# Presentation: 457015

## IX. Transient ModelSensitivity Analysis

## Sensitivity Analysis for the Initial Model

**One-percent sensitivities**: Can be explained using principle of superposition.
- Flow budget for simulation with pumping only:

## 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.

## One-Percent Sensitivities for HK_1

- Figure 9.6 of Hill and Tiedeman

## One-Percent Sensitivities for HK_1: Flow System with Pumping Only (No Recharge)

- One-Percent Sensitivities for HK_1: Flow System with Pumping Only (No Recharge)

- Figure 9.9 of Hill and Tiedeman

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

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

## 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.

## 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.

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

## 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

## 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.

## 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.

## Composite scaled sensitivities at the starting parameter values for the transient problem

- Figure 9.11 of Hill and Tiedeman (page 243)

## Parameter correlation coefficients at the starting parameter values for the transient problem

- Table 9.5 of Hill and Tiedeman (page 244)