Technical Remarks on Smoother Algorithms

Among the currently existing data assimilation algorithms, 4D variational data assimilation (4D-VAR), 4D-PSAS, fixed-lag Kalman smoother (FLKS), and representer method as well as Kalman smoother belong to the smoother category. In this Office Note, the formulations of these smoothing algorithms are discussed from the Bayesian point of view. Their relationships are further explored for linear dynamics in the context of fixed-interval smoothing. The implementation approaches and computational aspects of the smoothing algorithms are also discussed and intercompared for the purpose of retrospective data assimilation. Finally, the extensions of the algorithms to nonlinear dynamics are presented. iii Contents Abstract iii 1 Introduction 1 2 Formulations of smoother algorithms in probabilistic framework 2 2.1 FLKS formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 3D-PSAS-like formulation of FLKS . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2...