# Inverse modeling of groundwater flow using model reduction

Inverse modeling of groundwater flow using model reduction

Numerical groundwater flow models often have a very high number of model cells (greater than a million). Such models are computationally very demanding, which is disadvantageous for inverse modeling. This paper describes a low-dimensional formulation for groundwater flow that reduces the computational burden necessary for inverse modeling. The formulation is a projection of the original groundwater flow equation on a set of orthogonal patterns (i.e., a Galerkin projection). The patterns (empirical orthogonal functions) are computed by a decomposition of the covariance matrix over an ensemble of model solutions. Those solutions represent the behavior of the model as a result of model impulses and the influence of a chosen set of parameter values. For an interchangeable set of parameter values the patterns yield a low-dimensional model, as the number of patterns is often small. An advantage of this model is that the adjoint is easily available and most accurate for inverse modeling. For several synthetical cases the low-dimensional model was able to find the global minimum efficiently, and the result was comparable to that of the original model. For several cases our model even converged where the original model failed. Our results demonstrate that the proposed procedure results in a 60% time reduction to solve the groundwater flow inverse problem. Greater efficiencies can be expected in practice for large-scale models with a large number of grid cells that are used to compute transient simulations. Copyright 2005 by the American Geophysical Union.

SubjectCells

Computational methods

Computer simulation

Functions

Galerkin methods

Groundwater flow

Inverse problems

Mathematical models

Inverse modeling

Large-scale models

Low-dimensional formulation

Parameter values

Groundwater resources

flow modeling

groundwater flow

http://resolver.tudelft.nl/uuid:ba159cf5-7e65-4cd0-8437-8b3776ade91b

DOI TNO identifier238525

0043-1397

Water Resources Research, 41 (6), 1-13

Document typearticle

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