Paleoclimate data assimilation with adaptive observation error inflation and adaptive localization

Abstract. Paleoclimate data assimilation methods significantly enhance the accuracy, spatiotemporal continuity, and global relevance of climate reconstructions by integrating Earth system models with proxy records. In this study, we further improve the algorithm by implementing two adaptive strategies – adaptive observation error inflation and adaptive localization – and systematically evaluate their performance in reconstructing temperature data over equatorial regions. For the adaptive observation error inflation experiments, two distinct methods were employed: the adaptive observation error inflation (AOEI) method yields significant improvements in specific regions but also introduces local biases, whereas the Huber Robust Estimation (HAOEI) method provides more robust and spatially consistent enhancements overall. In the adaptive localization experiments, the localization radius and weight matrix at each grid point are dynamically adjusted based on observational density and correlation information. This strategy effectively utilizes sparse observational data, suppresses spurious teleconnections, accurately reproduces the spatial structure of dominant climate variability modes, and thereby enhances the overall stability of the analyzed field.