## 1 Introduction  
Surface transport distance of sediment is an important consideration when evaluating and predicting sediment transportation and landscape evolution resulting from rainfall-induced soil erosion in mountainous regions. The process chronologically includes (1) precipitation producing the runoff and related soil detachment; (2) the eroded soil accumulating as sediment and related maximum transport distance. For the runoff and soil erosion rate, widely used prediction models include: (1) a model based on real statistic data like the Universal Soil Loss Equation (USLE), composed of six factors to predict average annual soil weight [1; 2]; (2) a physical mechanism-based model such as the Water Erosion Prediction Project (WEPP) model, which is capable of predicting spatial and temporal distributions of soil detachment and deposition, both for single rainfall events or on a continuous basis, on both small (hill slopes, roads, small parcels) and large (watershed) scales [3]; (3) the European Soil Erosion Model (EUROSEM) model, a dynamic distributed model able to simulate sediment transport, erosion, and deposition by rill and inter-rill processes in single storms for both individual fields and small catchments [4]; and (4) the Kinematic Runoff and Erosion Model (KINEROS) model, which is an event-oriented, physically based model describing the processes of interception, infiltration, surface runoff, and erosion from agricultural and urban watersheds [5]. For the eroded soil sediment and related transport distance, two approaches are typically used to describe transport: (1) considering complex physical equations or (2) empirical coefficients. (1) For example, Limburg Soil Erosion Model (LISEM) is a physically based, hydrological, and soil erosion model for simulating the hydrology and sediment transport during and immediately after a single rainfall event applied in an agricultural catchment of a size ranging from 1 hectare up to approximately 100 km\({}^{2}\)[6]; [PERSON] [7] provides three equations that describe the movement of suspended sediment particles in a one-dimensional, infinitely wide, free-surface flow. The first two equations describe the continuity of mass and momentum in the flow of water. The third describes the conservation of mass for sediment transport. Unfortunately, this model involves seven parameters that are not easily obtained. (2) An exponential transport-distance model (as used by [PERSON] _et al._[8]) is used to simulate splash. Routing of splash is described in the four cardinal directions away from the source point, with relative weightings for upslope and downslope movement. Widespread overland flow is simulated using an exponential distribution parameterized by the calculated median travel distance. Although these data only relate to relatively coarse particle sizes, [PERSON] _et al._[9] find that they adequately predict rates of movement of finer particles. Sediment distribution and deposition follow the spatial pattern of the flow-routing algorithm directly. Concentrated flows are simulated with an exponential distribution function parameterized using the median transport distances, based on the review of available data by [PERSON] _et al._[10]. It should be noted that this equation is based on the ordinary regression results of [PERSON] _et al._[10], rather than the functional relationship form. These equations are relatively simple but some parameters, particularly those involving energy, are not easily estimated. In addition, the transport distance of soil particles of a particular size, not whole sediment mass, is the output in these equations. Since these models require many parameters and are relatively complex, here we use a simple fitting equation to link the rainfall events and soil erosion. Based on this fitting equation, we develop a straightforward soil erosion transport-distance model in which a geometric relationship is used to predict the maximum transport distance of soil erosion.