Sensitivity analysis 95% confidence interval HELP!!!

[Lisbeth]

Hi

When I run a sensitivity analysis I am supoposed to be able to see the 95% confidence interval of my parameters in the *.rec file under optimisation results. However I do not. I get this message: "Covariance matrix and parameter confidence intervals cannot be determined:- Some form or regularisation was implemented so these are not applicable."

Do any of you have an idea what I might have done wrong?

[Bill Dolinar]

You may be able to see the confidence interval by going into the MODFLOW | Parameters dialog, importing optimal values, then going into the MODFLOW | Parameter Estimation dialog and turning off both types of regularization, setting the maximum number of iterations (NOPTMAX) to -1, and then running MODFLOW. If the problem isn't "well-posed" you won't be able to get the information. It talks about this in John Doherty's PDF entitled "Getting the Most out of PEST" (http://www.pesthomepage.org/getfiles.php?file=pest_settings.pdf) on page 10:

When PEST is run in “estimation” mode and when it does not use singular value decomposition to solve the inverse problem, it records a parameter covariance matrix, together with parameter correlation coefficients and other uncertainty data, at the bottom of its run record file. However if any form of regularization is used (either Tikhonov regularization – as when it is run in “regularization” mode - or SVD/LSQR) these items are not recorded.

This is why. If a post-calibration parameter covariance matrix is to be computed using the traditional formula σ2(JtQJ)-1 where J is the Jacobian matrix and σ2 is the reference variance, then the inverse problem must be well-posed for this matrix to be calculable, and very well posed for it to have validity as an indicator of posterior parameter uncertainty. This does not happen often, for most problems that we encounter in environmental modelling embody more parameters than can be estimated uniquely. This is fine if regularization is used in solution of the inverse problem (either Tikhonov, SVD/LSQR, or both); PEST remains numerically stable and, if regularization is properly used, a minimum error variance solution to the inverse problem of model calibration can thereby be attained. However under these circumstances the posterior covariance matrix calculated under the assumption of problem well-posedness is incorrect (if it can be calculated at all).