Engr.Dr, Evans Ohaji PhD Thesis

MULTIPURPOSE DAM PROJECT MODELING OF CROSS RIVER BASIN USING

BAYESIAN DECISION THEORY

BY

OHAJI, EVANS PAULINUS CHUKWUDI

REG. NO. 2016101001

(M.Eng)

A THESIS IN THE DEPARTMENT OF CIVIL ENGINEERING, FACULTY OF

ENGINEERING, CHUKWUEMEKA ODUMEGWU OJUKWU UNIVERSITY

SUBMITTED TO THE SCHOOL OF POSTGRADUATE STUDIES,

CHUKWUEMEKA ODUMEGWU OJUKWU UNIVERSITY, IN PARTIAL

FULFILLMENT OF THE REQUIREMENTS FOR THE AWARD OF DEGREE OF

DOCTOR OF PHILOSOPHY OF THE CHUKWUEMEKA ODUMEGWU OJUKWU

UNIVERSITY

DECEMBER, 2019

i

DECLARATION

“I Ohaji Evans P.C. hereby declared that this work, Multipurpose Dam Project Modeling

of Cross River Basin Using Bayesian Decision Theory is a product of my own research

efforts, undertaken under the supervision of Engr. Assoc. Prof. Eme, L. C. and Engr. Dr.

Ezugwu C.N. and the work has not been presented elsewhere for the award of degree or

certificate. All sources have been appropriately acknowledged.”

OHAJI, EVANS PAULINUS CHUKWUDI

REG. NO. 2016101001

ii

CERTIFICATION

The undersigned certify that they have read and recommended to the School of Post Graduate

Studies for acceptance, a thesis entitled “MULTIPURPOSE DAM PROJECT

MODELING OF CROSS RIVER BASIN USING BAYESIAN DECISION THEORY ”

submitted to the Department of Civil Engineering by Evans P.C. Ohaji in partial fulfillment

of the requirements for the award of Doctor of Philosophy Degree in Civil Engineering

[Water Resources and Environmental Engineering] Chukwuemeka Odumegwu Ojukwu

University, Uli Anambra State.

………………………………

Engr. Assoc. Prof. Eme, L. C.

(Supervisor I)

..………………………

Date

………………………………

Engr. Dr. Ezugwu C.N

(Supervisor II)

…………………………

Date

………………………………

Engr. Assoc. Prof. Eme, L. C.

(Head of Department)

…………………………

Date

……………………………...

Engr. Assoc. Prof. A.J. Atuchukwu

(Dean, Faculty of Engineering)

…………………………

Date

………………………………

Professor M.N. Chendo

(Dean, School of Post Graduate Studies)

………………………...

Date

………………………………

External Examiner

………………………….

Date

iii

ACKNOWLEDGEMENTS

I wish to express my profound gratitude to all who made efforts in one way or the other in

contributing to this Research work, especially Late Engr. Prof. Anyata B. U., may his gently

soul rest in peace Amen.

My indebtedness goes to my project supervisor and Head of Civil Engineering Department,

Engr. Assoc. Prof. Eme, L. C. for his tireless effort in going through this Research work. I

sincerely owe him a lot for his sacrifice, his life style especially his life of humanity and

tolerance has made an indelible impression on me. Special thanks to Engr. Dr. Ezugwu C.N

the supervisor II and the entire staff of Civil Engineering Department. I will not forget to

thank the Dean of Engineering faculty, Engr. Assoc. Prof. A.J. Atuchukwu for his tireless

effort in the discharge of his duties. Also, Special thanks to the Dean of Post-Graduate studies,

Professor M.N. Chendo for the excellent coordination of the affairs of Post-Graduate school.

I also have to thank my beloved wife Mrs. Nneoma Ohaji and my son Master Prince

Chukwudi Ohaji for their prayers.

I express my profound gratitude to Almighty God for his Grace, Mercy, Provision and

Protection throughout my stay in the University.

Ohaji Evans P.C.

December, 2019

iv

TABLE OF CONTENTS

TITLE PAGE

DECLARATION

CERTIFICATION

ACKNOWLEDGEMENTS

TABLE OF CONTENTS

LIST OF TABLES

LIST OF FIGURES

LIST OF NOMENCLATURES

APPENDIX

ABSTRACT

i

ii

iii

iv

v

xii

xvi

xviii

xix

xx

CHAPTER ONE

1.0 Introduction 1

1.1 Background to the Study 3

1.1.1 Cross River Basin Development Authority (CRBDA) 3

1.1.2 Planning and Management Challenges in Cross River Basin Authority 4

1.2 Statement of the Problem 8

1.3 Aim and Objectives of the Study 10

1.4 Research Questions 11

1.5 Hypotheses 12

1.6 Justification of the Study 13

1.7 Area of Study 13

1.8 Scope of Study 16

1.9 Limitation of Study 16

v

CHAPTER TWO

LITERATURE REVIEW 17

2.0 Introduction 17

2.1 Theoretical Framework 17

2.1.1 Overview of Simulation Modeling 18

2.1.2 Experimental Design for simulation 20

2.1.3 Overview of Multipurpose Dam Project 22

2.1.4 World Multi-Purpose Dams 30

2.1.5 Multipurpose Benefits Framework 38

2.1.6 Water Transfer in Water Resources System 44

2.1.7 History of Nigerian River Basins 45

2.1.8 Nigerian Navigation-Water Ways 46

2.1.8.1 Federal Navigable Waterways 46

2.1.8.2 States Accessible By Navigable Inland Waterways in Nigeria 48

2.1.9 Inventory of Dams and Reservoirs 48

2.1.10 Hydropower Technologies and Resources 49

2.2 Conceptual Framework 61

2.2.1 Bayesian Decision theory 61

2.2.2 Steps of Decision-Making Process 62

2.2.3 Decision-Making under Uncertainty/Risk 63

2.2.4 Expected Monetary Value (EMV) 63

2.2.5 Steps for calculating EMV 64

2.2.6 Expected Opportunity Loss [EOL] 64

2.2.7 Steps for Calculating EOL 65

2.2.8 Expected Value of Perfect Information [EVPI] 65

vi

2.2.9 Conversion infinite to finite Bayesian Decision Model 66

2.2.10 Net Present Value Project Cashflow 68

2.2.11 Capital Projects Using Net Present Value 68

2.2.12 Net Present Value Decision Rules 69

2.3 Empirical Framework 70

2.3.1 Empirical Model 70

2.4 Research gap of the Literatures Reviewed (Gap Analysis) 89

2.5 Summary of the Literatures reviewed 90

CHAPTER THREE

METHODOLOGY 96

3.0 Methods 96

3.1 Experimental Model 96

3.1.1 Data Collection for the Experiments 97

3.2 Basic Concept of Bayesian Decision Model Infinite Equations 98

3.3 Estimation of payoff values of Economic efficiency of the Multi-purpose dam

projects 104

3.3.1 Data Collection of Economic Efficiency 104

3.4 Data Collection of payoff values of the Net benefits of Multi-purpose and Multiobjective

109

3.4.1 Estimation of the Net benefit nf Multipurpose and Federal Economic Redistribution 109

3.4.2 Estimation on Net Benefit of Multipurpose and Regional Economic Redistribution 116

3.4.3 Estimation on Net benefit of Multipurpose and State Economic Redistribution 124

3.4.4 Estimation on Net benefit of Multipurpose and Local Economic Redistribution 131

3.4.5 Estimation on Net benefit of Multipurpose and Social Well-Being 138

vii

3.5 Total Net-Benefits of Multi-Purposes under various Multi-Objectives 146

3.6 Raw Data Analysis and Discussion of Results 146

3.6.1 Introduction 146

3.6.2 Analyses 147

3.6.3 Observed Data Distribution 153

3.6.4 Expected Data Distribution 155

3.6.5 Data Validation 156

CHAPTER FOUR

DATA ANALYSIS AND DISCUSION OF RESULTS 163

4.1 Multipurpose and Multiobjective Variables Designation 165

4.2 Estimation of Required Number and Prior Probability of Multipurpose 165

4.2.1 Estimation of Required Number of Multipurpose 165

4.2.2 Estimation of Prior Probability of the Multipurpose. 167

4.3 Bayesian Decision Model Simulation, Likelihood Forecast, Marginal

Distribution, Posterior Distribution, Expected Value of System Information

(EVSI) and Expected Opportunity Loss (EOL) at 1 st Iteration. 169

4.3.1 Bayesian Decision Model Simulation of Expected Monetary Value at 1 st Iteration 169

4.3.2 Estimation of EPPI and EVPI in the 1 st Iteration. 171

4.3.2.1 Expected Profit in Perfect Information (EPPI) 171

4.3.2.2 Expection of Value of Perfect Information (EVPI) 171

4.3.3 Bayesian Decision Model Likelihood Forecast 172

4.3.3.1 Sample Mean Value, Standard Deviation, Variation Coefficient and Product of

Variation Coefficient & Payoff Values 175

4.3.3.2 Evaluation of Sample Value ti 176

4.3.3.3 Standardization of ti Values 177

viii

4.3.3.4 Estimation of Likelihood Function 2(1- Фǀtiǀ) 178

4.3.3.5 Normalization Likelihood function 2(1- Фǀtiǀ) 179

4.3.3.6 Likelihood Distribution Curves of the Multi-purpose and Multi-Objectives 180

4.3.4 Estimation of Marginal Probability in the 1 st Iteration 186

4.3.5 Estimation of Posterior probability in the 1 st Iteration 188

4.3.6 Estimation of Summation of Expected Opportunity Loss (∑EOL) of the

Multipurpose in the 1 st Iteration 190

4.3.7 Estimation of Expected value of System Information 1 st Iteration 192

4.3.8 Bayesian Decision Model Simulation of Multipurpose/Multiobjective Conditional

Opportunity Loss (COL) and EOL in 1 st Iteration 194

4.4 Dynamics of EMV and EOL at 1st Iteration 195

4.4.1 Expressing the Multipurpose EMV and EOL in Percentage at Ist Iteration 196

4.5 Simulation Modeling of Multipurpose and MultiObjective 2 nd Iteration [Optimum

Solution] 199

4.5.1 Estimation of EPPI and EVPI in the 2nd Iteration. 201

4.5.2 Estimation of likelihood in 2nd Iteration 202

4.5.2.1 Estimation of Marginal Probability in 2 nd Iteration 202

4.5.2.2 Estimation of Posterior probability in the 2 nd Iteration 204

4.5.2.3 Estimation of Summation of EOL in 2 nd Iteration [Point of Optimum Solution] 207

4.5.2.4 Estimation of EVSI in the 2 nd Iteration 208

4.5.2.5 Bayesian Decision Model Simulation of Multipurpose/Multiobjective Conditional

Opportunity Loss (COL) and EOL in 2 nd Iteration [ At Optimum Solution] 210

4.6 Dynamics of EMV and EOL in 2 nd Iteration 211

4.6.1 Expressing the Multipurpose EMV and EOL in Percentage at 2 nd Iteration 213

4.6.2 EMV and EOL in order of Priority 216

ix

4.7 Model Optimization of Multipurpose EMV of Cross River Basin System 219

4.7.1 Expected Monitory Value (EMV) of the Multi-Purpose in 1 st and 2 nd Iteration 219

4.7.2 Model Optimization of Multipurpose EOL of Cross River Basin System 222

4.7.3 Model Optimization of EPPI, EVPI and EVSI 225

4.8 Bayesian Decision Model Validation 225

4.8.1 Bayesian Decision Model Validation using Graphical Method 226

4.8.2 Bayesian Decision Model Validation Using Pearson Moment correlation 227

4.8.3 Bayesian Decision Model Validation Using T-test 229

4.8.4 Bayesian Decision Model (BDM) Efficiency 231

4.9 Application of BDM optimum strategies and policy in Cross River Basin 231

4.9.1 Allocation of FGN ₦10.9 Billion Development funds to Multipurpose Dam Project

Using EMV Ratio 232

4.9.2 Maximization of Net Return Per unit of Investment in Percentage For CRBDA 234

4.9.3 Allocation of ₦10.9 Billion to the CRBDA Multipurpose Using EOL Ratio 236

4.9.4 Minimization of Net Return Per unit of Investment in Percentage For CRBDA 237

4.9.5 Integration of Dam Multipurpose 238

4.9.6 Development and Utilization of a Small Hydropower Plant 238

4.9.6.1 Hydropower Plant Plan Selection 239

4.9.6.3 Cross River Rating Curve at Ikom 242

4.9.6.4 Rating curve of exceedance Probability (A) 243

4.9.6.5 Rating curve of exceedance Probability(B) 244

4.9.6.6 Cross River (Ikom) Location (5.79, 8.79) at 38m Elevation 245

4.9.5.7 Cross River (Ikom) Location (5.79, 8.79) at 29m Elevation 247

4.9.6.8 Working Areas of different Turbine types 248

4.9.6.9 Hydropower-Turbine Sizing Details 249

x

4.9.6.9.1 Selection of Turbine Type 249

4.9.6.9.2 Working Areas of different Turbine types 250

4.9.6.9.3 Cross section of the Small Hydropower Plant at Ikom 251

4.9.6.9.4 Kaplan Turbine Sizing Details 252

4..9.6.9.5 Kaplan Efficiency and Generator Representation 253

4.9.6.9.6 Kaplan Energy Calculator 254

4.9.6.10 Leverage Cost of Electricity (LCOE) of Small Hydropower Project at Ikom 255

4.9.6.10.1 Investment Costs as A Function of Installed Capacity and Turbine Head 257

4.9.6.10.2 Leverage Cost of Electricity (LCOE) of Small Hydropower Plant of 7MW

Turbine Capacity at Ikom (Cross River). 258

4.9.6.10.3 Percentage cost of Small Hydropower (SHP) station Components at Ikom town,

Cross River State 260

4.9.6.10.4 Components Cost of building a Small Hydropower Project (SHP) at Ikom, River

Cross. 262

4.10: Net Present Value (NPV)- Payback Duration and Monetary Value of Small

Hydropower Project investment at Ikom 263

4.10.1 The Small Hydropower Pay Back Duration 265

4.10.2 The Small Hydropower Payback Monetary Value 265

4.11 Allocation of Resources to the Multiobjective of the Cross-River Basin 266

CHAPTER FIVE

CONCLUSION, RECOMMENDATION AND CONTRIBUTION TO KNOWLEDGE 271

5.1 Conclusion 271

5.2 Recommendations 276

5.3 Contribution to Knowledge 277

REFERENCES 279

xi

LIST OF TABLES

Table 2.1: Prices of Electricity per Kilowatt-hour 39

Table 2.2: Inventory of Dams and Reservoirs in Cross River Basin 49

Table 3.1: Bill of Engineering Measurement and Evaluation (BEME) on Economic

Efficiency of Power Generation 105

Table 3.2: BEME on Economic Efficiency of Water Supply 106

Table 3.3: BEME on Economic Efficiency of Navigation 106

Table 3.4: BEME on Economic Efficiency of Irrigation 107

Table 3.5: BEME on Economic Efficiency of Flood Control 108

Table 3.6: BEME on Economic Efficiency of Recreation 108

Table 3.7: BEME on Net benefit of Hydropower and Federal Economic Redistribution 110

Table 3.8: BEME on Net benefit of Water Supply and Federal Economic Redistribution 111

Table 3.9: BEME on Net benefit of Navigation and Federal Economic Redistribution 112

Table 3.10: BEME on Net Benefits of Irrigation and Federal Economic Redistribution 113

Table 3.11: BEME on Net benefit of Flood control and Federal Economic Redistribution 114

Table 3.12: BEME on Net benefit of Recreation and Federal Economic Redistribution 115

Table 3.13: BEME on Net Benefit of Hydropower and Regional Economic Redistribution 117

Table 3.14: BEME on Net benefit of Water Supply and Regional Economic Redistribution 118

Table 3.15: BEME on Net benefit of Navigation and Regional Economic Redistribution 119

Table 3.16: BEME on Net benefit of Irrigation and Regional Economic Redistribution 121

Table 3.17: BEME on Net benefit of Flood control and Regional Economic Redistribution 122

Table 3.18: BEME on Net benefit of Recreation andRegional Economic Redistribution 123

Table 3.19: BEME on Net benefit of Hydropower and State Economic Redistribution 125

Table 3.20: BEME on Net benefit of Water Supply and State Economic Redistribution 126

Table 3.21: BEME on Net benefit of Navigation and State Economic Redistribution 127

xii

Table 3.22: BEME on Net benefit of Irrigation and State Economic Redistribution 128

Table 3.23: BEME on Net benefit of Flood Control and State Economic Redistribution 129

Table 3.24: BEME on Net benefit of Recreation and State Economic Redistribution 130

Table 3.25: BEME on Net benefit of Hydropower and Local Economic Redistribution 132

Table 3.26: BEME onNet Benefit of Water Supply and Local Economic Redistribution 133

Table 3.27: BEME on Net benefit of Navigation versus Local Economic Redistribution 134

Table 3.28: BEME onNet benefit of Tourism and Local Economic Redistribution 135

Table 3.29: BEME on Net benefit of Flood Control versus Local Economic Redistribution 136

Table 3.30: BEME on Net benefit of Recreation versus Local Economic Redistribution 137

Table 3.31: BEME on Net benefit of Hydropower and Social Well Being 140

Table 3.32: BEME on Net Benefit of Water Supply and Social Well-Being 141

Table 3.33: BEME on Net benefit of Navigation versus Social Well-Being 142

Table 3.34: BEME on Net benefit of Irrigation and Social Well-Being 143

Table 3.35: BEME on Net benefit of Flood Control versus Social Well-being 144

Table 3.36: BEME on Net benefit of Recreation versus Social Well-being 145

Table 3.37: Net benefits of Cross River basin Multi-Purpose and Multi-Objective 146

Table 3.38: Observed Contingency Table 149

Table 3.39: Expected contingency Table 150

Table 3.40: Computed Chi-square Table 151

Table 3.41: Expected and Observed Data 156

Table 3.42: Pearson Moment Coefficient of the Expected and Observed Data 158

Table 3.43: T-test on the Expected and Observed Data correlation (r) 159

Table 4.1: Estimation of Prior using Breakdown of economic benefits by installed capacity 168

Table 4.2: Payoff Table of the Multipurpose and Objectives of the River Basin 1 st Iteration 169

xiii

Table 4.3: Mean , Standard deviation, variation coefficient and Product of Variation

Coefficient & Payoff Values [equation. 3.1 to 3.3] 176

Table 4.4: Calculation of ti [Equation 3.4] 176

Table 4.5: Standardized ti Values [ǀtiǀ] using Equation 3.4 177

Table 4.6: Estimation of Likelihood Function 2(1- Фǀtiǀ) 178

Table 4.7: Calculation of P(x/y) of Equation 3.5 179

Table 4.8: Marginal Probability of 1 st Iteration 187

Table 4.9: Posterior (Model) probability of 1 st Iteration 189

Table 4.10: Summation of Expected Opportunity Loss (EOL) at 1 st Iteration 191

Table 4.11: Expected Value of System Information (EVSI) 1 st Iteration 192

Table 4.12: Payoff table of Conditional Probability at 1 st Iteration 194

Table 4.13: Dynamics of EMV and EOL at 1 st Iteration 195

Table 4.14: Expressing the Multipurpose EMV and EOL in Percentage at Ist Iteration 196

Table 4.15: Payoff Table of the Multipurpose and Objectives of the River Basin 2 nd Iteration 200

Table 4.16: Estimation of Marginal Probability in 2 nd Iteration 203

Table 4.17: Estimation of Posterior (Model) probability in the 2 nd Iteration 205

Table 4.18: Estimation of EOL in 2 nd Iteration 207

Table 4.19: Estimation of EVSI in the 2 nd Iteration 208

Table 4.20: Payoff table of Conditional Opportunity Loss 2 nd Iteration 210

Table 4.21: Dynamics of EMV and EOL in 2 nd Iteration 212

Table 4.22: Expressing the Multipurpose EMV and EOL in Percentage at 2 nd Iteration 213

Table 4.23: EMV & EOL of Multipurpose in Priority 216

Table 4.24: Expected Monetary Value of the Multipurpose 1 st Iteration and 2 nd Iteration 219

Table 4.25: Optimization of Expected Opportunity Loss of the Multipurpose 1 st Iteration

and 2 nd Iteration 222

xiv

Table 4.26: Optimization of EPPI, EVPI and EVSI at 1 st and 2 nd Iteration 225

Table 4.27: Validation Using Graphical Method 225

Table 4.28: Validation Using Pearson Moment correlation 227

Table 4.29: Validation using T-test 229

Table 4.30: FGN Appropriation of ₦10.9 Billion to CRBDA 232

Table 4.31: Allocation of ₦10.9 Billion to the CRBDA Multipurpose Using EMV Ratio 232

Table 4.32: Maximization of Net Return Per Unit of Investment in Percentage For CRBDA 234

Table 4.33: Allocation of ₦10.9 Billion to the CRBDA Multipurpose Using EOL Ratio 236

Table 4.34: Minimization of Net Return Per Unit of Investment in Percentage For CRBDA 237

Table 4.35: Cross River (Ikom) Rating Table at Ikom 241

Table 4.36: Kaplan Turbine Sizing Details 252

Table 4.37: Typical Installed Costs And Lcoe Of Hydropower Projects 259

Table 4.38: NPV Values Computed per year 264

Table 4.39: Allocation of ₦550,368,000,000.00 billion Generated by the Small

Hydropower Plant in 12 years 266

xv

LIST OF FIGURES

Figure 1.1: How Nigerian agency-wasted ₦2.5 billion on failed contracts, fraudulent

approvals, others-audit report.html/attachment/crbda-2 7

Figure 1.2: Map showing Cross River Basin coverage 15

Figure 2.1: Monthly payment per household for water services in Nigeria, 2011-2013 40

Figure 2.2: Typical “low head” hydropower plant with storage 52

Figure 2.3: Working areas of different turbine types 55

Figure 2.4: Cost breakdown of hydropower projects in developing countries 60

Figure 2.5: Conversion of Infinite Bayesian Model to Finite Bayesian Linear Model 67

Figure 3.1: Observed Data Distribution 154

Figure 3.2: Expected Data Distribution 155

Figure 3.3: Plot of Expected against observed data 157

Figure 3.4: Bayesian Decision Theory Model-Flow Chart 162

Figure 4.1: Frequency distribution of authorized uses based on installed hydropower capacity 166

Figure 4.2: Breakdown of economic benefits by installed capacity. 167

Figure 4.3: Likelihood distribution of Multiobjective benefits vs. Hydropower Project. 180

Figure 4.4: Likelihood distributions of Multiobjectives benefits vs. Water supply Projects 181

Figure 4.5: Likelihood distributions of Multiobjective benefits vs. Navigation Project 182

Figure 4.6: Likelihood distributions of Multiobjectives benefits vs.Irrigation Project. 183

Figure 4.7: Likelihood distributions of Multiobjective benefits Vs Flood Control Project 184

Figure 4.8: Likelihood distributions of Multiobjective benefit Vs Recreation Project 185

Figure 4.9: Graphical relationship between EVSI and EOL 193

Figure 4.10: Graphical relationship between EMV and EOL at 1st Iteration 198

Figure 4.11: Graphical representations of EVSI and EOL 209

Figure 4.12: Graphical dynamics of EMV and EOL of Cross River Basin at 2 nd Iteration 214

Figure 4.13: EMV and EOL Interaction 217

xvi

Figure 4.14: Optimization of EMV 220

Figure 4.15: Graphical Representation of the Optimized EOL of the Multipurpose 223

Figure 4.16: Validation using Graphical Method 226

Figure 4.17: Maximization of cost Per Unit of Investment for CRBDA 235

Figure 4.18: Minimization of cost Per Unit of Investment for CRBDA 237

Figure 4.19: Cross river (Ikom). Location (5.79, 8.79) Elevation: 38m. 239

Figure 4.20: Cross River (Ikom) rating Curve at Ikom, location:( 5.79, 8.79) 243

Figure 4.21: Rating curve exceedance Probability(A) 244

Figure 4.22: Rating curve of exceedance Probability(B) 245

Figure 4.23: Cross River (Ikom) Location (5.79, 8.79) at 38 Elevation 246

Figure 4.24: Cross River Location (5.79, 8.77) at 29m Elevation 247

Figure 4.25: Working Areas of different Turbine types 248

Figure 4.26: Working Areas of different Turbine types 250

Figure 4.27: Cross section of Small Hydropower Plant at Ikom 251

Figure 4.28: Turbine Efficiency 253

Figure 4.29: Energy Calculator 254

Figure 4.30: Hydropower costing Chart. Sources: International Renewable Energy Agency 255

Figure 4.31: Investment Costs as A Function of Installed Capacity and Turbine Head 257

Figure 4.32: Percentage cost of Small Hydropower station Components at Ikom town,

Cross River State 260

Figure 4.33: Graphical representation of Component Cost of building Hydropower

station at Ikom, River Cross in Naira. 262

Figure 4.34: Allocation of funds to the Multipurpose (Various level of Government

& Social Well-Being) 268

Figure 4.35: Allocation of funds to the Multipurpose (Various level of Government &

Social Well-Being) 269

xvii

LIST OF NOMENCLATURES

Ho

H1

= Null Hypothesis

= Alternative Hypothesis

CRBDA = Cross River Basin Development Authority

E

O

Ф

r

C

NPV

FMWR

X 2

ai

σ

C v

Pij

Y

X

EMV

EMV*

EOL

EOL*

EPPI

EVPI

EVSI

MPDP

PRIOR

= Expected sample values

= Observed sample values

= Data distribution function

= Pearson’s Product Moment Correlation

= Correlation Coefficient

= Net Present Value

= Federal Ministry of Water Resources

= Chi-Square

= Data mean

= Standard deviation

= Variation Coefficient of Payoff-values

= Payoff-Values

= Multipurpose Independent variable

= Multiobjective dependent variable

= Expected monetary values

= Maximum Monetary Value

= Expected Opportunity Loss

= Minimum Expected Opportunity Loss

= Expected Profit in Perfect Information

= Expected Value of Perfect Information

= Expected Value of System Information

= Multipurpose Dam Project

= Prototype (CRBDA)

POSTERIOR = Model (BDM

IGR

BEME

= Internally Generated Revenue

= Bill of Engineering Measurement and Evaluation

xviii

APPENDIX

APPENDIX A1: Chi-square Probabilities 297

APPENDIX A2: T-Test Table 298

APPENDIX A3: Bayesian Decision Theory Model-Flow Chart 299

APPENDIX A4: Sizing details for Cross River Hydro-Power Design [Ikom] 300

APPENDIX A5: Turbine efficiency 302

APPENDIX A6: Energy calculator 303

APPENDIX A7: Key Scheme Characteristics of Cross River Basin Development

Authority 304

APPENDIX A8: Computer Simulation of 1 st Iteration Input & Output 305

APPENDIXA9: Computer Simulation of 2 nd Iteration Input & Output 315

APPENDIX A10: FMWR Allocation to Cross River Basin Development

Authority(CRBDA) 320

APPENDIX A11: 2017 FGN Budget Allocation 321



APPENDIX A14: 2014 FGN Budget Proposal 324


APPENDIX A16: 2016 Annual Audit Report-Sheet-1 326

APPENDIX A17: Pearson Critical Values 329

APPENDIX A18: Data Collection Letter 330

APPENDIX A19: Questionnaires 331

APPENDIX A20: Research Visit to Cross River Basin Development Authority 336

xix

ABSTRACT

This research is aimed at examining simulation modeling in Bayesian Decision Theory

(BDT) and its application in Planning and Management of Cross River Basin. The

objectives were: to determine Prior (Prototype) and Posterior (Model) Probability,

Expected Monetary Value (EMV), Marginal Probability, Expected Value of Perfect

Information (EVPI), Expected Profit in Perfect Information (EPPI), Expected Value of

System Information (EVSI). The problems the study attempts to solve were: inadequate

capacity utilization of multipurpose scheme, inefficient economic benefits and losses,

inappropriate and unsustainability issues. The methodology applied involves data which

were collected from the Cross-River Basin Development Authority (CRBDA), Parastatals

and Ministries. The methods used in the experiments for the dam projects were as follows:

estimating the performance of economic efficiency of the multipurpose dam projects,

estimating performance of the net benefits of the interaction between multi-purpose and

the multi-objective, assembling the total net benefits of the interaction between

multipurpose and the multi-objective, analyzing the data obtained as the total net benefits

to ascertain the reliability and validation of the sources of data by using: Contingency

coefficient and association, Pearson moment correlation coefficient and T- distribution test.

A payoff table of the net benefits between multipurpose and multi-objective was applied

as a background for Bayesian Decision Model (BDM) using Simulation Flowchart and

Excel Spreadsheet developed. Consequently, results with respect to Posterior probability

and EMV of the multipurpose were obtained as follows: Hydropower (0.194160209),

Water supply (0.122369749); Navigation (0.020456291), Irrigation (0.183962646), Flood

control (0.06085393), Recreation (0.418197175) and led to the following interpretations:

Hydropower (₦ 1.698394464 trillion), Water supply (₦0.280792063 trillion), Navigation

(₦0.03732123 trillion), Irrigation (₦1.303730403 trillion), Flood control (₦0.302028085

trillion), Recreation (₦0.9206949 trillion) respectively. Therefore, the correlation of the

Prototype and Model of the multipurpose dam projects, resulted in a coefficient equal to

1.0 which, indicates 100% a higher performance of the Model in relation to the Prototype.

Similarly, the experimentation carried out using EMV ratio generated by BDM, justified

that the ₦10.9 billion apportioned by the Federal Government of Nigeria (FGN) to the

Basin was strategically allocated for various purpose. Thus, the Model concluded that

Hydropower is in high demand as it has the Maximum EMV of ₦1.698394464 trillion,

hence the study on Small Hydropower Project (SHP) was conducted (Head = 8m &

Discharge = 100m 3 /s), and Kaplan turbine generator was selected. This gave a design

output of 7.0 MW and its development cost was estimated at ₦7.8 billion. Prognosis into

the future, the Net Present Value (NPV) of the SHP cash flow for Payback duration of

minimum capacity utilization of the basin assets showed at 1 st year with a recovery cost of

₦7.8billion, while full capacity utilization of the basin assets at 12 th year accrued to

₦558billion. From the research work, it is recommended` that the FGN should deploy

strategic policies model like BDM that will empower CRBDA to invest allocations given

to it as an instrument of sustainability and payback on investment made. With this, the

Country will attain Sustainable Development Goals (SDGs) of vision 2030 as well as

vision 2020 for inclusion of Hydropower as renewable Energy in this research. Ultimately,

the research work indicated that BDM is at its best when inferences are made on present

and historical information. In the contribution to knowledge the research uses BDM as one

of the new inventory Models to solve the dynamic programming that had problem of curse

of dimensionality.

xx

CHAPTER ONE

1.0 Introduction

Most of the previous works on multipurpose water resources and environmental engineering

development project planning with regards to optimization have considered a single objective,

this objective in question is economic optimization. However, in real life situation this is not

always the case; other objectives can play significant roles alongside economic efficiency to

determine levels of development to be apportioned to various purposes involved in water

resources projects, such other objectives include: Regional Economic Redistribution, Local

Economic Redistribution, State Economic Redistribution, Federal Economic Redistribution,

Environmental Quality Improvement, and Youth Employment. These objectives are

becoming increasingly important due to some political, ecological, health and many other

reasons (Eme, 2013).

River basins Planning Engineer has considered benefits accruing from objectives outside

economic efficiency as either too difficult and too abstract to measure or intangible. However,

the fact is that these other objectives are considered very vital by interest group at the level of

authorization. Hence, the myth of immeasurability and intangibility of benefits accruing from

them must be destroyed. Scientifically, all measures are relative. Therefore, intangibility and

immeasurability cannot be in absolute terms. Hence there must be a measure of benefits that

exist. As a matter of facts a thorough analysis of benefits in light of, for instance, a

multipurpose dam project can show that tangible benefits are accruable under each of the

objectives. It can also be plausible to consider benefits accruable by each purpose

(development) to vary with respect to each objective. Moreover, this point can be buttressed

by data available from such areas of learning such as social, statistics, medical, geography,

welfare, ecology, and environmental engineering. In view of the foregoing, it becomes

1

necessary in multipurpose water resources planning to consider not only economic efficiency

but also any other benefits that may be deemed necessary at planning stage for explicit,

exhaustive and effective decision making (Eme, 2013)

Global Water Partnership (2000): “States that the Integrated Water Resources Management

(IWRM) is a process which supports the coordinated development and management of water,

land and related resources, in order to maximize the ensuing economic and social wellbeing

in a justifiable manner without compromising the sustainability of vital ecosystems”. In order

to implement the IWRM process, some technical (i.e. analysis of the properties of, and

interactions among, the resources in the region), economic (i.e. water as an economic good),

and institutional (i.e. water governance) aspects need to be carefully considered and possible

courses of action defined. Integrated Water Resources Management means River Basin

Management or Watershed Management or River Valley Management.

The use of analytical modeling tools in integrated water resources management (IWRM)

provides important instruments both for finding the best water use solutions and achieving

water security for multiple purposes in a sustainable and equitable manner. It also facilitates

the management and mitigation of extreme climate events. Water security needs and taking

into account present and future overall social economic and environmental goals (Global

Water Partnership (GWP), 2013).

Therefore, the implementation of the IWRM requires from water managers and planners a

good understanding of the system dynamics, which most of the time is hold by specialists

from different scientific fields. Since the management and science interchange is still limited

in many countries, proper mechanisms are needed to guarantee a continuous information

transfer to decision makers and water regulators.

2

More so, possible decision needed to be taken in river basin operations are: selection of River

basin purpose among alternatives that gives the optimal benefits, Standardized method of

resources allocation to the Multipurpose and Multiobjective and selection of types and

number of purposes that can be integrated for optimal benefits.

This research work, explored Bayesian Decision Model (BDM), in the integrated Water

Resources Management of Cross river watershed. However, simulation modeling in BDM

was applied in decision making in planning toward resolving conflict which may arise in the

management of Watershed operations.

Ultimately, this research work explored BDM as experienced in a case of the farmer’s

decision problem, where the modeler assisted the farmer who was faced with the choice of

selecting a high yielding crop among various alternative crops in making a useful decision

that will enable high crop production(Eme and Ohaji, 2019).

1.1 Background to the Study

This subsection covers: Cross River Basin Development Authority and Planning and

Management Challenges in Cross River Basin Authority.

1.1.1 Cross River Basin Development Authority (CRBDA)

The Cross-River Basin Development Authority assumed its present geographical entity

(Figure 1.2) courtesy of Decree No. 87 of 28th September, 1979.

Functions: The functions of the Cross-River Basin Development Authority as spelt out by

section 41(a)-(e) of the River Basin Development Authorities Act; cap R9, LFN, 2004 are as

follows;

(i)

To undertake comprehensive development of both surface and underground water

resources for multi-purpose use with the particular emphasis on the provision of

3

(ii)

irrigation infrastructure and the control of floods and erosion and for watershed

management;

To build, manage dams and other water resources necessary for the achievement of

the Authority’s functions and hand over all lands to be cultivated under the irrigation

scheme to farmers;

(iii) To supply water from the Authority’s completed storage schemes to all users for a fee

to be determined by the Authority with the approval of the Minister

(iv)

To build, manage infrastructural services such as roads and bridges linking project

sites; provided that such infrastructural services are included and form integral part of

the list of approved projects

(v)

To develop and keep up-to-date comprehensive water resources master plan,

identifying all water resources requirements in the Authority’s area of operation,

through adequate collection and collation of water resources, water use, socioeconomic

and environmental data of the River Basin.

1.1.2 Planning and Management Challenges in Cross River Basin Authority

CRBDA was established in1979, and this is nearly 40 years of its creation. Inventory (Table

2.2) conducted on the basin dams revealed that the existing dams were not functioning

properly and the ones under planning and design cannot be fully implemented due to

management challenges. The management challenges bedeviling CRBDA (See

AppendixA16-Auditor General of the Federation (AuGF) 2016 Annual Audit Report of

CRBDA) were as following:

Transfer of Project Fund Without Contract Agreement

A sum of N10.8 million was transferred from the Authority to a company without any

contract agreement and whose line of business does not include consultancy and supervision

between August and December 2015.According to the report, the transfer of project fund to

4

the said company without any contract agreement for a job to be carried out seems to be a

diversion of public funds for an ulterior purpose.More so, the task of supervising the agency’s

projects lies with a relevant department designated and trained for such a task.The auditor

general demanded that the managing director justifies the transfer of project funds or recover

the sum of N10,888,880. (Office of Auditor General of the Federation (OAuGF)-Audit

Report, 2016).

Abandoned Projects

“A contract for the construction of Itu irrigation/drainage/flood control project was awarded

in December 2008 to a company at the sum of N1.9 billion. Itu is a local government in

Akwa Ibom. According to the Executive Director, Planning and Design Department of the

agency, the project had not been able to take off smoothly due to youth restiveness, land

donor issues, compensation, slow progress of work and several changes in the management

of the company. He said the agency had expended N617.8 million out of the total contract

value. According to the Auditor General of the Federation(AuGF) report, a visit to the project

site revealed that the total area for the project is about 1,265 hectares, while only about 500

hectares were cleared, the project had been abandoned, no value was derived from the money

spent so far and obsolete equipment were abandoned on the site. In a meeting held in

February 2015 between the agency and the contractor, it was resolved that the contract be

ended since the completion period had lapsed. The Managing Director was however

requested to involve the Federal Ministry of Works to determine the work done so far,

terminate the contract and recover money paid to the contractor since he (contractor) did not

abide by the contract’s terms of agreement, blacklist the contractor and demote the staff

concerned.” (Office of Auditor General of the Federation (OAuGF)-Audit Report, 2016).

5

Incompetent Companies Engaged

“Another concern in the report is the Itagui irrigation project in Cross River State which was

first contracted to a company in August 2009 for N485.9 million but was terminated due to

non-progress of work in November 2012. The supervising ministry was asked to recover the

sum of N196 million from the contractor. According to the report, the same project was

awarded to another company in December 2012 for N505.6 million, with an expected

completion period of 24 months. It was later discovered that the company which the project

was awarded to, was unable to implement the project but sub-awarded the project to another

company, in violation of the provision of the Public Procurement Act 2007. Even so, no

progress was recorded at the end of 24 months. The Managing Director was requested to

make available to the office of the Accountant General of the Federation, evidence of

recovery and remittance of the sum of N196 million from the first contractor, also provide

evidence which shows that due process was followed in re-awarding the contract and give

reasons why the contract was re-awarded in the first place to incompetent contractor. He was

also asked also to terminate the contract and recover any unearned amount paid to the second

company.” (Office of Auditor General of the Federation (OAuGF)-Audit Report, 2016).

Project Funds Siphoned

About N50 million was paid to a multipurpose cooperative society for the purpose of training

communities in Odukpani Local Government Area of Cross River State, on agro-business in

2015 without evidence of how the money was utilized. According to the report, a visit to the

project site revealed that the center was not functional as it was under lock, overgrown by

weed; there was also no sign of agricultural activity going on at the center and no evidence of

any ongoing training. The report stated that the Managing Director was requested to justify

the abandonment of the center after spending such a huge amount of money, provide

evidence that the communities benefited from the purported training, otherwise recover the

6

sum of N50 million. (Office of Auditor General of the Federation (OAuGF)-Audit Report,

2016).

Figure 1.1: How Nigerian agency-wasted ₦2.5 billion on failed contracts, fraudulent

approvals, others-audit report.html/attachment/crbda-2

Source: Office of Auditor General of the Federation (OAUGF)-2016 Annual Audit Report-

Unauthorized Virement

“The audit report also revealed how the CRBDA spent N8.6 million which was a capital

project fund to pay overhead expenses in 2015. This, it added amounted to virement without

recourse to National Assembly’s approval, as well as abuse of the 2015 Appropriations Act.

7

The managing director was asked by the Auditor General to justify the unauthorized virement.

The auditor general also stated that the managing director did not respond to his audit

inspection dated June 2017, hence said he (official) should be properly sanctioned and forced

to enforce the recommendation contained in the report.” (Office of Auditor General of the

Federation (OAuGF)-Audit Report, 2016).

1.2 Statement of the Problem

Cross river basin with economic and great water resources cannot prosper without the

benefits of optimum resources allocation, development and utilization. The problems that

overwhelmed the system must be fully evaluated and remedial steps taken for the full

capacity utilization of the abundant resources in the basin. In the delineation of the problem,

most of the problems were decision problems for the decision maker. However, this research

work statement of the problem were as follows:

(i)

Transfer of Projects Funds without contract Agreement.

Decision Problem: ₦10.8 million was transferred from the Authority to a company

without any Contract Agreement and whose line of business was not included in

consultancy or supervision between August and December, 2015. This was a decision

problem because all line departments that processes contract agreed to the foregoing

prior engagement and disbursement of funds.

(ii)

Abandoned Projects.

Decision Problem: A contract for the construction of Itu irrigation/drainage/flood

control projects was awarded in December 2008 to a company at the sum of ₦ 1.9

billion Naira. The project could not be completed due to youth restiveness, land

donor issues, compensation, slow progress of work and several changes in the

management of the company. This is a decision problem, as Planning Engineers and

8

Management of CRBDA should have factored the root causes that lead to the

stoppage of the contract in their plan and management processes.

(iii)

Incompetent Companies Engaged

Decision Problem: In August 2009, a company was awarded a contract for ₦ 485.9

million, the contract job was not executed. Same job awarded in December 2012 to

another contractor to the tune of ₦505.6million with expected completion period of

24months, but the company lacked requisite technical expertise to handle the contract.

The foregoing was a decision problem because: The management gave out the first

contract and it was not executed and the money not recovered. Still on the same job a

second contract was given out without traceability to past failure, checks on

technicality, processes and procedures prior considering a second contract.

(iv)

Funds Siphoned through fictitious services and Projects

Decision Problem: ₦ 50 million naira was paid to a Cooperative Society for the

purpose of training communities in Odukpani Local Government Area of Cross River

State on Agro Business in 2015 without evidence of how the money was utilized.

This indeed was a decision problem because the management board of Cross River

Basin approved to it.

(v)

Unauthorized Virement

Decision Problem: CRBDA spent ₦8.6 million which was a capital project funds to

pay overhead expenses in 2015. The CRBDA Management board reached a decision

to execute the foregoing without recourse to National Assembly approval as well as

abuse of 2015 appropriations Act.

9

(vi)

Non-Continuity of awarded Project

Decision Problem: Contract awarded by Predecessors most a time are not continued

by the current authority. This is a decision problem because the current management

has decided not to continue Projects initiated by their predecessors.

(vii) Insufficient funds released by the Government (FGN)

Decision Problem: The Federal Government of Nigeria (FGN) through the Ministry

of Water Resources function as the funding, regulatory and supervisory agency, in

their process of planning and management releases insufficient funds to the basin.

Also, funds not released as at when due.

(viii)

Unstandardized method of resource allocation in the system

Decision Problem: Non deployment of standardized algorithm for resources

allocation is a decision problem.

(ix)

Underutilization of the River basin abundant resources by the Planning engineers

and Manager

Decision Problem: Managers and planning engineers non utilization of full capacity

of dams in the system is a decision problem because they have the inventory of the

Multipurpose and Multiobjective at their disposal, as well as resources appropriated

by the Federal Government of Nigeria. Therefore, they decide what to do with what is

available.

1.3 Aim and Objectives of the Study

This research was aimed at examining Simulation Modeling in Bayesian Decision Theory

(BDT) and its application in Planning and Management of Cross River Basin. The specific

objectives were to:

(i)

determine expected monetary value (EMV) and expected opportunity loss (EOL)

ratios of the multipurpose dam project (MPDP),

10

(ii)

determine maximum expected monetary value (EMV*) and minimum expected

opportunity loss (EOL*) of the MPDP.

(iii) determine marginal probability ratio of the multiobjective.

(iv)

determine expected value of perfect information (EVPI) and expected value of system

information (EVSI) of Cross River Basin Development Authority (CRBDA) and

(v)

investigate dynamics and interaction between EMV and EOL of the MPDP.

1.4 Research Questions

Research Questions were as follows:

(i)

Does the transfer of funds without contract agreement leads to inadequate decisionmaking

problem?

(ii)

Does the nonfactoring of the root causes of abandoned project by the CRBDA

management and planning engineers a decision-making problem?

(iii)

Does CRBDA management not following procedures prior award of contract to

incompetent companies a decision-making problem?

(iv)

Does the approval of fictitious services and projects by CRBDA management a

decision problem?

(v)

Does the execution of unauthorized virement by CRBDA management without

recourse to the national assemble or appropriation bill a decision problem?

(vi)

Does non-continuity of previous awarded contract by the present management of

CRBDA a decision problem?

(vii)

(viii)

Does the release of insufficient funds by FGN/FMWR to CRBDA a decision problem?

