Rainfall and runoff erosivity in the alpine climate of north Slovenia: a comparison of different estimation methods

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1 Hydrological Sciences Journal ISSN: (Print) (Online) Journal homepage: Rainfall and runoff erosivity in the alpine climate of north Slovenia: a comparison of different estimation methods MATJAŽ MIKOŠ, DARJA JOŠT & GREGOR PETKOVŠEK To cite this article: MATJAŽ MIKOŠ, DARJA JOŠT & GREGOR PETKOVŠEK (2006) Rainfall and runoff erosivity in the alpine climate of north Slovenia: a comparison of different estimation methods, Hydrological Sciences Journal, 51:1, , DOI: /hysj To link to this article: Published online: 19 Jan Submit your article to this journal Article views: 415 View related articles Citing articles: 17 View citing articles Full Terms & Conditions of access and use can be found at

2 Hydrological Sciences Journal des Sciences Hydrologiques, 51(1) February Rainfall and runoff erosivity in the alpine climate of north Slovenia: a comparison of different estimation methods MATJAŽ MIKOŠ 1, DARJA JOŠT 1 & GREGOR PETKOVŠEK 2 * 1 University of Ljubljana, Faculty of Civil and Geodetic Engineering, Jamova 2, SI-1000 Ljubljana, Slovenia mmikos@fgg.uni-lj.si 2 CGS Ltd Computer Aided Design, GIS and Ecology, Brnčičeva 13, SI-1000 Ljubljana, Slovenia Abstract Rainfall and runoff erosivity is often assessed by using the R factor. For its computation different methods may be used. The aim of this study was to compare some estimation methods for the alpine climate in the Slovenian Alps. Monthly and annual R factor values were calculated according to the RUSLE, using daily precipitation data for the period in Solčava, which is typical of the alpine region in Slovenia. In this alpine area with rather low rainfall intensities, the expression for computing the rainfall kinetic energy proposed by van Dijk et al. yielded on average 17.9% higher rainfall erosivities than the RUSLE approach. The newly proposed A index yielded on average 40% lower rainfall erosivities than the RUSLE approach. These lower values of rainfall erosivity were caused by the structure of rainfall during erosive events in the alpine region. The analysis in the alpine climate in Slovenia does not support the use of the proposed A index as a replacement for the usually used R factor when assessing rainfall erosivity. Key words R factor; RUSLE; rainfall intensity; rainfall and runoff erosivity; soil erosion; Slovenia Érosivité des pluies et du ruissellement en climat alpin du nord de la Slovénie: comparaison de différentes méthodes d estimation Résumé L érosivité de la pluie et du ruissellement est souvent estimée grâce au facteur R. Différentes méthodes peuvent être utilisées pour son calcul. Le but de cette étude est de comparer quelques méthodes d estimation en climat alpin dans les Alpes Slovènes. Les valeurs mensuelles et annuelles du facteur R ont été calculées selon l approche RUSLE, à partir de données journalières de précipitation observées pendant la période à Solčava, typique des Alpes Slovènes. Dans cette région alpine aux intensités pluvieuses plutôt faibles, l expression de l énergie cinétique de la pluie de van Dijk et al. a abouti à des érosivités de la pluie en moyenne 17.9% plus fortes qu avec l approche RUSLE. Le nouvel indice A a impliqué des érosivités de la pluie en moyenne 40% plus faibles qu avec l approche RUSLE. Ces valeurs inférieures d érosivité de la pluie ont été causées par la structure de la pluie lors des événements érosifs dans la région alpine. L analyse en climat alpin en Slovénie ne permet pas d utiliser l indice A proposé comme alternative du facteur R communément utilisé lors de l appréciation de l érosivité de la pluie. Mots clefs facteur R; RUSLE; intensité des pluies; érosivité des pluies et du ruissellement; érosion du sol; Slovénie INTRODUCTION Rainfall erosivity is one of the most important factors in the process of soil erosion, especially on bare ground or with sparse vegetation cover. The rainfall detaches soil from the ground by impact of raindrops. Soil can also be detached and transported downslope by shear force caused by the overland flow generated from precipitation. To assess the rainfall erosivity, the important parameters include the amount of precipitation, intensity (its temporal distribution), type of precipitation, kinetic energy and the distribution and velocity of raindrops. All these parameters are mutually dependent: two of them amount of rainfall and intensity of rainfall are of practical importance for estimation of rainfall erosivity. The two parameters are measured at standard meteorological stations and, therefore, are widely available. In many parts of the world, direct measurements of rainfall kinetic energy are rare, and it is common to use empirical equations. The in-depth discussion on kinetic energy of rain and its * Formerly at: Faculty of Civil and Geodetic Engineering, University of Ljubljana, Jamova 2, SI-1000 Ljubljana Open for discussion until 1 August 2006

