IDF curves and GEV reparameterization: verification and application across Brazilian territory

Código

I-EBHE0223

Autores

Alan de G. Barbosa

Tema

WG 1.02: Decomposing Complexity

Resumo

Intensity-duration-frequency (IDF) relationships are ubiquitous tools for the design and operation of stormwater drainage systems and flood control structures. Among several empirical formulations for deriving IDF curves, the model proposed by Koutsoyiannis, Kozonis e Manetas (1998) have stood out. These researchers suggested a reparametrization for the Generalized Extreme Value distribution (GEV) which, as opposed to the independent estimation of distinct models for a set of predefined times scales ? the most widespread procedure for rainfall frequency analysis ?, allows inferring all model parameters at once by aggregating information across time scales. This is particularly useful for estimating the GEV shape parameter, which is an acknowledge troubling procedure when only small samples are available ? a common situation when one is dealing with subdaily rainfall amounts. In effect, as demonstrated by Nadarajah, Anderson and Tawn (1998), the tail index of (heavy-tailed) variates is preserved during aggregation/averaging at distinct time scales, which increases the information content for inference and bypasses the usual problems of estimating unreasonable heavy tails from a few sample points. Despite of this fact, proper verification of the model assumptions ? constant tail index and coefficient of variation across durations ? is usually not performed when the reparametrization of Koutsoyiannis, Kozonis e Manetas (1998) is utilized by researchers and practitioners. Hence, this paper aims at providing a comprehensive asssessment of the empirical agreement between hourly precipitation data, as obtained from the Instituto Nacional de Meteorologia (INMET), and the theoretical reparametrized GEV model. For this, the distribution transformed parameters were estimated with the maximum likelihood estimators. We observed that, for most rainfall gauging stations, the model assumptions appear reasonable. Nonetheless, at some locations, we could not validate the reparametrized model, which indicates that further research is necessary for identifying possible reasons, from a physical perspective, for the lack-of-fit.