Multiparameter probability distributions for heavy rainfall modeling in extreme southern Brazil

Abstract

a b s t r a c t Study region: The study was conducted in the Rio Grande do Sul state -Brazil. Study focus: Studies about heavy rainfall events are crucial for proper flood management in river basins and for the design of hydraulic infrastructure. In Brazil, the lack of runoff monitoring is evident, therefore, designers commonly use rainfall intensity-duration-frequency (IDF) relationships to derive streamflow-related information. In order to aid the adjustment of IDF relationships, the probabilistic modeling of extreme rainfall is often employed. The objective of this study was to evaluate whether the GEV and Kappa multiparameter probability distributions have more satisfying performance than traditional two-parameter distributions such as Gumbel and Log-Normal in the modeling of extreme rainfall events in southern Brazil. Such distributions were adjusted by the L-moments method and the goodness-of-fit was verified by the Kolmogorov-Smirnov, Chi-Square, Filliben and Anderson-Darling tests. New hydrological insights for the region: The Anderson-Darling and Filliben tests were the most restrictive in this study. Based on the Anderson-Darling test, it was found that the Kappa distribution presented the best performance, followed by the GEV. This finding provides evidence that these multiparameter distributions result, for the region of study, in greater accuracy for the generation of intensity-duration-frequency curves and the prediction of peak streamflows and design hydrographs. As a result, this finding can support the design of hydraulic structures and flood management in river basins.

Hydrological regionalization of maximum stream flows using an approach based on L-moments

“…According to the Anderson-Darling non-parametric test (AD), the GEV model was the best PDF for most of the annual maximum stream flow series ( Table 2). This non-parametric test was specifically used for being quite robust and restrictive in identifying probabilistic models appropriate to represent asymptotic series, agreeing with the findings of other scientific studies (BEN-ZVI, 2009;FRANCO et al, 2014;BESKOW et al, 2015).…”

“…The Kappa, with parameters scale α, position ξ, and shape к and h, was the best fitted, according to the AD test, for two historical series. The superior applicability of Kappa, over the GEV, Gumbel and LN-2P PDFs, was observed by Beskow et al (2015) when analyzing the annual maximum daily rainfall in the state of Rio Grande do Sul, Brazil. Beskow et al (2015) were one of the pioneers in the use of the Kappa PDF applied to rainfall series in Brazil.…”

“…Because maximum stream flow tends to follow an asymptotic distribution, a better fit of the distribution tails is necessary (BESKOW et al, 2015). In this context, the Anderson Darling test (AD), which is considered superior (L'ECUYER; SIMARD, 2007) and more appropriate for this situation, as it assigns a greater importance to the extremes of the cumulative probability functions (HEO et al, 2013), was applied to evaluate the performance of the PDFs.…”

“…Hydraulic structures such as bridges, dams, culverts, collection and drainage systems, among others, require information on design stream flows, which are related to maximum stream flow events associated with predefined return periods (RPs) (BESKOW et al, 2015;KUMAR et al, 2003). In water resources management, the understanding of the hydrological behavior of a given basin related to the flood events aids in mitigating the impact of natural disasters and with flooded-area management.…”

Finding Probability Distributions for Annual Daily Maximum Rainfall in Pakistan Using Linear Moments and Variants

“…Different methods have been used for the goodness-of-fi t measure such as including the Chi-square method, quantile-quantile plots, mean absolute deviation index, LMRD, RMSE, KST, and ADT. These tests have been used by many authors [8,16,36,[41][42][43][44][45][46][47]. In this study we implemented three GOF tests -RMSE, KS, and AD -and one graphical method, i.e., LRD for visual inspection.…”