Non-stationary frequency analysis of extreme daily rainfall in Sao Paulo, Brazil



This work is an assessment of frequency of extreme values (EVs) of daily rainfall in the city of Sao Paulo, Brazil, over the period 1933–2005, based on the peaks-over-threshold (POT) and Generalized Pareto Distribution (GPD) approach. Usually, a GPD model is fitted to a sample of POT values selected with a constant threshold. However, in this work we use time-dependent thresholds, composed of relatively large p quantiles (for example p of 0.97) of daily rainfall amounts computed from all available data. Samples of POT values were extracted with several values of p. Four different GPD models (GPD-1, GPD-2, GPD-3, and GDP-4) were fitted to each one of these samples by the maximum likelihood (ML) method. The shape parameter was assumed constant for the four models, but time-varying covariates were incorporated into scale parameter of GPD-2, GPD-3, and GPD-4, describing annual cycle in GPD-2, linear trend in GPD-3, and both annual cycle and linear trend in GPD-4. The GPD-1 with constant scale and shape parameters is the simplest model. For identification of the best model among the four models we used rescaled Akaike Information Criterion (AIC) with second-order bias correction. This criterion isolates GPD-3 as the best model, i.e. the one with positive linear trend in the scale parameter. The slope of this trend is significant compared to the null hypothesis of no trend, for about 98% confidence level. The non-parametric Mann–Kendall test also showed presence of positive trend in the annual frequency of excess over high thresholds, with p-value being virtually zero. Therefore, there is strong evidence that high quantiles of daily rainfall in the city of Sao Paulo have been increasing in magnitude and frequency over time. For example, 0.99 quantiles of daily rainfall amount have increased by about 40 mm between 1933 and 2005. Copyright © 2008 Royal Meteorological Society