UDK/UDC: 504.121:556.121(497.4) Prejeto/Received: 19.08.2016 Izvirni znanstveni članek - Original scientific paper Sprejeto/Accepted: 12.10.2016 Analysis of rainfall erosivity using disdrometer data at two stations in CENTRAL SLOVENIA Analiza erozivnosti padavin na dveh merilnih mestih v osrednji Sloveniji Z UPORABO PODATKOV Z DISDROMETROV Arturo Ciaccioni1, Nejc Bezak2, Simon Rusjan2^ 'Department of Agricultural, Food and Environmental Sciences, University of Perugia, Borgo XX Giugno 74, 06121 Perugia, Italy 2Faculty of Civil and Geodetic Engineering, University of Ljubljana, Jamova cesta 2, 1000 Ljubljana, Slovenia Abstract Erosive rainfall events can cause significant problems in agriculture and other fields because of fertile soil losses. Therefore, high-frequency measurements of rainfall data are useful in order to improve our knowledge about this issue. This study presents rainfall measurements in years 2013, 2014 and 2015 at two locations in central Slovenia, namely Ljubljana and Črni vrh nad Polhovim Gradcem, which are located in temperate-continental climate. 1-minute rainfall data analysed in this study was measured using optical disdrometer. Results indicate large variability in rainfall erosivity at relatively short distances. Some specific extreme events can lead to rainfall erosivity values up to average annual rates. Large seasonal variability of erosivity was also observed in the measured data. Moreover, several KE-I equations were tested and the results show that locally developed equations are more suitable to estimate rainfall erosivity in cases where no disdrometer data is available. Keywords: rainfall measurements, disdrometer, rainfall erosivity, seasonal variability. Izvleček Erozivni padavinski dogodki lahko povzročijo velike probleme v kmetijstvu in ostalih dejavnostih zaradi izgub rodovitne zemljine. Meritve padavin z visoko frekvenco zajema podatkov so s tega vidika uporabne za izboljšanje našega razumevanja o procesih erodiranja zemljine. V prispevku je predstavljena analiza meritev padavin v letih 2013, 2014 in 2015 na dveh lokacijah v osrednjem delu Slovenije, Ljubljani in Črnem Vrhu nad Polhovih Gradcem, ki ju lahko okarakteriziramo z zmernimi celinskimi podnebnimi značilnostmi. Minutni padavinski podatki uporabljeni v tej raziskavi so bili pridobljeni z optičnima disdrometroma. Rezultati kažejo na veliko spremenljivost erozivnosti padavin na relativno kratkih razdaljah. Erozivnost posameznih ekstremnih opazovanih padavinskih dogodkov lahko doseže letne vrednosti erozivnosti padavin na posamezni postaji. Na osnovi merjenih podatkov je bila opažena tudi velika sezonska spremenljivost erozivnosti. Nadalje so bile testirane različne enačbe, ki povezujejo kinetično energijo dežnih kapljic in intenziteto padavin (t.i. KE-I enačbe). Rezultati kažejo, da so enačbe pridobljene na osnovi lokalno merjenih *Stik / Correspondence: simon.rusjan@fgg.uni-lj.si © Ciaccioni A. et al.; Vsebina tega članka se sme uporabljati v skladu s pogoji licence Creative Commons Priznanje avtorstva -Nekomercialno - Deljenje pod enakimi pogoji 4.0. © Ciaccioni A. et al.; This is an open-access article distributed under the terms of the Creative Commons Attribution - Non Commercial - Share Alike 4.0 Licence. podatkov bolj primerne za oceno erozivnosti dežja v primerih, ko ni lokalno razpoložljivih podatkov z naprav kakršen je disdrometer. Ključne besede: meritve padavin, disdrometer, erozivnost padavin, sezonska spremenljivost. 