Upscaling and Inverse Modeling of Groundwater Flow and Mass ...

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124 CHAPTER 5. JOINTLY MAPPING HYDRAULIC . . . Piezometric Head [m] Piezometric Head [m] Piezometric Head [m] Piezometric Head [m] 0 -1 -2 -3 -4 -5 -6 -7 0 -1 -2 -3 -4 -5 -6 -7 0 -1 -2 -3 -4 -5 -6 -7 0 -1 -2 -3 -4 -5 -6 -7 S1: Well # 2 S2: Well # 2 S3: Well # 2 S6: Well # 2 100 200 300 400 500 Time [day] 100 200 300 400 500 Time [day] 100 200 300 400 500 Time [day] 100 200 300 400 500 Time [day] Piezometric Head [m] Piezometric Head [m] Piezometric Head [m] Piezometric Head [m] 0 -1 -2 -3 -4 0 -1 -2 -3 -4 0 -1 -2 -3 -4 0 -1 -2 -3 -4 S1: Well # 10 100 200 300 400 500 Time [day] S2: Well # 10 100 200 300 400 500 Time [day] S3: Well # 10 100 200 300 400 500 Time [day] S6: Well # 10 100 200 300 400 500 Time [day] Figure 5.8: Piezometric head time series for the reference field (black) and simulated ones (gray lines) for the S1,S2,S3 and S6 scenarios at the conditioning well W2 (left column) and verification well W10 (right column).
CHAPTER 5. JOINTLY MAPPING HYDRAULIC . . . 125 Table 5.4: Bias and spread of predicted piezometric heads at time t = 67.7 days for the different scenarios. Scenario S1 S2 S3 S4 S5 S6 AAB(ht=67.7) 0.690 0.503 0.169 0.170 0.179 0.179 AESP (ht=67.7) 0.901 0.649 0.175 0.172 0.169 0.162 duction of AESP (h) is achieved by conditioning to head data. The reductions of AAB(h) and AESP (h) almost can be ignored when concentration data are used for conditioning in S4, S5 and S6. The main conclusions are: (1) of all the data, the measured piezometric head data are most informative for improving head predictions and reducing the prediction uncertainty; (2) the impact of concentration data for characterizing piezometric head is very small. Concentrations Reproduction Figure 5.9 to 5.12 show the ensemble mean and variance of 500 concentration realizations at time 300 and 500 days resulting from the transport simulation for all the six scenarios. These ensemble mean maps of concentration for scenario 1 show that even though each realization will have a non-Gaussian plume similar to those in the reference, the random location of high and low concentrations makes that the ensemble mean maps of plume show a Gaussian shape. Introducing the hydraulic conductivity data (S2) rectifies the plume but still does not reproduce the reference. The ensemble mean of the plume is further rectified when the conductivity, porosity and head data are jointly used for conditioning (S3). The reproduction of piezometric heads is very good in S3, but the limited improvement of the plume characterization indicates the importance of further conditioning on concentration data. The results for scenarios S4 and S6 show that conditioning remarkably improves the characterization of the plume. Conditioning to concentration data at t = 300 days (S4) also improves strongly the prediction for 500 days (although the concentration data sampled at t = 500 days are not used for conditioning in scenario S4). For scenarios S5 and S6 the additional concentration data from t = 400 and 500 days improve further the characterization of the plume so that they are very close to the reference plumes. The ensemble variance maps of the concentration fields show that the ensemble variance decreases away from the barycenter of the plume and is
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Upscaling and Inverse Modeling of G
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c⃝ Copyright by Liangping Li 2011
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Abstract The need to reduce the com
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improved as more data is assimilate
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Resumen La necesidad de reducir el
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Por último, en el tercer bloque, e
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Resum La necessitat de reduir el co
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flux i el transport (conductivitat
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Acknowledgements I want to thank my
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xx CONTENTS 3 Transport Upscaling U
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xxii CONTENTS
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xxiv LIST OF FIGURES 2.7 Flow compa
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xxvi LIST OF FIGURES 4.4 Reference
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xxviii LIST OF FIGURES
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1.1 Motivation and Objectives 1 Int
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CHAPTER 1. INTRODUCTION 3 Chapter 2
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6 CHAPTER 2. A COMPARATIVE STUDY OF
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8 CHAPTER 2. A COMPARATIVE STUDY OF
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10 CHAPTER 2. A COMPARATIVE STUDY O
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38 BIBLIOGRAPHY Berkowitz, B., Sche
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40 BIBLIOGRAPHY Gómez-Hernández,
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42 BIBLIOGRAPHY Salamon, P., Fernà
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44 CHAPTER 3. TRANSPORT UPSCALING U
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70 BIBLIOGRAPHY Dagan, G., 1994. Up
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72 BIBLIOGRAPHY Lawrence, A. E., Sa
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Page 168 and 169: 136 BIBLIOGRAPHY Chen, Y., Zhang, D
Page 170 and 171: 138 BIBLIOGRAPHY Journel, A., 1974.
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174 BIBLIOGRAPHY Yeh, W., 1986. Rev
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176 CHAPTER 7. CONCLUSIONS travels
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178 CHAPTER 7. CONCLUSIONS predicti
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180 APPENDIX A. FLOWXYZ3D - A THREE
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182 APPENDIX A. FLOWXYZ3D - A THREE
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