Emprego da simulação de Monte Carlo na estimativa do fator de frequência adotado no cálculo da Precipitação Máxima Provável (PMP) pontual em uma região de clima equatorial sujeita a atuação convectiva

Abstract

The Maximum Probable 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, as it 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, the present research aimed to estimate K for calculating the PMP from series of maximum annual precipitation simulated by the Monte Carlo Method (MMC), for durations equal to and greater than 24 hours, in Barcarena/PA (latitude : -1.5058°; longitude: -48.6271°), an equatorial, hot and humid location in the North of Brazil, which is close to Belém/PA and bathed by Baia de Marajó. Furthermore, the results were evaluated and discussed in relation to other methods established in the literature: Original Hershfield Method (1961a, 1961b and 1965), Statistical Method with Regionalized Envelope, based on the work of Sarkar and Maity (2020), and Hydrometeorological Method. 52 rainfall stations were selected for the study, using climatological arguments of a convective nature, located around Barcarena/PA, with data between 1949 and 2023 and an average temporal extension of 34 years, of which 42 were suitable for the synthetic simulation, which comprised a MMC process with random generation of 5,000 random variables through extreme distributions. In the region under study, the highest maximum annual rainfall recorded in 24 hours was 467.4 mm. The results of the Statistical Method with Regionalized Envelope, based on the work of Sarkar and Maity (2020), presented a K of 24 hours, associated with the VILA DO CONDE Station (00148011) which represented the city of Barcarena/PA, equal to 8.42, the synthetic simulation with percentiles of 99% and 95% exposed Ks equal to 6.92 and 5.33, respectively. What can be concluded is that these frequency factor estimates were much lower than the K obtained by the Original Hershfield Envelope, which would promote a factor of 14.94. It was noted that the magnitude of the frequency factors of the Regional Envelopes decreases as the duration of precipitation increases (between 24 hours and 30 days). It is also reported that the construction of statistical models that better represent the local climatological condition, such as the synthetic simulation of frequency factors and the Regional Envelope of 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. One of the great advantages of synthetic simulation is to reduce the negative influence of series that have a short temporal duration or low data quality.