Space-time interpolation of daily air temperatures

We propose a model to describe the mean function as well as the spatio-temporal covariance structure of 15 years of both maximum and minimum daily temperature data from 190 stations throughout the region of Catalonia (Spain), with daily data covering the period 1994-2008. Our aim is threefold: (a) estimation of the long-term trend of maximum and minimum temperatures; (b) assessing the spatial and temporal variability of temperatures, and (c) interpolation of the spatial temperatures at any given time. Long-term trend, annual harmonics and winds were considered as explanatory variables of the mean function. The parameters associated with these variables were allowed to vary between stations and within each year. We controlled temporal autocorrelation by means of ARMA models. For the spatial covariance structure we used the Matérn family of covariance functions and a nugget term. Spatio-temporal models were built as Bayesian hierarchical models with two stages following the integrated nested place Laplace approximation (INLA) for Bayesian inference. For the final model estimation we used a two-stage approach, in which we first assumed the stations were spatially independent, and then we modeled the spatio-temporal covariance using the interim posterior from the residuals of the model in the first-stage as prior distributions of replications of a spatial process. We allowed all spatial parameters to also vary with time.