A primary objective of this paper is to change the input data requirement of the Modified Universal Soil Loss Equation (MUSLE) for the calculation of its runoff factor for possible application in data-scarce areas. Basically, the MUSLE was developed for a small agricultural watershed, where the extent of erosion is from sheet to rill erosion, but we cannot exactly tell whether it considers gully erosion or not. The underlying physical assumption to improve the MUSLE is that the amount of potential energy of runoff is proportional to the shear stress for sediment transport from a slope field and the kinetic energy of the runoff at the bottom of the slope field for gully formation. The improved MUSLE was tested at four watersheds in Ethiopia, and it showed better performance (i.e., the minimum performance is 84%) over the original MUSLE (i.e., the minimum performance was 80%), for all four watersheds under our consideration. We expect the same to be true for other watersheds of Ethiopia.

Soil erosion and sediment transport are quite complex processes as they depend on physical, biological, mechanical, and chemical processes within a particular catchment. Therefore, it is highly essential to better explain engaged physical processes and means of accounting for site-specific conditions, for soil loss and sediment yield estimation. This paper mainly focuses on physical explanations behind erosion and common erosion models like Universal or Revised Universal Soil Loss Equation(USLE/RUSLE) and Modified Universal Soil Loss Equation(MUSLE). Based on the physical explanations and overall limitations, the MUSLE is selected for the application of sediment yield estimation. To regionalize the MUSLE, the main parameters of the MUSLE which directly affect the erosion process such as cover, conservation practice, soil erodibility, and topographic factors are estimated based on the past experiences from literature and comparative approaches, whereas the other parameters which do not directly affect the erosion process or which do not have physical meaning (i.e coefficient a and exponent b ) are estimated through calibration. The best exponent (b) of the Modified Universal Soil Loss Equation is 1, which results in Nash-Sutcliffe efficiency of approximately 1. The regionalized MUSLE shows good performance for all four watersheds under our consideration and we expect the same for other watersheds of Ethiopia.

Soil erosion and sediment transport are quite complex processes as they depend on physical, biological, mechanical, and chemical processes within a particular catchment. Therefore, it is highly essential to better explain engaged physical processes and means of accounting for site-specific conditions, for soil loss and sediment yield estimation. This paper mainly focuses on physical explanations behind soil erosion and common soil erosion models like Universal or Revised Universal Soil Loss Equation(USLE/RUSLE) and Modified Universal Soil Loss Equation(MUSLE). Based on the physical explanations and overall limitations, the MUSLE is selected for the application of sediment yield estimation. The main objective of this paper is to estimate the best exponent of the MUSLE, and to estimate the best combination of the exponent and topographic factor of the MUSLE under hydro-climatic conditions of Ethiopia. For the sake of calibration procedure, the main parameters of the MUSLE which directly affect soil erosion process such as cover, conservation practice, soil erodibility, and topographic factors are estimated based on the past experiences from literature and comparative approaches, whereas the other parameters which do not directly affect the erosion process or which have no any physical meaning (i.e coefficient a and exponent b) are estimated through calibration. It is verified that the best exponent of the MUSLE is 1 irrespective of the topographic factor, which results in the maximum performance of the MUSLE (i.e approximately 100\%). For the best combination of the exponent and topographic factor, the performance of the MUSLE is greater than or equal to 80\% for all four watersheds under our consideration, we expect the same for other watersheds of Ethiopia.

The effect of the topographic factor of the Modified Universal Soil Equation (MUSLE) on soil erosion and sediment yield is not clear. Except for the coefficient, soil erodibility, cover, and conservation practice factors of the MUSLE, an individual effect of the exponents and topographic factors of the MUSLE on soil erosion and sediment yield can be seen by applying the model at different watersheds. A primary objective of this paper is to estimate the best exponents and topographic factors of the MUSLE under the hydro-climatic conditions of Ethiopia. For the sake of the calibration procedure, the main factors of the MUSLE that directly affect the soil erosion process, such as cover, conservation practice, soil erodibility, and topographic factors, are estimated based on past experiences from the literature and comparative approaches, whereas the parameters that do not directly affect the erosion process or that have no direct physical meaning (i.e., coefficient a and exponent b) are estimated through calibration. We verified that the best exponent of the MUSLE is 1 irrespective of the topographic factor, which results in the maximum performance of the MUSLE (i.e., approximately 100%). The best exponent that corresponds to the best equation of the topographic factor is 0.57; in this case, the performance of the model is greater than or equal to 80% for all watersheds under our consideration. We expect the same for other watersheds of Ethiopia, while for other exponents and topographic factors, the performance of the model decreases. Therefore, for the conditions of Ethiopia, the original exponent of the MUSLE is changed from 0.56 to 0.57, and the best equations of the topographic factor are provided in this paper.

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