ESTIMATING RAINFALL EROSIVITY BY DROP SIZE DISTRIBUTIONS

Water soil erosion is a process of detachment and transport of soil particles due to rainfall and runoff and it is the main cause of the modeling of extended portions of the earth's surface. The acceleration of the process through anthropogenic perturbation has severe impacts on soil and environmental quality. Soil erosion above a certain level will reduce soil productivity over the long haul. It exposes subsoil, which has often poor qualities for crop establishment and growth, and it can lead to stand loss by sediment deposition. A fundamental property of rainfall for understanding how it is made up is the raindrop size distribution (DSD). The knowledge of the raindrop size distribution at the surface is fundamental for understanding the precipitation mechanisms at upper levels, and so it has a direct influence on soil erosion processes. Rainfall erosivity, i.e. the capability of rainfall to detach soil particles, is the most important parameter for quantifying erosion processes and it can be represented by its kinetic energy per unit time and area, named kinetic power, Pn. Many researchers proposed empirical relationships estimating kinetic power by rainfall intensity and having different mathematical forms (polynomial, exponential, logarithmical, and power type) (Salles et al., 2002). The most commonly used relationship estimating Pn as function of rainfall intensity is that proposed by Wischmeier and Smith (1978) according to which the ratio between kinetic power and rainfall intensity, Pn/I, increases for rainfall intensity value less than or equal to a threshold value of rainfall intensity, It, equal to 76 mm h-1 and then it becomes constant for rainfall intensity greater than It. Wischmeier and Smith (1978) justified this threshold value suggesting that the median volume diameter, D0, (i.e. the diameter that divides the drop size distribution (DSD) in two parts of equal volume) does not increase when rainfall intensities exceed It. For describing this trend Kinnell (1981) proposed an exponential relationship between the kinetic power and the rainfall intensity, according to which the kinetic power per unit volume of rainfall has a finite positive value at zero intensity and approaches to an asymptotic value at high intensities. The rainfall kinetic power may be also determined by adding the contribution of single raindrops once their mass and terminal velocity are known. In other words, detachability of soil due to a rainfall event can be indirectly measured if the DSD and a relationship between terminal velocity and drop diameter are known. In particular, combining the Gamma distribution of Ulbrich (1983) and the terminal velocity relationship proposed by Ferro (2001), Carollo and Ferro (2015) deduced theoretically a relationship linking the ratio between kinetic power and rainfall intensity, Pn/I, to  and  parameters of Ulbrich’s distribution, underlining that Pn/I depends on the intrinsic characteristics of rainfall. In this thesis at first a review concerning the Rain Drop Size Distribution measurement techniques that have been used and improved during the years, Rain Drop Size Distribution types, focusing mostly the exponential and gamma distributions, Raindrop terminal velocity and Rainfall energetic characteristics is presented in the Chapter 1. In the other chapters the analysis on DSD measurements carried out at Palermo (Italy) and at El Teularet (Spain), using an optical disdrometer are presented. In particular in the period June 2006 – March 2014 the disdrometer was installed at the experimental site of SAF Department of the University of Palermo, registering during the 544 rainfall events more than 45000 DSDs. From July 2015 to May 2016, the disdrometer was installed at El Teularet and, during the 79 rainfall events over than 5000 DSDs were recorded. For both datasets at first the DSD analysis was carried out, highlighting the high variability of the main statistical index (mean diameter, (D), standard deviation (D), median diameter, D50, median volume diameter, D0) with I. However despite the dispersion of the data the standard deviation (D) and median volume diameter, D0, of the distribution seem to show a slight trend with I and the pairs (I, (D)) and (I, D0) referred to Palermo and El Teularet datasets are overlapped. This result suggests that the same rainfall intensity could generate different raindrop size distributions. The reliability of Ulbrich’s law for reproducing measured DSDs in both sites was positively verified using both maximum likelihood method and momentum methods (MM1 and MM2) for estimating  and  parameters of the distribution. The raindrop size measurements were used to determine the experimental rainfall kinetic power values, Pn. The experimental pairs (I, Pn/I) obtained by the two datasets are overlapped and it seems that the ratio Pn/I tends to increase when rainfall intensity increases. The measured Pn values