Inverse modelling of groundwater flow using model reduction

This paper describes a reduced model for groundwater flow that reduces the computational burden necessary for inverse modeling. 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 finites differences.