# Soil Depth Prediction Model Using Terrain Attributes in Gangwon-do, South Korea
## 3 Predicted Soil Depth Model  
Previous studies to predict soil depth using TAs have been attempted continuously, and as a result, statistical models for soil depth prediction have been proposed. Representative statistical models for soil depth prediction are summarized in Table 4.  
The soil depth prediction model derived in this study is shown in Table 5, and the soil depth prediction model results for the study area are shown in Figure 7a. In addition, the scatter plot for each representative rock type is shown in Figure 7b-d. \(R_{adj}^{2}\) for representative rock types are 0.698 (Igneous rock), 0.676 (Metamorphic rock), 0.683 (Sedimentary rock), and the RMSE for representative rock types are 0.870 (Igneous rock), 0.876 (Metamorphic rock), and 0.981 (Sedimentary rock). For the verification of the developed regression equation, the measurement data and regression equation are compared with the data for the three regions not included in the development of the regression model. The soil depth distribution of the target area is prepared (Table 6). The numbers of data in igneous, metamorphic, and sedimentary rock areas for verification are 18, 30, and 29 sites, respectively, and the determinants between regression and instrumentation data are 0.867, 0.801, and 0.814, respectively. Additionally, \(R_{adj}^{2}\) for representative rock types are 0.859 (Igneous rock), 0.794 (Metamorphic rock), 0.807 (Sedimentary rock), and RMSE for representative rock types are 0.724 (Igneous rock), 1.104 (Metamorphic rock), 0.288 (Sedimentary rock). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Rock Type** & **R** & **R\({}^{2}\)** & **R\({}_{adj}^{2}\)** & **RMSE** & **\(p\)-Value** & **Number of Datapoints** \\ \hline Igneous & 0.931 & 0.867 & 0.859 & 0.724 & \textless{}0.001 & 18 \\ \hline Metamorphic & 0.895 & 0.801 & 0.794 & 1.104 & \textless{}0.001 & 30 \\ \hline Sedimentary & 0.902 & 0.814 & 0.807 & 0.288 & \textless{}0.001 & 29 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results of soil depth prediction models at the verification site. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Proposer** & **Model** & **Range of Soil Thicknesses (cm)** & **Number of Datapoints** \\ \hline [PERSON] [33] & \(88.8+1.020\text{AS}+0.057\text{AL}-2.491\text{S}\) & 40–160 & 553 \\ \hline [PERSON] [41] & \(-57.95+12.83\text{CV}_{\text{PL}}+21.46\text{TWI}\) & 0–200 & 30 \\ \hline [PERSON] [4] & \(97.883-1.457\text{S}+2.688\text{TWI}-0.073\text{AL}\) & 3.1–198.4 & 137 \\ [PERSON] [55] & \(17.918\text{TWI}+0.550\text{(Cell size}=10\text{m)}\) & 30–150 & 79 \\ \hline [PERSON] [2] & \(122.13-0.11\text{S}+0.012\text{TWI}+0.012\text{CA}-0.23\text{STI}\) & 30–150 & 100 \\ \hline \hline \end{tabular}  
* AS: Aspect, AL: Altitude, S: Slope, \(\text{CV}_{\text{PL}}\): Plane Curvature.  
\end{table} 
Table 4: Previously proposed statistical soil depth prediction models. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Rock Type** & **Model** & **\(p\)-Value** & **Number of Data** \\ \hline Igneous & \(0.626-0.536\text{STI}+0.509\text{TWI}-0.021\text{SLOPE}\) & \textless{}0.001 & 101 \\ \hline Metamorphic & \(4.442-0.702\text{STI}+0.228\text{TWI}-0.034\text{SLOPE}\) & \textless{}0.001 & 101 \\ \hline Sedimentary & \(4.289-0.667\text{STI}+0.242\text{TWI}-0.041\text{SLOPE}\) & \textless{}0.001 & 95 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The result of soil depth prediction models in this study. The distribution of soil depth for the entire area to be verified (Figure 8a,c,e) and the model verification results for each rock distribution (Figure 8b,d,f) are shown in the below figures. As a result of the verification, the \(R^{2}_{adj}\) is from 0.794 to 0.859, which is judged to be an appropriately predictable model. However, RMSE is relatively large in metamorphic rock regions. It is considered that this is because the soil depth data of the metamorphic rock verification in the target area are too concentrated near the valley, and a significant amount of the data includes values measured inside the valley.