Climate variables interpolation by using INLA and the SPDE approach

Gridded observational datasets of the main climate variables are essential in climate science. However, common interpolation approaches (e.g., classical kriging-based methods), often lack of a proper propagation and representation of uncertainty. In this study, a Bayesian spatio-temporal regression model based on the Integrated Nested Laplace Approximation (INLA) and the Stochastic Partial Differential Equation (SPDE) is introduced. Although the effective use of INLA and SPDE is documented in several envitonmental studies, their use among climate practitioners is still quite limited. Here, based on high-resolution monthly 2-meter maximum (Tmax) and minimum (Tmin) air temperature, we employ INLA and SPDE to derive gridded monthly temperature climatologies for Italy both for the most recent standard 30-year period (1991–2020) and three previous standard periods (1961-1990, 1971-2000, 1981-2010). Our regression model includes three spatial predictors (elevation, latitude and distance to sea) and a linear time effect accounting for the  temporal trend in the observed monthly temperatures. A Matern field is used to capture the residual spatio-temporal correlation. Because of the large space-time domain of our study, the regression analysis is run separately for each month (January-December) and for each variable (Tmax/Tmin). Despite its simplicity, this approach provides a flexible model to produce accurate continuous gridded surfaces equipped with model-based uncertainties. Through simulation, we generate  a distribution of plausible gridded surfaces of Tmax and Tmin monthly means, which we summarize through measures of central tendency (posterior mean)  and variability (standard deviation). We use the standard deviation maps to investigate how uncertainty affects our estimates of the 1991-2020 monthly climatologies and where, and the 95% credible intervals maps to assess the regions where the  1991-2020 period is significantly warmer than the previous 30-year standard periods.