Use of Chosen Methods for Determination of the USLE Soil Erodibility Factor on the Example of Loess Slope

The investigations were carried out on a loess slope in the Brzeźnica village, in the Rudnik commune. Nine points were chosen, in which particular parameters being parts of the examined models, were determined. On the basis of the literature, eight models for the Universal Soil Loss Equation (USLE) erodibility factor determination were designated. The chosen models were the ones proposed by: Wishmeier, Monchareonm, Torii et al. and Walker (all based on texture and organic matter content, Wischmeier and Smith (based on texture organic matter content and additionally on aggregate classes), Wiliams et al. (based on texture and organic carbon content), Renard et al. as well as Stone and Hilborn (both based only on texture). The investigated site was characterized as well. The statistical conclusions were drawn and the obtained results were compared with the results presented in the literature.


INTRODUCTION
Water erosion, along with salinity [Boroń et al. 2010, Boroń et al. 2016, Klatka et al. 2015, drought, floods and heavy metals contamination, belongs to the most dangerous forms of soil degradation. Soil water erosion can be determined in various ways, including modelling, the approach used most often. Among many published soil erosion models, Universal Soil Loss Equation (USLE) is the most popular. One of the factors used in creating this model is the soil erodibility factor, which depends on the mechanical properties of the soil. The main factors determining it are textural properties (granulometry and sorting), structural properties (presence of stable soil aggregates), the void ratio and soil moisture [Klatka 2020]. The USLE erodibility factor K USLE expresses the mass of eroded soil (Mg·ha -1 ) from a standard plot per erodibility unit Je (h·ha -1 ·MJ -1 ·cm -1 ). A slope of length 22,1 m, width 1.87 m and 9% inclination was taken as the standard plot in the USLE model [Wischmeier and Smith 1978], assuming that agricultural practices are conducted along the slope and that there is no plant cover for at least two years prior to measurements. For standard conditions, the coefficients L, S, C and P are defined as 1 [Wischmeier and Smith 1978]. Determination of the soil erodibility factor K USLE is problematic due to the number of elements characterizing the soil cover, so various methods have been developed to quantify it. These methods can be divided into direct (field) and indirect approaches (by means of equations and nomograms). As the field investigations that involve installing measurement systems for effluents on test plots are costly and time-consuming, they are sometimes impossible to be carried out on a large scale [Shabani et al. 2014]. In practice, this coefficient is therefore calculated by means of empirical functions (pedotransfer functions), taking into account various parameters. Such functions describe the relationships between the easilymeasurable parameters and the parameters which are more difficult to measure.
Wischmeier presented the first method for determining the K USLE coefficient in 1977 [Torri et al. 1997, Ryczek et al. 2013a]. The method was based on the 0.1-0.002 mm and < 0.002 mm fractions and organic matter content. Wischmeier and Smith [1978] introduced a modification of the equation [Chodak et al. 2008 Baryła [2012] carried out the investigations on the soil mass eroded in the area of the Agricultural Farm Puczniew (Łódź province). The arable lands of the farm consist mostly of loam and sand. The K USLE coefficient was determined by use of the Wischmeier and Smith [1978] nomogram. Święchowicz [2016] investigated the K USLE factor in the Łazy village located on the Brzesko Foreland, in the area of the Agricultural Pilot Plant of the Jagiellonian University 'Łazy'. The texture was uniform and the sand content was low (below 10%), with high silt content (50-70%) and clay content (8-18%). The organic matter content in the humus horizon was between 0.5 and 1.6%. Relief was characterised by the occurrence of curved hilltop hummocks with sections of flattened surfaces, and mainly low-gradient (3-10°) concavo-convex slopes. Kruk  The aim of this work was to compare these methods for determination of the soil erodibility factor, K USLE , for use in the USLE model.

Study site
The study site was an area located in the province of Silesia, Racibórz administrative district, Rudnik commune. The investigated site is geomorphologically part of the Silesia Plain subprovince, covering all of the western and middle parts of the Racibórz administrative district in the Oder river valley. Two mesoregions occur within the commune, Głubczyce Plateau and Racibórz Valley [Kondracki 2000]. According to the Gumiński agricultural-climatic province categories, the area belongs to the Sub Sudety-XVIII province. Masses of wet air from the Atlantic Ocean reach the area often, with rarer masses of dry continental air from the east. Total rainfall is 650 mm per year, and there are approximately 40-55 days with snow cover each year. The mean yearly temperature is 8.0°C. The warmest month is July (mean temperature about 18°C), and lowest temperatures are recorded in January (mean -2.1°C). There are typically 30 frosty days and 120 days with ground-frost each year. The growing season starts early, in the second week of March, and lasts an average of 210 -220 days. Southern and western winds prevail over the area [Radomski 1987, Woś 1993]. The study site was covered by winter wheat during fieldwork on 20 June 2017. Before sowing, traditional tillage was used.

