3.3 Modeling and applying the V–L relationship
In 2021, the total volume of 2,312 ephemeral gullies was 19,175.95
m3 (per ephemeral gully average 8.29 ± 6.34
m3), with 82.70% of the single ephemeral gully volume
concentrated within 13.0 m3, and only 3.46% of the
single ephemeral gully volume exceeding 20 m3. The
regression model fit the following equation for ephemeral gully volume
and length (Fig. 6(a)):
\(V=0.0842L^{1.1932}\ (R^{2}=0.80,\ n=1,594)\) (8)
where \(V\) is ephemeral gully volume (m3) and \(L\)is ephemeral gully length (m).
The above regression function indicated a power function relationship
between ephemeral gully volume and ephemeral gully length
(R2 = 0.80). Previous studies also used a power
function of the form V=aLb to reveal the
relationship between ephemeral gully volume (V ) and ephemeral
gully length (L ), where the values of constant a ranged
from 0.0082–2.94 and exponent b ranged from 1.12–2.1622 (Capra
et al., 2005; Frankl et al., 2013; Li et al., 2017; Muñoz-Robles et al.,
2010; Zucca et al., 2006). In this study, constant a (0.0842) and
exponent b (1.1932) were within the corresponding intervals
reported in previous studies, and ephemeral gully length can be
accurately and conveniently extracted based on large-scale DOM or DEM.
Moreover, the volumes of the ephemeral gullies were modeled using Eq.
(8) and compared to measured ephemeral gully volumes. Linear regression
between the predicted and measured ephemeral gully volumes produced
R2 and RMSE values of 0.97 and 0.85
m3, respectively (Fig. 5(b)). There was no observable
systematic bias between the predicted and measured ephemeral gully
volumes using the V–L relationship. Therefore, the V–Lmodel can be used to assess ephemeral gully volume in the hilly and
gully region of the Loess Plateau.