## 2 Materials and Methods
### Sediment Delivery Ratio  
The concept of gross soil loss (GSL) proposes to identify the areas that are most susceptible to erosion, considering a combination of natural and climatic conditions, as well as the impacts of human activities on soil erosion susceptibility. By incorporating these multifaceted factors, the GSL provides a comprehensive assessment of erosion-prone regions, helping in the formulation of targeted soil conservation and erosion control strategies to safeguard the landscape's integrity and ecological balance. However, it is important to note that the predicted GSL does not encompass the aspect of sediment deposition dimension, and it does not align with the concept of net soil loss (NSL).  
The sediment delivery ratio is a metric that gauges the proportion of sediment transported to a stream or water body about the quantity of sediment eroded from a specific area. This factor takes into account the complex dynamics of sediment movement, shedding light on how eroded soil particles are transported and ultimately deposited in aquatic systems, influencing their overall health and resilience [15,35].  
The sediment delivery ratio is a useful parameter in soil erosion modeling and sediment yield estimation. It is calculated by dividing the sediment yield leaving the erosion site by the total sediment produced by that site. The SDR value spans a scale from 0 to 1. It is influenced by many factors such as land use, slope, soil type, and vegetation cover. The SDR can be employed to estimate the quantity of sediment that reaches a specific location. This is crucial for comprehending the effects of sediment on ecosystems and for formulating management strategies aimed at reducing the silting up of reservoirs. The SDR is widely used in soil erosion and sediment transport modeling, and it is an important parameter in many soil conservation and water management programs.  
In a raster GIS context, the sediment delivery ratio can serve as a model for sediment distribution, representing the likelihood that eroded particles mobilized from a given catchment cell will be carried to the nearest stream cell [35]. This can be calculated using the following Formula (4):  
\[NSLi=GSLi\times SDRi \tag{4}\]  
where \(NSLi\) is the net soil loss at a pixel. \(GSLi\) and \(SDRi\) are, respectively, the \(GSLi\) and \(SDRi\) at the same pixel.  
\(SDRi\) can be calculated using the following Formula (5):  
\[SDRi=exp\left(-\beta\times\frac{Li}{Ri\times\left(Si\right)^{1/2}}\right) \tag{5}\]  
where \(\beta\) is a routing coefficient set \(-0.0051\).  
The parameter \(Li\) represents the length of segment \(i\) in the flow path, and its value is derived from either the length of the side or the diagonal of each cell, depending on the flow direction within the cell. The length is measured in meters (m).  
The map of the Li values is obtained from the ASTER GDEM using hydrological routines that calculate the \"flow length\". Ri is the surface roughness coefficient (m/s) derived based on the findings of [PERSON] et al. (1994). The parameter Si denotes the slope gradient, expressed in meters per meter (m/m). It is derived from the surface slope \(\alpha\), which is obtained from the GDEM (Global Digital Elevation Model). Si is calculated as follows (6):  
\[Si=tan(\alpha+0.01) \tag{6}\]  
The roughness of the soil surface plays a significant role in shaping hydrodynamic friction [23], consequently exerting an impact on the movement of water and the transportation of sediment. Additionally, it influences the process of sediment re-deposition across the landscape [5]. All coefficients for the various LULC classes were utilized based on the values presented in the work of [PERSON] et al. [17].