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IX. Transient Model Sensitivity Analysis

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Sensitivity Analysis for the Initial Model One-percent sensitivities: Can be explained using principle of superposition. Flow budget for simulation with pumping only:

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Sensitivity Analysis for the Initial Model DO EXERCISE 9.6a: Evaluate one-percent scaled sensitivity maps for the transient flow system. One-percent scaled sensitivities for the full transient problem are shown for selected parameters in Figures 9.6 to 9.8 of Hill and Tiedeman. One-percent scaled sensitivities for the pumping only simulation are shown for selected parameters in Figures 9.9 to 9.10.

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One-Percent Sensitivities for HK_1 Figure 9.6 of Hill and Tiedeman

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One-Percent Sensitivities for HK_1: Flow System with Pumping Only (No Recharge) Figure 9.9 of Hill and Tiedeman

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One-Percent Sensitivities for HK_1 (at 4 days): Calculating Using Superposition

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One-Percent Sensitivities for HK_1 (at 283 days): Calculating Using Superposition

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One-Percent Sensitivities for HK_1: Understanding Using Darcy’s Law Flow system with pumping only, at early time Main source of water to well is water released from storage in vicinity of well. When HK_1 is increased, the gradient towards the well needs to decrease in order to maintain similar amount of flow to the well through layer 1.

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One-Percent Sensitivities for HK_1: Understanding Using Darcy’s Law Flow system with pumping only, at later time Main source of water to well is inflow from river. When HK_1 is increased, the gradient from the river towards the well needs to decrease in order to maintain similar amount of flow to the well through layer 1.

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One-Percent Sensitivities for K_RB (at 58 days): Calculating Using Superposition

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One-Percent Sensitivities for K_RB: Understanding Using Darcy’s Law Recap: Flow system with recharge only Increase K_RB, hydraulic gradient across riverbed must decrease to maintain same discharge to the river. In the system with recharge only, h > Hriv; therefore, h must decrease when K_RB increases

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One-Percent Sensitivities for K_RB: Understanding Using Darcy’s Law Flow system with pumping only Reason that heads increase in response to an increase in K_RB: Increase K_RB, hydraulic gradient across riverbed must decrease to maintain similar inflow to the aquifer. In the system with pumpage only, h < Hriv; therefore, h must increase when K_RB increases. Reason for slight increase in hydraulic gradient away from the river: An increase in K_RB causes a slight increase in Q riv and a slight decrease in Q storage. The increased gradient is needed for this increased river water to flow to the well.

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Sensitivity Analysis for the Initial Model DO EXERCISE 9.6b: Use composite scaled sensitivities to evaluate the information provided by observations for the defined parameters. Composite scaled sensitivities for the starting parameter values are shown in Figure 9.11 of Hill and Tiedeman. DO EXERCISE 9.6c: Evaluate parameter correlation coefficients to assess parameter uniqueness. The parameter correlation coefficient matrices for the starting parameter values for the transient problem, calculated using MODFLOW-2000, are shown in Table 9.5.

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Composite scaled sensitivities at the starting parameter values for the transient problem Figure 9.11 of Hill and Tiedeman (page 243)

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Parameter correlation coefficients at the starting parameter values for the transient problem Table 9.5 of Hill and Tiedeman (page 244) Q_1&2SS_1HK_1K_RBVK_CBSS_2HK_2RCH_1RCH_2 Q_1&21.00-0.91-0.99-0.057-0.67-0.41-0.96-0.66-0.83 SS_1 1.000.88-0.0780.800.0430.890.580.75 HK_1 1.00-0.0290.680.410.920.670.82 K_RB 1.00-0.360.380.220.0510.055 VK_CB 1.00-0.230.610.430.55 SS_2 symmetric 1.000.410.300.35 HK_2 1.000.620.81 RCH_1 1.000.16 RCH_2 1.00

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V. Nonlinear Regression Objective-Function Surfaces Thus far, we have: Parameterized the forward model Obtained head and flow observations and their weights.

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