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\begin{document}

\title{Evolution and Development of Ephemeral Gully Erosion in Hilly and Gully
Region of the Loess Plateau in China}



\author[1]{Boyang Liu}%
\author[1]{Biao Zhang}%
\author[2]{Ziming Yin}%
\author[3]{Bai Hao}%
\author[1]{Dr. Shufang Wu}%
\author[1]{Hao Feng}%
\author[4]{K Siddique}%
\affil[1]{Northwest A\&F University}%
\affil[2]{Northwest A\&F University College of Natural Resources and Environment}%
\affil[3]{Sichuan Expressway Construction \& Development Group Co Ltd}%
\affil[4]{The University of Western Australia}%


\vspace{-1em}



  
  \date{May 23, 2024}


\begingroup
\let\center\flushleft
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\selectlanguage{english}
\begin{abstract}
Ephemeral gully erosion is a primary mode of soil erosion that is highly
visible, affecting soil productivity and restricting land use. Watershed
is the basic unit of soil erosion control; existing research has focused
on several typical ephemeral gullies or slopes, which do not fully
display changes in ephemeral gullies at a watershed scale. This study
analyzed the spatial-temporal evolution and development rate of
ephemeral gully erosion at the watershed scale on the Loess Plateau from
2009 to 2021 using remote sensing images (0.5 m resolution), unmanned
aerial vehicles (UAV), and field investigations. The results revealed
that: (1) most ephemeral gullies occurred in southwestern parts of the
watershed, with many hills and large slope gradients; (2) average growth
rates of each ephemeral gully frequency, length, density, dissection
degree, and width were 2.87 km \textsuperscript{2} y
\textsuperscript{--1}, 1.66 m y \textsuperscript{--1}, 0.12 km km
\textsuperscript{--2} y \textsuperscript{--1}, 0.0125\% y
\textsuperscript{--1}, and 0.04 m y \textsuperscript{--1} ,
respectively; (3) ephemeral gully erosion volume ( \emph{V}) and length
( \emph{L}) had a good power function relationship: V = 0 . 0842 L 1 .
1932 ~ ( R 2 = 0 . 80 ) . The root mean square error (RMSE) and
coefficient of determination (R \textsuperscript{2}) between the
measured and predicted ephemeral gully volumes suggest that the
\emph{V--L} relationship has a good predictive ability for ephemeral
gully volume. Thus, the \emph{V--L} model was used to evaluate the
development rate of ephemeral gully erosion volume in small watersheds
from 2009 to 2021, revealing an average value of 743.20 m
\textsuperscript{3} y \textsuperscript{--1}. This study proposed a
feasible model for assessing ephemeral gully volume and volume changes
at a watershed scale using high-resolution remote sensing images,
providing a reference for understanding the development of ephemeral
gully erosion in small watersheds over time.%
\end{abstract}%



\sloppy


\textbf{Evolution and Development of Ephemeral Gully Erosion in Hilly
and Gully Region of the Loess Plateau in China}

Boyang Liu\textsuperscript{a,b}, Biao Zhang\textsuperscript{a,b}, Ziming
Yin\textsuperscript{c}, Bai Hao\textsuperscript{d}, Shufang
Wu\textsuperscript{a,b}*, Hao Feng\textsuperscript{a}, Kadambot H.M.
Siddique\textsuperscript{e}

\textsuperscript{a} Key Laboratory of Agricultural Soil and Water
Engineering in Arid and Semiarid Areas, Ministry of Education, Northwest
A \& F University, Yangling 712100, China

\textsuperscript{b} Institute of Water Saving Agriculture in Arid Areas
of China, Northwest A \& F University, Yangling 712100, China

\textsuperscript{c} College of Natural Resources and Environment,
Northwest A\&F University, Yangling 712100, China

\textsuperscript{d} Sichuan Expressway Construction \& Development Group
Co., Ltd., Chengdu, Sichuan 610041, China

\textsuperscript{e} The UWA Institute of Agriculture and School of
Agriculture \& Environment, The University of Western Australia, Perth,
WA 6001, Australia

\textbf{*Corresponding Author:}

Shufang Wu, College of Water Resources and Architectural Engineering,
Northwest A\&F University, Yangling 712100, Shaanxi, PR China.
E-mail:\emph{wsfjs@163.com}

\textbf{Highlights}

\begin{itemize}
\tightlist
\item
  Used the SegNet model to extract ephemeral gully at the watershed
  scale.
\item
  Clarified the spatial-temporal evolution of ephemeral gully from
  2009--2021.
\item
  Evaluated the development rate of ephemeral gully morphological
  parameters.
\item
  Bulit an empirical model to assess ephemeral gully erosion volume.
\end{itemize}

