4.2 V–L relationship
The V–L relationship was best described by a power equationV=aLb , with Eq. 8 revealing an R2 value of 0.80, constant a of 0.0842, and exponent b of 1.1932, all within the corresponding intervals reported in previous studies (Capra et al., 2005; Frankl et al., 2013; Li et al., 2017; Muñoz-Robles et al., 2010; Zucca et al., 2006) and indicating that ephemeral gully length was a good predictor of ephemeral gully erosion volume. However, Li et al. (2017) showed that the relationship between gully volume and gully area had a larger Nash-Sutcliffe efficiency (Ens) and coefficient of determination (R2) and smaller relative error (Er) than the relationship between gully volume and gully length, indicating that theV–Ag prediction model performed better than the V–Lrelationship.
Ephemeral gullies are those transitioning from rill to gully. Due to the characteristics of ephemeral gullies and the limitation of DOM/DEM resolution, it is difficult to accurately obtain ephemeral gully areas. Ephemeral gully length is the most easily and accurately obtained morphological parameter from high-resolution remote sensing images, with good R2 and RMSE between the V–L models established in this study, and thus has great application potential for estimating ephemeral gully erosion volume in the hilly and gully region of the Loess Plateau in China.