Development of a frequency factor upper envelope curve to calculate Probable Maximum Precipitation (PMP) in an equatorial climate region subject to convective activity

Código

I-EBHE0090

Autores

Vitor Matheus Passos Martins, Eber José de Andrade Pinto

Tema

WG 1.10: Hydrologic Design - Solutions & Communication

Resumo

The Probable Maximum Precipitation (PMP) is fundamental in the design of safety structures for large reservoirs. WMO (2009) presents two methods for estimating PMP: Hydrometeorological and Hershfield Statistical. In many situations, the Statistical Method is chosen, which is simpler, and only uses precipitation data. However, this methodology was developed by Hershfield in the early 1960s and with estimates for up to 24 hours. The data used in the construction of the method were located in the northern hemisphere, with 90% of the rainfall levels in the USA, a region with a temperate and cold climate. Tropical, hot and humid regions were not considered by the patriarch of the Statistical Method. Given this context, this article aimed to estimate K for calculating the Statistical PMP through Regional Envelopes, according to the work of Sarkar and Maity (2020), in Barcarena/PA (latitude: -1.5058°; longitude: - 48.6271°), an equatorial, hot and humid location in Northern Brazil, which is close to Belém/PA and bathed by Baia de Marajó. The envelope curve was drawn up for a duration of 24 hours through 52 pluviometric stations selected by climatological arguments of a convective nature within a radius of 200 km, located around Barcarena/PA, with data between 1949 and 2023 and an average temporal extension of 34 years. In the region under study, the maximum annual precipitation for 1 day was 467.4 mm. The frequency factors were estimated using the following equation: K=((X_máx- X ?_(n-1) ))?S_(n-1) , where X ?_(n-1) and S_(n-1) are, respectively, the mean and standard deviation excluding the maximum value of the series X_máx. The values of Ks used in the elaboration of the envelope curve (local frequency factors) ranged between 1.98 and 9.46, with a mean of 3.50, standard deviation of 1.38, median of 3.33, coefficient of variation of 0.39 and asymmetry of 1.91. The 24-hour envelope curve published by Hershfield (1965) presents higher Ks values than the regional curve. For example, using data from the Vila do Conde station, code 00148011, located in Barcarena/PA, the K associated with 24 hours extracted from the Regional Envelope was 8.42 and from the Original Hershfield Envelope, 14.94. Therefore, based on the Regional Envelope, the Statistical Point PMP is 480.4 mm, and if the Original Hershfield Envelope were adopted, it would be equal to 761.5 mm. These results indicate the need for caution when applying methods developed with data from other regions. Additionally, the Mann-Kendall test was applied to verify the stationarity of the 24-hour series and, of the 4 that indicated non-stationarity, all showed positive trends. Finally, it was concluded that the construction of Regional Envelopes of the Ks, according to Sarkar and Maity (2020), must be taken into consideration compared to the Envelope proposed by Hershfield, which contemplates a climatic reality very different from that seen in the North of Brazil and with an out-of-date rainfall data.