Revista Recursos Hdricos

DOI:10.5894/rh34n2-1
O texto deste artigo foi submetido para reviso e possvel publicao em setembro de 2013, tendo sido aceite pela Comisso de Editores Cientficos Associados em outubro de 2013. Este artigo parte integrante da Revista Recursos Hdricos, Vol. 34, N 2, 5-12, novembro de 2013.

Anlise de frequncia de mximos anuais baseada em sries de durao parcial. Combinao das distribuies de Poisson inflacionada de zeros e generalizada de Pareto, modelo ZIP-GP

The peak-over-threshold approach applied to the flood frequency analysis of annual maximum discharges. A combined model of Zero-Inflated Poisson (ZIP) and generalized Pareto distributions

Artur Tiago Silva¹, Maria Manuela Portela¹, Mauro Naghettini²

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1 - Instituto Superior Tcnico, Lisboa, Portugal
2 - Universidade Federal de Minas Gerais, Belo Horizonte, Brasil

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RESUMO
Na anlise de frequncia de extremos hidrolgicos com recurso a sries de durao parcial, utiliza-se frequentemente um procedimento baseado na modelao do nmero de excedncias relativas a um dado limiar (ou seja, do nmero de picos) pela distribuio de Poisson e da magnitude dessas excedncias pela lei Generalizada de Pareto (GP) – modelo Poisson-GP. Tal modelo requer que seja validada a hiptese de que o nmero anual picos apresenta uma distribuio de Poisson, a qual, contudo, nem sempre se verifica em termos prticos. O presente artigo analisa uma distribuio alternativa para modelar o nmero anual de excedncias, nomeadamente, o modelo distributivo ZIP (zero-inflated Poisson), de dois parmetros. Adicionalmente, apresenta-se o formalismo resultante da combinao das distribuies ZIP e GP – modelo ZIP-GP – para anlise de frequncia de magnitudes mximas anuais apoiada em sries de durao parcial. Este ltimo modelo menos restritivo do que o de Poisson-GP, uma vez que propicia uma descrio mais precisa do processo de ocorrncia de cheias a partir de sries de durao parcial, designadamente, quando a fraco de anos sem picos excede a massa terica no ponto zero da distribuio de Poisson. O artigo contm um exemplo de aplicao do modelo ZIP-GP anlise da magnitude de cheias baseada em registos de caudais mdios dirios acima de dado limiar, incluindo a avaliao do desempenho de tal modelo relativamente ao modelo Poisson-GP. Os resultados alcanados evidenciam a superioridade do modelo ZIP-GP, principalmente para os menores quantis, e, consequentemente, validam a distribuio ZIP como alternativa distribuio Poisson para modelar a distribuio dos picos anuais numa abordagem baseada em sries de durao parcial.

Palavras-chave: Anlise de frequncia de extremos, sries de durao parcial, distribuio de Poisson inflaccionada de zeros, distribuio generalizada de Pareto.

ABSTRACT
In frequency analysis of hydrological extremes under a peaks-over-threshold (POT) approach, the model with Poisson arrival counts and Generalized Pareto (GP) distributed exceedances – Poisson-GP model is widely used. Such model requires the validation of the hypothesis that the distribution of the annual number of extreme events may be described by a Poisson distribution (Poisson hypothesis), which is not always verifiable in practical terms. The present study concerns the use of an alternative distribution for modeling the annual number of hydrological extremes - the Zero-Inflated Poisson (ZIP) distribution with two parameters.
A ZIP-GP model for extreme frequency analysis is proposed. This model is less restrictive than the Poisson-GP model since it allows for a more accurate description of the occurrence process in a POT framework if the fraction of years with no exceedances is significantly higher than the theoretical mass at zero of the Poisson distribution. An application of the ZIP-GP model to flood data from Northern Portugal and the evaluation of its performance relative to the Poisson-GP model is presented. The results show that the ZIP-GP model outperforms the Poisson-GP model, especially for lower quantiles, hence the ZIP distribution is a valid alternative to the Poisson distribution for modeling the annual occurrence counts of peaks in a POT approach for flood frequency analysis.

Keywords: Frequency analysis of hydrological extremes, peaks-over-threshold, zero-inflated Poisson distribution, generalized Pareto distribution.

 

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