1. Introduction Soil loss due to water erosion is an alarming phenomenon that leads to degradation of millions of hectares of croplands each year (Casazza, 2016). Several models for estimating soil loss are available (Angulo-Martínez et al., 2016), among these one of the most frequently used is the RUSLE method (Revised Universal Soil Loss Equation), developed by the USDA (United States Department of Agriculture) (USDA, 1997; Mikos et al., 2006). RUSLE equation consist of six factors that take into account the effect of rainfall erosivity (R), soil erodibility (K), slope length (L), slope steepness (S), land-use cover management (C) and support practice (P) (USDA, 1997). Direct measurements of erosion are needed to calibrate these models in different environmental conditions (Todisco et al., 2009). The erosivity of a rainfall is its ability to erode soil particles by splash and runoff (Angulo-Martínez et al., 2016). Technically it indicates detachment and transport capacity (Casazza, 2016), whereas physically it describes the process of disaggregation and detachment of soil particles due to the raindrop impact. Drop's diameter, mass, velocity, shape, fall height, force and impact pressure all influence the rainfall erosivity and consequently also soil erosion (Pandit and Isaac, 2015). The rainfall erosivity factor can be estimated using rainfall data and is frequently analysed in different environmental studies. Moreover, due to the climate change, the rainfall erosivity factor may change, which could lead to higher soil loss rates in the future (Zhang et al., 2010). To simplify the calculation and in order to correctly identify the erosivity one should use a single or few estimators that include the most important properties of these factors (Van Dijk et al., 2002). Both momentum and kinetic energy (KE) are good for this purpose (Fornis et al., 2005). As an example, RUSLE methodology uses KE to estimate rainfall erosivity (USDA, 1997). We can assume that each falling raindrop causes disaggregation and mobilization of soil particles because of its KE (Angulo-Martinez et al., 2016). Thus, the erosivity of a specific rainfall event is the sum of erosivity of all the drops (Carollo and Ferro, 2011). KE is a function of velocity and mass (KE=0.5mv2) and both quantities are functions of the dimension of the drops. Using the Drop-Size Distribution (DSD) and velocity data one can estimate KE. If the DSD is available, it is possible to calculate final fall velocity using various formulas (Kinnel, 1976; Hinkle et al., 1987; Cerro et al., 1998; Van Dijk et al., 2002; Angulo-Martinez et al., 2016; Casazza, 2016; Carollo et al., 2016). For practical purposes, a good estimation of the KE can be calculated based on the rainfall intensity (I), because of data availability and its relationship to the DSD. However, this indicator is only an approximation, because factors other than I determine the DSD (Van Dijk et al., 2002; Fornis et al., 2005; Carollo and Ferro, 2011; Pandit an Isaac, 2015; Angulo-Martinez et al., 2016). Large number of papers deal with this issue and several linear, polynomial, exponential, power low and logarithmic equations has been proposed (Table 1), confirming that a single relationship valid for all climate conditions around the world does not exist. In the area close to the location of measurements, the KE-I relationship usually fits well. Thus, it can be useful to develop equations for regions where they are still not available (Cerro et al., 1998; Pandit and Isaac, 2015; Angulo-Martinez et al., 2016; Casazza, 2016). Sometimes also local equations show spurious fit to different kinds of measured rainfall (Cerro et al., 1998; Van Dijk et al., 2002; Fornis et al., 2005; Angulo-Martinez and Barros, 2015) or at different elevation (even though studies are discordant on this issue) (Angulo-Martinez and Barros, 2015; Pandit and Isaac, 2015; Angulo-Martinez et al., 2016). A measuring equipment such as disdrometer is needed in the phases of developing and calibration of the KE-I relationship because it allows measurements of direct values of KE using the DSD information. Optical or laser disdrometers are the most recommended and also most widely used (Cerro et al., 1998; Fornis et al., 2005; Angulo-Martinez et al., 2016). Nevertheless, their measurements are affected by several errors due to intrinsic factors (limits of detection, simultaneous detection of drops, impact of raindrops on the device), and external factors (wind, natural coalescence and breaking of raindrops) (Salles and Poesen, 1999; Van Dijk et al., 