Does the unstandardized method of funds allocation by the CRBDA a decision

problem?

(ix)

Does the underutilization of CRBDA assets amidst sufficient resources a decision

problem?

11

1.5 Hypotheses

(i)

Comparing Pearson moment correlation coefficient calculated value (rcalculated value)

with the Critical value (rcritical value) using table of critical values (AppendixA17):

Pearson moment correlation critical value at 5% (0.05) significant figure and

degree of freedom of 4, is rcritical value = 0.2336 and rcalculated value = 0.968

(approximated to 3 significant figures) Therefore, rcalculated value > rcritical value i.e.

0.968 > 0.2336, therefore reject Null Hypothesis. This clearly implied that, there

is a significant relationship between means of observed and expected data.

( Subsection 3.6.5, Table 3.42 and Appendix A17).

(ii) Therefore, the Tcalculated value = 4.135895543, while T critical value = 2.032245 at 5%

(0.05) significant figure. t value ˃ t critical, therefore reject Null Hypothesis. This

clearly indicates that, there is a significant relationship between means of

observed and expected data. (Section 3.6.5, Table 3.43 and Appendix A2).

(iii)

Comparing rcalculated value with rcritical value using table of critical values: Pearson

correlation. At 5% (0.05) significant figure and degree of freedom of 4, is the

rcritical value = 0.811 and rcalculated value = 1. Therefore, rcalculated value > rcritical value i.e.

1 > 0.811, therefore reject Null Hypothesis. It implied a high performance of the

posterior (model) in relation to the prior (Prototype) probability. The model

performance indicates high level capability prediction of the system (subsection

4.8.2, Table 4.28, Appendix A17 ).

(iv) Therefore, the T calculated value = 18.15, while T critical value = 2.776 at 5% (0.05)

significant. t value ˃ t critical, therefore reject Null Hypothesis, It indicates a high

12

performance of the posterior (model) in relation to the prior (Prototype)

probability. (Subsection 4.8.2, Table 4.29 and Appendix A2)

(v)

Type-1 and type-2 errors were not found or committed (Subsection 3.6.5 and

4.8.2).

1.6 Justification of the Study

This study is useful because it is applicable in assessing the performance and improvement of

systems, such as parameter of water resources Capacity, Multi-purpose/Multi-Objective

water resources engineering, project planning and management, cash flow management and

inventory. This is also significant in handling maximization and minimization of expected

monetary values and expected opportunity Loss respectively in decision making. Other

justification of this study is:

(i)

(ii)

(iii)

Provides a system where resources are channeled to its strategic needs and uses.

It creates a system that discourages misappropriation of funds.

It creates a system that provide food for the region and nation at all times through

irrigation.

(iv)

(v)

It creates a system that contributes to reduction in global warming.

It creates a system that supports and encourage renewable energy, hence

contribute to the use of safe energy and further protection of our environment

against natural disaster like flooding, drought and desertification.

1.7 Area of Study

The area of study is Cross River watershed which extends between latitudes 48000N and

68500N and longitudes 78400E and 98400E. Bounded by lower Benue basin to the North, the

Anambra-Imo basin to the West, the Niger Delta basin to the South-West and Cameroon to

the East, the Cross River basin includes parts of both Akwa Ibom and Cross river states in

13

South-eastern Nigeria. With an estimated landmass of 28 620.33 km 2 , the main drainage

systems are the Cross, Great and Little Kwas, Calabar, Akpa Yafe, Kwa Ibo and Imo rivers.

The Cross-River basin has a tropical rainy climate with high rainfall (varying between

1250mm and 4000 mm per annum depending on location); high temperature and high relative

humidity. Groundwater resources vary depending on the location. In the coastal plain, the

aquifer is composed of sands with lenses of clay and gravel and the water table is near the

surface. The strength of artesian flow varies with the state of the tide. The Water table rises

more gently than the ground so that in the North of the coastal plain the water table is up to

50m below the surface. The two states have an estimated population of 9.1 million people.

14

N

Figure 1.2: Map showing Cross River Basin coverage

Sources: Ohaji, 2019/Goggle Earth, 2019

15

1.8 Scope of Study

The research work was limited to studying the simulation modeling of Bayesian decision

theory on the dynamics between six river basin purposes and six river basin Objectives from

2013 to 2017 that is 5 years. Data interaction, reliability and viability was measured using

Contingency and association test, while Pearson moment correlation and T-test were used to

test the research hypotheses. The basin covers two states namely, Cross Rivers and Akwa-

Ibom States. The Dams identified among others were Obudu, Yakurr, Ijegu-Yala and Nkari.

The first three dams are located in Cross river state and the last Nkari Dam is located Akwa-

Ibom state.

1.9 Limitation of Study

The limitation of the research work was on, the inability of the researcher obtaining the 2016

Annual Audited Report of the basin directly from the CRBDA which was later sourced from

the Office of Auditor General of the Federation (AUGF). It is most likely, that there would

have been more embellishing information if the report was sourced directly from CRBDA.

16

CHAPTER TWO

LITERATURE REVIEW

2.0 Introduction

The literature of this research work were on, Theoretical, Conceptual and Empirical

framework, and their relationship with the research under review.

However, sources of the literature review were from textbooks, journals, past research

projects, internets, and other related documents. Various opinions have been expressed at

various times in the general direction of the problems bothering on the following headings

and

sub headings: a) Theoretical Framework: (i) Overview of simulation Modeling (ii)

Experimental Design for simulation, (ii) Overview of Multipurpose Dam, (iii) World

Multipurpose Dam, (iv) Overview of Water Transfer, (v) History of Nigerian Waters, (vi)

Nigerian Water Ways, (vii) , Hydropower Technology and Resources.

b) Conceptual Framework: (i) Bayesian Decision Theory, (ii) Steps of Decision Making

Process, (iii) Decision Making under Uncertainty and Risk, (iv) Expected Monetary Value, (v)

Expected Opportunity Loss, (vi) Steps of Calculating EOL, (vii) Expected Value of perfect

Information, (viii) Converting infinite to finite Bayesian Decision Model, (ix) Bayesian

Decision Model Components, (x) Net Present Value of Project Cashflow.

(c) Empirical Framework: (i) Empirical Models, (ii) Research gap of the Literatures

Reviewed and Summary of Literatures Reviewed.

2.1 Theoretical Framework

This section covers the following: overview of simulation modeling, Experimental Design for

simulation, Overview of Multipurpose Dam Project, World Multi-Purpose Dams, Overview

of Water Transfer in Water Resources System, History of Nigerian River Basins, Nigerian

17

Navigation-Water Ways, Inventory of Dams and Reservoirs and Hydropower Technologies

and Resource.

2.1.1 Overview of Simulation Modeling

Simulation modeling may be defined as a technique that imitates the operation of a real-world

system as it evolves over a period of time. There are two types of simulation models: and

static simulation model. A static model simulation model depicts a system at a given point in

time. A dynamic simulation model depicts system as it transformed over time. Simulations

can be deterministic or stochastic simulation. A deterministic simulation contains no random

variables, whereas a stochastic simulation may be depicted by either discrete or continuous

models. A discrete simulation is one in which the state variables change only at discrete point

in time. In a continuous simulation, the state variables change continuously over time.

Simulation gives us the flexibility to study systems that are too complex for analytical

methods. However, it must be put into proper perspectives. Simulation models are time

consuming and costly to construct and run. Additionally, the result may not be very precise

and are often hard to validate. Simulation can be powerful tool, but only if it used properly

(Wayne, 2004).

In summary, simulation modeling has the following important features:

Simulation model is a technique that imitates the operation of a real-world system as

it evolved over a period of time.

Simulation model can be classified into two types of models namely static [System at

particular pointing time] and Dynamic [System as it evolves over time]

Simulation model can be deterministic [Random variable] or Stochastic [Discrete or

continuous variable]

Simulation model can be a powerful tool if properly used.

18

Simulation models are time consuming and costly to construct and run

Willemain (1994) recommended that “effective operation Research Practice requires more

than analytical competence: it also requires, among other attributes technical (e.g., when and

how to use the given technique) and Model Construction skills Communication and

Organization survival”

Model Construction, involves translating the problem definition into mathematical

relationships. If the resulting model fits into one of the standards mathematical models, such

as linear programming, a solution is usually attainable algorithms. Alternatively, if the

mathematical relationships are too complex to allow the determination of an analytical

solution, the operation Research team may opt to simplify the model and use a heuristic

approach or the team may consider the use of simulation, if appropriate. In some cases, a

combination of mathematical, simulation and heuristic models may be appropriate for solving

the decision problem.

Model solution, by far, is the simplest of all Operation Research phases because it entails the

use of well-defined optimization algorithms. An important aspect of the model solution phase

is sensitivity analysis.

Sensitivity analysis, it deals with obtaining additional information about the behavior of the

“Optimum” Solution when the model under goes some parameter variations. Sensitivity

analysis is mainly needed when the parameters of the model cannot be estimated accurately.

In this case, it is important to study the behavior of the optimum solution in the neighborhood

of the initial estimates of the model’s parameter.

Model Validity, checks whether or not the proposed model does what it supposed to do that

is, does the model provide a reasonable prediction of the behavior of the system under study?

Initially, the Operation Research team should be convinced that the output of the model does

not contain “surprises”. In other word does the solution make sense? Are the results

19

initiatively acceptable? On the formal side a Common Method for checking the validity of a

model is to compare its output with historical output date. The model is effective if, under

similar input conditions, it reproduces past performance. Generally, however, there is no

guarantee that future performance will continue to duplicate past behavior. Also, because the

model is usually based on careful examination of past data, the proposed comparison should

be favorable.

If the proposed model is depicting a new (non-existing) system, no historical data would be

available to make the comparison. In such cases, we may resort to the use of simulation as an

independent tool for verifying the output of the mathematical model. Application, of the

solution of a validated model involves the conversion of the model results into operating

instructions issued in undesirable form the individual who will administer the recommended

system. The burden of this task lies primary with the Operation Research.

2.1.2 Experimental Design for simulation

A Modeled system cannot be inclusive without been subjected to a test, where its reliability

will be confirmed prior operation, Stamatelatos et al (2002) and Vesely et al (2002) against

the foregoing states that “Risk analysis is a very broad field, utilizing a variety of quantitative

approaches. In the present context, however, we are largely concerned with risk analysis of

complex engineering system (e.g., nuclear power plants, infrastructure such as dams, and

space and defense systems) that are made up of highly reliable and frequently redundant

components, which in most cases are required to have an extremely low risk of catastrophic

failure. The normal method to risk analysis for such systems focus on the analysis of

initiating events and subsequent events sequences that could lead to failure, and on

enumerating and calculating the probabilities of different out comes through tree-based

analytical procedures. For many types of systems (e.g., nuclear power plant probabilistic risk

assessments), these approaches work well. However, systems that are highly dynamic can be

20

very difficult to model realistically using event treat/fault tree approaches, and they require a

tremendous amount of preprocessing effort.

As a result, an approach like Gold Sims that facilitates explicit representation of dynamic and

variability potential provides a powerful complement to existing methods. Gold Sim is a

general-purpose dynamic, probabilistic (Monte carol) simulator. Dynamic simulation allows

the analyst to develop a representation of a system whose reliability is to be determined, and

then observe that system’s performance over a specified period of time. The primary

advantages of dynamic probabilistic simulation are:

The system can evolve into any feasible state and its properties can change suddenly

or gradually as the simulation progresses.

The system can be affected by random processes which may be either internal (e.g.,

failure models) or external,

If some system properties are uncertain, the significance of those uncertainties can be

determined.

The continued that “in Monte Carlo simulation the model is run many times with uncertain

variables sampling different values each time (each run is called a realization) these

realizations are each considered equally likely (unless specialized sampling techniques are

used), and can be combined to provide not only a mean, but also confidence bounds and

range on the performance of the system. In addition to the performance of the statistical data

these realizations provide, multiple realizations may also reveal failure modes and scenarios

that may not be apparent, even to experienced task and reliability modelers. In addition to

providing a more accurate representation of uncertainty, Gold Sim (Monte Carlo simulator)

also allows you to create a more detailed and accurate representation of your systems that can

be achieved with even the most sophisticated risk and reliability methodology, with Monte

Carlo simulation, you can:

21

Model components that have multiple failure modes: It allows you to create multiple

modes for components, each of which can either be defined by a distribution do not have to

use time as the control variable. For example, a vehicle might use mileage to define failure,

while aircraft might use the number of cycles.

Model Complex Interdependencies: In addition to providing a logic-tree mechanism to

define relationship Monte Carlo simulation also allows you to model the more subtle effects

of failure on the other portions of the system. For example, you can easily model a situation

where the failure of one component causes another component to wear more quickly.

Model the External Environment: Reliability element in Goldsim (Monte Carol Simulation

is fully compactable with all other Goldsim operates can also be modeled and can affect and

interact with the system. These features and capability provide a powerful engine for realistic

modeling the risk and reliability of complex engineering system”

2.1.3 Overview of Multipurpose Dam Project

Multi-purpose dam as called, support navigation, recreation, flood control, irrigation, water

supply and hydro-power with each benefit providing significant, economic impacts on a local

regional and national level. According to UNESCO-WWAP, (2003), Dams have been

constructed for millennia, influencing the lives of humans and the ecosystems they inhabit.

Remnants of one such man-made structure dating back 5,000 years are still standing in

northeast Africa.

Around 2950-2750 B.C., the first dam known to exist was built by the ancient Egyptians,

measuring 11.3 meters tall, with a crest length of 106 m and foundation length of 80.7 m

(Yang, et al, 1999). The dam composed of 100,000 tons of rubble, gravel, and stone, with an

outer shell of limestone. The immense weight was enough to contain water in a reservoir

estimated to have been 570,000 cubic meters in capacity (Yang, et al, 1999).

22

Skinner, et al (2009), stated that “West African countries have built over 150 large dams on

the region’s rivers, increasing water storage capacity and regulation of water courses to

support the economic development of the countries of the region. Over the next 30 years,

many more will be built, not least as a response to increasingly fluctuating rainfall. However,

the construction of these dams has often led to the complex and difficult displacement and

relocation of populations, often affecting thousands of people: 80,000 people in the case of

Ghana’s Lake Volta created by the dam at Akosombo; 75,000 people with the dam at Kossou

in Ivory Coast. The construction of large dams in West Africa is one government response to

the challenges of water management to meet national needs for irrigation or for electricity.

However, their construction has often generated major socioeconomicand environmental

impacts that require heavy investments to mitigate them. From the dam operator perspective,

benefit sharing promotes good community relations that reduce the risk of project delays.

From the perspective of potential investors, realistic provisions for local benefit sharing mean

that locally affected communities and the public are more likely to support a dam project. As

a consequence, the investor’s risk exposure is reduced and investors are more inclined to

become financing partners. Benefit sharing also helps to address past shortcomings in dam

planning and management that are well documented. These include failures to honour social

commitments made to project-affected communities and failures to finance environmental

mitigation measures. It addresses the need to ensure that there is a stream of financing to

meet such needs over the longer term.

Types of Multi-Purpose Dams

World Commission on Dams (2000), stated that, the world has almost 900,000 dams built on

the numerous rivers across six continents, of those structures, 45,000 are classified as large

dams for having 15 m and a reservoir volume exceeding 3 million m3. The four types of

dams are gravity, embankment, arch, and buttress (Polaha & Ingraffea, 1999; BDS,2009).

23

The gravity dam uses the sheer weight of the earth, rock, and concrete to contain water

(Polaha & Ingraffea, 1999). An embankment dam is made of earth or rock with the addition

of an impermeable core (BDS, 2009). Arch dams require less material than the previous two

types and depend on the strength of arch action to hold back the water and are typically

located in “narrow spaces with strong abutments“ (Polaha & Ingraffea, 1999). Buttress dams

rely on added structures to support the wall against the pressure of the water and can vary in

shape from “flat to circular” (Polaha & Ingraffea, 1999). Depending on the site, design, and

materials available, any of the above types of dams may suit the needs and as most large

project, will serve more than one purpose. The basic benefits of these barriers include: flood

reduction and flow regulation, storage of water for food crop irrigation and daily use,

generation of electricity, and increased port access. These benefits do intertwine with

consequences impacting humans and the environment through species/habitat loss, inundated

fertile land and archeological sites, and relocation of inhabitants.

(a) Benefits Multi-Purpose Dams

Flood Control and Flow Regulation: Before diversion schemes and other methods were

used to move water, humans and other flora and fauna resided along brooks, streams, and

rivers. These surface waters are part of a watershed, which is a defined area where rain falls

to the earth and travels either across the surface or infiltrates into the ground; the water

eventually converging into rivers flowing to a sea or ocean (CTIC, 2009). One component of

a watershed is the floodplain, the area outside the bank of a river where water covers the

ground during a flood.

Every year, “floods kill thousands and affect the lives of millions

(Clarke & King, 2004). The number of floods is on the rise. In 1992, 57 floods were recorded

worldwide and by 2001, 156 floods were reported (Clarke & King, 2004). During President

Roosevelt’s term, the Mississippi Delta suffered from reoccurring floods in 1912-13, 1916,

and 1927, the latter event being the most devastating. Roosevelt called on the U.S. Army

24

Corps of Engineers, a separate federal branch of the army created to perform civil

engineering works throughout the nation (U.S. ACE, 2007). The Corps built dams upstream

of the affected area on the Mississippi River to alleviate any further damages from flood

control (U.S. ACE, 2007).

Irrigation and Water Usage: With the construction of dams, the demand of water increases.

Transporting water for irrigation purposes has been performed for generations. A civilization

dating back to 1000 B.C., called the city of Marib, was found to use an intricate diversion

method for irrigating their fields (Lanz, 1995). In Africa and the Middle East, 1,272 and 793

large dams, respectively, are used primary for irrigation. Though dams may not be necessary

for irrigating fields, the incorporation of such structures allows for increased amount of land

to be cultivated. “Half the world’s large dams were built exclusively or primarily for

irrigation and some 30-40% of the 271 million hectares irrigated worldwide rely on dams”

(WCD, 2000). With the population increasing, the agriculture sector will face the increasing

demand for food production. Today, the agriculture sector is presently the number one water

consumer and will likely remain so for years to come (United Nations, 2002). In addition to

food production, water is also required for human consumption. Reservoirs have enabled

water supplies to also be diverted to serve populations. The Hetch Hetchy Dam, constructed

in the1920s, was built to supply water to San Francisco 150 miles away (Bily, 2000). Lake

Mead, created by the Hoover Dam, provides 84% of Las Vegas’ water needs.

Power Generation: In the mid 1770’s, Bernard Forest de Bélidor, a French hydraulic and

military engineer, wrote a four volume series about using falling water to derive electricity

(EERE, 2008). The energy potential would certainly be able to provide many people and

companies with sufficient, inexpensive power. The initial capital costs for construction may

be significant, but many lenders are able to help fund the efforts. The World Bank had

assisted many countries in projects in Africa, India, Asia, and elsewhere. Industries across the

25

world are using this type of energy, which supplies five to nineteen percent of the total

electricity produced in the U. S. (Leslie, 2005; Clarke & King, 2004).

Although advances in technology enable the production of hydropower without a dam

present, seasonal changes in water flow make a containment barrier an ideal fix. Rivers

fluctuate throughout the year with the waxing and waning of precipitation, freezing, and

melting (Peterson, 1954). The variation makes production operations difficult to maintain

without steady electricity. To circumvent this inconvenience, a dam is used to control the

release of water to generate consistent energy, improving efficiency, which are typically

regarded as best practices in managing most aspects of life. Many advocates promote water

generated power from a pollution perspective “because it does not foul the air or

conspicuously degrade water…there [are] no invisible radioactive emissions, no possibility of

meltdowns” (Echeverria, et al, 1989). With water power, businesses and people living next to

the river are not required to live tangentially any longer. Power lines are utilized to bring

electricity to the locations significantly long distances away from the source (USGS, 2008).

Navigation: When the design and topography allow for increased navigation inland and aid

in the transport of manufactured goods, these dams provide an addition benefit. After

construction of a dam, the area is filled, increasing the depth of the water, hence enabling

larger ships to navigate to newly accessible ports (BDS, 2009). International trade relies on

major rivers to transport product around the world. Markets for imports and exports were

limited to seas, oceans, and the largest rivers, but with advancements in dam technology,

accessibility has increased (FEMA, 2006).

Recreation: Water access is not limited to cargo transport. FEMA found the primary function

of almost 40% of all reservoirs in the U.S. to be for recreation (2006). Not only do large dams

supply water for food production and storage, provide electricity, and increase navigation, but

26

create new locations for humans and wildlife to enjoy and inhabit. Essentially a large lake, a

reservoir provides many people with opportunities to enjoy swimming, fishing, and boating

(FEMA, 2006). Although dams have provided several benefits for humans, improving the

lives of many; negative environmental and social impacts also occur (Richter & Thomas,

2008).

(c) Costs

The number of people served, the water capacity, new habitats, energy potential, increased

irrigable land, are all benefits and can be measurable. However, dams and the accompanying

reservoirs also cause another series of issues, such as ecosystems being altered, people

relocated, and species, land, and archeological sites lost. These factors are more difficult to

quantify.

(d) Species Loss

The aquatic species inhabiting the waterways being dammed are immediately affected. The

several species of salmon traversing the Skagit in the northwest of the United States, once

abundant numbering about 2 million, have been reduced to under 9,000 (Rothfeder, 2000).

Due to the dozens of dams built over the last 50 years to generate electricity, state fisheries

biologists now transport the juvenile salmon 250 miles downstream to the ocean in order for

the fish to complete their life cycle (Rothfeder, 2000). On the opposite side of the earth,

China has species issues which cannot be remedied by tanker trucks.

The Chang Jiang basin is one of the richest ecosystems in China and concern for its

sustainability foresees a number of species significantly declining, including the river

dolphins, alligators, and paddlefish (Pitzl, 2007). The earth has five species of river dolphins,

one of which resides in the Chang Jiang in China (Dudgeon, 2000). Dams fragmented the

river and the increase of pollution from industries and the general population have affected

27

the Lipotes vexillifer species; approximately 200 individuals remained in 2000 (Dudgeon,

2000).

(e) Environmental Alterations and Degradation

As the world population continues to grow, the environment on which people depend will

ultimately be negatively affected. The Aral Sea is acknowledged as the worst case of

environmental degradation. The sea has lost 80% of its volume because of the diversion of

the Amu and Syr rivers to irrigate the deserts of Uzbek and Kazakh for cotton production

(Barlow & Clarke, 2002). Flora and fauna are also affected by degradation to the landscape

from the flood control upstream of dams and the lack thereof downstream. Significant

portions of land have been inundated by dam reservoirs, flood control approximately “one

million square kilometers (about 380,000 square miles)”worldwide (Barlow & Clarke, 2002).

The sediment once carried down rivers now accumulates behind the barriers reducing the

fertility of flood plains downstream and causing “erosion of riverbanks, coastal deltas, and

even distant coastlines” (Pearce, 2006). West Africa’s coastal lagoons are all being washed

away because limited particulate material is available to replenish the shoreline (Pearce,

2006). “The solids in the Nile River have decreased to such an extent that the Delta coastline

is already showing signs of receding” (Parker, 1995a). The lack of flood waters is also

causing similar situations in the Californian Imperial Valley, the Netherlands, and the

Australian Snowy Mountain project, where the soil salinity is increasing, affecting soil

quality and crop production (Davidson & Brooke, 2006). Further inland, flood control rivers

do cover the ground, periodically sluicing areas inhabited by humans and cause millions of

dollars in damage.

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(f)Dam Failures

The environment is an intricate system, all its parts interconnected to work together. Though

lack of water has had severe outcomes, too much water is also taking its toll in other parts of

the world. The reason for the failure could be linked to design, material, site, attack, or a

combination. The Carbora Bassa Dam in Mozambique, built by the Portuguese, has been a

target of sabotage over many years of civil wars within the country, which has weakened the

structure (Rothfeder, 2001). In 2000, Mozambique experienced the most devastating flood on

record when the spillway of the Carbora Bassa broke open causing a torrent of water to flood

the villages downstream (Rothfeder, 2001). People, having found safety in trees, were

stranded for five days in order to escape the muddy water lapping at their feet (Rothfeder,

2001). Mozambicans had to deal with their homes being flooded during the rainy season, but

for people living next to largerivers where large dams have been built or are in the process of

being constructed, their homes are or soon will be permanently underwater.

(g) Social Effects

“… Dams have physically displaced 40-80 million people worldwide, and most of these

people have never regained their former livelihoods (WCD, 2000). Inhabitants along rivers

will not only be affected by water quality issues, but their way of life will be altered

indefinitely. People living downstream of a dam are also forced into social change. Senegal

and Mauritania are two locations where the altered flow of the river upstream “had severe

implications for [their] cultural traditions and livelihoods” (Skinner, 2000).

They are

powerless watching their towns, “ancestral shrines, cultural patterns”, their way of life, as it is

swallowed up by a flood control river (Goldsmith & Hildyard, 1984). The loss of homes

includes the land on which they were built. The land along rivers is typically prime soil for

growing crops. A dam creates a permanent flooded condition causing the river fills its banks,

saturates the floodplains, and engulf the land below (Leslie, 2005).

“In general, those people

29

relocating worked relatively flat and fertile area and now must move to steeper and infertile

hillsides and upland areas” (Heming, et al, 2001). In the new locations, they will still need

food and fuel, which then requires them to “cultivate the steep slopes in order to grow the

necessities” (Heming, et al, 2001). As the new residents strive to survive, they will indirectly

cause increases in water runoff and soil erosion because of forest and grassland destruction

for crops (Heming, et al, 2001). Many people are asked to move to villages or cities. In Porto

Velho, Brazil, natives of the area are finding difficulty visualizing a new life, one that does

not include fishing in the river rapids or living from a vegetable farm; their new homes are

locate in a village without access toeither (Partlow, 2008). The dam near Porto Velho was not

the first and will most likely not be the last to bring about such controversy. The following

case studies analyze dams built on four continents and selected benefits and costs of each.

2.1.4 World Multi-Purpose Dams

There various kinds of multi-purpose dams constructed across the globe providing various

functions and benefits and this is reviewed in this section as follows:

(i)

Multi-purpose Dam in North America and Features

Hoover Dam : In the first instance, Hoover Dam was established to provide job to a teaming

jobless nation among others. The contract was awarded to Six Companies and the

construction schedule was advanced in order to provide jobs due to the massive

unemployment caused by the Great Depression (Corfield, 2007). Over 21,000 people from 47

states plus foreign workers were involved in building the dam and began work in 1932

(USBR, 2004a; USBR, 2004b; Clarkin, 2000).

The Area: The Colorado River, located in the Great Basin of the southwest United States,

flows through an area fairly dry throughout, varying mainly in temperature from north to

south. The Colorado River Basin covers an area of 637,000 square kilometers and expands

30

across seven states consisting of Arizona, California, Colorado, Nevada,New Mexico, Utah,

and Wyoming, and the northeast area of bordering Mexico (Atkins, 2007; USBR, 2008).

Configuration: The design entailed a concrete arch-gravity type dam (PBS, 2001; USBR,

2008). The complete dam, including all structures, was finished in 1936 almost 2 years ahead

of schedule (NID, 2004). The barrier spans 379 meters across the Black Canyon, measures

201 m (660 ft) at the base and 13.7 m at the crest, and stands at 221 m tall and contains over 3

million m3 of concrete (NID, 2004; DWMI, 2009; Gibbs, 2002; USBR, 2008). Hoover Dam

cost more than US$165 million to complete, holds back an artificial body of water known as

Lake Mead, which is a 35 million m3 reservoir, and the power plant within the dam generates

4 billion kilowatt-hours of hydroelectric power annually (PBS, 2001; Gibbs, 2002; DWMI,

2009).

Benefits: When proposed, the purposes for building the Hoover Dam were flood control,

sediment regulation, irrigation, municipal and industrial water supply, and generation of

electrical power (Davidson & Brooke, 2006). The population of the Colorado River Basin has

continued to grow and now is home to between 17 and 28 million people who depend on the

river as their primary source of water (USBR, 2008; Atkins, 2007; MSNBC, 2007). Lake

Mead, the reservoir behind Hoover dam, has created “new wildlife habitats along the shores

where, in 1985, 250 species of birds were identified in theregion” (Clarkin, 2000). The area

has also become a prime recreation location where nine million people visit Lake Mead each

year for swimming, boating, skiing, fishing, etc (USBR, 2008).

Issues and Constrains: However, the creation of a new habitat and recreational area has

caused places downstream to deteriorate. The lack of sediment deposits in the Gulf of

California delta has altered the area habitat to the point that wildlife, such as deer, birds, and

bobcats, have begun to disappear (Clarkin, 2000).

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(ii)

Multi-purpose Dam in South America and Features

Itaipú Dam: During the 1960s, the area experienced consecutive years of drought, lacking

waterneeded for drinking, irrigation, and industry (Parker, 1995b). As a result of the drought,

the leaders of Brazil and Paraguay forged a partnership in 1966 by signing an agreement to

create a mutually beneficial dam.They formed the Itaipú Binacional and worked with the

International Engineering Company to build the Itaipú Dam (PBS, 2001).

The Area: The Paraná River is the seventh largest in the world and second longest in South

America, running along the border between Brazil and Paraguay (Parker, 1995b; Lopez, et al,

2000). To the east of the river is Brazil, the fifth largest country in the world, covering an

area of 8.5 million square kilometers and having a population over 170 million people (Perz,

2007; Parker, 1995b). Brazil’s southern uplands and Rio Grande do Dul are subtropical in

climate characterized by hot summers and cold winters (Parker, 1995b). On the west bank of

the Paraná is the country of Paraguay, significantly smaller in comparison, composed of

406,750 square kilometers with a population just under 7 million (CIA, 2009).

Configuration: The project complex stretches 7.7 kilometers across the river, with the Itaipú

Dam making up 1 kilometer of the total length and standing 196 meters in height (Davidson

& Brooke, 2006). The barrier is a hollow concrete gravity dam, which allowed 35% less

material to be used without reducing the strength, though this section of the project still used

12.8 million cubic meters of concrete (Davidson & Brooke, 2006; Krauter, 1998).

Benefits: More than 30,000 workers were employed during the building of Itaipú dam over

the seven years from 1995 to 2002 (Krauter, 1998; Davidson & Brooke, 2006). The reservoir

the dam created, Itaipú Reservoir, is calculated to have a 29 billion m3 (PBS, 2001). The

energy production capacity is 12,600 megawatts with an annual production of 93,428

gigawatt-hours, the energy equivalent of 11 billion tonnes of coal (PBS, 2001; Roluti, 2008).

32

The project took around 18 years to materialize and over US$18 billion to build (PBS, 2001).

With the water capacity of Itaipú, the governments were able to provide water to homes,

farms, and industry. Issues and Constrains: The US$18 billion-dollar project, though

providing benefits for a large amount of people, also necessitated a half million people being

resettled, as well as affecting the local ecosystems to a great extent (Davidson & Brooke,

2006).

(iii)

Multi-purpose Dams in Asia and Features

The Three Gorges Dam: During the monsoon season, the Chang Jiang is subject to recurring,

damaging floods (Pitzl,2007). The uncontrollable floods claimed thousands lives: in 1931-

145,000 people, 1935-142,000 people, 1949-5,699 people, 1954-33,169 people; and 1998-

1,526 people (CTGP, 2002). In the 1950s, due to the series of floods, Mao Tse-tung, the

Chinese Communist leader from 1893-1976, ordered feasibility studies to be conducted on

potentially damming the river (Pitzl, 2007).

The Area: One cannot talk of Asia without mentioning China. China is the biggest economic

player in the region. China is the fourth largest country in the world with a land area of 9.3

million km2 of which about 15% is arable (CIA, 2009; Pitzl, 2007). Of China’s one billion

plus population, 96% of the people inhabit half the national territory (Parker, 1995c). Much

of the population relies on two major rivers that run through the country. The river that

supplies Beijing, with headwaters in the Mongolian mountains, is the Huang He (Yellow

River) in the north central part of China (Parker, 1995c). The Chang Jiang (Yangtze River),

the third-longest river in the world, is the other which runs through south central China and

has a more regular flow pattern compared to the Huang He (Parker, 1995c). With a more

dependable water source, the Chinese connected the Chang Jiang and Huang He through the

construction of the Grand Canal” (Pitzl,2007).

33

Configuration: The country’s engineers found Three Gorges to have the best combination of

topographical and geological conditions for building a dam (CTGP, 2002). About 20,000

people have been working almost non-stop to complete the 2.3 km , 185 m high structure by

2009 (CTGP, 2002; PBS, 2001). The gravity dam contains 14.86 million m3 of concrete and

creates a reservoir extending up to 600 km upstream, with a capacity of 39.3 billion m of

water (PBS, 2001; Carmichael, 2000).

Benefits: The major city of Chongqing, located in an area of rich manufacturing and

agriculture activities, is now a major port city due to the reservoir flood waters increasing

access for ocean-going vessels (Pitzl, 2007). The Three Gorges Dam Project included a 5

series lock allowing larger ships to navigate inland, upgrading navigation from ten million

tons to fifty million tonnage fleets (CTGP, 2002).

With such a development, the effort

approved by the Peoples’ Congress to transform the “largely rural agrarian society to a

developed economy” will move towards fruition (Carmichael, 2000). Another aspect of

industrialization is having sufficient electricity for manufacturing and other elements of

living. In terms of energy generation, the dam’s powerhouse will have a production capacity

of 18,200MW (CTGP, 2002).

Issues and Constrains: Though the dam provides benefits to people in other locations of

China, the area is significantly affected. Immediate effects will be the “reduction in numbers

of species in the river basin, most notably river dolphins, alligators, and paddlefish” (Pitzl,

2007).

(iv)

Multi-purpose Dams in Africa and Features

Aswan High Dam: In 1952, Egyptian president Gamal, Abdal-Nasser pledged to control his

country’s annual flood with an expensive dam across the Nile River (PBS, 2001). The dam

34

would control flooding, provide water for irrigation year-round, and supply hydroelectric

power (PBS, 2001).

The Area: Egypt, the most northeast country in Africa.. The land area of the country is

995,450 km and the water occupies an additional 6,000 km (CIA, 2009).

Configuration: The structure measures 3,829 m in length, 111 m in height, and widths of 40

m at the crest and 980 m at the base (Thompson, 2000). With the twelve Francis turbines,

each with an output of 175 megawatts, the electrical energy generation is an annual average

of 10 billion kilowatt-hours (1,228 tonnes of coal equivalent) (Ford, 2007). The reservoir

“Lake Nasser, contains some 200 billion ft3. (5.7 billion m3) of water” (Kich,2007).

Benefits: After completion, “the dam controls flood, ensures reliable and regular water

supply to irrigated farms along the river, and provides hydroelectric power and water for

human consumption and industrial use” (Kich, 2007).

Issues and Constrains: However, without the natural nutrient input provided by past flood,

the harvests of up to three crops a year require “massive support of fertilizer” (Parker, 1995a).

Prior annual floods not only cleansed the soils of salts and deposited nutrients, but also

reduced the number of rats and disease-bearing snails. With the decline of flood, incidences

of disease have been on the increase” (Thompson, 2000). Egyptians have been affected by the

construction of the dam which required ten thousand people to relocate, altered natural

habitats, submerged ancient temples and monuments that were not able to be moved to higher

locations (Davidson & Brooke, 2006; Thompson, 2000).

(v)

Multi-purpose Dams in Nigeria and Features

Kainji Dam: Kainji Dam is a dam build across the Niger River in Niger State of

Northern Nigeria. The total cost was estimated at US$209 million. Kainji Dam extends for

35

about 10 kilometers, including its saddle dam, which closes off a tributary valley. The dam

was designed to have a generating capacity of 960 megawatts; however, only 8 of its 12

turbines have been installed, reducing the capacity to 760 megawatts. (Daily Trust Online,

2012)

(vi)

Multi-purpose Dams in Cross River State and Features

Obudu Dam: The Obudu Dam is an earth-fill structure with a height of 15 m and a total

crest length of 425 m, and has a capacity of 4.2 million m3.(Enplan Group, 2004), The dam

is located within the Obudu crystalline basement plateau, a low-lying undulating region of

low seismic activity.( ESU E.O et al, 2010)The dam was commissioned in 1999 for use in

farm irrigation, fishing, and also for recreational and tourism purposes.( Etiosa Uyigue,

March 2006). In September 2000, the paramount ruler of Obudu local government area, his

Royal Highness Uti Agba, promised that his community would protect the facilities installed

at the dam . (Obudu Community, 2000).

The dam was hit by a massive rainstorm in July 2003, combined with release of excess water

from the Lagdo Dam in Cameroon, damaged the spillway and caused flood control that

destroyed over 200 houses. The estimated cost of repairing the damage and also completing

the irrigation works was estimated at about N350 million.( Etiosa Uyigue,2006) A 2004

safety review reported that immediate work was required to restore the spillway, at an

estimated cost of N272 million.( Enplan Group, 2004) In July 2009, the Federal government

issued a tender for engineering supervision of remedial work on the dam including

refurbishing or replacing hydro-mechanical parts, electrical installation and civil engineering

infrastructure.(FMAWR, 2010) The dam has reduced downstream water volumes in Obudu

town, causing acute scarcity of drinking water in the dry season.(Agnes Ingwu, 2012).

36

Conclusion: Most rivers have already been managed in some form. The World Commission

on Dams (WCD) has reported on the effects of large dams, and small, after their two year

study. In view of the planned technical, financial, and economic performance versus the

actual outcomes, the WCD found large dams to fall short of meeting any of the expected

goals.The ecosystems, biodiversity and downstream livelihoods are well documented and

were found to be degraded, along with limited success in predicting and avoiding loss in

these areas (WCD, 2000). For example, the Commission found “the use of fish passes to

mitigate the blockage of migratory fish has had little success, as the technology has often not

been tailored to specific sites and species”(WCD, 2000). Most facilities do not even have fish

passages (Marmulla, 2001). Most relocatees are not adequately provided for either. Knowing

one way of life and being asked to move where the population is denser, or the land is lower

quality, or acquiring skills are necessary for a new career, can be a shock many may not be

able to overcome. For the engineers, they have been asked to build a dam that will enable

people to have more food, possibly year round, as well as electricity, drinking water, and

recreation. Those who are asked to sacrifice their homes may get overlooked for a presumed

great good. Declines in fish populations to burying homes and cultures, other methods should

be explored in greater depth. The designers of the Three Gorges Project (TGP) were advised

to go the route of several smaller dams, but chose to move forward with the plan in hand. On

the TGP website, several pages boast of being the largest in a number of categories. Many

years prior, not long after the Hoover Dam was completed, Francis Crowe, “the [Bureau of

Reclamation] surveyor on the project, later put it, “I was wild to build this dam-the biggest

dam built by anyone, anywhere” (Pearce, 2006).

Ezugwu (2013) postulated that “Nigeria has abundant surface water bodies and good dam

sites that could be utilized for dam construction to create reservoirs for various water uses

including hydropower generation, flood control, water supply, irrigation, navigation, tourism,

37

sanitation, fish and wild life development and ground water recharge. Dam development and

disasters on people and the environment were examined. Various parts of our country are

presently seriously ravaged by flood control. Moreover, impacts of dams and dam failures in

the past were outlined. Various causes of dam failure were enumerated. Recommendations

on how to avert future dam disasters in our country were also captured. Dam development in

this country started many decades ago. These dams store water for various purposes including

hydro power development, irrigation, water supply, flood control, navigation, tourism,

sanitation, etc. Inadequate attention is being paid to the issue of flood control and other

disasters arising from dam projects in our country.”

2.1.5 Multipurpose Benefits Framework

In this research work there are six data categories that structure the multipurpose benefits framework.

These categories are referred to herein as “uses”, and they represent a culmination of operations and

services made possible due to existence of a reservoir. These uses are broadly classified to identify

categories associated with a reservoir project, and serve as a foundation for assessing collective and

inter-dependent relationships (Marisol Bonnet et al, 2015):

(i)

Power Generation

To quantify hydropower generation, the total annual kilowatt-hours of energy production

from a power plant is multiplied by the average wholesale rate at which it is sold. The unit

price for energy varies between and within the agencies as they cater to different regions of

the nation, each with unique energy markets and demand. This current preliminary analysis

does not include the value of capacity or ancillary services, which could further differentiate

the distribution of overall hydropower benefits. The Nigeria Electricity regulatory

commission, NERC, has put into operation Multi-year Terrific order, MYTO for the

determination of the cost of electricity sold by distribution/retails companies for the period

38

1June 2012-13 to May 2017[Vanguard News]. However, the following are the Electricity rate

according to NERC/DISCO: 250 kWh per household.

Table 2.1: Prices of Electricity per Kilowatt-hour

S/N Electricity consumption is measured in Naira per Kilowatt-hour Year

1 11.37 per KWh 2012-2013

2 11.37 per KWh 2013-2014

3 11.94 per KWh 2014-2015

4 12.54 per KWh 2015-2016

5 13.16 per KWh 2016-2017

Source: Nigerian Electricity Regulation Commission (NERC), 2017.

(ii)

Municipal Water Supply

To produce the benefit of M&I uses, the volume of water stored for municipal and industrial

use is multiplied by the national average price of water per unit volume. In general,

contractors and municipalities reserve a volume of water under contract to be made available

each year for their consumption. This data is largely found within project operating plans that

outline the storage allocations of each reservoir, or in public reports on water use. It is likely

that available water supply sector data in Nigeria are not only fragmentary but at times

deceptive. Only Nigeria and Sudan have practically no metering. IBNET data suggest that

average O&M cost in Nigeria are US$0.28; the African Infrastructure Country Diagnostic

(AICD) reports US$0.60 per cubic meter, which attests to the relatively high cost of water

services in Africa. Although metering is practically absent, the International Benchmarking

Network for Water & Sanitation Utilities [IBNET] estimate of nonrevenue water in Nigeria

in 2012 was 37%. Apparently, data on the Nigeria water sector are unreliable-possibly

because many operators do not enjoy the Administrative and financial autonomy that would

force them to collect and analyze key operating data. Since the Nigeria constitution gives

states considerable latitude in applying federal policies, it is not surprising to find that state

39

water tariffs vary significantly. Borno and Bayelsa even provide water free to residential

customers. Only Abuja, Oyo, Cross Rivers, and parts of Lagos meter consumption and bill

based on that. [Water Supply Tariff setting and Structure and the Effects on the poor- State

Water Agencies [SWA] in Nigeria.

Figure 2.1: Monthly payment per household for water services in Nigeria, 2011-2013

Source: International Benchmarking Network for water and sanitation Utilities (IBNET)

(iii)

Navigation

This benefit is manifested as Shipper savings (S.S), or the amount of money saved by

shippers who send commodities by barge (typically the cheapest shipping option) rather than

by truck or rail (usually the second least expensive option). A national value of S.S. was

provided by the Planning Center of Expertise for Inland Navigation.

To estimate the navigation benefit, the tonnage passed through a powered lock is multiplied

by the national S.S. value. The S.S. units are given in dollars per ton, reflecting the dollar

value saved over the entire length of a shipment. A typical shipment passes through multiple

locks and, consequently, the raw tonnage value at each lock cannot be used directly to

40

estimate the navigation benefit as it would result in double counting over the trajectory of a

shipment. In an effort to eliminate the double counting of goods passing through multiple

locks, the individual lock tonnage is divided by the total tonnage passed through all locks.

This tonnage is multiplied by the national S.S. to generate the navigation benefit. We can

only navigate 30% of Nigeria’s water ways-NIWA [Anna Okon-Punchng.com, Nov17, 2016]

the adequacy of inland waterways infrastructure helps determine Nigeria’s success or failure

in diversifying its production, expanding trade (domestic and foreign), reducing poverty and

improving economic growth. Inland water structures are one of the major infrastructural

factors among others. Nigeria natural endowment in inland waterways was about 10,000

kilometers [only 3000 km is navigable], which if developed through dredging and provision

of auxiliary facilities would provide all-round navigation for transportation of bulk cargo and

passengers.

Let say an average vessel or boat plying the waterways in Cross River Basin is 2000 naira per

day and Vessel tonnage per year.

(iv)

Irrigation

The benefit for irrigation is quantified by multiplying the total acres of land irrigated by the

value of crops grown on those acres. An estimate of crops produced is developed using

geographic information system (GIS) imagery to map the type and acreage of crops that

benefit from supplied irrigation water. A total dollar value is obtained by combining crop

yield data from the state level with nationwide crop prices supplied by the U.S. Department

of Agriculture (USDA). These values were provided by USBR, which keeps yearly data on

the number of acres, types of crops, and regional value of those crops for each of their

projects authorized for irrigation. A total dollar value is obtained by combining crop yield

data from the state level with nationwide crop prices supplied by the U.S. Department of

Agriculture (USDA). These values were provided by USBR, which keeps yearly data on the

41

number of acres, types of crops, and regional value of those crops for each of their projects

authorized for irrigation.

