A FIXED-LAG KALMAN SMOOTHER FOR RETROSPECTIVE DATA ASSIMILATION

Data assimilation has traditionally been employed to provide initial c onditions for numerical weather prediction (NWP). A multiyear time seq uence of objective analyses produced by data assimilation can also be used as an archival record from which to carry out a variety of atmosp heric process studies. For this latter purpose, NWP analyses are not a s accurate as they could be, for each analysis is based only on curren t and past observed data, and not on any future data. Analyses incorpo rating future data, as well as current and past data, are termed retro spective analyses. The problem of retrospective objective analysis has not yet received attention in the meteorological literature. In this paper, the fixed-lag Kalman smoother (FLKS) is proposed 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 e ach analysis time. A computationally efficient form of the FLKS is der ived. A simple scalar examination of the FLKS demonstrates that incorp orating future data improves analyses the most in the presence of dyna mical instabilities, for accurate models and for accurate observations . An implementation of the FLKS for a two-dimensional linear shallow-w ater model corroborates the scalar analysis. The numerical experiments also demonstrate the ability of the FLKS to propagate information ups tream as well as downstream, thus improving analysis quality substanti ally in data voids.