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, which yields significant extreme improvements in specific regions but introduces notable local biases, and Huber Robust Estimation (HAOEI) method, which provides more robust and spatially consistent enhancement overall. In the adaptive localization experiments, observational density and correlation data were utilized to adjust the localization radius and weight matrix at each grid point. This approach effectively leverages sparse observational information, reduces spurious teleconnections, accurately reproduces the spatial structure of dominant climate variability modes, and optimizes the overall stability of the analyzed field.