Although more complicated to use, the increasing availability of climate proxies has led many studies to innovate and develop new approaches to reconstruct past climate indices or spatial fields (PAGES2k Consortium, 2019). While instrumental observations document climate variability over a relatively short period subject to anthropogenic forcing, climate proxies covering the Common Era (CE) are spatially sparser, less precise with a time resolution of about a year and provide partial information on the natural climate variability beyond the instrumental period (PAGES2k Consortium, 2017). Much of what is known about the climate system has been deduced from climate models, instrumental observations, climate proxies derived from natural archives (corals, speleothems, marine sediments, etc.) and our physical understanding of robust identified phenomena. This climate model emulator is then used to simulate large sets of particles that are optimally combined with the information provided by proxy records to deduce skillful spatial climate fields reconstructions and their low-frequency variability over the Common Era. Here we present a new Proxy Data Assimilation strategy that relies on a statistical model called LIM to reproduce the spatiotemporal dynamics of the surface temperatures simulated by costly CMIP-class climate models. These approaches are however confronted with limitations due to the use of expensive global climate models over long periods and the very large number of simulations required to correctly describe the space of possible climate states, which increases exponentially with the dimension of the problem. The field of paleoclimate data assimilation offers a way to extend the window of observation and provide physically consistent spatial fields by combining information from both CMIP-class climate models and proxy records documenting the last 2000 years. The length of the instrumental period is relatively short for investigating slow climate features and their regional impacts. To detect and attribute anthropogenic climate changes, it is necessary to quantify and understand the wide range of the natural climate variability. Our results indicate that the LIM yields dynamical memory improving climate variability reconstructions and support the use of the LIM as a GCM-emulator in real reconstruction to propagate large ensembles of particles at low cost in SIR PF. The PDA further provides a set of physically consistent spatial fields allowing robust uncertainty quantification related to climate models biases and proxy spatial sampling. Our results show that the LIMs allow for skillful ensemble forecasts at 1-year lead-time based on GCMs dynamical knowledge with best prediction in the tropics and the North Atlantic. We examine in a perfect-model framework the skill of the various LIMs to forecast the dynamics of the surface temperatures and provide spatial field reconstructions over the last millennium in a SIR PF. Here we present a new PDA approach based on a sequential importance resampling (SIR) Particle filter (PF) that uses Linear Inverse Modeling (LIM) as an emulator of several CMIP-class GCMs. Paleoclimate data assimilation (PDA) offers a powerful way to extend the short instrumental period by optimally combining the physics described by General Circulation Climate Models (GCMs) with information from available proxy records while taking into account their uncertainties. Assessing climate models ability to reproduce such natural variations is crucial to understand climate sensitivity and impacts of future climate change. Proxy records that document the last 2000 years of climate provide evidence for the wide range of the natural climate variability from inter-annual to secular timescales not captured by the short window of recent direct observations.
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