Estimation Theory in Atmospheric Data Assimilation: Simplified Methods for Filtering and Smoothing.

In this presentation we outline how the approach of state augmentation, in estimation theory, can be used to derive a fixed-lag smoothing algorithm for nonlinear dynamics and observation processes. This extended fixed-lag Kalman smoother will be seen to involve the commonly-known extended Kalman filter and a corresponding nonlinear extension of the smoother counterpart. The purpose of the fixed-lag smoothing is to design a retrospective data assimilation system to be utilized at the NASA/ Data Assimilation Office with the purpose of generating very accurate data sets for climate research. For many reasons, this algorithm is impractical for applications to atmospheric data assimilation, which motivates the investigation of approximate schemes. In this regard, we evaluate the performance of approximations to the Kalman filter and the fixed-lag Kalman smoother applied to a linear shallow-water model, for which there is an exact performance evaluation procedure. Results will be shown for this problem, and comments on the status of implementation of a retrospective analysis algorithm for the Goddard Earth Observing System 1 (click here for documentation) will be made.