Suboptimal Schemes for Retrospective Data Assimilation Based on the Fixed-Lag Kalman Smoother

The fixed--lag Kalman smoother was proposed recently as a framework for providing retrospective data assimilation capability in atmospheric reanalysis projects (Cohn et al. 1994, Mon. Wea. Rev., 122, 2838--2867). Retrospective data assimilation refers to the dynamically--consistent incorporation of data observed well past each analysis time into each analysis. Like the Kalman filter, the fixed--lag Kalman smoother requires statistical information that is not available in practice and involves an excessive amount of computation if implemented by brute force, and must therefore be approximated sensibly to become feasible for operational use. In this article the performance of suboptimal retrospective data assimilation systems (RDASs) based on a variety of approximations to the optimal fixed--lag Kalman smoother is evaluated. Since the fixed--lag Kalman smoother formulation employed in this work separates naturally into a (Kalman) filter portion and an optimal retrospective analysis porti..