An ensemble recentering Kalman filter with an application to Argo temperature data assimilation into the NASA GEOS-5 coupled model

A two-step ensemble recentering Kalman filter (ERKF) analysis scheme is introduced. The algorithm consists of a recentering step followed by an ensemble Kalman filter (EnKF) analysis step. The recentering step is formulated such as to adjust the prior distribution of an ensemble of model states so that the deviations of individual samples from the sample mean are unchanged but the original sample mean is shifted to the prior position of the most likely particle, where the likelihood of each particle is measured in terms of closeness to the assimilated observations. The computational cost of the ERKF is essentially the same as that of a same size EnKF. KF is applied to the assimilation of Argo temperature profiles into the OGCM component of an ensemble of NASA GEOS-5 coupled models. Unassimilated Argo salt data are used for validation. These data serve as a proxy to assess the potential of the ERKF to improve estimates of unobserved model variables. A surprisingly small number (16) of model trajectories is sufficient to significantly improve model estimates of salinity over estimates from an ensemble run without assimilation. The two-step algorithm also performs better than the EnKF although its performance is degraded in poorly observed regions. The efficacy of the recentering is attributed to its ability to preserve balance relationships between observed and unobserved variables, even when the ensemble size is too small for the EnKF to accurately estimate cross-field error covariances.