2002; Lanzinger et al., 2006; Sasi Kumar et al., 2007; Angulo-Martinez et al., 2016). The difference among sensors causes difficulties in data comparison (Angulo-Martinez and Barros, 2015), while Lanzinger et al. (2006) showed disagreement among disdrometers of the same model. When comparing measurements of intensity and rainfall depth using disdrometers with the same data from a rain gauge, some studies noticed an overestimation (Fornis et al., 2005; Lanzinger et al., 2006, Petan et al. 2010), while others noticed an underestimation (Salles and Poesen, 1999; Sasi Kumar et al., 2007; Angulo-Martinez and Barros, 2015) of the data measured with disdrometer. KE itself is not sufficient to represent rainfall erosivity. Another factor that should be taken into account is the temporal distribution of rain intensity. Usually rainfall has low average intensity with some peaks. In order to obtain the rainfall erosivity index (EI) for RUSLE equation, KE must be multiplied with the highest thirty-minute intensity (IJ0) (USDA, 1997; Van Dijk et al., 2002; Mikoš et al., 2006; Angulo-Martinez et al., 2016; Casazza, 2016). The main aim of this study was to analyse rainfall erosivity using 1-minute rainfall data measured at two locations in Slovenia. The specific aims of the study were as follows: (i) to calculate the KE and EI using the DSD data for the stations in Ljubljana and Črni vrh nad Polhovim Gradcem, (ii) to evaluate suitability of several KE-I equations and (iii) to analyse temporal variability in the rainfall erosivity. 2. Methodology Data from two optical disdrometers located in Črni vrh nad Polhovim Gradcem and in Ljubljana (Figure 1) was used in this study in order to observe and analyse properties of rainfall erosivity. Rainfall depth data from these two disdrometers are available in real-time at (KSH, 2016): http://ksh.fgg.uni-lj.si/avp/DisCrniVrh/ (more information about these disdrometers including photos is also available). The elevation of the disdrometers is about 310 and 810 m.a.s.l. for the Ljubljana and Črni vrh disdrometer, respectively. Figure 2 shows the annual precipitation for these two stations for the period from 1981 to 2010 (ARSO, 2016). Average annual precipitation in the period from 1981 to 2010 was about 1360 and 1580 mm for the Ljubljana and Črni vrh stations, respectively. The rainfall variability at both locations is generally large, whereas summer thunderstorms mostly have the maximum rainfall erosivity. The intensity-duration-frequency curves derived for these two stations are available at: http ://meteo .arso.gov .si/uploads/probase/www/cli mate/table/sl/by variable/return-periods/Ljubljana%20Bezigrad.pdf and http: //meteo.arso.gov .si/uploads/probase/www/cli mate/table/sl/by_variable/return-periods/Crni%20Vrh%20nad%20Polhovim%20Gr adcem.pdf for the Ljubljana and Črni vrh stations, respectively. Disdrometer data from Ljubljana was collected in the periods from 08/08/2013 to 14/07/2014, from 12/08/2015 to 08/09/2015, and from 01/10/2015 to 25/01/2015. Parsivel 1 disdrometer by OTT, which classifies the raindrops into 32 classes of diameter and 32 classes of speed, producing 1024 classes in total, was used (OTT, 2008). This disdrometer was used in previous studies of rainfall erosivity in Slovenia (e.g., Petan, 2010). Data from Črni vrh nad Polhovim Gradcem was collected in the period from 16/07/2014 to 17/12/2015. Laser Precipitation Monitor 5.4110 by Thies Clima, which classifies raindrops in 22 classes of diameter and 20 classes of speed, producing 440 classes in total (Thies Clima, 2006), was used in this case study. Figure 1: Location of the optical disdrometers on the topographic map of Slovenia. Slika 1: Lokacija dveh optičnih disdrometrov na topografski karti Slovenije. 