Adaptive Covariance Hybridization for the Assimilation of SST Observations Within a Coupled Earth System Reanalysis

Ensemble data assimilation methods, such as the Ensemble Kalman Filter (EnKF), are well suited for climate reanalysis because they feature flow-dependent covariance. However, because Earth System Models are heavy computationally, the method uses a few tens of members. Sampling error in the covariance matrix can introduce biases in the deep ocean, which may cause a drift in the reanalysis and in the predictions. Here, we assess the potential of the hybrid covariance approach (EnKF-OI) to counteract sampling error. The EnKF-OI combines the flow-dependent covariance computed from a dynamical ensemble with another covariance matrix that is static but less prone to sampling error. We test the method within the Norwegian Climate Prediction Model, which combines the Norwegian Earth System Model and the EnKF. We test the performance of the reanalyzes in an idealized twin experiment, where we assimilate synthetic sea surface temperature observations monthly over 1980–2010. The dynamical and static ensembles consist respectively of 30 members and 315 seasonal members sampled from a pre-industrial run. We compare the performance of the EnKF to an EnKF-OI with a global hybrid coefficient, referred to as standard hybrid, and an EnKF-OI with adaptive hybrid coefficients estimated in space and time. Both hybrid covariance methods cure the bias introduced by the EnKF at intermediate and deep water. The adaptive EnKF-OI performs best overall by addressing sampling noise and rank deficiencies issues and can sustain low analysis errors by doing smaller updates than the standard hybrid version.