Bayesian geoadditive modelling of climate extremes with nonparametric spatially varying temporal effects

Abstract

Non-stationary modelling of climate extremes has attracted significant attention in recent years. Generalized extreme value (GEV) distribution is the standard approach for modelling block extremes. The non-stationary form of GEV distribution with location and scale parameters linearly regressing to time has been widely used for single-site time series of climate extremes. In the present paper, such a model is extended to be geoadditive for regional climate extremes with nonparametric spatially varying temporal effects. The model is implemented through the Bayesian hierarchical approach and is applied to the annual minimum surface air temperature in Mainland China as a demonstration. The five bivariate functions representing the regional regression parameters in the model are approximated by low-rank thin plate regression splines. All the necessary software tools for producing a thin plate regression spline basis and Markov Chain Monte Carlo sampling can be seamlessly integrated and called through the R software environment. Results show that the model can capture the spatial inhomogeneity and temporal non-stationarity features of regional climate extremes. Expressions for return levels with different return periods and their trends are also derived accordingly. Trends in different return levels, especially those in the ‘extreme state’ (e.g., 50-year return level) that cannot be inferred by usual observational trend analysis, can also be derived through samples drawn from posterior predictive distributions. The regional trend in a 50-year return level is quite different to that in a 2-year return level. More attention should be paid to trends in the extreme state of climate under climate change.