A Hybrid Gain Analog Offline EnKF for Paleoclimate Data Assimilation

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. 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. 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