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Rainfall erosivity in Slovenia: Sensitivity estimation and trend detection
Environmental Research 167 (2018) 528–535
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Rainfall erosivity in Slovenia: Sensitivity estimation and trend detection Manca Petek, Matjaž Mikoš, Nejc Bezak
⁎
T
University of Ljubljana, Faculty of Civil and Geodetic Engineering, Slovenia
A R T I C LE I N FO
A B S T R A C T
Keywords: Rainfall erosivity Trend detection Sensitivity analyses Slovenia
Slovenia is one of the EU countries with the largest values and largest amounts of variability in rainfall erosivity, with maximum annual values exceeding 10,000 MJ mm ha-1 h-1 yr-1. Five-minute rainfall data was analysed from 10 Slovenian rainfall stations with data-length availability longer than 25 years with a maximum data length of 69 years and a total data-station length equal to 443 years. Trends in the rainfall erosivity R-factor were detected for four different sub-samples using monthly, half-year, and annual rainfall erosivity values. The results indicate that rainfall erosivity trends for the selected Slovenian stations are mostly statistically insignificant, with the selected significance level of 0.05. However, a larger share of identified trends are positive than negative. The maximum annual rainfall erosivity values were obtained for one specific mountain station. Furthermore, a sensitivity analysis regarding the rainfall erosivity factor R calculation showed that the rainfall threshold parameter (12.7 mm) that is used to remove the small-magnitude rainfall events in order to reduce the computational burden can attribute up to 10% of the average annual R-values in cases where this threshold is not used. Other parameters have, on average, a smaller impact on the calculated rainfall erosivity. Furthermore, the application of local kinetic energy equations resulted in, on average, about 20% higher annual rainfall erosivity values compared to the equation that is proposed by the Revised Universal Soil Loss Equation (RUSLE) manual and was not developed specifically for this region.
1. Introduction As soil erosion is one of modern agriculture's major challenges, rainfall erosivity as one of its parameters plays an important role in estimating and modelling both soil erosion and its overall impacts on society and the environment. The increased interest in rainfall erosivity studies and increased global research is inter alia attested by the number of research papers published; the number of papers indexed in the Web of Science under the topic “rainfall erosivity” grew from less than a few papers a year in 1980's and 1990's to over 50 papers a year in the last few years. The most widely used soil erosion models around the world (especially at large spatial scales (Panagos et al., 2014, 2016a)) are the Universal Soil Loss Equation (USLE; Wischmeier and Smith, 1978) and the Revised Universal Soil Loss Equation (RUSLE; Renard et al., 1997); the modern definition of rainfall erosivity began with the development of USLE (Nearing et al., 2017). The two models correlate the estimated quantitative value of soil loss per unit area (A) as the interaction among rainfall erosivity and runoff (R), soil erodibility (K), slope length (L) and slope steepness (S), land cover (C), and protective measures (P). The rainfall erosivity factor is one of the most frequently studied parameters
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among a set of RUSLE parameters (e.g. Panagos et al., 2017a, 2017b). Moreover, this parameter is often characterised by high spatial and temporal variability (e.g. Panagos et al., 2016a, 2017b), which makes it interesting to investigate, since it can have significant impact on the soil erosion rates. High-quality and high-frequency precipitation data is needed to accurately estimate the R-factor (e.g. Petan et al., 2010). While many authors have tried to determine R for various time resolutions with the intention of modelling the rainfall erosivity factor for areas with insufficient rainfall records (Angulo-Martínez and Beguería, 2009; Borrelli et al., 2016; Hernando and Romana, 2016; Renard and Freimund, 1994; Yin et al., 2015), studies spanning across countries and regions often struggle to use the uniform time step of rainfall data and long-time series (Ballabio et al., 2017; Panagos et al., 2015a). However, in the past decade a few studies have also investigated rainfall erosivity at larger spatial scales (e.g. Panagos et al., 2017a, 2017b). In Europe the highest values of the R-factor are characteristic of the Mediterranean and alpine regions (Panagos et al., 2017a). Studies have classified Slovenia and its western areas as one of the most rainfall erosive areas in Europe and even worldwide (Borrelli et al., 2016; Panagos et al., 2015b). Previous studies saw the average values for Rfactor estimated at above 2000 MJ mm ha −1h−1yr−1 in the north of
Corresponding author. E-mail address: [email protected] (N. Bezak).
https://doi.org/10.1016/j.envres.2018.08.020 Received 12 December 2017; Received in revised form 10 August 2018; Accepted 13 August 2018 Available online 15 August 2018 0013-9351/ © 2018 Elsevier Inc. All rights reserved.
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2.2. Rainfall erosivity R-factor
Slovenia (Mikoš et al., 2006). The average value of rainfall erosivity was estimated at 3393 MJ mm ha −1h−1yr−1 by Petan (2010), with values over 10,000 MJ mm ha −1h−1yr−1 in the Julian Alps, and the average value of R-factor dropping below 2000 MJ mm ha −1h−1yr−1 in the northeast of the country (Bezak et al., 2015). This means that local lower rainfall erosivity values (below 2000 MJ mm ha −1h−1yr−1) that are characteristic for the Slovenia northeast lead to lower average rainfall erosivity despite some local extremes. Soil loss in Slovenia is also an important environmental issue, as Slovenia is one of the EU countries with the highest local rainfall erosivity values (Panagos et al., 2017a). While the high values of the R-factor are correlated with areas of predominately frequent convective precipitation, Panagos et al. (2015b) concluded that the value of the R-factor is correlated with geographical latitude, precipitation seasonality, and altitude. Moreover, the high local R-values that were detected in Slovenia are also relatively high on a global scale, where values above 7000 MJ mm ha −1h−1yr−1 are characteristic of mostly tropical areas (Panagos et al., 2017b). On the other hand, for temperate climates the mean R-value is about 3700 MJ mm ha −1h−1yr−1 (Panagos et al., 2017b), which is relatively similar to the mean R annual value in Slovenia, which is predominantly covered by a temperate climate (Ogrin, 1996; Petan, 2010). Studies investigating trends in rainfall erosivity are rare because high-frequency data, which are needed to estimate the R-factor, are only available for the past 10 or 20 years. Some exceptions can be found around the world (e.g. Verstraeten et al., 2006). One of the few such studies was carried out by Mueller and Pfister (2011), who showed that a statistically significant increasing trend has been present for the last 35 years in a number of high-intensity rainfall events for the EmscherLippe catchment in Germany. Thus, various sources of information can be used to estimate future rainfall erosivity factor values. For example, estimations of future rainfall erosivity were made using climate change scenarios for several regions (Nearing et al., 2004; Panagos et al., 2017a; Plangoen and Babel, 2014; Zhang et al., 2006). Among these studies, a projected increase in future rainfall erosivity is common to a varying degree. In the study encompassing European countries (Panagos et al., 2017a) Slovenia was one of the three countries with a projected decrease in its rainfall erosivity factor, namely by 22.7% by 2050 (Panagos et al., 2017a). Since Slovenia has 10 stations with more than 25 years of high frequency data (5-min time step), this information can be used to evaluate consistency of projected future rainfall erosivity factor values with actual trends in the measured data. The aims of the study are as follows: (i) to evaluate the presence of trends in the rainfall erosivity Rfactor in Slovenia using a relatively long time series (10 stations between 25 and 69 years of data), and (ii) to perform a sensitivity analysis regarding parameters that are used to define erosive events and calculate R-factor according to the RUSLE methodology (Renard et al., 1997).
Rainfall erosivity, as one of the driving forces of soil erosion, encompasses particle detachment, the breaking up of agglomerates, and the transport of eroded particles by runoff (Wischmeier and Smith, 1978). As such, rainfall erosivity is determined by the various characteristics of a rainfall event, such as rainfall intensity and duration, the kinetic energy of raindrops, their size (diameter), and velocity (e.g. Petan et al., 2010). The rainfall erosivity factor R, as proposed by the (R)USLE methodology, is defined by the following equation (Renard et al., 1997):
R=
∑n E∙I30 N
(1)
where R represents the rainfall erosivity (in MJ mm ha −1h−1), E is the kinetic energy of a specific rainfall event (MJ ha −1), and I30 is the maximum 30-min intensity (mmh−1) of erosive event n , which occurred within a time span of N years. The kinetic energy E of a rainfall event can, however, be determined according to several different authors and equations (Brown and Foster, 1987; Ciaccioni et al., 2016; Petkovšek and Mikoš, 2004; Renard et al., 1997; van Dijk et al., 2002; Wischmeier and Smith, 1958). For Slovenia Petan (2010) developed equations for several stations located in three of Slovenia's climate types using the 1min rainfall data that was measured using an optical disdrometer for specific locations in Slovenia (Petan, 2010): i. mountain climate (station Bovec)
eB = 0.336∙ [1 − 0.60∙exp( −0.047∙I )]
(2)
sub-Mediterranean climate (station Kozjane)
eB = 0.318∙ [1 − 0.56∙exp( −0.056∙I )]
(3)
temperate continental climate (station Ljubljana)
eB = 0.310∙ [1 − 0.60∙exp( −0.074∙I )]
(4)
where eB is specific kinetic energy (MJ ha-1 mm-1) and I is rainfall intensity (mm h-1). Often the equation proposed by Brown and Foster (1987) is also used (e.g. Panagos et al., 2015b):
eB = 0.29∙ [1 − 0.72∙exp( −0.05∙I )]
(5)
or the equation suggested by van Dijk et al. (2002), which was formulated based on a review of the literature:
eB = 0.283∙ [1 − 0.52∙exp( −0.042∙I )]
(6)
The relationship between E and eB can be defined by (e.g. Renard et al., 1997):
E = eB ∙I∙∆t
(7)
where Δt is the time interval (h). In this study rainfall erosivity was calculated using Brown and Foster (1987), van Dijk et al. (2002) and local equations, developed for specific Slovenian gauging stations (Eqs. 2–4; Petan, 2010). Eq. (5) was used for the trend analysis. Meanwhile, all the equations listed above (Eqs. 2–6) were used for the sensitivity analysis. However, the Brown and Foster (1987) equation was used in order to evaluate the sensitivity of parameters that are used to calculate the rainfall erosivity. This equation is most frequently used (e.g. Panagos et al., 2016b) and it is also included in the Rainfall Intensity Summarisation Tool (RIST) software, which can be used to calculate rainfall erosivity (USDA, 2014). An erosive rainfall event, according to Renard et al. (1997), is an event with at least 12.7 mm of rain, or 6.35 mm of rain within 15 min. Events are split into two separate events if there is less than 1.27 mm of rain within 6 h. For stations listed in Table 1 the rainfall erosivity factor R was calculated using the above described procedure for the entire data period shown in Table 1.
