Title: A spatial modeling approach to high dimensional statistical paleoclimate reconstructions

Abstract: The study of climate over the earth's history is a topic of current interest whose relevance has increased rapidly with the growing concern over climate change. Reconstructing climates of the past (sometimes referred to as the "hockey stick" problem) has been used to understand whether the current climate is anomalous in a millennial context. To this end, various statistical climate field reconstructions (CFR) methods have been proposed to infer past temperature from (paleoclimate) multiproxy networks. We propose a novel statistical climate field reconstruction method that aims to use recent advances in statistics, and in particular, high dimensional sparse covariance estimation to tackle this problem. The new CFR method provides a flexible framework for modeling the inherent spatial heterogeneities of high-dimensional spatial fields and at the same time provide the parameter reduction necessary for obtaining precise and well-conditioned estimates of the covariance structure of the field, even when the sample size is much smaller than the number of variables. Our results show that the new method can yield significant improvements over existing methods, with gains uniformly over space. We also show that the new methodology is useful for regional paleoclimate reconstructions, and can yield better uncertainty quantification. We demonstrate that the increase in performance is directly related to recovering the underlying structure in the covariance of the spatial field. We also provide compelling evidence that the new methodology performs well even at spatial locations with few proxies. (Joint work with D.Guillot and J. Emile-Geay).