Background The Loess Plateau is one of the most severely eroded areas in the world, and quantification of soil erosion has been an important research work in the Loess Plateau of China.Although there exist many different soil erosion models for simulating soil erosion, few studies have used ensemble models to simulate soil erosion.

Methods To investigate whether ensemble simulation can effectively improve soil erosion simulation, this study used the techniques of Bates-Granger (BG), equal weight (EW) and Granger-Ramanathan (GR) to integrate three widely used empirical-based soil erosion models, being Morgan-Morgan-Finney (MMF), Revised Universal Soil Loss Equation (RUSLE), and Chinese Soil Loss Equation (CSLE), respectively, for simulating soil erosion and sediment yield of a loess watershed, i.e., Xinshui River watershed.The training period (1991-2000) was for estimating the weight of each model, and the testing period (2001-2005) was for examining the applicability of the various ensemble approaches.The model performance was evaluated in terms of Nash coefficient (NSE), correlation coefficient (R), and root mean square error (RMSE), by against the measured sediment yield at the outlet of the watershed.Uncertainties of the model simulation were also evaluated by means of confidence interval.

Results 1) The three individual models differed in their performances, with MMF performing the best compared with the other two.2)Ensemble techniques greatly improved the performance of soil erosion simulation, and reduced uncertainties among various modelling tools.Comparing the best ensemble simulation with the best individual model, performances of NSE, R, and RMSE were improved by 23.6%, 15.8%, and 46.4%, respectively.3)BG technique provided more accurate predictions than the other methods did, the width of the confidence interval for BG technique smaller than that of the others, indicating a more stable and reliable performance.

Conclusions The performance of the widely used empirical soil erosion models (e.g., RUSLE, CSLE) could be further enhanced by using the technique of ensemble simulation combined with uncertainty analysis in their applications.