2. Data and methods 2.1. Data High temporal resolution rainfall data from 10 pluviographic gauging stations located throughout Slovenia was analysed (Table 1) to achieve the aims of this study. The gauging stations were chosen among an existing network in Slovenia (ARSO, 2017), based on their geographic location (Fig. 1), their altitude, and a sufficient data length (a minimum of 25 years of data was selected). These 10 stations are the only ones that met the data length requirement. The time step of the selected data was 5 min. Data through the end of the year 2016 was used in the analyses (Table 1). Analysed stations are located in three different climate types: mountain, temperate continental, and subMediterranean (Table 1; Ogrin, 1996).
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Table 1 Basic characteristics of stations that were analysed in this study and have more than 25 years of 5-min rainfall data available. Station name
Altitude [m.a.s.l.]
Data start year
Data length [years]
Climate type
Rateče Postojna Šmarata Ljubljana Bežigrad Novo mesto Celje Slovenske Konjice Murska Sobota Vogel Portorož
864 533 80 299 220 242 330 187 1535 2
1975 1970 1975 1948 1970 1970 1975 1970 1982 1992
42 47 42 69 47 47 42 47 35 25
mountain temperate continental temperate continental temperate continental temperate continental temperate continental temperate continental temperate continental mountain sub-Mediterranean
because for this time period all the selected stations have data available (Table 2). Furthermore, sub-samples were defined in consideration of the entire year (from January until December) for the MK trend test, while in the second case only the period from May until October (halfyear) was considered. The reason for the selection of the latter scenario was snow precipitation, which is present during the winter in Slovenia. Different stations therefore have quite diverse amounts of snow precipitation. Thus, additional sub-samples were added in order to make the trend detection independent of the snow precipitation. A description of the sub-samples used in this study is given in Table 2. Additionally, trends were identified in the monthly rainfall erosivity values for May, June, July, August, and September. This analysis used the complete available data lengths shown in Table 2.
2.3. Trend detection The non-parametric Mann-Kendall test was used for trend detection in annual, half-year and monthly rainfall erosivity R-factor values for the 10 investigated stations (Fig. 1). The rainfall erosivity factor R was calculated using the method shown in Section 2.2 and using the Eq. (5) that was proposed by Brown and Foster (1987). More details about the Mann-Kendall test are available in Kendall (1975) or Douglas et al. (2000). The null hypothesis of this test is that there is not a trend present in the sample and the alternative hypothesis is that a monotonic trend exists in the sample. The Mann-Kendall test is frequently used to detect changes in the different types of environmental data (e.g. Bezak et al., 2016; Burn and Elnur, 2002; Douglas et al., 2000; Xiong and Guo, 2004). Moreover, one of the advantages of the Mann-Kendall test is robustness against tied values (Douglas et al., 2000) and also its low sensitivity to the breaks caused by the inhomogeneous data (Jaagus, 2006; Tabari et al., 2011). Since data availability differs for the selected stations, four sub-samples were defined: two including all the available data for specific station and two for the period from 1992 to 2016,
2.4. Sensitivity analysis The next aim of the study was to carry out a sensitivity analysis regarding the parameters that are used to define erosive events and calculate the R-factor according to the RUSLE methodology (Renard
Fig. 1. Location of the analysed stations on the map of Slovenia with the elevation legend [m]. The geographical coordinates are also shown on a map in order to indicate country location. 530
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Table 2 Sub-samples used in order to detect trends in rainfall erosivity R-factor values. Sub-sample
Sub-sample description
MK1
The complete available data lengths presented in Table 1 were used in order to derive annual rainfall erosivity values (it should be noted that not all stations had the same sub-sample size) The period from 1992 till 2016 was used for all stations in order to derive annual rainfall erosivity values (all stations had the same sub-sample size) The complete available data lengths presented in Table 1 were used (it should be noted that not all stations had the same sub-sample size) but only the period between May and October was considered in order to derive half-year rainfall erosivity values The period from 1992 till 2016 was used for all stations (all stations had the same sub-sample size) but only the period between May and October was considered in order to derive half-year rainfall erosivity values
MK2 MK3 MK4
Table 3 Initial parameter and changed parameter values that were used to calculate SRC and NSI. Parameter
Initial parameter value (equation) according to RUSLE
Modified parameter values (equations) used to calculate SRC and NSI
Time parameter t Rainfall amount parameter p Rainfall amount parameter k Time parameter l Rainfall amount parameter c
6h 1.27 mm 12.7 mm 15 min 6.2 mm
2 h, 4 h, 8 h, 10 h, and 12 h 0 mm, 0.32 mm, 0.64 mm, 1.59 mm, and 2.54 mm 0 mm, 3.18 mm, 6.35 mm, 15.88 mm, and 25.4 mm 5 min, 10 min, 20 min, 25 min, and 30 min 0 mm, 3.1 mm, 9.3 mm, 12.4 mm, and 15.5 mm
Murska Sobota stations can be regarded as typical mountain and lowland stations, respectively. These two stations also have the highest and the lowest number of erosive events according to the methodology proposed by Renard et al. (1997) among the 10 analysed stations in this study (Table 4). All the investigated stations have a similar temporal rainfall erosivity pattern with the highest rainfall erosivity values in the summer (i.e., July, August and September) (e.g. Panagos et al., 2016b). Fig. 2 shows temporal rainfall and rainfall erosivity distribution for four Slovenian stations where Eq. (5) was used for specific kinetic energy calculation. The trends were investigated due to the relatively long data series. Table 5 shows Mann-Kendall trend results for the annual rainfall erosivity R-values for the 10 analysed stations and four sub-samples. Trend results for the sub-sample MK2 (period 1992–2016) indicate that for eight stations the trend is positive, and for two stations located in the temperate continental climate the trend is negative. However, it should be noted that only for one of these eight stations the trend in annual Rvalues is statistically significant with the selected significance level of 0.05 (Table 5). For all other stations the calculated trend is not statistically significant with the selected significance level of 0.05. Furthermore, taking into account only half-year period from May to October for the precipitation data from 1992 until 2016 (MK4) results are relatively similar (Table 5). For six stations the Mann-Kendall test is positive and it is negative for four stations. However, only for two stations is the trend statistically significant with the selected significance level of 0.05 (one positive and one negative). Both stations are located in the temperate continental climate region. Mann-Kendall results for the MK1
et al., 1997). The sensitivity analysis used the methods presented in Section 2.2 to calculate the R-factor. According to Renard et al. (1997) only events with more than 12.7 mm (parameter k) are included in the computation of the R-factor unless 6.2 mm (parameter c) of rain fell in 15 min (parameter l). Moreover, a storm period with less than 1.27 mm (parameter p) in over 6 h (parameter t) is used to separate two consecutive rainfall events (Renard et al., 1997). This 12.7 mm threshold was at first used in order to reduce the computational burden in the Rfactor calculation (Wischmeier and Smith, 1978; Renard et al., 1997). Other parameters are used to separate individual erosive events (Renard et al., 1997). Thus, the idea of the sensitivity analysis was to detect which of these parameters have the largest influence on the rainfall erosivity calculation. In order to quantify the influence of an individual parameter, two local sensitivity methods were used, namely the Standard Regression Coefficient (SRC) and the Normalized Sensitivity Index (NSI) (Bezak et al., 2015; Gan et al., 2014). SRC computes regression between a vector of model input variables (in the case of rainfall erosivity the various parameter values shown in Table 3 were used) and model outputs (in our case the annual rainfall erosivity values). The higher the SRC result, the more sensitive the investigated parameter is (Gan et al., 2014). More information about the SRC can be found in Gan et al. (2014). NSI compares initial and changed parameter values (shown in Table 3) and model outputs (i.e. annual rainfall erosivity values calculated using initial and changed parameter values). High NSI values indicate that the investigated parameter had a large impact. More information about NSI can be found in Bezak et al. (2015). Program R package sensitivity was used to calculate SRC (Pujol et al., 2017). Table 3 shows initial parameter values and changes in the parameter values that were used in order to compute the SRC and NSI values. Moreover, the influence of the I-eb equation that is used to calculate specific kinetic energy on rainfall erosivity was also investigated. Eqs. (2)–(6) were used for this purpose. The calculated annual rainfall erosivity values using the various equations were evaluated.
