Intensity-Duration-Frequency equations (IDF) for the state of Paraíba, Brazil, and regionalization of its parameters

Abstract

In the design of major hydraulic structures, a key element is the design discharge, determined from the time series of flow or through runoff models such as the rational method, which relates the peak surface flow with a rainstorm. The design storm is generally established from the Intensity-Duration-Frequency (IDF) relationships via recording gauges data. In the absence/scarcity of these data, daily data from the rain gauge network can be used via the disaggregation process. Thus, the objective of this study is to develop the IDFs for the state of Paraíba, Brazil, where there is an extensive network of rain gauges (263 stations). For this purpose, daily precipitation data were disaggregated for various durations between 5 min and 24 hours and the best fit distribution was chosen among the Gumbel, Weibull, Pearson, Log-Pearson and Generalized Extreme Values (GEV) distributions for the time series of these durations. From the fitted distribution, rainfall for various durations and frequencies were obtained to generate the IDF curves for each location. No single satisfactory distribution was identified for all cases, with Pearson III and Log-Pearson III being the most common. For the IDF curves, the four-parameter equation was fitted and the parameter values were determined by non-linear regression. These varied a lot within the Paraíba state and were regionalized to obtain the IDF equation for any location in the state. The rainfall intensities obtained from the parameters determined in this study, when compared with those derived from the previously existing equations, show large differences and need updating.