Modeling of driving factors and headcut rates of ephemeral gullies in the loess plateau of China using high-resolution remote sensing images

Figures & data

Figure 1. Location of the study area. (a) Geographical location, (b) remote sensing image, and (c) ephemeral gully samples in the Zhoutungou watershed on the Loess Plateau.

Figure 2. Monthly cumulative precipitation (orange bars) and average temperature (red curves) from 2009 to 2021 in the Zhoutungou watershed.

Figure 3. Flowchart of the methodology used in this study.

Figure 4. Spatial discretization parameter optimization for each continuous variable.

Figure 5. (a) Spatial distribution and (b) the relative frequency of ephemeral gully head advance rates from 2009 to 2021.

Figure 6. Ephemeral gully head advancement from 2009–2021 at two ephemeral gully sites: (a) ephemeral gully 68 and (b) ephemeral gully 85.

Table 1. Multi-collinearity testing indices for the independent variables in the study area.

Driving factors	Collinearity statistics
	Tolerance	VIF
Slope degree	0.82	1.22
Slope aspect	0.87	1.15
Profile curvature	0.85	1.17
Catchment area	0.84	1.19
FVC	0.80	1.25
Rainfall erosivity	0.89	1.13

Table 2. Ephemeral gully head advance rates in other global sites.

Continent	Region	Ephemeral gully head advance rate (m yr^–1)	References
Africa	Morocco	0–0.31	Marzolff and Ries (2007)
	Ethiopia	0.53–18.40	Yibeltal et al. (2019), Frankl et al. (2012), Nyssen et al. (2002)
	South Africa	0.33–1.67	Grellier et al. (2012)
	Kenya	0.8–1.5	Oostwoud Wijdenes and Bryan (2001)
	Tunisia	0.29–0.46	Maaoui et al. (2012)
Europe	Spain	0.07–0.8	Marzolff and Ries (2007), Martı́nez-Casasnovas (2003)
	Romania	0.92	Ionita (2006)
	Poland	0.21–0.52	Malik (2008)
Asia	Iran	0.1–2.57	Nazari Samani et al. (2010), Nazari Samani et al. (2018)
	Loess Plateau in China	0.23–2.39	Jiang et al. (2021), Xu et al. (2019)

Figure 7. OPGD-based explanatory variable exploration of ephemeral gully head advance rate: (a) factor detector, (b) interaction detector, (c) ecological detector, and (d) risk detector.

Figure 8. Regression function fitting curves for ephemeral gully head advance rate and (a) catchment area, (b) FVC, (c) rainfall erovisity, and (d) slope degree.

Figure 9. Ephemeral gully head advance rates from the field survey (measured values) and the prediction model (predicted values).

Table 3. Summary of global prediction models for ephemeral gully head advance rate

Study region	Prediction model for ephemeral gully head advance rate	References
USA	$R=0.15A^{0.49}{S}^{0.14}{P}^{0.74}E$ where $R$ is ephemeral gully head advance rate (m yr^–1), $A$ is drainage area above gully head (m^2), $S$ is slope of the approach channel above the gully head (%), $P$ is the sum of rainfall from 24-hour rains ≥12.7 mm, and $E$ is the soil clay percentage	Thompson (Thompson 1964)
USA	$R=1.5A^{0.46}{P}^{0.2}$ where $R$ is ephemeral gully head advance rate (m yr^–1), $A$ is drainage area above gully head (ha), and $P$ is the sum of rainfall from 24-hour rains ≥12.7 mm during gully development (mm)	SCS Ⅰ (USDA 1966)
USA	$R_A=R_1{\left(\frac{A_1}{A_2}\right)}^{0.46}{\left(\frac{P_2}{P_1}\right)}^{0.2}$ where $R_A$ is ephemeral gully head advance rate (m yr^–1), $R_1$ is past average annual ephemeral gully head advance rate (m yr^–1), $\frac{A_1}{A_2}$ is the ratio of the mean drainage area of the reaches to the average drainage area of the reach through which the gully has moved, and $\frac{P_2}{P_1}$ is the ratio of the amount of rainfall from 24-hour rains ≥12.7 mm during the study period	SCS Ⅱ (USDA 1966)
Hilly and gully region of Loess Plateau in China	$R=9.26\times {10}^{-4}{S}^{0.187}{C}_A^{0.597}(R-1855.87{)}^{0.498}(1+F{)}^{-0.565}$ where $R$ is ephemeral gully head advance rate (m yr^–1), S is slope of the approach channel above the ephemeral gully head (°), $C_A$ is catchment area above the ephemeral gully head (m^2), R is annual average rainfall erosivity (MJ mm hm^–2 h^–1 yr^–1), and F is fractional vegetation cover (%)	This research

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