Efficient identification of uncertain parameters in a large-scale tidal model of the European continental shelf by proper orthogonal decomposition

The adjoint method can be used to identify uncertain parameters in large-scale shallow water flow models. This requires the implementation of the adjoint model, which is a large programming effort. The work presented here is inverse modeling based on model reduction using proper orthogonal decomposition (POD). An ensemble of forward model simulations is used to determine the approximation of the covariance matrix of the model variability and 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 with the classical variational method, the adjoint of the tangent linear model is replaced by the adjoint of a linear reduced forward model. The minimization process is carried out in reduced subspace and hence reduces the computational costs. In this study, the POD-based calibration approach has been implemented for the estimation of the depth values and the bottom friction coefficient in a large-scale shallow sea model of the entire European continental shelf with approximately 10 ⁶ operational grid points. A number of calibration experiments is performed. The effectiveness of the algorithm is evaluated in terms of the accuracy of the final results as well as the computational costs required to produce these results. The results demonstrate that the POD calibration method with little computational effort and without the implementation of the adjoint code can be used to solve large-scale inverse shallow water flow problems.