Calibration and Reliability in Groundwater Modelling: Credibility of Modelling

(Proceedings of ModelCARE 2007 Conference, held in Denmark, September 2007). IAHS Publ. 320, 2008, 235-239.

Using many pilot points and singular value decomposition in groundwater model calibration

Steen Christensen¹ & John Doherty²

1 Department of Earth Sciences, University of Aarhus, Ny Munkegade building 1520, DK-8000 Århus, Denmark

sc@geo.au.dk

2 Watermark Numerical Computing, 336 Cliveden Ave, Corinda 4075, Queensland, Australia

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 modeller 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 normal matrix is used to reduce the large number of pilot point parameters to a smaller number of so-called super parameters that can be estimated by nonlinear regression from the available observations. A number of Eigenvectors corresponding to significant Eigen values (resulting from the decomposition) is used to transform the model from having many pilot point parameters to having a few super parameters. A synthetic case model is used to analyse and demonstrate the application of the presented method of model parameterization and calibration.

Key words pilot point; singular value decomposition; parameter estimation