(v)

Flood Control

Flood control benefits are quantified as damages avoided, or the reduction in potential or

realized damages to structures, contents of structures, and land use in areas that would have

been inundated had the structure not been in place. Flood plain curves, using geographic and

local data, allow both the acreage and depth of a prevented flood to be estimated. When a

dam regulates a flood control event, the volume stored is used in the flood plain model. A

fraction of the value of land, buildings, goods, and activities that lie within the flood plain

and would have been destroyed are assigned to the flood event based on its severity. This

ultimately allows a dollar amount of potential damages to be reached. When a dam regulates

a flood control event, the volume stored is used in the flood plain model. A fraction of the

value of land, buildings, goods, and activities that lie within the flood plain and would have

been destroyed are assigned to the flood event based on its severity. This ultimately allows a

dollar amount of potential damages to be reached.

Since the benefit for preventing these natural events can be substantial, each agency performs

a proprietary analysis to estimate damages avoided based on derived flood-stage-damage

relationships for particular regions. This value is commonly assigned to an entire river system

or agency project incorporating the flood benefits of multiple reservoirs with and without

hydropower. To obtain the benefit from a single reservoir, the fraction of total system flood

storage provided by an individual reservoir is multiplied by the damages prevented. In most

cases cumulative damages for the past fifty years were provided, and the benefit was

calculated as an average annual benefit. In some cases, the benefit was obtained from

publicly available annual reports, system-wide flood studies, or district level presentations.

42

(vi) Recreation

Reservoirs are popular destinations for a wide variety of recreation activities including

fishing, boating, camping, swimming, water sports, and wildlife observation. Three common

procedures are available to estimate recreation spending:

(i)

(ii)

The travel cost method (TCM),

The contingent valuation method (CVM), and

(iii) Unit day values (USACE, 2000).

TCM models assume the travel and time costs spent by visitors to get to a reservoir increase

with distance. A demand curve is derived that values the reservoir using travel and time as

‘price’ surrogates. The CVM relies on surveys that ask an individual their willingness to pay

for recreation activities (for which they are not currently paying) at a given location. The unit

day value approach assumes the total benefit of the reservoir can be estimated by multiplying

the number of visitors to the reservoir by the average amount spent per visitor per trip.

Visitation data is produced from surveys and regional economic and population models,

while spending profiles are generally obtained via direct survey (USACE, 2000; Black,

McKinney, Unworthy, & Flores, 1998). However, this research work is based on Unit day

values.

To estimate the economic benefit of recreation, most agencies rely on the unit day value

approach, with visitor counts to reservoirs and related recreation areas obtained through an

agency survey or provided by state and national park services. In this research, the economic

benefit of recreation is computed by multiplying the number of annual visitors to a reservoir

by a daily spending average. In most cases either the average spending amount or the number

of visitors contain regional and temporal multipliers to capture spending trends in a specific

region and account for the amount of time each visitor participates in recreation activities.

Common spending amounts range from $10/visitor/day for local visitors participating in day

43

use activities like bird watching or hiking, to $40/visitor/day or more non-local visitors

participating in leisure or multi-day recreation activities , including water sports and

overnight camping (Stynes, 2005; Stynes and Chang, 2007; Cardno Entrix, 2011; Chang et al.,

2012; White et al., 2013).

Most recreation data represent an estimate based on trends observed at sites around the world.

When survey data are not available at a particular site, it is common for agencies to estimate a

number for that site based on other national recreation areas with similar characteristics. This

approach, in combination with the diverse activities and preferences of recreationists at

reservoirs, lends itself a great deal of uncertainty in number of visits and spending amounts

per activity. In a pure economic benefits analysis, this uncertainty cannot be easily quantified.

To mitigate the uncertainty in a national level analysis, the approach used in this research

restricts valuation to two metrics and relies primarily on data provided by individual agencies.

2.1.6 Water Transfer in Water Resources System

Introduction of Water Transfer: Water transfer is the process by which water is transferred

from one river catchment to another. Transfer can take place by river pipelines or diversion.

There is often too little water in one area and excess of water in another. Water transfer

should as much as possible be improved on both technological and scientifically scale, this is

very necessary to cushion the effects of the changing world. Water transfer can be used as

measures to mitigate the effects of global warming, desertification, flooding, droughts.

Historically, advances in water system management have been motivated by socio-economic

and environmental concerns.

Since the 1970s, the cumulative expense and environmental

impact of developing traditional water supplies have encouraged innovative use of existing

facilities and have led to extended demand management efforts. Currently, growth in water

demands and environmental concerns have caused even these innovations to yield

44

"diminishing marginal returns." These economic and environmental conditions, combined

with recent droughts, have incited further efforts to improve traditional supply augmentation

and demand management measures and have inspired the recent consideration and use of

water transfers. The use of water transfers in many parts of the world, especially in the West,

can be seen as a natural development of the water resources line of work which is seeking to

explore and implement new methods in water management.

This research work identifies the many forms of water transfers available to water managers

and their uses in the engineering of water resource systems.

However, water can be

transferred through the various means as listed below:

(i)

Pipes, pipes that hold water and transfer it to points of needs (e.g. Domestic and

industrial water supply as well as for irrigation)

(ii)

Aqueduct, used to transfer fresh water to highly populated areas.

(iii) Natural and Artificial channels

(iv)

Penstock in the case of powering a turbine through gravity.

2.1.7 History of Nigerian River Basins

The idea of creating River Basin or Water Authorities grew from the success of the

Tennessee Valley Authority in the United States of America in the early 1930s. This idea was

replicated in many countries of the world and it guided the Federal Government in the 60s in

the commissioning of studies which eventually led to the establishment of River Basin

Development Authorities in Nigeria, starting with Chad and Sokoto-Rima River Basin

Development Authorities.

At present, Nigeria has twelve (12) River Basin Development Authorities; their creation

started when the Federal Government passed the River Basin Development Decrees Nos. 32

and 33 of 14th August 1973 to give a legal backing to the establishment of the Chad and

45

Sokoto-Rima River Basin Development Authorities. Afterward, the River Basin

Development Authorities Decrees No. 25 of 15th June, 1976 and the Niger Delta Basin

Development Authority Decree No.37 of 3rd August, 1976 were also promulgated

These Decrees created 11 River Basin Development Authorities. In January, 1994,

Government approved the division of Niger Basin Development Authority into Upper and

Lower Niger Basin Development Authorities, thus bringing the number of River Basin

Development Authorities to 12.

Decrees Nos. 25 and 37 of 1976 established 11 River Basin Development Authorities,

including the Cross-River Basin Development Authority. In 1979, the Cross-River Basin

Development Authority assumed its present geographical entity courtesy of Decree No. 87 of

28th September, 1979.

2.1.8 Nigerian Navigation-Water Ways

Nigeria is endowed with a large resource base of waterways spanning 10,000 km; about

3,800 km is navigable seasonally. Twenty-eight (28) of the nation’s 36 States can be accessed

through water. Nigeria can also link five of its neighboring countries– Equatorial Guinea,

Benin Republic, Cameroon, Chad and Niger Republic by water.

The Rivers Niger and Benue set up the major channels for inland navigation which include

but not limited to the Port Novo- Badagry-Lagos waterways, Cross River, Lekki and Ogun-

Ondo waterways, Lagos Lagoons, Benin River, Escravos channel, Nun River, Orashi River,

Imo River, Ethiope , Lake Chad, Ugwuta lake, and the numerous creeks in the Niger delta.

2.1.8.1 Federal Navigable Waterways

The following are the Navigable water ways in Nigeria:

46

(i)

The River Niger all the way from the Nigerian/Niger/Benin border, through the Nun

and Forcados distributaries to the Atlantic Ocean.

(ii)

The River Benue sources all the way from the Nigerian/Cameroun border to its

confluence with River Niger at Lokoja.

(iii)

The River Cross (Cross River) from the Nigerian/Cameroun border to the Atlantic.

Ocean, and all its distributaries.

(iv)

Major rivers such as: Rivers Sokoto. Kaduna. Geriny. Gongola. Taraba. Donga.

Katsina-Ala. Anambra. Ogun. Oluwa. Osse, Benin, Imo. Kwa Ibo.

(v)

The Intra-coastal route from Badagry, down to the Badagry Creek to Lagos through

Lagos Lagoon to Epe, Lekki Lagoon lo Iwopin. along Omu Creek, Talifa Kivei io

Atijere, Akata. Aboto. Oluwa River to Okitipupa and onto Gbekebo. Arogbo.

Ofunama. Benin Creek to Warri. Also, the canal running from Araromi through

Aiyetoro. Imelumo to Benin River and from Aiyetoro through Mahin Lagoon to

Igbokoda.

(vi)

The waterway from Warri down to the Forcados River, through Frukana, Siama.

Bomadi. Angalabiri. Patani. Torofani. down River Nun to Agberi, Kiama. Sabagreia.

Gbaran Creek, Agudama, Ekpetional into Ekole Creek to Yanaka. Agoribiri Creek to

Egbema, Yenegoa, Sangala to Mbiakpaba. onto Okokokiri, Ofokpota, Olagaga.

Nembe, Adema., Degema, Sombreiro River to Hanya Town, Ogbakiri to Port

Harcourt.

(vii)

The waterway from Port Harcourt, water ways to Amadi Creek down to Bonny River,

into Opobo Channel Adoni River, through Andoni Flats, Tellifer Creek, Imo River.

Shooter Creek. Kwa Ibo Creek, Kwa Ibo River, Stubbs Creeks. Widenham Creek,

Effiat-Mbo Creek, Cross River estuary to Oron and Calabar.

47

(viii)

Rivers Benin, down to Ethiope, Ossiomo. Onne, Aba. Azumini, Olomum. Siluko,

Talifa, Forcados, Penington, Escravos, Warri, Ramos, Dodo, Bonny, Middleton,

Fishtown, Sengana, Brass of Nicholas, Santa Barbara. San Batholomew, Sambriero,

New Calabar, Mbo, Rio del Rey, Uruan, Akwayafe.

(ix)

Creeks Odiama, down to Agamama Tora, Nembe, Krakama, Buguma, Bille, Finima,

New Calabar, Ekole, Cawthprne Channel, Ikane-Bakassi, Omu, Kwato (Gwato),

Adagbrassa, Chananomi, Okpoko, Jones Kulama, Ikebiri, Nikorogba, Sagbama,

Egbedi, Kolo, Laylor, Hughes Channel.

(x)

(xi)

Lakes Mahin, down to Oguta, Osiam Ehomu.

The Orashi River from Oguta Lake moves to Ebocha, Omoku, Kreigani, Moiama.,

Okariki, Egbema, Sombreiro River.

(xii)

Lake Chad, the part within Nigeria.

2.1.8.2 States Accessible By Navigable Inland Waterways in Nigeria

The longest river in Nigeria are the Niger River and its tributary, the Benue River but the

most used, especially by larger powered boats and for commerce, are in the Niger Delta and

all along the coast from Lagos Lagoon to Cross River. (https://niwa.gov.ng/waterways

2.1.9 Inventory of Dams and Reservoirs

Inventory of Dams and Reservoirs in cross river basin were depicted in the table 2.2.

However, judging from the inventory, it appears that none of the said facilities are working in

full capacity most of the facilities are in design and construction stages. Inaddition most the

water facilities either in design state or constructed are mainly for irrigation purposes. This

research work most likely will be providing explanation for the prevailing irrigation

structures in Cross River basin when compared with other River basin purposes.

48

Table 2.2: Inventory of Dams and Reservoirs in Cross River Basin

Source: Cross River Basin Development Authority (2017)

2.1.10 Hydropower Technologies and Resources

Hydropower is a renewable energy source hinged on the natural water cycle. Hydropower is

reliable and cost-effective renewable power generation technology available (Brown, 2011).

Hydropower system often have significant flexibility in their design and can be designed to

content base-load demands with relatively high capacity factors, and a lower capacity factor,

but content with a much larger share of peak demand.

Hydropower is the leading renewable energy source, and it produces around 16% of the

world’s electricity and over 4/5 th

of the world’s renewable electricity. Presently, more

countries in the world depend on hydropower for their electricity supply. Hydropower

generates the bulk of electricity in most countries and plays some role in more than 150

countries. United States, Canada, China are the countries which have the leading hydropower

generation capability (International Panel on Climate Change (IPCC), 2011; Renewable

Energy21 (REN21, 2011; and International Hydropower Association (IHA), 2011).

49

Hydropower is the leading flexible source of power generation available and is capable of

responding to demand fluxes in minutes, delivering base-load power and, when a reservoir is

present, storing electricity over weeks, months, seasons or even years (Brown, 2011 and

IPCC, 2011).

Hydroelectric generating units have the capacity to start up quickly and operate ably almost

instantly, even when used only for one or two hours. This is in contrast to thermal plant

where start-up can take several hours or more, during which time efficiency is significantly

below design levels. In addition, hydropower plants can operate efficiently at partial loads,

which is not the case for many thermal plants. Pumped and Reservoir storage hydropower

can be used to reduce the frequency of start-ups and shutdowns of conventional thermal

plants and maintain a balance between demand and supply, thereby reducing the loadfollowing

burden of thermal plants (Brown, 2011).

Hydropower is the only all-encompassing and cost-efficient storage technology available

today. Despite promising developments in other energy storage technologies, hydropower is

still the only technology offering economically feasible large-scale storage. It is also a

relatively effective energy storage option. (IEA, 2010c). Systems with significant shares of

large-scale hydro with significant reservoir storage will therefore be able to incorporate

higher levels of variable renewables at low cost than systems without the benefit of

hydropower. Hydropower can serve as a power source for both large, centralized and small,

isolated grids. Small hydropower can be a cost-competitive option for rural electrification for

remote communities in developed and developing countries and can displace a significant

proportion of diesel-fired generation. Hydropower projects account for a projected half of all

“certified emissions reduction” credits in the CDM pipeline for renewable energy projects

(Branche, 2012). “Hydropower Sustainability Assessment Protocol” according to The

50

International Hydropower Association enables the production of a sustainability profile for a

project from the assessment of performance within important sustainability. Integrated river

basin management; silt erosion resistant materials, environmental and hydrokinetics issues

will provide continuous improvement of environmental performance and, in several cases,

costs reductions (IPCC, 2011). Hydropower converts the potential energy of water flowing in

a river with a certain vertical fall. The apparent annual power generation of a hydropower

project is directly related to the head and flow of water. Hydropower plants use a relatively

simple concept to transform the energy potential of the flowing water to turn a turbine, which,

then, provides the mechanical energy required to drive a generator and produce electricity

(Figure 2.2).

The key components of a normal hydropower plant are:

(i)

Dam: Most hydropower plants depend on a dam that holds back water, creating a large

water reservoir that can be used as storage.

(ii) Intake, penstock and surge chamber: Gates on the dam open and gravity conducts the

water through the penstock to the turbine. There is sometimes a head race before the

penstock. A surge chamber is used to reduce surges in water pressure that could

potentially cause damage to the turbine.

(iii) Turbine: The water strikes the turbine blades and turns the turbine, which is attached to

a generator by a shaft. There is a range of Configuration possible with the generator

above or next to the turbine.

(iv) Generators: As the turbine blades turn, the rotor inside the generator also turns and

electric current is produced as magnets rotate inside the fixed-coil generator to produce

alternating current (AC).

51

Figure 2.2: Typical “low head” hydropower plant with storage

Sources: Picture adapted from hydropower news and information (http://www.alternative-energynews.info/technology/hydro/)

(v)

Transformer: The transformer inside the powerhouse takes the AC voltage and

converts it into higher-voltage current for more efficient (lower losses) long-distance

transport.

(vi)

Transmission lines: Send the electricity generated to a grid-connection point, or to a

large industrial consumer directly, where the electricity is converted back to a lower

voltage current and fed into the distribution network. In remote areas, new

transmission lines can represent a considerable planning hurdle and expense.

(vii) Outflow: Finally, the used water is carried out through pipelines, called tailraces, and

re-enters the river downstream. The outflow system may also include “spillways”

which allow the water to bypass the generation system and be “spilled” in times of

flood or very high inflows and reservoir levels.

52

Hydropower plants usually have very long lifetimes and, depending on the particular

component, are in the range 30 to 80 years. There are many examples of hydropower plants

that have been in operation for more than 100 years with regular upgrading of electrical and

mechanical systems but no major upgrades of the most expensive civil structures (dams,

tunnels) (IPCC, 2011).

The water used to drive hydropower turbines is not “consumed” but is returned to the river

system. This may not be immediately in front of the dam and can be several kilometers or

further downstream, with a not insignificant impact on the river system in that area. However,

in many cases, a hydropower system can facilitate the use of the water for other purposes or

provide other services such as irrigation, flood control and/or more stable drinking water

supplies. It can also improve conditions for navigation, fishing, tourism or leisure activities.

The components of a hydropower project that require the most time and construction effort

are the dam, water intake, head race, surge chamber, penstock, tailrace and powerhouse. The

penstock conveys water under pressure to the turbine and can be made of, or lined with, steel,

iron, plastics, concrete or wood. The penstock is sometimes created by tunneling through

rock, where it may be lined or unlined.

The powerhouse contains most of the mechanical and electrical equipment and is made of

conventional building materials although in some cases this maybe underground. The primary

mechanical and electrical components of a small hydropower plant are the turbines and

generators.

Turbines are devices that convert the energy from falling water into rotating shaft power.

There are two main turbine categories: “reactionary” and “impulse”. Impulse turbines extract

the energy from the momentum of the flowing water, as opposed to the weight of the water.

Reaction turbines extract energy from the pressure of the water head.

53

The most suitable and efficient turbine for a hydropower project will depend on the site and

hydropower scheme design, with the key considerations being the head and flow rate (Figure

2.2). The Francis turbine is a reactionary turbine and is the most widely used hydropower

turbine in existence. Francis turbines are highly efficient and can be used for a wide range of

head and flow rates. The Kaplan reactionary turbine was derived from the Francis turbine but

allows efficient hydropower production at heads between 10 and 70 meters, much lower than

for a Francis turbine. Impulse turbines such as Pelton, Turgo and cross-flow (sometimes

referred to as Banki-Michell or Ossberger) are also available. The Pelton turbine is the most

commonly used turbine with high heads. Banki Michell or Ossberger turbines have lower

efficiencies but are less dependent on discharge and have lower maintenance requirements.

There are two types of generators that can be used in small hydropower plants: asynchronous

(induction) figure 2.3: and synchronous machines (NHA and HRF, 2010). Asynchronous

generators are generally used for micro hydro projects.

Small hydropower, where a suitable site exists, is often a very cost-effective electric energy

generation option. It will generally need to be located close to loads or existing transmission

lines to make its exploitation economic. Small hydropower structures typically take less time

to construct than large-scale ones although planning and approval processes are often similar

(Egre and Milewski, 2002).

Large-scale hydropower plants with storage can largely de-couple the timing of hydropower

generation from variable river flows. Large storage reservoirs may be sufficient to buffer

seasonal or multi-seasonal changes in river flows, whereas smaller reservoirs may be able to

buffer river flows on a daily or weekly basis. With a very large reservoir relative to the size

of the hydropower plant, hydropower plants can generate produce power at a near-constant

level throughout the year (i.e. operate as a base-load plant). Alternatively, if the scheme is

54

designed to have hydropower capacity that far exceeds the amount of reservoir storage, the

hydropower plant is sometimes referred to as a peaking plant and is designed to be able to

generate large quantities of electricity to meet peak electricity system demand. Where the site

allows, these are design choices that will depend on the costs and likely revenue streams from

different Configuration.

Figure 2.3: Working areas of different turbine types

Source: Based on NHA and HRF, 2010.

(i)

Hydropower Classification by Type

Hydropower plants can be built in a variety of sizes and with different characteristics. In

addition to the importance of the head and flow rate, hydropower structures can be put into

the following categories:

55

(a) Run-of-river (ROR) hydropower projects have no, or very little, storage capacity

behind the dam and generation is dependent on the control and size of river flows.

(b) Reservoir hydropower structures have the ability to store water behind the dam in a

reservoir in order to de-couple generation from hydro inflows. Reservoir capacities can

be small or very large, depending on the characteristics of the site and the economics

of dam construction.

(c) Pumped storage hydropower structures use off-peak electricity to pump water from a

reservoir located after the tailrace to the top of the reservoir, so that the pumped

storage plant can generate at peak times and provide grid stability and flexibility

services.

These three types of hydropower plants are the most common and can be developed across

size and capacity from the very small to very large, depending on the hydrology and

topography of the watershed. They can be grid-connected or form part of a remote local

network.

(ii)

Run-Of-River (ROR) Technologies

In run-of-river hydropower systems and reservoir systems, electricity production is driven by

the natural flow and elevation drop of a river. Run-of-river structures have little or no storage,

although even run-of-river structures without storage will sometimes have a dam. Hence, runof-river

hydropower plants with storage are said to have “pondage”. This allows very shortterm

water storage. Plants with pondage can regulate water flows to some extent and shift

generation a few hours or more over the day to when it is most needed. A plant without

pondage has no storage and therefore cannot schedule its production. The timing of

generation from these structures will depend on river flows. Where a dam is not used, a

portion of the river water might be diverted to a channel or pipeline (penstock) to convey the

water to the turbine.

56

Run-of-river structures are often found downstream of reservoir projects as one reservoir can

regulate the generation of one or many downstream run-of-river plants. The major advantage

of this approach is that it can be less expensive than a series of reservoir dams because of the

lower construction costs. However, in other cases, systems will be constrained to be run-ofriver

because a large reservoir at the site is not viable.

The operation regime of run-of-river plants, with and without pondage, depends heavily on

hydro inflows. Although it is difficult to generalize, some systems will have relatively stable

inflows while others will experience wide variations in inflows. A drawback of these systems

is that when inflows are high and the storage existing is full, water will have to be “spilled”.

This represents a lost opportunity for generation and the plant design will have to trade off

capacity size to take advantage of high inflows, with the average amount of time these high

inflows occur in a normal year. The value of the electricity produced will determine what the

trade-off between capacity and spilled water will be and this will be taken into account when

the scheme is being designed.

(iii)

Hydropower Schemes with Reservoirs for Storage

Hydropower structures with large reservoirs behind dams can store substantial quantities of

water and effectively act as an electricity storage system. As with other hydropower systems,

the amount of electricity that is generated is based the volume of water flow and the amount

of hydraulic head available. The advantage of hydropower plants with storage is that

generation can be decoupled from the control of rainfall or glacial melt. For instance, in areas

where snow melt provides the bulk of inflows, these can be stored through spring and

summer to meet the higher electricity demand of winter in cold climate countries, or until

summer to meet peak electricity demands for cooling. Hydropower structures with large-scale

reservoirs thus offer incomparable flexibility to an electricity system.

57

The design of the hydropower plant structures and the type and size of reservoir that can be

built are very much reliant on opportunities offered by the topography and are defined by the

landscape of the plant site. However, developments in civil engineering techniques that

reduce costs mean that what is economic is not fixed. Reduced costs for tunneling or canals

can open up increased opportunities to generate electricity.

Hydropower can ease the low-cost integration of variable renewables into the grid, as it is

able to respond almost instantaneously to changes in the amount of electricity running

through the grid and to efficiently store electricity generated by wind and solar by holding

inflows in the reservoir rather than generating. This water can then be released when the sun

is not shining or the wind not blowing. In Denmark, for example, the high level of variable

wind generation is managed in part through interconnections to Norway where there is

considerable hydropower storage (Nordel, 2008a).

(iv)

Large and Small Hydropower Schemes

A classification of hydropower by head is interesting because it is this that controls the water

pressure on the turbines, which, together with discharge, are the most significant parameters

for deciding the type of hydraulic turbine to be used. Generally speaking, hydropower is

usually classified by size and the type of structure (run-of-river, reservoir, pumped storage).

Although there is no agreed definition, the following bands are typical to describe the size of

hydropower projects:

(a) Large-hydropower: 100 MW, feeding into a large electricity grid;

(b) Medium-hydropower: From 20 MW to 100 MW almost always feeding a grid;

(c) Small-hydropower: From 1 MW to 20 MW usually feeding into a grid;

(d) Mini-hydropower: From 100 kW to 1 MW that can be either stand-alone, mini-grid

or grid connected;

58

(e) Micro-hydropower: From 5 kW to 100 kW that provide power for a small

community or rural industry in remote areas away from the grid; and

(f) Pico-hydro: From a few hundred watts up to 5 kW (often used in remote areas away

from the grid).

(v)

Breakdown of Hydropower Costs by Source

The largest share of installed costs for large hydropower plant is typically taken up by civil

works for the construction of the hydropower plant. Electrical and mechanical equipment

usually contributes less to the cost. However, for hydropower projects where the installed

capacity is less than 5 MW, the costs of electro-mechanical equipment may dominate total

costs due to the high specific costs of small-scale equipment. The cost breakdown for small

hydro projects in developing countries reveals the diversity of hydropower projects and their

site-specific constraints and opportunities. The electro-mechanical equipment costs appear to

be higher than for large-scale projects, contributing from 18% to as much as 50% total costs.

For projects in remote or difficult to access locations, infrastructure costs can dominate total

costs.

59

Figure 2.4: Cost breakdown of hydropower projects in developing countries

Source: (IRENA); Renewable Energy Technologies: Cost Analysis Series

60

2.2 Conceptual Framework

This section includes all the steps in decision making using Bayesian Decision theory.

2.2.1 Bayesian Decision theory

Bayesian decision theory was developed by an English reverend Thomas Bayes (1701-1761)

and published posthumously (1763). The essence of Bayesian inference is in the rule, known

as Bayes' theorem that tells us how to update our initial probabilities P (Y) if we see evidence

X, in order to find out P (Y|X) [Posterior Probability]

Bayesian inference comprises the following three principal steps:

i. Obtain the initial probabilities P (Y) for the unknown things. (Prior distribution.)

ii.

iii.

Calculate the probabilities of the evidence X (data) given

Different values for the unknown things, i.e., P (X | Y). (Likelihood or conditional

distribution.)

iv.

Calculate the probability distribution of interest P (Y | X) using Bayes' theorem.

(Posterior distribution.)

Bayes' theorem can be used sequentially; such as:

i. If we first receive some evidence X (data), and calculate the posterior probability P(Y

| X), and at some later point in time receive more data X', the calculated posterior can

be used in the role of prior to calculate a new posterior P (Y | X, X’) and so on.

ii.

The posterior probability P (Y | X) expresses all the necessary information to perform

predictions.

iii.

The more evidence we get, the more certain we will become of the unknowns, until

all but one value combination for the unknowns have probabilities so close to zero

that they can be neglected.

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Bayesian method: (i) Is parameter-free and the user input is not required, instead, prior

distributions of the model offer a theoretically justifiable method for affecting the model

construction; (ii) Works with probabilities and can hence be expected to produce robust

results with discrete data containing nominal and ordinal attributes; (iii) Has no limit for

minimum/maximum sample size; (iv) Is able to analyze both linear and non-linear

dependencies; (v) Assumes no multivariate normal model; (vi) Allows prediction. (Petri,

2011).

The farmer’s example as mention introduction underlined the philosophy that paraphrases

several important applications in the areas of real life, inventory, maintenance, cash flow

management, regulation of electric power, water resources and hydropower management.

2.2.2 Steps of Decision-Making Process

The decision-making process involves the following steps:

(i)

Identify and define the problem.

(ii) List of all possible future events, called states of nature, which can occur in the

context of the decision problem. Such events are not under the control of the decisionmaker

because these are erratic in nature.

(iii) Identification of all the courses of action (alternatives or decision choices) which are

available to the decision-maker. The decision-maker has control over these courses of

action.

(iv) Expressing the payoffs (Pij) resulting from each pair of course of action and state of

nature, payoffs are normally expressed in a monetary value

(v) Applying an appropriate mathematical decision theory model to select best course of

action from the list on the basis of some criterion (measure of effectiveness) that

results in the optimum (desired) payoff.

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2.2.3 Decision-Making under Uncertainty/Risk

Decision-making under risk is a probabilistic decision state of affairs, in which more than one

state of nature exists and the decision-maker has adequate information to assign probability

values to the likely occurrence of each state of these states. Knowing the probability

distribution of the state of natures, the best decision is to select that course of action which

has the leading expected payoff value. The expected average payoff value of an alternative is

the sum of all possible payoffs of that alternative weighted by the probabilities of those

payoffs occurring.

The most widely used criterion for evaluating various courses of action (alternative) under

risk is the Expected Monetary Value (EMV).

2.2.4 Expected Monetary Value (EMV)

The expected monetary value (EMV) for a given course of action is the weighted sum of

possible payoffs for each alternative. It is obtained by summing the payoffs for each course of

action multiplied by the probabilities associated with each state of nature. The expected (or

mean) value is the long-run average value that could result if the decision were repeated a

large number of times. Mathematically EMV is stated as follows:

EMV (Course of action, SJ) = ΣPij*Pj 2.1

Where

m = number of possible states of nature

Pj = Probability of occurrence of each state of nature Nj

Pij = Payoff associated with each state of nature Nj and course of action Sj

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2.2.5 Steps for calculating EMV

The various steps involved in the calculation of EMV are as follows:

(a) Construct a payoff matrix listing all possible states of nature and courses of action.

Enter conditional payoff values associated with each possible combination of course

of action and state of nature along with the probability of the occurrence of each state

of nature.

(b) Calculate the EMV for each course of action by multiplying by the conditional

payoffs by the associated probabilities and add these weighted values for each course

of action.

(c) Select the course of action that yields the optimum EMV.

2.2.6 Expected Opportunity Loss [EOL]

An alternative approach to maximizing expected monetary value (EMV) is to minimize the

expected opportunity loss (EOL), also called expected value of regret. The EOL is defined as

the difference between the highest profit (or payoff) for a state of nature and the actual profit

obtained for the particular course of action taken. In order words, EOL is the amount of

payoff that is lost by not selecting the course of action that has the greatest payoff for the

state of nature that actually occurs. The courses of action due to which EOL minimum was

recommended.

Since EOL is an alternative decision criterion for decision-making under risk, therefore, the

results will always be the same as those obtained by EMV criterion discussed earlier. Thus,

only one of the two methods should be applied to reach a decision. Mathematically, it is

stated as follows:

EOL (State of nature, NJ) = Σ Lij*Pj 2.2

Where

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2.2.10 Net Present Value Project Cashflow

Net present value is one of many capital budgeting methods used to evaluate potential

physical asset projects in which a company might want to invest. Usually, these capital

investment projects are large in terms of scope and money, such as purchasing an expensive

set of assembly-line equipment or constructing a new building.

Net present value uses discounted cash flows in the analysis, which makes the net present

value more precise than of any of the capital budgeting methods as it considers both the risk

and time variables.

A net present value analysis involves several variables and assumptions and evaluates the

cash flows forecasted to be delivered by a project by discounting them back to the present

using information that includes the time span of the project (t) and the firm's weighted

average cost of capital (i). If the result is positive, then the firm should invest in the project. If

negative, the firm should not invest in the project.

2.2.11 Capital Projects Using Net Present Value

Before you can use net present value to evaluate a capital investment project, you'll need to

know if that project is a mutually exclusive or independent project. Independent projects are

those not affected by the cash flows of other projects.

Mutually exclusive projects, however, are different. If two projects are mutually exclusive, it

means there are two ways of accomplishing the same result. It might be that a business has

requested bids on a project and a number of bids have been received. You wouldn't want to

accept two bids for the same project. That is an example of a mutually exclusive project.

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When you are evaluating two capital investment projects, you have to evaluate whether they

are independent or mutually exclusive and make an accept-or-reject decision with that in

mind.

2.2.12 Net Present Value Decision Rules

Every capital budgeting method has a set of decision rules. For example, the payback period

method's decision rule is that you accept the project if it pays back its initial investment

within a given period of time. The same decision rule holds true for the discounted payback

period method.

Net present value also has its own decision rules, which include the following:

Independent projects: If NPV is greater than $0, accept the project.

Mutually exclusive projects: If the NPV of one project is greater than the NPV of

the other project, accept the project with the higher NPV. If both projects have a

negative NPV, reject both projects.

Following is the basic equation for calculating the present value of cash flows, NPV (p),

when cash flows differ each period:

NPV(p) = CF (0) + CF (1)/ (1 + i) t + CF (2)/ (1 + i) t + CF (3)/ (1 + i) t + CF (4)/ (1 + i) t 2.7

Where:

i = firm's cost of capital

t = the year in which the cash flow is received

CF (0) = initial investment

To work the NPV formula:

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Add the cash flow from Year 0, which is the initial investment in the project, to the

rest of the project cash flows.

The initial investment is a cash outflow, so it is a negative number. In this research

work, the cash flows hydropower project for 1 through 12 years are all positive

numbers.

2.3 Empirical Framework

This section details with research works and studies done in decision making processes using

decision making models such as Bayesian decision theory, Game theory and Markovian

decision theory as it relates to Scientific Innovation, Agriculture and Water resources and

Environmental Engineering Management.

2.3.1 Empirical Model

Mike Joy (1994) and Simon Gardner (1999) stated that “Empirical modeling is concerned

with the modeling of situations that can be directly linked to real world scenarios. The

purpose of this is to create the mental link between the model and the real world. This allows

for further thought into the application of models and the principles that surround the state of

real-world entities. When developing modeling using empirical modeling the focus of

thought should be on how the model relates to its real-world context and whether the model is

a true representation of this scenario. With such wide-ranging applications, an early

understanding of its principles is essential. The purpose of this research work is to show how,

through the use of empirical modeling, a model can be created that presents these principles

and relates them to the real-world situation”. Empirical applications of Bayesian decision

model were stated below:

Lakawathana(1970): Presented “Selected empirical results of a study employing decisionmaking

theory as a framework for considering decision making under risk. The particular

70

problem involves choices between alternative crop rotations for Sevier County farmers. The

study demonstrates the usefulness of the Bayesian theory that gives more than point

estimation. A multiple regression model using two linear terms was employed to determine

the influence of snow pack and reservoir storage on water availability for irrigation purposes

during July, August, and September. The Bayesian approach was employed. The optimum

action or decision was first determined where only the knowledge of the priori probabilities

of the states of nature was available. Optimum strategies were then determined where run-off

observation was available and the posteriori probabilities of the states of nature were

determined.Study results indicate that the expected value of the additional information is

substantial and come out very close to the expected value of a perfect predictor and higher

than the expected value of the "no data" problems. It means that the Bayesian approach gives

more than a point estimation and is useful for farm management decision making under risk.”

Lakawathana(1970) research work indicates the following;

(i)

Decision making in a farm where there is the need for the selection of alternative

crops, and this was made possible using Bayesian decision theory.

(ii)

(iii)

The study demonstrated the usefulness of Bayesian theory that gives more estimation.

The study demonstrated the importance of perfect forecaster in the use of Bayesian

model.

Thomas and Robert (1975): “In their Remote Sensing of Photogrammetric Engineering and

provide valuable information for decision-making in a wide variety of problems. The

inability of the data producer to express the capabilities of remote sensing in monetary terms

inhibits its use as an information source. Bayesian Decision Theory can provide monetary

information for evaluating the worth of data, in some cases. An outline of Bayesian Decision

Theory for finite-discrete problems is presented. An example in land use identification for

water resources planning is discussed.”

71

Summary:

Thomas and Robert (1975) research work indicates the following;

(i)

Decision making in Remote Sensing Photographic Engineering is made possible using

Bayesian decision theory

(ii)

The study demonstrated the capabilities of Bayesian Decision Theory as it provides

monetary information for evaluating the worth of data.

(iii)

The study demonstrated that Bayesian Decision Theory can handle both finite and

finite-discrete problems.

Eme, (2012) “In his applies markovian decision theory in multi-purpose/multi-objective dam

development optimization. The problem investigated was decision problem on how to

apportion (allocate) a development fund so as to optimize the returns under the worst

condition of conflict. It considers a hypothetical case where N100 million is to be spent on a

multi-purpose/multi-objective water resources development project. The purpose of interest

are irrigation, hydro-electric power generation, and water supply. The returns (objectives) to

be optimized in stages as a multi-stage decision problem are economic efficiency, regional

redistribution and social well-being and a benefit (return) study of the three purposes under

each of the three objectives was carried out. In conclusion, policy five yields the highest

expected yearly benefit of N9.12 million under the worst conflicting condition”.

Eme, (2012) research work indicates the following;

(i)

Decision making in Multipurpose/Multi-objective dam development optimization is

made possible using Markovian Decision Theory

(ii)

Problem the research work investigated was decision problem on how to apportion

(allocate) a development fund so as to optimize the returns under the worst condition

of conflict.

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Eme, (2015) “Applied the Exhaustive Enumeration method of Markovian Decision theory

while considering N12.3billion

funds released from 2007 to 2011 for capital projects to

Anambra/ Imo River Basin Development Authority, Nigeria under the supervision of federal

Ministry of water Resources in Nigeria, with the sole aim at optimization of allocation to

various projects and maximization of expected revenue to the authority. The developmental

projects are: Irrigation, Water supply, Hydro-electric Power Generation, Flood control,

Drainage, Navigation, Recreation/Tourism, and Erosion Control. The objectives optimized in

stages as a multi-stage decision problem: Economic Optimization, Federal, Regional state

and Local Economic Redistribution, Social well-being, Youth Employment and

Environmental Quality Improvement. The problem then becomes how to allocate (apportion)

the N12.3billion limited development funds among the various projects so as to optimize the

returns even under the worst conflict situation. Methodology involves methods and

experiments and data were collected from Anambra/Imo River Basin Authority, Owerri,

Ministries and Parastatals. From interpretation of the results of the experiments, Policy 10

yields the largest expected yearly revenue of N2.7billion under the worst conflict condition.

The developmental projects should be apportioned by the planning and management engineer

as follows: irrigated

Agriculture (N0.24billion), water supply (N.54billion), Hydroelectric

Power generation (N.84billion), Flood control (N1.08billion), Drainage (N1.42billion),

Navigation (N1.57billion), Recreation (N2.82billion) and Erosion Control (N3.8billion) for

optimum solution in maximization of investment on the River Basin which has limited fund

allocated to it from Federal budget”.


(i)

Applied Exhaustive Enumeration method of Markovian Decision theory for capital

allocation of funds to projects in Anambra/ Imo River Basin Development Authority,

for optimum solution in maximization of investment on the River Basin.

73

(ii)

The objectives optimized in stages as a multi-stage decision problem.

Eme, (2015) stated that “Non-parametric experiment is aimed at modeling an alternative

method of testing null hypothesis for Anambra/Imo River Basin (prototype) and the

contingency, reliability theory (model). The work assesses the relationship between the

experimental and theoretically expected result and tests the null hypothesis, as follows: (a) if

no maintenance is applied by the decision maker next year’s productivity depends on this

year’s productivity depends on this year’s condition of the basin. (b) if maintenance is

applied by the decision maker, next year’s productivity depends on this year’s condition of

the basic (c) if the cost function depends on the strategy (courses of action) of the decision

maker in terms of loss during a -1- year period. (d) if the return function depends on the

course of action of the decision maker in terms of gain during an -1- year period, (e) if

simulation optimization depends on the minimization of expected cost (f) if simulation

optimization depends on the maximization of the expected revenue. The methodology

involves contingency, reliability test and alternative interactive model of Pearson product

moment correlation. Data were collected for the model and prototype from the Ministries,

parastatals and Anambra-Imo River Basin Development Authority Owerri. The problem of

providing more information about a phenomenon or interactions in the analysis of variance

was solved. The study shows that there is a significant difference between the actual

experimentation of the Anambra-Imo River Basin schemes and expected theoretical result for

both maintenance and without maintenance of the scheme, which led to the rejection of (H0).

To further test the hypothesis the researcher analyzed the data with other powerful parametric

tests such as Pearson’s product moment correlation and scatter diagrams which coincided

with r=1.00 as height of perfection of performance of the basin when compared with the

theory”.


74

(i)

Non-parametric experiments aimed at modeling an alternative method of testing null

hypothesis for Anambra/Imo River Basin (prototype) and the contingency, reliability

theory (model). The objectives optimized in stages as a multi-stage decision problem.

(ii)

To further test the hypothesis the researcher analyzed the data with other powerful

parametric tests such as Pearson’s product moment correlation and scatter diagrams

which coincided with r=1.00 as height of perfection of performance of the basin when

compared with the theory.

Eme, (2015) “In this paper aims at studying simulation modeling in Markovian Decision

theory considers its relationship to linear programming and adapts exhaustive enumeration

method, policy iteration methods of certain stochastic systems of the finite and infinite stage

models for solution of the gardener’s problems. The objective of the problem is to determine

the optimum policy or strategy or action that maximizes the expected return (revenue) within

the available fund over the planning period. Consequently, most of the problems are decision

problems for the decision maker (the gardener) such as: (as” apply fertilizer or do not apply

fertilizer: (b) “Whether the gardening activity will continue for a limited number of years or

indefinitely”. In the basic concept of Markovian Decision theory, the number of transitional

probabilities and computational efforts required to solve a Markov chain grows exponentially

with the number of states. The linear programming formulation in this paper is interesting,

but it is not as efficient computationally as the exhaustive enumeration method or the policy

iteration algorithm methods of markovian decision problems, particularly for large values of

stationary policies. In conclusion, alternatively contingency and reliability tests were

performed as a check which show no significant difference between the experimental and

theoretical expected results and led to the acceptance of null hypothesis”.

75


(i)

Markovian Decision theory relationship to linear programming and exhaustive

enumeration method, policy iteration methods of certain stochastic systems of the

finite and infinite stage models for solution of the gardener’s problems.

(ii)

The linear programming formulation in this paper is interesting, but it is not as

efficient computationally as the exhaustive enumeration method or the policy iteration

algorithm methods of markovian decision problems, particularly for large values of

stationary policies.

Eme, (2015) “Investigate a case where N100 billion is to be spent on the maintenance of the

twelve Nigeria River Basin Engineering Development Schemes. The purposes of interest are;

irrigation, water supply, hydro-electric power generation, flood control, Drainage, Navigation,

Recreation and Erosion control. The returns (objectives) to be optimized in stages as a multistage

decision problem are: Economic Efficiency, Federal, Regional, State and Local

Economic Redistribution, social well-being, Being, Youth Employment and Environmental

Quality Improvement. The problem them becomes how to apportion (allocation) the N100

billion development funds among the various purposes so as to optimize the returns

(objectives) even under the worst conflict situation to avoid flooding of the lower regions or

plains. A benefit (return) study of the eight purposes under each of the eight objectives was

carried out. The conception of the study is as shown in table 1 with maintenance and table 2

without maintenance. Methods of experiments involve the gardener’s problem case 1 and

steady state probabilities and mean return times of ergodic chains of markov chain. In

conclusion result of the performance of experiment 1 shows that for years 1, 2, and 3. The

planning and management engineer should maintain the river basin engineering development

regardless of the state of the system to return to a very excellent state and 10 o 16 years for

76

poor and very poor state. The total expected revenue for the eight years ranges from

N828.5billion to N822billion”.


(i)

The problem on how to apportion (allocation) development funds among the various

purposes so as to optimize the returns (objectives) even under the worst conflict

situation to avoid flooding of the lower regions or plains.

(ii)

The type of Markovian Decision Model applied is steady state probabilities and mean

return times of ergodic chains of markov chain.

Eme, & Anyata (2015) “In their work aim at measuring the marginal effect of a key variable

such as a hydropower generation/ water supply or railway system upon a set of relevant

policy variable such as Economic variables, Environmental Impact Analysis. Only the

impacts of the social-economic subsystem (E) and geographic-demographic subsystem (G)

upon the environmental subsystem (M) is assessed. Therefore, the environmental profile is

the central pivot of the analysis. Cost-benefit analysis was criticized for several reasons such

as neglect of the equity criteria, does not incorporate uncertainties etc. In the survey of

environmental evaluation, it is evident that in the framework of neoclassical or cost benefit

analysis the evaluation of environmental commodities has to be based on marked prices.

When market prices do not exist for environmental commodities artificial price e.g. shadow

prices have to be calculated in order to ensure an operational result. Methodology involves an

integrated structure of Economic-environmental survey which was investigated in greater

detail. In conclusion several methods developed and employed so far cannot be regarded as

satisfactory evaluation techniques in an operational environmental policy analysis, because

intangible and incommensurable effects are very hard to incorporate in all these methods. The

conclusion is justified that any attempt to transform an un-priced impact into a single

77

dimension must fail, unless corrected with Bayesian decision model or Markov chains, which

could take care of uncertainties, equity, risk, time effect, and poor data availability etc.”.

Eme, & Anyata (2015) research work indicates the following;

(i)

Their work aims at measuring the marginal effect of a key variable such as a

hydropower generation/ water supply or railway system upon a set of relevant policy

variable such as Economic variables, Environmental Impact Analysis.

