Comparing different multiple flow algorithms to calculate RUSLE factors of slope length (L) and slope steepness (S) in Switzerland

Abstract

The topographic LS-factor is one of the most difficult factors of the Revised Universal Soil Loss Equation (RUSLE) to define in a landscape with varying topography. For the application of the RUSLE not only at the plot but at catchment or landscape level, different multiple flow algorithms (MFA) have been developed and applied in various studies. However, these different MFAs in combination with various convergence values and applied at different resolutions of digital elevation models (DEM) have not been addressed so far. This publication focuses on filling this gap in the context of the agricultural area of Switzerland.To evaluate different factors of slope steepness (S-factor) and slope length (L-factor), we tested four different multiple flow algorithms (MFA) (Deterministic Infinity (DINF), Multiple Flow Direction (MFD), Multiple Triangular Flow Direction (MTFD), Watershed (WAT)) and compared them with the MFA approach (Flow 95 in MUSLE87) used in the existing erosion risk map of Switzerland with a resolution of two metres. The MFAs we tested, used three different convergence settings and two digital terrain models (DEM) – one with a very fine two metre resolution (DEM2) and one with a coarser resolution of 25 m (DEM25) – enabling us to examine the influence of DEM resolution on the LS-factor. In total, we evaluated 21 L-factor variations to assess the significance for the prediction of the potential erosion risk. The calculations were applied at a local (test area Frienisberg, 88.7 ha) and at a regional scale (Lyss, 11,855 ha) in the agricultural Swiss Plateau. Both test areas were segmented into field blocks with an average size of 5 ha (14 field blocks in Frienisberg and 2305 field blocks in Lyss). A field block can contain several fields with different types of agricultural land use and is delineated by surrounding hydrological barriers. For these field blocks, the various L-factors were calculated automatically using Geographic Information Systems (GIS). Finally, the LS-factors were calculated for two selected MFAs.The L-factors calculated with the various MFAs and the high-resolution DEM2 differed negligibly in terms of statistical values (mean values, standard deviation) and in the spatial distribution of the pixels both among each other and in comparison to the L-factor of the existing erosion risk map. As expected, using the coarser DEM25 resulted in considerably lower S-factors but surprisingly in higher L-factors, so that there was little difference in the average LS values between the DEM25 and the DEM2. However, spatial distribution of the L-factor values and the soil erosion risk was much more differentiated in the DEM2 and better reflected the topography compared with the DEM25. Erosion risk hotspots such as slope depressions with concentrated runoff and thalweg erosion could be reliably identified. Moreover, the lower-resolution DEM25 was not well suited to the chosen approach with field blocks of a mean size of 5 ha, as the intersection of polygon and raster data produced edge errors depending on the clipping method. This study showed that a high-resolution DEM was more important for the calculation of the LS-factor and potential soil erosion risk than the choice of MFA, and that the calculation of LS-factors based on field blocks offered a number of advantages mainly in determining the channel network and maximum flow length.