Table 4 Average number of erosive events per year according to the methodology proposed by Renard et al. (1997) and total number of rainfall events per year (without using the k parameter 12.7 mm threshold; k = 0 mm).
3. Results and discussion 3.1. Trend analysis Slovenia is one of the EU countries with the highest rainfall erosivity values (e.g. Bezak et al., 2015). The maximum rainfall erosivity values are characteristic of mountain climates (in the NW part of the country); while, on the other hand, the smallest rainfall erosivity values are generally observed in the NE part of the country (Fig. 1). The Vogel and 531
Station name
Average number of erosive events per year
Total number of rainfall events per year
Rateče Postojna Šmarata Ljubljana Bežigrad Novo mesto Celje Slovenske Konjice Murska Sobota Vogel Portorož
23.0 27.5 26.4 28.3 25.4 24.7 24.5 17.2 30.9 23.7
101.0 110.1 124.0 128.9 133.3 122.8 99.8 122.5 104.3 132.2
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Fig. 2. Temporal rainfall [mm] and rainfall erosivity [(MJ mm)/(ha h month)] distribution for different stations (a) Vogel, b) Murska Sobota, c) Ljubljana, d) Portorož). It should be noted that rainfall erosivity for all rainfall events (parameter k value 0 mm) is shown and not just for the erosive ones based on the RUSLE methodology.
continental climate had a negative trend in rainfall erosivity values for all four sub-samples. However, again the detected trend was statistically significant only for one sub-samples. Thus, the measured rainfall data up to the year 2016 indicate that rainfall erosivity in Slovenia generally is not decreasing. However, future rainfall erosivity for Slovenia is projected to decrease by 22.7% through 2050 (Panagos et al., 2017a). Moreover, this projected decease cannot (yet) be detected in the rainfall erosivity data calculated, as based on the measured rainfall. Furthermore, for two stations (Rateče and Ljubljana Bežigrad, with the longest data length located in the mountain and temperate continental climates) the trend results for both MK1 and MK3 sub-samples are positive and statistically significant with the selected significance level 0.05. A possible explanation for the disagreement between observed trends in the measured data (this study) and future rainfall erosivity projections (Panagos et al., 2017a) could be that the European projections were made with a consideration of larger areas and without considering individual stations. Moreover, also the authors of the study indicated that results should be handled with care due to uncertainties related to the General Circulation Models (GCMs) and Regional Circulation Models (RCMs) (Panagos et al., 2017a). The results presented in this study are in line with the Mueller and Pfister (2011) study, who found a statistically significant increasing trend in the rainfall intensity data for the Emscher-Lippe catchment in Germany. However, Verstraeten et al. (2006) found no significant monotonic trend in
sub-sample are as follows; for nine stations the trend in annual R-values is positive and it is negative only for one station (Table 5). For this subsample the trends for five stations are statistically significant (all positive) with the selected significance level of 0.05. Furthermore, similar results were obtained for the MK3 sub-sample where only a half-year period was considered (May-October) (Table 5). For nine stations the Mann-Kendall trend results were positive and for one station negative (i.e. a station located in the temperate continental climate). However, for three stations the trend results were statistically significant with the selected significance level of 0.05 (two positive and one negative). The Mann-Kendall trend results can be summarized as follows; most of the detected trends were not statistically significant with the selected significance level of 0.05 (Table 5). However, a larger percent of statistically significant trends were positive than negative (Table 5). It is evident that some stations (Postojna, Ljubljana and Vogel) showed a different trend depending on the selected sub-sample (Table 5). Similar results were also obtained by Bezak et al. (2016) when analysing changes in the flood data, where annual maxima (AM) or peaks over threshold (POT) sub-samples resulted in different trends. Furthermore, for Rateče, Šmarata, Celje, Slovenske Konjice, Murska Sobota, and Portorož the stations trends were positive for all four tested sub-samples, yet mostly statistically insignificant with the selected significance level of 0.05. These stations are located in different climate zones (Table 1). The Novo mesto station that is located in the temperate
Table 5 Mann-Kendall trend test results (τ ) with corresponding p-values (p) for the four different sub-samples defined in Table 2 for 10 analysed rainfall stations in Slovenia. Station name / Sub-sample
Rateče Postojna Šmarata Ljubljana Bežigrad Novo mesto Celje Slovenske Konjice Murska Sobota Vogel Portorož
MK1
MK2
MK3
MK4
τ
p
τ
p
τ
p
τ
p
0.333 0.247 0.275 0.218 − 0.175 0.230 0.022 0.179 0.166 0.16
0.002 0.015 0.010 0.008 0.085 0.023 0.845 0.078 0.164 0.272
0.073 − 0.213 0.107 0.013 − 0.133 0.007 0.08 0.387 0.127 0.16
0.624 0.141 0.469 0.944 0.362 0.981 0.591 0.007 0.387 0.272
0.217 0.003 0.166 0.176 − 0.201 0.186 0.038 0.164 0.039 0.007
0.044 0.985 0.124 0.032 0.048 0.067 0.729 0.107 0.755 0.981
0.053 − 0.327 0.120 − 0.02 − 0.147 0 0.153 0.387 − 0.087 0.007
0.726 0.023 0.414 0.907 0.315 1 0.293 0.007 0.559 0.981
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Table 6 Mann-Kendall trend test results (τ ) for May, June, July, August, and September using all the available data shown in Table 1. Test results that are indicated with * are statistically significant with the selected significance level of 0.05. Station/Month
May
June
July
August
September
Rateče Postojna Šmarata Ljubljana Bežigrad Novo mesto Celje Slovenske Konjice Murska Sobota Vogel Portorož
0.131 0.039 0.182 − 0.004 0.214 * 0.202 0.264 * 0.137 − 0.016 0.203
0.090 − 0.014 − 0.010 0.057 0.001 0.067 − 0.046 0.145 0.095 0.056
0.038 0.096 0.161 0.083 − 0.091 0.142 − 0.264 * 0.087 0.032 0.228
0.002 − 0.114 0.123 0.047 − 0.183 0.085 0.215 0.134 0.032 0.088
0.027 0.061 0.017 0.032 0.056 0.176 0.015 0.004 0.012 0.004
Table 7 SRC and average NSI values for 10 analysed stations for five different parameters (t (time parameter, usually 6 h), p (rainfall amount parameter, usually 1.27 mm), k (rainfall amount parameter, usually 12.7 mm), l (time parameter, usually 15 min), and c (rainfall amount parameter, usually 6.2 mm)) that are used to define erosive events and are consequently used to calculate rainfall erosivity R-factor values according to the RUSLE methodology (Renard et al., 1997). A detailed description of these different parameters is given in Section 2.4. Table 3 shows the initial and modified parameter values that were used to calculate SRC and NSI. Station/parameter
Test
t
p
k
l
c
Rateče
SRC NSI SRC NSI SRC NSI SRC NSI SRC NSI SRC NSI SRC NSI SRC NSI SRC NSI SRC NSI
0.962 0.109 0.975 0.119 0.966 0.111 0.961 0.106 0.977 0.104 0.964 0.096 0.976 0.098 0.977 0.085 0.951 0.084 0.960 0.082
− 0.950 0.049 − 0.914 0.053 − 0.935 0.051 − 0.927 0.052 − 0.918 0.054 − 0.930 0.049 − 0.915 0.050 − 0.962 0.050 − 0.970 0.028 − 0.945 0.044
− 0.994 0.130 − 0.995 0.115 − 0.995 0.117 − 0.993 0.117 − 0.995 0.170 − 0.994 0.164 − 0.994 0.160 − 0.994 0.185 − 0.994 0.034 − 0.995 0.089
0.820 0.005 0.719 0.006 0.912 0.005 0.858 0.007 0.872 0.011 0.837 0.007 0.809 0.007 0.838 0.014 0.855 0.002 0.580 0.010
− 0.845 0.030 − 0.878 0.031 − 0.843 0.029 − 0.864 0.029 − 0.853 0.044 − 0.863 0.039 − 0.869 0.039 − 0.870 0.051 − 0.864 0.008 − 0.910 0.031
Postojna Šmarata
annual R-values calculated using 105 years of 10-min data for a gauging station in Belgium. However, a standard normal homogeneity test indicated lower R-values for the period 1898–1990 in comparison to the period 1991–2002 (Verstraeten et al., 2006). Because in Slovenia the highest monthly rainfall erosivity is in the summer (Fig. 2), we also calculated Mann-Kendall test for May, June, July, August, and September (Table 6). Only in three cases was the detected trend statistically significant with the selected significance level of 0.05 (in two cases positive and in one case negative) (Table 6). Moreover, a larger percent of statistically insignificant trends was positive than negative, which is in line with results presented in Table 5. Milošević et al. (2016) found decreasing trends in rainfall amounts with some differences between seasons for Slovenia. Furthermore, for most of the country summer rainfall amounts were decreasing as well (Milošević et al., 2016). Similar results were also obtained by Bezak et al. (2016). This could be explained by the fact that the most intense rainfall events are more frequent (i.e. more frequent and more intense summer thunderstorms due to higher air temperature) and these events have the largest impact on the rainfall erosivity and consequently also on soil erosion and sediment transport in rivers.
