Assessment of alternative methods for analysing maximum rainfall spatial data based on generalized extreme value distribution

The present study aimed to analyze and spatially model maximum rainfall in the southern and southwestern regions of Minas Gerais using spatial statistical methods. Daily data on maximum rainfall were collected from 29 cities in the region. To obtain predictions of maximum rainfall for return periods of 2, 5, 10, 50, and 100 years, Bayesian Inference was employed, utilizing the most appropriate prior for each locality. The spatial analysis of the phenomenon based on results obtained through Bayesian Inference was conducted using interpolation methods, including Inverse Distance Weighting (IDW) and Kriging (Ordinary Kriging (OK) and Log-Normal Kriging (LK)). Different semivariogram models were used, and the most suitable one was selected based on cross-validation results for each method, which were also compared to those of IDW. Additionally, a spatial analysis was carried out using max-stable processes and spatial Generalized Extreme Value (GEV) distribution, with the models evaluated based on Takeuchi's Information Criteria. All models were also assessed by calculating the mean prediction error for six locations that were not used in model fitting. The results indicated that the most suitable models among Kriging and IDW for return periods of 2, 5, and 10 years were Gaussian (LK), Spherical (OK), and Wave (OK), respectively. Among the max-stable models and spatial GEV, the most suitable for modeling was the Smith max-stable model. Consequently, for spatial prediction over 50- and 100-year return periods, OK (Wave) and the Smith max-stable model were employed. The non-informative prior distribution showed better results for more cities compared to the informative one. Techniques from the Theory of Extreme Values, Bayesian Inference and Geostatistics were applied jointly. Predictions of up to approximately 180 mm of daily rainfall were obtained.