Methods
Field experimentation was carried out on 20 June 2017. Nine measuring points were chosen (Fig. 1a). Three replicates for each sample were taken from the upper part of soil, using 100 cm 3 rings for determination of physical properties ( Fig. 1b) and using plastic bags for the remaining analyses. The following soil properties were analysed: texture by means of the Casagrande method [PN-R-04032 1998], bulk density (ρ o ), solid phase density (ρ s ), total porosity (n) [Mocek et al. 1997[Mocek et al. , 2015, organic matter content (OM), organic carbon content (C) [Oleksynowa et al. 1991 The statistical analyses were performed using the Statistica 13.0 software package, using the Least Significant Difference (LSD) test and basic statistical analysis (Tukey and Fischer-Snedecor procedures). The LSD method allowed determining which differences are statistically significant. In the case where the absolute value of the difference between the means is greater than LSD | ̅ − ̅ | ≥ , it is assumed that differences are significant. The LSD values were calculated using the Tukey test, based on the Student t-distribution. The mathematical model is described as: where: x i,j is the hypothetical value of the investigated feature of replicate i (i = 1, 2, …..) and object j (j = 1, 2, …..), μ is the state value estimated by the mean of all observations, r is the number of repetitions (blocks), and k is the number of factor objects.
The mean value for each group and object mean (from all data), total sum of squares (total variability), total sum of squares between groups (from all data) and sum of squares within each group (intragroup variability) were determined. The F-statistics were then calculated and compared with the table values. The results are presented in Table 3. The total sum of squares (G) was calculated according to the equation the sum of squares of factors (T) was calculated according to the equation and the sum of block squares (R) was calculated according to the equation Correction P is calculated according to the equation .
The sum of squared errors (E) is calculated according to the equation LSD was calculated as a product of the standard deviation of the means difference s D (based on error due to variance) and the t D -value of the dependent variable in relation to significance level α, degrees of freedom for the error (ν) and the number of compared means (m): where: t(α; k, N -k) is the critical value of the standardised Student t-test range. The standard deviation of the difference between the means was calculated as:

RESULTS AND DISCUSSION
The soil texture was analysed for 9 sample locations, based on the PN-R-04032 [1998]   d10diameter of particles, that mass with the mass of lower diameter is 10% of sample mass, ntotal porosity,%    Table 4. The classification of granular groups was performed according to the methods of PTG [2008]. The analysis of the results showed that the soils in the study area are not differentiated by texture, but rather are all loamy silt. The sand content was 13-18%, the silt content was 70-79% and the clay content was 5-12%. Three replicate measurements of bulk density (ρ o ), solid phase density (ρ s ), organic matter content (OM), organic carbon content (C) and total porosity (n) were carried out for each point, with results presented in Table 5. Bulk density (ρ o ) varied between 1.41 and 1.57 Mg·m -3 , while solid phase density (ρ s ) varied between 2.52 and 2.75 Mg·m -3 . OM varied from 0.85 to 1.35%, and C fell between 0.52 and 0.78%. Total porosity (n) was between 40 and 46% (table 5).
Saturated hydraulic conductivity varied between 0.003111 and 0.009097 m·d -1 . Saturated hydraulic conductivity plays an important role in forming surface runoff. High values show low surface runoff, while low values indicate higherintensity runoff. Saturated hydraulic conductivity was classified as very low, k < 3.0 ·10 -5 [USDA Soil Survey Manual 1951], in all samples. These results show that high runoff can occur in the study area. Figure 2 shows soil material transported as a result of runoff on the day of field investigations (20 July 2017). Table 6 presents the values of parameters used to determine the value of K USLE . For the Wischmeier method [1977], the required percentage content of grains in the size range 0.1-0.002 mm was determined based on the grain size distribution Factor   [1978] were 8% for sites 1-3, 5, and 9, 6% for site 4, and 7% for sites [6][7][8]. The values of the a parameter were between 0.85 and 1.35%; in all samples the value of parameter b was found to be 2 (indicating that aggregates have a fine aggregate structure (1 -2 mm)), and parameter c was found to be 6 (indicating that the ground has very low permeability). The values of the K USLE parameter were found to be between 0.63 and 0.75 t·ha -1 ·Je -1 . The values of K USLE determined based on the Monchareon (1982) method (based on the geometric mean between 3 neighbouring values) were between 0.55 and 0.57 t·ha -1 ·Je -1 . The K USLE values determined with the Williams method (1984), taking into account texture, organic matter (OM) and organic carbon content (C), fell between 0.16 and 0.18 t·ha -1 ·Je -1 . The values of K USLE calculated using the Renard et al. method [1997] were between 0.41 and 0.43 t·ha -1 ·Je -1 . In the analysis using the Torri et al. equation [1997], calculations were carried out assuming that the lowest grain size value of separates is 0.000005 mm; the results fell between 0.27 and 0.29 t·ha -1 ·Je -1 .

