Abstract
Abstract. Probabilistic spatial reconstructions of past climate states are valuable to quantitatively study the climate system under different forcing conditions because they combine the information contained in a proxy synthesis into a comprehensible product. Unfortunately, they are subject to a complex uncertainty structure due to complicated proxy–climate relations and sparse data, which makes interpolation between samples difficult. Bayesian hierarchical models feature promising properties to handle these issues, like the possibility to include multiple sources of information and to quantify uncertainties in a statistically rigorous way. We present a Bayesian framework that combines a network of pollen and macrofossil samples with a spatial prior distribution estimated from a multi-model ensemble of climate simulations. The use of climate simulation output aims at a physically reasonable spatial interpolation of proxy data on a regional scale. To transfer the pollen data into (local) climate information, we invert a forward version of the probabilistic indicator taxa model. The Bayesian inference is performed using Markov chain Monte Carlo methods following a Metropolis-within-Gibbs strategy. Different ways to incorporate the climate simulations into the Bayesian framework are compared using identical twin and cross-validation experiments. Then, we reconstruct the mean temperature of the warmest and mean temperature of the coldest month during the mid-Holocene in Europe using a published pollen and macrofossil synthesis in combination with the Paleoclimate Modelling Intercomparison Project Phase III mid-Holocene ensemble. The output of our Bayesian model is a spatially distributed probability distribution that facilitates quantitative analyses that account for uncertainties.
Highlights
Spatial or climate field reconstructions of past near-surface climate states combine information from proxy samples, which are mostly localized, with a model for interpolation between those samples
These properties transfer to the cross-validation experiments (CVEs) in which the models with a shrinkage covariance matrix perform better, too
The over-dispersiveness of the shrinkage models should be an indicator that this model is not underdispersed even in real-world applications that face additional challenges from potentially biased or under-dispersed transfer functions and a more sophisticated spatial structure of the climate state than in the earth system models (ESMs) climatologies
Summary
Spatial or climate field reconstructions of past near-surface climate states combine information from proxy samples, which are mostly localized, with a model for interpolation between those samples. They are valuable for comparisons of the state of the climate system under different external forcing conditions because they produce a comprehensible product containing the joint information in a proxy synthesis. Spatial reconstructions are subject to a complex uncertainty structure due to uncertainties in the proxy–climate relation and the sparseness of available proxy data, which leads to additional interpolation uncertainties. To account for uncertainties due to the sparseness of proxy data, we suggest the use of stochastic interpolation techniques.
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