Estimating rainfall erosivity by aggregated drop size distributions

Abstract

Abstract:Rainfall erosivity is defined as the potential of the rain to cause erosion, and it can be represented by rainfall kinetic power. At first in this paper, the raindrop size distributions (DSD) measured by an optical disdrometer located at Palermo in the period June 2006-March 2014 and aggregated for intensity classes, are presented. Then an analysis of raindrop size characteristics is carried out, and the reliability of Ulbrich's distribution, using both the maximum likelihood and momentum estimate parameter methods, is tested. The raindrop size measurements are used to determine the experimental rainfall kinetic power values, which are compared with the ones calculated by a theoretically deduced relationship. This analysis demonstrates that the kinetic power is strictly related to the median volume diameter of DSD. Finally, the reliability of the simplest Marshall and Palmer exponential DSD for estimating the rainfall kinetic power is demonstrated.

Reliability of rainfall kinetic power-intensity relationships

“…In particular, they showed that the median volume diameter, D 0 , increases with rainfall intensity until I = 40 mm h −1 , and then it assumes a quasi‐constant value. A similar trend was observed by Carollo et al () in the scatterplot P n / I versus I : P n / I increases with I for I < 40 mm/h and assumes a quasi‐constant value for I ≥ 40 mm/h. This result confirms the approach of Wischmeier and Smith () even if a lower intensity threshold value than I t = 76 mm/h was identified.…”

“…Carollo et al () demonstrated that the exponential distribution of Marshall and Palmer (), when it is referred to the unit area and time, can be assumed formally identical to a Gamma distribution (Ulbrich, ) with μ = 0.67 (Uijlenhoet & Stricker, ) and, as a consequence, from Equation it follows that provides the rainfall kinetic power when Λ parameter of Marshall and Palmer () distribution is known. Carollo et al (), using the following relationship (Uijlenhoet & Stricker, ; Ulbrich, ): obtained the following estimate of Λ parameter by momentum method and μ = 0.67: in which D 0 is equal to the one deduced from the measured DSD.…”

Characterizing rainfall erosivity by kinetic power - Median volume diameter relationship

“…Many other researches (Laws and Parsons, 1943;Atlas, 1953;Kelkar, 1959;Zanchi and Torri, 1980;Brandt, 1990;Jau-yau et al, 2008) propose a power law for describing the relationship D 0 -I implying that D 0 continues to increase indefinitely with I. This result is in contrast with other researchers which state that a maximum median volume diameter value is reached at high rainfall intensities (usually above 70-100 mm/h), after which the D 0 either stabilizes (Kinnell, 1981;Rosewell, 1986;Brown and Foster, 1987;Carollo et al, 2016a) or even decreases (Hudson, 1965;Baruah, 1973;Carter et al, 1974;Assouline and Mualem, 1989;Van Dijk et al, 2002).…”

“…This choice allows to exclude both rainfall having a low erosive power and DSDs having a small sample size (Carollo and Ferro, 2015;Carollo et al, 2016a). This procedure provided 45802 DSDs for Palermo and 5537 DSDs for El Teularet with a sampling time of 1 min (named single DSDs) characterized by I, determined by Eq.…”

“…This choice is justified by a previous analysis (Carollo et al, 2016b) which demonstrates that the available DSDs can be aggregated into rainfall intensity class since the DSDs falling into each class are not statistically different. In particular, the intensity class range was set equal to 1 mm/h for I < 30 mm/h, 2 mm/h for 30 < I < 50 mm/h, 5 mm/h for 50 < I < 100 mm/h and 10 mm/h for I > 100 mm/h (Carollo et al, 2016a). For each class, the rainfall intensity was calculated as average of the intensities of the single DSDs falling into the class.…”