3 116 Matjaž Mikoš et al. functional relationship with intensity is beyond the scope of this study. Not having local measurements of rainfall kinetic energy available, the main aim of the study was less oriented towards precise computation of real values of rainfall erosivity in the study area; rather, the focus was on its annual and seasonal variability using measured rainfall rates and intensities. Also, a comparison was performed between two selected empirical equations for kinetic energy among many applicable equations for rainfall erosivity estimation. Rainfall and runoff erosivity factor R Usually, rainfall and runoff erosivity is expressed by the so-called R factor. Wischmeier & Smith (1958) first introduced the factor for use in the universal soil loss equation (USLE). Later, the entire equation was revised, which included a modification of rainfall and runoff erosivity factor as well. The result was the revised universal soil loss equation (RUSLE) (Renard et al., 1997). In general, the R factor is calculated as a product of the total energy of rainfall, E and its maximum 30-min intensity, I 30 : R = E (1) I 30 The total energy of the rainfall is computed on the base of unit energy e (per unit of precipitation). The unit energy is a function of rainfall intensity, i. The total energy is a sum of the products of instantaneous unit energy, e j and amount of precipitation, p j for each time interval, j: E = e j p j (2a) j e = f (i) (2b) Overview of methods used Rain is extremely variable in place and time. For example, Lal (1998) did not find a correlation between kinetic energy and momentum of rainfall in Ibadan, western Nigeria in 1980, whereas he found a significant relationship in In recent years, several reviews of rainfall parameterization have appeared (Uijlenhoet & Stricker, 1999; Steiner & Smith, 2000; Salles et al., 2002; van Dijk et al., 2002). Some of the proposed equations for the relationship between rainfall kinetic energy, e and rainfall intensity, i are summarized in Fig. 1. From the theoretical point of view, the best fit to the measured data would be obtained by the power-law relationship (Steiner & Smith, 2000; Salles et al., 2002). But also other proposed relationships lie between the limits given for one standard deviation about the mean (Steiner & Smith, 2002) and thus, they are also applicable. Out of many proposed e i relationships, two were selected for computation of the R factor. USLE/RUSLE In this paper, the reference equation for the R factor was that of USLE (Wischmeier & Smith, 1958) or RUSLE (Renard et al., 1997). In both cases, R is computed from

4 Rainfall and runoff erosivity in the alpine climate of north Slovenia van Dijk (2002) RUSLE + Brown & Foster (1987) Marshall-Palmer DSD (1948) + Uplinger (1981) stratiform rain i^0.3 (Salles et al., 2002) convective rain i^0.2 (Salles et al., 2002) Steiner & Smith (2000) Steiner & Smith (2000) i^0.25 e (MJ / (ha h)) i^ i (mm/h) Fig. 1 Relationship between rainfall intensity, i, and kinetic energy of rainfall, e, for selected equations. For Marshall-Palmer (1948) DSD, N(D) = N 0 e - D, values of N 0 = 8000 m -3 mm -1 and = 4.1R mm -1 were used. The Uplinger (1981) equation for the raindrop terminal fall velocity is v(d) = 3.25D equation (1). In SI units, USLE uses the following relationship between unit energy e (MJ ha 1 mm 1 ) and intensity i (mm h -1 ) (Foster et al., 1981): = log i i 76 mm h 1 (3a) e 10 () e = i > 76 mm h 1 (3b) It was found that, from the limit value of intensity (at 76 mm h -1 ), the mean size of raindrops no longer increases and, therefore, their velocity does not increase either. As the raindrops reach their terminal size, the unit energy stabilizes at the value of e = MJ ha -1 mm -1. Later studies showed that the exponential relationship between unit energy e and intensity i is more appropriate: [ 1 a ( bi) ] e = e exp max (4)

