Parameterization of Bernard’s Mathematical Model to Estimate Intensity-Duration-Frequency Curves in the Curitiba and São José dos Pinhais Sub-basins Belonging to the Upper Iguaçu River Basin, Brazil

Abstract

Abstract The main objective of this research was to generate the parameters of a mathematical model for predicting precipitation behavior in the Curitiba and São Jose dos Pinhais sub-basins, which belong to the upper Iguaçu basin. Initially, a time series of pluviographic records from five meteorological stations was acquired. These data underwent goodness-of-fit tests and probability distribution function analyses, revealing that the Gumbel distribution provided the best fit for the data from all five analyzed stations. Subsequently, the Gumbel distribution and the polynomial regression method determined the relationship between precipitation, intensity, duration, and frequency (IDF). IDF curves for different return periods were plotted using this established model as a function of precipitation event duration. The results showed that the Curitiba station recorded the highest rainfall (146.2 mm) within 24 hours in February 1990. Statistical analysis based on the Mann-Kendall test indicated that the rainfall values from the five stations analyzed exhibited a homogeneous distribution. These findings reveal that the future IDF curves will rise as time goes by, and a possible climate change may occur, which could be due to the various factors that affect the climate. In conclusion, this research successfully derived the parameters necessary for calculating the intensity of future precipitation events across different durations and return periods for the five stations analyzed.