Testing The Exchangeability Of Two Ensembles Of Spatial Processes - Evaluating Proxy Influence In Assimilated Paleoclimate Reconstructions

Climate field reconstructions (CFR) attempt to estimate spatiotemporal fields of climate variables in the past, using climate proxies such as tree rings, ice cores and corals. CFRs have emerged as important datasets for studying the mechanisms of climate change and for assessing climate model performance. While many different CFR products and methods exist, Data Assimilation (DA) methods are a recent and promising new means of deriving CFRs that optimally fuse large collections of proxies with climate model information. Despite the growing application of DA-based CFRs, the extent of assimilation, i.e., how much the proxies have changed the statistical properties of the climate model data, is still poorly understood. To address this question, we propose a robust and computationally efficient method, based on functional data depth, to evaluate the differences in the distributions of two spatiotemporal processes. We apply our test to study global and regional proxy influence in DA-based CFRs by comparing the background and analysis states. We find that the analysis states are significantly altered from the climate-model-based background states due to the assimilation of paleoclimate proxies. Moreover the difference between the analysis and background states increases as the number of assimilated proxies increases, even in regions far beyond proxy collection sites. Our approach allows us to characterize the added value of proxies, indicating where and when the reconstructed fields are distinct from the climate model.