5 118 Matjaž Mikoš et al. where e max is maximum unit energy (e), when intensity approaches infinity (MJ ha -1 mm -1 ), and a and b are coefficients. Coefficient a, together with e max, determines the minimum unit energy. Coefficient b (h mm -1 ) defines the shape of the exponential curve. Kinnell (1981) proposed an exponential relationship. Several other authors (cf. van Dijk et al., 2002) confirmed that this relationship describes well the relationship between the energy and intensity in different geographical regions. In the revised RUSLE, the logarithmic relationship between e and i (equations (3a) and (3b)) was also replaced by the exponential relationship. The coefficients e max = 0.29 MJ ha -1 mm -1, a = 0.72 and b = 0.05 h mm -1 were proposed by Brown & Foster (1987). From Fig. 1 it can be seen that, when compared to the others selected from the literature, this widely used relationship predicts very low kinetic energies, and its usage will underestimate rainfall erosivity. Computation of rainfall kinetic energy after van Dijk et al. (2002) Van Dijk et al. (2002) reviewed a set of studies on the distribution of the size of raindrops and/or kinetic energy rainfall intensity relationships. Based on the most reliable studies from around the world, a new relationship was proposed (referred to herein as the van Dijk et al. equation). As the RUSLE relationship, it is also of exponential form (equation (4)), but the values of the coefficients are now: e max = MJ ha -1 mm -1, a = 0.52 and b = h mm -1. Having in mind the aim of the study, these values were chosen as an available estimate without having local measurements of rainfall kinetic energy e, and thus not claiming their strict validity for the alpine climate under study. From Fig. 1 it can be seen that, for low rainfall intensities (i < 2 mm h -1 ), the van Dijk et al. equation resembles the convective type of rain and, for higher rainfall intensities (10 < i < 20 mm h -1 ), it resembles the stratiform type of rain. Both types of rain are defined after Salles et al. (2002). The A index after Sukhanovski et al. (2002) Sukhanovski et al. (2002) suggested the use of a new method for computation of the rainfall erosivity factor. The factor was named A index (Sukhanovski & Khan, 1983). The difference between the A index and the USLE R factor (equations (1) (3b)) is in the intensity parameter. While the USLE R factor uses maximum 30-min intensity (I 30 ), effective intensity (I eff ) is used for computation of the A index. The authors state that their method is more physically based and give the details of its derivation. On the basis of three study areas they concluded that, on the annual basis, the A index can replace the R factor without adjustments of other coefficients, i.e. their ratio is 1:1. This was not true for individual events. For individual events, the ratio A/R was not always equal or close to one. The differences were most significant in the case of the events with highly variable intensities. Since I 30 does not take into account the characteristics of the whole event, Sukhanovski et al. (2002) suggested the use of effective intensities I eff, being the weighted average of the rainfall intensity of the whole event:

6 Rainfall and runoff erosivity in the alpine climate of north Slovenia 119 E a j b I I eff = (5) E j where E j is the energy and I j the intensity in the jth time interval and a and b are the coefficients. Tools for computation of rainfall erosivity Petkovšek (2002) developed the computer program RF for calculation of rainfall erosivity. Originally, it served as a tool for computation of the RUSLE R factor. The current version enables the computation with any method that uses the exponential e i relationship (equation (4)). The input file consists of data on rainfall. These are usually obtained from automatic raingauges. The program reads the standard format of the operator of the Slovenian automatic raingauge network, i.e. the Environmental Agency of the Republic of Slovenia (ARSO), other text files or Matlab binary format (MathWorks, 2002). From the given precipitation data, erosive events are extracted and, for each of them, the following variables are computed: precipitation, P; energy of rainfall, E; maximum 30-min intensity, I 30 ; and the R factor. The computation of the A index is performed within a spreadsheet program. For the given beginning and end of an event the tool also computes the R factor using exponential (equation (4)) and logarithmic equations (equation (3)). MEASURING SITE AND DATA The climatological station at Solčava is a part of the network of the Environmental Agency of the Republic of Slovenia. It is located at the elevation of 658 m a.s.l. at Ν; Ε. At the station, the precipitation is measured with a Hellman pluviometer with an area of 200 cm 2 and a Russian type P-2 pluviograph with an area of 500 cm 2, the latter having a mechanical clock and registers on a band. Reviewed data for the 13-year period were obtained from ARSO (Zupancic, personal communication, 2003) and were imported directly into the RF program. The average annual precipitation for this period was mm. In this period, there were seven separate intervals together 22 days (0.46% of this period) when the pluviograph did not operate. On these days, the pluviometer recorded mm precipitation, which is 1.95% of total precipitation for this period. In these cases, the RUSLE R factor was calculated indirectly from the daily rainfall data, P d. The equation that best describes the relationship between the square of daily rainfall P d and the R factor was used: 2 R = k P d (6) Values of coefficient k were determined for each month separately, as proposed by Petkovšek & Mikoš (2004). For those months where data on 5-min intensities were missing, the corresponding coefficient of determination r 2 is as follows: k = (r 2 = 0.837) for February, k = (r 2 = 0.501) for September, k = (r 2 = 0.909) for October and k = (r 2 = 0.904) for November.

7 120 Matjaž Mikoš et al. RESULTS The average annual R factor was evaluated as MJ ha 1 mm h 1, using also the daily rainfall data for the days when the pluviograph did not operate. The range between the maximum ( MJ ha 1 mm h 1 in 1998) and minimum ( MJ ha 1 mm h 1 in 2001) is about 75% of the mean value, which is much higher than for precipitation. The number of erosive events, n, was between 40 (in 1995) and 61 (in 1999) with an average of 48.4 events per year. Years with the maximum (in 1998) or minimum R factor (in 2001) do not correspond to the years with maximum (in 2000) or minimum annual precipitation (in 2002), nor to the years with the maximum (in 1999) or minimum number of erosive events (in 1995). For the analysed period, Fig. 2 shows the annual precipitation, P, and Fig. 3 shows the annual distribution of the average monthly precipitation, in both cases as a function of the RUSLE R factor. Further computations and hence comparisons in this paper were done using only 5-min rainfall data excluding days when the pluviograph did not operate. The annual values of R factor for the analysed period, calculated by the van Dijk et al. equation (R D in Table 1) and by the RUSLE equation (R R in Table 1) are given in Fig. 4. The mean values of the R factor for individual months and the differences between both equations are given in Table 1. The average annual R factor calculated by van Dijk equation was estimated at MJ ha 1 mm h 1, as compared to the average annual RUSLE R factor value of MJ ha 1 mm h 1. Furthermore, a logarithmic equation (equation (3)) was used to compute the rainfall energy for the computation of the RUSLE R factor (R R,log ) to achieve compatibility between the R factor and A index. In this way, the effect of the different methods of computation of rainfall intensity on the rainfall erosivity could be determined. The annual values of A index for the analysed period and a comparison to the R factor computed using logarithmic equation (R R,log ) are given in Fig. 5. The average annual RUSLE R factor calculated with the logarithmic equation was estimated at MJ ha 1 mm h 1 compared to the average annual A index value of MJ ha 1 mm h P R R (MJ mm / (ha h)) P (mm) Year Fig. 2 Total annual precipitation P and RUSLE rainfall and runoff erosivity factor R.