\section*{Abstract}

{\label{abstract}}

Ephemeral gully erosion is a primary mode of soil erosion that is highly
visible, affecting soil productivity and restricting land use. Watershed
is the basic unit of soil erosion control; existing research has focused
on several typical ephemeral gullies or slopes, which do not fully
display changes in ephemeral gullies at a watershed scale. This study
analyzed the spatial-temporal evolution and development rate of
ephemeral gully erosion at the watershed scale on the Loess Plateau from
2009 to 2021 using remote sensing images (0.5 m resolution), unmanned
aerial vehicles (UAV), and field investigations. The results revealed
that: (1) most ephemeral gullies occurred in southwestern parts of the
watershed, with many hills and large slope gradients; (2) average growth
rates of each ephemeral gully frequency, length, density, dissection
degree, and width were 2.87 km\textsuperscript{2}y\textsuperscript{--1},
1.66 m y\textsuperscript{--1}, 0.12 km km\textsuperscript{--2}
y\textsuperscript{--1}, 0.0125\% y\textsuperscript{--1}, and 0.04 m
y\textsuperscript{--1} , respectively; (3) ephemeral gully erosion
volume (\emph{V} ) and length (\emph{L} ) had a good power function
relationship:\(V=0.0842L^{1.1932}\ (R^{2}=0.80)\). The root mean square error (RMSE) and
coefficient of determination (R\textsuperscript{2}) between the measured
and predicted ephemeral gully volumes suggest that the\emph{V--L}
relationship has a good predictive ability for ephemeral gully volume.
Thus, the \emph{V--L} model was used to evaluate the development rate of
ephemeral gully erosion volume in small watersheds from 2009 to 2021,
revealing an average value of 743.20 m\textsuperscript{3}
y\textsuperscript{--1}. This study proposed a feasible model for
assessing ephemeral gully volume and volume changes at a watershed scale
using high-resolution remote sensing images, providing a reference for
understanding the development of ephemeral gully erosion in small
watersheds over time.

\textbf{Keywords:}

\emph{soil erosion, ephemeral gully, remote sensing and UAV,
morphological features, development rate}

\section*{1. Introduction}

{\label{introduction}}

Soil is fundamental for life on earth, impacting global issues such as
food and water security (Koch et al., 2013; McBratney et al., 2014), and
is increasingly considered the main contributor to extensive ecosystem
services (Dominati et al., 2010). Soil erosion is the greatest threat to
soil function at the global scale (Montanarella et al., 2016) and is
recognized as the most dominant land degradation process, severely
damaging infrastructure, causing land degradation and water pollution in
developed regions, and threatening the safety of human production and
life in many developing regions (Hao et al., 2020; Mohammed et al.,
2020; Pennock, 2019). Ephemeral gully erosion is a linear erosion
pattern occurring on steep cultivated slope farmland, formed by the
combined action of runoff erosion and human cultivation, and with a
connecting role in the slope-gully system (Liu \emph{et al.}, 1988;
Poesen \emph{et al.}, 2003; Wang \emph{et al.}, 2003). Ephemeral gully
erosion is a major contributor to soil erosion worldwide, adversely
affecting water quality in the receiving water courses and impacting
aquatic life (Fox et al., 2016; Gholami et al., 2019; Gupta et al.,
2019; Anache et al., 2018; Dev\selectlanguage{ngerman}átý et al., 2019; Eekhout and de Vente,
2022; Sun et al., 2014; Tamene et al., 2020).

Research has focused on measuring ephemeral gully morphological
parameters and determining their development at temporal and spatial
scales. Some studies have used ground-based methods (e.g. field plots,
erosion pins, tape method, volume replacement method) to garner relevant
ephemeral gully data (Boardman et al., 2015; Casalí et al., 2006; Evans
and Lindsay, 2010; Gómez-Gutiérrez et al. 2014; Kearney et al., 2018;
Perroy et al., 2010; Romanescu et al., 2012; Shen \emph{et al.} , 2021;
Wang \emph{et al.} , 2020a; Wang \emph{et al.} , 2021a), but the limited
data significantly impacts the reliability of the research conclusions
for practical application. Further verification is needed to determine
whether the conclusions under small-scale conditions can be extrapolated
to larger scales. However, large-area field surveys are needed to
accurately grasp the spatial distribution characteristics of ephemeral
gully morphological features, requiring a large workload with low
efficiency. In recent decades, the spatial resolutions, revisiting
times, and detail of remote sensing data and digital elevation models
(DEM) have significantly increased, providing crucial data support for
accurately identifying the spatial position and morphological parameters
of ephemeral gullies (Arabameri et al., 2019; Cao \emph{et al} ., 2020;
Dai \emph{et al} ., 2020; Karydas and Panagos, 2020; King \emph{et al}
., 2005; Liu \emph{et al} ., 2022; Vallejo Orti et al., 2019;
Yermolayev\emph{et al} ., 2020). Ephemeral gully volume is an important
morphological parameter of ephemeral gullies and an indicator of the
contribution of ephemeral gully erosion to sediment yield (Kompia-Zare
et al., 2011; Woodward, 1999). Understanding ephemeral gully development
over time is important for predicting their future behavior, which can
be done directly by measuring volume change (Li et al., 2017).
Unfortunately, due to ephemeral gully characteristics and the inherent
accuracy limitations of DEM, measuring ephemeral gully volume using DEM
data has not been widely used. However, ephemeral gully length is the
most easily obtained morphological parameter, with several studies
exploring the relationship between ephemeral gully volume (\emph{V} )
and length (\emph{L} ) using the power
equation\emph{V=aL\textsuperscript{b}} (Capra et al., 2005; Frankl et
al., 2013; Kompani-Zare et al., 2011; Li et al., 2017; Muñoz-Robles et
al., 2010; Zhang et al., 2007; Zucca et al., 2006).