(ii)

Transformation of an un-priced impact into a single dimension must fail, unless

corrected with Bayesian decision model or Markov chains, which could take care of

uncertainties, equity, risk, time effect, and poor data availability.

(iii)

Cost-benefit analysis was criticized for several reasons such as neglect of the equity

criteria, does not incorporate uncertainties.

Eme, & Anyata (2015) explained “In their paper that attention for tourism and recreation in

advanced and underdeveloped regions is the result of many socio-economic and

environmental elements. This paper investigates with models why these regions consider

tourism and recreation as a major source of an accelerated growth process. These socioeconomic

and environmental elements gave: (i) rise in leisure time (ii) rise in welfare

especially the increase of discretionary income, (iii) increase accessibility of many regions

and infrastructure etc. it is found that the rise of mass tourism and recreation has led to

several negative externalities such as congestion, environmental decay, destruction of

traditional social structures, increase in socio-economic inequality an likes. The methodology

and analysis were based on the local or regional attractiveness in the form of the set of

physical and environmental quality and quantity of tourism and recreational behavior such as:

family size, family composition, education, income etc., residential characteristics and

characteristic of recreational areas such as: ecological quality accessibility etc. their

attractiveness activities have fairly high income elasticity with respect to the demand for

78

tourism services. In Nigeria case that is full of uncertainty which should be a true-life

situation the models used for the analyses of the elements could not justify these uncertainties;

therefore, the work recommends the Gardener’s model of the Markovian Decision Theory to

take care of these lapses”.

Eme, & Anyata (2015) research work indicates the following;

(i)

The methodology and analysis were based on the local or regional attractiveness in

the form of the set of physical and environmental quality and quantity of tourism and

recreational behavior such as: family size, family composition, education, income etc.,

residential characteristics and characteristic of recreational areas such as: ecological

quality accessibility etc. their attractiveness activities have fairly high income

elasticity with respect to the demand for tourism services.

(ii)

In Nigeria case that is full of uncertainty which should be a true-life situation the

models used for the analyses of the elements could not justify these uncertainties;

therefore, the work recommends the Gardener’s model of the Markovian Decision

Theory to take care of these lapses.

Xuan Wang et al (2015): “In their paper, considered the complexity of the water resources

system and the uncertainty of the assessment of information, a method based on the Bayesian

theory was developed for performing WRV assessments while using the constructed indicator

system. This system includes four subsystems, the hydrological subsystem, the

socioeconomic subsystem, the Eco environmental subsystem and the hydraulic engineering

subsystem. The WRV degree for each subsystem and the integrated water resources system

were assessed. Finally, the assessment results and the characteristics of the Bayesian method

were compared with those of the grey relational analysis method and the parametric-system

method. The results showed the following. (1) The WRV of the integrated water resources

system of the entire Zhangjiakou region was very high; Zhangjiakou City and Xuanhua

79

County have tendencies to belong to Extreme WRV, with probabilities of 26.8% and 25%,

respectively, while the other seven administrative counties have tendencies to belong to High

WRV, with probabilities ranging from 24.6% to 27%. (2) Compared with the parametricsystem

method and the grey relational analysis method, the Bayesian method is simple and

can effectively address the uncertainty issues with the reliable WRV assessment results.”

Xuan Wang et al (2015) research work indicates the following;

(i)

Water Resources Vulnerability Assessment was investigated using three method

namely: the parametric-system, the grey relational analysis method and the Bayesian

method.

However, Bayesian method was found to be simple and can effectively

address the uncertainty issues with the reliable WRV assessment results.

Eme and Ohaji (2019): “In their paper examined simulation modeling in Bayesian Decision

theory and its application in day to day decision making as well as planning in water

resources and Environmental engineering. It also gives more insight in the validation of prior

probability. The research objectives deal with the multi-objective value of water for its wide

range of purposes such as Power generation, water supply, Navigation, Irrigation, and Flood

control, in the Cross-River basin using Bayesian Modeling. In line with foregoing objectives,

the research aim to achieve the following: (i) to lay bare the usefulness of the Bayesian theory

that gives more than point estimation. It measures the magnitude of the difference between

alternative actions and provides a variety of estimates for consideration, (ii) to present

selected empirical results of a study employing decision-making theory as a framework for

considering decision making under uncertainty. (iii) to evaluate the optimum policy or

strategy or action that maximizes the expected benefit in the River Basin within the available

limited resources and funds over the planning period of a course of action or alternatives. The

multi-objectives arising from the development that were optimized include: Economic

Efficiency, Regional Economic Distribution, State and Local Economic Redistribution,

80

Youth Employment and Environmental Quality Improvement, which are primarily essential

in Cross Rivers State and Nigeria. Methodology applied involving methods, experiments and

data were collected for the River Basin Engineering Development, from Parastatals and

Ministries. The conceptual framework on Bayesian Decision Model (BDM) as presented in

chapter 3 captured the iterative updates of prior probability toward achieving an optimum

solution of a set problem. The analysis and presentation of results in chapter 4 were based on

simulation of Bayesian Models Iterations. Chi-square, Contingency and association and

Pearson Product Moment Correlation were carried out as Interaction, reliability and Validity

tests respectively. The study applied Bayesian Decision Model, where the following

parameters were obtained: (a)Posterior Probabilities of the States of Nature (b) Marginal

Probability of the Courses of action, (c) Maximum Expected Monetary Value[EMV*] (d)

Expected Profit in a Perfect Information[EPPI], (e) Expected Value of Perfect

Information[EVPI], and (f) Expected Value of System Information[EVSI]. In the process of

Iteration in chapter 4, and at some point, the Prior becomes equal to the Posterior Probability,

when this occurs an optimum solution is said to be achieved. However, the correlation of

prior and posterior probability is equal to one (1) at the optimum solution. Ultimately, the

research paper indicates that Bayesian decision theory is at best when there is little or no data

requirement for decision making. It also infers that no reasonable decision can be achieved

without making references to present, historical information, knowledge, pattern and

sequence. In order words, the use of BDM in future prediction will depend on historical and

present information. The various purposes under consideration at the 2nd iteration with

expected profit for perfect information has the following demand values(Table 18):

Hydropower = 20.43; Water Supply = 34.28; Navigation = 2; Irrigation =34.4; Environmental

= 1 The result above gave the indication that there is relatively high demand for water supply

for domestic use and irrigation for agricultural crops. However, the researcher is

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recommending inter dam water transfer within the watershed to take care of water demand

imbalance in the system. If this management decision is imbibed on, it will increase the

production of cereal in the eastern part of Nigeria comparative with that of Northern Nigeria.

These decisions also support FGN Initiatives in establishing more Dams in Cross River

watershed to checkmate on food security, most especially Rice production which has been

confirmed to be doing extremely well based on research and information received.

Eme and Ohaji (2019) research work on “Bayesian Decision Modeling In Watershed

Management-Cross River Basin, Nigeria indicates the following;

(i)

Examining simulation modeling in Bayesian Decision theory and its application in

day to day decision making as well as planning in water resources and Environmental

engineering.

(ii)

The study applied Bayesian Decision Model, where the following parameters were

obtained: (a) Posterior Probabilities of the States of Nature (b) Marginal Probability of

the Courses of action, (c) Maximum Expected Monetary Value where the optimum

policy or strategy or action that maximizes the expected benefit in the River Basin

was determined (d) Expected Profit in a Perfect Information, (e) Expected Value of

Perfect Information, and (f) Expected Value of System.

(iii)

The research work gives more insight in the validation of prior probability.

Eme and Ohaji (2019): “In their applied Prior-Posterior decision theory based models to

analyze and solve the Farmer’s Decision problem who is faced with decision of determining

among alternatives crops [Sorghum, Rice, Wheat & Corn] the best crop to invest on, that will

give a high yield and profit under the prevailing state of nature on a 100 acres land located in

Obudu LGA in Cross River State. However, the study aimed to (i) laid bare the usefulness of

the Prior-Posterior theory that gives more than point estimation. (ii) Measures the magnitude

of the difference between alternative actions and provides a variety of estimates for

82

consideration and (ii) to present selected empirical results of a study employing decisionmaking

theory as a framework for considering decision making under uncertainty, (ii) To

evaluate the optimum policy or strategy or action that maximizes the expected yield of cereal

crop within the study area. Consequently, given the prior probabilities of the state of nature

and the likelihood of the alternatives courses of action, and applying Prior-Posterior Decision

Model to the uncertain system,

the following decision parameters were generated:

(a)Posterior Probabilities of the States of Nature (b) Marginal Probability of the Course of

Action, (c) Maximum Expected Monetary Value[EMV*] (d) Expected Profit in a Perfect

Information[EPPI], (e) Expected Value of Perfect Information[EVPI], and (f) Expected Value

of System Information[ EVSI]. The determination of the parameters gave a clear indication

that Rice has the Maximum Expected Monetary [EMV*] value of $17,178.21 at 40 th model

iteration, making it the most suitable crop for the farmer to invest on, for maximum high

yield; therefore, a decision was made. EMV* of rice was also observed to be optimized from

the 1 st and 40 th model iteration at the value of $14,175.66 and $17,178.21 respectively. The

result of the analyses attests to the fact that rice production in Obudu the study area is

currently the most yielding crop. The methodology involves experiments and data were

collected from United State Department of Agriculture (USDA). The analysis and

presentation of results were based on Simulation of Prior-Posterior decision Model. Policy

iterations and Pearson Product Moment Correlation were carried out as interaction, validity,

reliability tests. The validity of Prior-Posterior decision model on the farmer’s decision

problem was evaluated by comparing prior probability of 1 st iteration with posterior

probability of 40 th probability of the state of nature which gave the Pearson correlation

coefficient(r) = 1.0. Ultimately, Prior-Posterior Decision Model Excel Algorithms [Payoff

Matrix table] having been used in solving the farmer’s decision problem can also be applied

in a wide variety of fields, most especially in River Basin Management and Environmental

83

Engineering. The researcher also produces Prior-Posterior Decision Theory Model Flow

Chart to demystify difficulties encountered in understanding of BDM”

Eme and Ohaji (2019) research work on “Prior-Posterior Decision Theory-A Case Study of

Farmers’ Decision Problem indicates the following;

(i)

This study applied Prior-Posterior decision theory based models to analyze and solve

the Farmer’s Decision problem who is faced with decision of determining among

alternatives crops [Sorghum, Rice, Wheat & Corn] the best crop to invest on, that will

give a high yield and profit under the prevailing state of nature on a 100 acres land

located in Obudu LGA in Cross River State.

(ii)

Excel Algorithms [Payoff Matrix table] having been used in solving the farmer’s

decision problem can also be applied in a wide variety of fields, most especially in

River Basin Management and Environmental Engineering.

Eme and Ohaji (2019): Markovian Decision Modeling in Dam Projects - Niger Delta River

Basin. Presented “simulation modeling in Markovian Decision theory and its application in

decision making as well as planning in water resources and environmental engineering. The

research objectives deal with the multi-objective values of a River basin for its wide range of

purposes such as Economic Efficiency, Regional Economic distribution, State Economic

distribution, Social Well-being, and Environmental Quality control. In line with foregoing

objectives, the researchers aim at achieving the following: (i) Measures the magnitude of the

difference between alternative actions (ii) to present a framework for considering decision

making under uncertainty. (iii) to evaluate the optimum policy or strategy or action that

maximizes the expected benefit in the River Basin within the available limited resources and

funds over the planning period of a course of action or alternatives. The Methodology applied

involved Markovian decision model method for River basin. Data collection was based on

technical literatures from books, journals, and newspapers, River Basin Engineering

84

Development, Parastatals. The analysis and presentation of results were based on simulation

of Markovian Models. Furthermore, Contingency association, Chi-square, Pearson Product

Moment Correlation were carried out as interaction, reliability and validity tests. However,

simulating the river basin variables using Markov chain Homogeneous analysis and policy

iterations resulted to a decision policy of allocating resources to the river basin objectives

based on a federal government budgetary appropriation of 100 billion Naira. In conclusion

the model had policy decision made as follows: Economic Efficiency [64%], Regional

Economic Distribution [9%], State Economic Distribution [19%], Social Well-Being [5%]

and Environmental Control [3%]. The results indicate that Markov Chain can be successfully

applied in optimum policy investment decision making in multi-objective water resources

management. Numerous major multiple-purpose reservoir systems have been constructed

throughout the nation during the past several decades. Public needs and objectives and many

factors affecting operation of these reservoirs change over time. Reservoir system operations

are complex and often offer substantial increases in benefits for relatively small

improvements in operating efficiency. Consequently, evaluation of refinements and

modifications to the operations of existing reservoir systems is becoming an increasingly

important activity. However, Reservoir operation for municipal and industrial water supply is

based on meeting demands subject to institutional constraints related to project ownership.

However, against the foregoing the research work was initiated out of the concern of

allocating budgetary resources to the various river basin purposes for functionality

requirement as well as sustainability of the system arrangement.

Based on the findings and conclusions reached on the study the following recommendations

are made: Niger delta has more water available; therefore, it is recommended that

Hydropower in this region should be considered and encouraged because of it immediate and

long-term benefits when compared to gas powered electric plants. Also, clean environment

85

should be embraced for a healthy land, water and air; and in turn increase the level of tourism

as well as reduces flood control caused by environmental abuse. The study can provide an

organized baseline for future work, mainly in obtaining superior estimates for institutional

water use and planning by the aid of Markovian decision theory. However, the findings of the

study can be vital input into the demand management process for long term sustainable water

supply within Niger Delta River Basin and beyond.”

Eme and Ohaji (2019): Markovian Decision Modeling in Dam Projects - Niger Delta River

Basin research work indicates the following;

(i)

The results indicate that Markov Chain can be successfully applied in optimum policy

investment decision making in multi-objective water resources management.

(ii)

(iii)

It can handle multivariate uncertainty problems.

The model uses inventory as bases of operation.

Eme and Ohaji (2019): Game Theory Modeling in River Valley Projects-Benin Owena River

Basin. “This study applied game theory-based model to analyze and solve sharing conflicts

on funds allocation to the multi-purpose and the multi-objectives in Benin-Owena River

Basin. The model provides strategic decisions geared toward resolving the problem of

apportioning N100 billion Naira development fund each to the two players, multi-objective

[economic efficiency, regional economic distribution, state economic distribution, youth

employment and environmental control] and the multi-purpose. [irrigation, hydropower,

water supply, recreation, and erosion control]. The game simulation comprised five players

on both the multi-purpose and multi-objective axis and the game theory converted to a linear

programming problem and was analyzed using Simplex method. The analysis and

presentation of results in this paper were based on Game Theory Simulation Model. However,

Contingency and Association, Chi-square and Pearson Product Moment Correlation were

carried out as Interaction, reliability and Validity tests. The result indicates the following

86

proportional funds allocated in percentages to the multi-objectives: economic efficiency,

regional economy distribution, state economic distribution, youth employment and

environmental control are 23, 72, 0.00, 0.00, and 5%, respectively. And funds apportioned to

the multipurpose are in the following order: Irrigation, hydroelectric power, water supply,

and recreation and erosion control are: 0.0, 0.0, 0.26, 0.16, and 58%, respectively. This study

gave the indication that funds were available for water supply, recreation and erosion control

for the multipurpose, which gave rise to solving economic efficiency and regional Economic

Distribution for the multi-objective. In additional, to avoid conflict, the results suggest a need

to design a mechanism to reduce the risk of losses of those players by a side payment, which

provides them with economic incentives to cooperate. Game theory application in River basin

management is invaluable; it gives optimum solution on government investment and

wellbeing of people within the region for both multi-purpose and multi-objectives

simultaneously.

This study applied game theory-based models to analyze and solve seem sharing conflicts

concerning funds allocation to the multi-purpose and the multi-objectives in Benin-Owena

River Basin. This study covers the dynamics between five river basin purposes and five river

Objectives and how the relation of the duo can be optimized using Game theory model for the

benefit of the inhabitant of the basin. The horizon for the study was designed to cover a

period of 5 years (2013 – 2017). The Ondo State Government in 1976, commissioned the

design of the Owena River Dam with the objective of supplying raw water from the resulting

reservoir for the existing water scheme, but taken over by the Federal Government of Nigeria

(through Benin-Owena River Basin Development Authority)

and converted it to a

multipurpose use in line with the functions of the River Basin Development Authorities. The

design was reviewed to include in addition to provision of potable water, usage for irrigation

of 3,000 hectares of farmland, fisheries, as well as generation of hydro-electric power. The

87

dam sited on the Owena River and was designed to create an impoundment of 36.25 million

cm3 gross capacity, covering an area of approximately 7.38 km2 at the normal water level.

Thus, this study examined the Owena multipurpose/multi-objective River basin, as a key

activity in managing the water source.

This study gave the indication that funds were only available for water supply, recreation and

erosion control for the multipurpose, while funds are available for only economic efficiency

and regional Economic Distribution for the multi-objective. In additional, to avoid conflict,

the results suggest a need to design a mechanism to reduce the risk of losses of those players

by a side payment, which provides them with economic incentives to cooperate. The

application of Game Decision theory on Benin-Owena River basin resulted to the following

outputs: -Funds allocated to Objectives in percentage are: Economic efficiency, Regional

economy, State economy, Youth Employment and Environment are 23, 72, 0.00, 0.00, and

5%respectively. The allocations in monetary values are depicted in Table 6. -Funds allocated

to Purposes in percentages are: Irrigation, Hydroelectric Power, Water Supply, and

Recreation and Erosion Control are: 0.0, 0.0, 0.26, 0.16, and 58%.”

Eme and Ohaji (2019): Game Theory Modeling in River Valley Projects-Benin Owena River

Basin. Research work indicates the following;

(i)

The game simulation comprised five players on both the multi-purpose and multiobjective

axis and the game theory converted to a linear programming problem and

was analyzed using Simplex method.

(ii)

This model has deficiency that it cannot effectively handle multivariate variable

under risk and uncertain situations.

88

2.4 Research gap of the Literatures Reviewed (Gap Analysis)

This research work further filled the literature gap with the following:

(i)

Contrast to Game and Makovian theory in modeling of river basin operation,

Bayesian Decision Model simulation incorporated procedure that obtain Profit

maximization and minimization of losses and wastages when Perfect information was

used, and this is inform of Expected profit in perfect information (EPPI).

(ii)

Also, Contrast to Game and Makovian theory in modeling of river basin operation,

the Bayesian Decision Model simulation incorporated monetary provision for the

model forecaster in the form of Expected value of system information (EVSI).

(iii)

The dynamic relationship between EMV and EOL reveals or gave an indication of

Multipurpose dam integration for optimum benefits, and this is the first time is being

applied in Multipurpose dam operation.

(iv)

Empirical prior that is based on experiment was used in this research work contrary to

previous research works that used Expert opinions (Objective prior), Personal view

(Subjective prior) and Questioners as they appear to be bias sources of information.

(v)

Ohaji (2019): developed Excel spreadsheet algorithm as a tool for the evaluation of

the curse of dimensionality experienced in the denominator of the infinite Bayesian

model equation. However, the denominator of Bayesian Model equation termed

“fixed Normalizing factor”, is (usually) extremely difficult to evaluate. The excel

spread sheet developed was found easy to use, when compared with previous aid like,

Win BUGS software and Markov Chain Monte Carlo as used by (Eme, 2012) in his

research work.

89

2.5 Summary of the Literatures reviewed

The summary of the literature reviewed are as follows:

(i)

Wayne (2004). Postulated that Simulation models are time consuming and costly

to construct and run. Additionally, the result may not be very precise and are often

hard to validate. Simulation can be powerful tool, but only if it used properly

(ii)

Willemain (1994) recommended that “effective operation Research Practice

requires more than analytical competence: it also requires, among other attributes

technical (e.g., when and how to use the given technique) and Model Construction

skills Communication and Organization survival”

(iii)

UNESCO-WWAP, (2003) stated: “Dams have been constructed for millennia,

influencing the lives of humans and the ecosystems they inhabit. Remnants of one

such man-made structure dating back 5,000 years are still standing in northeast

Africa.”

(iv) World Commission on Dam (2000), stated that, the world has almost 900,000

dams built on the numerous rivers across six continents, of those structures,

45,000 are classified as large dams having 15 m and a reservoir volume exceeding

3 million m 3 .

(v)

Ezugwu (2013) postulated that “Nigeria has abundant surface water bodies and

good dam sites that could be utilized for dam construction to create reservoirs for

various water uses including hydropower generation, flood control, water supply,

irrigation, navigation, tourism, sanitation, fish and wild life development and

ground water recharge. Dam development and disasters on people and the

environment were examined.

(vi)

Hydropower is the leading flexible source of power generation available and is

capable of responding to demand fluxes in minutes, delivering base-load power

90

and, when a reservoir is present, storing electricity over weeks, months, seasons or

even years (Brown, 2011 and (International Panel on Climate Change (IPCC),

2011).

(vii)

Hydropower is the only all-encompassing and cost-efficient storage technology

available today. Despite promising developments in other energy storage

technologies, hydropower is still the only technology offering economically

feasible large-scale storage. It is also a relatively effective energy storage option.

(IEA, 2010).

(viii)

Hydropower can ease the low-cost integration of variable renewables into the grid,

as it is able to respond almost instantaneously to changes in the amount of

electricity running through the grid and to efficiently store electricity generated by

wind and solar by holding inflows in the reservoir rather than generating. This

water can then be released when the sun is not shining or the wind not blowing. In

Denmark, for example, the high level of variable wind generation is managed in

part through interconnections to Norway where there is considerable hydropower

storage (Nordel, 2008a).

(ix)

Ohaji, 2019 developed “Excel spread sheet algorithm for solving Bayesian

Decision Model curse of dimensionality of fixed Normalizing factor and Normal

likelihood function of Multiobjective/Multiobjective dam projects”.

(x)

Lakawathana(1970) research work indicates the following; decision making in a

farm where there is the need for the selection of alternative crops, and this was

made possible using Bayesian decision theory, the study demonstrated the

usefulness of Bayesian theory that gives more estimation, the study demonstrated

the importance of perfect forecaster in the use of Bayesian model.

91

(xi)

Thomas and Robert (1975) research work indicates the following; decision

making in Remote Sensing Photographic Engineering is made possible using

Bayesian decision theory, the study demonstrated the capabilities of Bayesian

Decision Theory as its provide monetary information for evaluating the worth of

data, the study demonstrated that

Bayesian Decision Theory can handle both

finite and finite-discrete problems.

(xii) Eme, (2012) research work indicates the following; decision making in

Multipurpose/Multi-objective dam development optimization is made possible

using Markovian Decision Theory Problem the research work investigated was

decision problem on how to apportion (allocate) a development fund so as to

optimize the returns under the worst condition of conflict.

(xiii) Eme, (2015) research work indicates the following; applied Exhaustive

Enumeration method of Markovian Decision theory for capital allocation of funds

to projects in Anambra/ Imo River Basin Development Authority, for optimum

solution in maximization of investment on the River Basin, The objectives

optimized in stages as a multi-stage decision problem.

(xiv)

Eme, (2015) research work indicates the following; non-parametric experiments

aimed at modeling an alternative method of testing null hypothesis for

Anambra/Imo River Basin (prototype) and the contingency, reliability theory

(model). The objectives optimized in stages as a multi-stage decision problem, to

further test the hypothesis the researcher analyzed the data with other powerful

parametric tests such as Pearson’s product moment correlation and scatter

diagrams which coincided with r=1.00 as height of perfection of performance of

the basin when compared with the theory.

92

(xv)

Eme, (2015) research work indicates the following; Markovian Decision theory

relationship to linear programming and exhaustive enumeration method, policy

iteration methods of certain stochastic systems of the finite and infinite stage

models for solution of the gardener’s problems, the linear programming

formulation in this paper is interesting, but it is not as efficient computationally as

the exhaustive enumeration method or the policy iteration algorithm methods of

markovian decision problems, particularly for large values of stationary policies.

(xvi)

Eme, (2015) research work indicates the following; The problem on how to

apportion (allocation) development funds among the various purposes so as to

optimize the returns (objectives) even under the worst conflict situation to avoid

flooding of the lower regions or plains. The type of Markovian Decision Model

applied is steady state probabilities and mean return times of ergodic chains of

markov chain.

(xvii)

Eme, & Anyata (2015) research work indicates the following; Their work aim at

measuring the marginal effect of a key variable such as a hydropower generation/

water supply or railway system upon a set of relevant policy variable such as

Economic variables, Environmental Impact Analysis. Transformation of an unpriced

impact into a single dimension must fail, unless corrected with Bayesian

decision model or Markov chains, which could take care of uncertainties, equity,

risk, time effect, and poor data availability. Cost-benefit analysis was criticized for

several reasons such as neglect of the equity criteria, does not incorporate

uncertainties.

(xviii) Eme, & Anyata (2015) research work indicates the following; The methodology

and analysis were based on the local or regional attractiveness in the form of the

set of physical and environmental quality and quantity of tourism and recreational

93

behavior such as: family size, family composition, education, income etc.,

residential characteristics and characteristic of recreational areas such

as:

ecological quality accessibility etc. their attractiveness activities have fairly high

income elasticity with respect to the demand for tourism services. In Nigeria case

that is full of uncertainty which should be a true-life situation the models used for

the analyses of the elements could not justify these uncertainties; therefore, the

work recommends the Gardener’s model of the Markovian Decision Theory to

take care of these lapses.

(xix)

Xuan Wang et al (2015) research work indicates the following; Water Resources

Vulnerability Assessment was investigated using three method namely: the

parametric-system, the grey relational analysis method and the Bayesian method.

However, Bayesian method was found to be simple and can effectively address

the uncertainty issues with the reliable WRV assessment results.

(xx)

Eme and Ohaji (2019) research work on “Bayesian Decision Modeling in

Watershed Management-Cross River Basin, Nigeria indicates the following;

Examining simulation modeling in Bayesian Decision theory and its application in

day to day decision making as well as planning in water resources and

Environmental engineering. The study applied Bayesian Decision Model, where

the following parameters were obtained: (a) Posterior Probabilities of the States of

Nature (b) Marginal Probability of the Courses of action, (c) Maximum Expected

Monetary Value where the optimum policy or strategy or action that maximizes

the expected benefit in the River Basin was determined (d) Expected Profit in a

Perfect Information, (e) Expected Value of Perfect Information, and (f) Expected

Value of System. The research work gives more insight in the validation of prior

probability.

94

(xxi)

Eme and Ohaji (2019) research work on “Prior-Posterior Decision Theory-A Case

Study of Farmers’ Decision Problem indicates the following; This study applied

Prior-Posterior decision theory based models to analyze and solve the Farmer’s

Decision problem who is faced with decision of determining among alternatives

crops [Sorghum, Rice, Wheat & Corn] the best crop to invest on, that will give a

high yield and profit under the prevailing state of nature on a 100 acres land

located in Obudu LGA in Cross River State. Excel Algorithms [Payoff Matrix

table] having been used in solving the farmer’s decision problem can also be

applied in a wide variety of fields, most especially in River Basin Management

and Environmental Engineering.

(xxii)

Eme and Ohaji (2019): Markovian Decision Modeling in Dam Projects - Niger

Delta River Basin research work indicates the following; The results indicate that

Markov Chain can be successfully applied in optimum policy investment decision

making in multi-objective water resources management. It can handle multivariate

uncertainty problems. The model uses inventory as bases of operation.

(xxiii) Eme and Ohaji (2019): Game Theory Modeling in River Valley Projects-Benin

Owena River Basin. Research work indicates the following; the game simulation

comprised five players on both the multi-purpose and multi-objective axis and the

game theory converted to a linear programming problem and was analyzed using

Simplex method. This model has deficiency that it cannot effectively handle

multivariate variable under risk and uncertain situations.

95

CHAPTER THREE

METHODOLOGY

3.0 Methods

The methods of carrying out this research work were based on simulation modeling technique of

the Bayesian Decision Model (BDM). And the application of the Farmer’s example as a model

is described below. More so, data collection methods employed for this research work were

covered in this section.

3.1 Experimental Model

The experiment assessed the performance of the Cross-River Basin Development Authority

(Prototype) based on the actions of the Farmer as the decision maker in terms of his

application of BDM model in selecting the most suitable crop among alternative crops that

will give highest yield or production.

Consequently, the above farmer’s decision problem is an experimental model which was used

to assess the performance of the prototype (Multipurpose/Multiobjective river basin

engineering development planning and management). Thus, the farmer’s decision problem is

hinged on the choice to select the highest yielding crop among alternatives using BDM. (Eme

and Ohaji, 2019). However, the concept of the farmer’s decision model was used to evaluate

the performance of the experimental phase of the Cross-River Basin Engineering

Development planning and management, it also falls back to a decision problem for the

decision maker resulting from absence of inherited management experience, shortage of

administrative and technical manpower, system inadequacies, financial constrains etc.

96

The foregoing application of the Farmer’s decision problem experience on the River basin

(Prototype), will resolve the inadequacies in the planning and management of system assets.

3.1.1 Data Collection for the Experiments

The methodology also involves data collection by estimation of net economic efficiency of

the multipurpose dam project and benefits accrued to the multiobjectives from the multipurpose

developed using information obtained from (CRBDA), Parastatals, Ministries,

Articles, Journals and Books. The total net benefits of the multipurpose dam project- and the

multi-objective were assembled in a payoff value table where y and x represent multipurpose

dam project and multiobjective respectively, here referred to as data. The data obtained was

analyzed for source reliability and validation by using: Contingency coefficient and

association, T- distribution and Pearson moment correlation coefficient test. The payoff value

table prepared, served as a background for Bayesian Decision Model (BDM) Simulation

using Flowchart and Excel Spreadsheet developed. However, summary of the aforementioned

steps, preceding detailed methodology were stated below with references:

(i)

Data collection of payoff values of net economic efficiency of the Multi-purpose

dam project. (Subsection 2.1.5 and Section 3.3).

(ii) Data collection of payoff values of the net benefits accrued to the Multi-objective

from Multi-purpose dam project developed (Section 3.4).

(iii)

Assembling the payoff values of total net economic efficiency of the Multipurpose

dam project and net benefits accrued to the Multi-objective from Multipurpose

dam project developed. (Section 3.5).

(iv)

Analyzed the payoff values of total net benefits between Multi-purpose and the

Multi-objective data source reliability and validity using (a) Contingency

97

The denominator of equation 3.22 and 3.27 is rigorous to solve and is called

“Curse of Dimensionality” problem. Therefore, Ohaji, (2019): developed Excel

spreadsheet algorithm as an aide and a tool for the evaluation of the curse of

dimensionality experienced in the denominator of the infinite Bayesian model

equation. However, the denominator of BDM equation termed “fixed Normalizing

factor”, is (usually) extremely difficult to evaluate. The excel spread sheet

developed was found easy to use, when compared with previous aid like, Win

BUGS software and Markov Chain Monte Carlo as used by (Eme, 2012) in his

research work.

3.3 Estimation of payoff values of Economic efficiency of the Multi-purpose dam

projects

As far as optimization is concerned, economic efficiency of a water resources development

project is achieved by economic optimization of cost and benefit. On the other hand,

economic optimization is achieved by either minimization of cost (Wastages) function or

maximization of benefit (Profits) function or both.

3.3.1 Data Collection of Economic Efficiency

The factors that determine the benefits accruing to various purposes under economic

efficiency as an objective vary with purposes as stated and estimated below:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

Hydropower (Net returns from electrical energy sales)

Water supply (Net returns from water rates)

Navigation (value of length of the river for improvement)

Irrigation (values of land and Agricultural yield)

Flood Control (Value of lands area & Properties protected from flood water)

Recreation (Values of land area for recreational purposes)

104

Data necessary for determining the above benefit factors were obtained from Ministry of

Agriculture and Natural Resources, Ministry of lands, Ministry of Water Resources, National

Population Commission, National Offices of Statistics, Public Utilities Boards, and Ministry

of Works. The specific securing of data was achieved thus:

(i)

(ii)

(iii)

Value of Land-Ministry of lands and National office of Statistics

Agricultural yield-Ministry of Agriculture and National Office of Statistics

Net returns from Water Supply-Ministry of Works, Public Utilities Board, and

National Office of statistics

(iv)

Nets returns from Electrical energy sales-Ministry of Mines and Power, Ministry

of Industries, National Office of Statistics and National Population Commission.

(i)

Value of land area and building protected from flood water, Ministry of Water

Resources, Ministry of Environment, Ministry of Housing and National Office of

Statistics.

(ii)

Value of length of river for improvement-Ministry of Water Resources, Ministry

of Environment, and National Office of Statistic.

(iii)

Values of land area for recreational purposes-Ministry of Environment, and

National Office of Statistic.

The technical information provided in subsection 2.1.5 were also used in the estimation of

Economic efficiency of the watershed Purposes. Find raw data estimation in Tables 3.1, 3.2,

3.3, 3.4, 3.5 and 3.6.

Table 3.1: Bill of Engineering Measurement and Evaluation (BEME) on Economic

Efficiency of Power Generation

Hydropower

Naira/KW

Population

[9.1 x 10 6

House hold

House

Hold

Months/year year KW/Month Amount (₦)

Revenue(A) 13.16 9,100,000 1 12 5 250 1,796,340,000,000

105

Less 25%

O&M(B)

Economic

Efficiency

449,085,000,000

A - B 1,347,255,000,000

The Bill of Engineering Measurement and Evaluation (BEME) of Table 3.1 calculated

Economic efficiency for Power generation using the details of the multipurpose framework in

chapter 2 and table 2.1. However table 3.1 explains the calculation of Economic efficiency of

Hydropower within cross river basin system, considering the following: (i) cost of electricity

in Naira/Kilowatt; (ii) use of the entire population, (iii) cost of Electricity in Naira/kilowatt,

(iv) Number of persons per house hold, (v) kWh per household, (vi) Duration or period under

consideration.

Table 3.2: BEME on Economic Efficiency of Water Supply

Water Supply

Naira/Month

Population

[9.1 x 10 6 ]

House hold

House

Hold

Months/year year Amount (₦)

Revenue(A) 750 9,100,000 1 12 5 409,500,000,000

Less 25% O&M

(B)

Economic

Efficiency

102,375,000,000

A - B 307,125,000,000

The Bill of Engineering Measurement and Evaluation (BEME) of table 3.2 calculated

Economic efficiency for Water supply using the details of the multipurpose framework in

chapter 2 and figure 2.1. However, table 3.2 explains the calculation of Economic efficiency

of Water supply within cross river basin system, considering the following: (i) cost of water

supply in Naira/Month; (ii) use of the entire population, (ii) number of persons per

households, (iii) Duration or period under consideration.

Table 3.3: BEME on Economic Efficiency of Navigation

Cost of Dredging

(A)

Navigation

Naira/Kilometer Kilometer Year Amount (₦)

106

Revenue

Generated (B)

110,000,000 900 5 495,000,000,000

495,000,000,000

Navigation

National Shippers Savings Vessels Tonnage per year Year Billion Naira

32,000 1,000,000 5 160,000,000,000

Economic

A-B 335,000,000,000

Efficiency

The Bill of Engineering Measurement and Evaluation (BEME) of Table 3.3 explains the

calculation of Economic efficiency of Navigation within cross river basin system, considering

the following: (i) cost of dredging in Naira/kilometer; (ii) Kilometers navigable, (iii) period

under consideration.

Table 3.4: BEME on Economic Efficiency of Irrigation

BEME of Economic Efficiency of Irrigation

No

A

B

Description

Estimated cost of Land After

Irrigation

Estimated cost of Land before

Irrigation

Cost of Land [Billion

Naira]

Year [2013 –

2017]

Amount (₦)

190,000,000,000 5 950,000,000,000.00

100,000,000,000 5 500,000,000,000.00

C Benefit from Land [A – B] 90.000.000.000 5 450,000,000,000.00

D

E

F

Estimated Agricultural yield after

irrigation

Estimated Agricultural yield before

irrigation

Benefit from Agricultural Yield[D-

E]

180,000,000,000 5 900,000,000,000.00

90,000,000,000 5 450,000,000,000.00

90,000,000,000 5 4,500,00,000,000.00

G Gross benefit from Irrigation [ C+F] 180000000000.00 5 900,000,000,000.00

H

Cost of Irrigation [Separable of

Joint]

154,290,000,000 5 771,450,000,000.00

I Net Benefit from Irrigation[G-H] 128,550,000,000.00

The Bill of Engineering Measurement and Evaluation (BEME) of Table 3.4 estimates the

economic efficiency of irrigation in the basin, where irrigable arable land was estimated to

cost about 128.6 billion naira; while the economic benefit was calculated using the

descriptions in the second column of the table.

107

Table 3.5: BEME on Economic Efficiency of Flood Control

Flood control

Flood control Cost [Billion Naira] Year Amount (₦)

Estimated Values of Houses

and properties within the flood

plain (A)

130,050,000,000 5 650,250,000,000

Flood control structures in

place (B)

10,000,000,000 5 50,000,000,000

Economic Efficiency A - B 600,250,000,000

The Bill of Engineering Measurement and Evaluation (BEME) of Table 3.5, estimates the

economic efficiency of flood control, considering the estimated of Houses and Properties

within the basin flood plain.

Table 3.6: BEME on Economic Efficiency of Recreation

Recreation

Description

Number of Visitors

per Annum

Unit rate per

Person [Naira]

Year Amount (₦)

Estimated number of

Visitors accessing

recreational activities

(A).

9,100,000 500 5 22,750,000,000.00

Less 25% O & M (B) 5,687,500,000.00

Economic

Efficiency(A-B)

17,062,500,000.00

The Bill of Engineering Measurement and Evaluation (BEME) of Table 3.6, estimates the

economic efficiency of Recreational activities, considering the estimated values of Natural

environment with tourist potential.

108

3.4 Data Collection of payoff values of the Net benefits of Multi-purpose and Multiobjective

The net payoff values benefit of Multipurpose and Multiobjective [ Federal, Regional, State

and Local Economic distribution as well as Social Wellbeing] were covered in this section.

3.4.1 Estimation of the Net benefit nf Multipurpose and Federal Economic

Redistribution

This is measured through benefits derived from water resources projects by various

benefiting localities within a federated unit as a result of allocation and size of project and

with regards to various purposes involved. Such benefits vary with respect to decision

variables (purposes) - the factors determining the benefits are: Industrialization, Urbanization,

Man-power availability, improved property value.

The benefits derivable as a result of the above factors are in the form of:

(i) Tax to regional authority from attracted new industries.

(ii) Savings on road user cost as a result of attracted infrastructures and roads.

(iii)Saving on skilled service charge.

(iv)Enhance property value, rent and rates.

Data on the above items (i) to (iv) was collected as follows:

Item (i) - From Ministry of Industries and Board of Internal revenue

Item (ii) – From Federal Office of Statistics and Ministry of Works

Item (iii) –From Federal Office of Statistic and Ministry of Labor

Item (iv) – From Ministry of Works and Housing, and local government authorities:

Therefore, the benefit accruing to each purpose considering Federal economic redistribution

is a summation of item (i) to (iv) above with regards to each specific purpose in the

multipurpose water resources development. That is, benefits due to the inclusion of that

109

purpose in question as a part of the multi-purpose but considering only federal economic

redistribution as the objective. Find raw data in Tables 3.7, 3.8, 3.9, 3.10, 3.11 and 3.12

Table 3.7: BEME on Net benefit of Hydropower and Federal Economic Redistribution

S/N

1

2

3

4

Description

(i)Tax on new

industries attracted

as a result of

inclusion of H.E.P

in the development

(ii) Saving on road

–user cost as result

of new roads built

due to inclusion of

H.E.P in the

development

(iv)Savings on

skilled labor due to

attracted manpower

as a result of the

inclusion of H.E.P

in the development

(v)Increase in

Property value, rent

and rate as a result

of inclusion of

H.E.P in the

development

Quantities

[Population affected]

No years Rate [Naira] Amount [Naira]]

9,100,000 5 6,588 299,754,000,000.00

9,100,000 5 8,796 400,218,000,000.00

9,100,000 5 13,188 600,054,000,000.00

9,100,000 5 65,934 2,999,997,000,000.00

Net benefit on Hydropower and Federal Economic Distribution 4,300,023,000,000

The Bill of Engineering Measurement and Evaluation (BEME) of Table 3.7 details the

benefit accrued to the Federal Economic Distribution in the occurrence of Hydropower one of

110

the six multi-purpose dam projects. However, the net benefit on Hydropower and Federal

Economic Distribution is 4.3 trillion Naira

Table 3.8: BEME on Net benefit of Water Supply and Federal Economic Redistribution

S/

N

Description

Quantities [Population

affected]

No

years

Rate

[Naira]

Amount [Naira]]

1 (i)Tax on new

industries attracted as

a result of inclusion

of WS in the

development

2 (ii)Saving on road –

user cost as result of

new roads built due

to inclusion of WS in

the development

3 (iii)Savings on


attracted manpower

as a result of the

inclusion of WS in

the development

4 (iv)Increase in


and rate as a result of

inclusion of WS in

the development

9,100,000 5 6,784 308,672,000,000

9,100,000 5 2,799 127,354,500,000

9,100,000 5 3,500 159,250,000,000

9,100,000 5 4,500 204,750,000,000

Net benefit on water supply and Federal Economic Distribution

111


benefit accrued to the Federal Economic Distribution in the occurrence of Water Supply one

of the six multi-purpose dam projects. However, the net benefit on water supply and Federal

Economic Distribution is 0.2 trillion Naira.

Table 3.9: BEME on Net benefit of Navigation and Federal Economic Redistribution

S/N Description Quantities [Population affected] No years Rate [Naira] Amount [Naira]]

1

(i)Tax on new

industries attracted as a

result of inclusion of

Navigation in the

development

9,100,000 5 0 0.00

2

(ii)Saving on road –


new roads built due to

inclusion of

Navigation in the

development

9,100,000 5 2,199 100054500000.00

3

(iii)Savings on skilled

labor due to attracted

manpower as a result

of the inclusion of

Navigation in the

development

9,100,000 5 2,305 104877500000.00

4

(iv)Increases in



inclusion of

Navigation in the

development

9,100,000 5 2,090 95095000000.00

Net benefit on Navigation and Federal Economic Distribution 300,027,000,000

112


benefit accrued to the Federal Economic Distribution in the occurrence of Navigation one of

the six multi-purpose dam projects. However, the net benefit on Navigation and Federal


Table 3.10: BEME on Net Benefits of Irrigation and Federal Economic Redistribution

S/N

1

2

3

4

Description

(i)Tax on new



of Irrigation in the

development



new roads built due

to inclusion of

Irrigation in the

development




of the inclusion of

Irrigation in the

development

(iv)Increase in



inclusion of Irrigation

in the development


affected]

No

years

Rate

[Naira]

Amount [Naira]

9,100,000 5 18,900 859,950,000,000

9,100,000 5 19,500 887,250,000,000

9,100,000 5 20,500 932,750,000,000

9,100,000 5 20,500 932,750,000,000

Net benefit on Irrigation and Federal Economic Redistribution 3,612,700,000,000


benefit accrued to the Federal Economic Distribution in the occurrence of Irrigation, one of

113

the six multi-purpose dam projects. However, the net benefit on Irrigation and Federal


Table 3.11: BEME on Net benefit of Flood control and Federal Economic

Redistribution

S/N

1

2

3

4

Description

(i)Tax on new


as a result of

inclusion of Flood

Control in the

development

(ii)Saving on road

user cost as result

of new roads built

due to inclusion of

Flood Control in

the development

(iii)Savings on


attracted

manpower as a

result of the

inclusion of Flood

Control in the

development

(iv)Increase in

Property value,

rent and rate as a

result of inclusion

of Flood Control

in the development


affected]

No

years

Rate [Naira]

Amount [Naira]]

9,100,000 5 25,000 1,137,500,000,000

9,100,000 5 8,000 364,000,000,000

9,100,000 5 8,000 364,000,000,000

9,100,000 5 25,000 1,137,500,000,000

114

Net benefit on Flood Control and Federal Economic Distribution 3,003,000,000,000


benefit accrued to the Federal Economic Distribution in the occurrence of flood control one

of the six multi-purpose dam projects. However, the net benefit on Flood Control and Federal

Economic Distribution is 3 trillion Naira.

Table 3.12: BEME on Net benefit of Recreation and Federal Economic Redistribution


1

(i)Tax on new


a result of inclusion of

Recreation in the

development

9,100,000 5 10,000 455,000,000,000

2




inclusion of

Recreation in the

development

9,100,000 5 1000 45,500,000,000

3




of the inclusion of

Recreation in the

development

9,100,000 5 1,000 45,500,000,000

4

(iv)Increase in



inclusion of

Recreation in the

development

9,100,000 5 10,000 455,000,000,000

115

Net benefit on Recreation and Federal Economic Distribution 1,001,000,000,000


benefit accrued to the Federal Economic Distribution in the occurrence of Recreation, one of

the six multi-purpose dam projects. However, the net benefit on Recreation and Federal

Economic Distribution is 1trillion Naira.

