[M-GI29] Data assimilation: A fundamental approach in geosciences

[MGI29-10] An iterative ensemble-based variational method with ensemble generation in random subspaces

*Shin ya Nakano^1,2 (1.The Institute of Statistical Mathematics, 2.Center for Data Assimilation Research and Applications, Joint-Support Center for Data Science Research)

Keywords:ensemble-based variational method, data assimilation

The ensemble-based method for variational data assimilation problems, referred to as the 4-dimensional ensemble variational method (4DEnVar), is a useful tool for data assimilation problems. Although the 4DEnVar is originally based on a linear approximation, highly uncertain problems, where system nonlinearity is significant, can be solved by an iterative algorithm which minimizes a quadratic function at each iteration. This iterative method can be regarded as an approximation of the Gauss-Newton method for solving 4-dimensional variational problems. Since ensemble-based methods basically seek the solution within a lower-dimensional subspace spanned by the ensemble members, it appears that the solution of this iterative method is confined within the subspace. However, the conditions for monotonic convergence to a local maximum of the objective function can be satisfied even if the ensemble is distributed in different subspace at each iteration. This study demonstrates that the iterative ensemble-based algorithm can solve high-dimensional problems if it is allowed that the ensemble can be generated in different subspace at each iteration.