General Method Based on Regressive Relationships to Parameterize the Three-Parameter Depth–Duration–Frequency Curve

Abstract

This paper aims to present simple regressive equations to estimate the parameters of the three-parameter depth–duration–frequency (DDF) curve (3p-DDF), which accurately expresses, for a preassigned return period, the relationship between the rainfall depth and the rainfall duration over large duration ranges, from below 1 h (i.e., tens of minutes) to above 1 h (up to 24 h). These equations are developed to relate their parameters to those of the two-parameter DDF curve (2p-DDF), which can be estimated more easily being based on more readily available data related to rainfall durations above 1 h. In the applications, the regressive equations are first calibrated using recent pluviographic data in northern Italy, Germany, and Sweden. Two validation steps are then carried out to test the equations in terms of estimated rainfall depths using the same data as those used in the calibration step and data of stations from other geographic areas, i.e., Sicily in southern Italy, and from the past century, respectively. The results obtained prove this methodology capable of providing reliable estimation of short-duration rainfalls with various return periods in the absence of measurements with fine temporal resolution.

Keywords

• depth–duration–frequency curves
• extreme events
• Gumbel distribution
• sub-hourly rainfall