Predictive error dependencies when using pilot points and singular value decomposition in groundwater model calibration |
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| Authors: | Steen Christensen John Doherty |
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| Institution: | 1. Department of Earth Sciences, University of Aarhus, Ny Munkegade Building 1520, DK-8000 Aarhus C, Denmark;2. Watermark Numerical Computing, 336 Cliveden Avenue, Corinda 4075, Queensland, Australia |
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| Abstract: | A significant practical problem with the pilot point method is to choose the location of the pilot points. We present a method that is intended to relieve the modeler from much of this responsibility. The basic idea is that a very large number of pilot points are distributed more or less uniformly over the model area. Singular value decomposition (SVD) of the (possibly weighted) sensitivity matrix of the pilot point based model produces eigenvectors of which we pick a small number corresponding to significant eigenvalues. Super parameters are defined as factors through which parameter combinations corresponding to the chosen eigenvectors are multiplied to obtain the pilot point values. The model can thus be transformed from having many-pilot-point parameters to having a few super parameters that can be estimated by nonlinear regression on the basis of the available observations. (This technique can be used for any highly parameterized groundwater model, not only for models parameterized by the pilot point method.) |
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| Keywords: | Pilot point Singular value decomposition Parameter estimation Calibration Prediction error Nonlinearity Tikhonov regularization |
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