A line-search optimization method for non-Gaussian data assimilation via random quasi-orthogonal sub-spaces

This paper enhances the optimization method in [6] by using quasi-orthogonal vector bases and band matrices. Our approach employs the three-dimensional-variational (3D-Var) cost function to estimate posterior modes of error distributions. The proposed method works as follows: at each iteration, we estimate the 3D-Var cost function's negative gradient via a first-order Taylor approximation. This vector is then multiplied by random positive definite matrices to obtain a set of potential descent directions. We employ these directions to build an initial sub-space onto which partial analysis increments can be computed. Subsequently, we create a set of orthogonal directions to previous sub-spaces in a least-square sense; we search for additional analysis contributions onto the new directions via line-search optimization. Sub-space analysis increments are mapped back onto model spaces as they are found. We theoretically prove the convergence of our proposed optimization method. Experimental tests are performed by using the Lorenz-96 model. The results reveal that additional directions can improve the quality of analysis corrections during assimilation steps. Even more, as the sub-space dimension increases, the optimization method can converge faster to posterior modes of analysis distributions.

Automated summary

This study enhances the optimization method by employing 3D-Var cost function and specific matrix structures, and experimentally verifies the advantages of the new method in analysis correction quality and convergence speed.