Abstract
Probabilistic studies of hydrological variables, such as heavy rainfall daily events, constitute an important tool to support the planning and management of water resources, especially for the design of hydraulic structures and erosive rainfall potential. In this context, we aimed to analyze the performance of three probability distribution models (GEV, Gumbel and Gamma two parameter), whose parameters were adjusted by the Moments Method (MM), Maximum Likelihood (ML) and L - Moments (LM). These models were adjusted to the frequencies from long-term of maximum daily rainfall of 8 rain gauges located in Minas Gerais state. To indicate and discuss the performance of the probability distribution models, it was applied, firstly, the non-parametric Filliben test, and in addition, when differences were unidentified, Anderson-Darlling and Chi-Squared tests were also applied. The Gumbel probability distribution model showed a better adjustment for 87.5% of the cases. Among the assessed probability distribution models, GEV fitted by LM method has been adequate for all studied rain gauges and can be recommended. Considering the number of adequate cases, MM and LM methods had better performance than ML method, presenting, respectively, 83% and 79.2% of adequate cases.
Highlights
Probabilistic studies of hydrological variables such as heavy rainfall constitute an important element for supporting water resources planning and management
The Anderson - Darling test is an alternative at to the ChiSquare and Kolmogorov-Smirnov tests, as it gives more weight to the tails of the frequency distribution, being more recommended for asymptotic distributions (Naghettini; Pinto, 2007). We developed this studied aiming to analyze the performance of three probability distribution models (GEV, Gumbel and Gamma two-parameter), whose parameters were adjusted by Moments, Maximum Likelihood and L-moments methods, applied to longterm series of maximum rainfall daily events from eight rain gauges located in Minas Gerais state
It can be seen that Barbacena rain gauge shows the lowest dispersion statistical indicators, represented by the standard deviation (SD), range of variation (RV) and coefficient of variation (CV), followed by Estiva and Ouro Preto rain gauges
Summary
Probabilistic studies of hydrological variables such as heavy rainfall constitute an important element for supporting water resources planning and management. Among the features of great interest is the study of rainfall frequency associated to the maximum daily rainfall, whose behavior is strongly associated with the asymptotic distributions (Mello; Silva, 2005). Several studies in the literature have investigated the probability distribution models for extreme values of climate variables, especially the Gumbel and Generalized Extreme Value (GEV) models, which have produced better adjustments or performances. In the study of intense rainfall for the São Francisco Basin, Silva and Clarke (2004) concluded that the use of the Gumbel distribution could not be recommended for data sets throughout the San Francisco basin. Sansigolo (2008), comparing the Normal, Gumbel, Fréchet, Weibull, LogNormal and Pearson probability distribution models, adjusted to maximum daily rainfall and maximum absolute temperature data sets, for Piracicaba city, SP state, concluded that the Gumbel distribution obtained the best performance. Araújo et al (2010) evaluated the Gumbel, Gamma, Log-Normal, Normal, Weibull and Beta probability distribution models applied to
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