Watershed is the basic hydrological response unit, an ideal spatial
scale for studying soil and water losses, and the fundamental unit for
managing ecological environments. Studies on soil erosion at the
watershed scale have focused on estimating soil erosion and sediment
(Cao \emph{et al.} , 2022; Galdies \emph{et al.} , 2022; Lufira \emph{et
al.} , 2022), assessing erosion susceptibility (Pandey \emph{et al.} ,
2021; Tahouri \emph{et al.} , 2022; Tesema, 2022; Wang \emph{et al.} ,
2022), and analyzing the factors affecting soil erosion
(Aneseyee\emph{et al.} , 2020; Choudhury \emph{et al.} , 2022; Guduru
and Jilo, 2022; Zhao \emph{et al.} , 2022). However, most scholars chose
typically representative ephemeral gullies or slopes as research objects
to analyze changes in ephemeral gullies (Capra et al., 2009; Karydas and
Panagos, 2020; Li et al., 2016; Wang \emph{et al.} 2021b; Zheng et al.,
2006), but typical ephemeral gullies or slopes do not fully display
changes in ephemeral gullies at a watershed scale. Therefore, clarifying
the temporal and spatial development processes of ephemeral gullies at
the watershed scale is valuable for determining soil and water
conservation practices and understanding the characteristics of each
ephemeral gully and other geomorphologic processes related to ephemeral
gully erosion.

The Loess Plateau of China is a typical loess geomorphic region and one
of the most serious soil erosion regions in China, if not the world
(Fu\emph{et al.} , 2011). Ephemeral gully erosion on the Loess Plateau
accounts for more than 70\% of its ravines, with erosion accounting for
26.60--59.20\% of total slope erosion (Cheng et al., 2007; Zheng et al.,
2006). Ephemeral gully erosion control has been underway on the Loess
Plateau since 1999 when the Chinese government implemented `Grain for
Green Project' (Fu et al., 2017; Ran et al., 2013; Wang et al., 2014),
with some areas still requiring attention. This study used 0.50 m
resolution remote sensing images integrated with a deep learning image
semantic segmentation model (deep learning can scientifically build
high-level features from raw datasets, deliver forecasting results, and
perform better than machine learning in various research areas) to
identify ephemeral gullies and extract morphological features at the
watershed scale, analyze the temporal and spatial distribution and
evolution law of ephemeral gullies, and clarify the development
processes and rate of ephemeral gully erosion at the watershed scale in
the hilly and gully region of the Loess Plateau. This research will help
select the most effective countermeasures to prevent and control soil
erosion and provide more effective measures to protect limited land
resources and ecological environments.

\textbf{2. Materials and Methods}

\textbf{2.1 Study area}

The research area of this study is the Zhoutungou watershed (36°42'10''
N to 36°47'10'' N, 109°09'00'' E to 109°13'45'' E), a typical small
watershed in the hilly and gully region of the Loess Plateau, with an
average altitude of 1,235.37 m (Fig. 1 (a) and (b)). The annual average
temperature is 8.80\selectlanguage{english} and annual average rainfall is 550 mm (74\% falls
from July to Sept.). The soil type is loessial soil of the Zhoutungou
watershed. The total watershed area is 33.60 km\textsuperscript{2}, with
18.70 km\textsuperscript{2} (55.57\%) of valleys (Jiang \emph{et al.} ,
1999). The ephemeral gullies are distributed mainly on slope surfaces in
the southern region, accounting for about one-third of the slope area.
The main measure for ephemeral gully regional governance is planting
grasses and shrubs. The main valley in the watershed runs southwest to
northeast, with the number of branch valleys gradually increasing from
northeast to southwest. The valley and branch valley sections have a `U'
or `V' shape, with the terrain of each valley comprising hills, slopes,
and channels. In addition, we selected two slope types for field
investigations to obtain measured values of ephemeral gully
morphological parameters. Slope A is on sunny slopes, with an area of
22,532 m\textsuperscript{2}. Slope B is on shady slopes, with an area of
11,004 m\textsuperscript{2} (Fig.1 (c)). We investigated 13 ephemeral
gullies on slope A and six ephemeral gullies on slope B.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

Figure 1. Location of the study area. (a) Geographical location map of
the study area on the Loess Plateau. (b) Digital elevation model (DEM)
of the Zhoutungou watershed. (c) Detailed information of field survey
sites (Slope A located on a sunny slope, and Slope B located on a shady
slope).

\textbf{2.2 Data sources}

This study used three different spatial scale survey methods to monitor
ephemeral gully: satellite remote sensing monitoring, unmanned aerial
vehicle (UAV) monitoring, and field investigations (Fig. 2). The remote
sensing image data included 0.50 m high-resolution satellite images
(digital orthophoto map, DOM) in 2009, 2012, and 2018 and 0.50 m
high-resolution DOM images by UAV in 2021 (11,720 images). A DEM with
0.15 m resolution and DOM with 0.50 m resolution were created using
Agisoft Metashape (Windows1.7.3, Agisoft, Russia). The 1:10,000 DEM data
used in this study were obtained from the Shaanxi Geomatics Center of
the Ministry of Natural Resources of China, and the 0.15 m resolution
DEM data were obtained by the authors using UAV (Table 1). In order to
avoid the influence of different DEM resolutions on the extraction
accuracy of ephemeral gully morphological parameters, we changed the
resolution of 0.15 m to 5 m by resampling in ArcGIS software (ArcGIS
10.2, Esri, U.S.A). The remote sensing and UAV images were obtained from
April to June each year when the vegetation was not yet lush and thus
had no significant impact on ephemeral gully recognition.

