Using Model Reduction Methods within Incremental Four-Dimensional Variational Data Assimilation

Abstract

Incremental four-dimensional variational data assimilation is the method of choice in many operational atmosphere and ocean data assimilation systems. It allows the four-dimensional variational data assimilation (4DVAR) to be implemented in a computationally efficient way by replacing the minimization of the full nonlinear 4DVAR cost function with the minimization of a series of simplified cost functions. In practice, these simplified functions are usually derived from a spatial or spectral truncation of the full system being approximated. In this paper, a new method is proposed for deriving the simplified problems in incremental 4DVAR, based on model reduction techniques developed in the field of control theory. It is shown how these techniques can be combined with incremental 4DVAR to give an assimilation method that retains more of the dynamical information of the full system. Numerical experiments using a shallow-water model illustrate the superior performance of model reduction to standard truncation techniques.