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

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62 CHAPTER 3. TRANSPORT UPSCALING USING MULTI- . . . 3.3.4 Propagation of Uncertainty Due to the inherent lack of information in groundwater modeling, an uncertainty assessment is commonly requested in solute transport simulations (e.g., Salamon et al., 2007; Riva et al., 2008). Quantifying the uncertainty associated with flow and transport modeling should be important for the decision maker to assess the degree of confidence of his decisions. Here, we have analyzed how the uncertainty is estimated from the ensemble of realizations at the fine scale and after flow and transport upscaling. We will analyze the propagation of uncertainty through the upscaling process, along the same line as Fernàndez-Garcia and Gómez-Hernández (2007). The use of 30 realizations may seem a small number to perform an uncertainty evaluation in such a heterogeneous aquifer. However, our purpose is not so much to analyze the number of realizations needed to obtain a good estimation of model uncertainty, but rather to compare the uncertainty derived from 30 realizations, before and after upscaling. If uncertainty upscales well for 30 realizations, it should do so for a larger number of realizations. We evaluate uncertainty by calculating the spread in the ensemble of cumulative breakthrough curves at all the control planes. More precisely, we quantified uncertainty by the 95% confidence interval related with the early, median, and late arrival time of particles to each control plane. The early arrival time reflects the fastest pathways between source and control plane, which is for example of importance for the safety assessment of nuclear waste repositories. The late arrival time constitutes important information for the calculation, for example, of clean-up times in contaminated aquifer remediation. The evolution of uncertainty with the travel distance is shown in Figure 3.6. We can see that: (1) For the early arrival time, the advection-only model and double-rate mass transfer model show a slight overestimation of the uncertainty. (2) For the median arrival time, the double-rate mass transfer model is better in reproducing the uncertainty estimated at the fine scale than the advective-only model. (3) For the late time, it is evident that the use of doublerate mass transfer model clearly outperforms the advective-only for distances larger than 60 m, and less clearly (because of the scale the results are plotted) for the shorter distances. In highly heterogeneous formulations, hydraulic conductivity upscaling is not sufficient to preserve the uncertainty. Transport upscaling, through the use of a mass transfer process at the coarse scale is needed for proper upscaling of the uncertainty associated with solute transport predictions.
CHAPTER 3. TRANSPORT UPSCALING USING MULTI- . . . 63 Evolution of Uncertaity Early Arrival Time, T05 [day] Evolution of Uncertaity Median Arrival Time, T50 [day] Evolution of Uncertaity Late Arrival Time, T95 [day] 140 120 100 80 60 40 20 0 240 200 160 120 80 40 0 5000 4000 3000 2000 1000 0 180 x 120 x 60, Fine 18 x 12 x 12, Coarse: advection-only 18 x 12 x 12, Coarse: double-rate Model 0 20 40 60 80 100 120 140 160 180 x 120 x 60, Fine X - Travel Distance [m] 18 x 12 x 12, Coarse: advection-only 18 x 12 x 12, Coarse: double-rate Model 0 20 40 60 80 100 120 140 160 180 x 120 x 60, Fine X - Travel Distance [m] 18 x 12 x 12, Coarse: advection-only 18 x 12 x 12, Coarse: double-rate Model 0 20 40 60 80 100 120 140 160 X - Travel Distance [m] Figure 3.6: Evolution of uncertainty as a function of travel distance for the early, median, and late travel times, as measured by the width of the 95% confidence interval derived from an ensemble of 30 realizations. Calculations were performed at the fine scale, and at the coarse scale for two different upscaling approaches.
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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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Page 70 and 71: 38 BIBLIOGRAPHY Berkowitz, B., Sche
Page 72 and 73: 40 BIBLIOGRAPHY Gómez-Hernández,
Page 74 and 75: 42 BIBLIOGRAPHY Salamon, P., Fernà
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Page 102 and 103: 70 BIBLIOGRAPHY Dagan, G., 1994. Up
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112 CHAPTER 5. JOINTLY MAPPING HYDR
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136 BIBLIOGRAPHY Chen, Y., Zhang, D
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138 BIBLIOGRAPHY Journel, A., 1974.
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140 BIBLIOGRAPHY Wen, X., Deutsch,
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142 CHAPTER 6. GROUNDWATER FLOW INV
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170 BIBLIOGRAPHY Deutsch, C. V., Jo
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172 BIBLIOGRAPHY Lee, S., Carle, S.
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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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