Ljubljana Bežigrad Novo mesto Celje Slovenske Konjice Murska Sobota Vogel Portorož
smaller number of events. For example, for the Murska Sobota station, which has the maximum SRC for the t parameter, the use of the 12 h k parameter results in about a 7% higher average annual R-value compared to the initial t value (6 h) proposed in the RUSLE methodology (Renard et al., 1997). The other three parameters (p, l, and c) that are used to define erosive events have, on average, a smaller impact for these 10 stations on average annual R-values (Table 7). More specifically, higher p parameter values result in smaller R-values and viceversa. For example, for the Murska Sobota station the use of 2.54 mm instead of 1.27 mm for the p parameter results in about 3% lower average annual R-values. The influence of the l and c parameters, which are used to include short duration erosive events in the R-values calculation, is even smaller (Renard et al., 1997). Higher l parameter values correspond to an increase in the duration of the short-duration events. The maximum SRC for the l parameter was obtained for the Šmarata station (Table 7). Smaller c parameter values result in higher R-values. The maximum absolute SRC for parameter c is obtained for the Portorož station (Table 7). More specifically, a higher c parameter value (15.5 mm instead of initial 6.2 mm) results in about a 2% smaller average annual R-value. The sensitivity of five parameters that are used to define erosive events according to the RUSLE methodology (Renard et al., 1997) was also investigated using the NSI (Table 7). Similarly to SRC, also the application of NSI indicates that on average k and t parameters have the largest impact on the average annual R-values (Table 7). It can be seen that average k and t parameter value for 10 stations is 0.13 and 0.10, respectively (Table 7). On the other hand, average NSI values for p, l, and c parameters are 0.05, 0.08, and 0.03, respectively (Table 7). The sensitivity analysis results can be summarized as follows: the development of computer processing power and software development such as RIST (USDA, 2014) has made it possible to analyse large amounts of high-frequency data in a few minutes. This means that rainfall erosivity R-factor calculation is faster today than it was in times of Wischmeier and Smith (1978) or even Renard et al. (1997) and larger amounts of data can be processed. Thus, applying the k parameter that was initially defined only due to the reduced computational burden is meaningful only because it can yield results that
3.2. Sensitivity analysis Table 7 shows calculated SRC values for analysed stations in Slovenia for 5 parameters that were used to define the erosive events and are presented in Table 3. The higher the SRC value, the more sensitive the investigated parameter (Gan et al., 2014) is. It can be seen that on average the highest SRC values are obtained for the rainfall amount parameter k, which is used to define erosive events. With a decreasing k value (e.g. from 12.7 mm to 0 mm), which means that we also take into consideration rainfall events with small rainfall erosivity, higher R-values are obtained. Fig. 3 shows the decrease in the annual rainfall erosivity for the increasing k parameter values. One can notice that all stations indicate a similar decrease in rainfall erosivity with the increase in the k parameter. This relationship is relatively linear for most of the stations. Using the k parameter value of 0 mm resulted in approximately 10% higher average annual R-values than when using the initial k parameter value (12.7 mm) proposed by the Renard et al. (1997) for the Murska Sobota station. Moreover, similar results were also obtained for other analysed stations (Table 7 and Fig. 3). However, it should be noted that lowering the k parameter also introduces smallmagnitude rainfall events in the rainfall erosivity data that do not even result in surface runoff or soil erosion processes. On the other hand, using a higher k parameter (e.g. in order to additionally reduce the computational burden) of 25.4 mm results in up to about 15% lower average annual R-values depending on the station. The second-most sensitive parameter is the time parameter t, used to separate (or merge) consecutive rainfall events (Table 7). Using larger t values (e.g. 12 h instead of 6 h) results in larger average annual R-values. Larger t values result in the lumping of several consecutive rainfall events into a 533
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Fig. 3. Relationship between annual rainfall erosivity values and the k parameter used to select only events with more than k mm of rain (usually 12.7 mm is used) for the 10 Slovenian stations. The Vogel station is shown on its own figure in order to improve the readability of figures due to large differences in annual rainfall erosivity values among stations.
decades have generally been decreasing (Milošević et al., 2016). This decrease is also evident in summer rainfall amounts (Milošević et al., 2016), which could indicate that most erosive events that have the largest impact on the annual and monthly rainfall erosivity are more frequent (i.e. summer thunderstorms). Moreover, the observed trends for monthly rainfall erosivity for May, June, July, August, and September were also mostly statistically insignificant (significance level of 0.05) with a larger percentage of positive trends, which could indicate a slight (statistically non-significant) increase in summer extreme events. ii) The sensitivity analysis showed that the k parameter (rainfall amount threshold; usually 12.7 mm is used) that was initially defined in order to reduce the computational burden in the R-factor calculations (and remove the small-magnitude events that could have minor impact on the soil erosion rates) can attribute to up to 10% of the average annual R-factor if this threshold is removed (k parameter value 0 mm). Moreover, the decrease in the annual rainfall erosivity with the increasing k parameter value is relatively linear (Fig. 3). This parameter has the largest impact on the R-factor calculation among the analysed parameters that are used to define the erosive events. Moreover, it was also found that t (the time parameter, usually 6 h) and p (the rainfall amount parameter, usually 1.27 mm) parameters have a larger influence on the R-factor calculation than c (rainfall amount parameter, usually 6.2 mm) and l (time parameter, usually 15 min) parameters. Furthermore, selection of the kinetic energy equation has even larger impact on the calculated annual rainfall erosivity. More specifically, this study indicated that the use of local Slovenian equations (Eq. (2)–(4)) resulted in, on average, about 20% higher annual rainfall erosivity values compared to the Brown and Foster (1987) equation (Eq. (5)).
are comparable with previous studies. However, it would also be relevant to report R-values of all rainfall events (k parameter value 0 mm) and not just erosive (according to the Renard et al., 1997 definition) ones, since differences in average annual R values can amount up to 10% (using the k parameter 0 mm). However, it should be noted that these small magnitude rainfall events do not always result in soil erosion processes. Another important step that must be made when calculating rainfall erosivity is the selection of the kinetic energy equation. Lobo and Bonilla (2015) have shown that differences in erosivity can amount up to three times with the application of various equations. Moreover, differences were the largest for rainfall events with lower intensities and smaller for rainfall events with higher intensities. Furthermore, also Angulo-Martínez et al. (2016) found that none of the kinetic energy equation should be used universally and applying the equation far from the location for which it was developed should be limited. A comparison that was made in this study indicated that the use of Eqs. (5) and (6) results in, on average, about 20% and 12% lower annual rainfall erosivity values, respectively, than the use of local equations that were developed specifically for Slovenian climate conditions (Eqs. (2)–(4)). Thus, it seems that the impact of the kinetic energy equation is larger than the impact of different parameters that are used to define erosive events. Moreover, differences between the local equation (Eqs. (2)–(4)) and the equation proposed by Brown and Foster (1987) were slightly larger for the station located in the sub-Mediterranean climate than for stations located in the other two climate zones in Slovenia. However, it should be noted that only one station from the sub-Mediterranean climate was analysed in this study. For other stations in Slovenia the calculated differences were relatively similar. 4. Conclusions
Acknowledgment The presented study shows results of the rainfall erosivity R-factor evaluation for the 10 analysed stations with at least 25 years (maximum is 69 years of data) of high-frequency data (5-min) from Slovenia (Europe). The analysed stations are located in three different climate types, namely sub-Mediterranean, temperate continental, and mountain climate. Trends were analysed using the Mann-Kendall test and with the application of four different sub-samples. Sensitivity analysis was carried out using the SRC and NSI. Based on the presented results the following conclusions can be made:
We wish to thank the Environmental Agency of the Republic of Slovenia for providing data. The critical and useful comments of two anonymous reviewers and the guest editor improved this work, for which the authors are very grateful. We also gratefully acknowledge Mr. J. Rocchio for his English language editorial support. Funding The results of the study are part of the research Programme P2–0180: “Water Science and Technology, and Geotechnical Engineering: Tools and Methods for Process Analyses and Simulations, and Development of Technologies” that is financed by the Slovenian Research Agency (ARRS) (Grant number P2-0180).
