Model-reduced Variational Data Assimilation in Groundwater Modeling

This paper describes a new approach to variational data assimilation that with a comparable computational efficiency does not require implementation of the adjoint of the tangent linear approximation of the original model. In classical variational data assimilation, the adjoint implementation is used to efficiently compute the gradient of the criterion to be minimized. Our approach is based on model reduction. Using an ensemble of forward model simulations, the leading EOFs are determined to define a subspace. The reduced model is created by projecting the original model onto this subspace. Once this reduced model is available, its adjoint can be implemented very easily and be used to approximate the gradient of the criterion. The minimization process can now be solved completely in reduced space with negligible computational costs. If necessary, the procedure can be repeated a few times by generating new ensembles closer to the most recent estimate of the parameters. The reduced model based method has been tested on several nonlinear synthetic cases for which the hydraulic conductivity was estimated.