Analysis of regional and global mean temperatures based on instrumental observations has typically been based on aggregating temperature measurements to grid cells. A potential deficiency in the uncertainty estimates for such gridded data is that the spatial statistical dependence between temperature anomalies is partly ignored or misspecified, in particular with respect to effects of the spherical geometry of the earth.
From a modelling perspective, a more natural approach is to construct a spatial stochastic model for the temperature field directly on the globe, together with a model for the measurements, without aggregation. Such a model can incorporate non-stationary spatial dependencies due to differences between the tropical and polar regions, as well as local covariate information such as topography.
Local and global yearly temperature means are then computed along with uncertainty estimates using a fast Bayesian numerical integration scheme. By using recent advances (Lindgren et al., 2010) in methods for constructing spatially consistent Markov random fields, the variations in statistical dependence between geographical locations can be estimated in a computationally efficient way. We use these methods to calculate reconstructions of the global climate in the past century, with fine spatial resolution in regions with dense data coverage, and coarse resolution in other regions. The full statistical uncertainty of the model parameters is included in the analysis.
F. Lindgren, H. Rue, and J. Lindström “An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach”, J. R. Statist. Soc. B, 73, Part 4 (2011).
Keywords: Climate reconstruction; spatial models; Gaussian Markov random fields; efficient computations
Biography: Finn Lindgren has a background in statistical image analysis, and is currently focusing on methodology for general spatial and spatio-temporal models for environmental data, using Gaussian Markov random fields based on stochastic partial differential equations. He has a special interest in developing accessible and computationally efficient software for large spatial data sets.