2.5 Assessing the V–L relationship and ephemeral gully
erosion volume change
The data for ephemeral gully recognition and DEM (0.15 m resolution)
were imported into ArcGIS software to extract each ephemeral gully
erosion volume using Spatial Analyst and 3D Analyst tools. The empirical
relationship between ephemeral gully volume (V) and length
(L ) was established with curve fitting analysis, which calculated
the root mean square error (RMSE) and coefficient of determination
(R2) to examine the effect of ephemeral gully length
on measured and predicted ephemeral gully erosion volume. Finally, we
calculated ephemeral gully erosion volume in 2009 using the constructedV–L relationship and analyzed the change in ephemeral gully
erosion volume from 2009 to 2021.
RMSE was calculated as Eq. (7):
\(RMSE=\sqrt{\frac{1}{n}\sum_{i=1}^{n}\left(P_{i}-M_{i}\right)^{2}}\)(7)
where M is measured ephemeral gully erosion volume, P is
predicted ephemeral gully erosion volume, and n is the number of
modeled gullies.