Table 1 Basic information on the DOM and DEM data used in this study.\selectlanguage{english}
\begin{longtable}[]{@{}lllll@{}}
\toprule
\begin{minipage}[b]{0.17\columnwidth}\raggedright\strut
Data type\strut
\end{minipage} & \begin{minipage}[b]{0.17\columnwidth}\raggedright\strut
Product name\strut
\end{minipage} & \begin{minipage}[b]{0.17\columnwidth}\raggedright\strut
Data time (year)\strut
\end{minipage} & \begin{minipage}[b]{0.17\columnwidth}\raggedright\strut
Spatial resolution (m)\strut
\end{minipage} & \begin{minipage}[b]{0.17\columnwidth}\raggedright\strut
Data source\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
DOM\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
QuickBird-02\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
2009\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.50\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Maxar Technologies\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Pleiades\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
2012\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
CNES\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
SuperView\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
2018\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
China Centre for Resources Satellite Data and Application\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
PHANTOM 4 RTK\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
2021\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.50\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Authors used UAV\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
DEM\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
1:10000 DEM\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
2009 and 2012\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
5\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Shaanxi Geomatics Center of Ministry of Natural Resources of China\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.15 m DEM\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
2021\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.15\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Authors used UAV\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

Note: DOM, DEM and UAV refer to digital orthophoto map, digital
elevation model and unmanned aerial vehicle, respectively,\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

Figure 2. Three spatial scale ephemeral gully monitoring methods.

\textbf{2.3 Selection of ephemeral gully identification model}

The SegNet model is a convolutional neural network for pixel-level image
segmentation proposed by Badrinarayanan \emph{et al.} (2017) using
end-to-end and pixel-to-pixel training to achieve image segmentation.
Its core component is an encoder network and corresponding decoder
network, followed by a pixel-level classifier, which outputs the
probability map of the K channel, where K is the number of
classification categories. Compared with other models, SegNet has fewer
training parameters, smaller memory occupation, and shorter network
training time (Deng et al., 2022; Jiang et al., 2020; Manickam et al.,
2020). In 2021, six indexes (Accuracy, Precision, Recall, F1 value, ROC
curve, and AUC) were used to compare the ephemeral gully recognition
results and accuracy evaluation with U-Net, R2U-Net, and SegNet, with
SegNet ranked first for ephemeral gully recognition in the hilly and
gully region of the Loess Plateau, followed by R2U-Net and U-Net
(Liu\emph{et al.} , 2022). Ephemeral gully length and width between
predicted and field measured values had RMSE values of 6.78 m
(R\textsuperscript{2} = 0.9817) and 0.50 m (R\textsuperscript{2} =
0.8573), respectively, using the SegNet model, indicating its superior
performance for ephemeral gully recognition and morphological feature
extraction. Hence, this study used the SegNet model for ephemeral gully
recognition and morphological feature extraction at the watershed scale.
The process of identifying ephemeral gullies with the SegNet model was
performed as follows: SegNet model carries out iterative cyclic training
based on the data set until the loss value is minimum and obtains the
corresponding optimal weight of the model. Based on the optimal weight
and network structure of the SegNet model, ephemeral gullies were
recognized using the sliding window and ignoring edge detection methods
at the watershed scale (Fig. 3).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

Figure 3. Network structure diagram of the SegNet model.

The SegNet model is a symmetric structure, mainly including Encoder and
Decoder stages. The Encoder stage classifies and analyzes low-level
local pixel values of images through Convolution Layer, ReLU function,
Batch Normalization function, and Pooling Layer to obtain high-level
semantic information. The Decoder stage uses Pooling Indices, UpSampling
Layer, Convolution Layer, ReLU function, and Batch Normalization
function to improve the geometric shape of objects and make up for the
loss of detail caused by shrinking the object in the Pooling Layer of
the Encoder stage. Finally, the extracted feature image is output as a
segmentation map through the Sigmoid function. This model inputs an
image with three RGB channels and outputs a segmentation map with one
channel.

\textbf{2.4 Extraction of ephemeral gully morphological parameters}

The data for ephemeral gully recognition and DEM were imported into
ArcGIS software to extract the morphological features of ephemeral
gullies (e.g., number, length, width, area, frequency, density, and
dissection degree) using Spatial Analyst and 3D Analyst tools. For
ephemeral gully length (\emph{L} ), the distance measurement function
was used to obtain the projected ephemeral gully length, which was
divided by the cosine value of the corresponding gradient to obtain the
ephemeral gully length using Eq. (1). For ephemeral gully width
(\emph{W} ), five positions were selected on the ephemeral gully length
to measure ephemeral gully width, and calculate the average value of the
five position widths to obtain the average ephemeral gully width using
Eq. (2). Ephemeral gully area (\emph{A} ) is the average ephemeral gully
width multiplied by the corresponding length using Eq. (3). Ephemeral
gully fequency (\emph{F} ) is the ephemeral gully number per unit area
of the watershed, reflecting the erosion intensity of ephemeral gullies
in the watershed using Eq. (4). Ephemeral gully density
(\(\rho\)) is the total ephemeral gully length per unit area
of the watershed, reflecting ephemeral gully length characteristics in
the watershed and degree of surface fragmentation using Eq. (5).
Ephemeral gully dissection degree (\emph{D} ) is the total ephemeral
gully area per unit area of the watershed, reflecting watershed
ephemeral gully development using Eq. (6).

