Abstract
Intensity–duration–frequency (IDF) curves are empirical mathematical formulations that have been used for years in engineering for planning, design, and operation of hydraulic projects. The expression proposed by Sherman (1931) has been validated and used largely by many researchers. In all cases, the four parameters of this formulation are obtained through a numerical procedure. Although these parameters are obtained from historical rainfall observations, the optimization of these parameters implies an infinite combination between them and all those solutions would be valid. Of the four parameters, only one of them (C) has units, and for this reason, a physical sense of parameter C is searched for. Having certainty that some of them can be measured in situ would represent a great advance for modern hydrology. With data from 523 storms monitored every minute, a parametric adjustment was made to the Sherman equation and the typical duration of storms at each site was also obtained. To demonstrate how rainfall intensities vary with the change in C value, rainfall intensities calculations for of 5, 10, 15, and 20 min rainfall duration are used to validate the proposed methodology. The results show that typical storm duration is correlated with the additive parameter of Sherman’s formula.
Highlights
Rain is defined by two variables: magnitude and frequency, which is known as the precipitation regime
The magnitude of rainfall is the total precipitation that occurs in millimeters, while the frequency is associated with the storm duration
The precipitation intensity is directly proportional to the return period and inversely proportional to the storm duration
Summary
Rain is defined by two variables: magnitude and frequency, which is known as the precipitation regime. The frequency in terms of probability is expressed by the return period. The precipitation intensity is directly proportional to the return period and inversely proportional to the storm duration. The authors in [1] define intensity–duration–frequency curves (IDF) as the relationship between the mean precipitation intensity and the frequency of occurrence (inverse of the return period). Intensity–duration–frequency curves are applied worldwide in hydrological calculations to obtain the design precipitation depth, precipitation intensity, and return periods. These IDF curves are hydrologic risk analysis tools used in engineering for planning, design, and construction of hydraulic works, e.g., flood protection works [2]. The first researcher to find the relationship between 24-h precipitation and short-term precipitation was [3], who found that
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