A new approach for calculating the slope length factor in the Revised Universal Soil Loss Equation

Abstract

This paper proposes a flow-path-network-triangular-facet-network (FPN_TFN) method based on a flow path network (FPN) and triangular facet network (TFN) constructed from a digital elevation model (DEM) to enhance the calculation of the slope length factor (<i>L</i>) in the Revised Universal Soil Loss Equation (RUSLE). First, the slope length was derived from a FPN, which is traced by the flow path network model. Then, a TFN was used to estimate the slope, and finally, <i>L</i> was obtained by combining slope length with slope using the equation in RUSLE. Experiments were conducted to (1) quantitatively validate the accuracy of the FPN_TFN method using 5 m DEMs that were generated from four mathematical surface models; and (2) qualitatively evaluate the error by using a 30 m DEM of a real-world mountainous region located in central Ganzi Tibetan Autonomous Prefecture of Sichuan Province, China. The performance of the four algorithms proposed by Moore and Burch (1986a), Böhner and Selige (2006), Desmet and Govers (1996), and Hickey (2000) were compared with that of the new approach. In the former two algorithms, two single flow direction and four multiple flow direction algorithms were selected for calculating the upslope contributing area (CA) and specific catchment area (SCA), such that 14 algorithms would be used for the comparison. The <i>L</i> estimates computed with the proposed algorithm were closer to the theoretical value. The root mean standard errors (RMSE) of the proposed algorithm are 79%, 96%, 69%, and 90% less than the same errors generated by the best of 14 comparison algorithms on the ellipsoid, inverse ellipsoid, saddle, and plane, respectively. The mean absolute errors (MEs) of the proposed algorithm are 0.83, 0.14, 1.00, and 0.39 m using the aforementioned order of surfaces, obviously lower than that of the comparison algorithms. The spatial error of the proposed algorithm is distributed between –1 and 1 for the inverse ellipsoid and plane surfaces, and falls mainly between –1 and 1 on the ellipsoid and saddle surfaces. They are still lower than that for the other algorithms. The new approach also produces better spatial distributions of <i>L</i> on the real-world mountainous region.