3.4.2 Estimation on Net Benefit of Multipurpose and Regional Economic

Redistribution


benefiting localities within a region as a result of allocation and size of project and with

regards to various purposes involved. Such benefits vary with respect to decision variables

(purposes) - the factors determining the benefits are: Industrialization, Urbanization, Manpower

availability, improved property value.


(i)

(ii)

Tax to regional authority from attracted new industries.

Savings on road user cost as a result of attracted infrastructures and roads.

(iii) Saving on skilled service charge.

(iv)

Enhance property value, rent and rates.




116



Therefore, the benefit accruing to each purpose considering Regional Economic

Redistribution is a summation of item (i) to (iv) above with regards to each specific purpose

in the multipurpose water resources development. That is, benefits due to the inclusion of that

purpose in question as a part of the multi-purpose but considering only Regional economic

distribution as the objective. Find raw data in Tables 3.13, 3.14, 3.15, 3.16, 3.17, and 3.18

Table 3.13: BEME on Net Benefit of Hydropower and Regional Economic

Redistribution


1

2

3

4

(i)Tax on new industries

attracted as a result of

inclusion of Recreation

in the development

(ii)Saving on road –user

cost as result of new

roads built due to


in the development



manpower as a result of

the inclusion of

Recreation in the

development

(iv)Increase in Property

value, rent and rate as a


Recreation in the

development

9,100,000 5 2,179 99,144,500,000

9,100,000 5 44 2,002,000,000

9,100,000 5 22 1,001,000,000

9,100,000 5 1,978 89,999,000,000

Net benefit on Hydropower and Regional Economic Redistribution 192,146,500,000


benefit accrued to the Regional Economic Redistribution in the occurrence of Hydropower,

117

one of the six multi-purpose dam projects. However, the net benefit on Hydropower and

regional economic redistribution is 0.192 trillion Naira.

Table 3.14: BEME on Net benefit of Water Supply and Regional Economic

Redistribution


1



inclusion of WS in the

development

9,100,000 5 1400 63,700,000,000

2



roads built due to

inclusion of WS in the

development

9,100,000 5 1000 45,500,000,000

3




the inclusion of WS in

the development

9,100,000 5 1000 45,500,000,000

4




WS in the development

9,100,000 5 1,000 45,500,000,000

Net benefit on Water Supply and Regional Economic Distribution 200,200,000,000

118


benefit accrued to the Regional Economic Redistribution in the occurrence of Water supply,

one of the six multi-purpose dam projects. However, the net benefit on water supply and

Regional economic redistribution is 0.2 trillion Naira.

Table 3.15: BEME on Net benefit of Navigation and Regional Economic Redistribution


1

2

3

4



inclusion of Navigation

in the development



roads built due to

inclusion of Navigation

in the development




the inclusion of

Navigation in the

development

(iv)Increases in Property



Navigation in the

development

9,100,000 5 100 4,550,000,000

9,100,000 5 10 455,000,000

9,100,000 5 10 455,000,000

9,100,000 5 100 4,550,000,000

Net benefit on Navigation and Regional Economic Redistribution 10,010,000,000


benefit accrued to the Regional Economic Redistribution in the occurrence of Navigation, one

of the six multi-purpose dam projects. However, the net benefit on Navigation and regional

economic redistribution is 0.01 trillion Naira.

119

120

Table 3.16: BEME on Net benefit of Irrigation and Regional Economic Redistribution


1



inclusion of Irrigation in

the development

9,100,000 5 220 10,010,000,000

2



roads built due to


the development

9,100,000 5 4,396 200,018,000,000

3




the inclusion of

Irrigation in the

development

9,100,000 5 110 5,005,000,000

4




Irrigation in the

development

9,100,000 5 879 39,994,500,000

Net benefit on Irrigation and Regional Economic Distribution 255,027,500,000


benefit accrued to the Regional Economic Redistribution in the occurrence of Irrigation, one

of the six multi-purpose dam projects. However, the net benefit on Irrigation and regional

economic redistribution is 0.255trillion Naira.

121

Table 3.17: BEME on Net benefit of Flood control and Regional Economic Redistribution

S/N Description Quantities No years Rate [Naira] Amount [Naira]]

1

(i)Tax on new



of Flood Control in

the development

9,100,000 5 132 6,006,000,000

2

3



new roads built due

to inclusion of Flood

Control in the

development

(iii)Savings on


attracted manpower

as a result of the

inclusion of Flood

Control in the

development

9,100,000 5 1,319 60,014,500,000

9,100,000 5 220 10,010,000,000

4

(iv)Increase in



inclusion of Flood

Control in the

development

9,100,000 5 2,198 100,009,000,000

Net benefit on Flood control and Regional Economic Distribution 176,039,500,000


benefit accrued to the Regional Economic Redistribution in the occurrence of Flood Control,

one of the six multi-purpose dam projects. However, the net benefit on Flood control and

regional economic redistribution is 0.176 trillion Naira.

122

Table 3.18: BEME on Net benefit of Recreation andRegional Economic Redistribution

S/N Description Population No years Rate [Naira] Amount [Naira]]

1

(i)Tax on new industries attracted as a result

of inclusion of Recreation in the development

9,100,000 5 10 455,000,000

2

(ii)Saving on road –user cost as result of new

roads built due to inclusion of Recreation in

the development

9,100,000 5 130 5,915,000,000

3

(iii)Savings on skilled labor due to attracted

manpower as a result of the inclusion of

Recreation in the development

9,100,000 5 14 637,000,000

4

(iv)Increase in Property value, rent and rate as

a result of inclusion of Recreation in the

development

9,100,000 5 22 1,001,000,000

Net benefit on Recreation and Regional Economic Distribution 8,008,000,000


benefit accrued to the Regional Economic Redistribution in the occurrence of Recreation, one

of the six multi-purpose dam projects. However, the net benefit on Recreation and regional

economic redistribution is 0.0086billion Naira. This is approximated to 0.008trillion Naira.

123

3.4.3 Estimation on Net benefit of Multipurpose and State Economic Redistribution


benefiting localities within a state(s) as a result of allocation and size of project and with


(purposes) - the factors determining the benefits are: Industrialization, Urbanization, Manpower

availability, and improved property value.


(i)

(ii)

(iii)

(iv)



Saving on skilled service charge.







Therefore, the benefit accruing to each purpose considering State Economic Distribution

redistribution is a summation of item (i) to (iv) above with regards to each specific purpose in

the multipurpose water resources development. That is, benefits due to the inclusion of that

purpose in question as a part of the multi-purpose but considering only State economic

distribution as the objective. Find raw data in Tables 3.19, 3.20, 3.21, 3.22, 3.23 and 3.24.

124

Table 3.19: BEME on Net benefit of Hydropower and State Economic Redistribution

S/N

1

Description

(i)Tax on new

industries

attracted as a

result of

inclusion of

H.E.P in the

development


affected]

No

years

Rate [Naira]

Amount [Naira]]

9,100,000 5 13,500 614,250,000,000

2

3

4

(ii)Saving on

road –user cost

as result of new

roads built due

to inclusion of

H.E.P in the

development

(iii)Savings on

skilled labor

due to attracted

manpower as a

result of the

inclusion of

H.E.P in the

development

(iv)Increase in

Property value,

rent and rate as

a result of

inclusion of

H.E.P in the

development

9,100,000 5 12,500 568,750,000,000

9,100,000 5 5,450 247,975,000,000

9,100,000 5 14,800 673,400,000,000

Net benefit on Hydropower and State Economic Distribution 2,104,375,000,000


benefit The accrued to the State Economic Distribution in the occurrence of Hydropower, one of

the six multi-purpose dam projects. However, the net benefit on Hydropower and State


125

Table 3.20: BEME on Net benefit of Water Supply and State Economic Redistribution


1

2

3

4

(i)Tax on new

industries

attracted as a

result of

inclusion of

WS in the

development

(ii)Saving on

road –user cost

as result of new

roads built due

to inclusion of

WS in the

development

(iii)Savings on

skilled labor

due to attracted

manpower as a

result of the

inclusion of

WS in the

development

(iv)Increase in

Property value,

rent and rate as

a result of

inclusion of

WS in the

development

9,100,000 8 179 13,031,200,000

9,100,000 5 2,198 100,009,000,000

9,100,000 5 220 10,010,000,000

9,100,000 5 720 32,760,000,000

Net benefit on Water Supply and State Economic Distribution 155,810,200,000

Bill of Engineering Measurement and Evaluation (BEME) of Table 3.20 details the benefit

accrued to the State Economic Distribution in the occurrence of Water Supply, one of the six

multi-purpose dam projects. However, the net benefit on water supply and State Economic

Distribution is 0.156 trillion Naira.

126

Table 3.21: BEME on Net benefit of Navigation and State Economic Redistribution

S/

N

1

2

3

4

Description

(i)Tax on new

industries

attracted as a

result of

inclusion of

Navigation in

the development

(ii)Saving on

road –user cost

as result of new

roads built due

to inclusion of

Navigation in

the development

(iii)Savings on

skilled labor due

to attracted

manpower as a

result of the

inclusion of

Navigation in

the development

(iv)Increases in

Property value,

rent and rate as a

result of

inclusion of

Navigation in

the development

Quantities [Population affected]

No

years

Rate

[Naira]

Amount [Naira]]

9,100,000 5 2,198 100,009,000,000

9,100,000 5 0 0

9,100,000 5 2,198 100,009,000,000

9,100,000 5 0 0

Net benefit on Navigation and State Economic Distribution 200,018,000,000


benefit accrued to the State Economic Distribution in the occurrence of Water Supply, one of the

six multi-purpose dam projects. However, the net benefit on Navigation and State Economic


127

Table 3.22: BEME on Net benefit of Irrigation and State Economic Redistribution

S/N

1

Description

(i)Tax on new

industries

attracted as a

result of

inclusion of

Irrigation in the

development


affected]

No

years

Rate

[Naira]

Amount [Naira]]

9,100,000 5 18,242 830,011,000,000

2

(ii)Saving on

road –user cost

as result of new

roads built due to

inclusion of

Irrigation in the

development

9,100,000 5 1,604 72,982,000,000

3

4

(iii)Savings on

skilled labor due

to attracted

manpower as a

result of the

inclusion of

Tourism in the

development

(iv)Increase in

Property value,

rent and rate as a

result of

inclusion of

Irrigation in the

development

9,100,000 5 6,154 280,007,000,000

9,100,000 5 13,560 616,980,000,000

Net benefit on Irrigation and State Economic Redistribution 1,799,980,000,000


benefit accrued to the State Economic Distribution in the occurrence of Irrigation, one of the six

multi-purpose dam projects. However, the net benefit on Irrigation and State Economic


128

Table 3.23: BEME on Net benefit of Flood Control and State Economic Redistribution


1



inclusion of Flood

Control in the

development

9,100,000 5 681 30,985,500,000

2



roads built due to

inclusion of Flood

Control in the

development

9,100,000 5 1,099 50,004,500,000

3




the inclusion of Flood

Control in the

development

9,100,000 5 506 23,023,000,000

4




Flood Control in the

development

9,100,000 5 176 8,008,000,000

Net benefit on Flood Control and State Economic Redistribution 112,021,000,000


benefit accrued to the State Economic Redistribution in the occurrence of Flood Control one of

the six multi-purpose dam projects. However, the net benefit on Flood Control and State

Economic Redistribution is 0.112 trillion Naira.

129

Table 3.24: BEME on Net benefit of Recreation and State Economic Redistribution


1




in the development

9,100,000 5 68 3,094,000,000

2



roads built due to


in the development

9,100,000 5 1 45,500,000

3




the inclusion of

Recreation in the

development

9,100,000 5 45 2,047,500,000

4




Recreation in the

development

9,100,000 5 18 819,000,000

Net benefit on Recreation and State Economic Redistribution 6,006,000,000


benefit accrued to the State Economic Redistribution in the occurrence of Recreation one of

the six multi-purpose dam projects. However, the net benefit on Recreation and State


130

3.4.4 Estimation on Net benefit of Multipurpose and Local Economic Redistribution


benefiting localities within a state(s) as a result of allocation and size of project and with


(purposes) - the factors determining the benefits are:

Industrialization,

Urbanization,

Man-power availability,

Improved property value.




Saving on skilled service charge.







Therefore, the benefit accruing to each purpose considering Local economic redistribution is

a summation of item (i) to (iv) above with regards to each specific purpose in the

multipurpose water resources development. That is, benefits due to the inclusion of that

131

purpose in question as a part of the multi-purpose but considering only State economic

distribution as the objective. Find raw data in Tables: 3.25, 3.26, 3.27, 3.28, 3.39 and 3.30.

Table 3.25: BEME on Net benefit of Hydropower and Local Economic Redistribution

S/N Description Quantities [Population affected] No years Rate [Naira] Amount [Naira]

1

(i)Tax on

new

industries

attracted as a

result of

9,100,000 5 4,396 200,018,000,000

inclusion of

H.E.P in the

development

2

(ii)Saving on

road –user

cost as result

of new roads

built due to

9,100,000 5 2,198 100,009,000,000

inclusion of

H.E.P in the

development

3

(iii)Savings

on skilled

labor due to

attracted

manpower as

9,100,000 5 2,198 100,009,000,000

a result of the

inclusion of

H.E.P in the

development

4

(iv)Increase

in Property

value, rent

and rate as a

result of

9,100,000 5 8,791 399,990,500,000

inclusion of

H.E.P in the

development

Net benefit on Hydropower and Local Economic Distribution 800,026,500,000


benefit accrued to the Local Economic Distribution in the occurrence of Hydropower, one of

the six multi-purpose dam projects. However, the net benefit on Hydropower and Local

Economic Distribution is 0.8 trillion Naira

132

Table 3.26: BEME onNet Benefit of Water Supply and Local Economic Redistribution


1

(i)Tax on

new

industries

attracted as

a result of

9,100,000 5 2,198 100,009,000,000

inclusion of

WS in the

development

2

(ii)Saving

on road –

user cost as

result of

new roads

9100000 5 2,198 100,009,000,000

built due to

inclusion of

WS in the

development

3

(iii)Savings

on skilled

labour due

to attracted

manpower

9100000 5 4,396 200,018,000,000

as a result of

the inclusion

of WS in the

development

4

(iv)Increase

in Property

value, rent

and rate as a

result of

inclusion of

WS in the

development

9100000 5 6,593 299,981,500,000

Net benefit on Water Supply and Local Economic redistribution 700,017,500,000


benefit accrued to the Local Economic Distribution in the occurrence of Water Supply, one of

the six multi-purpose dam projects. However, the net benefit on water supply and Local


133

Table 3.27: BEME on Net benefit of Navigation versus Local Economic Redistribution

S/N Description


affected]

No years Rate [Naira] Amount [Naira]

(i)Tax on new

industries

1

attracted as a

result of inclusion

9,100,000 5 0 0

of Navigation in

the development

(ii)Saving on road

user cost as result

2

of new roads built

due to inclusion

9,100,000 5 2,198 100,009,000,000.00

of Navigation in

the development

3

(iii)Savings on

skilled labor due

to attracted

manpower as a

result of the

inclusion of

Navigation in the

development

9,100,000 5 0 0

4

(iv)Increases in

Property value,

rent and rate as a

result of inclusion

of Navigation in

the development

9,100,000 5 0 0

Net benefit on Navigation and Local Economic Distribution 100,009,000,000


benefit accrued to the Local Economic Distribution in the occurrence of Navigation, one of

the six multi-purpose dam projects. However, the net benefit on Navigation and Local

Economic Distribution is 0.1trillion Naira

134

Table 3.28: BEME onNet benefit of Tourism and Local Economic Redistribution

Quantities [Population No

S/N Description

Rate [Naira] Amount [Naira]

affected]

years

1




the development

9,100,000 5 6,400 291,200,000,000

2

3

4



roads built due to


the development




the inclusion of Irrigation

in the development




Irrigation in the

development

Net benefit on Irrigation

and Local Economic

Redistribution

9,100,000 5 10,000 455,000,000,000

9,100,000 5 5,000 227,500,000,000

9,100,000 5 5,000 227,500,000,000

1,201,200,000,000


benefit accrued to the Local Economic Distribution in the occurrence of Irrigation, one of the

six multi-purpose dam projects. However, the net benefit on Irrigation and Local Economic


135

Table 3.29: BEME on Net benefit of Flood Control versus Local Economic Redistribution

Quantities

S/N Description

[Population

affected]

No years Rate [Naira] Amount [Naira]

1

(i)Tax on new

industries attracted as a



development

9,100,000 5 22,000 1,001,000,000,000

2




inclusion of Flood

Control in the

development

9100 5 2,500 113,750,000

3


labour due to attracted


the inclusion of Flood

Control in the

development

9100 5 2,300 104,650,000

4





development

9100 5 3,400 154,700,000

Net benefit on Flood Control and Local Economic Redistribution 1,001,373,100,000


benefit accrued to the Local Economic Redistribution in the occurrence of Flood Control, one

of the six multi-purpose dam projects. However, the net benefit on Flood Control and Local


136

Table 3.30: BEME on Net benefit of Recreation versus Local Economic Redistribution

Quantities

No

S/N Description

[Population

Rate [Naira] Amount [Naira]

years

affected]

1

(i)Tax on new


a result of inclusion of

Recreation in the

development

9,100,000 5 35 1,592,500,000.00

2




inclusion of

Recreation in the

development

9,100,000 5 17 773,500,000.00

3


labour due to attracted


of the inclusion of

Recreation in the

development

9,100,000 5 18 819,000,000.00

4

(iv)Increase in



inclusion of

Recreation in the

development

9,100,000 5 150 6,825,000,000.00

Net benefit on Recreation and Local Economic Redistribution 10,010,000,000.00


benefit accrued to the Local Economic Redistribution in the occurrence of Recreation, one of

the six multi-purpose dam projects. However, the net benefit on Recreation and Local

Economic Redistribution is 0.01trillion Naira, and is approximated to 0.1 billion Naira.

137

3.4.5 Estimation on Net benefit of Multipurpose and Social Well-Being

When considering Youth Employment as a development objective in multipurpose water

resources planning, all factors that contribute towards furtherance of Youth Employment in

. society are taken into consideration when determining the benefits that accrue to various

purposes involved in the development such factors are: -Food, shelter, and clothing Industrial

and collective security, Luxury and convenience. Health Education, Harmonious Family and

Community relations, Pleasant work and living conditions, Clean and stimulating,

Environment, Certain level of culture and level of morality.

Of the above ten factors, the first five are the most important and determining whereas the

rest are incidental.

Benefits derivable as a result of the above five main factors, that is (a) to (e), are in the form

of savings:

On food, Shelter and clothing;

As a result of reduced theft, workers strike and better security in industries, homes and in

public places;

On extra-home luxury expenses;

As a result of better health;

Better family and community relations, improved level of culture as well as morality

education.

Therefore, the benefit accruing to each purpose considering social well-being is a summation

of

items (i) to (v) above with regards to each specific purpose in the multipurpose water

resources development.

138

Data on the above items (i) to (v) were collected as follows:

Item (i)-from Ministry of Social Welfare, National Population commission and National

Office of Statistic.

Item (ii) - from police dept., Ministry of Labor, Ministry of Internal Affairs, and National

Office of Statistics

Item (iii) - from Ministry of Industries, State Tourism Commission and National Office of

Statics.

Item (iv) - from Ministry of Health and Ministry of Social Welfare.

Find raw data on Social Well-Being as the objective can be found in Tables 3.31, 3.32, 3.33,

3.34, 3.35, and 3.36.

139

Table 3.31: BEME on Net benefit of Hydropower and Social Well Being

S/

Quantities [Population No Rate

Description

N

affected]

years [Naira]

Amount [Naira]

1

(i)Tax on new


as a result of

inclusion of H.E.P

in the development

9,100,000 5 440 20020000000

2

3

4



new roads built due

to inclusion of

H.E.P in the

development

(iii)Savings on


attracted manpower

as a result of the

inclusion of H.E.P

in the development

(iv)Increase in


and rate as a result

of inclusion of

H.E.P in the

development

9,100,000 5 220 10010000000

9,100,000 5 220 10010000000

9,100,000 5 1,319 60014500000

Net benefit on Hydropower and Social Well-Being

100,054,500,000


benefit accrued to the Social Well-Being in the occurrence of Hydropower, one of the six

multi-purpose dam projects. However, the net benefit on Hydropower and Social Well-Being

is 0.10 trillion Naira.

140

Table 3.32: BEME on Net Benefit of Water Supply and Social Well-Being


1

(i)Tax on new



9,100,000 5 5.49 249,795,000.00

of Water Supply in

the development

2



new roads built due

to inclusion of Water

Supply in the

development

9,100,000 5 5.49 249,795,000.00

3

4

(iii)Savings on


attracted manpower

as a result of the

inclusion of Water

Supply in the

development

(iv)Increase in



inclusion of Water

Supply in the

development

9,100,000 5 3,297 150,013,500,000.00

9,100,000 5 1 45,500,000.00

Net benefit on Water Supply and Social well-being 150,558,590,000.00


benefit accrued to the Social Well-Being in the occurrence of Water Supply, one of the six

multi-purpose dam projects. However, the net benefit on water supply and Social Well-Being


141

Table 3.33: BEME on Net benefit of Navigation versus Social Well-Being


S/N Description

Amount [Naira]

affected]

years [Naira]

1

(i)Tax on new


as a result of

inclusion of

Navigation in the

development

9,100,000 5 0 0.00

2

(ii)Saving on road

user cost as result

of new roads built

due to inclusion of

Navigation in the

development

9,100,000 5 4,396 200,018,000,000.00

3

4

(iii)Savings on

skilled labor due

to attracted

manpower as a

result of the

inclusion of

Navigation in the

development

(iv)Increases in

Property value,

rent and rate as a

result of inclusion

of Navigation in

the development

9,100,000 5 0 0.00

9,100,000 5 0 0.00

Net benefit on Navigation and Social Well-Being 200,018,000,000.00


benefit accrued to the Social Well-Being in the occurrence of Navigation, one of the six

multi-purpose dam projects. However, the net benefit on Navigation and Social Well-Being is

0.2 trillion Naira.

142

Table 3.34: BEME on Net benefit of Irrigation and Social Well-Being

Quantities

No Rate

S/N Description

Amount [Naira]

[Population affected] years [Naira]

1

2

(i)Tax on new



of Irrigation in the

development



new roads built due

to inclusion of

Irrigation in the

development

9,100,000 5 1,099 50,004,500,000

9,100,000 5 2,198 100,009,000,000

3




of the inclusion of

Irrigation in the

development

9,100,000 5 330 15,015,000,000

4

(iv)Increase in



inclusion of Irrigation

in the development

9,100,000 5 330 15,015,000,000

Net benefit on Irrigation and Social Well-being 180,043,500,000


benefit accrued to the Social Well-Being in the occurrence of Irrigation, one of the six multipurpose

dam projects. However, the net benefit on water supply and Social Well-Being is

0.18 trillion Naira.

143

Table 3.35: BEME on Net benefit of Flood Control versus Social Well-being


S/N Description

Amount [Naira]

affected]

years [Naira]

1

(i)Tax on new

industries

attracted as a

result of

inclusion of

Flood Control in

the development

9,100,000 5 2,198 100,009,000,000.00

2

3

4

(ii)Saving on

road –user cost as

result of new

roads built due to

inclusion of

Flood Control in

the development

(iii)Savings on

skilled labor due

to attracted

manpower as a

result of the

inclusion of

Flood Control in

the development

(iv)Increase in

Property value,

rent and rate as a

result of

inclusion of

Flood Control in

the development

9,100,000 5 1.1 50,050,000.00

9,100,000 5 0.055 2,502,500.00

9,100,000 5 220 10,010,000,000.00

Net benefit on Flood Control and Social Well-Being 110,071,552,500.00


benefit accrued to the Social Well-Being in the occurrence of Flood Control, one of the six

multi-purpose dam projects. However, the net benefit on water supply and Social Well-Being


144

Table 3.36: BEME on Net benefit of Recreation versus Social Well-being

S/N

Description


affected]

No

years

Rate [Naira]

Amount [Naira]

1

(i)Tax on new

industries

attracted as a

result of

inclusion of

Recreation in

the

development

9,100,000 5 10,000 455,000,000,000.00

2

3

4

(ii)Saving on

road –user cost

as result of new

roads built due

to inclusion of

Recreation in

the

development

(iii)Savings on

skilled labor

due to attracted

manpower as a

result of the

inclusion of

Recreation in

the

development

(iv)Increase in

Property value,

rent and rate as

a result of

inclusion of

Recreation in

the

development

9,100,000 5 3000 136,500,000,000.00

9,100,000 5 1900 86,450,000,000.00

9,100,000 5 10,000 455,000,000,000.00

Net benefit on Recreation and Social Well-Being 1,132,950,000,000


benefit accrued to the Social Well-Being in the occurrence of Recreation, one of the six

multi-purpose dam projects. However, the net benefit on Recreation, and Social Well-Being

is 1.13 trillion Naira,

145

3.5 Total Net-Benefits of Multi-Purposes under various Multi-Objectives

Gross Benefit of N10.9 Billion released from Federal Government of Nigeria from 2013 to

2017 for Capital Projects to Cross River basin Development Authority (CRBDA) under

various Objectives as in section 3.4.1 to 3.4.5.

Table 3.37: Net benefits of Cross River basin Multi-Purpose and Multi-Objective

Multiobjective

Multipurpose/Courses of Action/ Alternatives

State of Nature Hydropower

Water

Supply Navigation Irrigation

Flood

Control Recreation

Economic

Efficiency

1.35 0.31 0.335 0.129 0.6 0.017

Federal Economic

Redistribution

4.3 0.8 1 3.6 3 1

Regional Economic

Redistribution

0.192 0.2 0.01 0.255 0.176 0.008

State Economic

Redistribution

2.1 0.156 0.2 1.8 0.112 0.006

Local Economic

Redistribution

0.8 0.7 0.1 1.2 1 0.01

Social Well-Being 0.1 0.151 0.2 0.18 0.11 1.13

The table 3.37 shows the net benefit in trillions of Naira of the multi-purpose and multiobjectives.

This table is very important because it determines the best multi-purpose project

among others that can be further developed for optimum system benefits. The foregoing is

achieved by the products of the empirical prior distribution and the payoff values.

consequently, the multipurpose that has the Maximum Expected Monetary Value (EMV*)

will be selected as a project worth investing on for the benefit of the Rivers Basin inhabitant,

the region and the country at large.

3.6 Raw Data Analysis and Discussion of Results

3.6.1 Introduction

This chapter discussed raw data analysis, interaction, reliability and validity of the raw data

source using analysis of variance [ANOVA].

146

3.6.2 Analyses

This subsection deals with analysis of the raw data. The raw data were analyzed for

interaction, reliability and validity.

However, to carry the analysis the following test were

employed namely:

I. Contingency coefficient & association

II.

Pearson moment correlation coefficient

(i) Contingency Coefficient and its Associates

Chi-Square(X2) Contingency Test

The Chi-square test is a measure of relationships, association or independence. Introduced by

Karl Pearson in 1990, the chi-square test is probably the best known and the most important

of all non-parametric method. It involves a measure of reliability by comparing observed

frequency distribution failure mode with theoretical or expected distribution failure when that

hypothesis is false.

Non-parametric tests process the advantage of being fairly robust with respect to violations of

assumptions having more power-efficiency (the power of a test relative to the sample size

which permits one to compare the power of two different statistical tests. The power of a

statistical test is then probability that the test will correctly reject the null hypothesis when

that hypothesis is false) and sometimes providing more information about a phenomenon (i.e.

interactions in the analysis of variance).

There are five basic conditions that must be met for Chi-square analysis to be validly applied.

These are (a) the sample observations are independent of each other (b) sample data are

drawn at random from the population (c) Sample data are expressed in original unites. (d)

The sample should contain at least 50 observations. (e) There should be not less than five

observations in any one cell. (f) Not more than 20% of the expected frequency should be less

than 5.

147

Table 3.40: Computed Chi-square Table

O E 0-E (0-E) 2 (0-E) 2 /E

1.35 0.886561144 0.463439 0.21477557 0.242256921

0.31 0.232318726 0.077681 0.00603438 0.025974576

0.335 0.184992684 0.150007 0.02250219 0.121638296

0.129 0.718313056 -0.58931 0.34728988 0.483479835

0.6 0.501134653 0.098865 0.00977436 0.019504452

0.017 0.217679738 -0.20068 0.04027236 0.185007377

4.3 4.431188499 -0.13119 0.01721042 0.003883929

0.8 1.161169843 -0.36117 0.13044366 0.112338136

1 0.924625965 0.075374 0.00568125 0.006144371

3.6 3.590254966 0.009745 9.4966E-05 2.6451E-05

3 2.504759118 0.495241 0.24526353 0.097919009

1 1.08800161 -0.088 0.00774428 0.007117897

0.192 0.272016754 -0.08002 0.00640268 0.023537818

0.2 0.071280572 0.128719 0.01656869 0.232443296

0.01 0.056759886 -0.04676 0.00218649 0.038521693

0.255 0.220394484 0.034606 0.00119754 0.005433629

0.176 0.153759301 0.022241 0.00049465 0.003217033

0.008 0.066789004 -0.05879 0.00345615 0.051747245

2.1 1.414745876 0.685254 0.46957322 0.331913472

0.156 0.370726781 -0.21473 0.04610759 0.124370811

0.2 0.295205399 -0.09521 0.00906407 0.030704276

1.8 1.146260965 0.653739 0.42737473 0.372842432

0.112 0.799694626 -0.68769 0.4729239 0.591380614

0.006 0.347366353 -0.34137 0.11653099 0.33546999

0.8 1.232323225 -0.43232 1.66464645 -2.096969675

0.7 0.322923876 0.377076 -0.05415225 0.431228372

0.1 0.257140506 -0.15714 0.41428101 -0.571421517

1.2 0.998457768 0.201542 0.79691554 -0.595373304

1 0.696578996 0.303421 0.39315799 -0.089736987

0.01 0.30257563 -0.29258 0.59515126 -0.88772689

0.1 0.605164502 -0.50516 0.25519117 0.421688935

0.151 0.158580203 -0.00758 5.7459E-05 0.000362337

0.2 0.126275561 0.073724 0.00543529 0.043043111

0.18 0.490318762 -0.31032 0.09629773 0.196398224

0.11 0.342073307 -0.23207 0.05385802 0.157445842

1.13 0.148587665 0.981412 0.96317017 6.482167754

27.337 27.337 0.00 7.80 6.937979762

151

X 2 (6.937979762) < X 2 0.10 (34.382). DF = 25 [Reference Chi-square Table in Appendix 1]

Contingency coefficient, C is given by

C = X² N + X²

Where C = Contingency Coefficient

X² = Chi-square

N = Grand total of subjects or cases

X² = 6.937979762

N = 27.337

C = 6.937979762 27.337 + 6.937979762

C = 0.505519, the maximum Contingency coefficient can go is 0.8.

Therefore C = 0.505519/0.8

C = 0.632

Correlation of attributes r, is given as:

r = X² N(K − 1)

r = 6.937979762 27.337(6 − 1)

r = 0.2518901= 0.252

Analysis and Discussion on Raw Data

(i) The Contingency of the raw data is = 0.632

(ii) The correlation of attributes of the raw data = 0.252

(iii) The X 2 value 6.94 is interpreted from the X 2 table of probability values at 0.10

level of significance [Appendix-1]. The degree of freedom necessary to intercept

X 2 values are always determined from the frequency table by the number of rows

minus one time the number of columns minus one (r-1) (c-1) i.e. (6-1) (6-1) = 25

152

(iv) Since the obtained X 2 value of 6.94 is less than the critical value of 34.382, therefore the

Alternate Hypotheses was accepted. i.e.: X 2 (6.94) ˂ X 2 0.10 (34.382). The Alternate

Hypotheses is accepted and the null hypothesis is rejected, a clear indication that there is a

relationship between the River basin purposes and the Objectives.

- Therefore, there is relationship between the state of the system (Dam Purposes) and the

Dam Objectives.

- The Chi Square was not based on a fictitious data, in the case of Bayesian Decision

Modeling in River Basin Management.

- In the test of how well the linear estimator, y=a + bx fits the raw data, the correlation

coefficient r = 0.252 resulting in a good fit or relationship for the raw data

3.6.3 Observed Data Distribution

153

The distribution curve of the observed data presented the limit value of spread at 99.9% (Probability

of 0.999) and that in turn gave the distribution function(Ф) equal to 0.001(highlighted in yellow in the

table as shown in the figure 3.1) at both tail of the curve. More so, the mean of the observed data was

equal to 0.759. The total area under the curve is equal to 1.0 (Which implies probability of 1).

Therefore, the distribution function [Ф = area under the curve – probability of curve spread] was used

in the evaluation of the likelihood function P(x/y) in the proceeding chapter 4, subsection 4.3.3.4.

Figure 3.1: Observed Data Distribution

Source: (Ohaji. E, 2019)

154

3.6.4 Expected Data Distribution

Similarly, the distribution curve of the expected data presented the limit value of spread at 99.9%

(Probability of 0.999) and that in turn gave the distribution function(Ф) equal to 0.001 (highlighted in

yellow in the table as shown in the figure 3.2) at both tail of the curve. More so, the mean of the

expected data is equal to 0.759. The total area under the curve is equal to 1.0 (Which implies

probability of 1). Therefore, the distribution function [Ф = area under the curve – probability of curve

spread] was used in the evaluation of the likelihood function P(x/y) in the proceeding chapter 4,

subsection 4.3.3.4.

Figure 3.2: Expected Data Distribution

Source: (Ohaji. E, 2019)

155

3.6.5 Data Validation

(i) Graphical Method

Table 3.41: Expected and Observed Data

Observed Data

Expected Data

1.35 0.886561144

0.31 0.232318726

0.335 0.184992684

0.129 0.718313056

0.6 0.501134653

0.017 0.217679738

4.3 4.431188499

0.8 1.161169843

1 0.924625965

3.6 3.590254966

3 2.504759118

1 1.08800161

0.192 0.272016754

0.2 0.071280572

0.01 0.056759886

0.255 0.220394484

0.176 0.153759301

0.008 0.066789004

2.1 1.414745876

0.156 0.370726781

0.2 0.295205399

1.8 1.146260965

0.112 0.799694626

0.006 0.347366353

0.8 1.232323225

0.7 0.322923876

0.1 0.257140506

1.2 0.998457768

1 0.696578996

0.01 0.30257563

0.1 0.605164502

0.151 0.158580203

0.2 0.126275561

0.18 0.490318762

0.11 0.342073307

1.13 0.148587665

156

Figure 3.3: Plot of Expected against observed data

From Table 3.41, the expected data was plotted against observed data and figure 3.3

indicates the graphical expression of the relationship; where the correlation coefficient R 2

indicates a good relationship between observed and expected data, hence the source of data.

157

(ii)

Pearson Moment Correlation Coefficient

Table 3.42: Pearson Moment Coefficient of the Expected and Observed Data

Table 3.42 is an extract of excel spreadsheet used for the computation of the Pearson moment

correlation coefficient of the observed and expected data. The result therein as R 2 = 0.9376

which gave a clear indication of a strong relationship between the observed and the expected

data. It also implies that the source of the data is credible and can be used as input to the

system model simulation.

158

Analysis and Discussion

(i)

Comparing rcalculated value with rcritical value using table of critical values: Pearson

correlation. At 5% (0.05) significant figure and degree of freedom of 4, rcritical value

= 0.2336 and rcalculated value = 0.968 (approximated to 3 significant figures)

Therefore, rcalculated value > rcritical value using i.e. 0.968 > 0.2336,

(ii)

therefore, reject Null Hypothesis, (Section 3.4.5 and Appendix A17). Ultimately,

there is a significant relationship between means of observed and expected data.

Table 3.43: T-test on the Expected and Observed Data correlation (r)

Formula

Out-put /Decision

total number of sample(n) 36

n - 2 34

R² 0.8791

R 0.9376

A (t = (n-2)) ⁄(1-r²) 19.45825658

B = SQRT OF A 4.411151389

C = B X r 4.135895543

t value 4.135895543

Degree of freedom(df) = n-2 34

Level of Confidence 95%

t critical 2.032245

Therefore, reject Null hypothesis

t value > critical 4.135895543 ˃ 2.032245

[Type-1 and type-2 errors were not

found or committed. Which implies

that there is significant relationship

between means of Observed and

Expected data.

Analysis and Results of table 3.43:

Table 3.43 above summarizes how to determine t value and t critical value. To find a critical

value, look up your confidence level in the bottom of t-table (See Appendix A2) this tells you

which column of the t-table you need. Intersect this column with the row for the degree of

159

(ii) t value ˃ t critical, therefore reject Null Hypothesis, this is a clear indication that the

correlation coefficient relationship between means of Observed and Expected data can

be used for prediction of data and simulation modeling.

(iii)Type-1 and type-2 errors were not found or committed

161

Figure 3.4: Bayesian Decision Theory Model-Flow Chart

Source: Ohaji. E, 2019

162

CHAPTER FOUR

DATA ANALYSIS AND DISCUSION OF RESULTS

This chapter deals with transforming and modeling data with the goal of discovering useful

information, informing conclusions, supporting decision-making, discussion of results,

optimum solution, policy’s and strategies and its applications in Cross River Basin System.

Details of the proceeding involves the followings:

i) Multipurpose and Multiobjective Variables Designation.

ii) Estimating Authorized Number and Prior Probability of Multipurpose:

a) Authorized Number of Multipurpose

b) Prior Probability of Multipurpose

iii) Bayesian Decision Model Simulation, Likelihood Forecast, Marginal Distribution,

Posterior Distribution, Expected Value of System Information (EVSI) and Expected

Opportunity Loss (EOL) at 1 st Iteration

a) Model Simulation of Multipurpose/Multiobjective payoff values toward

achieving Expected Monetary Value (EMV), Expected Value of Perfect

Information (EVPI) and Expected Profit in Perfect Information (EPPI).

b) Likelihood Simulation of Multiobjective/Multipurpose payoff values toward

achieving its Likelihood distribution, Marginal and Posterior Distribution, EVSI

c) Model Simulation of Multipurpose/Multiobjective payoff values toward

achieving Conditional Opportunity Loss (COL) of the System and EOL

iv) Dynamics of EMV and EOL at 1 st Iteration.

v) Bayesian Decision Model Simulation, Marginal Distribution, Posterior Distribution

and Expected Opportunity Loss (EOL) at 2 nd Iteration

163

a) BDM Simulation of Multipurpose/Multiobjective payoff values toward achieving

Expected Monetary Value (EMV), EVPI and EPPI.

b) Likelihood Simulation of Multi-objectives/Multipurpose payoff values toward

achieving its Likelihood distribution, Marginal and Posterior Distribution. and

EVSI

c) BDM Simulation of Multipurpose/Multi-objectives of COL payoff values toward

achieving Expected Opportunity Loss (EOL) of the System.

vi) Dynamics of EMV and EOL at 2 nd Iteration.

vii)Bayesian Decision Model Optimization:

a) Bayesian Decision Model Optimization of EMV

b) Bayesian Decision Model Optimization of EOL

c) Bayesian Decision Model Optimization of EPPI

d) Bayesian Decision Model Optimization EVPI

e) Bayesian Decision Model Optimization of EVSI

viii) Bayesian Decision Model Validation of Multipurpose Prior & Posterity distribution.

ix)

Bayesian Decision Model Application:

a) Allocation of Resources to the Multipurpose using the Optimum Solutions or

Policy.

b) Multipurpose Dam Integration

c) Development and Utilization of a Small Hydropower Plant, an outfall of decision

made by BDM for having the Maximum Expected Monetary Value (EMV) and

Minimum Expected Opportunity Loss (EOL).

x) Net Present Value (NPV): Payback Duration and Payback Monetary Value of Small

Hydropower Project investment at Ikom.

164

xi) Allocation of Resources to the Multiobjective of the Cross-River Basin.

4.1 Multipurpose and Multiobjective Variables Designation

In this section two watershed variables were simulated; the watershed Multipurpose, and

Multi-objectives and then likelihood forecast from the observed data. Thus:

(a) Let Yi denotes Courses of action or alternatives (I = 1,2,3,4,5) representing ‘Hydropower’,

‘Water Supply’ ‘Navigation’, ‘Irrigation’, Flood Control and, ‘Recreation’ respectively and

Xj be the State of nature (j = 1,2,3, 4) representing

‘Economic Efficiency’, ‘Regional

Economic Distribution’, ‘State Economic Distribution’, ‘Youth Employment’ and

‘Environmental Control’ respectively.

(b) Let P (Yi), (i = 1, 2, 3, 4. 5) denotes Prior Probability of Yi

(c) Let Xi, Xi+1, Xi+2, Xi+3 (i = 1) denote the outcome forecast for the State of nature such as:

‘Economic Efficiency’’, ‘Federal Economic Distribution’, ‘Regional Economic Distribution’,

‘State Economic Distribution’, ‘local Economic Distribution’, and Social wellbeing,

respectively.

(d) Therefore, Let P (Xi/Yi), P (Xi+1/Yi) ……… (i = 1, 2, 3, 4. 5) denotes. Likelihood values

generated as a function of the state of nature.

4.2 Estimation of Required Number and Prior Probability of Multipurpose

4.2.1 Estimation of Required Number of Multipurpose

The relationship between installed hydropower capacity and number of authorized purposes

shows a general trend of greater number of purposes as installed capacity increases (Figure

4.1).

165

Figure 4.1: Frequency distribution of authorized uses based on installed hydropower capacity.

Sources:

U.S. Department of Energy Wind and Water Program

The majority of plants with a capacity greater than 100 MW are authorized for four purposes,

while most plants with a capacity lower than 100 MW serve only three purposes. Reservoirs

authorized for six uses are almost equally distributed between plants with less than 10MW,

100-500 MW, and greater than 500 MW installed capacity. (Hadjerioua et al., 2015).

Analysis and Discussion on Number of Authorized Purpose:

(i) Cross river basin Multipurpose Dam can be authorized for six uses [Figure 4.1]

and are almost equally distributed between plants with less than 100 MW, 100-

500 MW, and greater than 500 MW installed capacity. (Hadjerioua et al., 2015).

(ii)

In this research work, less than 100MW of Hydropower plant was designed to

correspondingly support five (5) other River Basins multipurpose, making it Six

(6) Multipurpose in accordance with figure 4.2.

166

4.2.2 Estimation of Prior Probability of the Multipurpose.

In this case the prior probabilities of the river basin multipurpose is said to be objective, they

are objective because the prior knowledge of the multipurpose are based on an established or

Figure 4.2: Breakdown of economic benefits by installed capacity.

Source: U.S. Department of Energy Wind and Water Program

167

4.3.2 Estimation of EPPI and EVPI in the 1 st Iteration.

This subsection covers the evaluation of EPPI and EVPI as follows:

4.3.2.1 Expected Profit in Perfect Information (EPPI)

Expected Profit in Perfect Information [EPPI] was calculated using table 4.2; where prior

probability of each courses of action was multiplied across its row by the highest payoff

value of each row and then summed up. The steps in involved in this computation was

expressed as follows:

EPPI = 0.19*4.3+ 0.12*0.80 + 0.02*1 + 0.18*3.6 + 0.06*3 + 0.43*1.13 = ₦2.19 trillion

Also, at the bottom of the table 4.2 were the values of:

i. Maximum Expected Monetary value (EMV*) = ₦1.68 trillion,

ii.

Expected Profit in Perfect Information (EPPI) = ₦2.19 trillion

4.3.2.2 Expection of Value of Perfect Information (EVPI)

EVPI was calculated as the difference between EPPI and EMV*, thus:

EVPI = EPPI – EMV*

EVPI = ₦2.19 trillion - ₦1.68 trillion = ₦0.51 trillion

Expected Value of Perfect Information (EVPI) = ₦0.51 trillion. The EVPI is the monetary

value worth for providing perfect information and hence funds made for Research and

Development.

Expected Value of perfect information [EVPI] was calculated by the difference between the

EPPI and EMV*. See table 4.2.

171

P Y1

X1

X1

= [P (Y1) * P

Y1

] / P X1 3.15

P Y2

X1

X1

= [P (Y2) * P

Y2

] / P X1 3.16

P Y3

X1

X1

= [P (Y3) * P

Y3

] / P X1 3.17

P Y4

X1

X1

= [P (Y4) * P

Y4

] / P X1 3.18

P Y5

X1

X1

= [P (Y5) * P

Y5

] / P x1 3.19

P Y6

X1

X1

= [P (Y6) * P

Y6

] / P x1 3.20

(v) Validation of Posterior Probability

P Yn

X1

= P Y1

X1

+ P Y2

X1

+ P Y3

X1

+ P Y4

X1

+ P Y5

X1

+ P Y6

X1 = 1 3.21

4.3.3.1 Sample Mean Value, Standard Deviation, Variation Coefficient and Product of

Variation Coefficient & Payoff Values

Evaluation of sample mean, standard deviation, variation coefficient and product of variation

coefficient & payoff values was performed using equation 3.1 to 3.3 on an excel spread sheet

and extract of the sheet shown table 4.3.

