Inverse Shallow-Water Flow Modeling Using Model Reduction

Abstract

The idea presented in this paper is variational data assimilation based on model reduction using proper orthogonal decomposition. An ensemble of forward model simulations is used to determine the approximation of the covariance matrix of the model variability, and only the dominant eigenvectors of this matrix are used to define a model subspace. An approximate linear reduced model is obtained by projecting the original model onto this reduced subspace. Compared to the classical variational method, the adjoint of the tangent linear model is replaced by the adjoint of a linear reduced forward model. Thus, it does not require the implementation of the adjoint of the tangent linear model. The minimization process is carried out in reduced subspace and hence reduces the computational cost. Twin experiments using an operational storm surge prediction model in the Netherlands, the Dutch Continental Shelf Model are performed to estimate the water depth, with the findings that the approach with relatively little computational cost and without the burden of implementation of the adjoint model can be used in variational data assimilation.