\(L=\frac{L_{p}}{\cos\theta}\) (1)

\(W=\frac{\sum_{i=1}^{5}W_{i}}{5}\) (2)

\(A=WL\) (3)

\(F=N/A_{0}\) (4)

\(\rho=\frac{\sum_{i=1}^{n}L_{i}}{A_{0}}\) (5)

\(D=\frac{\sum_{i=1}^{n}A_{i}}{A_{0}}\) (6)

where \(L_{p}\) is projected ephemeral gully length,
\(\theta\) is ephemeral gully gradient, \(W_{i}\) (i=1,
2, 3, 4, 5) is the five position widths of the ephemeral gully,
\(N\) is ephemeral gully number, and \(A_{0}\)
is watershed area.

\textbf{2.5 Assessing the \emph{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 \emph{(V)} and length
(\emph{L} ) was established with curve fitting analysis, which
calculated the root mean square error (RMSE) and coefficient of
determination (R\textsuperscript{2}) 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
constructed\emph{V--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 \emph{M} is measured ephemeral gully erosion volume, \emph{P} is
predicted ephemeral gully erosion volume, and \emph{n} is the number of
modeled gullies.

\textbf{3. Results}

\textbf{3.1 Temporal and spatial changes in ephemeral gullies}

The SegNet model was applied to the UAV image of the whole Zhoutungou
watershed in 2021, with the sliding window and ignoring edge detection
methods used to identify ephemeral gullies at the watershed scale (Fig.
4 (a)). Comparing the ephemeral gully identification results with the
field survey in Fig. 4 (b), we found that the SegNet model had
\textgreater{}91.66\% accuracy for ephemeral gully number and spatial
distribution accuracy.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

Figure 4. Recognition results of the SegNet model in the Zhoutungou
watershed in 2021. Ephemeral gully recognition results at (a) the
watershed scale and (b) the sampling area.

The SegNet model extracted 1,153, 2,045, 2,413, and 2,312 ephemeral
gullies encompassing 34.32, 60.86, 71.82, and 68.81
km\textsuperscript{2} in 2009, 2012, 2018, and 2021, respectively, with
a frequency development rate of 2.87
km\textsuperscript{2}y\textsuperscript{--1} (Table 2). Most of the
ephemeral gullies were in the southern half of the Zhoutungou watershed
(Fig. 5), which has complex landforms and large slope gradients. From
2009 to 2012, many new ephemeral gullies formed in the northeast and
south of the watershed, but some disappeared. From 2012 to 2018, new
ephemeral gullies formed in the middle south and southeast regions of
the watershed, while others disappeared in the northeast and southwest
regions. From 2018 to 2021, only a few regions formed new ephemeral
gullies, with many disappearing in the western region.

Table 2 Statistical characteristics for ephemeral gully number and
frequency in the Zhoutungou watershed from 2009--2021.\selectlanguage{english}
\begin{longtable}[]{@{}lllll@{}}
\toprule
\begin{minipage}[b]{0.19\columnwidth}\raggedright\strut
Year\strut
\end{minipage} & \begin{minipage}[b]{0.19\columnwidth}\raggedright\strut
Number\strut
\end{minipage} & \begin{minipage}[b]{0.19\columnwidth}\raggedright\strut
Total area (km\textsuperscript{2})\strut
\end{minipage} & \begin{minipage}[b]{0.19\columnwidth}\raggedright\strut
Frequency (km\textsuperscript{--2})\strut
\end{minipage} & \begin{minipage}[b]{0.19\columnwidth}\raggedright\strut
Frequency development rate (km\textsuperscript{2}
y\textsuperscript{--1})\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
2009\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
1,153\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
33.60\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
34.32\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
2.87\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
2012\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
2,045\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
60.86\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
2018\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
2,413\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
71.82\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
2021\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
2,312\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
68.81\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image5/image5}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image6/image6}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image7/image7}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image8/image8}

\end{center}
\end{figure}

Figure 5. Spatial variation in ephemeral gully distribution from
2009--2021. (a) Ephemeral gully distribution in 2009. Spatial changes in
ephemeral gully distribution from (b) 2009--2012, (c) 2012--2018, and
(d) 2018--2021.

\textbf{3.2 Development rate of ephemeral gully morphological features}

In 2009, 2012, 2018, and 2021, ephemeral gully lengths ranged from
7.00--209.50, 5.00--228.00, 5.00--230.00, and 5.00--209.50 m (average
48.39, 46.58, 45.75, and 45.84 m) (Table 3), with total ephemeral gully
lengths of 55.79, 95.26, 110.40, and 105.98 km and densities of 1.66,
2.84, 3.59, and 3.15 km km\textsuperscript{--2}, respectively, and
development rates of 1.66 m y\textsuperscript{--1} (length) and 0.12 km
km\textsuperscript{--2} y\textsuperscript{--1} (density). From 2009 to
2021, ephemeral gully width ranged from 0.50 to 2.50 m, with more than
99\% between 0.50 and 1.50 m and an average width development rate of
0.04 m y\textsuperscript{--1}. The proportion of ephemeral gully widths
2.00--2.50 m decreased from 0.67\% in 2009 to 0.05\% in 2021. In 2009,
2012, 2018, and 2021, ephemeral gully area ranged from 6.50--230.71,
4.64--246.86, 4.64--230.00, and 5.36--209.50
m\textsuperscript{2}(average 49.12, 47.34, 46.05, and 46.36
m\textsuperscript{2}), total area was 0.0566, 0.0968, 0.1111, and 0.1072
km\textsuperscript{2}, and dissection degree was 0.17\%, 0.29\%, 0.33\%,
and 0.32\%, respectively, with development rates of 4,213.39
m\textsuperscript{2}y\textsuperscript{--1} (total area) and 0.0125\%
y\textsuperscript{--1}(dissection degree). This study found that the
development rate of all ephemeral gully morphological parameters
gradually decreased over time.