i) The detected trends in rainfall erosivity for different sub-samples are mostly statistically insignificant with the selected significance level of 0.05. However, a larger percentage of detected trends is positive than negative (both for statistically significant and non-significant trends). For six stations trends were always positive (all four subsamples) yet not always statistically significant. Only for one of the 10 analysed stations were negative trends observed for all four defined sub-samples (located in the temperate continental climate) despite the fact that annual rainfall amounts in Slovenia in recent
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Rainfall erosivity in Slovenia: Sensitivity estimation and trend detection Manca Petek, Matjaž Mikoš, Nejc Bezak
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University of Ljubljana, Faculty of Civil and Geodetic Engineering, Slovenia
A R T I C LE I N FO
A B S T R A C T
Keywords: Rainfall erosivity Trend detection Sensitivity analyses Slovenia
Slovenia is one of the EU countries with the largest values and largest amounts of variability in rainfall erosivity, with maximum annual values exceeding 10,000 MJ mm ha-1 h-1 yr-1. Five-minute rainfall data was analysed from 10 Slovenian rainfall stations with data-length availability longer than 25 years with a maximum data length of 69 years and a total data-station length equal to 443 years. Trends in the rainfall erosivity R-factor were detected for four different sub-samples using monthly, half-year, and annual rainfall erosivity values. The results indicate that rainfall erosivity trends for the selected Slovenian stations are mostly statistically insignificant, with the selected significance level of 0.05. However, a larger share of identified trends are positive than negative. The maximum annual rainfall erosivity values were obtained for one specific mountain station. Furthermore, a sensitivity analysis regarding the rainfall erosivity factor R calculation showed that the rainfall threshold parameter (12.7 mm) that is used to remove the small-magnitude rainfall events in order to reduce the computational burden can attribute up to 10% of the average annual R-values in cases where this threshold is not used. Other parameters have, on average, a smaller impact on the calculated rainfall erosivity. Furthermore, the application of local kinetic energy equations resulted in, on average, about 20% higher annual rainfall erosivity values compared to the equation that is proposed by the Revised Universal Soil Loss Equation (RUSLE) manual and was not developed specifically for this region.
1. Introduction As soil erosion is one of modern agriculture's major challenges, rainfall erosivity as one of its parameters plays an important role in estimating and modelling both soil erosion and its overall impacts on society and the environment. The increased interest in rainfall erosivity studies and increased global research is inter alia attested by the number of research papers published; the number of papers indexed in the Web of Science under the topic “rainfall erosivity” grew from less than a few papers a year in 1980's and 1990's to over 50 papers a year in the last few years. The most widely used soil erosion models around the world (especially at large spatial scales (Panagos et al., 2014, 2016a)) are the Universal Soil Loss Equation (USLE; Wischmeier and Smith, 1978) and the Revised Universal Soil Loss Equation (RUSLE; Renard et al., 1997); the modern definition of rainfall erosivity began with the development of USLE (Nearing et al., 2017). The two models correlate the estimated quantitative value of soil loss per unit area (A) as the interaction among rainfall erosivity and runoff (R), soil erodibility (K), slope length (L) and slope steepness (S), land cover (C), and protective measures (P). The rainfall erosivity factor is one of the most frequently studied parameters
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among a set of RUSLE parameters (e.g. Panagos et al., 2017a, 2017b). Moreover, this parameter is often characterised by high spatial and temporal variability (e.g. Panagos et al., 2016a, 2017b), which makes it interesting to investigate, since it can have significant impact on the soil erosion rates. High-quality and high-frequency precipitation data is needed to accurately estimate the R-factor (e.g. Petan et al., 2010). While many authors have tried to determine R for various time resolutions with the intention of modelling the rainfall erosivity factor for areas with insufficient rainfall records (Angulo-Martínez and Beguería, 2009; Borrelli et al., 2016; Hernando and Romana, 2016; Renard and Freimund, 1994; Yin et al., 2015), studies spanning across countries and regions often struggle to use the uniform time step of rainfall data and long-time series (Ballabio et al., 2017; Panagos et al., 2015a). However, in the past decade a few studies have also investigated rainfall erosivity at larger spatial scales (e.g. Panagos et al., 2017a, 2017b). In Europe the highest values of the R-factor are characteristic of the Mediterranean and alpine regions (Panagos et al., 2017a). Studies have classified Slovenia and its western areas as one of the most rainfall erosive areas in Europe and even worldwide (Borrelli et al., 2016; Panagos et al., 2015b). Previous studies saw the average values for Rfactor estimated at above 2000 MJ mm ha −1h−1yr−1 in the north of
Corresponding author. E-mail address: [email protected] (N. Bezak).
https://doi.org/10.1016/j.envres.2018.08.020 Received 12 December 2017; Received in revised form 10 August 2018; Accepted 13 August 2018 Available online 15 August 2018 0013-9351/ © 2018 Elsevier Inc. All rights reserved.
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2.2. Rainfall erosivity R-factor
Slovenia (Mikoš et al., 2006). The average value of rainfall erosivity was estimated at 3393 MJ mm ha −1h−1yr−1 by Petan (2010), with values over 10,000 MJ mm ha −1h−1yr−1 in the Julian Alps, and the average value of R-factor dropping below 2000 MJ mm ha −1h−1yr−1 in the northeast of the country (Bezak et al., 2015). This means that local lower rainfall erosivity values (below 2000 MJ mm ha −1h−1yr−1) that are characteristic for the Slovenia northeast lead to lower average rainfall erosivity despite some local extremes. Soil loss in Slovenia is also an important environmental issue, as Slovenia is one of the EU countries with the highest local rainfall erosivity values (Panagos et al., 2017a). While the high values of the R-factor are correlated with areas of predominately frequent convective precipitation, Panagos et al. (2015b) concluded that the value of the R-factor is correlated with geographical latitude, precipitation seasonality, and altitude. Moreover, the high local R-values that were detected in Slovenia are also relatively high on a global scale, where values above 7000 MJ mm ha −1h−1yr−1 are characteristic of mostly tropical areas (Panagos et al., 2017b). On the other hand, for temperate climates the mean R-value is about 3700 MJ mm ha −1h−1yr−1 (Panagos et al., 2017b), which is relatively similar to the mean R annual value in Slovenia, which is predominantly covered by a temperate climate (Ogrin, 1996; Petan, 2010). Studies investigating trends in rainfall erosivity are rare because high-frequency data, which are needed to estimate the R-factor, are only available for the past 10 or 20 years. Some exceptions can be found around the world (e.g. Verstraeten et al., 2006). One of the few such studies was carried out by Mueller and Pfister (2011), who showed that a statistically significant increasing trend has been present for the last 35 years in a number of high-intensity rainfall events for the EmscherLippe catchment in Germany. Thus, various sources of information can be used to estimate future rainfall erosivity factor values. For example, estimations of future rainfall erosivity were made using climate change scenarios for several regions (Nearing et al., 2004; Panagos et al., 2017a; Plangoen and Babel, 2014; Zhang et al., 2006). Among these studies, a projected increase in future rainfall erosivity is common to a varying degree. In the study encompassing European countries (Panagos et al., 2017a) Slovenia was one of the three countries with a projected decrease in its rainfall erosivity factor, namely by 22.7% by 2050 (Panagos et al., 2017a). Since Slovenia has 10 stations with more than 25 years of high frequency data (5-min time step), this information can be used to evaluate consistency of projected future rainfall erosivity factor values with actual trends in the measured data. The aims of the study are as follows: (i) to evaluate the presence of trends in the rainfall erosivity Rfactor in Slovenia using a relatively long time series (10 stations between 25 and 69 years of data), and (ii) to perform a sensitivity analysis regarding parameters that are used to define erosive events and calculate R-factor according to the RUSLE methodology (Renard et al., 1997).
Rainfall erosivity, as one of the driving forces of soil erosion, encompasses particle detachment, the breaking up of agglomerates, and the transport of eroded particles by runoff (Wischmeier and Smith, 1978). As such, rainfall erosivity is determined by the various characteristics of a rainfall event, such as rainfall intensity and duration, the kinetic energy of raindrops, their size (diameter), and velocity (e.g. Petan et al., 2010). The rainfall erosivity factor R, as proposed by the (R)USLE methodology, is defined by the following equation (Renard et al., 1997):
R=
∑n E∙I30 N
(1)
where R represents the rainfall erosivity (in MJ mm ha −1h−1), E is the kinetic energy of a specific rainfall event (MJ ha −1), and I30 is the maximum 30-min intensity (mmh−1) of erosive event n , which occurred within a time span of N years. The kinetic energy E of a rainfall event can, however, be determined according to several different authors and equations (Brown and Foster, 1987; Ciaccioni et al., 2016; Petkovšek and Mikoš, 2004; Renard et al., 1997; van Dijk et al., 2002; Wischmeier and Smith, 1958). For Slovenia Petan (2010) developed equations for several stations located in three of Slovenia's climate types using the 1min rainfall data that was measured using an optical disdrometer for specific locations in Slovenia (Petan, 2010): i. mountain climate (station Bovec)
eB = 0.336∙ [1 − 0.60∙exp( −0.047∙I )]
(2)
sub-Mediterranean climate (station Kozjane)
eB = 0.318∙ [1 − 0.56∙exp( −0.056∙I )]
(3)
temperate continental climate (station Ljubljana)
eB = 0.310∙ [1 − 0.60∙exp( −0.074∙I )]
(4)
where eB is specific kinetic energy (MJ ha-1 mm-1) and I is rainfall intensity (mm h-1). Often the equation proposed by Brown and Foster (1987) is also used (e.g. Panagos et al., 2015b):
eB = 0.29∙ [1 − 0.72∙exp( −0.05∙I )]
(5)
or the equation suggested by van Dijk et al. (2002), which was formulated based on a review of the literature:
eB = 0.283∙ [1 − 0.52∙exp( −0.042∙I )]
(6)
The relationship between E and eB can be defined by (e.g. Renard et al., 1997):
E = eB ∙I∙∆t
(7)
where Δt is the time interval (h). In this study rainfall erosivity was calculated using Brown and Foster (1987), van Dijk et al. (2002) and local equations, developed for specific Slovenian gauging stations (Eqs. 2–4; Petan, 2010). Eq. (5) was used for the trend analysis. Meanwhile, all the equations listed above (Eqs. 2–6) were used for the sensitivity analysis. However, the Brown and Foster (1987) equation was used in order to evaluate the sensitivity of parameters that are used to calculate the rainfall erosivity. This equation is most frequently used (e.g. Panagos et al., 2016b) and it is also included in the Rainfall Intensity Summarisation Tool (RIST) software, which can be used to calculate rainfall erosivity (USDA, 2014). An erosive rainfall event, according to Renard et al. (1997), is an event with at least 12.7 mm of rain, or 6.35 mm of rain within 15 min. Events are split into two separate events if there is less than 1.27 mm of rain within 6 h. For stations listed in Table 1 the rainfall erosivity factor R was calculated using the above described procedure for the entire data period shown in Table 1.
