Modeling of probability in obtaining intensity-duration-frequency relationships of rainfall occurrence for Pelotas, RS, Brazil

Abstract

Based on historical series, for each locality, equations can characterize the relationship between intensity, duration and frequency of rainfall occurrence. The objective of this study was to present two equations that can describe the occurrence of intense rainfall in Pelotas, RS state, over the period 1982-2015. The two equations were denominated conventional and hybrid, depending on the probabilistic model used. Following the conventional methodology, the parameters of Normal, Log-Normal, Gumbel and Gamma probability distributions were adjusted by the maximum likelihood method for return periods of 2, 5, 10, 20, 25, 50 and 100 years. The maximum intensity values for the hybrid equation were obtained using the empirical model of Weibull, considering return periods of 2, 5, 10, 20 and 25 years. On the other hand, the same theoretical distributions used in the conventional equation were applied to return periods of 50 and 100 years. The Kolmogorov-Smirnov test was used to select the best fitting distribution for the data. In order to verify the information acquired through the Weibull empirical model in comparison to the theoretical distributions, the t-test was applied to the angular coefficients. Significant differences were not verified between the values of maximum rainfall intensities obtained using the two methodologies, for the pre-established durations and return periods. Thus, considering the maximum rainfall intensities values (durations of 5-1440 min) and return periods of 2-100 years in the municipality of Pelotas, RS, Brazil, both the hybrid and the conventional intense rainfall equations can be used.

Seasonal intensity-duration-frequency relationships for Pelotas, Rio Grande do Sul, Brazil

“…The results for each duration and return period analyzed showed that the maximum rainfall adjusted for the summer using the Gumbel distribution was similar to that obtained through the IDF, as estimated by Dorneles et al (2019).…”

“…The results of the performance indices showed that the maximum summer rainfall series was similar to that obtained using the conventional method of Dorneles et al (2019). The RMSE values were 7.34 < x < 10.41, with the lowest RMSE value obtained for a 100-year return time.…”

“…The maximum rainfall values for 5-15 min durations showed the smallest differences between series across all return times analyzed, with the largest discrepancy corresponding to approximately 2.44 mm. Notably, however, although the maximum rainfall divergence for a two-year return time showed a greater divergence compared to those of Dorneles et al (2019), the maximum was 3.44 mm and lasted for 15 min.…”

“…The adjusted IDF relationships were compared with those obtained using conventional annual pluviographic data for the same location and period to determine the representativeness of the maximum intensities of seasonal rainfall. The following intensity equation was proposed by Dorneles et The maximum rainfall intensities associated with a given duration and return time corresponding to the summer and winter periods, and those conventionally determined by Dorneles et al (2019), were converted into maximum rainfall to examine the applicability of the results to engineering.…”

“…AER -aggregate error rate; NSC -Nash-Sutcliffe coefficient divided into three levels to evaluate: unsatisfactory (NSC < 0.50), satisfactory (0.50 < NSC < 0.65) and very good (0.75 < NSC < 1.00); h -number of terms in the series; Z i -maximum rainfall obtained from the IDF relationships determined using the conventional pluviographic method, mm (Dorneles et al, 2019); Z i -maximum rainfall determined based on the adjusted IDF relationships for the summer and winter periods, mm; and, Z i -the arithmetic mean of the maximum rainfall obtained from the IDF relationships determined using the conventional method, mm (Dorneles et al, 2019).…”