8 Rainfall and runoff erosivity in the alpine climate of north Slovenia P R R (MJ mm / (ha h)) P (mm) Jan Feb Mar Apr May June July Aug Sep Oct Nov Dec Month Fig. 3 Annual distribution of the average monthly precipitation P and R factors for the period at Solčava RR RD R (MJ mm / (ha h)) Year Fig. 4 Annual values of rainfall and runoff erosivity factor, R, after the van Dijk et al. equation R D and the original RUSLE equation R R. DISCUSSION Comparison of the RUSLE and van Dijk et al. equations From Fig. 4 it can be seen that the equation of van Dijk et al. (2002) gives consistently higher values of R factor than the RUSLE. The average annual R factor after van Dijk et al. (R D ) is MJ ha 1 mm h 1, which is 17.9% higher than the value of MJ ha 1 mm h 1 of RUSLE. The relationship between the annual R factor values of the two equations can be described by a linear equation of the form R D = 1.179R R, where r 2 = From Table 1 it can be seen that from December to April the rainfall erosivity is low (R < 100 MJ ha -1 mm h -1 ) and the relative difference between R D and R R is high,

9 122 Matjaž Mikoš et al. Table 1 Comparison of the mean values of the R factor in Solčava for individual months in the analysed period , excluding days when the pluviograph did not operate. Month I 30 (mm h -1 ) R D R R Absolute difference R D R R (MJ ha -1 mm h -1 ) January February March April May June July August September October November December Mean R D : after van Dijk et al. (2002); R R : after RUSLE; both in MJ ha -1 mm h -1. Relative difference (R D R R )/R R (%) R(R,log) A R, A (MJ mm / (ha h)) Year Fig. 5 The annual values of A index at Solčava for the period and comparison to the R factor computed using logarithmic equation (R R,log ). being highest in February (38.6%). In these months the mean values of the maximum 30-min erosivity of events are also low (I 30 < 5.5 mm h -1 ). The difference in the R factor between both equations is the lowest in summer (June August). The smallest relative difference of 9.2% is in August, when the R factor and the mean I 30 are maximum (I 30 = 16.4 mm h -1 ). Structurally, the van Dijk et al. and RUSLE equations are the same. In both cases, the R factor is computed as a product of rainfall energy (E) and maximum 30-min intensity (I 30 ) of an event. The values of I 30 are the same for both equations. The difference lies in the coefficients of the equation for unit energy e (equation (4)). From Fig. 1 it can be seen that, in the case of lower intensities (i < 26.7 mm h -1 ), the van Dijk et al. equation gives higher values of unit energy e than does the RUSLE equation. The opposite holds for higher intensities.

10 Rainfall and runoff erosivity in the alpine climate of north Slovenia 123 Table 2 Overview of distribution of maximum 30-min intensities, I 30. I 30 (mm h -1 ) Number of erosive events Percentage > Total For all the 629 erosive events at Solčava, low rainfall intensities <10 mm h -1 prevailed. Because the maximum 30-min intensity I 30 of each erosive event is taken to compute the R factor, data from Table 2 can be analysed. The percentage of erosive events with I 30 < 26.7 mm h -1 is 96.5%. Because the proportion of low intensities is so high, the van Dijk et al. equation yields higher annual and monthly rainfall erosivities than the RUSLE equation in the case of the analysed data for Solčava. Comparison between the R factor and A index From Fig. 4 it can be seen that the A index is consistently smaller than the RUSLE R R,log. The average annual A index is MJ ha 1 mm h 1, which is only 58.6% of the average annual value of R R,log ( MJ ha 1 mm h 1 ). The relationship between the annual values of the A index and R R,log can be given by the linear equation: A = R R,log, where r 2 = The results for the alpine climate in Solčava lead to different conclusions than those of Sukhanovski et al. (2002). In that study, the ratio of the annual value of A index to the annual value of R R,log was approximately 1, while in the case of Solčava, A/R R,log = If the energy for both methods is calculated in the same way (equation (3)), the following relationship between individual events can be written: A E Ief Ief = = (7) R E I 30 I 30 Table 3 Number and percentage of erosive events for different classes of I eff /I 30. I eff /I 30 Number of erosive events Percentage < % % % % > % Total %

