2.4 Extraction of ephemeral gully morphological parameters
The data for ephemeral gully recognition and DEM were imported into ArcGIS software to extract the morphological features of ephemeral gullies (e.g., number, length, width, area, frequency, density, and dissection degree) using Spatial Analyst and 3D Analyst tools. For ephemeral gully length (L ), the distance measurement function was used to obtain the projected ephemeral gully length, which was divided by the cosine value of the corresponding gradient to obtain the ephemeral gully length using Eq. (1). For ephemeral gully width (W ), five positions were selected on the ephemeral gully length to measure ephemeral gully width, and calculate the average value of the five position widths to obtain the average ephemeral gully width using Eq. (2). Ephemeral gully area (A ) is the average ephemeral gully width multiplied by the corresponding length using Eq. (3). Ephemeral gully fequency (F ) is the ephemeral gully number per unit area of the watershed, reflecting the erosion intensity of ephemeral gullies in the watershed using Eq. (4). Ephemeral gully density (\(\rho\)) is the total ephemeral gully length per unit area of the watershed, reflecting ephemeral gully length characteristics in the watershed and degree of surface fragmentation using Eq. (5). Ephemeral gully dissection degree (D ) is the total ephemeral gully area per unit area of the watershed, reflecting watershed ephemeral gully development using Eq. (6).
\(L=\frac{L_{p}}{\cos\theta}\) (1)
\(W=\frac{\sum_{i=1}^{5}W_{i}}{5}\) (2)
\(A=WL\) (3)
\(F=N/A_{0}\) (4)
\(\rho=\frac{\sum_{i=1}^{n}L_{i}}{A_{0}}\) (5)
\(D=\frac{\sum_{i=1}^{n}A_{i}}{A_{0}}\) (6)
where \(L_{p}\) is projected ephemeral gully length, \(\theta\) is ephemeral gully gradient, \(W_{i}\) (i=1, 2, 3, 4, 5) is the five position widths of the ephemeral gully, \(N\) is ephemeral gully number, and \(A_{0}\) is watershed area.