The Kalman Filter as Post-Processor for Analog Data–Model Assimilation in Paleoclimate Reconstruction

Abstract

We present an off-line paleo-data assimilation methodology that formally combines the analog assimilation method (AA) and the Kalman Filter (KF), utilizing the KF as a post-processor of the AA output. This methodology can be applied to reconstruct climate fields that are spatially separated from proxy-based reconstructions by using the spatial co-variability generated by a climate model. Our method is applied to a set of spatially resolved and spatially consistent climate reconstructions of several variables reflecting different seasons, incorporating the application of methodological variants that have undergone rigorous testing in terms of both improving statistical methodology and physical interpretation. This contrasts with applications primarily based on transfer relationships of annual means of local, single variable or bivariate, climate model priors into paleo proxy states. The gains from adding the KF post-processor are modest in our test case of reconstructing sea level pressure (SLP) geopotential height fields in the northeast Pacific, utilizing paleoclimatic temperature and moisture reconstructions in western North America. Notably, SLP reconstruction skill is enhanced in the oceanic region south of Alaska that is strongly associated with wet winters in western North America. The results suggest the AA method is approaching optimality in this test case, driven by the quality of the paleoreconstruction information used to drive the AA process, along with the realism of the climate model employed, to which the KF post-processing step is added. The derived reconstructions are then used for evaluation of the relationship between winter SLP and precipitation in California over the past ∼450 years.