Reduction of large-scale numerical ground water flow models

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Numerical models are often used for simulating ground water flow. Written in state space form, the dimension of these models is of the order of the number of model cells and can be very high (> million). As a result, these models are computationally very demanding, especially if many different scenarios has to be simulated. Therefore we introduce in this paper a model reduction approach to develop an approximate model with a significantly reduced dimension. The reduction method is based upon several simulations of the large-scale numerical model. By computing the covariance matrix of the model results, we obtain insight into the variability of the model behavior. Moreover, selecting the leading eigenvector of this covariance matrix, we obtain the spatial patterns that represent the directions in state space where the model variability is dominant. These patterns are also called Emperical Orthogonal Functions (EOFs). The original numerical model can now be projected onto the reduced space spanned by the dominant spatial patterns. The result is a low dimensional model that is still able to reproduce the dominant model behavior. In this paper we introduce the reduction approach and describe a real life application of the appraoch to a large-scale numerical ground water flow model.