175

Table 4.3: Mean , Standard deviation, variation coefficient and Product of Variation Coefficient & Payoff Values [equation. 3.1 to 3.3]

Multiobjective aj σj Cvj Multipurpose/Courses of Action/Alternatives

Hydropower Water Supply Navigation Irrigation

Flood

Control

Recreation

State of Nature

Mean Value Standard Deviation [σj/aj] Product of variation coefficient of sample and Payoff value [Cvij x Pij]

Economic Efficiency

0.46 0.537488333 1.176552 1.588346 0.364731 0.394145 0.151775254 0.70593 0.020001

Federal Economic

Redistribution

2.28 1.718162778 0.75248 3.235664 0.601984 0.75248 2.708928176 2.25744 0.75248

Regional Economic

Redistribution

State Economic

Redistribution

Local Economic

Redistribution

Social Well-Being

0.14 0.117418944 0.837709 0.16084 0.167542 0.0083771 0.213615914 0.14744 0.006702

0.73 1.065160786 1.461126 3.068364 0.227936 0.2922252 2.630026632 0.16365 0.008767

0.64 0.538690542 0.848332 0.678665 0.593832 0.0848332 1.017997875 0.84833 0.008483

0.31 0.450211293 1.443756 0.144376 0.218007 0.2887512 0.259876107 0.15881 1.631444

176


(i) The table 4.3 calculated sample mean value, standard deviation, variation coefficient

and product of variation coefficient and payoff table value using equation 3.1 to 3.3.

(ii) The product of variation coefficient with the payoff values equal to Cvij x Pij. However,

Cvij x Pij in turn serve as an input in table 4.4 for the calculation of ti.

4.3.3.2 Evaluation of Sample Value ti

Evaluation of sample value ti was performed using equation 3.4 on an excel spread sheet and

extract of the excel spread sheet shown table 4.4.

Table 4.4: Calculation of ti [Equation 3.4]

State of Nature

t i` (Standardizing the sample value)

(Expected sample value – Observed sample value)/ Cvij x Pij

Hydropower Water Supply Navigation Irrigation

Flood

Control

Recreation

Economic Efficiency -0.29177 -0.21298 -0.38059 3.882801 -0.14005 10.03329

Federal Economic

Redistribution

0.040545 0.599966 -0.10017 -0.0036 -0.21938 0.116949

Regional Economic

Redistribution

0.497492 -0.76828 5.581874 -0.162 -0.15085 8.772284

State Economic

Redistribution

-0.22333 0.94205 0.325795 -0.24857 4.202328 38.93873

Local Economic

Redistribution

0.63702 -0.63499 1.852348 -0.19798 -0.35767 34.48836

Social Well-Being 3.49896 0.03477 -0.25532 1.194103 1.461298 -0.60156

176

Sample value ti was estimated using equation 3.13 and simulated using the excel spreadsheet.


(i) The table 4.4 calculated the value of ti using equation 3.4.

(ii) The equation 3.4 and table 4.4 were used for the purpose of standardizing the sample

values and the absolute values ǀt iǀ were obtained in table 4.5 just to eliminate the negative

signs.

4.3.3.3 Standardization of ti Values

This section however, transform all the t i values in table 4.4 to absolute ǀtiǀ values vis-a-vis

converting all negative values to positives values, as follows :

Table 4.5: Standardized ti Values [ǀtiǀ] using Equation 3.4

ǀtiǀ

[Expected sample value – Observed sample value]/ [Cvij x Pij]

State of Nature

Hydropower Water Supply Navigation Irrigation Flood Control Recreation

Economic

Efficiency

Federal Economic

Redistribution

Regional Economic

Redistribution

State Economic

Redistribution

Local Economic

Redistribution

0.29177 0.21298 0.38059 3.882801 0.14005 10.03329

0.040545 0.599966 0.10017 0.0036 0.21938 0.116949

0.497492 0.76828 5.581874 0.162 0.15085 8.772284

0.22333 0.94205 0.325795 0.24857 4.202328 38.93873

0.63702 0.63499 1.852348 0.19798 0.35767 34.48836


177


The table 4.5 calculated the absolute values of the sample to eliminate the negative signs as in

table 4.4.

4.3.3.4 Estimation of Likelihood Function 2(1- Фǀtiǀ)

The likelihood function P(x/y) = 2(1- Фǀt iǀ) was estimated using Equation 3.5, as shown below:

Table 4.6: Estimation of Likelihood Function 2(1- Фǀtiǀ)

State of Nature

Economic

Efficiency

Federal

Economic

Redistribution

Regional

Economic

Redistribution

State Economic

Redistribution

Local

Economic

Redistribution

Social Well-

Being

Hydropower

Water

Supply

Sample Likelihood values = 2(1- Фǀtiǀ )

Sample Likelihood values = P(x/y)

Navigation

Irrigation

Flood

Control

Recreation

1.999416 1.999574 1.999239 1.992234 1.99972 1.979933

1.999919 1.9988 1.9998 1.999993 1.999561 1.999766

1.999005 1.998463 1.988836 1.999676 1.999698 1.982455

1.999553 1.998116 1.999348 1.999503 1.991595 1.922123

1.998726 1.99873 1.996295 1.999604 1.999285 1.931023

1.993002 1.99993 1.999489 1.997612 1.997077 1.998797

ΣP(X/y) 11.98962 11.99361 11.98301 11.98862 11.98694 11.8141

Analysis and Discussion:

(i)

The table 4.6 calculated the sample likelihood using equation 3.5. However, 2(1- Фǀtiǀ) or

P(x/y) represent the likelihood sample as shown on the table,

(ii)

The total values along the multipurpose column are summed up [ΣP(X/y)] as shown on

the last row of the table.

178

(iii) The summed values in each column were used to divided all the values along the

multipurpose column; the essence of doing this is to normalized all the values in each

column so that when summed up will be equal to 1, to comply with the Bayesian

likelihood constrain.

4.3.3.5 Normalization Likelihood function 2(1- Фǀtiǀ)

The normalization of Likelihood function was performed as shown in table 4.7, by summing all

the values along the P(xi/y1) column and then divided each of the values of each column with

summed value in such a way that, the sum of all the values along the column after the division

will be equal to 1.

Table 4.7: Calculation of P(x/y) of Equation 3.5

Normalizing sample likelihood = 2(1-Фǀtiǀ) [Normalized]

State of Nature

Forecast Likelihood

P(x i/y 1) P (x i /y 2) P (x i /y 3) P (x i /y 4) P (x i /y 5) P (x i /y 6)


Economic Efficiency 0.166762 0.16672 0.166839 0.166177 0.166825 0.167591

Federal Economic

Redistribution

Regional Economic

Redistribution

0.166804 0.166655 0.166886 0.166824 0.166812 0.169269

0.166728 0.166627 0.165971 0.166798 0.166823 0.167804

State Economic Redistribution 0.166774 0.166598 0.166849 0.166783 0.166147 0.162697

Local Economic Redistribution 0.166705 0.16665 0.166594 0.166792 0.166789 0.163451


ΣP (x i = 1….6/y n) 1 1 1 1 1 1

Analysis and Discussion on the Likelihood function P(X/y) [table 4.7]

(i)

(ii)

The table 4.7 indicates the normalized values of the sample likelihood.

However, values in table 4.7 represent the main likelihood of the sample.

179

(iii) The summation of the likelihood on the vertical-axis must give a value of one (1) to

conform with Bayesian decision model constrain.

4.3.3.6 Likelihood Distribution Curves of the Multi-purpose and Multi-Objectives

This subsection used table 4.7 in the plotting of likelihood distribution curves between the

Multiobjective benefits and Multipurpose projects (each Column 2,3,4,5,6,7 of table 4.7 were

plotted against column 1). It explains the benefits of purposes/projects (Multipurpose) to the

Multiobjective in the system.

Figure 4.3: Likelihood distribution of Multiobjective benefits vs. Hydropower Project.

Analysis and Discussion of Likelihood distribution of Multiobjectives benefits vs.

Hydropower Project.

(i)

(ii)

In figure 4.3, Numbers 1 to 6 along the horizontal-axis denotes Hydropower Project.

Whilst the Vertical-axis denotes the frequency of the Multi-objectives benefits.

180

(i)

The curve, in the figure 4.3 was elucidated on the basis of Economic Efficiency

among other objectives; hence the Economic efficiency benefit of Hydropower

project was relatively high, an indication that, it has potential for sustainability[Figure

4.3].

Figure 4.4: Likelihood distributions of Multiobjectives benefits vs. Water supply Projects

Analysis and Discussion of Likelihood distributions of Multiobjectives benefits vs. Water

supply Project.

(i)

(ii)

(ii)

In figure 4.4, numbers 1 to 6 along the horizontal-axis denotes Water Supply Project.



among other objectives; hence the Economic efficiency benefit of Water supply

project was relatively high, an indication that, it has potential for sustainability[Figure

4.4].

181

(iii)

The system has not been developed in such a way that will enable people pay for the

services of water supply, rather individual and co-operate organization provided

water for themselves by sinking boreholes and patronizing of water vendors.

Therefore, much revenue was not generated for the benefit of the River basin.

Figure 4.5: Likelihood distributions of Multiobjective benefits vs. Navigation Project

Analysis and Discussion of Likelihood distributions of Multiobjective benefits vs.

Navigation project:

(i)

(ii)

(iii)

In figure 4.5, numbers 1 to 6 along the horizontal-axis denotes Navigation Project.



benefit among other objectives; hence the Economic efficiency benefit of Navigation

project was relatively high, an indication that, it has potential for sustainability.

[Figure 4.5].

182

Figure 4.6: Likelihood distributions of Multiobjectives benefits vs.Irrigation Project.

Analysis and Discussion of Likelihood distributions of Multiobjectives benefits vs.

Irrigation Project

(i)

(ii)

(iii)

In figure 4.6, numbers 1 to 6 along the horizontal-axis denotes Irrigation Project.



benefit among other objectives; hence the Economic efficiency benefit of Irrigation

project was relatively low, an indication that it is not sustainable since Cross River

basin Development (CRBD) is not benefitting directly, but other Multiobjectives

were benefitting, hence could not return commensurate payback on investment or

probably subsidized by the Federal Government of Nigeria(FGN). And this is one of

the reasons the basin continually depends on Federal Government for allocations.

Nevertheless, Irrigation project has highest benefits next to Hydropower Project with

183

respect to other Multiobjective benefits other than the Economic Efficiency benefit.

[Figure 4.6]

Figure 4.7: Likelihood distributions of Multiobjective benefits Vs Flood Control Project

Analysis and Discussion of Likelihood distributions of Multiobjective benefits vs. Flood

Control Project.

(iv)

(v)

(vi)

In figure 4.7, numbers 1 to 6 along the horizontal-axis denotes Flood Control Project.

Whilst the Vertical-axis denotes the Multi-objectives benefits.


Project among other objectives; hence the Economic efficiency benefit of Flood

Control Project was relatively high, an indication that, it has potential for

sustainability.

184

Figure 4.8: Likelihood distributions of Multiobjective benefit Vs Recreation Project

Analysis and Discussion of Likelihood distributions of Multibjectives benefits vs.

Recreation Project

(i)

In figure 4.8, numbers 1 to 6 along the horizontal-axis denotes Recreation Project.

(ii) Whilst the Vertical-axis denotes the Multi-objectives benefits in relation to

Recreation Project.

(vii)


benefit among other objectives; hence the Economic efficiency beneft of Recreation

Project was relatively high, an indication that, it has potential for sustainability.

Summary: Figure 4.3 to 4.8 indicates that Hydropower, Irrigation and Flood control should be

selected for integration as a Multi-purpose for optimal benefits.

185

Table 4.8: Marginal Probability of 1 st Iteration

YJ [ P(Y)] P(X/Y) Pr(X) = P(Y)*P*X/Y)

Alternative

Dam

Projects

Prior

(Prototyp

e-

CRBDA)

likelihood

Economic

Efficiency

Federal

Economic

Redistribution

Regional

Economic

Redistribution

State Economic

Redistribution

Local

Governme

nt

Redistribu

tion

Social

Wellbeing

Hydropower 0.19 0.166762263 0.031685

0.16680417 0.031693

0.166727946 0.031678

0.16677368 0.031687

0.166704672 0.031674

0.166227269 0.031583181

Water

Supply

0.12 0.166719894 0.020006

0.166655362 0.019999

0.166627294 0.019995

0.166598317 0.019992

0.166649521 0.019998

0.166749611 0.020009953

Navigation 0.02 0.166839482 0.003337

0.166886285 0.003338

0.165971372 0.003319

0.166848628 0.003337

0.166593842 0.003332

0.16686039 0.003337208

Irrigation 0.18 0.166177098 0.029912

0.166824245 0.030028

0.16679782 0.030024

0.166783378 0.030021

0.166791818 0.030023

0.16662564 0.029992615

Flood

Control

0.06 0.16682493 0.010009

0.166811694 0.010009

0.166823128 0.010009

0.166147146 0.009969

0.16678862 0.010007

0.166604482 0.009996269

Recreation 0.43 0.167590744 0.072064

0.169269475 0.072786

0.167804219 0.072156

0.162697363 0.06996

0.163450763 0.070284

0.169187435 0.072750597

Verification 1

Marginal

Probability

0.167013 0.167852 0.167182 0.164965 0.165317 0.167669823

Analysis and Discussion on Marginal Probability at 1 st Iteration [of table 4.8]:

Marginal Probabilities of 1 st Iteration, were taken from the last row of table 4.8.

(i) Economic Efficiency = 0.167013

(ii) Federal Economic Redistribution = 0.167852

(iii) Regional Economic Redistribution = 0.167182

187

Table 4.9: Posterior (Model) probability of 1 st Iteration

State of Nature Marginal Probability Multipurpose

Prior (Prototype-CRBDA) x

Likelihood

Posterior (Model-BDM)

Probability

Economic

Efficiency

0.167013 Hydropower 0.031685 0.189714298

Water Supply 0.020006 0.119789114

Navigation 0.003337 0.019979173

Irrigation 0.029912 0.179098669

Flood Control 0.010009 0.059932291

Recreation 0.072064 0.431486455

Federal Economic

Redistribution

0.167852 Hydropower 0.031693 0.188813796

Water Supply 0.019999 0.119144433

Navigation 0.003338 0.019884921

Irrigation 0.030028 0.178897755

Flood Control 0.010009 0.059628099

Regional

Economic

Redistribution

Recreation 0.072786 0.433630997

0.167182 Hydropower 0.031678 0.189484176

Water Supply 0.019995 0.11960197

Navigation 0.003319 0.019855194

Irrigation 0.030024 0.179586556

Flood Control 0.010009 0.059871268

Recreation 0.072156 0.431600836

State Economic

Redistribution

0.164965 Hydropower 0.031687 0.192082613

Water Supply 0.019992 0.121187772

Navigation 0.003337 0.020228309

Irrigation 0.030021 0.181983585

Flood Control 0.009969 0.060429789

Recreation 0.06996 0.424087932

Local Economic

Redistribution

0.165317 Hydropower 0.031674 0.191594421

Water Supply 0.019998 0.12096697

Navigation 0.003332 0.020154426

Irrigation 0.030023 0.18160539

Flood Control 0.010007 0.06053397

Recreation 0.070284 0.425144824

Social Well-Being 0.16767 Hydropower 0.031583 0.188365327

Water Supply 0.02001 0.119341411

Navigation 0.003337 0.019903449

Irrigation 0.029993 0.178879029

Flood Control 0.009996 0.059618772

Recreation 0.072751 0.433892012

189

Analysis and Discussion on Posterior Probabilities of 1st Iteration of [table-4.9]:

Posterior (Model-BDM) Probabilities of 1st Iteration is taken from column-5 and the rows

corresponding to the State economic redistribution of table 4.9. The foregoing selection was

made because the posterior corresponding to the state economic redistribution has the same

pattern with the prior probability. Therefore, posterior probabilities selected were as follows:

(i) Hydropower = 0.192082613

(ii) Water supply = 0.121187772

(iii)Navigation = 0.020228309

(iv)Irrigation = 0.181983585

(v) Flood control = 0.060429789

(vi)Recreation = 0.424087932

The Posterior probability gave the indication of the futuristic status of the Multipurpose of Cross

River Basin.

4.3.6 Estimation of Summation of Expected Opportunity Loss (∑EOL) of the

Multipurpose in the 1 st Iteration

The essence of estimating the summation of expected opportunity loss of the various objectives

ws to enable the researcher estimate optimization in relation to losses in the system; this will in

turn generate the Expected value of system information (EVSI). However, Summation of EOL

was calculated as shown in the 6 th column of table 4.10.

190

Table 4.10: Summation of Expected Opportunity Loss (EOL) at 1 st Iteration

Multiobjective

Multipurpose

Posterior (Model-

BDM) COL EOL ΣEOL

Economic Efficiency Hydropower 0.189714298 0.00 0

Water Supply 0.119789114 1.04 0.124580678

Navigation 0.019979173 1.02 0.020278861

Irrigation 0.179098669 1.22 0.218679475

Flood Control 0.059932291 0.75 0.044949219

Recreation 0.431486455 1.33 0.575171444 0.983659677

Federal Economic

Redistribution Hydropower 0.188813796 0.00 0

Water Supply 0.119144433 3.50 0.417005515

Navigation 0.019884921 3.30 0.065620238

Irrigation 0.178897755 0.70 0.125228429

Flood Control 0.059628099 1.30 0.077516528

Recreation 0.433630997 3.30 1.43098229 2.116353

Regional Economic

Redistribution Hydropower 0.189484176 0.01 0.001515873

Water Supply 0.11960197 0.00 0

Navigation 0.019855194 0.19 0.003772487

Irrigation 0.179586556 -0.06 -0.009877261

Flood Control 0.059871268 0.02 0.00143691

Recreation 0.431600836 0.19 0.082867361 0.079715371

State Economic


Water Supply 0.121187772 1.94 0.235589028

Navigation 0.020228309 1.90 0.038433787

Irrigation 0.181983585 0.30 0.054595075

Flood Control 0.060429789 1.99 0.120134421

Recreation 0.424087932 2.09 0.88804013 1.336792442

Local Economic

Redistribution Hydropower 0.191594421 -1.99 -0.380889709

Water Supply 0.12096697 -0.04 -0.005322547

Navigation 0.020154426 -0.09 -0.001773589

Irrigation 0.18160539 -1.69 -0.306549898

Flood Control 0.06053397 0.00 0

Recreation 0.425144824 0.11 0.045065351 -0.649470392

Social Well-Being Hydropower 0.188365327 -2.09 -0.394436994

Water Supply 0.119341411 -0.15 -0.017901212

Navigation 0.019903449 -0.19 -0.003861269

Irrigation 0.178879029 -1.79 -0.320908978

Flood Control 0.059618772 -0.11 -0.00631959

Recreation 0.433892012 0.00 0 -0.743428043

Analysis and Discussion on Summation of Expected Opportunity Loss (∑EOL) at 1 st

Iteration [Table 4.10]:

Sum of Expected Opportunity Loss of the various purpose with respect to the objectives in 1 st

Iteration were as follows:

(i)

Economic Efficiency = ₦0.983659677trillion

191

(ii)

(iii)

(iv)

(v)

(vi)

Federal Economic Redistribution = ₦2.116353 trillion

Regional Economic Redistribution = ₦0.079715371 trillion

State Economic Redistribution = ₦1.336792442 trillion

Local Economic Redistribution = ₦-0.649470392 trillion

Social Well-Being = ₦-0.743428043 trillion

The Summation of Expected Opportunity Loss were input values for the evaluation of Expected

Value of System Information (EVSI). And these values (sum EOL) when multiplied with

Marginal probabilities Produces Expected value of system information (EVSI).

4.3.7 Estimation of Expected value of System Information 1 st Iteration

In this process of 1 st Iteration the value of EVSI obtained is ₦ 0.52135 trillion. However, the

graphical representation between EOL and EVSI is linear in nature (see figure 4.9); it implies

that EOL is directly proportional to EVSI. As the expected opportunity loss increases, the

Expected value of system information also increases. However, expected value of system

information was calculated as shown in column 4 of table 4.11.

Table 4.11: Expected Value of System Information (EVSI) 1 st Iteration

Outcome

Marginal

Probability ΣEOL EVSI

Economic Efficiency 0.17 0.98366 0.164284

Federal Economic Redistribution 0.17 2.116353 0.355234

Regional Economic Redistribution 0.17 0.079715 0.013327

State Economic Redistribution 0.16 1.336792 0.220525

Local Economic Redistribution 0.16531738 -0.64947 -0.10737

Social Well-Being 0.167669823 -0.74343 -0.12465

EVSI 0.52135

192

Analysis and Discussion on EVSI at the 1 st Iteration [table 4.11]

The Expected Value of System Information (EVSI) ₦ 0.52135 trillion indicates the money which

the River basin Authority has to pay for hiring the services of a Consultant.

Figure 4.9: Graphical relationship between EVSI and EOL

Analysis and Discussion of Figure 4.9:

The figure 4.9 indicates the following:

(i) The EVSI is a function of the ∑EOL and the duo are directly proportional.

(ii) As ∑EOL increase the Monetary values of EVSI increase

(iii) As ∑EOL decrease the Monetary value of EVSI decreases.

193

Analysis and Discussion of Table 4.12:

Table 4.12 evaluates the Expected Opportunity Loss at 1 st iteration as follows:

(i) To obtain the value of Conditional Opportunity Loss (COL) the highest value per row

was used to subtract it self and every other value in the same row. This same process was

done for the rest of the rows.

(ii) The payoff values within the matrix table 4.12 represent the Conditional Opportunity

Loss (COL).

(iii) The 4 th row within matrix table 4.12 represent the prior probability.

(iv) The products of (ii) and (iii) gave the values of Expected Opportunity Loss (EOL).

4.4 Dynamics of EMV and EOL at 1st Iteration

The summation of Expected Monetary Value and Expected Opportunity Loss equals to a

constant. EMV and EOL were used for decision making differently or the two can complement

and verify the each other. Hydropower which was selected for investment as can be seen in table

4.13 below has the maximum EMV and minimum EOL.

Table 4.13: Dynamics of EMV and EOL at 1 st Iteration


EMV 1.67998 0.27804 0.0369 1.28952 0.29988 0.93353

EOL -0.77406 0.7548 0.12246 -0.23688 0.23736 3.02075

CONSTANT 0.90592 1.03284 0.15936 1.05264 0.53724 3.95428


The table 4.13 described the relationship between Expected Monitory Value and Expected

Opportunity Loss as follows:

195

(i)

(ii)

(iii)

(iv)

Row 1 of the table indicates the River Basin Purposes

Row 2 indicates the Expected Monetary value of the river basin Purpose

Row 3 indicates the Expected Opportunity Loss of the River Basin.

Row 4 indicates the Sum values of the EMV and EOL which also referred to as the

constant.

(v)

EMV or EOL has the capacity to evaluates the optimum strategy or solution of the

system and can as well complement and verify each other.

(vi)

(vii)

The summation of EMV and EOL must equal to a constant.

However, the monetary value of EOL as can be seen in table 4.13 were as follows:

EOL(Hydropower) = N -0.77406 trillion,

EOL (Water Supply) = N 0.7548trillion

EOL(Navigation) = N 0.12246trillion

EOL(Irrigation) = N -0.23688 trillion

EOL (Flood Control) = N 0.23736trillion

EOL(Recreation) = N 3.02075trillion

4.4.1 Expressing the Multipurpose EMV and EOL in Percentage at Ist Iteration

This subsection expresses the summation of EMV and EOL to be equal to 100, where the 100

was express as a system constant. The system must be 100% efficient for optimal operations. In

other word this is called EMV and EOL dynamic (Ohaji, E. 2019).

Table 4.14: Expressing the Multipurpose EMV and EOL in Percentage at Ist Iteration


EMV 185.4446 26.91995 23.15512 122.5034 55.81863 23.60809

EOL -85.4446 73.08005 76.84488 -22.5034 44.18137 76.39191

CONSTANT 100 100 100 100 100 100

196


To obtain the optimum values for decision making the EOL Values in table 4.14 were converted

to percentage as follows:

(i) From the Constant in the fourth row of the table 4.14, it is clear that the system has

varying constant per each River Basin purpose.

(ii) The constant need to be of the same value and to actualize that the values of the constant

in row 4 of table 4.13 were taken to be equivalent to 100%, with that, the value EMV

and EOL under the Hydropower purpose will be 185.4446% and -85.4446% respectively,

using this process, all the constant will be normalized and the constant value = 100% as

can been in table 4.14.

197

Figure 4.10: Graphical relationship between EMV and EOL at 1st Iteration

198

(v)

(vi)

(vii)

Flood control EMV =₦ 0.302028085 trillion and

Recreation EMV = ₦ 0.9206949 trillion.

At the bottom of the table were the values of the Maximum Expected Monetary value

= ₦ 1.698 trillion,

(viii)

(ix)

Expected Profit in Perfect Information (EPPI) = ₦2.20 trillion and

Expected Value of Perfect Information (EVPI) = ₦0.51trillion. The EVPI is the

monetary value worth for providing perfect information as well as funds made

available for Research and Development(R&D).

(x)

Comparing the EMV values of the 1st and 2nd Iteration one can see that there are

slight differences in values and also that there were little or no difference between the

prior and posterior at this point and one can say that the simulation process has gotten

to optimum point, hence optimization of the process has taken placed or occurred.

The simulation process optimized the Maximum Expected Monetary values from ₦

1.67998 trillion to ₦ 1.698394464 trillion. With an optimized value =

₦0.01841trillion.

4.5.1 Estimation of EPPI and EVPI in the 2nd Iteration.

This subsection covers the evaluation of EPPI and EVPI as follows:

4.5.1.1 Expected Profit in Perfect Information (EPPI)

Expected Profit in Perfect Information [EPPI]-is calculated using table 4.15; where prior

probability of each course of action is multiplied across its row by the highest payoff value of

each row and then summed up. The steps in involved in this computation were expressed below:

201

EPPI = 0.192082613*4.3+ 0.12118777*0.80 + 0.02022831*1 + 0.181983585*3.6 +

0.060429789*3 + 0.424087932*1.13 = ₦2.20 trillion

Also, at the bottom of the table 4.15 were the values of:

i. Maximum Expected Monetary value (EMV*) = ₦ 1.698394464 trillion,

ii.

Expected Profit in Perfect Information (EPPI) = ₦2.20 trillion.4.5.1.2 -Expected Value of

Perfect Information (EVPI)

EVPI was calculated as the difference between EPPI and EMV*, thus:

EVPI = EPPI – EMV*

EVPI = ₦2.2trillion - ₦ 1.7trillion = ₦0.51trillion

Expected Value of Perfect Information (EVPI) = ₦0.51trillion. This fund was made available for

Research and Revelopment.

Expected Value of perfect information [EVPI] - was calculated by the difference between the

EPPI and Expected Monetary Value. See table 4.15.

4.5.2 Estimation of likelihood in 2nd Iteration

The likelihood of the second iteration remain the same does not change no matter the number of

iterations.

4.5.2.1 Estimation of Marginal Probability in 2 nd Iteration

Marginal probability is the Normalization constant or the evidence of Bayesian decision model;

it is defined as the summation of the product of prior probability and the Likelihood of the

observed data. Therefore, the Marginal probabilities of the Bayesian decision model were

calculated using equation 3.7 and table 4.16.

202

Table 4.17: Estimation of Posterior (Model) probability in the 2 nd Iteration


Prior (Prototype-

CRBDA) x

Likelihood


Probability

Economic Efficiency 0.167007336 Hydropower 0.032032131 0.191800744

Water Supply 0.020204412 0.12097919

Navigation 0.003374881 0.020207978

Irrigation 0.030241504 0.181078897

Flood Control 0.010081195 0.060363787

Recreation 0.071073212 0.425569404

Federal Economic

Redistribution 0.167837411 Hydropower 0.032040181 0.190900114

Water Supply 0.020196592 0.120334266

Navigation 0.003375827 0.020113676

Irrigation 0.030359274 0.180885025

Flood Control 0.010080395 0.06006048

Recreation 0.071785141 0.427706439

Regional Economic


Water Supply 0.02019319 0.12079048

Navigation 0.00335732 0.020082628

Irrigation 0.030354465 0.181572618

Flood Control 0.010081086 0.060302471

Recreation 0.071163744 0.425683248

State Economic


Water Supply 0.020189679 0.122369749

Navigation 0.003375066 0.020456291

Irrigation 0.030351837 0.183962646

Flood Control 0.010040237 0.06085393

Recreation 0.068997988 0.418197175

Local Economic


Water Supply 0.020195884 0.12215001

Navigation 0.003369912 0.020382111

Irrigation 0.030353373 0.183585172

Flood Control 0.010079001 0.060960446

Recreation 0.069317496 0.419250424


Water Supply 0.020208014 0.120534009

Navigation 0.003375304 0.020132551

Irrigation 0.030323131 0.180867287

Flood Control 0.010067874 0.060051483

Recreation 0.071750349 0.42796672

Analysis and Discussion on Posterior Probabilities of 2 nd Iteration [table 4.17]:

Posterior (Model-BDM) Probabilities of 2 nd

Iteration [Optimum Solution] were taken from

column-5 and the rows corresponding to the State economic redistribution of table 4.17. The

foregoing selection was made because the posterior corresponding to the state economic

redistribution has the same pattern with the prior probability. Therefore, posterior probabilities

selected were as follows:

205

(i) Hydropower = 0.194160209

(ii) Water supply = 0.122369749

(iii)Navigation = 0.020456291

(iv)Irrigation = 0.183962646

(v) Flood control = 0.06085393

(vi)Recreation = 0.418197175

The Posterior probability gave indication of the futuristic status of the Multipurpose of Cross

River Basin. At this point of 2 nd iteration an optimum solution was reached.

206

4.5.2.3 Estimation of Summation of EOL in 2 nd Iteration [Point of Optimum Solution]

Table 4.18: Estimation of EOL in 2 nd Iteration

OBJECTIVES/BENEFITS

STATE OF

NATURE

POSTERIOR(Model-

BDM) COL EOL ΣEOL


Water Supply 0.12097919 1.04 0.125818357

Navigation 0.020207978 1.02 0.020511098

Irrigation 0.181078897 1.22 0.221097333

Flood Control 0.060363787 0.75 0.045272841

Recreation 0.425569404 1.33 0.567284015 0.97998364

Federal Economic


Water Supply 0.120334266 3.50 0.421169931

Navigation 0.020113676 3.30 0.066375132

Irrigation 0.180885025 0.70 0.126619517

Flood Control 0.06006048 1.30 0.078078624

Recreation 0.427706439 3.30 1.411431249 2.10367445

Regional Economic


Water Supply 0.12079048 0.00 0

Navigation 0.020082628 0.19 0.003815699

Irrigation 0.181572618 -0.06 -0.009986494

Flood Control 0.060302471 0.02 0.001447259

Recreation 0.425683248 0.19 0.081731184 0.0785402

State Economic


Water Supply 0.122369749 1.94 0.237886793

Navigation 0.020456291 1.90 0.038866952

Irrigation 0.183962646 0.30 0.055188794

Flood Control 0.06085393 1.99 0.120977612

Recreation 0.418197175 2.09 0.875704884 1.32862504

Local Economic


Water Supply 0.12215001 -0.04 -0.0053746

Navigation 0.020382111 -0.09 -0.001793626

Irrigation 0.183585172 -1.69 -0.309891771

Flood Control 0.060960446 0.00 0

Recreation 0.419250424 0.11 0.044440545 -0.6576391


Water Supply 0.120534009 -0.15 -0.018080101

Navigation 0.020132551 -0.19 -0.003905715

Irrigation 0.180867287 -1.79 -0.324475913

Flood Control 0.060051483 -0.11 -0.006365457

Recreation 0.42796672 0.00 0 -0.7516252


Sum values of EOL from the six column of table 4.18, when multiplied with Marginal

probabilities produced EVSI.

207

4.5.2.4 Estimation of EVSI in the 2 nd Iteration

EVSI was estimated by the product of Expected Marginal probability and Sum of Expected

opportunity loss. The values calculated can be seen in column 4 of table 4.19

Table 4.19: Estimation of EVSI in the 2 nd Iteration

Outcome

Marginal



Federal Economic Redistribution 0.17 2.103674 0.353075





EVSI 0.51433

Analysis and Discussion on EVSI at 2 nd Iteration [table 4.19]:

The EVSI value of ₦0.51433 trillion indicates the money which the River basin Authority has to

pay for hiring the services of a forecaster. [ Consultant]. The consultant forecasted the following

corrected (evidence by the model validation and constrains):

(i)

(ii)

The system prior and Posterior distribution as it relates to the Multipurpose

The system Expected Opportunity Loss as it relates to the Multipurpose operational

wastages or losses.

(iii)

The system Likelihood distribution as it relates to the Multiobjectives in the

perspective of Multipurposes.

(iv)

(v)

The system Marginal distribution.

The money received by the Consultant was dependent on the number of River basin

purposes that has less losses or wastages.

208

Figure 4.11: Graphical representations of EVSI and EOL

209


Table 4.20 evaluated the Minimum Posterior Expected Opportunity Loss at 2 nd Iteration as

follows:

(i)

To obtain the value of Conditional Opportunity Loss (COL) the highest value per row

was used to subtract it self and every other value in the same row. This same process was

done for the rest of the rows.

(ii) The payoff values within the matrix table 4.20 represent the Conditional Opportunity

Loss (COL).

(iii) The 4 th row within the matrix table 4.20 represent the prior probability.

(iv) The products of (ii) and (iii) gives the values of Minimum Posterior Expected

Opportunity Loss (EOL). However, the monetary value of EOL as can be seen in table

4.13 were as follows:

EOL(Hydropower) =₦ -0.791008691 trillion

EOL (Water Supply) = ₦0.769705721 trillion

EOL(Navigation) = ₦0.12525387 trillion

EOL(Irrigation) = ₦-0.24209 trillion

EOL (Flood Control) = ₦0.240738147trillion

EOL(Recreation) = ₦2.937835154 trillion

4.6 Dynamics of EMV and EOL in 2 nd Iteration

This subsection demonstrated the dynamics between EMV and EOL and its application in the

optimal integration of dam project in the system.

211

Table 4.21: Dynamics of EMV and EOL in 2 nd Iteration


EMV 1.698394464 0.280792063 0.03732123 1.303730403 0.302028085 0.9206949

EOL -0.791008691 0.769705721 0.12525387 -0.242094842 0.240738147 2.937835154

CONSTANT 0.907385773 1.050497784 0.1625751 1.061635561 0.542766233 3.858530055


The table 4.21 described the relationship between Expected Monitory Value and Expected

Opportunity Loss as follows:

(i)

(ii)

(iii)

(iv)

Row 1 of the table indicates the River Basin Purposes

Row 2 indicates the Expected Monetary value of the river basin Purpose

Row 3 indicates the Expected Opportunity Loss of the River Basin.

Row 4 indicates the Sum values of the EMV and EOL which also, referred to as

the constant.

(v)

Each of EMV or EOL has the capacity to evaluates the optimum strategy or

solution of the system and can as well complement and verify each other.

(vi)

The summation of EMV and EOL must equal to a constant.

The Maximum Expected Monetary value (EMV*) and the Minimum Opportunity Loss (EOL*)

were ₦1.698394464 trillion and ₦ -0.791008691 trillion respectively.

212

4.6.1 Expressing the Multipurpose EMV and EOL in Percentage at 2 nd Iteration

To obtain the optimum values for decision making, the EOL and EMV values were converted to

percentage as shown in table 4.22 as follows:

Table 4.22: Expressing the Multipurpose EMV and EOL in Percentage at 2 nd Iteration

Hydropower

Water


Flood

Control

Recreation

EMV

187.1744649 26.72942935 22.95630151 122.80395 55.64607143 23.86128622

EOL -87.17446485 73.27057065 77.04369849 -22.80394997 44.35392857 76.13871378

CONSTANT 100 100 100 100 100 100


To obtain the optimum values for decision making the EMV and EOL values in table 4.21 were converted

to percentage as shown in table 4.22:

(i)

From the Constant in the fourth row of the table 4.21, it was clear that the system has varying

constant per each River Basin purpose.

(ii) The constant need to be of the same value and to actualize that the values of the constant in row 4

of table 4.21 were taken to be equivalent to 100%, with that,

the value of EMV and EOL under the

Hydropower purpose became 187.1744649% and -87.17446485% respectively, using this

process, all the constant will be normalized and the constant value = 100% as seen in table 4.22.

213

Figure 4.12: Graphical dynamics of EMV and EOL of Cross River Basin at 2 nd Iteration

This Chart type was used for the following reasons:

(i)

Compared the percentages that each value [ EMV + EOL] contributed to a total

[Constant]

(ii)

Showed the percentage that each value contributed changes overtime

214

(iii)

And this was another way to find out the Multipurpose which has the Maximum

EMV and at the same time the Minimum EOL

Analysis and Discussion on EMV and EOL Dynamics [table 4.22 and figure 4.12]

Table 4.21 & 4.22 and figure 4.12 demonstrated in two different cases that Hydropower was best

selected for investment for the following reasons:

(i)

The figure 4.12 demonstrated the relationship between EMV and EOL in optimum

decision of the River basin. However, from table 4.22 and figure 4.12, the following

deduction were made in the order of best decision:

(ii)

1st and best decision indicates the choice of Hydropower Project which was

represented by the First bar on the figure shows that the EMV = 187.17% and EOL =

-87.17% and the constant = 100%.

(iii)

2nd decision indicates the Irrigation Project which was represented by the fourth bar

on the figure shows that EMV = 122.80% and EOL = -22.80% and the Constant =

100%.

(iv)

The item (ii) and (iii) were indication that Hydropower and Irrigation should be

integrated or optimized as Multipurpose dam project.

215

4.6.2 EMV and EOL in order of Priority

This subsection selected the multipurpose dam project from table 4.22 in the order of maximum

and minimum EMV and EOL values respectively. The foregoing was done to enable the

determination of dam projects that can be integrated for optimal benefits of the system. The

priority listing of the EMV and EOL values enables the plotting of EMV and EOL dynamics or

interaction graph as shown in figure 4.13 below.

Table 4.23: EMV & EOL of Multipurpose in Priority

Priority Multipurpose EMV % EOL %

1 Hydropower 187.1744649 -87.17446485

2 Irrigation 122.80395 -22.80394997

3 Flood Control 55.64607143 44.35392857

4 Water Supply 26.72942935 73.27057065

5 Recreation 23.86128622 76.13871378

6 Navigation 22.95630151 77.04369849


Table 4.23 detailed the maximum and minimum EMV and EOL respectively.

The table also explained that EMV is inversely proportional to EOL.

The table indicates that the most viable projects has the maximum and the minimum EMV and

EOL respectively.

216

Figure 4.13: EMV and EOL Interaction

217


The outcome of the interaction between EMV and EOL as represented in figure 4.13 were

explained below:

(i)

Hydropower has the highest value of EMV* and the lowest value EOL*, this is an

indication that satisfied the condition of been the dam project that will yield more profit

and benefit for the system when developed.

(ii)

Irrigation took the second position where the EMV and EOL values were next to

hydropower.

(iii)

Flood control was found to be at third position, this is also in line with most world dam

integrated projects (Check subsection 2.1.4: Review on world multipurpose dams).

(iv)

Current trends in water resources management is calling for Integrated Management, a

system where two or more projects are managed at the same time using same resources

and labor for more benefit of the system. Against the foregoing, it becomes very clear

that Hydropower and Irrigation can be integrated.

(v)

EMV is defined as the expected monetary value. “Expected value under uncertainty” is

the expected or average return that we would realize if we were to repeat the decision an

infinite number of times, each time having “perfect” or complete information and making

the “best” possible decision on that information. In line with the foregoing definition,

Hydropower according to the figure was selected as the Basin Purpose/Project with the

Maximum EMV and Minimum EOL. Therefore, more money should be allocated to

Hydropower for development or investment

218

4.7 Model Optimization of Multipurpose EMV of Cross River Basin System

This subsection demonstrated the optimization of the system under the heading: EMV and EOL

of the dam projects.

4.7.1 Expected Monitory Value (EMV) of the Multi-Purpose in 1 st and 2 nd Iteration

The difference between the Expected Monetary Value at the 1 st and 2 nd iteration gave the

Optimized value. Details of these were shown in the 5 th column of Table 4.24:

Table 4.24: Expected Monetary Value of the Multipurpose 1 st Iteration and 2 nd Iteration

S/N

Multipurpose

EMV 1 st iteration (trillion

naira)

EMV 2 nd Iteration(trillion

naira)

Optimized

values(trillion naira)

1 Hydropower 1.67998 1.698394464 0.018414464

2 Water supply 0.27804 0.280792063 0.002752063

3 Navigation 0.0369 0.03732123 0.00042123

4 Irrigation 1.28952 1.303730403 0.014210403

5 Flood Control 0.29988 0.302028085 0.002148085

6 Recreation 0.93353 0.9206949 -0.0128351

Analysis and Discussion of Table 4.24

The Table 4.24 indicates the optimization of EMV at 1 st and 2 nd Iteration.

The optimization process of EMV took place between the 1 st and 2 nd Iteration. The resultant optimized

values were shown in table 4.24.

219

Figure 4.14: Optimization of EMV

220

Analysis and Discussion on figure 4.14

The Multipurpose dam Project that appears in the positive and negative quadrant above the

horizontal line and with maximum and minimum EMV and EOL values respectively (figure 4.14)

were as follows:

i. Hydropower Project

ii.

Irrigation Project

Analysis and Discussion on Model Optimization of EMV:

Table 4.24 represents the Expected Monetary values of Cross river basin Multipurpose, at this

point the Hydropower which has the Maximum Monetary Value was selected for an Investment

and if fully implemented will generate more money for the River basin multiobjective such as

Federal, Regional, State, Local Economic Redistribution and Social well-being. However, figure

4.14 depicts graphically the expected monetary values at 2 nd Iteration (Optimum solution).

However, the following were observed:

(i)

The difference between EMV at 1 st and 2 nd gave the optimization values of the

multipurpose. [ table 4.24]

(ii)

(iii)

(iv)

(v)

(vi)

Optimization was achieved at the point of optimum solution.

Optimization value for Hydropower = ₦0.018 trillion.

Optimization value for irrigation = ₦0.014trillion

Optimization value for Flood control = ₦0.002trillion

The result of (ii) and (iii) strongly recommends Hydropower and Irrigation

integrationn in Cross River Basin.

221

4.7.2 Model Optimization of Multipurpose EOL of Cross River Basin System

The difference between the Expected Monetary Value at the 1 st and 2 nd iteration gave the

Optimization values. Details of these were shown in Table 4.25.

Table 4.25: Optimization of Expected Opportunity Loss of the Multipurpose 1 st Iteration and 2 nd

Iteration

S/N

Multipurpose

EOL 1 st iteration

(trillion Naira)

EOL 2 nd Iteration

(trillion Naira)

Optimized values

(trillion Naira)

1 Hydropower -0.77406 -0.791008691 -0.0169487

2 Water supply 0.7548 0.769705721 0.0149057

3 Navigation 0.12246 0.12525387 0.0027939

4 Irrigation -0.23688 -0.242094842 -0.0052148

5 Flood Control 0.23736 0.240738147 0.0033781

6 Recreation 3.02075 2.937835154 -0.0829148

222

Figure 4.15: Graphical Representation of the Optimized EOL of the Multipurpose

Analysis and Discussion of table 4.25

The Table 4.25 indicates the optimization of EOL at 1 st and 2 nd Iteration.

a) Table 4.25 represents the Expected Opportunity Loss of Cross river basin Multipurpose,

at this point the Hydropower which has the Minimum Expected Opportunity Loss was

selected for an Investment, if fully implemented will generate more funds for the river

223

basin, Federal, Regional, State, Local Economic Redistribution and Social wellbeing.

However, figure 4.15 depicts graphically the expected opportunity Loss at 2 nd Iteration

optimum solution. However, the following were observed:

(i)

The difference between EOL at 1 st and 2 nd gave the optimization value of the

multipurpose. [ table 4.25]

(ii)

(iii)

Optimization was achieved at the point of optimum solution.

Optimization occurred for Hydropower and also optimization took place in Irrigation

though very small.

(iv)

The result of (iii) is an indication that Hydropower and Irrigation were strongly

recommended for integrated management in Cross River Basin.

224

4.7.3 Model Optimization of EPPI, EVPI and EVSI

This subsection demonstrated the optimization of the system under the heading of EPPI, EVPI

and EVSI.

