The Role of Interpolation Methods for the Production of R factor to Estimate Soil Erosion of Basins Using RUSLE Model (Case Study: Balarood Basin)

Introduction:

 There are many equations to prepare the R factor using synoptic stations data in the basin areas (Kamaludin et al. 2013 and Nikolova, 2016). The amount of this factor is estimated using different interpolation methods for the study areas. In addition, there are various methods to estimate the R factor at unknown points such as algebraic methods (linear regression and IDW ) and geostatistics methods (ordinary kriging, simple kriging and ....). Some researchers used ordinarily kriging (Men and Zhenrong, 2009, Moradi Motlagh, 2017 and Shabani, 2011), regression-kriging (De Mello et al. 2015), Co-kriging (Khorsandi et al. 2012), local polynomial (Hoyos et al. 2005), distinctive kriging (Zhang et al. 2009) and Linear Regression interpolation methods (Moradi Motlagh, 2017 and Sazab Pardazan cons. Eng. Co, 1998) to estimate the R factor. Instead of using synoptic data, some researchers used TRMM satellite images to produce R factor (Kumar Das and Guchait, 2016 and Zhu et al. 2011). Some rough topographic lands in the small basins such as the Balarood basin have valleys and elevations; the R factor estimate lower in valleys than in elevations by using the linear regression interpolation method (algebra); while the rainfall is seen uniformly over the elevations and valleys. This problem fix in different kriging interpolation methods and its predictions are close to the reality; therefore, the purpose of this study is to investigate the role of linear regression and geostatistics interpolation methods to produce the R factor and their effect on estimating the erosion of basins by the RUSLE model.Study area The geo-location of the study area (Fig. 1) is between 3601770.582860 mN and 3654377.5862609 mN and 328342.235576 mE and of 534721.260746 mE. 

 Materials and Methods:

 In this study, satellite image and their processing methods, GIS techniques and the RUSLE erosion model are used. Fig. 3 illustrates the materials and methods in the research, which describe as the following. 3.1. RUSLE soil erosion model Universal Soil Loss Equation presented for the first time by Whishmeier and Smith (1977). This model estimates the soil erosion by Eq. (1): (1) A=R×K×L×S×C×P Where A is the estimated soil loss per area and time unit and in this study, is in tons per hectare unit (metric system). R, K, L, S, C and P are the rainfall-runoff erosivity factor (MJ.mm.ha-1.hr-1.yr-1), soil erodibility factor (ton.ha.h. (MJ.mm.ha)-1), the slope length factor, the slope steepness, the cover-management factor and the support practice factor alternatively. 3.1.1. Calculating the R factor for each synoptic station The R factor indicates the power of rainfall erosivity and Renar and Freimund (1994) equation have been used to calculate it (Eq. (3, 4 and 5)). 3.1.2. Topographic Factor (LS) LS is the topographic factor, where L is the slope length factor and calculated by the ratio of lost soil from the sloped area to the lost soil from the experimental plots when the soil type and the degree of the slope are similar. This factor is calculated using Eq. (6). Interpolation methods use the R factor calculated at each station to prepare the R-layer in the basin area. In this study in order to provide the R layer, algebraic (linear regression) and ordinary kriging interpolation methods are used. 3.2. Semivariogram and its application in choosing the best R-factor interpolated. A large number of studies have proved the efficiency of the semivariogram in spatial analysis and environmental studies. Semivariogram equations (Eq. (11)) with different models (Spherical, Gaussian, Linear, Exponential, and Circular) use to estimate spatial auto-correlation. 3.3. Pearson Correlation Coefficient (r) Generally, the most common equation to express the correlation between two variables over time and place is the Pearson correlation coefficient. This coefficient shows the direction and degree of correlation and can be calculated using standard deviation and standard methods (Eq. (12 and 13) respectively). 3.4. The coefficient of determination (R2) Correlation coefficient shows the correlation between two variables but does not give us more information about the nature of this correlation. It determines the high, low, or relative correlation (Balyani and Hakimdost, 2014). The accuracy of the model is higher and we can determine the optimal model for fitting if the coefficients of determination of data go towards 1. 3.5. Data resources In this study, to produce LS, P, C, K, and the R factors, 1:25000 topographic maps, ASTER satellite image, area soil map and precipitation data of 12 synoptic stations (Table 5) have been used respectively (Table 4)

Conclusions:

The results indicated the R factor interpolated by linear regression method has more auto-correlation (R2=0.985) than once interpolated by ordinary kriging method (R2=0.964). Though the coefficients of determination are close, this difference could justify the use of linear regression interpolation method in the preparation of the R factor. The R factor interpolated by linear regression is higher than the R factor interpolated by ordinary kriging method on average.The maps of soil erosion risk indicated that by using the linear regression and ordinary kriging interpolation methods to prepare the R factor, the risk of soil erosion at the basin (ton per hectare) estimate 0 to 77824.5 and 0 to 55277.2 respectively. The mean annual erosions from linear regression and ordinary kriging interpolations have been estimated 19315/135 t.ha-1.yr-1 and 14223/726 t.ha-1.yr-1 alternatively. It demonstrated using linear regression interpolation method in preparing the R factor layer leads to the higher estimation of this factor and ultimately to the higher estimation of the erosion by the RUSLE experimental model. The average of the erosion estimated using the R factor interpolated by linear regression method has less difference (1651/865 t.ha-1.yr-1) then another one in the previous study (Sazab Pardazan Cons. Eng. Co, 1998). Comparison of estimated erosions with each of their factors indicated both of the estimated erosions have the lowest and highest correlation with their R and LS factors, respectively. This study also demonstrates that remote sensing and GIS are valuable tools in assessing soil erosion and its factors.