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.