Multiscale Methods of Data Assimilation

Achi Brandt
Department of Mathematics, Univeristy of California Los Angeles and Weizmann Institute

Following an introduction to general nonlinear multigrid algorithms, their many potential benefits for solving inverse PDE problems are explained, focusing on the problem of atmospheric data assimilation. The equations of very stable and adaptable implicit time steps can be solved at a cost comparable to that of explicit steps. The multiscale computation allows the data assimilation to account for correlation at all scales, at a cost again just comparable to solving the direct PDEs. Such computations can also facilitate full (not just initial-condition) control (which is more sensitive and accurate), yield flexible multiscale representation and fast inversion of full-matrix covariances, improve regularization (e.g., exploiting scale-dependent statistical theories), continuously fast-assimilate new observations, organize observational data in efficient hierarchical structures, and allow scale-dependent data types.

Last Update: September 27, 2005