Global temperature analysis with non-stationary random field models

Analysis of regional and global mean temperatures based on instrumental observations has typically been based on aggregating temperature measurements to grid cells. Due to the uneven data coverage, this makes analysis of the associated uncertainties difficult. We here present an alternative model based approach, where the climate and weather are modelled as random fields generated by a stochastic partial differential equation. Using the efficient Markov representations developed by Lindgren et al. (2011), direct numerical optimisation and integration with the R-INLA software provides Bayesian temperature reconstructions and associated uncertainties.