Table 4.26: Optimization of EPPI, EVPI and EVSI at 1 st and 2 nd Iteration

Description

1 st Iteration (trillion

Naira)

2 nd Iteration (trillion

Naira)

Optimized values

(trillion Naira)

EPPI 2.19 2.2 0.01

EVPI 0.51 0.51 0

EVSI 0.52135 0.51433 0.00702

Analysis and Discussion OF Table 4.26

i. EPPI was Optimized with a gain = 0.01 trillion Naira

ii. EVPI, no Optimization observed = 0

iii.

EVSI, was optimized with a gain = 0.00702 trillion Naira

4.8 Bayesian Decision Model Validation

Table 4.27: Validation Using Graphical Method

Multipurpose

Prior (Prototype-CRBDA)

Probability


Probability-1


Probability -2

Hydropower 0.19 0.192082613 0.194160209

Water supply 0.12 0.121187772 0.122369749

Navigation 0.02 0.020228309 0.020456291

Irrigation 0.18 0.181983585 0.183962646

Flood Control 0.06 0.060429789 0.06085393

Recreation 0.43 0.424087932 0.418197175

225

4.8.1 Bayesian Decision Model Validation using Graphical Method

Plotting prior probability value in table 4.29, column 2 against Posterior (Prototype-CRBDA)

Probability of second iteration in table 4.29 column 4, the resulted graph is shown in the figure

4.16.

Figure 4.16: Validation using Graphical Method

226


i. Comparing the graph equation y = 0.9881x with Bayesian infinite linear equation,

y =βx +α

ii. Therefore β = 0.9881 and α = 0

iii. The correlation coefficient of the relationship (r) = 0.994

4.8.2 Bayesian Decision Model Validation Using Pearson Moment correlation

This subsection covers the validation of the of the prior and posterior probability of BDM using

Pearson moment correlation coefficient as demonstrated below:

Table 4.28: Validation Using Pearson Moment correlation

227


i. Pearson Moment Correlation Coefficient R² = 0.999996

ii. Where r = 1

iii.

The correlation coefficient being equal to 1 indicates that the model simulation got to the

point of Optimum solution and was close to perfection, hence results generated was

suitable for strategic planning and management of the River Basin system.

iv. Comparing rcalculated value with rcritical value using Pearson correlation critical table. At 5%

(0.05) significant figure and degree of freedom of 4, rcritical value = 0.811 and rcalculated

value = 1 (approximated to 3 significant figures) Therefore, rcalculated value > rcritical value

using i.e. 1 > 0.811, therefore reject Null Hypothesis, (Appendix A17). This indicate high

performance of the model (Posterior Probability) in relation to the prototype (Prior

Probability).

.

228

4.8.3 Bayesian Decision Model Validation Using T-test

This subsection covers the validation of posterior (BDM) and prior (Prototype) probabilities

using T-test as demonstrated in table 4.29 below:

Table 4.29: Validation using T-test

Formula

Out-put /Decision

total number of sample(n) 6

n - 2 4

R² 0.988

R 0.994

A (t = (n-2)) ⁄(1-r²) 333.3333333

B = SQRT OF A 18.25741858

C = B X r 18.14787407

t value 18.14787407

Degree of freedom(df) = n-2 4

Level of Confidence 95%

t critical 2.776

Therefore, reject Null hypothesis. Type 1 and 2 errors were

t value > t critical 18.15 ˃ 2.776

not found. This indicate high performance of the model

(Posterior Probability) in relation to the prototype (Prior

Probability).

Analysis and Results of table 4.29:

Table 4.29 above summarized how to determine t value and t critical value. To find a critical

value, look up your confidence level in the bottom of t-table (See Appendix A2) this tells you

which column of the t-table you need. Intersect this column with the row for the degree of

freedom(df), the number you see is the critical value (or the t * value) for your confidence interval.

t-test for the correlation significant between Observed and expected data using the equation

229

In this subsection EMV and EOL ratio were applied as standardized method for the allocation of

funds appropriated by the Federal Government of Nigerian (FGN) to CRBDA as a Development

funds for the Multipurpose dam project. More so, the Development or Investment on the selected

Hydropower accrued to internally generated revenue funds which were allocated to the

Multiobjective using Marginal Probability ratio as show in the proceeding subsections:

4.9.1 Allocation of FGN ₦10.9 Billion Development funds to Multipurpose Dam Project

Using EMV Ratio

The optimum solution presented by Bayesian decision theory can be used for allocation of Funds

to the River basin. This is done by using optimum strategy or policy. However, the Federal

Government of Nigeria (FGN) appropriated of ₦10.9 billion through the Federal Ministry of

Water Resources (FMWR) to Cross River Basin Development Authority (CRBDA) for the

horizon (2013 to 2017). This research work uses the table 4.31, below for the demonstration of

optimum funds allocation. (See Appendix 10-15 for details of the FGN/FMWR appropriation to

CRBDA).

Table 4.30: FGN Appropriation of ₦10.9 Billion to CRBDA

Year Budgeted Allocation Budget Released

2013 1,737,370,960.00 1,737,370,960.00

2014 1,392,415,715.00 1,392,415,715.00

2015 617,959,580.00 617,959,580.00

2016 2,191,973,627.00 2,191,973,627.00

2017 4,966,764,419.00 4,966,764,419.00

Total Allocation 10,906,484,301.00 10,906,484,301.00

Table 4.31: Allocation of ₦10.9 Billion to the CRBDA Multipurpose Using EMV Ratio

232

Policy Multipurpose EMV % Allocation Ratio

1 Hydropower 187.1744649 42.61990212

Gross Allocation of

10,906,484,301.00 billion

Naira

4,648,332,934.01

2 Irrigation 122.80395 27.9626408 3,049,741,029.13

3 Flood Control 55.64607143 12.67069266

4 Water Supply 26.72942935 6.086330543

5 Recreation 23.86128622 5.433250116

1,381,927,105.36

663,804,685.22

592,576,570.97

6 Navigation 22.95630151 5.227183761

570,101,976.30

Using Multipurpose EMV allocation ratio, ₦10.9 billion appropriated by the FGN, were

apportioned as follows (Table 4.31):

439.1715034 100 10,906,484,301

(i)

(ii)

(iii)

(iv)

(v)

(vi)

Hydropower = ₦4,648,332,934.01billion

Irrigation = ₦3,049,741,029.13 billion

Flood Control = ₦1,381,927,105.36 billion

Water Supply = ₦ 663,804,685.22 million

Recreation = ₦592,576,570.97 million

Navigation = ₦ 570,101,976.30 million

233

4.9.2 Maximization of Net Return Per unit of Investment in Percentage For CRBDA

This subsection used table 4.32 to demonstrate the investment benefit of the multipurpose of

CRBDA in a scale of 100, using EMV ratio as follows:

Table 4.32: Maximization of Net Return Per Unit of Investment in Percentage For CRBDA

Policy

Developmental Projects for

Investment

Maximization of net return per

unit of Investment for CRBDA

1 Hydropower 42.61990212 of Investment

2 Irrigation 27.9626408 of Investment

3 Flood Control 12.67069266 of Investment

4 Water Supply 6.086330543 of Investment

5 Recreation 5.433250116 of Investment

6 Navigation 5.227183761 of Investment

100

For CRBDA to enhance its share of the new funds available for expansion with respect to

maximization of cost per unit of investment, it should invest as shown in table 4.32.

234

Figure 4.17: Maximization of cost Per Unit of Investment for CRBDA

Analysis and Discussion of Subsection 4.9.1 & 4.9.2 and figure 4.17

(i) Table 4.31 indicates allocation process of N10.9 billion appropriation funds from Federal

Government of Nigeria (FGN) to Cross River Basin Authority.

(ii) Multipurpose EMV expressed in percentage was used for the generation of EMV ratio

that formed the bases of the allocation process.

(iii)The viable Multipurpose as seen in the figure 4.17 has maximization of cost per unit

investment for CRBDA.

(iv)The viable Multipurpose were Hydropower and Irrigation.

235

4.9.3 Allocation of ₦10.9 Billion to the CRBDA Multipurpose Using EOL Ratio

This subsection used the EOL ratio in the allocation of 10.9 billion FGN appropriated

development funds to CRBDA as demonstrated in the table as follows:

Table 4.33: Allocation of ₦10.9 Billion to the CRBDA Multipurpose Using EOL Ratio

Priority Multipurpose EOL % EOL Allocation

Ratio

Gross Allocation of

₦10,906,484,301.00 billion

1 Hydropower -87.17446485

-54.20336983 -5,911,682,021.66

2 Irrigation -22.80394997 -14.17904814 -1,546,435,659.71

3 Flood Control 44.35392857

4 Water Supply 73.27057065

5 Recreation 76.13871378

27.57840152 3,007,834,032.23

45.55820154 4,968,798,099.00

47.3415566 5,163,299,438.43

6 Navigation 77.04369849

47.90425832 5,224,670,412.71

160.8284967 100 10,906,484,301.00

For CRBDA to enhance its share of the new funds available for expansion with respect to

minimization of cost per unit of investment, it should invest as shown in table 4.33.

Using Multipurpose EOL allocation ratio, ₦10.9 billion appropriated by the FGN, were

apportioned in table 4.33 as follows:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

Hydropower = ₦-5,9911,682,021.66 billion

Irrigation = ₦-1,546,435,659.71 billion

Flood Control = ₦3,007,834,032.23 billion

Water Supply = ₦ 4,968,798,099.00 million

Recreation = ₦5, 163, 299,438.43 million

Navigation = ₦ 5,224,670,412.71 million

236

4.9.4 Minimization of Net Return Per unit of Investment in Percentage For CRBDA

This subsection used table 4.32 to demonstrate the investment benefit of the multipurpose of

CRBDA in a scale of 100, using EOL ratio as follows:

Table 4.34: Minimization of Net Return Per Unit of Investment in Percentage For CRBDA

Priority

Developmental Projects for Investment

Minimization of cost per unit of

investment for CRBDA

1 Hydropower -54.20336983% of Investment

2 Irrigation -14.17904814% of Investment

3 Flood Control 27.57840152 of Investment

4 Water Supply 45.55820154 of Investment

5 Recreation 47.3415566 of Investment

6 Navigation 47.90425832 of Investment

100

Figure 4.18: Minimization of cost Per Unit of Investment for CRBDA

237

Analysis and Discussion of Subsection 4.9.3 & 4.9.4 and figure 4.18

(i)

The viable Multipurpose as can be seen in the figure 4.18 has minimization of cost per

unit investment for CRBDA and this chart served as a control for the number of

Multipurpose to be integrated in CRBDA.

(ii)

(iii)

The viable Multipurpose were Hydropower & Irrigation.

The two viable Multipurpose should be integrated for maximum efficiency.

4.9.5 Integration of Dam Multipurpose

The analysis in subsection 4.9.1, 4.9.2, 4.9.3, 4.9.4 on EMV & EOL ratios allocation,

maximization of profit and minimization of losses on investment made, as well as Likelihood

distribution curves (Subsection 4.3.3.6) and Dynamics of EMV and EOL (section 4.6) informed

the following conclusion:

that the two Multipurpose stated below should be integrated for optimum benefits of the system:

i. Hydropower

ii.

Irrigation

4.9.6 Development and Utilization of a Small Hydropower Plant

The second application of

optimum solutions and strategies of the model is the selection of

Hydropower for development because it satisfied the models conditions of been the only

Multipurpose among the Six investigated in cross river basin having Maximum Expected

Monetary Value and Minimum Expected Opportunity Loss, and prior the development,

feasibility study of the project was

carried out in inform of Hydropower Plant selection as

detailed in the proceeding subsection.

238

4.9.6.1 Hydropower Plant Plan Selection

Also, in line with Bayesian Decision simulation model, decision for investment and further

development of Hydropower facilities as one of the river basin purposes selected among others;

becomes a necessary and pertinent task to be carried out in order to assist in sustain renewable

energy within the system. Then considering elevation deferential of 8 meters of the river at Ikom

and with reference to section 2.9 of the literature review, Small hydropower was designed as

well as the cost of its construction. Consequently, to carry out the foregoing task, the river at

Ikom was investigated for a potential for a hydropower, starting from a point as shown in figure

4.19, where differential Head and river discharge were also investigated. However, the head and

river discharge were obtained as follows 8m and 2840m3/s as can been seen in Table 4.35.

Figure 4.19: Cross river (Ikom). Location (5.79, 8.79) Elevation: 38m.

239


(i)

Figure 4.19 is the location proposed for the construction of weir or Aqueduct; and hence

a channel by which water was transferred from the channel to the fore bay and the

Penstock successfully.

(ii)

This process is called Run-off-River method, were water from the main river is diverted

through a channel to forebay and then a penstock that conveys water to the turbine, which

convert potential energy of the water to kinetic energy for generation of electricity.

4.9.6.2 Cross River (Ikom) Rating Table of Ikom

This subsection showed Cross River (Ikom) rating table at Ikom, location (5.79, 8.79) and

elevation 38m.

240

Table 4.35: Cross River (Ikom) Rating Table at Ikom

H(m) Q(m3/s) H(m) Q(m3/s) H(m) Q(m3/s) H(m) Q(m3/s) H(m) Q(m3/s)

0.05 1.67 2.35 444 4.65 1247 6.95 2294 9.25 3540

0.10 4.21 2.40 458 4.70 1267 7.00 2319 9.30 3569

0.15 7.43 2.45 472 4.75 1288 7.05 2344 9.35 3598

0.20 11 2.50 487 4.80 1309 7.10 2370 9.40 3628

0.25 16 2.55 502 4.85 1329 7.15 2395 9.45 3657

0.30 20 2.60 517 4.90 1350 7.20 2420 9.50 3686

0.35 25 2.65 532 4.95 1371 7.25 2446 9.55 3716

0.40 31 2.70 547 5.00 1392 7.30 2472 9.60 3745

0.45 37 2.75 563 5.05 1413 7.35 2497 9.65 3775

0.50 43 2.80 578 5.10 1435 7.40 2523 9.70 3805

0.55 50 2.85 594 5.15 1456 7.45 2549 9.75 3834

0.60 57 2.90 610 5.20 1477 7.50 2575 9.80 3864

0.65 64 2.95 626 5.25 1499 7.55 2601 9.85 3894

0.70 72 3.00 642 5.30 1521 7.60 2627 9.90 3924

0.75 79 3.05 658 5.35 1543 7.65 2654 9.95 3955

0.80 87 3.10 675 5.40 1564 7.70 2680 10.00 3985

0.85 96 3.15 691 5.45 1586 7.75 2706 10.05 4015

0.90 104 3.20 708 5.50 1609 7.80 2733 10.10 4045

0.95 113 3.25 725 5.55 1631 7.85 2760 10.15 4075

1.00 122 3.30 742 5.60 1653 7.90 2786 10.20 4076

1.05 131 3.35 759 5.65 1676 7.95 2813 10.25 4106

1.10 141 3.40 776 5.70 1698 8.00 2840 10.30 4168

1.15 151 3.45 793 5.75 1721 8.05 2867 10.35 4198

1.20 161 3.50 811 5.80 1744 8.10 2894 10.40 4229

1.25 171 3.55 828 5.85 1766 8.15 2921 10.45 4260

1.30 181 3.60 846 5.90 1789 8.20 2948 10.50 4291

1.35 192 3.65 864 5.95 1821 8.25 2976 10.55 4322

1.40 203 3.70 882 6.00 1836 8.30 3003 10.60 4358

1.45 214 3.75 900 6.05 1859 8.35 3031 10.65 4384

1.50 225 3.80 918 6.10 1882 8.40 3058 10.70 4416

241

1.55 236 3.85 937 6.15 1906 8.45 3086 10.75 4447

1.60 248 3.90 855 6.20 1926 8.50 3114 10.80 4449

1.65 260 3.95 974 6.25 1953 8.55 3142 10.85 4510

1.70 272 4.00 993 6.30 1977 8.60 3169 10.90 4542

1.75 284 4.05 1011 6.35 2000 8.65 3197 10.95 4573

1.80 296 4.10 1030 6.40 2024 8.70 3226 11.00 4605

1.85 309 4.15 1050 6.45 2048 8.75 3254 11.05 4637

1.90 322 4.20 1069 6.50 2072 8.80 3282 11.10 4669

1.95 334 4.25 1088 6.55 2097 8.85 3310 11.15 4701

2.00 348 4.30 1108 6.60 2121 8.90 3339 11.20 4733

2.05 361 4.35 1127 6.65 2145 8.95 3367 11.25 4765

2.10 374 4.40 1147 6.70 2170 9.00 3396 11.30 4797

2.15 388 4.45 1167 6.75 2195 9.05 3425 11.35 4829

2.20 401 4.50 1187 6.80 2219 9.10 3453 11.40 4862

2.25 415 4.55 1207 6.85 2244 9.15 3482 11.45 4894

2.30 429 4.60 1227 6.90 2269 9.20 3511 11.50 4926

Source: Nigerian-Inland Water Ways Cross River (Ikom) rating table span between 1914 to 1959]


(i) The table 4.35 represents Cross River (Ikom) rating Table at Ikom. Location (5.79, 8.79).

(ii) the stage ranges from 0.05 to 11.50.

(iii) the Discharge ranges from 1.67 to 4926 m3/s.

(iv)

Note Stages and River Discharge were collected on daily bases for 30/31 days within a period of

45 years.

4.9.6.3 Cross River Rating Curve at Ikom

This subsection plotted values of Head and Discharge in table 4.35 into a curve called rating

curve as shown below.

242

Figure 4.20: Cross River (Ikom) rating Curve at Ikom, location:( 5.79, 8.79)


(i)

The figure 4.20 represents Cross River (Ikom) rating curve of at Ikom where the Stage or

height ranges from 0.05 to 14m

(ii)

the Discharge ranges from 1.67 to 4765m3/s.

(iii) At the height of 8m the peak flow was about 2840 m3/s.

(iv)

this implies the River discharge within 100years will be within 2840 m3/s and this should

be considered in designing a duct and fore bay to avoid flooding.

4.9.6.4 Rating curve of exceedance Probability (A)

Exceedance probability can be calculated as percentage of given flow to be equal or exceeded.

This probability measures the chance of experiencing hazardous event such as flooding. Factors

needed in its calculation include inflow value and total number of events on record which is 98%

to 1% for a peak flow range of 1000 to 100,000.

243

Figure 4.21: Rating curve exceedance Probability(A)


(i)

The figure 4.21 represents Cross River (Ikom) rating curve of exceedance at Ikom where

the peak flow ranges from 1000 to 100000.

(ii) he exceedance probability ranges from 99.99 to 0.01.

(iii) At an exceedance of 99.99 the peak flow is about 2840 m3/s.

(iv)

(v)

This implies the River discharge in 100 years will be within 2840 m3/s.

The foregoing should be considered in designing a duct and fore bay to prevent it from

flooding.

4.9.6.5 Rating curve of exceedance Probability(B)

Exceedance probability can be calculated as percentage of given flow to be equal or exceeded.

This probability measures the chance of experiencing hazardous event such as flooding. Factors

needed in its calculation include inflow value and total number of events on record which is 98%

to 1% for a peak flow range of 200 to 20,000.

244

Figure 4.22: Rating curve of exceedance Probability(B)

Analysis and Discussion on the Rating Curve of exceedance Probability at Ikom

(i)

The figure 4.22 represents Cross River (Ikom) rating curve of exceedance at Ikom where

the peak flow ranges from 2000 to 20000

(ii) the exceedance probability ranges from 99.99 to 0.01.

(iii) At an exceedance of 98.89 the peak flow is about 2840 m3/s

4.9.6.6 Cross River (Ikom) Location (5.79, 8.79) at 38m Elevation

This subsection showed the headrace and point where the river was channeled to the forebay.

245

Figure 4.23: Cross River (Ikom) Location (5.79, 8.79) at 38 Elevation

Source: Goggle Earth (2019)


(i) The figures 4.23 represent the cross-sectional area of elevation 38m.

(ii)

It is the point that indicates the turbine headrace location.

(iii) A point where a reservoir will be constructed taking advantage of the narrow path, it is

also a point where the river will be diverted making provision for a channel, forebay and

then a penstock.

246

4.9.5.7 Cross River (Ikom) Location (5.79, 8.79) at 29m Elevation

This subsection showed the Tailrace point and where the water that powered the Turbine flows

back to the River. The foregoing demonstrated the concept of hydropower as a renewable energy.

Figure 4.24: Cross River Location (5.79, 8.77) at 29m Elevation

Source: Goggle Earth (2019)


(i) The figures 4.24 represent the cross-sectional area of elevation 29m.

(ii)

It is the point where the turbine tailrace will be constructed, where water will return back

to the river after powering the turbine

247

4.9.6.8 Working Areas of different Turbine types

This subsection used the chart below to determine the working areas of the selected turbine using

Head and Discharge parameter of the Turbine.

Figure 4.25: Working Areas of different Turbine types

Source: Based on NHA and HRF, 2010

248


(i)

The figure 4.25 represents the working areas of different Turbine types.

(ii) The designed height for the proposed small hydropower dam station at Ikom is 8m.

(iii) However, taking 8m on the vertical axis of figure which corresponded to the design of

penstock flow of 100m3/s.

(iv)

from the figure it is clear that anything below 10m and flow of 1 to 1000m3/s indicates

Kaplan Turbine.

(v)

It implies that judging by the inputs data [H=8m, Q = 100m3/s], a suitable turbine that

must be selected is Kaplan.

4.9.6.9 Hydropower-Turbine Sizing Details

This subsection covers the Turbine sizing details based on the Head and Discharge parameters

using HPP-Design software.

4.9.6.9.1 Selection of Turbine Type

HPP is defined as Hydro Power Plants Design; it is a simple tool for hydro power preliminary

investigation. Design is the first step to find the main parameters for your hydro power plant.

One of the main questions for hydropower projects developers is: which turbine is the best

choice for HPP? Should it be a Francis, a Pelton, a Kaplan, an Archimedes’ screw, a Cross flow,

or a Pat (pump as turbine)? What is the fundamental dimension of hydro turbine, the weight, the

efficiency? HPP-design using the chart below can answer to the foregoing questions. (HPP,

2019).

249

4.9.6.9.2 Working Areas of different Turbine types

This subsection used the chart below for the selection of Turbine type based on the Head and

Discharge parameters already determined.

Figure 4.26: Working Areas of different Turbine types

Source: HPP-design.com

The discharge of the river is 2840 m3/s and this was reduced via the channel and fore bay to 100

m3/s and that flow through the penstock, therefore the effective input for the Turbine selection

are: H = 8 meter, Discharge = 100 m3/s; with the foregoing two parameters, and the application

of the concept shown in figure 4.27 the hydropower Turbine was designed and a suitable

Turbine[ Head = 8m and Discharge = 100m 3 /s] was selected using Hydropower plant chart as

shown in the figure 4.26 above using HPP tool: The 8m head loss on the graph corresponds with

250

100m3/s discharge through the penstock and that clearly justify the selection of Kaplan turbine.

Find in table 4.36 Kaplan turbine sizing details.

4.9.6.9.3 Cross section of the Small Hydropower Plant at Ikom

This subsection detailed the working cross section of the Hydropower plant shown figure 4.27.

Flow through Penstock = 100 m3/s

Figure 4.27: Cross section of Small Hydropower Plant at Ikom

Source: Ohaji (2019)


(i) The cross section of the small hydropower is represented in figure 4.27.

(ii)

The total river discharge was reduced by constructing a duct and a channel which leads to

a fore bay and then a penstock which in turn transport the water at an input water

251

discharge of 100m3/s converting potential energy at the fore bay to Kinetic energy

through the penstock.

(iii) The forebay is constructed to be at an elevation of 38m (Head race), same elevation of

the river at location (5.79, 8.79).

(iv) The tailrace is at an elevation of 29m. Location (5.79, 8.77)

(v) while the axis of the turbine is position at an elevation 30m.

(vi)

The head loss is the differential between the head race and the tailrace.

(vii) The water that eventually powered the turbine was returned back to the river and this is

term a renewable process because no water was wasted eventually.

4.9.6.9.4 Kaplan Turbine Sizing Details

This subsection detailed result sheet of hydropower plants sizing as shown Table 4.36 (appendix

A3)

Table 4.36: Kaplan Turbine Sizing Details

252

4..9.6.9.5 Kaplan Efficiency and Generator Representation

This subsection demonstrated Kaplan efficiency and generator representation using the figure

below (appendix A4)

Figure 4.28: Turbine Efficiency

Sources: HPP.Design.com

253

4.9.6.9.6 Kaplan Energy Calculator

This subsection demonstrated Kaplan energy calculator using the figure below (appendix A5)

Figure 4.29: Energy Calculator

Sources: HPP.Design.com

254

Analysis and Discussion of Small Hydropower Sizing

However, the design sheets and chart were generated using Hydropower plant online software

(HPP Design). However, the Max Turbine Power [Ptm] was estimated at 6.73 [MW] and was

consequently approximated to 7MW.

4.9.6.10 Leverage Cost of Electricity (LCOE) of Small Hydropower Project at Ikom

Using figure 4.30 below the percentage cost of the various components that make up a small

hydropower was calculated as follow:

Figure 4.30: Hydropower costing Chart. Sources: International Renewable Energy Agency

Source: (IRENA); Renewable Energy Technologies: Cost Analysis Series

255

(i)

Figure 4.30 gave the various percentages of the components that makeup a hydropower

system. The percentage proportions were taken from the base of the figure where 7MW

was taken as design output of the turbine.

(ii)

Here the percentage of the Hydropower components were represented in the y-axis, while

the turbine capacities were represented in the x-axis.

(iii) However, along the y-axis are the corresponding columns which are broken down as

representation of the Hydropower components such as Equipment, electrical connections,

infrastructure and logistic, civil work, planning and other installation costs

256

4.9.6.10.1 Investment Costs as A Function of Installed Capacity and Turbine Head

This subsection covered the investment cost of the Small Hydropower plant.

Figure 4.31: Investment Costs as A Function of Installed Capacity and Turbine Head

Sources: International Renewable Energy Agency (IRENA); Renewable Energy Technologies:

Cost Analysis Series.

Analysis and Discussion of Small Hydropower Sizing

(i)

The figure 4.31 was used for the estimation of Investment cost of turbine installed

capacity given the turbine head of 8m.

(ii)

The corresponding installed monetary value per Kilowatt is 2,800 UDS/Kilowatt.

257

(iii)

When 10% cost of capital was considered, corresponding installed monetary value per

Kilowatt is 3,080 UDS/Kilowatt.

(iv)

On multiplying this with the Turbine design value of 7000 Kilowatt (7MW), the turbine

installed capacity now equal = UDS 19,600,000.00.

(v)

(vi)

The Turbine install capacity in Naira at the rate of N360/UDS = N7,056,000,000.00.

More so, adding the cost of money brings the value to = ₦7,761,600,000.00 Find table

4.37 for details.

4.9.6.10.2 Leverage Cost of Electricity (LCOE) of Small Hydropower Plant of 7MW

Turbine Capacity at Ikom (Cross River).

This section evaluated the cost of various electricity components using LCOE.

Table 4.37: Leverage Cost of Electricity (LCOE) of Small Hydropower Plant of 7MW Turbine

Capacity at Ikom (Cross River)

S/N Description % USD NAIRA

1 Planning 8 1,568,000 564,480,000

2 Infrastructure and Logistic 1 196,000 70,560,000

3 Civil work 62 12,152,000 4,374,720,000

4 Total Equipment 22 4,312,000 1,552,320,000

5

Electrical Connections and

Construction

7 1,372,000 493,920,000

Total cost [1+2+3+4+5] 19,600,000 7,056,000,000

6 Cost of Capital

10% of

19,600,000

1,960,000 705,600,000

Total 21,560,000 7,761,600,000

258

The cost of building and powering 7MW Turbine Capacity in Ikom town is 7.8 billion Naira.

Therefore, it will take 1 years to recover the cost of building Hydropower Plant and additional

accrued funds to be allocated to the Multipurpose.

Table 4.37: Typical Installed Costs And Lcoe Of Hydropower Projects

Types of Hydropower Installed Cost Operation and Capacity Factor

Levelized cost of

(USD/KW)

Maintenance

(%)

electricity (2010

cost (% year of

USD/KWh)

installed costs)

Large hydro 1050 - 7650 2 – 25 25 - 90 0.02 – 0.19

Small hydro 1300 - 8000 1 – 4 20 - 95 0.02 – 0.27

Refurbishment/upgrade 500 – 1000 1 – 6 0.01 – 0.05

Note: The levelized cost of electricity calculation assume a10% cost of capital

Source: Renewable Energy Technologies: Cost Analysis Series, 2012.


From Table 4.37 above it was estimated that installed cost of Small Hydropower Plant at Ikom

was 3,080 USD/KW [ 21,560,000 USD/7000 KW]. The foregoing is within the range of values

as stipulated in Table 4.38.[ Small hydro: 1300USD/KW – 8000USD/KW], cost analysis series

2012.

The cost of Small Hydropower Project Development as estimate as ₦7,761,600,000 is within the

range of Typical installed costs and LCOE of Hydropower Projects as depicted in Table 4.37.

259

4.9.6.10.3 Percentage cost of Small Hydropower (SHP) station Components at Ikom town,

Cross River State

The percentage cost of the SHP components proposed to be at ikom was illustrated in figure 4.32

as follows:

Figure 4.32: Percentage cost of Small Hydropower station Components at Ikom town, Cross River State

260


Table 4.37 shows the cost of the small hydropower and its various components and from

figure 4.32, the percentage cost of building Hydropower station at Ikom Cross River were

as follows:

(i) Planning = 8%;

(ii) Total Equipment = 22%;

(iii) Electrical Connections and Construction = 7%;

(iv) Infrastructure and Logistics = 1%

(v) and Civil Works = 62%.

(vi) The hydropower percentage distribution is represented in a graphical chart in

Figure 4.32 & 4.33; from this chart it is clear that the civil works as a component

of Hydropower takes largest cost of investment at 62% cost, whiles Infrastructure

and logistics takes the least cost of investment at 1%

261

4.9.6.10.4 Components Cost of building a Small Hydropower Project (SHP) at Cross River

(Ikom).

The percentage cost of the SHP components proposed to be at ikom was illustrated in figure 4.33

as follows:

Figure 4.33: Graphical representation of Component Cost of building Hydropower station at Cross River

(Ikom) in Naira.

262

Analysis and Discussion on figure 4.32 and 4.33:

(i) It is very clear that civil works took a larger chunk of the entire project funds at 62%

followed by the equipment cost.

(ii) the next in line to civil works in terms of heavy cost is Total Equipment which is placed

at 22% of the total hydropower cost.

4.10: Net Present Value (NPV)- Payback Duration and Monetary Value of Small

Hydropower Project investment at Ikom

Recall Net Present Value (NPV) equation 2.7 in literature review as follows:

NPV(p) = CF (0) + CF (1)/ (1 + i) t + CF (2)/ (1 + i) t + CF (3)/ (1 + i) t + CF (4)/ (1 + i) t

Where:

(i)

(ii)

(iii)

i = firm's cost of capital

t = the year in which the cash flow is received

CF (0) = initial investment

The computation of NPV using the equation is expressed in the table below:

263

Table 4.38: NPV Values Computed per year

Formula Per Year NPV = CF(N)/(1+i)) t [₦] NPV = CF(N)/(1+i)) t [$] t [year]

CF (0) 7,761,600,000 22,176,000.00 0

CF(1)/(1+i)) t 7,056,000,000 20,160,000.00 1

CF(2)/(1+i)) t 14,112,000,000.00 40,320,000.00 2

CF(3)/(1+i)) t 21,168,000,000.00 60,480,000.00 3

CF(4)/(1+i)) t 28,224,000,000.00 80,640,000.00 4

CF(5)/(1+i)) t 35,280,000,000.00 100,800,000.00 5

CF(6)/(1+i)) t 42,336,000,000.00 120,960,000.00 6

CF(7)/(1+i)) t 49,392,000,000.00 141,120,000.00 7

CF(8)/(1+i)) t 56,448,000,000.00 161,280,000.00 8

CF(9)/(1+i)) t 63,504,000,000.00 181,440,000.00 9

CF (10)/(1+i)) t 70,560,000,000.00 201,600,000.00 10

CF (11)/(1+i)) t 77,616,000,000.00 221,760,000.00 11

CF (12)/(1+i)) t 84,672,000,000.00 241,920,000.00 12

NPV(Hydropower) NGN 558,129,600,000.00 $1,594,656,000.00

Effective NPV = 558,129,600,000.00 - 7,761,600,000

= ₦550,368,000,000.00 billion

264

4.10.1 The Small Hydropower Pay Back Duration

NPV duration of the Small Hydropower Project: from table 4.38, it will take 1 years for the

money invested in Small Hydropower Plant to pay back on the investment made. The NPV

evaluation is demonstrated in subsection 4.10.2 below.

4.10.2 The Small Hydropower Payback Monetary Value

The SHP payback monetary value was evaluated below:

(i) NPV = CF(0) + CF(1)/(1+i))t + CF(2)/ (1+i))t + CF(3)/ (1+i))t + CF(4)/ (1+i))t +

CF(5)/ (1+i))t + CF(6)/ (1+i))t + CF(7)/ (1+i))t + CF(8)/ (1+i))t + CF(9)/ (1+i))t +

CF(10)/ (1+i))t + CF(11)/ (1+i))t + CF(12)/ (1+i))t.

Therefore:

NPV = 22,176,000 + 20,160,000 + 40,320,000 + 60,480,0000 + 100,800,000 +

120,960,000 + 141,120,000 + 141,120,000 + 161,280,000 + 181,440,000 +

210,600,000 + 221,760,000 + 241,920,000 = $1,594,656,000 billion

(₦558,129,600,000 billion)

(ii) Assuming that the plant was built in 2017, therefore, in 12 years’ time i.e. 2030

the Hydropower plant must have payback of its initial cost of development and

investment plus addition money of $1,594,656,000 billion (₦558,129,600,000

billion).


(i)

The cost of development and investment of Small Hydropower Project at Ikom is

recovered at the 1 st year after investment. (see second row of table 4.38).

265

(ii)

The Net Present Value (NPV) of Hydropower Project investment at Ikom is NGN

₦558,129,600,000 billion, which means that if CRBDA invests in the project, it

adds (₦558,129,600,000 billion in value to its worth.

(iii)

The Net Present Value of the Hydropower Project development and utilization for

12 year (2017 to 2030) is ₦558,129,600,000 billion and this adds in value to

CRBDA worth if implemented.

(iv) The ₦550,368,000,000.00 billion [Effective NPV = 558,129,600,000.00 -

7,761,600,000] is for allocation to the multiobjective.

4.11 Allocation of Resources to the Multiobjective of the Cross-River Basin

This subsection covered the allocation of ₦550,368,000,000.00 billion generated by the Small

Hydropower Plant within 12 years to the Multiobjective using Marginal Probability ratio as shown

column-2 and the allocated funds were depicted in column-3 of table 4.39.

Table 4.39: Allocation of ₦550,368,000,000.00 billion Generated by the Small Hydropower Plant in 12

years

Multiobjective Allocation Ratio Allocated Funds (₦550,368,000,000.00 billion)

Economic Efficiency 0.167007336

Federal Economic Red 0.167837411

Regional Economic

Red

0.167175346

State Economic Red 0.16498913

Local Economic Red 0.16533673

Social Well-Being 0.16765404

91,915,493,499.65

92,372,340,217.25

92,007,960,827.33

90,804,737,499.84

90,996,045,416.64

92,271,418,686.72

266


Allocation of the Small Hydropower plant Internally Generated Revenue (IGR) to the

Multiobjective using Marginal Probability ratio were as follows:

Multiobjective

(a) Economic Efficiency

(b) Federal Economic Red’

(c) Regional Economic Red’

(d) State Economic Red’

(e) Local Economic Red’

(f) Social Well-Being

Allocated Fund (₦550,368,000,000.00 billion)

₦91,915,493,499.65 billion

₦92,372,340,217.25 billion

₦92,007,960,827.33 billion

₦ 90,804,737,499.84 billion

₦90,996,045,416.64 billion

₦92,271,418,686.72 billion

267

Figure 4.34: Allocation of funds to the Multipurpose (Various level of Government & Social

Well-Being)

268

Figure 4.35: Allocation of funds to the Multipurpose (Various level of Government & Social

Well-Being)

Analysis and Discussion of figure: 4.34 & 4.35

i. The following Multiobjectives: Economic Efficiency, Federal Economic Redistribution,

Regional Economic Redistribution and Social Well-being received 17% each While State

Economic Redistribution and Local Economic Redistribution received 16% each from

₦550,368,000,000.00 billion as Internally Generated revenue (IGR) from the Small

Hydropower.

ii.

The allocation of funds as observed in item (i) should be the ultimate desire of the Basin

and our country Nigeria, this is because funds generated from the developed (Investment)

River basin purpose(SHP) were allocated for the benefits of the Multiobjective as return on

investment made.

iii.

Economic Efficiency received ₦ 91,915,493,499.65 billion from the funds generated from

the Small Hydropower Plant and this fund will be used for Operation & Maintenance and

Cost of Overhead.

269

iv.

The process of allocating resources to the Multiobjective will assist in achieving the

Sustainable Development Goal (SDG) Vision 2030 as well as the system optimization.

v. Social Well-Being received ₦ ₦92,271,418,686.72 billion from the funds generated from

the SHP and this funds will be used for Health care Scheme, Housing and Employment.

vi.

Local Government received ₦92,271,418,686.72 billion from the funds generated from

SHP and this fund will be used for Rural development at the same pace with the Federal,

Regional and State level.

vii.

Bayesian Decision Model method of standardized funds allocation enhances equal

development at all level of government.

270

CHAPTER FIVE

CONCLUSION, RECOMMENDATION AND CONTRIBUTION TO KNOWLEDGE

5.1 Conclusion

The research work concluded as follows:

(i) Prior (Prototype-CRBDA) Probabilities of Multipurpose using Breakdown of

economic benefits by installed capacity of less than 100MW are: Hydropower

(0.19); Water supply (0.12); Navigation (0.02); Irrigation (0.18); Flood control

(0.06) and Recreation (0.43).

(ii)

The expected monetary values of the CRBDA multipurpose are as follows:

(a)

(b)

(c)

(d)

(e)

(f)

Hydropower, EMV = 1.698394464 trillion,

Water supply EMV = ₦ 0.280792063 trillion,

Navigation EMV = ₦ 0.03732123 trillion

Irrigation EMV = ₦ 1.303730403 trillion,

Flood control EMV =₦ 0.302028085 trillion and

Recreation EMV = ₦ 0.9206949 trillion.

(iii) Maximum Expected Monetary (EMV*) of the multipurpose is equal to ₦ 1.698

trillion. BDM selected Hydropower for having EMV* among another alternative of

CRBDA multipurpose.

(iv)

Expected Value of Perfect Information (EVPI) value of CRBD = ₦0.51trillion. This

fund is made available for research and development of CRBDA.

(v)

Expected Profit in Perfect Information (EPPI) of CRBD = ₦2.20 trillion. This fund

is the profit expected to be made by CRBDA for the use of the perfect information

for the modeling process.

271

(vi)

Marginal Probabilities of Cross River Basin at Optimum Solution as reveal by the

Model are:

(a) Economic Efficiency = 0.167007336

(b) Federal Economic Redistribution = 0.167837411

(c) Regional Economic Redistribution = 0.167175346

(d) State Economic Redistribution = 0.16498913

(e) Local Economic Redistribution = 0.16533673

(f) Social Well-Being = 0.16765404

(vii)

The Expected Value of System Information (EVSI) = ₦0.51433 trillion. The fund is

payment made for hiring the services of a consultant.

(viii)

BDM Efficiency: The ratio of EVSI (= ₦0.51433 trillion) and EVP1 (= ₦0.51trillion)

indicates the model efficiency as applied in CRBDA Operation, thus: Efficiency of

BDM on CRBDA Operation = ₦0.51433 trillion/₦0.51trillion x 100% = 100%

efficiency.

(ix)

The posterior (Model-BDM) Probability of Multipurpose dam projects of CRBDA are

as follows:

(a) Hydropower = 0.194160209

(b) Water supply = 0.122369749

(c) Navigation = 0.020456291

(d) Irrigation = 0.183962646

(e) Flood Control = 0.06085393

(f) Recreation = 0.418197175

272

(vix) The Expected opportunity Loss (EOL) of Multipurpose dam projects of CRBDA are as

follows:

(a) Hydropower = ₦-0.791008691 trillion

(b) Water supply = ₦ 0.769705721 trillion

(c) Navigation = ₦ 0.12525387 trillion

(d) Irrigation = ₦ -0.242094842 trillion

(e) Flood Control = ₦ 0.240738147 trillion

(f)

Recreation = ₦ 2.937835154 trillion

(x) Minimum Opportunity Loss(EOL*) = ₦-0.791008691trillion. BDM selected

Hydropower for having EOL* among other alternative of CRBDA multipurpose.

(xi)The Optimization of the system (difference in Monetary value between the 1 st and the last

Iteration) were observed at optimum point as follows:

a. Optimized value of Expected Monetary (EMV) Value = ₦0.018 trillion

b. Optimized value of Expected Profit in Perfect Information (EPPI) = ₦0.01

trillion

c. Optimized value of Expected Value of System Information (EVSI) = ₦0.007

trillion

(xii)

The Dynamics between EMV and EOL of Bayesian Decision Models expressed in

percentage reveal the following CRBDA Multipurpose for integration for having the

best extreme values of Maximum and Minimum EMV and EOL respectively as

follows:

a. Hydropower (EMV = 187.17, EOL = -87.17)

b. Irrigation (EMV = 122.80, EOL = -22.80)

273

(xiii) The validation of the Bayesian decision model gave the following results: Pearson

moment correlation coefficient (r) = 0.994, approx. = 1, also T-test (where t value > t

critical) result further confirm performance of the model [Posterior (Model-BDM)].

relation to the Prior (Prototype-CRBDA).

(xiv) The proposed cost of building a Small Hydropower of 7MW capacity[Head =8m &

Discharge = 100m 3 /s] at Ikom was put at = NGN 7,761,600,000 billion.

(xv)

₦10.9 billion naira appropriated by the FGN were allocated to the multipurpose using

EMV ratio as follows:

a. Hydropower = ₦4,648,332,934.01billion

b. Irrigation = ₦3,049,741,029.13 billion

c. Flood Control = ₦1,381,927,105.36 billion

d. Water Supply = ₦ 663,804,685.22 million

e. Recreation = ₦592,576,570.97 million

f. Navigation = ₦ 570,101,976.30 million

(xvi) The Net Present Value (NPV) of Small Hydropower Project investment at Ikom has the

following:

(a) ₦55,036,800,000.00 billion accrued for 12 years for full capacity utilization.

(b) ₦7,761,600,000 billion accrued for 1 st year for return on investment made, this

is called payback value for minimum capacity investment.

(xvii) Allocation of the Small Hydropower plant Internally Generated Revenue (IGR) to the

Multiobjective using Marginal Probability ratio as follows:

Multiobjective

Allocated Fund (₦550,368,000,000.00 billion)

274

(g) Economic Efficiency ₦91,915,493,499.65

(h) Federal Economic Red ₦92,372,340,217.25

(i) Regional Economic Red ₦92,007,960,827.33

(j) State Economic Red ₦ 90,804,737,499.84

(k) Local Economic Red ₦90,996,045,416.64

(l) Social Well-Being ₦92,271,418,686.72

(a) The following Multiobjectives: Economic Efficiency, Federal Economic Redistribution,

Regional Economic Redistribution and Social Well-being received 17% each, while State

Economic Redistribution and Local Economic Redistribution received 16% each from

₦550,368,000,000.00 billion of the Small Hydropower Internally Generated revenue

(IGR).

(b) The allocation of funds as observed in item (a) should be the ultimate desire of the Basin

and our country Nigeria, for with this the country economy will be sustainable, this is

because streams of funds will be continually generated from the various River basin

purposes (Investment) which in turn be allocated (Return on Investment) to the

Multiobjective.[ Federal, Regional, State, Local Economic Redistribution and Social

Wellbeing]. With the foregoing arrangement the country will depend less on oil as a

source of revenue. Hence reduction in the use of fossil fuel as well as decrease in

contribution to global warming.

(c) Allocation of ₦ 91,915,493,499.65 to the Economic Efficiency of the River Basin,

support the Hydropower Plant in the area of Operation, Maintenance and Cost of

Overhead.

275

(d) The process of allocating resources to the Multiobjective will assist in achieving the

Sustainable Development Goal (SDG) Vision 2030 as well as the system optimization.

(e) Allocation of funds to the Social Well-Being supports improvement of Health care

Scheme, Housing and Employment.

(f) Funds allocated to Local Government level will promotes Rural development at the same

pace with the Federal, Regional and State level.

(g) Bayesian Decision Model method of funds allocation will boosts equal development at all

level of government.

