## 2 Materials and Methods
### Methods
#### 2.2.2 The USLE Calculation  
The USLE was developed by [PERSON] and [PERSON] in the year of 1978 [46]. The initial purpose of this equation was to measure the average soil loss per year for gentle terrain [47; 48]. Recently, the Revised Universal Soil Loss Equation (RUSLE) has been developed and applied with similar structure of the USLE, but contains some improvements of input factors based on an updated database in the United States (US) [49]. For example, the data from more than 1000 locations were analyzed to calculate the rainfall erosivity. These modifications are useful to help the accuracy of the model in the US, but not for other regions in the world like Vietnam [9]. The USLE is expressed by Equation (1):  
\[\mathrm{A}=\mathrm{R}\times\mathrm{K}\times\mathrm{LS}\times\mathrm{C}\times \mathrm{P} \tag{1}\]  
where A is the average soil loss (t/ha/year); R is rainfall erosivity (MJ-mm/ha-h-year); K is the soil erodibility factor (t-h/MJ-mm); LS is the topographic factor (unitless); C is the cropping management factor (unitless); P is the practice support factor (unitless). Rainfall Erosivity (R)  
There are many models that use rainfall data to calculate the rainfall erosivity factor [50], most of them are in relation to annual rainfall as the input data for R calculation [51; 52]. Because of the lack of available rainfall intensity data as well as the unique characteristic of each eco-region, the formula could be used in different ways [53]. In this research, the R was calculated based on the suggestion (Equation (2)) of [PERSON] [54], who conducted research by the observed data of 253 hydrometeorology stations in the entire country over 54 consecutive years. This was used to calculate the rainfall erosivity in relation to the sloped land specifically in the conditions present in Vietnam. \[\mathrm{R}=0.548257\mathrm{P}-59.9 \tag{2}\]  
where P is precipitation (mm). The annual rainfall in this study was calculated on the observed measurement of six hydrometeorology stations around the research site with the shortest and longest distances to the center of Song Kon commune being 13 km and 27 km respectively. The data of rainfall were collected in the period from 2008 to 2018. The map of R factor was obtained by inverse distancing weight (IDW) interpolation method using ArcGIS 10.2. Erodibility Factor (K)  
Soil texture and soil organic matter content are often used for the measurement of the K factor [55; 56]. The information needed to acquire these soil indicators is dependent on K identification. As a result, K is one of the most challenging factors to determine. In Vietnam, most of the soil erosion researches that have been conducted in the Central region have used the K factor suggested by [PERSON] [57]. This research was conducted in Central Vietnam based on soil analysis of a vast area which stretches over 50.000 square kilometers. For the Song Kon commune, there are three soil types: Arenic Acrisols (86% of total area), Ferralic Arcrisols (12%), and Dystric Fluvisols (2%). The soil type was extracted from the soil map (1:100,000) of Quang Nam province which was mapped by Vietnam National Institute of Agricultural Planning and Projection (NIAPP) in 2005 [58], and its K value is presented by Table 1.  
Topographic Factor (LS)  
In Central Vietnam, the topography is the most significant feature to have impact on the soil erosion rate [9]. The topographic factor is combined with the impact of slope length (L) and slope steepness (S) to determine the rate of soil erosion. Most of the research [9; 12] measured the LS factor by using the formula proposed by [PERSON] and [PERSON] [59] or [PERSON] and [PERSON] [60]. In addition, the use the Digital Elevation Model (DEM) in Geographical Information Systems (GIS) is a popular approach to enable researchers to calculate the LS factor [61]. Moreover, the resolution of DEM data has influenced the accuracy of LS value, especially in the complex terrain regions [62; 63]. The flow direction algorithm is also an effective tool in determining the LS value [64; 65].