An operational improvement of A-4DEnVar and its application to the estimation of the spatially varying bottom friction coefficients of the M2 constituent in the Bohai and Yellow seas

Abstract

The analytical four-dimensional ensemble variational (A-4DEnVar) data assimilation scheme inherits the advantages of the conventional four-dimensional variational (4D-Var) data assimilation scheme and removes the adjoint model. However, compatible operational improvements such as the reduction of the computational costs and the localization method should be considered when it is used in realistic systems. In this paper, the computational complexity of calculating the inverse of background error covariance (the B matrix) is decreased by a precondition transform method, i.e., introducing a new state variable whose product with the B matrix is the original state variable to be optimized in the cost function. Furthermore, an independent point (IP) scheme is combined to construct an implicit localization method and further decreases the computational cost. Based on the Princeton Ocean Model with the generalized coordinate system (POMgcs), the operational improved A-4DEnVar is applied to optimize the spatially varying bottom friction coefficients (BFCs) of the M2 constituent in the Bohai and Yellow seas. A twin experiment with idealized observations is designed to validate the effectiveness of the proposed method. In practical experiments, with no more than 10 IPs, the algorithm can assimilate observations from the National Astronomical Observatory (NAO) dataset and obtain a good simulation. The experimental performances increase with the increase of either the IPs or observations, which indicates the efficacy of the proposed algorithm.