Reduced models for linear groundwater flow models using empirical orthogonal functions

In this paper we describe two reduced models that describe the hydraulic head h within three-dimensional groundwater flow models. We defined a reduced model structure as a linear combination of a set of spatial patterns P with time-varying coefficients r. The patterns were obtained by a data-driven indentification technique (Empirical Orthogonal Functions, EOFs), and they span a subspace of model results that captures most of the relevant information of the original model. Due to those patterns, we constructed two different formulations for dr/dt, by applying different projections: (1) a State-Space Projection (SSP) that projects a state-space formulation for groundwater flow; and (2) a Galerkin Projection (GP) that substitutes h within the PDE for groundwater flow by the reduced model structure P-T r, and projects the outcome onto the patterns. The SSP and GP have been both applied to a realistic case study with a negligible loss of model accuracy (Relative Mean Absolute Error< 0.5%). The dimension of r (16) was significantly reduced compared to the dimension of h (32,949) and hence we achieved a maximal reduction in computational time for the SSP approximate to 1/625 and for the GP approximate to 1/70 of the original time. Both reduced models have a promising prospect as their time reduction increases whenever the number of grid cells increases and the parameterization of the original model grows in complexity. (C) 2003 Elsevier Ltd. All rights reserved.