2500 1= £ 2000 £ 1000 a i 500 □ Ljubljana ■ Črni vrh ooooooooooooooooooaiait^t^aiaiaiaiaic^ 1111111111111111111 Year oooooooooo^h 00000000000 22222222222 Figure 2: Annual precipitation values for the Ljubljana and Črni vrh nad Polhovim Gradcem stations. Slika 2: Povprečne letne vrednosti padavin za postaji Ljubljana in Črni vrh nad Polhovim Gradcem. Both devices are laser disdrometers that produce a laser beam that is detected (as voltage) by a sensor on the other side of the detection area; the reduction in voltage due to the raindrops passing through the beam makes it possible to determine the dimension of raindrops. In the same way, from the interfering time the device determines the speed of each raindrop (Thies Clima, 2006; OTT, 2008). Both disdrometers measure several rainfall characteristics such as DSD, rainfall intensity, rainfall depth and precipitation type at 1-minute time intervals. Therefore, 1-minute disdrometer data was used in this study. Before calculating the 0 rainfall erosivity it was necessary to pre-process the data. Classes with diameter larger than 7 mm were not considered in the calculations of the rainfall erosivity because, according to Petan et al. (2010), such large drops are often artefacts of the device, which detects multiple overlapping raindrops as one drop. Since disdrometers detect the type of precipitation for each 1-minute time interval, it was relatively straightforward to discard minutes with solid winter precipitation (SYNOP code wawa table 4680 types from 67 to 88). Hail (code SYNOP wawa table 4680 types 88 and 89) is usually associated with very intense rainfall, thus it should also be considered for erosivity. Nevertheless, minutes of hail were also detected during snow events. Preprocessing of the data showed that hail events in winter were not meaningful. Thus, minutes with hail during the meteorological winter (December, January and February) (Trenberth, 1983) were not considered in further calculations. Intensity (I in mmh-1) was calculated from DSD measured by the disdrometer using the formula from Petan et al. (2010) (equation 1): I = n 6-A-At ni ■ C'lD?dD, (1) Ob,l-Oa,l where A (mm2) is the area of detection, At (1/60 h) is the interval of data collection, ni is the number of detected raindrops in the size class I and Di (mm) is the raindrop class diameter ranging from Da,i to Db,i. According to the RUSLE methodology, minutes with rain intensity lower than 0.1 mm h-1 were considered as not rainy (Petan, 2010). Furthermore, minutes with I calculated from DSD larger than the selected threshold level (0.1 mmh-1), but with zero value of I measured from disdrometer, were not considered in the analysis, because they are probably the result of an incorrect measurement. Rainfall events were considered as separate if there was a 6-hour interval with no rain between two consecutive events. Moreover, according to the RUSLE manual (USDA, 1997) only rainfall events larger than 12.7 mm, or with more than 6.35 mm in 15 minutes were considered for the calculations of the rainfall erosivity factor (R). The R factor of the RUSLE equation is the sum of the event's EI (multiplied by 10-2 to obtain the result in MJ mm ha-1h-1). The calculation of average annual R factor is based on rainfall erosivity in multiple years (equation 2) (USDA, 1997): R _ zlEI N (2) where j is the number of events, N the number of years, and EI (Jmmm-2h-1) the erosivity index of each rainfall event. As stated in the introduction, EI of an event is calculated with the following equation (3) (USDA; 1997): EI=KEIsa, (3) where KE (Jm-2) is total kinetic energy of the rainfall and I30 (mm h-1) is the maximum 30-minute intensity. KE per hour (Jm-2h-1) was calculated using the disdrometer data with the formula from Petan et al. (2010): KE = p-n 12-W3-A-At 1 rVhi 22 Vb,i-Va,i Jva,l J-- JlDbji-Da,i 1 I^Df'dD ■ r'vfdv, (4) where, in addition to abovementioned terms, p (kg m-3) is the water density and vi (m s-1) is the raindrop fall velocity of the class i ranging from vai to vb,i. The results calculated using the disdrometer data were compared with KE estimations using 13 different KE-I relationships, chosen from different references (Table 1). The equations were selected based on the geographical criterion, meaning that equations developed for regions close to Slovenia or with similar climate characteristics were used. All equations that had been developed for Europe were tested. Some others equations were also selected due to the following reasons: • Equation from Van Dijk et al. (2002) since it was defined as general for all climate types; • Equation from Brandt (1990) because it is used in the EUROSEM (EUROpean Soil Erosion Model) (Morgan et al., 1998); Equations from Brown and Foster (1987), and USDA (1997) because they are used for USLE-RUSLE model, considered good for Slovenian Alps by Mikoš et al. (2006). 