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.