AFixed-Lag Kalman Smoother for RetrospectiveData 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 xed{lag Kalman smoother (FLKS) as a means of providing retrospective analysis capability in data assimilation. The FLKS is a direct generalization of the Kalman lter. It incorporates all data observed up to and including some xed amount of time past each analysis time. We derive a computationally e cient form of the FLKS. A simple scalar examination of the FLKS demonstrates that incorporating future data improves analyses the most in the presence of dynamical instabilities, for accurate models, and for poor observations. An implementation of the FLKS for a two{dimensional linear shallow{water model corroborates the scalar analysis. The numerical experiments also demonstrate the ability of the FLKS to propagate information upstream as well as downstream, thus improving analysis quality substantially in data voids. -2