| Abstract: The accurate modeling of extreme events is growing in relevance, particularly in the environmental sciences in which such events can be seen as a result of climate change. In particular, measuring rainfall risk is also important for the design of hydraulic structures (dams, levees, drainage systems, bridges, etc.) and for flood mapping and zoning. The Brazilian regulatory agency, Agência Nacional de Águas (ANA), makes available rainfall series for 11,368 rain stations throughout Brazil, some of them dating from the 19th century. One of our goals was to produce, using the framework of extreme value theory, maps with reliable estimates of the 25-year return level of a extreme rainfall for each locality covered by ANA. Such dataset present many complex challenges: first, evaluating its quality; then, modeling spatial extremes over large random fields; modeling temporal nonstationarity of the extreme rainfall process due to natural climate seasonality and due to a possible trend owing to climate change; correcting biases resulting from misspecification of the model or from a small sample. In this study, we tackle all these issues. We perform a detailed quality control, and we make a deep discussion of biases resulting either from misspecification of the model or from a small sample, while providing important information regarding the modeling of rainfall extremes, and complementing recent previous studies. In particular, the shape parameter of the extreme-value model seems to have a mean asymptotic value of 0.06. |