Simplified Kalman smoother and ensemble Kalman smoother for improvingocean forecasts and reanalyses

Dong et al. 2021 presented a post processing smoothing method for application inoperational ocean reanalysis products using the archive of sequential filterincrements. This simple smoother, based on a temporal decay parameter, iscapable of effectively reducing errors in global ocean reanalyses, especially where orwhen no observations are being assimilated (through assessment againstindependent data). Here we further exploit this smoothing method by implementingit in the Kalman filter (KF) and ensemble Kalman filter (EnKF), and comparing it’sperformance with traditional extended Kalman smoother (KS) and ensembleKalman smoother (EnKS) in the Lorenz 1963 model.We demonstrate that our smoothing algorithm is equivalent to the KS and EnKSexcept that the cross-time error covariances in the Kalman smoothers are modifiedas the Kalman filter error covariance multiplied by a cross-time decay term. Thesimplified KS and EnKS provide substantial improvement over the KF and EnKF withsmaller RMSE, while incurring very little computational or additional storage cost,such that there is significant potential of implementing these methods inoperational ocean forecasts and reanalyses.