A Preconditioning Algorithm for Four-Dimensional Variational Data Assimilation

Abstract

A preconditioning method suitable for use in four-dimensional variational (4DVAR) data assimilation is proposed. The method is a generalization of the preconditioning previously developed by the author, now designed to include direct observations, as well as different forms of the cost function. The original approach was based on an estimate of the ratio of the expected decrease of the cost function and of the gradient norm, derived from an approximate Taylor series expansion of the cost function. The generalized method employs only basic linear functional analysis, still preserving the efficiency of the original method. The preconditioning is tested in a realistic 4DVAR assimilation environment: the data are direct observations operationally used at the National Centers for Environmental Prediction (formerly the National Meteorological Center), the forecast model is a full-physics regional eta model, and the adjoint model includes all physics, except radiation. The results of five 4DVAR data assimilation experiments, using a memoryless quasi-Newton minimization algorithm, show a significant benefit of the new preconditioning. On average, the minimization algorithm converges in about 20?25 iterations. In particular, after only 10 iterations, about 95% of the cost function decrease was achieved in all five cases. Especially encouraging is the fact that these results are obtained with physical processes present in the adjoint model.