Physical Parameterization of IDF Curves Based on Short-Duration Storms

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. the rainfall depths of 5, 10, 15, and 30 min are inversely correlated with the rainfall depth of one hour, establishing empirical factors 0.29, 0.45, 0.57, and 0.79 respectively. Using data from nearly 200 rain gauges, Hershfield found values for non-dimensional factors that allowed the transformation of daily rainfall data to calculate IDF curves. In this research, frequency analysis was performed by fitting the Gumbel and Lognormal probability functions, using the maximum rainfall depth accumulated in 24 h to provide functional mathematical relationships for desegregation of rainfall in minutes. Even today, the same distributions are used for the analysis of the maximum annual precipitation associated with duration of 1, 2, 3, 6, 12, 18, 24, 48, and 72 h [4]. There are different methods or approaches to obtain IDF curves. A considerable literature on IDF curves has been published. The reference studies for IDF curves for Australia were conducted by [5][6][7]. In Belgium, the reference IDF curves were presented by [8,9]. In Canada, a number of investigations in the field of IDF curves were published by [10][11][12][13][14][15][16]. In Denmark [17,18] used Sherman's formulation to define IDF curves. In Sweden, detailed studies have also been formalized to define IDF curves [19][20][21]. To date, various methods have been developed and introduced in Spain to compute IDF curves [22][23][24]. In Taiwan, IDF curves were prepared according to the procedure used by [25][26][27]. Reference [28] have recently developed a methodology for select IDF curves in China. In Peninsular Malaysia, a software tool for estimated IDF curves has been developed as an Excel add-in by using Visual Basics for Applications [29]. A site in Java, Indonesia, wa...

Methodological Guide to Forensic Hydrology

“…Landslide type (by origin) and height Landslide direction / movement type Landslide velocity Landslide impact pressure and soil material Note(s): 1 Physical flood vulnerability indicators-weighted in [26]. 2 Physical Parameterization of IDF Curves based on short-duration storms in [21]. 3 Suggested debris-flow magnitude classifications in [70].…”

“…The regime should understand the magnitude and frequency of an extreme event. In addition, particular interest should be focused on the increase in the frequency of high-intensity and short-duration storms [21]. The key to responding to this is the appropriate management of intervention protocols for an urban environment under rainy seasons, as well as effective hydraulic urban network operational procedures [22][23][24][25][26][27].…”

Journal of Water and Land Development

“…The reliability of the empirical model was investigated against the other formula, namely Sherman and Ishiguro, considering it is commonly used in the upstream area of the basin [GUTIERREZ-LOPEZ et al 2019]. The Sherman formula can be derived from Equation (2), while Equation (3) denotes the Ishiguro formula.…”

Estimation of the G2P Design Storm from a Rainfall Convectivity Index

“…However, this is not always possible, and many design storms are derived from statistical characterizations of maximum average intensities for different time scales to which a frequency or return period is associated (IDF curves). Nevertheless, the temporal structure may vary according to the selected storm duration and IDF parameters, as [21] demonstrated when using the Sherman equation, one of the most widely used IDF curve.…”