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We evaluate Linear Inverse Models (LIMs) trained on last millennium model data to predict Arctic sea‐ice concentration, thickness, and other atmospheric and oceanic variables on monthly timescales. We find that more than 500 years of training data and 100 years of validation data are needed to reliably estimate LIM forecast skill. The best LIM has skill up to 8 months lead time and outperforms an autoregressive model of order one (AR1) forecast at all locations, with particularly large outperformance near the ice edge. However, for out‐of‐sample validation tests using data from various different model simulations and reanalysis products, they underperform an AR1 model due to differences in the location of the sea‐ice edge from the training data. We present a metric for predicting LIM forecast skill, based on the spatial correlation of the variance in the training and validation data sets.

 

Linear transformations are widely used in data assimilation for covariance modeling, for reducing dimensionality (such as averaging dense observations to form “superobs”), and for managing sampling error in ensemble data assimilation. Here we describe a linear transformation that is optimal in the sense that, in the transformed space, the state variables and observations have uncorrelated errors, and a diagonal gain matrix in the update step. We conjecture, and provide numerical evidence, that the transformation is the best possible to precede covariance localization in an ensemble Kalman filter. A central feature of this transformation in the update step are scalars, which we term canonical observation operators (COOs), that relate pairs of transformed observations and state variables and rank‐order those pairs by their influence in the update. We show for an idealized problem that sample‐based estimates of the COOs, in conjunction with covariance localization for the sample covariance, can approximate well the true values, but a practical implementation of the transformation for high‐dimensional applications remains a subject for future research. The COOs also completely describe important properties of the update step, such as observation‐state mutual information, signal‐to‐noise and degrees of freedom for signal, and so give new insights, including relations among reduced‐rank approximations to variational schemes, particle‐filter weight degeneracy, and the local ensemble transform Kalman filter.

 

Abstract Scientific understanding of low-frequency tropical Pacific variability, especially responses to perturbations in radiative forcing, suffers from short observational records, sparse proxy networks, and bias in model simulations. Here, we combine the strengths of proxies and models through coral-based paleoclimate data assimilation. We combine coral archives ( δ 18 O, Sr/Ca) with the dynamics, spatial teleconnections, and intervariable relationships of the CMIP5/PMIP3 Past1000 experiments using the Last Millennium Reanalysis data assimilation framework. This analysis creates skillful reconstructions of tropical Pacific temperatures over the observational era. However, during the period of intense volcanism in the early nineteenth century, southwestern Pacific corals produce El Niño–Southern Oscillation (ENSO) reconstructions that are of opposite sign from those from eastern Pacific corals and tree ring records. We systematically evaluate the source of this discrepancy using 1) single-proxy experiments, 2) varied proxy system models (PSMs), and 3) diverse covariance patterns from the Past1000 simulations. We find that individual proxy records and coral PSMs do not significantly contribute to the discrepancy. However, following major eruptions, the southwestern Pacific corals locally record more persistent cold anomalies than found in the Past1000 experiments and canonical ENSO teleconnections to the southwest Pacific strongly control the reconstruction response. Furthermore, using covariance patterns independent of ENSO yields reconstructions consistent with coral archives across the Pacific. These results show that model bias can strongly affect how proxy information is processed in paleoclimate data assimilation. As we illustrate here, model bias influences the magnitude and persistence of the response of the tropical Pacific to volcanic eruptions. 

Abstract We use theNorthern Hemisphere Tree-RingNetwork Development (NTREND) tree-ring database to examine the effects of using a small, highly-sensitive proxy network for paleotemperature data assimilation over the last millennium. We first evaluate our methods using pseudo-proxy experiments. These indicate that spatial assimilations using this network are skillful in the extratropical Northern Hemisphere and improve on previous NTREND reconstructions based on Point-by-Point regression. We also find our method is sensitive to climate model biases when the number of sites becomes small. Based on these experiments, we then assimilate the real NTREND network. To quantify model prior uncertainty, we produce 10 separate reconstructions, each assimilating a different climate model. These reconstructions are most dissimilar prior to 1100 CE, when the network becomes sparse, but show greater consistency as the network grows. Temporal variability is also underestimated before 1100 CE. Our assimilation method produces spatial uncertainty estimates and these identify treeline North America and eastern Siberia as regions that would most benefit from development of new millennial-length temperature-sensitive tree-ring records. We compare our multi-model mean reconstruction to five existing paleo-temperature products to examine the range of reconstructed responses to radiative forcing. We find substantial differences in the spatial patterns and magnitudes of reconstructed responses to volcanic eruptions and in the transition between the Medieval epoch and Little Ice Age. These extant uncertainties call for the development of a paleoclimate reconstruction intercomparison framework for systematically examining the consequences of proxy network composition and reconstruction methodology and for continued expansion of tree-ring proxy networks. 

Winds and pressure over the Southern Ocean are critical to many aspects of the climate system, but the brevity of climate data in this region makes it challenging to interpret recent changes. Here, we reconstruct 20th century sea level pressure and zonal surface wind anomalies over the Southern Ocean, using data assimilation with a global paleoclimate proxy database and four climate‐model priors. The reconstructions agree well with instrumental reanalysis products, especially in the circumpolar westerly and Pacific regions. We observe significant strengthening in the midlatitude Pacific westerlies, associated with a deepening Amundsen Sea Low, throughout the 20th century in all four reconstructions. When the prior includes anthropogenic forcing, we observe poleward‐shifting circumpolar westerlies throughout the 20th century. Our results highlight the combined roles of natural variability and anthropogenic forcing, and the zonally asymmetric character of atmospheric circulation changes at high southern latitudes, with implications for Antarctic ice sheet change.

 

Abstract. Reconstructions of past temperature and precipitation are fundamental to modeling the Greenland Ice Sheet and assessing its sensitivity to climate. Paleoclimate information is sourced from proxy records and climate-model simulations; however, the former are spatially incomplete while the latter are sensitive to model dynamics and boundary conditions. Efforts to combine these sources of information to reconstruct spatial patterns of Greenland climate over glacial–interglacial cycles have been limited by assumptions of fixed spatial patterns and a restricted use of proxy data. We avoid these limitations by using paleoclimate data assimilation to create independent reconstructions of mean-annual temperature and precipitation for the last 20 000 years. Our method uses oxygen isotope ratios of ice and accumulation rates from long ice-core records and extends this information to all locations across Greenland using spatial relationships derived from a transient climate-model simulation. Standard evaluation metrics for this method show that our results capture climate at locations without ice-core records. Our results differ from previous work in the reconstructed spatial pattern of temperature change during abrupt climate transitions; this indicates a need for additional proxy data and additional transient climate-model simulations. We investigate the relationship between precipitation and temperature, finding that it is frequency dependent and spatially variable, suggesting that thermodynamic scaling methods commonly used in ice-sheet modeling are overly simplistic. Our results demonstrate that paleoclimate data assimilation is a useful tool for reconstructing the spatial and temporal patterns of past climate on timescales relevant to ice sheets.