A Fixed-Lag Kalman Smoother for Retrospective Data Assimilation

Data assimilation has traditionally been employed to provide initial conditions for numerical weather prediction (NWP). A multi--year time sequence of objective analyses produced by data assimilation can also be used as an archival record from which to carry out a variety of atmospheric process studies. For this latter purpose, NWP analyses are not as accurate as they could be, for each analysis is based only on current and past observed data, and not on any future data. Analyses incorporating future data, as well as current and past data, are termed retrospective analyses. The problem of retrospective objective analysis has not yet received attention in the meteorological literature. In this paper, we propose the fixed--lag Kalman smoother (FLKS) as a means of providing retrospective analysis capability in data assimilation. The FLKS is a direct generalization of the Kalman filter. It incorporates all data observed up to and including some fixed amount of time past each analysis time...