Model selection in extreme value regression for estimation of changes in return values over time applied to extreme annual regional CMIP6 desert temperatures

Abstract Estimating changes in extremes quantiles from environmental processes which are non-stationary in time from small samples is challenging, since it is difficult to characterise the nature of tail non-stationarity adequately, and hence to estimate extreme quantiles in time. Using annual maxima and minima of near-surface temperature () from Coupled Model Intercomparison Project Phase 6 (CMIP6) output for a number of the Earth’s desert regions as illustration, we use generalised extreme value (GEV) regression to characterise changes in extreme quantiles over the next century. We consider a set of candidate models with different parametric forms for the variation of GEV parameters with time, estimating parameters using Bayesian inference. We seek to select the optimal candidate model using one of a number of model selection criteria, including the Akaike, Bayesian, divergence and widely-applicable “information criteria”. However, in an extreme value setting, the performance of different model selection criteria is unreliable. We therefore undertake a simulation study using ground truth models generating data qualitatively similar to annual temperature extrema, to assess the relative performance of the criteria to minimise error in prediction of change $$\Delta Q$$ in the 100-year return value of over the period (2015, 2125). In our application, the Bayesian information criterion (BIC) provides best performance, clearly out-performing the divergence and widely-applicable information criteria in particular. We compare BIC model selection with a stacked Bayesian model average. Using BIC-selected GEV regression models, we estimate joint posterior distributions of $$\Delta Q$$ , coupled over three climate scenarios, for different combinations of desert region, global climate model and climate ensemble. Aggregating posterior estimates over climate models and ensembles, we find evidence for significant increases in $$\Delta Q$$ for regional annual maxima under the stronger forcing scenarios for all desert regions. Similar but weaker and less significant trends are observed for regional annual minima. There is evidence that extreme minima are warming more rapidly than extreme maxima in Antarctica, whereas most hot desert regions exhibit the opposite effect.