3. Results and discussion 3.1 Calculation of KE and EI using disdrometer data As a result of the procedure described in Methodology, 39 independent rainfall events were recognised as erosive according to the mentioned criteria (RUSLE methodology) for the Črni vrh nad Polhovim Gradcem measuring station, while at the Ljubljana measuring station 52 erosive events were identified. In the next step the EI values were calculated for these events for both stations. EI values vary among events in the range from 3.79 MJmmha-:h-1 to 1025.42 MJmmha-1h-1 in Ljubljana and from 6.08 MJmmha-1h-1 to 2926.96 MJmmha-:h-1 for the Črni vrh nad Polhovim Gradcem station. In both cases the distribution of the EI values is asymmetric, with median considerably lower than mean; this indicates that EI for the majority of events is quite low, but in the observed time periods some relatively high or even extreme events occurred (Figure 3). Furthermore, one can also see that mean EI value for events measured in the Črni vrh stations is higher than for the Ljubljana station. Moreover, also the maximum EI value for the Črni vrh station is much higher than for the Ljubljana station. This high value is associated with an extreme flood that occurred in the headwaters of the Gradaščica River catchment in August 2014 (Bezak et al., 2016). However, direct comparison of calculated EI values between the two stations is not possible because different time period of data was used in this study. In the period of data collection three events occurred that had return period of maximum 30-minute intensity larger than 5 years (Table 2). These return periods were determined using the intensity-duration-frequency (IDF) curves derived by the Slovenian Environment Agency (ARSO) and are available at: http://meteo.arso.gov.si. Rainfall event that occurred on the 5th of August 2014 had a return period larger than 100 years. This event caused intense soil erosion and sediment transport processes with flash floods in the Gradaščica River catchment (Bezak et al., 2016). The consequences of this event were the worst in the headwater part of the Gradaščica catchment (e.g. Mačkov graben area). The other two events that happened in autumn 2014 were not so extreme in the headwater part and the damage was more uniformly distributed around the entire catchment. More information about these events can be found in Rusjan et al. (2015). 1100 1000 900 800 700 600 500 400 300 200 100 0 Lu median 3000 t 2500 ™ 2000 -E 1500 -- • 1000 500 0 -----mean median SJ Events (b) Figure 3: EI for events recorded in Ljubljana (a) and Črni vrh nad Polhovim Gradcem (b). Slika 3: EI vrednosti za erozivne dogodke, ki so bili izmerjeni v Ljubljani (a) in Črnem vrhu nad Polhovim Gradcem (b). Table 1: An overview of KE-I relationships (equations in bold were used in this study). Preglednica 1: Pregled enačb KE-I (enačbe označene s krepkim tiskom so bile uporabljene v tej študiji). Authors Equation KE-I (KE: Jm-2h-1) I range for development (mmh-1) Location Blanchard (1953)a 12.7I(1-0.98e"0011/) <25 Honolulu, HI, USA Blanchard (1953)a 23.7-I-(1-0.71- e"0 031 /) <127 Honolulu, HI, USA Brandt(1988)a 30^(1-0.56^e_0'044/) <105 Manaus, AM, Brasil Brandt (1990)b /•(8.95+8.44 log/) Elaboration of data from Marshall and Palmer (1948) Brown and Foster (1987) b 29•/•(1-G.72•e"0'05'/) <250 MS, USA Carter et al. (1974) c I(11.32+0.5546 I--0.5009 10"2I2+0.12610"4I3) <260 MS/LA, USA Cerro et al. (1998) 