An “offline” approach to DA is used, where static ensemble samples are drawn from existing CMIP climate‐model simulations to serve as the prior estimate of climate variables. We use linear, univariate forward models (“proxy system models (PSMs)”) that map climate variables to proxy measurements by fitting proxy data to 2 m air temperature from gridded instrumental temperature data; the linear PSMs are then used to predict proxy values from the prior estimate. Results for the LMR are compared against six gridded instrumental temperature data sets and 25% of the proxy records are withheld from assimilation for independent verification. Results show broad agreement with previous reconstructions of Northern Hemisphere mean 2 m air temperature, with millennial‐scale cooling, a multicentennial warm period around 1000 C.E., and a cold period coincident with the Little Ice Age (circa 1450–1800 C.E.). Verification against gridded instrumental data sets during 1880–2000 C.E. reveals greatest skill in the tropics and lowest skill over Northern Hemisphere land areas. Verification against independent proxy records indicates substantial improvement relative to the model (prior) data without proxy assimilation. As an illustrative example, we present multivariate reconstructed fields for a singular event, the 1808/1809 “mystery” volcanic eruption, which reveal global cooling that is strongly enhanced locally due to the presence of the Pacific‐North America wave pattern in the 500 hPa geopotential height field.

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The efficacy of a novel ensemble data assimilation (DA) technique is examined in the climate field reconstruction (CFR) of surface temperature. A minimalistic, computationally inexpensive DA technique is employed that requires only a static ensemble of climatologically plausible states. Pseudoproxy experiments are performed with both general circulation model (GCM) and Twentieth Century Reanalysis (20CR) data by reconstructing surface temperature fields from a sparse network of noisy pseudoproxies. The DA approach is compared to a conventional CFR approach based on principal component analysis (PCA) for experiments on global domains. DA outperforms PCA in reconstructing global-mean temperature in all experiments and is more consistent across experiments, with a range of time series correlations of 0.69–0.94 compared to 0.19–0.87 for the PCA method. DA improvements are even more evident in spatial reconstruction skill, especially in sparsely sampled pseudoproxy regions and for 20CR experiments. It is hypothesized that DA improves spatial reconstructions because it relies on coherent, spatially local temperature patterns, which remain robust even when glacial states are used to reconstruct nonglacial states and vice versa. These local relationships, as utilized by DA, appear to be more robust than the orthogonal patterns of variability utilized by PCA. Comparing results for GCM and 20CR data indicates that pseudoproxy experiments that rely solely on GCM data may give a false impression of reconstruction skill.

Hydroclimate extremes critically affect human and natural systems, but there remain many unanswered questions about their causes and how to interpret their dynamics in the past and in climate change projections. These uncertainties are due, in part, to the lack of long-term, spatially resolved hydroclimate reconstructions and information on the underlying physical drivers for many regions. Here we present the first global reconstructions of hydroclimate and associated climate dynamical variables over the past two thousand years. We use a data assimilation approach tailored to reconstruct hydroclimate that optimally combines 2,978 paleoclimate proxy-data time series with the physical constraints of an atmosphere—ocean climate model. The global reconstructions are annually or seasonally resolved and include two spatiotemporal drought indices, near-surface air temperature, an index of North Atlantic variability, the location of the intertropical convergence zone, and monthly Niño indices. This database, called the Paleo Hydrodynamics Data Assimilation product (PHYDA), will provide a critical new platform for investigating the causes of past climate variability and extremes, while informing interpretations of future hydroclimate projections.