304017

Calibration and Reliability in Groundwater Modelling: From Uncertainty to Decision Making (Proceedings of ModelCARE’2005, The Hague, The Netherlands, June 2005). IAHS Publ. 304, 2006. pp.113–119.

Inverse modelling of groundwater flow using model reduction

P. T. M. Vermeulen¹ & a. w. heemink²

1 Netherlands Institute of Applied Geoscience TNO – National Geological Survey (TNO-NITG), PO Box 80015, NL-3508 TA Utrecht, The Netherlands

peter.vermeulen@tno.nl

2 Delft University of Technology, Faculty of Electrical Engineering, Mathematics and Computer Science, Department of Applied Mathematical Analysis, PO Box 5031, NL-2600 GA Delft,
The Netherlands

Abstract This paper describes a reduced model for groundwater flow that reduces the computational burden necessary for inverse modelling. The formulation follows from a projection of the original groundwater flow equation upon a set of basis vectors (i.e. patterns). Those patterns are computed by a decomposition of the covariance matrix for an ensemble of model evaluations. These represent the model behaviour with respect to model forces and a set of estimation parameters. By projecting (mapping) the original equations upon those patterns, a reduced model is obtained that can be used to solve a minimization problem with negligible computational costs. For several synthetic cases this reduced model found the global minimum more efficiently than the original model using adjoints or finite differences.

Keywords adjoint; Galerkin projection; inverse modelling; reduced model