Table 3 Ephemeral gully morphological features from 2009 to 2021 in the
Zhoutungou watershed.\selectlanguage{english}
\begin{longtable}[]{@{}llllll@{}}
\toprule
Morphological features & Year & Minimum & Maximum & Mean &
Total\tabularnewline
\midrule
\endhead
Length (m) & 2009 & 7.00 & 209.50 & 48.39 & 55792.50\tabularnewline
& 2012 & 5.00 & 228.00 & 46.58 & 95295.00\tabularnewline
& 2018 & 2.00 & 230.00 & 45.75 & 110400.00\tabularnewline
& 2021 & 5.00 & 209.50 & 45.84 & 105980.00\tabularnewline
Density (km km\textsuperscript{--2}) & 2009 &
2.08\selectlanguage{ngerman}×10\textsuperscript{--4} & 6.24\selectlanguage{ngerman}×10\textsuperscript{--3} &
1.44\selectlanguage{ngerman}×10\textsuperscript{--3} & 1.66\tabularnewline
& 2012 & 1.49\selectlanguage{ngerman}×10\textsuperscript{--4} & 6.79\selectlanguage{ngerman}×10\textsuperscript{--3} &
1.39\selectlanguage{ngerman}×10\textsuperscript{--3} & 2.84\tabularnewline
& 2018 & 5.95\selectlanguage{ngerman}×10\textsuperscript{--5} & 6.85\selectlanguage{ngerman}×10\textsuperscript{--3} &
1.36\selectlanguage{ngerman}×10\textsuperscript{--3} & 3.29\tabularnewline
& 2021 & 1.49\selectlanguage{ngerman}×10\textsuperscript{--4} & 6.24\selectlanguage{ngerman}×10\textsuperscript{--3} &
1.36\selectlanguage{ngerman}×10\textsuperscript{--3} & 3.15\tabularnewline
Width (m) & 2009 & 0.50 & 2.50 & 1.01 & 1168.21\tabularnewline
& 2012 & 0.50 & 2.00 & 1.01 & 2073.07\tabularnewline
& 2018 & 0.50 & 2.00 & 1.00 & 2423.00\tabularnewline
& 2021 & 0.50 & 2.00 & 1.01 & 2339.43\tabularnewline
Area (m\selectlanguage{ngerman}²) & 2009 & 6.50 & 230.71 & 49.12 & 56600.00\tabularnewline
& 2012 & 4.64 & 246.86 & 47.34 & 96800.00\tabularnewline
& 2018 & 4.64 & 230.00 & 46.05 & 111100.00\tabularnewline
& 2021 & 5.36 & 209.50 & 46.36 & 107200.00\tabularnewline
Dissection degree (\%) & 2009 & 1.93\selectlanguage{ngerman}×10\textsuperscript{--5} &
6.87\selectlanguage{ngerman}×10\textsuperscript{--4} & 1.46\selectlanguage{ngerman}×10\textsuperscript{--4} &
0.17\tabularnewline
& 2012 & 1.38\selectlanguage{ngerman}×10\textsuperscript{--5} & 7.35\selectlanguage{ngerman}×10\textsuperscript{--4} &
1.41\selectlanguage{ngerman}×10\textsuperscript{--4} & 0.29\tabularnewline
& 2018 & 1.38\selectlanguage{ngerman}×10\textsuperscript{--5} & 6.85\selectlanguage{ngerman}×10\textsuperscript{--4} &
1.37\selectlanguage{ngerman}×10\textsuperscript{--4} & 0.33\tabularnewline
& 2021 & 1.60\selectlanguage{ngerman}×10\textsuperscript{--5} & 6.24\selectlanguage{ngerman}×10\textsuperscript{--4} &
1.38\selectlanguage{ngerman}×10\textsuperscript{--4} & 0.32\tabularnewline
\bottomrule
\end{longtable}

\textbf{3.3 Modeling and applying the \emph{V--L} relationship}

In 2021, the total volume of 2,312 ephemeral gullies was 19,175.95
m\textsuperscript{3} (per ephemeral gully average 8.29 \selectlanguage{ngerman}± 6.34
m\textsuperscript{3}), with 82.70\% of the single ephemeral gully volume
concentrated within 13.0 m\textsuperscript{3}, and only 3.46\% of the
single ephemeral gully volume exceeding 20 m\textsuperscript{3}. 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
(m\textsuperscript{3}) and \(L\)is ephemeral gully length
(m).

The above regression function indicated a power function relationship
between ephemeral gully volume and ephemeral gully length
(R\textsuperscript{2} = 0.80). Previous studies also used a power
function of the form \emph{V=aL\textsuperscript{b}} to reveal the
relationship between ephemeral gully volume (\emph{V} ) and ephemeral
gully length (\emph{L} ), where the values of constant \emph{a} ranged
from 0.0082--2.94 and exponent \emph{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 \emph{a} (0.0842) and
exponent \emph{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
R\textsuperscript{2} and RMSE values of 0.97 and 0.85
m\textsuperscript{3}, respectively (Fig. 5(b)). There was no observable
systematic bias between the predicted and measured ephemeral gully
volumes using the \emph{V--L} relationship. Therefore, the
\emph{V--L}model can be used to assess ephemeral gully volume in the
hilly and gully region of the Loess Plateau.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image9/image9}

\end{center}
\end{figure}

Figure 6. Establishment and verification of the \emph{V--L} model. (a)
Power relationshi between ephemeral gully volume (\emph{V} ) and
ephemeral gully length (\emph{L} ). (b) Comparison of predicted
ephemeral gully volume with measured ephemeral gully volume.