2. Data and methods 2.1. Data High temporal resolution rainfall data from 10 pluviographic gauging stations located throughout Slovenia was analysed (Table 1) to achieve the aims of this study. The gauging stations were chosen among an existing network in Slovenia (ARSO, 2017), based on their geographic location (Fig. 1), their altitude, and a sufficient data length (a minimum of 25 years of data was selected). These 10 stations are the only ones that met the data length requirement. The time step of the selected data was 5 min. Data through the end of the year 2016 was used in the analyses (Table 1). Analysed stations are located in three different climate types: mountain, temperate continental, and subMediterranean (Table 1; Ogrin, 1996).
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Table 1 Basic characteristics of stations that were analysed in this study and have more than 25 years of 5-min rainfall data available. Station name
Altitude [m.a.s.l.]
Data start year
Data length [years]
Climate type
Rateče Postojna Šmarata Ljubljana Bežigrad Novo mesto Celje Slovenske Konjice Murska Sobota Vogel Portorož
864 533 80 299 220 242 330 187 1535 2
1975 1970 1975 1948 1970 1970 1975 1970 1982 1992
42 47 42 69 47 47 42 47 35 25
mountain temperate continental temperate continental temperate continental temperate continental temperate continental temperate continental temperate continental mountain sub-Mediterranean
because for this time period all the selected stations have data available (Table 2). Furthermore, sub-samples were defined in consideration of the entire year (from January until December) for the MK trend test, while in the second case only the period from May until October (halfyear) was considered. The reason for the selection of the latter scenario was snow precipitation, which is present during the winter in Slovenia. Different stations therefore have quite diverse amounts of snow precipitation. Thus, additional sub-samples were added in order to make the trend detection independent of the snow precipitation. A description of the sub-samples used in this study is given in Table 2. Additionally, trends were identified in the monthly rainfall erosivity values for May, June, July, August, and September. This analysis used the complete available data lengths shown in Table 2.
2.3. Trend detection The non-parametric Mann-Kendall test was used for trend detection in annual, half-year and monthly rainfall erosivity R-factor values for the 10 investigated stations (Fig. 1). The rainfall erosivity factor R was calculated using the method shown in Section 2.2 and using the Eq. (5) that was proposed by Brown and Foster (1987). More details about the Mann-Kendall test are available in Kendall (1975) or Douglas et al. (2000). The null hypothesis of this test is that there is not a trend present in the sample and the alternative hypothesis is that a monotonic trend exists in the sample. The Mann-Kendall test is frequently used to detect changes in the different types of environmental data (e.g. Bezak et al., 2016; Burn and Elnur, 2002; Douglas et al., 2000; Xiong and Guo, 2004). Moreover, one of the advantages of the Mann-Kendall test is robustness against tied values (Douglas et al., 2000) and also its low sensitivity to the breaks caused by the inhomogeneous data (Jaagus, 2006; Tabari et al., 2011). Since data availability differs for the selected stations, four sub-samples were defined: two including all the available data for specific station and two for the period from 1992 to 2016,
2.4. Sensitivity analysis The next aim of the study was to carry out a sensitivity analysis regarding the parameters that are used to define erosive events and calculate the R-factor according to the RUSLE methodology (Renard
Fig. 1. Location of the analysed stations on the map of Slovenia with the elevation legend [m]. The geographical coordinates are also shown on a map in order to indicate country location. 530
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Table 2 Sub-samples used in order to detect trends in rainfall erosivity R-factor values. Sub-sample
Sub-sample description
MK1
The complete available data lengths presented in Table 1 were used in order to derive annual rainfall erosivity values (it should be noted that not all stations had the same sub-sample size) The period from 1992 till 2016 was used for all stations in order to derive annual rainfall erosivity values (all stations had the same sub-sample size) The complete available data lengths presented in Table 1 were used (it should be noted that not all stations had the same sub-sample size) but only the period between May and October was considered in order to derive half-year rainfall erosivity values The period from 1992 till 2016 was used for all stations (all stations had the same sub-sample size) but only the period between May and October was considered in order to derive half-year rainfall erosivity values
MK2 MK3 MK4
Table 3 Initial parameter and changed parameter values that were used to calculate SRC and NSI. Parameter
Initial parameter value (equation) according to RUSLE
Modified parameter values (equations) used to calculate SRC and NSI
Time parameter t Rainfall amount parameter p Rainfall amount parameter k Time parameter l Rainfall amount parameter c
6h 1.27 mm 12.7 mm 15 min 6.2 mm
2 h, 4 h, 8 h, 10 h, and 12 h 0 mm, 0.32 mm, 0.64 mm, 1.59 mm, and 2.54 mm 0 mm, 3.18 mm, 6.35 mm, 15.88 mm, and 25.4 mm 5 min, 10 min, 20 min, 25 min, and 30 min 0 mm, 3.1 mm, 9.3 mm, 12.4 mm, and 15.5 mm
Murska Sobota stations can be regarded as typical mountain and lowland stations, respectively. These two stations also have the highest and the lowest number of erosive events according to the methodology proposed by Renard et al. (1997) among the 10 analysed stations in this study (Table 4). All the investigated stations have a similar temporal rainfall erosivity pattern with the highest rainfall erosivity values in the summer (i.e., July, August and September) (e.g. Panagos et al., 2016b). Fig. 2 shows temporal rainfall and rainfall erosivity distribution for four Slovenian stations where Eq. (5) was used for specific kinetic energy calculation. The trends were investigated due to the relatively long data series. Table 5 shows Mann-Kendall trend results for the annual rainfall erosivity R-values for the 10 analysed stations and four sub-samples. Trend results for the sub-sample MK2 (period 1992–2016) indicate that for eight stations the trend is positive, and for two stations located in the temperate continental climate the trend is negative. However, it should be noted that only for one of these eight stations the trend in annual Rvalues is statistically significant with the selected significance level of 0.05 (Table 5). For all other stations the calculated trend is not statistically significant with the selected significance level of 0.05. Furthermore, taking into account only half-year period from May to October for the precipitation data from 1992 until 2016 (MK4) results are relatively similar (Table 5). For six stations the Mann-Kendall test is positive and it is negative for four stations. However, only for two stations is the trend statistically significant with the selected significance level of 0.05 (one positive and one negative). Both stations are located in the temperate continental climate region. Mann-Kendall results for the MK1
et al., 1997). The sensitivity analysis used the methods presented in Section 2.2 to calculate the R-factor. According to Renard et al. (1997) only events with more than 12.7 mm (parameter k) are included in the computation of the R-factor unless 6.2 mm (parameter c) of rain fell in 15 min (parameter l). Moreover, a storm period with less than 1.27 mm (parameter p) in over 6 h (parameter t) is used to separate two consecutive rainfall events (Renard et al., 1997). This 12.7 mm threshold was at first used in order to reduce the computational burden in the Rfactor calculation (Wischmeier and Smith, 1978; Renard et al., 1997). Other parameters are used to separate individual erosive events (Renard et al., 1997). Thus, the idea of the sensitivity analysis was to detect which of these parameters have the largest influence on the rainfall erosivity calculation. In order to quantify the influence of an individual parameter, two local sensitivity methods were used, namely the Standard Regression Coefficient (SRC) and the Normalized Sensitivity Index (NSI) (Bezak et al., 2015; Gan et al., 2014). SRC computes regression between a vector of model input variables (in the case of rainfall erosivity the various parameter values shown in Table 3 were used) and model outputs (in our case the annual rainfall erosivity values). The higher the SRC result, the more sensitive the investigated parameter is (Gan et al., 2014). More information about the SRC can be found in Gan et al. (2014). NSI compares initial and changed parameter values (shown in Table 3) and model outputs (i.e. annual rainfall erosivity values calculated using initial and changed parameter values). High NSI values indicate that the investigated parameter had a large impact. More information about NSI can be found in Bezak et al. (2015). Program R package sensitivity was used to calculate SRC (Pujol et al., 2017). Table 3 shows initial parameter values and changes in the parameter values that were used in order to compute the SRC and NSI values. Moreover, the influence of the I-eb equation that is used to calculate specific kinetic energy on rainfall erosivity was also investigated. Eqs. (2)–(6) were used for this purpose. The calculated annual rainfall erosivity values using the various equations were evaluated.