11 124 Matjaž Mikoš et al. From Table 3 it can be seen that the ratio I eff /I 30 is between 0.5 and 0.75 for most (65%) of the erosive events. In only 6% of the erosive events, the ratio exceeded 1. The definition of an erosive event defines the shortest possible duration of such an event as 6 hours. For 13 erosive events (for a typical event see Fig. 6(a)), for which the ratio I eff /I 30 was below 0.4, the following common features were identified: these events have a long duration, on average more than 36 h; duration of some events exceeds two days; depth of precipitation is high (90.5 mm on average), the event with the maximum rainfall amount in the analysed period (161.6 mm) is included in this group; and rainfall erosivity is high (average R R,log = 244 MJ ha -1 mm h -1 ). For 17 erosive events (for a typical event see Fig. 6(b)), for which I eff /I 30 > 1.25, the following was established: (a) I (mm h -1 ) (b) Time (min) I (mm h -1 ) Time (min) Fig. 6 Histograms of rainfall intensities for (a) the event between 31 October and 2 November 1990 (duration: 43 h 10 min;, total precipitation P = mm; 30-min intensity I 30 = 16.4 mm h -1 ; effective precipitation I eff = 5.6 mm h -1 ; and ratio I eff /I 30 = 0.34); and (b) the event of 13 August 1991 (duration <6 h; P = 12.6 mm; I 30 = 24.6 mm h -1, I eff = 35.7 mm h -1 ; and I eff /I 30 = 1.45)

12 Rainfall and runoff erosivity in the alpine climate of north Slovenia 125 these events have a short duration, with an average of just above 8 hours, while the average for all events is 16 h; rainfall depth is low, on average 8.9 mm, which is significantly lower than the average for all events (24.8 mm); and rainfall erosivity is also low (average R R,log = 22 MJ ha -1 mm h -1 ). CONCLUSIONS The analysis of typical rainfall data in the alpine climate in Slovenia showed that the erosive events with low rainfall intensities (i < 26.7 mm h -1 ) prevail (96.5% of all erosive events in the analysed period). That is why the van Dijk et al. equation produced higher R factor values in such a climate than the RUSLE, which underestimated rainfall erosivity. For rainfall intensities i < 26.7 mm h -1, the van Dijk et al. equation, e = 0.283[1 0.52exp( 0.042i)] predicted similar kinetic energy e and thus also the R factor as the theoretically based power-law equation of Salles et al. (2002) for a combination of convective (e = 0.135i 0.2 ) and stratiform rain (e = 0.192i 0.3 ). Local measurements of rainfall kinetic energy would be needed to further improve the validity of the estimated R factor values in the alpine climate. Unfortunately, the relationship between rainfall kinetic energy and rainfall rate is not constant for different types of rainfall. Thus, a separate analysis would be needed for each type of rainfall using different values of parameters in the selected e i relationship. Such detailed analysis for estimation of R factor values in the alpine climate, also in Slovenia, will be possible when long-term measurements of rainfall kinetic energy, covering all possible rainfall types, become available. The analyses performed did not support the use of the proposed A index as a replacement for the usually used R factor when assessing rainfall erosivity. The structure of rainfall during erosive events in this alpine region was the major reason why the A index yielded, on average, more than 40% lower rainfall erosivities than did the RUSLE approach. Acknowledgements The authors wish to thank the Environmental Agency of the Republic of Slovenia for providing the precipitation data. The in-depth review of the anonymous reviewers and personal communication with Jürgen Joss helped to improve earlier versions of the paper. REFERENCES Brown, L. C. & Foster, G. R. (1987) Storm erosivity using idealised intensity distribution. Trans. Am. Soc. Agric. Engrs 30, Foster, G. R., McCool, D. K., Renard, K. G. & Moldenhauer, W. C. (1981) Conversion of the universal soil loss equation to SI metric units. J. Soil Water Conserv. 36, Kinnell, P. I. A. (1981) Rainfall-kinetic energy relationships for soil loss prediction. Soil Sci. Am. J. 45, Lal, R. (1998) Drop size distribution and energy load of rain storms in Ibadan, western Nigeria. Soil Tillage Res. 48, Marshall, J. S. & Palmer, W. M. (1948) The distribution of rain drop with size. J. Met. 5, MathWorks (2002) Matlab User Guide. MathWorks Inc.

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