An Ensemble Kalman Smoother for Online Paleoclimate Data Assimilation

Abstract An integrated hybrid ensemble Kalman smoother (IHEnKS) is proposed to optimally utilize proxy data from the past to the future for paleoclimate data assimilation (PDA). As an extension of the integrated hybrid ensemble Kalman filter, IHEnKS assimilates future proxies through cross‐time error covariances, which are estimated from an online PDA by use of a deep learning‐based surrogate model. To mitigate the influences of sampling errors and model errors, an adaptively estimated covariance localization varying with spatial and temporal separations is adopted to eliminate the sampling errors in space and time. Moreover, a hybridization with climatological cross‐time error covariances through augmentation of lagged climatological perturbations are implemented. Consistent results are obtained from reconstructions of surface air temperature and sea surface temperature in both pseudoproxy and real proxy experiments. IHEnKS with spatial and temporal localizations and hybridization achieves the best reconstructions compared to various configurations of ensemble‐based assimilation methods. The advantages of IHEnKS become more pronounced as the proxy network becomes sparser.