# Soil Depth Prediction Model Using Terrain Attributes in Gangwon-do, South Korea
## 1 Introduction  
Soil depth is defined as the vertical distance from the ground surface to bedrock [1, 2, 3, 4]. The soil depth can be changed by erosion and weathering, and it is determined by various environmental variables, including slope, land use, curvature, parent material, weathering rate, climate, vegetation cover, upslope contributing area, and lithology [5, 6]. In addition, the weathering depth varies depending on the rock type [7], and the distribution of soil depth will be different accordingly.  
Soil depth plays an important role in landslide disaster prevention and management. The increasingly complex shallow landslide generation process integrates with physically based models such as SHALSTAB [8], SHETRAN [9], GEOtop FS+ [10], TRIGRS [11], and H-slider [12] to predict spatial patterns of landslide occurrences [13, 14, 15, 12]. However, most of the analysis methods using landslide analysis models are carried out under the assumption that the soil depth is constant without consideration of the spatial distribution for soil depth [16, 17, 18, 8, 12]. Additionally, the flow of groundwater and the formation of wetting front, which have a significant effect on the stability of the slope, are also significantly affected by the soil depth and its spatial distribution [19, 20].  
Many researchers have conducted studies on how to predict soil depth, and these studies can be classified broadly into three groups: (1) physically based, (2) interpolation-based, and (3) regression methods.  
The physically based model for soil depth prediction was developed as a landscape evolution model to solve the soil mass-balance equation over time [5]. Most landscape evolution models use linear sediment transport laws, which assume that the terrain slope and the sediment amount are equal. Although it develops into a simple analytical solution for mass balance, observational results report that landslides contribute to soil transport [5; 21; 22; 23; 24]. Recently, non-linear transport laws have been used to predict slope failure [23; 25; 26] and to describe the planar topography of steep slopes [27].  
Interpolation-based soil depth prediction methods include IDW [28], Kriging [29; 30], Co-Kriging [31], regression-kriging, and so on [3; 32]. These days, many researchers have suggested the interpolation method to predict the spatial distribution of the soil depth, and this method often shows high accuracy compared to other methods. [PERSON] and [PERSON] [33] reported that the co-kriging method showed higher accuracy than the ordinary kriging (OK), regression kriging (RK), and linear regression methods. However, although the interpolation method is convenient to use, it requires a large amount of data [5; 34; 35], and it cannot be said to show high accuracy in all cases because the deviation is significant due to the various environmental variables [36].  
Regression methods correlate soil depth with TAs from digital elevation maps (DEMs) [33; 37; 38; 39]. [PERSON] [40] reported that the coefficient of determination (\(R^{2}\)) of the slope angle, absolute height, and relative height with soil depth were 0.46, 0.36, and 0.37, respectively. [PERSON] et al. [41] also analyzed the statistical correlation between soil depth and plan curvature, compound topographic index, and upslope mean plan curvature. Additionally, [PERSON] et al. [4] suggested that the correlation coefficient between the regression model using slope and TWI as variables and soil depth was 64.1%, and [PERSON] et al. [2] reported that the correlation coefficient between slope, wetting index, catchment area, and STI with soil depth was 76%.  
In this paper, the study area was classified into igneous rock, metamorphic rock, and sedimentary rock, which are representative rock type in Korea. The correlation between TAs and soil depth in the study area is analyzed. Additionally, Using the multiple linear regression method, we propose a soil depth prediction model for each rock type that is suitable for the geological condition in Korea.