Table 4 Average number of erosive events per year according to the methodology proposed by Renard et al. (1997) and total number of rainfall events per year (without using the k parameter 12.7 mm threshold; k = 0 mm).
3. Results and discussion 3.1. Trend analysis Slovenia is one of the EU countries with the highest rainfall erosivity values (e.g. Bezak et al., 2015). The maximum rainfall erosivity values are characteristic of mountain climates (in the NW part of the country); while, on the other hand, the smallest rainfall erosivity values are generally observed in the NE part of the country (Fig. 1). The Vogel and 531
Station name
Average number of erosive events per year
Total number of rainfall events per year
Rateče Postojna Šmarata Ljubljana Bežigrad Novo mesto Celje Slovenske Konjice Murska Sobota Vogel Portorož
23.0 27.5 26.4 28.3 25.4 24.7 24.5 17.2 30.9 23.7
101.0 110.1 124.0 128.9 133.3 122.8 99.8 122.5 104.3 132.2
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Fig. 2. Temporal rainfall [mm] and rainfall erosivity [(MJ mm)/(ha h month)] distribution for different stations (a) Vogel, b) Murska Sobota, c) Ljubljana, d) Portorož). It should be noted that rainfall erosivity for all rainfall events (parameter k value 0 mm) is shown and not just for the erosive ones based on the RUSLE methodology.
continental climate had a negative trend in rainfall erosivity values for all four sub-samples. However, again the detected trend was statistically significant only for one sub-samples. Thus, the measured rainfall data up to the year 2016 indicate that rainfall erosivity in Slovenia generally is not decreasing. However, future rainfall erosivity for Slovenia is projected to decrease by 22.7% through 2050 (Panagos et al., 2017a). Moreover, this projected decease cannot (yet) be detected in the rainfall erosivity data calculated, as based on the measured rainfall. Furthermore, for two stations (Rateče and Ljubljana Bežigrad, with the longest data length located in the mountain and temperate continental climates) the trend results for both MK1 and MK3 sub-samples are positive and statistically significant with the selected significance level 0.05. A possible explanation for the disagreement between observed trends in the measured data (this study) and future rainfall erosivity projections (Panagos et al., 2017a) could be that the European projections were made with a consideration of larger areas and without considering individual stations. Moreover, also the authors of the study indicated that results should be handled with care due to uncertainties related to the General Circulation Models (GCMs) and Regional Circulation Models (RCMs) (Panagos et al., 2017a). The results presented in this study are in line with the Mueller and Pfister (2011) study, who found a statistically significant increasing trend in the rainfall intensity data for the Emscher-Lippe catchment in Germany. However, Verstraeten et al. (2006) found no significant monotonic trend in
sub-sample are as follows; for nine stations the trend in annual R-values is positive and it is negative only for one station (Table 5). For this subsample the trends for five stations are statistically significant (all positive) with the selected significance level of 0.05. Furthermore, similar results were obtained for the MK3 sub-sample where only a half-year period was considered (May-October) (Table 5). For nine stations the Mann-Kendall trend results were positive and for one station negative (i.e. a station located in the temperate continental climate). However, for three stations the trend results were statistically significant with the selected significance level of 0.05 (two positive and one negative). The Mann-Kendall trend results can be summarized as follows; most of the detected trends were not statistically significant with the selected significance level of 0.05 (Table 5). However, a larger percent of statistically significant trends were positive than negative (Table 5). It is evident that some stations (Postojna, Ljubljana and Vogel) showed a different trend depending on the selected sub-sample (Table 5). Similar results were also obtained by Bezak et al. (2016) when analysing changes in the flood data, where annual maxima (AM) or peaks over threshold (POT) sub-samples resulted in different trends. Furthermore, for Rateče, Šmarata, Celje, Slovenske Konjice, Murska Sobota, and Portorož the stations trends were positive for all four tested sub-samples, yet mostly statistically insignificant with the selected significance level of 0.05. These stations are located in different climate zones (Table 1). The Novo mesto station that is located in the temperate
Table 5 Mann-Kendall trend test results (τ ) with corresponding p-values (p) for the four different sub-samples defined in Table 2 for 10 analysed rainfall stations in Slovenia. Station name / Sub-sample
Rateče Postojna Šmarata Ljubljana Bežigrad Novo mesto Celje Slovenske Konjice Murska Sobota Vogel Portorož
MK1
MK2
MK3
MK4
τ
p
τ
p
τ
p
τ
p
0.333 0.247 0.275 0.218 − 0.175 0.230 0.022 0.179 0.166 0.16
0.002 0.015 0.010 0.008 0.085 0.023 0.845 0.078 0.164 0.272
0.073 − 0.213 0.107 0.013 − 0.133 0.007 0.08 0.387 0.127 0.16
0.624 0.141 0.469 0.944 0.362 0.981 0.591 0.007 0.387 0.272
0.217 0.003 0.166 0.176 − 0.201 0.186 0.038 0.164 0.039 0.007
0.044 0.985 0.124 0.032 0.048 0.067 0.729 0.107 0.755 0.981
0.053 − 0.327 0.120 − 0.02 − 0.147 0 0.153 0.387 − 0.087 0.007
0.726 0.023 0.414 0.907 0.315 1 0.293 0.007 0.559 0.981
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Table 6 Mann-Kendall trend test results (τ ) for May, June, July, August, and September using all the available data shown in Table 1. Test results that are indicated with * are statistically significant with the selected significance level of 0.05. Station/Month
May
June
July
August
September
Rateče Postojna Šmarata Ljubljana Bežigrad Novo mesto Celje Slovenske Konjice Murska Sobota Vogel Portorož
0.131 0.039 0.182 − 0.004 0.214 * 0.202 0.264 * 0.137 − 0.016 0.203
0.090 − 0.014 − 0.010 0.057 0.001 0.067 − 0.046 0.145 0.095 0.056
0.038 0.096 0.161 0.083 − 0.091 0.142 − 0.264 * 0.087 0.032 0.228
0.002 − 0.114 0.123 0.047 − 0.183 0.085 0.215 0.134 0.032 0.088
0.027 0.061 0.017 0.032 0.056 0.176 0.015 0.004 0.012 0.004
Table 7 SRC and average NSI values for 10 analysed stations for five different parameters (t (time parameter, usually 6 h), p (rainfall amount parameter, usually 1.27 mm), k (rainfall amount parameter, usually 12.7 mm), l (time parameter, usually 15 min), and c (rainfall amount parameter, usually 6.2 mm)) that are used to define erosive events and are consequently used to calculate rainfall erosivity R-factor values according to the RUSLE methodology (Renard et al., 1997). A detailed description of these different parameters is given in Section 2.4. Table 3 shows the initial and modified parameter values that were used to calculate SRC and NSI. Station/parameter
Test
t
p
k
l
c
Rateče
SRC NSI SRC NSI SRC NSI SRC NSI SRC NSI SRC NSI SRC NSI SRC NSI SRC NSI SRC NSI
0.962 0.109 0.975 0.119 0.966 0.111 0.961 0.106 0.977 0.104 0.964 0.096 0.976 0.098 0.977 0.085 0.951 0.084 0.960 0.082
− 0.950 0.049 − 0.914 0.053 − 0.935 0.051 − 0.927 0.052 − 0.918 0.054 − 0.930 0.049 − 0.915 0.050 − 0.962 0.050 − 0.970 0.028 − 0.945 0.044
− 0.994 0.130 − 0.995 0.115 − 0.995 0.117 − 0.993 0.117 − 0.995 0.170 − 0.994 0.164 − 0.994 0.160 − 0.994 0.185 − 0.994 0.034 − 0.995 0.089
0.820 0.005 0.719 0.006 0.912 0.005 0.858 0.007 0.872 0.011 0.837 0.007 0.809 0.007 0.838 0.014 0.855 0.002 0.580 0.010
− 0.845 0.030 − 0.878 0.031 − 0.843 0.029 − 0.864 0.029 − 0.853 0.044 − 0.863 0.039 − 0.869 0.039 − 0.870 0.051 − 0.864 0.008 − 0.910 0.031
Postojna Šmarata
annual R-values calculated using 105 years of 10-min data for a gauging station in Belgium. However, a standard normal homogeneity test indicated lower R-values for the period 1898–1990 in comparison to the period 1991–2002 (Verstraeten et al., 2006). Because in Slovenia the highest monthly rainfall erosivity is in the summer (Fig. 2), we also calculated Mann-Kendall test for May, June, July, August, and September (Table 6). Only in three cases was the detected trend statistically significant with the selected significance level of 0.05 (in two cases positive and in one case negative) (Table 6). Moreover, a larger percent of statistically insignificant trends was positive than negative, which is in line with results presented in Table 5. Milošević et al. (2016) found decreasing trends in rainfall amounts with some differences between seasons for Slovenia. Furthermore, for most of the country summer rainfall amounts were decreasing as well (Milošević et al., 2016). Similar results were also obtained by Bezak et al. (2016). This could be explained by the fact that the most intense rainfall events are more frequent (i.e. more frequent and more intense summer thunderstorms due to higher air temperature) and these events have the largest impact on the rainfall erosivity and consequently also on soil erosion and sediment transport in rivers.