38.4•/•(1-G.528•e"0'029'/) Barcellona, Spain Coutinho and Tomás (1995) b 35.9•/•(1-G.559•e"0'034'/) 0-120 Mértola, Portugal Fornis et al. (2005) 30.8^(1-0.55^-a03/) 2.8-142 Cebu, Philippines Fornis et al. (2005) 29.02^I"7167^3600 2.8-142 Cebu, Philippines Fornis et al. (2005) 12.05-I119-3600 2.8-142 Cebu, Philippines Fornis et al. (2005) I(11.93+7.82 logI) 2.8-142 Cebu, Philippines Hudson (1965)c 29.89I-128.23 Zimbawe Jayawardena and Rezaur (2000)d 36.8I(1-0.69e-0 038 /) 12-120 Hong Kong Kinnel(1973)c 30.13I-165.11 Miami, FL, USA Kinnell (1980) d 29.2-I-(1-0.89-e-a048'J) 19-229 Mozowe, Zimbawe Kinnell (1980) d 29.3^(1-0.28^-0018/) 2-309 Miami, FL, USA Laws and Parson (1943) a 28.9I(1-0.54e"0 059/) 0.4-114 Washington, DC, USA Lim et al. (2015) d 25.75I (1-0.54^e-0 05 /) 0.1-142 Daejeon, Korea Marshall and Palmer (1948) a 29^(1-0.74^e"0 039/) <23 Ottawa, ON, Canada McGregor and Mutchler (1976) c I^(27.3+21.68e"0048/-41.26e-0072í) Holly Springs, MS, USA McIsaac (1990) b 28.8•I•(1-0.45•e~0'033'I) 1,.5-194 Panama McIsaac (1990) a 24.6I(1-0.46e"0 037/) 1-193 Franklin, NC, USA McIsaac (1990) a 29.2I(1-0.51e"0011/) 2-170 Majuro, Marshall Islands McIsaac (1990) a 25.1I(1-0.4e"0 045 /) 14-148 Island Beach, NL, USA McIsaac (1990) a 26.8^(1-0.29^e_0'049/) 13-180 Bogor, Indonesia Onaga et al. (1988) a I(9.81+10.6logI) Okinawa, Japan Petan (2010) 31.6^(1-G.6^ e^61^) 0.1-247 Ljubljana, Slovenia Petan (2010) 34.1•/•(1-G.6•e"0'04'/) 0.1-254 Bovec, Slovenia Petan et al. (2010) 29.8/(1-G.6e-76 mm/h Van Dijk et al. (2002) 28.3•/•(1-G.52•e"0'042'/) Elaboration of published data Van Dijk et al. (2002) 30.4I(1-0.69e"0 06/) 0.3-124 Malangbong, Indonesia Zanchi and Torri (1980) b /•(9.81+11.25log/) 1-140 Firenze, Italy Cited by: a) Van Dijk et al. (2002) b) Petan et al. (2010) c) Roswell (1986) d) Angulo-Martínez et al. (2016) e) Morgan (2001) Table 2: An overview of rainfall events with return period of I30 larger than 5 years. Preglednica 2: Pregled dogodkov, ki so imeli povratno dobo glede na I30 večjo od 5 let. Occurrence of the event Place I30 (mmh-1) Return period of the event 09/09/2013 Ljubljana 48.6 >10 years 05/08/2014 Črni Vrh 77.6 >250 years 23/06/2015 Črni Vrh 41.1 >5 years 3.2 Evaluation of the KE-I relationships In the next step of the study, several KE-I equations (Table 1) were tested using the disdrometer data from the two stations. Values of one-minute I (calculated applying equation 1) were used to solve the equations; regardless of eventual ranges (shown in Table 1) of I utilized in the development of such equations. Logarithmic and linear equations yielded negative values of KE for I lower than the threshold levels shown in Table 3. These values were assumed to be zero in the calculation of the total KE for individual rainfall events. The last two equations shown in Table 3 do not actually yield negative values because their threshold level is lower than 0.1 mmh-1 and, as stated above, minutes with intensity lower than 0.1 mm/h were discarded from further analysis. KE calculated by applying various equations shown in Table 1 were visually compared with KE calculated using disdrometer data (Figure 4). Equations that gave the closest fit to the measured data are those that are close to the line that connects coordinates (0,0) and (4000,4000). In both stations the results were similar with differences in the magnitude scatter. The scatter was larger for the data from the Črni vrh nad Polhovim Gradcem than for the data from the Ljubljana station. This could be expected because for this station the EI and KE values were generally higher than for the Ljubljana station. Moreover, we also calculated the Pearson correlation coefficients (CORREL function in Excel was used for this purpose) between measured (calculated from the data) and calculated (estimated using the proposed equations) KE values using several equations for both analysed stations (Table 4). The results indicate that the equation proposed by Sempere-Torres et al. (1992) gave the worst fit to the measured disdrometer data (for the Ljubljana