GENERALISED WHOLE-FARM STOCHASTIC DYNAMIC ...

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Description of the multi-period risk programming model 69c D =H R IH G \\-H G IH R {2CU-\)]8-SCU>H,(C)(D)From Figure 4.4 it is clear that if H min is greater than H R loss will be minimised The averageamount (H A ) of water that contributes to H R is calculated as: H A = H R - H I) - H RH A is taken as the net irrigation amount taken up in the root zone of the SAPWAT water budget,whereas the rest (H D x H R ) enters the SAPWAT water budget as below the root zone.4.3.2 CROP YIELD ESTIMATIONSAPWAT calculates maximum evapotrans pi ration (ET m ) and actual evapotranspi ration (ET a )during each day of the growing season.Crop yield was calculated with the use crop yield response factors (ky) which relate relative yielddecrease (1-Ya/Ym) to relative evapotrans pi ration deficit (1-ETa/ETm). More specifically theStewart multiplicative (De Jager, 1994) relative evapotranspiration formula was used to calculatecrop yield taking the effect of water deficits in different crop growth stages into account:rrYa = Ym x \-ky t 1-(1)with:vvYmactual crop yield (ton/ha)maximum potential crop yield (ton/ha)actual evapotranspiration {mm.ha)ETmmaximum potential evapotranspiration (mm.ha)crop yield response factormgrowth stageslength of crop growth stage in daysCrop yields and water use on a weekly basis were estimated for 256 different combinations ofwater stress in each of the crop growth stages. The irrigation is triggered whenever the specifieddeficit was reached. Variability of the crop yields was estimated for each of the three states ofnature included in SAPWAT.
Description of the multi-period risk programming model 704.4 CALCULA TION OF RISK PARAMETERSA separate GAMS model was developed to generate the necessary variance-covanance matrixor deviation matrix for the Skeleton DLP model. These matrices are calculated fromappropriately correlated sequences of simulated crop yields over a period of 15 years for 100states of nature. Deterministic constant prices were assumed.Procedures developed by Richardson, Klose and Gray (2000) was used to simulate the cropyields from intra- and intertemporal correlation matrices. Since SAPWAT only includes normal,severe drought and favourable weather sets the triangle distribution is used to simulate thesequences.The cumulative probability distribution (F w ) of the triangular distribution is completely specifiedby the minimum (a), maximum (c) and the mode (b) (Hardaker, Huirne and Anderson, 1997).Through the use of the inverse transform method it is possible to simulate random values of xfor any uniformly distributed value (U) between zero and one. More specifically the inversetransform function of the triangular distribution is given by:x = a + (u(c - a\b - a)f s forO
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GENERALISED WHOLE-FARM STOCHASTICDY
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DISCLAIMERThis report has been revi
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A cknowledgements* Mr Abraham Bekke
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Executive Summar\-the season (Berna
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Executive Summaryseveral farmers us
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Table of contents2.6 CONCLUSIONS 22
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LIST OF TABLESTABLE 3.1: UTILISATIO
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Lys van figureFIGURE E1:ENVELOPE OF
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Introductioncrops compete for water
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IntroductionChapter 2 gives an over
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Literature reviewYieldY = /(ET)y- .
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Literature reviewThe Lagrangian mut
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Literature review 15water use betwe
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Literature review 17White, 1969). A
Page 36 and 37: Literature review 19the explicit ti
Page 38 and 39: Literature review 21The variance of
Page 40 and 41: CHAPTERSTUDYAREA3.1 GENERAL DESCRIP
Page 42 and 43: Study Area 25250Jan Feb Mar Apr May
Page 44 and 45: Study Area 27users. More specifical
Page 46 and 47: Study Area 29which the user may dis
Page 48 and 49: Descriplion of the multi-period ris
Page 50 and 51: Description of (he multi-period ris
Page 52 and 53: Description of the multi-period ris
Page 90 and 91: Results and conclusions 735.2 RE-AL
Page 92 and 93: Results and conclusions 755.3 RE-AL
Page 94 and 95: Results and conclusions 11unrealist
Page 96 and 97: RESEARCH IMPLICATIONSGeneralWhile S
Page 98 and 99: Research implications 81• The imp
Page 100 and 101: REFERENCESANNANDALE, J.G., BENADE,
Page 102 and 103: References 85DE JUAN, J.A, TARJUELO
Page 104 and 105: References 87MARE, H.G. (1995). Mar
Page 106 and 107: References 89Orange-Riet water user
Page 108 and 109: Appendix A 91pivotlpivotlpivotlpivo
Page 110 and 111: Appendix A 93flood2flood2flood2floo
Page 112 and 113: Appendix A 95labour.labour,labour.l
Page 114 and 115: Appendix A 97floodlfloodlflood2floo
Page 116 and 117: Appendix A 99pivot.ml.cropB.y3pivot
Page 118 and 119: Appendix A 101flood2flood2flood2.pi
Page 120 and 121: Appendix A 103CanalNetwork. gins04/
Page 122 and 123: Appendix A 105yipivot1.pivot.ml.cro
Page 124 and 125: Appendix A 107farm2.floodlfarm2.flo
Page 126 and 127: Appendix B 109C(I,J) Cholesky decom
Page 128 and 129: Appendix B 111DISPLAY VC;* Whistle
Page 130 and 131: Appendix B 113CUD(rnd,I,t)LE ((DATA
Page 132 and 133: APPENDIXENTERPRISE BUDGETWHEAT CENT
Page 134 and 135: Appendix C 118MAIZE: CENTRE PIVOTIt
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Appendix C120GROUNDNUTS CENTRE PIVO
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Appendix C 122LUCERNE: FLOOD 2003It
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Appendix C 124COTTON: FLOOD 2003Ite
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Appendix D 1265cl_5c3_off5c45c6offo
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Appendix D 128sec_to_ter(con,conl)
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Appendix D 130TABLEpg_to_p(pg,p) li
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Appendix D132wt25wt2 6wt27wt28wt2 9
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Appendix D 134pivot 10/TABLEprices(
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APPENDIXPRODUCTION FUNCTION ENVELOP
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Appendix E 1388.5»• •* •»
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Appendix E 1403.63.2* * * * ••
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