Ljubljana Bežigrad Novo mesto Celje Slovenske Konjice Murska Sobota Vogel Portorož
smaller number of events. For example, for the Murska Sobota station, which has the maximum SRC for the t parameter, the use of the 12 h k parameter results in about a 7% higher average annual R-value compared to the initial t value (6 h) proposed in the RUSLE methodology (Renard et al., 1997). The other three parameters (p, l, and c) that are used to define erosive events have, on average, a smaller impact for these 10 stations on average annual R-values (Table 7). More specifically, higher p parameter values result in smaller R-values and viceversa. For example, for the Murska Sobota station the use of 2.54 mm instead of 1.27 mm for the p parameter results in about 3% lower average annual R-values. The influence of the l and c parameters, which are used to include short duration erosive events in the R-values calculation, is even smaller (Renard et al., 1997). Higher l parameter values correspond to an increase in the duration of the short-duration events. The maximum SRC for the l parameter was obtained for the Šmarata station (Table 7). Smaller c parameter values result in higher R-values. The maximum absolute SRC for parameter c is obtained for the Portorož station (Table 7). More specifically, a higher c parameter value (15.5 mm instead of initial 6.2 mm) results in about a 2% smaller average annual R-value. The sensitivity of five parameters that are used to define erosive events according to the RUSLE methodology (Renard et al., 1997) was also investigated using the NSI (Table 7). Similarly to SRC, also the application of NSI indicates that on average k and t parameters have the largest impact on the average annual R-values (Table 7). It can be seen that average k and t parameter value for 10 stations is 0.13 and 0.10, respectively (Table 7). On the other hand, average NSI values for p, l, and c parameters are 0.05, 0.08, and 0.03, respectively (Table 7). The sensitivity analysis results can be summarized as follows: the development of computer processing power and software development such as RIST (USDA, 2014) has made it possible to analyse large amounts of high-frequency data in a few minutes. This means that rainfall erosivity R-factor calculation is faster today than it was in times of Wischmeier and Smith (1978) or even Renard et al. (1997) and larger amounts of data can be processed. Thus, applying the k parameter that was initially defined only due to the reduced computational burden is meaningful only because it can yield results that
3.2. Sensitivity analysis Table 7 shows calculated SRC values for analysed stations in Slovenia for 5 parameters that were used to define the erosive events and are presented in Table 3. The higher the SRC value, the more sensitive the investigated parameter (Gan et al., 2014) is. It can be seen that on average the highest SRC values are obtained for the rainfall amount parameter k, which is used to define erosive events. With a decreasing k value (e.g. from 12.7 mm to 0 mm), which means that we also take into consideration rainfall events with small rainfall erosivity, higher R-values are obtained. Fig. 3 shows the decrease in the annual rainfall erosivity for the increasing k parameter values. One can notice that all stations indicate a similar decrease in rainfall erosivity with the increase in the k parameter. This relationship is relatively linear for most of the stations. Using the k parameter value of 0 mm resulted in approximately 10% higher average annual R-values than when using the initial k parameter value (12.7 mm) proposed by the Renard et al. (1997) for the Murska Sobota station. Moreover, similar results were also obtained for other analysed stations (Table 7 and Fig. 3). However, it should be noted that lowering the k parameter also introduces smallmagnitude rainfall events in the rainfall erosivity data that do not even result in surface runoff or soil erosion processes. On the other hand, using a higher k parameter (e.g. in order to additionally reduce the computational burden) of 25.4 mm results in up to about 15% lower average annual R-values depending on the station. The second-most sensitive parameter is the time parameter t, used to separate (or merge) consecutive rainfall events (Table 7). Using larger t values (e.g. 12 h instead of 6 h) results in larger average annual R-values. Larger t values result in the lumping of several consecutive rainfall events into a 533
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Fig. 3. Relationship between annual rainfall erosivity values and the k parameter used to select only events with more than k mm of rain (usually 12.7 mm is used) for the 10 Slovenian stations. The Vogel station is shown on its own figure in order to improve the readability of figures due to large differences in annual rainfall erosivity values among stations.
decades have generally been decreasing (Milošević et al., 2016). This decrease is also evident in summer rainfall amounts (Milošević et al., 2016), which could indicate that most erosive events that have the largest impact on the annual and monthly rainfall erosivity are more frequent (i.e. summer thunderstorms). Moreover, the observed trends for monthly rainfall erosivity for May, June, July, August, and September were also mostly statistically insignificant (significance level of 0.05) with a larger percentage of positive trends, which could indicate a slight (statistically non-significant) increase in summer extreme events. ii) The sensitivity analysis showed that the k parameter (rainfall amount threshold; usually 12.7 mm is used) that was initially defined in order to reduce the computational burden in the R-factor calculations (and remove the small-magnitude events that could have minor impact on the soil erosion rates) can attribute to up to 10% of the average annual R-factor if this threshold is removed (k parameter value 0 mm). Moreover, the decrease in the annual rainfall erosivity with the increasing k parameter value is relatively linear (Fig. 3). This parameter has the largest impact on the R-factor calculation among the analysed parameters that are used to define the erosive events. Moreover, it was also found that t (the time parameter, usually 6 h) and p (the rainfall amount parameter, usually 1.27 mm) parameters have a larger influence on the R-factor calculation than c (rainfall amount parameter, usually 6.2 mm) and l (time parameter, usually 15 min) parameters. Furthermore, selection of the kinetic energy equation has even larger impact on the calculated annual rainfall erosivity. More specifically, this study indicated that the use of local Slovenian equations (Eq. (2)–(4)) resulted in, on average, about 20% higher annual rainfall erosivity values compared to the Brown and Foster (1987) equation (Eq. (5)).
are comparable with previous studies. However, it would also be relevant to report R-values of all rainfall events (k parameter value 0 mm) and not just erosive (according to the Renard et al., 1997 definition) ones, since differences in average annual R values can amount up to 10% (using the k parameter 0 mm). However, it should be noted that these small magnitude rainfall events do not always result in soil erosion processes. Another important step that must be made when calculating rainfall erosivity is the selection of the kinetic energy equation. Lobo and Bonilla (2015) have shown that differences in erosivity can amount up to three times with the application of various equations. Moreover, differences were the largest for rainfall events with lower intensities and smaller for rainfall events with higher intensities. Furthermore, also Angulo-Martínez et al. (2016) found that none of the kinetic energy equation should be used universally and applying the equation far from the location for which it was developed should be limited. A comparison that was made in this study indicated that the use of Eqs. (5) and (6) results in, on average, about 20% and 12% lower annual rainfall erosivity values, respectively, than the use of local equations that were developed specifically for Slovenian climate conditions (Eqs. (2)–(4)). Thus, it seems that the impact of the kinetic energy equation is larger than the impact of different parameters that are used to define erosive events. Moreover, differences between the local equation (Eqs. (2)–(4)) and the equation proposed by Brown and Foster (1987) were slightly larger for the station located in the sub-Mediterranean climate than for stations located in the other two climate zones in Slovenia. However, it should be noted that only one station from the sub-Mediterranean climate was analysed in this study. For other stations in Slovenia the calculated differences were relatively similar. 4. Conclusions
Acknowledgment The presented study shows results of the rainfall erosivity R-factor evaluation for the 10 analysed stations with at least 25 years (maximum is 69 years of data) of high-frequency data (5-min) from Slovenia (Europe). The analysed stations are located in three different climate types, namely sub-Mediterranean, temperate continental, and mountain climate. Trends were analysed using the Mann-Kendall test and with the application of four different sub-samples. Sensitivity analysis was carried out using the SRC and NSI. Based on the presented results the following conclusions can be made:
We wish to thank the Environmental Agency of the Republic of Slovenia for providing data. The critical and useful comments of two anonymous reviewers and the guest editor improved this work, for which the authors are very grateful. We also gratefully acknowledge Mr. J. Rocchio for his English language editorial support. Funding The results of the study are part of the research Programme P2–0180: “Water Science and Technology, and Geotechnical Engineering: Tools and Methods for Process Analyses and Simulations, and Development of Technologies” that is financed by the Slovenian Research Agency (ARRS) (Grant number P2-0180).
i) The detected trends in rainfall erosivity for different sub-samples are mostly statistically insignificant with the selected significance level of 0.05. However, a larger percentage of detected trends is positive than negative (both for statistically significant and non-significant trends). For six stations trends were always positive (all four subsamples) yet not always statistically significant. Only for one of the 10 analysed stations were negative trends observed for all four defined sub-samples (located in the temperate continental climate) despite the fact that annual rainfall amounts in Slovenia in recent
References Angulo-Martínez, M., Beguería, S., 2009. Estimating rainfall erosivity from daily precipitation records: a comparison among methods using data from the Ebro Basin (NE
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