station). Moreover, according to literature, its use is suitable only for intensities higher than 20 mm h-1 (Petan et al., 2010). The best agreement between disdrometer data and equations results were obtained using the formulas developed in Slovenia by Petan (2010) and Petan et al. (2010) (Fig. 4 shows results using equation for the Ljubljana region). However, some other equations also produced a similar fit to the data (Table 4). At high values of I equations from Coutinho and Tomás (1995) and Cerro et al. (1998) tend to slightly overestimate the disdrometer data, while all the other tested equations shown in Table 1 tend to slightly underestimate the data obtained from the disdrometer. Furthermore, Pearson correlation coefficients shown in Table 4 can be regarded as relatively high for almost all tested equations, which also indicates that changes among compared equations are generally not significant. Table 3: Values of I under which KE estimated with linear and logarithmic equation tested in this study are negative. Preglednica 3: Vrednosti I pri katerih so ocenjene vrednosti KE z uporabo linearnih ter logaritemskih enačb negativne. Equation KE negative when: Usón and Ramos (2001) I>0.76923 mm h-1 Sempere-Torres et al. (1992) I>5.58824 mm h-1 Zanchi and Torri (1980) I>0.13428 mm h-1 USDA (1997) I>0.04334 mm h-1 Brandt (1990) I>0.08701 mmh-1 a s o ■_■, rr C ,2 _a o t g s» m % (a) +■ / • ST X 1Ü0D 2000 3000 4DDQ tfF(MJ'haL) calculated from the data .5- g -c ^ w C 0 O m o ™ o !: m > -D "C o (U o 1 tt « o ^ o f o (0 Lu O Se +/ + / • * Z* x -K/ X - ¿ä T>í + iT X x < * - - - (b) 0 1000 2000 3000 4000 KE (MJ-ha1) calculated from the data + Cerro et al. (1998) • Petan (2010) X Brown and Foster (1987) Figure 4: Example of results for three selected KE-I relationships plotted versus KE estimated using the disdrometer data from Ljubljana (a) and from Črni vrh (b). Slika 4: Primer treh rezultatov izračunov z uporabo 3 izbranih KE-I enačb in KE vrednosti, ki so bile ocenjene z uporabo podatkov z disdrometra za postajo v Ljubljani (a) in Črnem vrhu nad Polhovim Gradcem (b). 3.3 Temporal variability of erosivity In the last part of the study the variability in rainfall erosivitiy was observed. Since a complete series of data is not available, it was not possible to determine the R factor for complete calendar years, but monthly R was determined for each month or part of the month, with data from at least one station (Figure 5). One can notice that rainfall erosivity in winter is generally smaller than in summer months, which can be expected for the climatic characteristics of Slovenia. In Ljubljana the average monthly R value for about 16 months was 380.1 MJ mm ha"'-h"1. This means that average annual R value for this period for the Ljubljana station was 4561.0 MJ-mmha"1-h"1'y"1. For the Crni vrh nad Polhovim Gradcem station the average monthly R value for about 17 months of records was 527.4 MJmmha-1h-1 and the average annual value was 6320.9 MJ-mmha"1-h"1y"1. The computation of average monthly R was based on data collected in different periods, and some months are more represented than others. This impedes the direct comparison with average values from other studies (Petan, 2010; Panagos et al., 2015) and also between the two stations. However, these results give an idea about the order of magnitude of erosivity in central Slovenia during the period considered. 4. Conclusions Disdrometer data used in this study allows an accurate estimation of KE and I30 factors that determine EI (Cerro et al., 1998). EI does not consider intra-storm intensity pattern (Angulo-Martínez et al., 2016) and intermittency (Dunkerley, 2015), and is not the most representative for the Mediterranean climate (Pandit and Isaac, 2015). Todisco (2014) showed that in central Italy the parameters used in RUSLE methodology to discern erosive and non-erosive events are not always correct; she proposed an adaption of the theory of runs to compare the patterns of intra storm intensity, given a threshold level of