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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. Plain Language Summary: Data assimilation is a statistical method that reduces uncertainty in a model, based on observations. Because of their ease of implementation, the ensemble data assimilation methods, that rely on the statistics of a finite ensemble of realizations of the model, are popular for climate reanalysis and prediction. However, observations are sparse—mostly near the surface—and the sampling error from data assimilation method introduces a deterioration in the deep ocean. We use a method that complements this ensemble with a pre‐existing database of model states to reduce sampling error. We show that the approach substantially reduces error at the intermediate and deep ocean. The method typically requires the tunning of a parameter, but we show that it can be estimated online, achieving the best performance. Key Points: Hybrid covariance handles sampling error and improves the update of deep water masses when assimilating surface observation with an Ensemble Kalman FilterThe method is well suited to provide a long coupled reanalysis of the past centuryHybrid covariance with adaptive hybrid coefficients explicitly estimated in space and time achieved the best performance [ABSTRACT FROM AUTHOR]

This study hybridizes the background error covariance (BEC) of the hourly atmospheric three-dimensional variational data assimilation (3DVar) in Local Analysis (LA) operated at Japan Meteorological Agency using the flow-dependent BEC derived from the singular vector-based Mesoscale Ensemble Prediction System (MEPS) and the static BEC. The impact of introducing the hybrid BEC into the 3DVar is examined, along with its sensitivities to various factors like the ensemble size that is augmented by using lagged ensemble forecasts, the weight given to the ensemble-based component of BEC, the localization scales, and the use (or not) of the cross-variable correlation. This hybrid 3DVar system can be operated with small additional computational cost because it has no coupling with another ensemble data assimilation system. In sensitivity experiments, this hybrid 3DVar is shown to yield smaller forecast root mean square errors than the pure 3DVar, especially for surface variables. Moreover, the hybrid 3DVar shows a better equitable threat score for strong precipitation. These improvements were greater in the experiments with larger ensemble sizes that were increased by using lagged ensemble forecasts because of the reduced sampling errors in the ensemble-based BEC. These results were sensitive to the weight given to the ensemble-based BEC and the horizontal localization scale, whose optimal values were found to be approximately 0.5 and 100 km, respectively. The longer vertical correlation scale and the cross-variable correlation were also found important to create dynamically-balanced analysis, which is especially true for heavy rain cases. [ABSTRACT FROM AUTHOR]

For Paleoclimate data assimilation (PDA), a hybrid gain analog offline ensemble Kalman filter (HGAOEnKF) is proposed. It keeps the benefits of the analog offline ensemble Kalman filter (AOEnKF) that constructs analog ensembles from existing climate simulations with joint information of the proxies. The analog ensembles can provide more accurate prior ensemble mean and "flow‐dependent" error covariances than randomly sampled ensembles. HGAOEnKF further incorporates the benefits of static prior error covariances that better capture large‐scale error correlations and mitigate sampling errors than the sample prior error covariances, through a hybrid gain approach within an ensemble framework. Observing system simulation experiments are conducted for various data assimilation methods, using ensemble simulations from the Community Earth System Model‐Last Millennium Ensemble Project. Results show that using the static prior error covariances estimated from a sufficiently large sample set is beneficial for the traditional offline ensemble Kalman filter (OEnKF) and AOEnKF. HGAOEnKF method is superior to the OEnKF and AOEnKF with and without static prior error covariances, especially for the reconstruction of extreme events. The advantages of HGAOEnKF over OEnKF and AOEnKF with and without static prior error covariances are persistent with varying sample sizes and presence of model errors. Plain Language Summary: Paleoclimate data assimilation (PDA) combines information from the climate simulations and proxy data, aiming to provide an optimal estimate of past climates. The relatively low predictive skill of the climate model and the noisy and sparse paleoclimate proxies have imposed great challenges on PDA. Previous studies have shown that offline ensemble assimilation methods are much more computationally efficient than online ensemble assimilation ones, and the offline analog ensemble can also provide "flow‐dependent" prior error covariances. However, the sample prior error covariances estimated from an ensemble with limited members can be contaminated by sampling errors. Hybridization of the "flow‐dependent" prior error covariances with the static ones can remedy the sampling error, and also infuse better representation of large‐scale error correlations from the static ones. Thus a hybrid gain analog offline ensemble Kalman filter (EnKF) is proposed, which retains the advantages of the analog ensemble and further adapts the benefits of static prior error covariances. The hybrid gain analog offline EnKF is superior to the traditional offline EnKF and the offline EnKF with analog ensembles. Key Points: Static B using sufficiently large samples can better capture large‐scale error correlations and mitigate sampling errors than the sampled BHybrid gain analog offline ensemble Kalman filter (HGAOEnKF) uses the ensemble mean prior from the analog ensemble and hybrid gains combining the static B and "flow‐dependent" BHGAOEnKF has advantages over OEnKF and analog offline ensemble Kalman filter with varying sample sizes and presence of model errors, especially for extreme years [ABSTRACT FROM AUTHOR]