5.2 Recommendations

This work is recommended to the Federal Government of Nigeria for realization of Sustainable

Development Goal 2030 as follows:

(i)

Multi-purpose Dam has major roles to play in sustainability. Many of the sustainable

development goals (SDGs) can be achieved by proper and functional water systems at

all levels. Therefore, FGN should come up with strategic policy that will empower

the river basin authority to sustain the basin and not always expecting funds from the

government, with this the country will attain SDGs goals by 2030.

(ii) In addition, FGN should further empower all professionals in engineering through

Nigerian Society Engineering(NSE) and Council for Regulation of Engineering In

Nigeria(COREN) to play key roles to actualize their respective obligations during

planning, construction and maintenance of water structures so as to maximize its

ability to provide food, water and energy,

by so doing, Sustainable water

infrastructure would go a long way to enhance water use efficiency (Goal 6).

276

(iii) The research recommends future research work on reconnaissance on the entire

length of

Cross River all the way from Ikom down to the point where the River

entered Atlantic Ocean for potential locations of hydropower station and possible

build

hydropower stations, for there is non existing anywhere in the basin and

renewable energy sources cannot be enough for the basin and the country.

(iv)

Hydropower as a matter of Urgency should be incorporated in the scheme of

development and utilization of Multipurpose in Cross River Basin to take care of the

following:

(a)

(b)

(c)

Reduce carbon emission in the system

to respond to increase Hydropower demand in the region and Nigeria at Large

to utilize abundant renewable energy already provided by nature inform of

networks of river and potential head loss for power generation.

(d)

Provide job for the teaming population

5.3 Contribution to Knowledge

The researcher is the first to have applied Bayesian decision model in the planning and

management of River Basin System; and has come up with following contribution to knowledge:

(i) In Contrast to Game and Makovian theory in modeling of river basin operation, Bayesian

Decision Model simulation incorporated procedure to obtain Profit maximization and

minimization of losses and wastages when Perfect information is provided, and this is

informed of Expected profit in perfect information (EPPI).

277

(ii) Also, in Contrast to Game and Makovian theory in modeling of river basin operation, the

Bayesian Decision Model simulation incorporated monetary provision for the model

forecaster in the form of Expected value of system information (EVSI).

(iii)The dynamic relationship between EMV and EOL reveals or gave an indication of

Multipurpose dam integration for optimal benefits, and this is the first time is being

applied in Multipurpose dam operation.

(iv)Empirical prior that is based on experiment was used in this research work instead of

Expert opinions (Objective prior) and Personal view (Subjective prior).

(v) Ohaji, (2019): developed Excel spreadsheet algorithm as a tool for the evaluation of the

curse of dimensionality experienced in the denominator of the infinite Bayesian model

equation. However, the denominator of Bayesian Model equation termed “fixed

Normalizing factor”, is (usually) extremely difficult to evaluate. The excel spread sheet

developed was found easy to use, when compared with previous aid like, Win BUGS

software and Markov Chain Monte Carlo as used by (Eme, 2012) in his research work.

(vi)Future researchers will need this research work as a baseline data and reference, because

it is the first of its kind using BDM application in the planning and management of River

basin system.

278

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296

APPENDIX A 1: Chi-square Probabilities

297

T-Test Table

APPENDIX A 2: T-Test Table

Confidence Level 80% 90% 95% 99% 99.9%

One tail P-Value 0.1 0.05 0.0025 0.005 0.0005

Two Tail P-Value 0.2 0.1 0.05 0.01 0.001

Degree of Freedoom

1 3.077684 6.313752 12.7062 63.65674 636.6192

2 1.885618 2.919986 4.302653 9.924843 31.59905

3 1.637744 2.353363 3.182446 5.840909 12.92398

4 1.533206 2.131847 2.776445 4.604095 8.610302

5 1.475884 2.015048 2.570582 4.032143 6.868827

6 1.439756 1.94318 2.446912 3.707428 5.958816

7 1.414924 1.894579 2.364624 3.499483 5.407883

8 1.396815 1.859548 2.306004 3.355387 5.041305

9 1.383029 1.833113 2.262157 3.249836 4.780913

10 1.372184 1.812461 2.228139 3.169273 4.586894

11 1.36343 1.795885 2.200985 3.105807 4.436979

12 1.356217 1.782288 2.178813 3.05454 4.317791

13 1.350171 1.770933 2.160369 3.012276 4.220832

14 1.34503 1.76131 2.144787 2.976843 4.140454

15 1.340606 1.75305 2.13145 2.946713 4.072765

16 1.336757 1.745884 2.119905 2.920782 4.014996

17 1.333379 1.739607 2.109816 2.898231 3.965126

18 1.330391 1.734064 2.100922 2.87844 3.921646

19 1.327728 1.729133 2.093024 2.860935 3.883406

20 1.325341 1.724718 2.085963 2.84534 3.849516

21 1.323188 1.720743 2.079614 2.83136 3.819277

22 1.321237 1.717144 2.073873 2.818756 3.792131

23 1.31946 1.713872 2.068658 2.807336 3.767627

24 1.317836 1.710882 2.063899 2.79694 3.745399

25 1.316345 1.708141 2.059539 2.787436 3.725144

26 1.314972 1.705618 2.055529 2.778715 3.706612

27 1.313703 1.703288 2.051831 2.770683 3.689592

28 1.312527 1.701131 2.048407 2.763262 3.673906

29 1.311434 1.699127 2.04523 2.756386 3.659405

30 1.310415 1.697261 2.042272 2.749996 3.645959

31 1.309464 1.695519 2.039513 2.744042 3.633456

32 1.308573 1.693889 2.036933 2.738481 3.621802

33 1.307737 1.69236 2.034515 2.733277 3.610913

34 1.306952 1.690924 2.032245 2.728394 3.600716

36 1.305514 1.688298 2.028094 2.719485 3.58215

39 1.303639 1.684875 2.022691 2.707913 3.55812

40 1.303077 1.683851 2.021075 2.704459 3.550966

298

APPENDIX A3: Bayesian Decision Theory Model-Flow Chart

Source: Ohaji, 2019

299

APPENDIX A4: Sizing details for Cross River Hydro-Power Design [Ikom]

Hydropower Plants sizing details:

300

Name:

Country:

CROSS RIVERHYDRO-POWER

[IKOM]

Lat: 5.79, Long: 8.82 Nigeria

DESIGN

Net head [H]:

Maxdischarge [Q]:

Frequency[f]:

MaxTurbinePower [Ptm]:

8[m]

100[m³/s]

50[Hz]

6.73[MW]

Mechanical data

Turbine specifications

Draft tube dimension

Turbine type:

Kaplan Turbine

Diffuserheight-T1:

9800[mm]

Turbine regulation:

Full Kaplan

Diffuserwidth-T4:

12030[mm]

Layout:

Vertical"S"

Diffuserlenght-T2:

29060[mm]

Speed-n:

116[rpm]

Dischargeheight-T3:

2490[mm]

Specific speed-K: Runaway

speed/Speed:

4.60

2.59

Generator specifications

MaximumRunAwayspeed:

299.73[rpm]

Generator type:

Synchronous

Flow run-away:

210.4[m³/s]

Number of poles:

6

Blades number:

3

Frequency-f:

50[Hz]

Hs:

2.4[m]

Power factor (nominal):

1.00

Peak hydraulic efficiency:

86.0[%]

Speed-n:

1000[rpm]

Max turbine mechanical power:

6730[kW]

Nominal power:

7218[kW]

Nominal Plant Efficiency:

82[%]

Apparent power:

7218[kVA]

Minimum flow:

15.00[m³/s]

Generator peak efficiency:

98.0[%]

Transformer peak efficiency:

99.5[%]

Turbine dimension

RunnerouterDiameter-D0:

Runner inner diameter-Di:

Guide vain height-B:

Pipe connection for valve- Dv:

4152[mm]

2341[mm]

1816[mm]

5400[mm]

Gearbox specifications

Gear box Ratio:

Numbers of stages:

Gearboxpeakefficiency:

8.64

2

97.5[%]

Gate circle diameter-Dc

4718[mm]

Other specifications

Numbers of guide vanes:

30

Hydraulic thrust (axial) -F1

1038.79[KN

Spiral case dimension

Runner Weight:

161.42[KN]

S1: S2: 5750[mm]

Turbine Weight:

4103.38[KN]

S3: S4: 8989[mm]

11789[mm]

7473[mm]


301

APPENDIX A5: Turbine efficiency

Q/Qmax

Efficiency

0.20 53.8

0.25 68.5

0.30 77.0

0.35 81.7

0.40 84.1

0.45 85.2

0.50 85.7

0.55 85.9

0.60 85.9

0.65 86.0

0.70 86.0

0.75 86.0

0.80 86.0

0.85 85.6

0.90 84.6

0.93 83.9

0.95 83.2

0.98 82.4

1.00 81.6

1.03 80.7

1.05 79.7

Efficiency η[%]

100

90

80

70

60

50

40

30

20

10

0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Q/Qmax

Fullkaplan

Turbine and Generator rappresentation


302

APPENDIX A6: Energy calculator

# Q[%] Q[m³/s]

1. 414.00 414.00

2. 157.00 157.00

Estimated energy production 1267.50 [MWh]

3. 100.00 100.00

4. 71.00 71.00

5. 53.00 53.00

6. 40.00 40.00

7. 31.00 31.00

8. 24.00 24.00

9. 18.00 18.00

10. 14.00 14.00

11. 9.00 9.00

12. 6.00 6.00

-

400

350

300

250

200

150

100

50

0

1 2 3 4 5 6 7 8 9 10 11 12


303

APPENDIX A7: Key Scheme Characteristics of Cross River Basin Development

Authority

CRBDA has 3,412ha of total planned Irrigable Area and 1% of it is 34.12ha which was

estimated at 1billion naira. That is 29.31million naira/ha.

1Source: http://www.fao.org/tempref/agl/AGLW/ROPISIN/ROPISINreport.

304

SHEET-2: Sample Mean Value, Standard deviation, Variation coefficient, Product of Variation Coefficient & Payoff Values [equation. 3.1 to 3.3]

Multiobjective aj σj Cvj Multipurpose/Courses of Action/Alternatives

Hydropower

Water


Flood

Control

Recreation

State of Nature

Mean

Value

Standard Deviation [σj/aj] Product of variation coefficient of sample and Payoff value [Cvij x Pij]

Economic

Efficiency

Fedral Economic

Redistribution

0.46 0.537488333 1.176552 1.588346 0.364731 0.394145 0.151775254 0.70593 0.020001

2.28 1.718162778 0.75248 3.235664 0.601984 0.75248 2.708928176 2.25744 0.75248

Regional Economic

Redistribution

State Economic

Redistribution

Local Economic

Redistribution

Social Well-Being

0.14 0.117418944 0.837709 0.16084 0.167542 0.0083771 0.213615914 0.14744 0.006702

0.73 1.065160786 1.461126 3.068364 0.227936 0.2922252 2.630026632 0.16365 0.008767

0.64 0.538690542 0.848332 0.678665 0.593832 0.0848332 1.017997875 0.84833 0.008483

0.31 0.450211293 1.443756 0.144376 0.218007 0.2887512 0.259876107 0.15881 1.631444

306

SHEET-3: Calculation of ti [Equation 3.4]

State of Nature

Economic

Efficiency

Federal

Economic

Redistribution

ti`(Standardizing the sample value)

(Expected sample value – Observed sample value)/ Cvij x Pij

Water

Flood

Hydropower

Navigation Irrigation

Recreation

Supply

Control

-0.29177 -0.21298 -0.38059 3.882801 -0.14005 10.03329

0.040545 0.599966 -0.10017 -0.0036 -0.21938 0.116949

Regional

Economic

Redistribution

0.497492 -0.76828 5.581874 -0.162 -0.15085 8.772284

State Economic

Redistribution

-0.22333 0.94205 0.325795 -0.24857 4.202328 38.93873

Local

Economic

Redistribution

0.63702 -0.63499 1.852348 -0.19798 -0.35767 34.48836

Social Well-

Being

3.49896 0.03477 -0.25532 1.194103 1.461298 -0.60156

307

SHEET-4: ǀtiǀ Equation 3.4

State of

Nature

Hydropower

ǀtiǀ

[Expected sample value – Observed sample value]/ [Cvij x Pij]

Water

Supply

Navigatio

n

Irrigation

Flood

Control

Recreatio

n

Economic

Efficiency

Federal

Economic

Redistribution

Regional

Economic

Redistribution

State

Economic

Redistribution

Local

Eonomic

Redistribution

Social Well-

Being

0.29177 0.21298 0.38059 3.882801 0.14005 10.03329

0.040545 0.599966 0.10017 0.0036 0.21938 0.116949

0.497492 0.76828 5.581874 0.162 0.15085 8.772284

0.22333 0.94205 0.325795 0.24857 4.202328 38.93873

0.63702 0.63499 1.852348 0.19798 0.35767 34.48836

3.49896 0.03477 0.25532 1.194103 1.461298 0.60156

308

SHEET-5:: Calculation of P(x/y) of Equation 3.5

State of Nature

Economic

Efficiency

Federal

Economic

Redistribution

Regional

Economic

Redistribution

State Economic

Redistribution

Local

Economic

Redistribution

Social Well-

Being

Hydropower

Water

Supply

Sample Likelihood values = 2(1- Фǀtiǀ )

Sample Likelihood values = P(x/y)

Navigation

Irrigation

Flood

Control

Recreation

1.999416 1.999574 1.999239 1.992234 1.99972 1.979933

1.999919 1.9988 1.9998 1.999993 1.999561 1.999766

1.999005 1.998463 1.988836 1.999676 1.999698 1.982455

1.999553 1.998116 1.999348 1.999503 1.991595 1.922123

1.998726 1.99873 1.996295 1.999604 1.999285 1.931023

1.993002 1.99993 1.999489 1.997612 1.997077 1.998797

ΣP(X/y) 11.98962 11.99361 11.98301 11.98862 11.98694 11.8141

309

SHEET-6: Calculation of P(x/y) of Equation 3.5

Normalizing sample likelihood = 2(1-φǀtiǀ) [Normalized]

State of Nature

Forecast Likelihood

P(x i/y 1) P(x i /y 2) P(x i /y 3) P(x i /y 4) P(x i /y 5) P(x i /y 6)


Economic Efficiency

0.166762 0.16672 0.166839 0.166177 0.166825 0.167591

0.166804 0.166655 0.166886 0.166824 0.166812 0.169269

Federal Economic

Redistribution

0.166728 0.166627 0.165971 0.166798 0.166823 0.167804

Regional Economic

Redistribution

State Economic

Redistribution

0.166774 0.166598 0.166849 0.166783 0.166147 0.162697

Local Economic

Redistribution

Social Well-Being

ΣP(x i = 1…..6/y n)

0.166705 0.16665 0.166594 0.166792 0.166789 0.163451

0.166227 0.16675 0.16686 0.166626 0.166604 0.169187

1 1 1 1 1 1

310

SHEET-7: Marginal Probability of 1 st Iteration

YJ [ P(Y)] P(X/Y)

Alternative

Dam

Projects

Prior

likelihood

Economic

Efficiency

Federal

Economic

Redistribution

Regional

Economic

Redistribution

State Economic

Redistribution

Local

Economic

Redistribu

tion

Social

Wellbeing

Hydropower 0.19 0.166762263 0.031685

0.16680417 0.031693

0.166727946 0.031678

0.16677368 0.031687

0.166704672 0.031674

0.166227269 0.031583181

Water

Supply

0.12 0.166719894 0.020006

0.166655362 0.019999

0.166627294 0.019995

0.166598317 0.019992

0.166649521 0.019998

0.166749611 0.020009953

Navigation 0.02 0.166839482 0.003337

0.166886285 0.003338

0.165971372 0.003319

0.166848628 0.003337

0.166593842 0.003332

0.16686039 0.003337208

Irrigation 0.18 0.166177098 0.029912

0.166824245 0.030028

0.16679782 0.030024

0.166783378 0.030021

0.166791818 0.030023

0.16662564 0.029992615

Flood

Control

0.06 0.16682493 0.010009

0.166811694 0.010009

0.166823128 0.010009

0.166147146 0.009969

0.16678862 0.010007

0.166604482 0.009996269

Recreation 0.43 0.167590744 0.072064

0.169269475 0.072786

0.167804219 0.072156

0.162697363 0.06996

0.163450763 0.070284

0.169187435 0.072750597

Verification 1

Marginal

Probability

0.167013 0.167852 0.167182 0.164965 0.165317 0.167669823

311

SHEET-9: Posterior probability of 1 st Iteration


Prior x

Likelihood

Posterior Probability

Economi

Efficiency

0.167013 Hydropower 0.031685 0.189714298

Water Supply 0.020006 0.119789114

Navigation 0.003337 0.019979173

Irrigation 0.029912 0.179098669

Flood Control 0.010009 0.059932291

Recreation 0.072064 0.431486455

Federal Economic

Redistribution

0.167852 Hydropower 0.031693 0.188813796

Water Supply 0.019999 0.119144433

Navigation 0.003338 0.019884921

Irrigation 0.030028 0.178897755

Flood Control 0.010009 0.059628099

Regional

Economic

Redistribution

Recreation 0.072786 0.433630997

0.167182 Hydropower 0.031678 0.189484176

Water Supply 0.019995 0.11960197

Navigation 0.003319 0.019855194

Irrigation 0.030024 0.179586556

Flood Control 0.010009 0.059871268

Recreation 0.072156 0.431600836

State Economic

Redistribution

0.164965 Hydropower 0.031687 0.192082613

Water Supply 0.019992 0.121187772

Navigation 0.003337 0.020228309

Irrigation 0.030021 0.181983585

Flood Control 0.009969 0.060429789

Recreation 0.06996 0.424087932

Local Economic

Redistribution

0.165317 Hydropower 0.031674 0.191594421

Water Supply 0.019998 0.12096697

- Navigation 0.003332 0.020154426

Irrigation 0.030023 0.18160539

Flood Control 0.010007 0.06053397

Recreation 0.070284 0.425144824


Water Supply 0.02001 0.119341411

Navigation 0.003337 0.019903449

Irrigation 0.029993 0.178879029

Flood Control 0.009996 0.059618772

Recreation 0.072751 0.433892012

312

SHEET-10: Summation of Expected Opportunity Loss (EOL) at 1 st Iteration

Multiobjective Multipurpose Posterior COL EOL ΣEOL


Water Supply 0.119789114 1.04 0.124580678

Navigation 0.019979173 1.02 0.020278861

Irrigation 0.179098669 1.22 0.218679475

Flood Control 0.059932291 0.75 0.044949219

Recreation 0.431486455 1.33 0.575171444 0.983659677

Federal Economic


Water Supply 0.119144433 3.50 0.417005515

Navigation 0.019884921 3.30 0.065620238

Irrigation 0.178897755 0.70 0.125228429

Flood Control 0.059628099 1.30 0.077516528

Recreation 0.433630997 3.30 1.43098229 2.116353

Regional Economic


Water Supply 0.11960197 0.00 0

Navigation 0.019855194 0.19 0.003772487

Irrigation 0.179586556 -0.06 -0.009877261

Flood Control 0.059871268 0.02 0.00143691

Recreation 0.431600836 0.19 0.082867361 0.079715371

State Economic


Water Supply 0.121187772 1.94 0.235589028

Navigation 0.020228309 1.90 0.038433787

Irrigation 0.181983585 0.30 0.054595075

Flood Control 0.060429789 1.99 0.120134421

Recreation 0.424087932 2.09 0.88804013 1.336792442

Local Economic


Water Supply 0.12096697 -0.04 -0.005322547

Navigation 0.020154426 -0.09 -0.001773589

Irrigation 0.18160539 -1.69 -0.306549898

Flood Control 0.06053397 0.00 0

Recreation 0.425144824 0.11 0.045065351 -0.649470392


Water Supply 0.119341411 -0.15 -0.017901212

Navigation 0.019903449 -0.19 -0.003861269

Irrigation 0.178879029 -1.79 -0.320908978

Flood Control 0.059618772 -0.11 -0.00631959

Recreation 0.433892012 0.00 0 -0.743428043

313

SHEET-11: Expected Value of System Information (EVSI) 1 st Iteration

Outcome

Economic Efficiency

Fedral Economic Redistribution

Regional Economic Redistribution

State Economic Redistribution

Marginal


0.17 0.98366 0.164284

0.17 2.116353 0.355234

0.17 0.079715 0.013327

0.16 1.336792 0.220525


Social Well-Being

0.167669823 -0.74343 -0.12465

EVSI 0.52135

314

COMPUTER SIMULATION OF PRIOR-1 INPUT & OUTPUT

SHEET-12: Estimation of Marginal Probability in 2 nd Iteration

Y J P(Y) P(X/Y) P( Y∩ X) = P(Y)*P(X/Y)

Alternative

Dam

Projects Prior likelihood

Economic

Efficiency

Federal

Economic

Redistributio

n

Regional

Economic

Redistributio

n

State

Economic

Redistributio

n

Local

Economic

Redistributi

on

Social

Wellbeing

Hydropower 0.19208261 0.166762263 0.032032131

0.16680417 0.032040181

0.166727946 0.03202554

0.16677368 0.03203432

0.166704672 0.03202107

0.166227269 0.031929368

Water Supply 0.12118777 0.166719894 0.020204412

0.166655362 0.020196592

0.166627294 0.02019319

0.166598317 0.02018968

0.166649521 0.02019588

0.166749611 0.020208014

Navigation 0.02022831 0.166839482 0.003374881

0.166886285 0.003375827

0.165971372 0.00335732

0.166848628 0.00337507

0.166593842 0.00336991

0.16686039 0.003375304

Irrigation 0.18198359 0.166177098 0.030241504

0.166824245 0.030359274

0.16679782 0.030354465

0.166783378 0.03035184

0.166791818 0.03035337

0.16662564 0.030323131

Flood Control 0.06042979 0.16682493 0.010081195

0.166811694 0.010080395

0.166823128 0.010081086

0.166147146 0.01004024

0.16678862 0.010079

0.166604482 0.010067874

Recreation 0.42408793 0.167590744 0.071073212

0.169269475 0.071785141

0.167804219 0.071163744

0.162697363 0.06899799

0.163450763 0.0693175

0.169187435 0.071750349

Verification 1

Marginal

Probability 0.167007336 0.167837411 0.167175346 0.16498913 0.16533673 0.16765404

316

SHEET-13: Estimation of Posterior probability in the 2 nd Iteration

State of Nature Marginal Probability Multipurpose Prior x Likelihood Posterior Probability

Economi Efficiency 0.167007336 Hydropower 0.032032131 0.191800744

Water Supply 0.020204412 0.12097919

Navigation 0.003374881 0.020207978

Irrigation 0.030241504 0.181078897

Flood Control 0.010081195 0.060363787

Recreation 0.071073212 0.425569404

Federal Economic


Water Supply 0.020196592 0.120334266

Navigation 0.003375827 0.020113676

Irrigation 0.030359274 0.180885025

Flood Control 0.010080395 0.06006048

Recreation 0.071785141 0.427706439

Regional Economic


Water Supply 0.02019319 0.12079048

Navigation 0.00335732 0.020082628

Irrigation 0.030354465 0.181572618

Flood Control 0.010081086 0.060302471

Recreation 0.071163744 0.425683248

State Economic


Water Supply 0.020189679 0.122369749

Navigation 0.003375066 0.020456291

Irrigation 0.030351837 0.183962646

Flood Control 0.010040237 0.06085393

Recreation 0.068997988 0.418197175

Local Economic


Water Supply 0.020195884 0.12215001

Navigation 0.003369912 0.020382111

Irrigation 0.030353373 0.183585172

Flood Control 0.010079001 0.060960446

Recreation 0.069317496 0.419250424


Water Supply 0.020208014 0.120534009

Navigation 0.003375304 0.020132551

Irrigation 0.030323131 0.180867287

Flood Control 0.010067874 0.060051483

Recreation 0.071750349 0.42796672

317

SHEET-14: Estimation of EOL in 2 nd Iteration

OBJECTIVES/BENEFITS STATE OF NATURE POSTERIOR COL EOL ΣEOL


Water Supply 0.12097919 1.04 0.125818357

Navigation 0.020207978 1.02 0.020511098

Irrigation 0.181078897 1.22 0.221097333

Flood Control 0.060363787 0.75 0.045272841

Recreation 0.425569404 1.33 0.567284015 0.97998364

Federal Economic


Water Supply 0.120334266 3.50 0.421169931

Navigation 0.020113676 3.30 0.066375132

Irrigation 0.180885025 0.70 0.126619517

Flood Control 0.06006048 1.30 0.078078624

Recreation 0.427706439 3.30 1.411431249 2.10367445

Regional Economic


Water Supply 0.12079048 0.00 0

Navigation 0.020082628 0.19 0.003815699

Irrigation 0.181572618 -0.06 -0.009986494

Flood Control 0.060302471 0.02 0.001447259

Recreation 0.425683248 0.19 0.081731184 0.0785402

State Economic


Water Supply 0.122369749 1.94 0.237886793

Navigation 0.020456291 1.90 0.038866952

Irrigation 0.183962646 0.30 0.055188794

Flood Control 0.06085393 1.99 0.120977612

Recreation 0.418197175 2.09 0.875704884 1.32862504

Local Economic


Water Supply 0.12215001 -0.04 -0.0053746

Navigation 0.020382111 -0.09 -0.001793626

Irrigation 0.183585172 -1.69 -0.309891771

Flood Control 0.060960446 0.00 0

Recreation 0.419250424 0.11 0.044440545 -0.6576391


Water Supply 0.120534009 -0.15 -0.018080101

Navigation 0.020132551 -0.19 -0.003905715

Irrigation 0.180867287 -1.79 -0.324475913

Flood Control 0.060051483 -0.11 -0.006365457

Recreation 0.42796672 0.00 0 -0.7516252

318

SHEET-15: Estimation of EVSI in the 2 nd Iteration

Outcome

Marginal



Fedral Economic Redistribution 0.17 2.103674 0.353075





EVSI 0.51433

319

APPENDIX A10: FMWR Allocation to Cross River Basin Development

Authority(CRBDA)

Year TOTAL CAPITAL TOTAL ALLOCATION

2013 1,325,000,000 1,737,370,960

2014 1,000,478,691 1,392,415,715

2015 220,000,000 655,693,584

2016 1,827,576,837 2,191,973,627

2017 4,589,999,067 4,966,764,419

Total allocation in 5years 8,963,054,595.00 10,944,218,305.00

320

FEDERAL MINISTRY OF WATER RESOURCES

APPENDIX A11: 2017 FGN Budget Allocation

2017 FGN BUDGET ALLOCATION

No Code MDA

Total

Personnel

Total

Overhead

Total

Recurrent

Total Capital

Total Allocation

1 252001001

2 252002001

3 252037001

4 252038001

FEDERAL MINISTRY

OF WATER

RESOURCES - HQTRS

NIGERIA

HYDROLOGICAL

SERVICE AGENCY

ANAMBRA/ IMO

RBDA

BENIN/ OWENA

RBDA

1,291,677,688 273,665,578 1,565,342,267 51,153,246,901 52,718,589,824

215,688,828 38,935,101 254,623,929 817,700,000 1,072,323,929

383,777,823 38,935,100 422,712,923 2,619,045,426 3,041,758,349

308,405,540 30,605,254 339,010,794 755,000,000 1,094,010,794

5 252039001 CHAD BASIN RBDA 340,647,380 35,576,963 376,224,343 1,672,545,395 2,048,769,738

6 252040001 CROSS RIVER RBDA 338,376,690 38,388,662 376,765,352 4,589,999,067 4,966,764,419

7 252041001

HADEJIA-

JAMAÄ»ARE RBDA

332,564,227 42,285,000 374,849,227 3,066,340,349 3,441,189,576

8 252042001 LOWER BENUE RBDA 347,775,559 27,233,559 375,009,118 1,400,800,000 1,775,809,118

9 252043001 LOWER NIGER RBDA 492,627,244 37,127,743 592,754,987 4,991,667,925 5,521,422,913

10 252044001 NIGER DELTA RBDA 517,412,412 43,441,662 560,854,074 1,003,000,000 1,563,854,074

11 252045001 OGUN/ OSUN RBDA 338,994,481 44,471,584 383,466,065 860,259,350 1,243,725,415

12 252046001 SOKOTO RIMA RBDA 416,819,417 46,736,791 463,556,208 3,450,303,591 3,913,859,799

13 252047001 UPPER BENUE RBDA 293,775,455 28,296,592 322,072,047 3,301,692,000 3,623,764,047

14 252048001 UPPER NIGER RBDA 311,268,823 25,902,342 337,171,165 2,998,116,380 3,335,287,545

15 252049001

16 252050001

17 252051001

NATIONAL WATER

RESOURCES

INSTITUTE- KADUNA

NIGERIA

INTEGRATED WATER

MANAGEMENT

COMMISSION

GURARA WATER

MANAGEMENT

AUTHORITY

350,739,786 22,657,000 373,396,786 1,377,676,751 1,751,073,537

119,457,046 69,193,750 188,650,796 423,000,000 611,650,796

14,908,286 42,807,918 57,716,204 665,912,306 723,628,510

6,414,916,685 886,260,599 7,364,176,285 85,146,305,441 92,447,482,383

321




No Code MDA

1. 0252001001

2. 0252002001

FEDERAL MINISTRY

OF WATER

RESOURCES - HQTRS

NIGERIA

HYDROLOGICAL

SERVICE AGENCY

Total

Personnel

Total

Overhead

Total

Recurrent

Total Capital

Total Allocation

1,267,112,688 273,665,579 1,540,778,267 22,296,609,745 23,837,388,012

201,669,054 38,935,101 240,604,155 786,127,100 1,026,731,255

3. 0252037001 ANAMBRA/ IMO RBDA 383,532,543 38,935,100 422,467,643 1,434,869,300 1,857,336,943

4. 0252038001 BENIN/ OWENA RBDA 301,729,810 30,605,254 332,335,064 646,000,000 978,335,064

5. 0252039001 CHAD BASIN RBDA 369,997,029 35,576,963 405,573,992 1,477,500,000 1,883,073,992

6. 0252040001 CROSS RIVER RBDA 326,008,128 38,388,662 364,396,790 1,827,576,837 2,191,973,627

7. 0252041001

HADEJIA-JAMAÄ»ARE

RBDA

335,596,689 29,647,313 365,244,002 865,000,000 1,230,244,002

8. 0252042001 LOWER BENUE RBDA 328,382,410 27,233,559 355,615,969 1,147,000,000 1,502,615,969

9. 0252043001 LOWER NIGER RBDA 456,313,683 37,127,744 493,441,427 1,020,516,449 1,513,957,876

10. 0252044001 NIGER DELTA RBDA 460,714,055 43,441,662 504,155,717 1,080,000,000 1,584,155,717

11. 0252045001 OGUN/ OSUN RBDA 344,444,067 44,471,585 388,915,652 766,000,000 1,154,915,652

12. 0252046001 SOKOTO RIMA RBDA 404,169,256 46,736,791 450,906,047 811,673,215 1,262,579,262

13. 0252047001 UPPER BENUE RBDA 304,725,034 28,296,592 333,021,626 623,000,000 956,021,626

14. 0252048001 UPPER NIGER RBDA 337,466,118 25,902,342 363,368,460 721,190,000 1,084,558,460

15. 0252049001

16. 0252050001

17. 0252051001

NATIONAL WATER

RESOURCES

INSTITUTE- KADUNA

NIGERIA INTEGRATED

WATER MANAGEMENT

COMMISSION

GURARA WATER

MANAGEMENT

AUTHORITY

361,713,782 22,657,000 384,370,782 746,576,541 1,130,947,323

135,282,216 69,193,750 204,475,966 380,000,000 584,475,966

13,939,247 42,807,927 56,747,174 370,360,813 427,107,987

6332795809 873,622,924 7,206,418,733 37,000,000,000 44,206,418,733

322




NO CODE MDA

1. 0252001001

2. 0252002001

FEDERAL MINISTRY OF

WATER RESOURCES -

HQTRS

NIGERIA

HYDROLOGICAL

SERVICE AGENCY

TOTAL

PERSONNEL

TOTAL

OVERHEAD

TOTAL

RECURRENT

TOTAL

CAPITAL

TOTAL

ALLOCATIO

N

1,355,200,736 323,490,274 1,678,691,010 2,707,588,523 4,386,279,533

215,688,828 51,034,824 266,723,652 108,746,270 375,469,922

3. 0252037001 ANAMBRA/ IMO RBDA 410,195,233 50,150,824 460,346,057 220,000,001 680,346,058

4. 0252038001 BENIN/ OWENA RBDA 322,705,679 40,509,370 363,215,049 219,999,998 583,215,047

5. 0252039001 CHAD BASIN RBDA 395,718,748 39,974,836 435,693,584 220,000,000 655,693,584

6. 0252040001 CROSS RIVER RBDA 348,671,794 49,287,786 397,959,580 220,000,000 617,959,580

7. 0252041001

HADEJIA-JAMAÄ»ARE

RBDA

358,926,940 38,241,429 397,168,369 220,000,000 617,168,369

8. 0252042001 LOWER BENUE RBDA 351,211,133 34,746,564 385,957,697 220,000,002 605,957,699

9. 0252043001 LOWER NIGER RBDA 488,036,025 48,342,594 536,378,619 220,000,000 756,378,619

10. 0252044001 NIGER DELTA RBDA 492,742,306 54,137,108 546,879,414 220,000,000 766,879,414

11. 0252045001 OGUN/ OSUN RBDA 368,389,377 51,212,965 419,602,342 220,000,000 639,602,342

12. 0252046001 SOKOTO RIMA RBDA 432,266,584 58,111,270 490,377,854 220,000,000 710,377,854

13. 0252047001 UPPER BENUE RBDA 325,909,127 37,033,605 362,942,732 220,000,000 582,942,732

14. 0252048001 UPPER NIGER RBDA 360,926,330 37,284,558 398,210,888 220,000,000 618,210,888

15. 0252049001

16. 0252050001

17. 0252051001

NATIONAL WATER

RESOURCES

INSTITUTE- KADUNA

NIGERIA INTEGRATED

WATER MANAGEMENT

COMMISSION

GURARA WATER

MANAGEMENT

AUTHORITY

386,859,660 29,988,998 416,848,658 350,000,000 766,848,658

144,686,862 85,477,566 230,164,428 41,665,216 271,829,644

14,908,286 56,660,933 71,569,219 150,000,000 221,569,219

6,773,043,648 1,085,685,504 7,858,729,152 5,998,000,010 13,856,729,162

323


APPENDIX A14: 2014 FGN Budget Proposal

2014 FGN BUDGET PROPOSAL

NO CODE MDA

1. 0252001001

2. 0252002001

3. 0252037001

FEDERAL MINISTRY

OF WATER

RESOURCES - HQTRS

NIGERIA

HYDROLOGICAL

SERVICE AGENCY

ANAMBRA/ IMO

RBDA

TOTAL

PERSONNEL

TOTAL

OVERHEAD

TOTAL

RECURRENT

TOTAL

CAPITAL

TOTAL

ALLOCATION

1,254,673,570 392,665,788 1,647,339,338 17,157,922,372 18,805,261,710

221,389,970 55,885,560 277,255,530 387,000,000 644,255,530

455,489,942 55,865,560 511,355,502 1,000,000,000 1,511,355,502

4. 0252038001

BENIN/ OWENA

RBDA

322,160,663 43,913,580 366,074,243 1,000,000,000 1,366,074,243

5. 0252039001 CHAD BASIN RBDA 307,422,039 51,047,178 358,469,217 1,002,634,900 1,361,104,116

6. 0252040001 CROSS RIVER RBDA 336,855,511 55,081,513 391,937,024 1,000,478,691 1,392,415,715

7. 0252041001

HADEJIA-

JAMAÄ»ARE RBDA

359,414,905 42,539,089 401,953,994 1,500,000,000 1,901,953,994

8. 0252042001 LOWER BENUE RBDA 325,353,085 39,075,742 384,428,837 1,000,372,750 1,364,801,587

9. 0252043001 LOWER NIGER RBDA 527,688,587 53,272,298 580,980,885 1,000,000,000 1,580,980,885

10. 0252044001 NIGER DELTA RBDA 507,219,018 62,331,745 589,550,763 1,000,000,000 1,569,550,783

11. 0252045001 OGUN/ OSUN RBDA 385,054,057 63,809,522 428,863,579 1,000,000,000 1,428,863,579

12. 0252046001 SOKOTO RIMA RBDA 415,585,401 67,059,723 482,625,124 1,000,000,000 1,482,625,124

13. 0252047001 UPPER BENUE RBDA 302,209,896 40,601,024 342,810,920 1,000,135,313 1,342,946,234

14. 0252048001 UPPER NIGER RBDA 346,499,885 37,165,665 383,685,550 1,000,000,000 1,482,625,124

15. 0252049001

16. 0252050001

17. 0252051001

NATIONAL WATER

RESOURCES

INSTITUTE- KADUNA

NIGERIA

INTEGRATED WATER

MANAGEMENT

COMMISSION

GURARA WATER

MANAGEMENT

AUTHORITY

253,004,750 32,509,128 285,513,878 353,000,000 1,342,946,234

137,582,483 99,281,819 238,864,301 145,199,716 1,383,605,550

18,139517 61,281,819 77,561,956 147,000,000 638,513,878

6,453,723,291 1,253,507,355 7,707,230,646 30,673,743,742 38,380,974,388

324




NO CODE MDA

1. 0252001001

2. 0252037001

FEDERAL MINISTRY

OF WATER

RESOURCES - HQTRS

ANAMBRA/ IMO

RBDA

TOTAL

PERSONNEL

TOTAL

OVERHEAD

TOTAL

RECURRENT

TOTAL

CAPITAL

TOTAL

ALLOCATION

1,083,024,657 434,615,687 1,517,640,344 22,531,340,812 24,048,981,156

464,161,638 69,652,538 533,814,176 1,473,000,000 2,006,814,176

3. 0252038001

BENIN/ OWENA

RBDA

316,287,249 48,517,004 364,804,253 1,173,000,000 1,537,804,253

4. 0252039001 CHAD BASIN RBDA 356,131,589 66,930,198 423,061,787 1,213,000,000 1,636,061,787

5. 0252040001 CROSS RIVER RBDA 343,099,138 69,271,822 412,370,960 1,325,000,000 1,737,370,960

6. 0252051001

7. 0252041001

GURARA WATER

MANAGEMENT

AUTHORITY

HADEJIA-

JAMAÄ»ARE RBDA

17,437,823 70,346,852 87,784,675 197,000,000 284,784,675

392,002,606 53,037,247 445,039,853 1,228,000,000 1,673,039,853

8. 0252042001 LOWER BENUE RBDA 311,818,910 49,183,926 361,002,836 1,213,000,000 1,574,002,836

9. 0252043001 LOWER NIGER RBDA 519,742,477 66,419,289 586,161,766 1,,317,000,000 1,903,161,766

10. 0252044001 NIGER DELTA RBDA 519,025,500 77,714,503 596,740,003 1,693,000,000 2,289,740,003

11. 0252050001

NATIONAL WATER

RESOURCES

INSTITUTE-KADUNA

146,023,657 89,122,355 235,146,012 239,000,000 474,146,012

12. 0252045001 OGUN/ OSUN RBDA 271,719,861 40,532,007 321,251,868 538,000,000 850,251,868

13. 0252048001 UPPER NIGER RBDA 394,809,520 79,556,978 474,366,498 1,400,000,000 1,874,366,498

14. 0252046001 SOKOTO RIMA RBDA 439,998,323 83,609,292 523,607,615 1,392,999,999 1,916,607,614

15. 0252047001 UPPER BENUE RBDA 313,588,316 45,802,443 359,390,759 1,213,000,000 1,572,390,759

16. 0252048001 UPPER NIGER RBDA 348,652,676 46,337,724 394,990,400 1,213,000,000 1,607,990,400

17. 0216001001

NIGERIA

HYDROLOGICAL

SERVICE AGENCY

229,075,735 76,537,019 305,612,754 517,000,000 822,612,754

6,466,599,675 1,467,186,884 7,933,786,559 39,876,340,812 47,810,127,371

325

APPENDIX A16: 2016 Annual Audit Report-Sheet-1

326

APPENDIX A16: 2016 ANNUAL AUDIT REPORT-SHEET-2

327

APPENDIX A16: 2016 ANNUAL AUDIT REPORT-SHEET-3

SOURCE: OFFICE OF THE AUDITOR GENERAL(OAuGF) OF THE FEDERATION(2016): 2016 ANNUAL AUDIT

REPORT, PP 190-193.

328

APPENDIX A17: Pearson Critical Values

329

APPENDIX A18: Data Collection Letter

330

APPENDIX A19: Questionnaires

Table 1: A Questionnaire for Planning and Management Decision on Assets operation

of Cross River Basin Development Authority (CRBDA) for Staff.

A

Name……………………………………………………………………………………………

Age………………………………………………Sex………………………………………….

Education Background………………………………………………………………………….

B

INSTRUCTION:

Please tick (√) where applicable in the space provided below.

STRONGLY AGREE (SA), AGREE (A), DISAGREE (D), STRONGLY DISAGREE (SA)

Gender: Male ( ), Female ( ), Marital status: Married ( ), Single ( )

Employment status: Employed: ( ), Contract ( )

S/NO QUESTIONS (4mrks)

SA

1 The transfer of funds without contract

agreement by CRBDA leads to inadequate

decision-making problem.


agreement by Consultant leads to

inadequate decision-making problem.


agreement by the Contractor leads to


4 The non-factoring of the root causes of

abandoned project by the CRBDA

management and planning engineers a



abandoned project by the Consultant




abandoned project by the Contractor



7 CRBDA management not following

procedures prior award of contract to

incompetent companies/contractor a


8 Consultant management not following



(3mrks)

A

(2maks)

D

(1mrk)

SD

(mean)

X

331


9 Contractor management not following




10 The approval of fictitious services and

projects by CRBDA management a

decision problem.


projects by Consultant management a

decision problem.


projects by Contractor management a

decision problem.

13 The execution of unauthorized virement by

CRBDA management without recourse to

appropriation bill is a decision-making

problem.


Consultant management without recourse

to appropriation bill is a decision-making

problem.


Contractor management without recourse to

appropriation bill is a decision-making

problem.

16 Non-continuity of previous awarded

contract by the present management of

CRBDA a decision problem.



Consultant a decision problem.



Contractor a decision problem.

19 The release of insufficient funds by

FGN/FMWR to CRBDA a decision

problem.


FGN/FMWR to Consultant a decision

problem.


FGN/FMWR to Contractor a decision

problem.

22 The unstandardized method of funds

allocation by the CRBDA a decision

problem.


allocation by the Consultant a decision

332

problem.


allocation by the Contractor a decision

problem.

25 The underutilization of CRBDA assets

amidst sufficient resources a decision

problem.

26 The underutilization of Consultant assets


problem.

27 The underutilization of Contractor assets


problem.

Table 2: A Questionnaire for Planning and Management Decision on Assets operation

of Cross River Basin Development Authority (CRBDA) for Contractors/ Consultants.

A

Name……………………………………………………………………………………………

Age………………………………………………Sex………………………………………….

Education Background………………………………………………………………………….

B

INSTRUCTION:

Please tick (√) where applicable in the space provided below.

STRONGLY AGREE (SA), AGREE (A), DISAGREE (D), STRONGLY DISAGREE (SA)

Gender: Male ( ), Female ( ), Marital status: Married ( ), Single ( )

Vendor status: Contractor: ( ), Consultant ( )

S/NO QUESTIONS (4mrks)

SA


agreement by CRBDA leads to



agreement by Consultant leads to



agreement by the Contractor leads to



abandoned project by the CRBDA



(3mrks)

A

(2mrks)

D

(1mrk)

SD

(mean)

X

333


abandoned project by the Consultant




abandoned project by the Contractor



7 CRBDA management not following




8 Consultant management not following




9 Contractor management not following





projects by CRBDA management a

decision problem.


projects by Consultant management a

decision problem.


projects by Contractor management a

decision problem.

13 The execution of unauthorized virement

by CRBDA management without

recourse to appropriation bill is a



by Consultant management without




by Contractor management without





CRBDA a decision problem.



Consultant a decision problem.



Contractor a decision problem.

334


FGN/FMWR to CRBDA a decision

problem.


FGN/FMWR to Consultant a decision

problem.


FGN/FMWR to Contractor a decision

problem.


allocation by the CRBDA a decision

problem.


allocation by the Consultant a decision

problem.


allocation by the Contractor a decision

problem.

25 The underutilization of CRBDA assets


problem.

26 The underutilization of Consultant

assets amidst sufficient resources a

decision problem.

27 The underutilization of Contractor

assets amidst sufficient resources a

decision problem.

335

APPENDIX A20: Research Visit to Cross River Basin Development Authority

336

Engr.Dr, Evans Ohaji PhD Thesis

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