Results of calculations of the K USLE soil erodibility factor
For the Stone and Hilborn [2000] method, the granular subgroups were distinguished based on the division of mineral deposits into groups and subgroups according to PTG [2008], and it was found that for all 9 points K USLE equalled 0,41 t·ha -1 ·Je -1 . Because of the lack of variability in the calculated results, the distribution isolines were not generated. During determination of the regression equation for the Walker method [2017], 3 random sampling points were chosen (1,5,9). This method produced the equation K = 0.0074·S + 0,0044·C -0,0925·OM, with K USLE values ranging between 0.52 and 0.58 t·ha -1 ·Je -1 . According Figure 2. Accumulation of soil material dislocated as a result of runoff to these authors' suggestion, the K USLE parameters for all 9 sampling locations were recorded based on the Wischmeier and Smith [1978] method. The percentage content of separates with grain sizes 2-0.1 and 0.1-0.002 mm, and the percentage content of organic matter (C) were used in the first approximation. In order to understand variability in the resulting K USLE values, a second approximation was made, taking into account soil structure and its permeability (Fig. 3). The results fell between 0.44 and 0.51 t·ha -1 ·Je -1 for the first approximation, and between 0.52 and 0.58 t·ha -1 ·Je -1 for the second approximation. The isolines of spatial distribution for the K USLE values calculated by these methods are presented in Figure 3. The statistical analyses were carried out based on Table 7, which shows the collected results of the K USLE calculations, with their mean values and object and block sums. The calculated value of the F coefficient (2880,000) is higher than the value indicated by the Fischer-Snedecor distribution tables (2,180), which suggests that statistically significant differences exist between all the means. The LSDs between the particular methods were calculated using the q Tukey test ( Table 8) (H) methods which make up group c, based on maximum and minimum grain diameters and their mass share (I), percentage organic matter content and soil type information (H). The Wischmeier [1977] method (A) and the Torri et al. [1997] method (G), which together compose group d and are based on the 0.1-0.002 and < 0.,002 mm grain size fractions and organic matter content, do not differ statistically from each other. However, they do differ from the other methods. Methods F and H both give the values closest to the mean (0.42 t·ha -1 ·Je -1 ) and median values (0.41 t·ha -1 ·Je -1 ), and thus can be taken as most reliable. This study was carried out on a low-inclination slope with uniform soil texture, and the site was covered by uniform plants and consisted of arable land; it can be therefore assumed that disagreement due to random factors was reduced to a minimum.
Comparing ·Je -1 were obtained mostly from silty clay. Lower values (≤0.41 Mg·ha -1 ·Je -1 ) obtained using the second method were mainly from sandy clay loam and loam. The values > 0.41 Mg·ha -1 ·Je -1 almost all occurred in silty clay. a-e -uniform groups The map of K USLE factor distributions across Europe produced by Panagos et al. [2014], based on the Wischmeier and Smith [1978] method, shows that the mean K USLE values for Europe averaged 0.320 Mg·ha -1 ·Je -1 . The mean value for Poland was 0.299 Mg·ha -1 ·Je -1 . For the Brzeźnica village, this value was between 0.46 and 0.55 Mg·ha -1 ·Je -1 .

CONCLUSIONS
Different methods of calculating the USLE soil erodibility factory (K USLE ) produce differing results. The maps of the K USLE distribution indicate that this coefficient shows high spatial variability. The proper determination of the K USLE coefficient is a very real, complicated and important problem. Detailed statistical analysis of the results obtained with various methods showed noticeable differences between the results calculated by means of the Wischmeier and Smith, and Williams methods, and between the Wischmeier, and