IX. Transient Model Sensitivity Analysis

1. IX. Transient ModelSensitivity Analysis

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

3. 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.

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

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

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

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

8. 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.

9. 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.

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

11. 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

12. 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 Qriv and a slight decrease in Qstorage. The increased gradient is needed for this increased river water to flow to the well.

13. 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.

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

15. Q_1&2 SS_1 HK_1 K_RB VK_CB SS_2 HK_2 RCH_1 RCH_2 Q_1&2 1.00 -0.91 -0.99 -0.057 -0.67 -0.41 -0.96 -0.66 -0.83 SS_1 1.00 0.88 -0.078 0.80 0.043 0.89 0.58 0.75 HK_1 1.00 -0.029 0.68 0.41 0.92 0.67 0.82 K_RB 1.00 -0.36 0.38 0.22 0.051 0.055 VK_CB 1.00 -0.23 0.61 0.43 0.55 SS_2 symmetric 1.00 0.41 0.30 0.35 HK_2 1.00 0.62 0.81 RCH_1 1.00 0.16 RCH_2 1.00 Parameter correlation coefficients at the starting parameter values for the transient problem Table 9.5 of Hill and Tiedeman (page 244)