## 4 Results
### Frequencies of the Topographic Indexes Based on the DEM Grid Cell Size  
Figures 4 and 5 show the frequency and cumulative frequency of the topographical indexes based on the grid cell size of the Dongkok and Ieemokjung watersheds, respectively. The curves in Figures 4 and 5 shifted from left to right as the grid cell size increased for both the Dongkok and Ieemokjung watersheds. These results indicate that the mean of topographic index (\(ln(\frac{a}{tan\beta})\)) increases as DEM cell resolution is coarser. It is because contributing area (a) increases, and the slope of watershed (\(tan\)\(\beta\)) decreases as DEM cell size increases. This analysis is coincided with Figure 6, which shows the log-transformed contributing area (\(ln(a)\)) and the log-transformed inverse slope of watershed (\(ln(\frac{1}{tan\beta})\)) increase as DEM cell resolution is coarser [13; 35].  
Figure 4: Frequency distribution of the topographic indexes (\(ln(\frac{a}{tan\beta})\)) based on the DEM grid cell size. (**a**) Dongkok watershed. (**b**) Ieemokjung watershed.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Description** & **Units** & **Calibration Range** \\ \hline \(m\) & Exponential storage parameter & m & 0.001–0.1 \\ \(ln(T_{0})\) & Soil–water permeability coefficient & ln(m\({}^{2}\)/h) & 1–50 \\ \(T_{d}\) & residence time in unsaturated zone & h & 1–50 \\ \(SR_{max}\) & Maximum vegetation storage & m & 0.1–1 \\ \(SR_{0}\) & Vegetation deficiency & m & 0.01–1 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Calibration parameters and ranges used in TOPMODEL in this study [32; 33].  
Figure 7 shows the variation in the contributing area of the grid cell size in the Dongkok and Ieemokjung watersheds, which depended on the Rainfall-runoff events. Figure 7a shows that the contributing area increased with respect to the grid cell size, but the slopes of the curves in the grid cell size in the Dongkok watershed were different depending on the Rainfall-runoff events. The slopes (ratio) of the curves in DK960826 and DK980815 were 0.239 and 0.337, respectively, and those in DK960616 and DK970715 were 0.609 and 0.803, respectively. The variation range in the slopes was between 0.239 and 0.803. Figure 7b shows the change in the slope of the curves in the grid cell size from 0.356 to 0.540 in the Rainfall-runoff events in the Ieemokjung watershed. Figure 7 shows that the contributing area in the Rainfall-runoff events and grid cell size varied. In other words, when the grid cell size was large, the contributing area increased, but the contributing area varied depending on the characteristics of the Rainfall-runoff events, even when the grid cell size was constant. The change of contributing area depending on rainfall events in Figure 6 shows a good agreement that the contributing area is not stationary but changes over both storm and seasonal timescales, reflecting  
Figure 5: Cumulative frequency of the topographic indexes (\(ln(\frac{d}{tamp})\)) based on the DEM grid cell size. (**a**) Dongkok watershed. (**b**) Ieemokjung watershed.  
Figure 6: Relation of mean topographic indexes (\(ln(\frac{d}{tamp})\)) to mean ln(a) and mean ln(1/tan\(\beta\)) values based on DEM cell size in Dongkok and Ieemokjung watersheds.  
changes in the average watershed water balance, topography, and soil conditions. Particularly, the contributing area differs from the mean watershed deficit related to the watershed water balance for the saturated zone [1; 36; 37]. It implies that rainfall events affect mean watershed deficit, and different mean watershed deficits influence the contributing area. Also, several studies found that the influence of DEM resolution was through its effect on the calculation of the contributing area [13; 35]. However, more results and studies need to be provided to clarify the relation among rainfall events, contributing area, input parameters, and DEM resolution.