allowed to verify positively the reliability of the relationship theoretically deduced by Carollo and Ferro (2015) for rainfall kinetic power estimate in Sicily and in Spain. The exponential distribution of Marshall and Palmer (1948), when it is referred to the unit area and time, can be assumed formally identical to a Gamma distribution (Ulbrich, 1983) setting  = 0.67. According to Ulbrich (1983), D0 is linked only to and  parameters so that, assuming =0.67, parameter can be deduced by only D0 value. Therefore, the relationship theoretically deduced by Carollo and Ferro (2015) for estimating kinetic power by  and values can be rewritten obtaining that the ratio Pn/I depends directly on median volume diameter D0. This relationship resulted fully applicable to estimate Pn/I in Mediterranean environments. For both datasets, in order to better focus the influence of rainfall intensity on DSD and rainfall energetic characteristics, the DSDs were aggregated in intensity classes. This procedure yields 59 DSDs for Palermo and 54 for El Teularet experimental sites characterized by rainfall intensity values ranging respectively from 0.8 to 203 mm/h and from 0.7 to 150 mm/h. The DSD analysis highlighted that, for a given rainfall intensity, the DSDs registered at Palermo present mean, median diameter and standard deviation values greater than the ones detected in El Teularet. Instead, the median volume diameter (D0) values are practically overlapped. In other words, for a given intensity, the rainfall occurring at El Teularet presents characteristics different from the one detected at Palermo. In any case, both datasets are characterized by similar trend with I: the mean and median diameter showed an increasing trend for the lowest values of rainfall intensity (I <15 mm/h), while no trend can be observed for I > 15 mm/h; the standard deviation and the median volume diameter of the distribution increase with rainfall intensity values until I = 40 mm/h and then become quasi-constant. The reliability of Ulbrich’s law for reproducing measured DSDs in both sites was positively verified using both maximum likelihood and momentum methods (MM1 and MM2) for estimating  and  parameters of the distribution. The aggregated raindrop size distributions were used to determine the experimental rainfall kinetic power values, Pn. The experimental pairs (I, Pn/I) obtained by the two datasets are overlapped. This circumstance implies that, in the two experimental sites, the same rainfall intensity determines different DSDs and similar kinetic power values. As well as D0, the ratio Pn/I increases with rainfall intensity for I less than or equal to 40 mm/h and then it becomes quasi-constant. This trend agrees with Wischmeier and Smith (1978) approach even if the threshold value of rainfall intensity (It = 40 mm/h) resulted less than the one proposed by Wischmeier and Smith (1978) (It = 76 mm/h). The measured kinetic power values were used for verifying in both sites the reliability of the most known empirical relationship for kinetic power estimate, i.e. Wischmeier and Smith (1978) and Kinnell (1981) relationships. The Wischmeier and Smith (1978) relationship is fully applicable for estimating the kinetic power of the rainfall both in Sicilian both in Spanish environments. In particular it does not need to be recalibrate but it is enough setting the threshold value of the rainfall intensity equal to 40 mm/h for obtaining a good estimate of the Pn. Instead of having an acceptable estimate of the rainfall kinetic power the relationship proposed by Kinnell (1981) needs to be calibrated on data. In fact for both datasets the use of the parameter values suggested by McGregor et al. (1995) allows a systematic underestimation of Pn, instead the parameter values suggested by Brown and Foster (1987) produce a systematic overestimation of the kinetic power for the highest values of rainfall intensity. Finally the comparison between the pairs (I, Pn/I and I, D0) corresponding to datasets of present investigation with the ones obtained in other sites of the world (Marshall Islands, New Jersey, Alaska, Indonesia, Oregon, Franklin, Hong Kong, Ethiopia) by different measurement techniques (drop camera, piezoelectric force transducer, blotting paper) was presented. In particular it highlighted that these datasets did not overlap. Therefore a single relationship Pn/I - I or D0-I is not reliable for estimating rainfall kinetic power at any site. Instead, the experimental pairs (D0, Pn/I) relative to all available datasets resulted quasi-perfectly aligned around a single increasing curve.The theoretically derived relationship linking Pn/I to D0 resulted fully applicable to all available datasets. This relationship represents a theoretical confirmation of the Wischmeier and Smith (1978) hypothesis according to which the Pn/I depends on median volume diameter that represents a variable free from at site effects and useful to characterized rainfall erosivity.