1. Calibration & Sensitivity Analysis

2. Head measured in an observation well is known as a target. Baseflow measurements or other fluxes (e.g., ET) are also used as targets during calibration. Targets in Model Calibration The simulated head at a node representing an observation well is compared with the measured head in the well. (Similarly for flux targets…) Residual error = observed - simulated During model calibration, parameter values (e.g., R and K) are adjusted until the simulated head matches the observed value within some acceptable range of error. Hence, model calibration solves the inverse problem.

3. Calibration Targets calibration value associated error 20.24 m  0.80 m Target with relatively large associated error. Target with smaller associated error.

4. Examples of Sources of Error Surveying errors Errors in measuring water levels Interpolation error Transient effects Scaling effects Unmodeled heterogeneities

5. Leave this box unchecked so that gwv will compare simulated heads at the node with the target values.

6. Head measured in an observation well is known as a target. Baseflow measurements or other fluxes are also used as targets during calibration. Targets in Model Calibration The simulated head at a node representing an observation well is compared with the measured head in the well. (Similarly for flux targets…) Residual error = observed - simulated During model calibration, parameter values (e.g., R and T) are adjusted until the simulated head matches the observed value within some acceptable range of error. Hence, model calibration solves the inverse problem.

7. Basecase simulation for the 2006 Final Project Perfect fit All heads are too low.

8. Residual = observed - simulated

9. 2006 values

10. Calibration parameters are parameters whose values are uncertain. Values for these parameters are adjusted during model calibration. Typical calibration parameters include hydraulic conductivity and recharge rate. Parameter values can be adjusted manually by trial and error. This requires the user to do multiple runs of the model. …or parameter adjustment can be done with the help of an inverse code. The inverse code will automatically find a set of parameters that matches the observed head values.

11. Automated calibration using inverse modeling Codes MODFLOWP – used in MODFLOW2000 GV Calibration PEST UCODE Available in GWV for use with MODFLOW 88/96

12. x y ocean 2L L Island Recharge Problem- Forward Problem well Parameters known with certainty: R= 0.003375 ft/d K= 100 ft/day Solve for head h =120.014

13. x yocean Island Recharge Problem – Inverse Problem Head in well = 120.014 feet (target) well Uncertain parameters Initial guesses R= 0.001 ft/d K= 50 ft/day Add a flux target to estimate both R and K F= -57120 ft 3 /day 2 parameters and 2 targets; Ideally should have at least 1 more target.

14. Targets h = 120.014 ft F = -57120 ft 3 /day We are trying to estimate R and K. Correct answers: K = 100 ft/day R = 0.003375 ft/day 2 parameters and 2 targets; Ideally should have at least 1 more target.

15. Sensitivity analysis is used: During calibration (Sensitivity coefficients =  sum of squared residuals/  parameter value or  h/  parameter value) As an uncertainty analysis after calibration

16. The Problem of Zonation Most inverse codes estimate parameters in pre-determined, fixed zones. Yet, the boundaries/existence of such zones is usually uncertain. Pilot points can be used instead. Parameters are estimated at arbitrarily selected points known as pilot points. Then parameter values are interpolated between pilot points.