\textbf{3.4 Estimation of ephemeral gully erosion volume and erosion
rate}

Ephemeral gully erosion volume was calculated based on the
\emph{V--L}model using the length of 1,153 ephemeral gullies interpreted
by remote sensing images in 2009, with the ephemeral gully erosion
volumes in 2009 and 2012 summarized in Table 4. In 2009, the total
erosion volume of 1,153 ephemeral gullies was 10,257.60
m\textsuperscript{3}, with an average erosion volume of each ephemeral
gully of 8.90 m\textsuperscript{3}. In 2021, the total erosion volume of
2,312 ephemeral gullies was 19,175.95 m\textsuperscript{3}, with an
average erosion volume of each ephemeral gully of 8.29
m\textsuperscript{3}. From 2009 to 2021, the ephemeral gully erosion
volume change was mainly in the south of the watershed (Fig. 7), where
the terrain is broken and has many steep slopes. In addition, the slope
area has damaged soil structure and less vegetation coverage after the
gully land consolidation project, so soil erosion can easily occur under
extreme rainfall. The average erosion volume of each ephemeral gully
increased by 3.54 m\textsuperscript{3} or 0.29
m\textsuperscript{3}y\textsuperscript{--1}, and the total erosion volume
of all ephemeral gullies (except for those that disappeared) increased
by 8,918.35 m\textsuperscript{3} or 743.20
m\textsuperscript{3}y\textsuperscript{--1} from 2009 to 2021.

Table 4 Ephemeral gully volume from 2009 to 2021 in the Zhoutungou
watershed.\selectlanguage{english}
\begin{longtable}[]{@{}lllllll@{}}
\toprule
\begin{minipage}[b]{0.14\columnwidth}\raggedright\strut
Year\strut
\end{minipage} & \begin{minipage}[b]{0.14\columnwidth}\raggedright\strut
Number\strut
\end{minipage} & \begin{minipage}[b]{0.14\columnwidth}\raggedright\strut
Minimum (m\textsuperscript{3})\strut
\end{minipage} & \begin{minipage}[b]{0.14\columnwidth}\raggedright\strut
Maximum (m\textsuperscript{3})\strut
\end{minipage} & \begin{minipage}[b]{0.14\columnwidth}\raggedright\strut
Mean (m\textsuperscript{3})\strut
\end{minipage} & \begin{minipage}[b]{0.14\columnwidth}\raggedright\strut
Total (m\textsuperscript{3})\strut
\end{minipage} & \begin{minipage}[b]{0.14\columnwidth}\raggedright\strut
Average annual development rate (m\textsuperscript{3}
y\textsuperscript{--1})\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
2009\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
1153\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.86\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
49.54\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
8.90\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
10257.60\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
743.20\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
2012\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
2045\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.57\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
54.80\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
8.50\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
17376.93\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
2018\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
2413\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.57\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
55.38\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
8.33\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
20110.76\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
2021\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
2312\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.01\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
53.16\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
8.29\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
19175.95\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image10/image10}

\end{center}
\end{figure}

Figure 7. Spatial distribution of ephemeral gully erosion volume in (a)
2009 and (b) 2021.

\textbf{4. Discussion}

\textbf{4.1 Ephemeral gully morphological parameters}

This study combined remote sensing imagery and the SegNet model to
analyze temporal and spatial changes of ephemeral gully morphological
features at a watershed scale. In 1999, Jiang \emph{et al.} (1999)
analyzed the distribution characteristics of ephemeral gullies using W-B
(White-Black) aerial photographs, identifying 4,495 ephemeral gullies in
the Zhoutungou watershed. We found that the ephemeral gully numbers in
the watershed decreased from 4,495 in 1999 to 1,153 in 2009 due to the
`Grain for Green Project' significantly improving vegetation coverage on
the Loess Plateau, reducing slope soil erosion and inhibiting the
formation and development of slope ephemeral gullies (Chen \emph{et al.}
, 2019; Dou \emph{et al.} , 2020; Liang \emph{et al.} , 2019). However,
ephemeral gully numbers changed after 2009 due to (1) the frequent
occurrence of extreme rainfall on the Loess Plateau increasing soil
erosion (Hu \emph{et al.} , 2019; Li \emph{et al.} , 2022; Wang\emph{et
al.} , 2020b; Zhao \emph{et al.} , 2021); (2) the gully land
consolidation project (implemented in 2011 to increase arable land by
excavating soil from the slopes on both sides of gullies, combined with
simultaneous comprehensive gully prevention and control measures);
despite reducing watershed erosion to a certain extent (Chen \emph{et
al.} , 2020; Han \emph{et al.} , 2018; Jin, 2014; Jin \emph{et al.} ,
2019; Kang \emph{et al.} , 2021), its associated engineering involving
topsoil stripping and ridge construction damaged the slope vegetation
(increased slope) and soil environment (loosened soil structure),
forming new ephemeral gullies on the slope.