instantaneous intensity. However, EI can still be considered a good indicator of rainfall erosivity (Van Dijk et al., 2002), and it is used in RUSLE methodology (USDA, 1997) that has often been applied all over the world. However, Casazza (2016) suggests going beyond this semi-empirical model and replacing it with a more physical-based model. despite its drawbacks; it is less data demanding and However, modelling rainfall erosivity using the will probably remain frequently used in the future. RUSLE methodology is relatively straightforward Table 4: Pearson correlation coefficients between measured and calculated KE values using several equations for the Ljubljana and Črni vrh nad Polhovim Gradcem stations. Preglednica 4: Izračunane vrednosti Pearsonovih koeficientov korelacije med izmerjenimi ter izračunanimi KE vrednostmi za postaji Ljubljana ter Črni vrh nad Polhovim Gradcem. Authors Equations Stations Ljubljana Črni vrh Petan et al. (2010) 29.8I(1-0.6e~0 071 /) 0.984 0.980 Petan et al. (2010) 31.9I(1-0.6e~0 055 /) 0.984 0.982 Usón and Ramos (2001) 23.47-18 0.979 0.966 Sempere-Torres et al. (1992) 34I-190 0.787 0.923 Coutinho and Tomás (1995) 35.9-I-(1-0.559-e-0 034/) 0.982 0.980 Cerro et al. (1998) 38.4I(1-0.538 e"0 029/) 0.981 0.978 Zanchi and Torri (1980) I- (9.81+11.25 - logI) 0.983 0.984 Wischmeier and Smith (1958) I(11.9+8.73logI) if I<76mm/h 0.984 0.977 28.3I if I>76mm/h Brown and Foster (1987) 29-I-(1-0.72-e"0 05 /) 0.976 0.986 Brandt(1990) I(8.95+8.44 logI) 0.984 0.982 Van Dijk et al. (2002) 28.3-I-(1-0.52-e"0042/) 0.982 0.977 Petan (2010) 31.6I(1-0.6e"0 061 /) 0.958 0.981 Petan (2010) 34.1I(1-0.6e"004/) 0.957 0.983 Figure 5: Monthly R in Ljubljana (a) and in Črni vrh nad Polhovim Gradcem (b). Data for months indicated with asterisk were incomplete. Slika 5: Mesečne vrednosti faktorja erozivnosti padavin R za postaji Ljubljana (a) in Črni vrh nad Polhovim Gradcem (b). Podatki za mesece, ki so označeni z zvezdico niso bili popolni. Slovenia has one of the highest rainfall erosivities among European countries. The average annual value of R for the Slovenian stations considered by Panagos et al. (2015) in the period 1999-2008 was 2302 MJ mm ha-1h-1, while the maximum was 5655.8 MJmmha-1h-1. Despite to the small size of the country, there is significant variability in the rainfall erosivity among the three climatic regions (mediterranean, alpine, and continental), with a lower R in the latter case, where extreme events are less frequent than in the other two climate regions. In view of these high erosivity values, rainfall erosivity results shown in this paper are still relatively high, especially compared with some other studies (Panagos et al., 2015; Ceglar et al., 2008). Petan (2010) reported mean R value of 3153.8 MJmmha-1h-1 for the Črni vrh nad Polhovim Gradcem and 3625.3 MJmmha-1h-1 for the Ljubljana station. However, some extreme events that occurred in the observed periods, which could explain the high values. Moreover, the results of this study indicate that one extreme event such as the one in August 2014 in the Gradaščica River catchment (Bezak et al., 2016) can lead to rainfall erosivity higher than average annual values. Data about this event collected in Črni Vrh show an EI of 2727.2 MJmmha^h"1, corresponding to about 40% of yearly R factor of the period August 2014-July 2015. Furthermore, 1-minute rainfall data measured with optical disdrometer was used in this study. This means that higher rainfall erosivity values can be expected than in the case of using e.g. 15 minute rainfall data where some information about the most extreme rainfall intensity can be lost. The highest values of rainfall erosivity were observed in summer and beginning of autumn due to extreme events. Similar conclusions about the seasonal distribution of rainfall erosivity was pointed out by Ceglar et al. (2008) and Diodato and Bellocchi (2012) in their works, regarding respectively western Slovenia and the Euro-Mediterranean region. 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