# The Definition of Perennial Streams Based on a Wet Channel Network Extracted from LiDAR Data
## 3 Results and Discussion
### The Relationship between the Wet Channel Ratio and Streamflow Excedance Probability  
To better understand the definition of perennial streams, the relationships between two non-dimensional variables were investigated (Figure 6): streamflow exceedance probability  
Figure 5: The relationship between streamflow (Q), presented in Table 1, and wet channel length (\(L_{W}\)) in the study watersheds. (\(E_{Q}\)) and the wet channel ratio (\(\alpha_{W}\)). \(E_{Q}\) values of 0% and 100% represented the highest and lowest streamflow, respectively. An \(E_{Q}\) of 0% was likely to be an underestimation as it was evaluated based on limited streamflow data. Despite this fact, it was assumed that all of the stream networks were flowing (i.e., \(\alpha_{W}=100\%\)) when the maximum streamflow occurred (i.e., \(E_{Q}=0\%\)). Under this assumption, the best fit function was an exponential function, \(\alpha_{W}=100e^{-0.024E_{Q}}\) with \(R^{2}=0.73\), as shown in Figure 6.  
From the fitted equation, an \(E_{Q}\) of 100% (i.e., the minimum streamflow) corresponded to an \(\alpha_{W}\) of 9.1%. Using the definition of a perennial stream from the literature, \(E_{Q}\) values of 90% and 80% corresponded to \(\alpha_{W}\) values of 11.4% and 14.7%, respectively. [PERSON] and [PERSON] [46] showed that perennial stream density declines from around 0.6 km/km\({}^{2}\) to 0.2 km/km\({}^{2}\) since the minimum streamflow decreases when \(E_{P}/P\) increases from 0.8 to 2.1 (i.e., less rainfall). The drainage density slightly increases (around 9-13 km/km\({}^{2}\)) for \(0.8\leq E_{P}/P\leq 2.1\) based on the dependence of drainage density on the climate. Therefore, the perennial stream ratio (\(PSR\)), defined as the perennial stream length over the total valley length, declines with \(E_{P}/P\) for a perennial stream. The perennial stream length of each watershed was obtained from the National Hydrography Dataset (NHD), and the valley length was extracted from LiDAR DEM to compute the perennial stream ratio (\(PSR\)). As shown in Figure 7a, the \(E_{Q}\) of the perennial streamflow for each watershed was calculated using the relationship between \(E_{Q}\) and \(\alpha_{W}\), as shown in Figure 6. The range of the perennial stream ratio (\(PSR\)) for the study watersheds was 1.2% to 29.4% with a mean of 11.0%; the range of \(E_{Q}\) corresponding to the perennial streamflow was from 49% to 100%, and the average value was 86%. Figure 7b shows the distribution of perennial streamflow \(E_{Q}\) for the study watersheds. The distribution was represented by normalized frequency, defined as the ratio of the number of watersheds in each bin to the total number of watersheds. Corresponding to the perennial streamflow, 71% of the study watersheds had \(E_{Q}\) values greater than 80%. Figure 6: The relationship between streamflow exceedance probability (\(E_{Q}\)) and the wet channel ratio (\(\alpha_{W}\)) in the study watersheds. The perennial streamflow for each watershed was directly calculated from the perennial stream length using the relationship between streamflow (\(Q\)) and wet channel length (\(L_{\text{W}}\)) in Figure 5. Subsequently, another \(E_{Q}\) of perennial streamflow was computed using the flow duration curve for each watershed. The range of \(E_{Q}\) regarding perennial streamflow was from 51% to 100%, and the average value was 88%. The ranges of \(E_{Q}\) associated with perennial streamflow were similar using both relationships, and the mean values were 86% and 88%, respectively, which were in the range of the reported values (i.e., 80% and 90%) from the literature [7; 8; 9]. However, caution should be exercised when using the mean \(E_{Q}\) value to define perennial streams because \(E_{Q}\) values associated with perennial streamflow depend on the characteristics of the watershed, such as groundwater, land use, soil, vegetation, and topography. The NHD perennial stream lengths (\(PSR\)), perennial streamflows, and the \(E_{Q}\) values for the perennial streamflows for the study watersheds are listed in Table 2.