An assessment on the shape parameter of the Generalized Extreme Value distribution of annual daily maximum precipitation in Brazil

Código

I-EBHE0202

Autores

Tomás Antonio Quezado Duval, Dirceu Silveira Reis Junior, SAULO AIRES DE SOUZA

Tema

WG 1.10: Hydrologic Design - Solutions & Communication

Resumo

An accurate description of the statistical behavior of extreme rainfall is critical for the design of many types of infrastructure, such as culverts, bridges and dams, and to assess the risk of large floods. One of the important questions in extreme precipitation analysis is which probability distribution should be used to statistically describe the pattern of extreme rainfall in a region. This paper reports an on-going effort to characterize the value of the shape parameter (?) of the Generalized Extreme Value (GEV) distribution, which ultimately defines which of the three distributions, Fréchet (?????), Gumbel (?????), or reversed Weibull (?????), should be used across different regions of Brazil. The shape parameter gains special attention here due to its importance in describing the tail of the distribution, which is closely related to the quality of representation of extreme events. For historical reasons and ease of computation, many extreme rainfall studies carried out in Brazil still use the Gumbel distribution as default, even though more recent studies developed by federal agencies have changed this picture by analyzing different possible distributions. Here, we employ approximately 3,800 rain gauges with at least 15 years of data to adjust the GEV distribution using three different estimators: L-moments (L-MOM), Maximum Likelihood (ML), and the Generalized Maximum Likelihood (GML), which uses a Beta prior distribution on ? with mean equal to ?0.10 and standard deviation equal to 0.122 to constrain the estimated ??to reasonable values. Results based on likelihood ratio test and information criteria (e.g. AIC and BIC) are not conclusive on which one of the three extreme value distribution is more adequate. However, regardless of the estimator used in the analysis, the majority of gauges are associated with a heavy tail distribution (Fréchet) with ?????. The average value of ??was equal to ?0.051 with standard deviation of 0.083. Restricting the sample size to gauges with at least 40 years of data, the average value of ??gets slightly lighter (?0.029) with standard deviation of 0.091. These results are relatively similar to those presented by Papalexiou & Koutsoyiannis (2013) with average equal to ?0.092 and a standard deviation of 0.12. Furthermore, we bring a discussion on how rain gauge record length might impact shape parameter values as we found ? estimates grew slightly as series length increased. As for quantile estimation, our analysis demonstrated that those obtained with the Gumbel distribution showed a tendency of being underestimated in relation to ones estimated with the other two GEV distributions. We observed that choosing to determine quantiles with the Gumbel over the other forms of the GEV distribution can lead to up nearly 10% of stations being underestimated by at least 15% for a 100-year return period, and that this underestimation increases with higher return periods.