Thursday, September 18, 2008

New Pest SVD Strategy

John Doherty recently suggested a new strategy for using Singular Value Decomposition (SVD) in Pest. This may be a bit confusing because the acronym SVD is used in two different ways in Pest and in Groundwater Vistas.

Many of you may be familiar with SVD-Assist, which is a way of reducing the number of estimated parameters, especially when calibrating a highly parameterized model (e.g. with pilot points). In Groundwater Vistas Advanced version, this is found on the Model/Pest/SVD Assist menu. To use this procedure, just start at the top and work down one menu item at a time. There are two big advantages of using SVD-Assist. The first is that you can often reduce the run time by a factor of 10. This is done by estimating a linear combination of model parameters called a super parameter. The number of super parameters is often only 5 to 10 percent of the total number of parameters. The utility SVDAPREP does all the work - you just need to tell it how many super parameters you want to use. The number of super parameters can be estimated using the utility SUPCALC (also now accessible in Groundwater Vistas on the SVD Assist menu). The other advantage is that the solution to the inverse problem is often more stable using this approach.

The other SVD used by Pest is a series of options in the Pest Control file. In Groundwater Vistas, this is accessed through Model/Pest/Options at the bottom of the dialog. Simply turn on the option that says "Use Singular Value Decomposition". The other key parameter here is the Eigenvalue threshold below the check-box. When using this type of SVD, the computational effort is the same as a normal Pest run. However, after making the model simulations to assemble the Jacobian Matrix, Pest will not try to estimate parameters that are insensitive (as determined by the Eigenvalue Threshold). This also makes the estimation more stable.

The new strategy suggested by John is to use both together. That is, you use SVD-Assist as you normally would but also turn on the regular SVD within the Pest Control file. In this way, if there are super parameters that are insensitive, Pest will not try to estimate them. The two SVD techniques together make the estimation even more stable. John suggests using an Eigenvalue Threshold of 1e-6 and estimate a few more super parameters than you might ordinarily try to estimate.


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