# Evaluating the Drainage Density Characteristics on Climate and Drainage Area Using LiDAR Data
## 3 Results and Discussion  
### Relationship between Drainage Density and Climate Aridity Index  
A total of 121 study watersheds in arid and humid regions were selected, then the valley networks were extracted using 1 m resolution LiDAR-based DEMs. The drainage area of most watersheds is less than 3 km\({}^{2}\), and the average drainage area is 1.31 km\({}^{2}\), with a minimum of 0.04 km\({}^{2}\) and a maximum of 8.19 km\({}^{2}\). The range of \(D_{d}\) is from 6.2 km/km\({}^{2}\) to 41.5 km/km\({}^{2}\). Figure 6 shows the obtained results from this study overlaid with the reported data by [PERSON] [31] and [PERSON] [39]. For the climate aridity index, \(E_{P}/P\leq 1\), the data points by [PERSON] [36] follow a decreasing trend, whereas such a declining trend does not exist for the watersheds in this study (Figure 6). The decreasing trend by [PERSON] [39] continues until \(E_{P}/P\) approaches \(\sim\)1.8. This discrepancy can be explained by the land use in Madduma Bandara's watersheds, in which the natural land cover has been consistently removed due to a tea plantation over a 100 year period. In Madduma Bandara's watersheds, the same vegetation cover exists in a different climates leading to the same resistance force against erosion enforced by rainfall. Given this circumstance, when \(E_{P}/P\) increases (i.e., less rainfall), the erosion force drops while the resistance force is constant. This condition results in decreasing \(D_{d}\) as \(E_{P}/P\) increases. Thus, those data points are affected by human interferences to drainage density. Figure 5: Curvature-based valley network extraction: (**a**) Contour curvature computed from the filtered DEM and (**b**) extracted valley network based on the curvature threshold in the Isleta Drain watershed located in New Mexico. Figure 6: Drainage density (\(D_{d}\)) versus climate aridity index (\(E_{P}/P\)) from Melton [33], Madduma Bandara [39], and this study. For \(1\leq E_{P}/P\leq 6\), the drainage densities from both Melton [33] and this study show increasing trends (Figure 7). However, the magnitude of \(D_{d}\) is higher than those of Melton [33]. This difference can be explained by the spatial resolution of topographic maps. The topographic maps with a scale of 1:24,000 were used for extracting drainage networks by Melton [33] for watersheds with \(E_{P}/P\) less than 6. These topographic maps with bare-earth contours are approximately equivalent to DEMs with a cell size of 30 m [56], from which small valleys are not detectable. Therefore, the drainage density is underestimated. However, the spatial resolution of LiDAR-based DEMs is 1 m in this study. The extracted drainage network from coarse topographic maps deviates significantly from the correspondingly observed one in the field [6; 57]. In order to demonstrate the effect of DEM resolution on drainage density, 1 m DEMs for the study watersheds were resampled to 30 m DEMs for generating a drainage network. Twenty watersheds with \(E_{P}/P\) less than six and drainage areas larger than 0.2 km\({}^{2}\) were randomly selected. As shown in Figure 7, drainage densities from 1 m DEMs are higher than those from 30 m DEMs. As a demonstration, Figure 8 shows the extracted valley lines from 1 m and 30 m DEMs for the Isleta Drain watershed in New Mexico. As indicated in Figure 6, the drainage densities from Melton [33] are higher than those in this study when \(E_{P}/P\geq 7\). The difference may be a result of the watersheds' size between the two studies. The six watersheds used in Melton [33] are located in Arizona, southwestern United States. The method that was used to map the valley networks in these six watersheds were field survey. The range of the watershed sizes is from 0.001 to 0.006 km\({}^{2}\), which was smaller than the current study. The study watersheds selected for the current study have an average watershed size of 0.40 km\({}^{2}\) when \(E_{P}/P\geq 7\). The difference in watershed sizes between [PERSON]'s [33] study and the current study may contribute to the difference in drainage density.