This study found that ephemeral gully lengths ranged from 5 to 230 m
(average 48.39 m)---more than 82.35\% ranged from 15 to 70 m---with an
average growth rate of 1.66 m y\textsuperscript{--1} from 2009 to 2021.
However, other studies reported ephemeral gully lengths ranging from
7.71 to 237 m (average 56.50 m), with 60\% from 30 to 60 m (Cheng et
al., 2006; Cheng et al., 2007; Jiang \emph{et al.,} 1999). The hilly and
gully region of the Loess Plateau has a unique and large undulating
terrain, prone to developing long ephemeral gullies. Compared with
previous studies, our study revealed shorter ephemeral gully lengths,
which may be due to ephemeral gullies being: (1) buried or cut off by
road construction and the gully land consolidation project, or (2)
greatly eroded by headward gully erosion or vertical wall collapse under
the influence of extreme rainfall.

\textbf{4.2 \emph{V--L} relationship}

The \emph{V--L} relationship was best described by a power
equation\emph{V=aL\textsuperscript{b}} , with Eq. 8 revealing an
R\textsuperscript{2} value of 0.80, constant \emph{a} of 0.0842, and
exponent \emph{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; Mu\selectlanguage{ngerman}ñoz-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
(R\textsuperscript{2}) and smaller relative error (Er) than the
relationship between gully volume and gully length, indicating that
the\emph{V--Ag} prediction model performed better than the
\emph{V--L}relationship.

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 R\textsuperscript{2} and RMSE between the \emph{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.

\textbf{4.3 Ephemeral gully erosion rate}

The world is under serious threat of soil erosion. The ephemeral gully
erosion rate in Europe and America is 90--6,490 t
km\textsuperscript{--2} y\textsuperscript{--1} (Capra et al., 2009; Li
et al., 2016; Maetens et al., 2012; Panagos et al., 2015; Valcárcel et
al., 2003). On the Loess Plateau, the ephemeral gully erosion rate
without vegetation coverage is about 1,000--12,000 t
km\textsuperscript{--2} y\textsuperscript{--1}, and with vegetation
coverage is 215 t km\textsuperscript{--2} y\textsuperscript{--1} in the
Loess Plateau (Zhang et al., 2017; Zheng, 2006). This study estimated an
ephemeral gully erosion rate of 22.12
m\textsuperscript{3}km\textsuperscript{--2} y\textsuperscript{--1} or
28.75 t km\textsuperscript{--2} y\textsuperscript{--1} (average soil
bulk density is 1.3 g cm\textsuperscript{--3}) based on high-resolution
remote sensing images in the watershed from 2009 to 2021, considerably
lower than previous results but attributed to the improved vegetation
coverage in the watershed since the Chinese government implemented the
`Grain for Green Project' in 1999.

The increased vegetation coverage and biomass results in a dense
vegetation canopy that can intercept and redistribute rainwater and
reduce the kinetic energy of raindrops, and the grassland cover and
plant litter can reduce runoff erosion by avoiding the direct impact of
raindrops on soil, increasing soil infiltration capacity and runoff
resistance and decreasing runoff velocity (Hayas et al., 2017; Mukai,
2017; Sun et al., 2016; Vanmaercke et al., 2016). In addition, the
well-developed root systems have great physical and chemical binding
effects for combining soil particles and soil aggregates to improve soil
cohesion and the shear strength and tensile strength of the soil--root
matrix, significantly enhancing soil resistance to erosion (Allen et
al., 2018; Barthès and Roose, 2002; De Baets and Poesen, 2015; Guo et
al., 2019; Khan and Lateh, 2015; Wang et al., 2021c; Zegeye et al.,
2018; Zhao et al., 2013). In summary, vegetation restoration has
improved soil erosion conditions and enhanced regional water and soil
conservation benefits.

\textbf{5. Conclusion}

The SegNet model was used to recognize ephemeral gullies and extract
their morphological features at a watershed scale from 2009 to 2021 to
analyze temporal and spatial distribution characteristics of ephemeral
gullies in the hilly and gully region of the Loess Plateau. This study
showed that ephemeral gullies are mainly located in the southern part of
the watershed, where there are complex landforms and steep slopes. The
increase in ephemeral gully number, length, width, total area,
frequency, density, dissection degree, and erosion volume was 97
y\textsuperscript{--1}, 1.66 m y\textsuperscript{--1}, 0.04 m
y\textsuperscript{--1}, 4,213.39
m\textsuperscript{2}y\textsuperscript{--1}, 2.87
km\textsuperscript{2}y\textsuperscript{--1}, 0.12 km
km\textsuperscript{--2}y\textsuperscript{--1}, 0.0125\%
y\textsuperscript{--1}, and 22.12 m\textsuperscript{3}
km\textsuperscript{--2} y\textsuperscript{--1}, respectively. The
regression analysis revealed a power function relationship between
ephemeral gully erosion volume and length:\(V=0.0842L^{1.1932}\ (R^{2}=0.80,\ n=1,594)\). Indeed,
The regression analysis revealed ephemeral gully length can be measured
accurately and easily from high-resolution satellite images. This study
demonstrated that assessing ephemeral gully erosion volume and volume
rate is feasible using a regression model of ephemeral gully erosion
volume and length from historical high-resolution remote sensing images
in the hilly and gully region of the Loess Plateau in China.

\textbf{Acknowledgments}

This research was supported by the National Natural Science Foundation
of China (41977064), National Key R\&D Program of China
(2021YFD1900700), Fundamental Research Funds for the Central
Universities (2452021158; 2452021036), and 111 Project of the Ministry
of Education and the State Administration of Foreign Experts Affairs
(B12007). The authors express their gratitude to colleagues in their
research group for their help with the experiments.

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