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Soil & Tillage Research 94 (2007) 4–14
Morphology parameters of ephemeral gully in characteristics
hillslopes on the Loess Plateau of China
Hong Cheng a,b,*, Xueyong Zou a,b, Yongqiu Wu a,b, Chunlai Zhang a,b,Qiuhong Zheng a,b, Zhangyan Jiang a,b
a Key Laboratory of Environment Change and Natural Disaster, The Ministry of Education of China,
Beijing 100875, People’s Republic of Chinab China Center of Desert Research at Beijing Normal University, Beijing Normal University, No. 19, Xinjiekouwaida Street,
Haidian District, Beijing 100875, People’s Republic of China
Received 16 November 2005; received in revised form 14 May 2006; accepted 18 June 2006
Abstract
The Loess Plateau of North China has one of the highest erosion rates in the world. Ephemeral gullies are an important erosion
type found on hill slopes of upland areas, and soil loss due to these gullies equals 30–70% of total soil loss. In this study, we used a
high-accuracy global positioning system (GPS) to measure the morphology of characteristic ephemeral gullies near Suide, Shaanxi
Province. We discuss the geomorphological characteristics of the gullies (their length, the distance between the head of ephemeral
gully and the watershed divide, the distance between two neighboring hill slope ephemeral gullies, the critical slope gradient, the
upslope drainage area, and the flow erosivity). The length and average distance between gullies both followed a Pearson IV
distribution function, but the function parameters differed. The product of upslope drainage area and the square of the critical slope
gradient ranged from 4.74 to 892.66 m2 and can be used to determine locations where gullies are likely to begin in a digital elevation
model with a 2 m � 2 m grid. The relationship between the upslope drainage area (A) and the critical slope gradient (S) could be
expressed as S = 0.058A�0.3. For the first time, this paper determined the relationship between gully length (L) and flow erosivity
(E): L = 0.0305E + 18.185 (R2 = 0.71). These results improve our understanding of the erosion process in ephemeral gullies.
# 2006 Elsevier B.V. All rights reserved.
Keywords: Soil erosion; Morphology parameters; GPS; The Loess Plateau; Ephemeral gully
1. Introduction
Ephemeral gullies develop a weakly incised channel
with accelerated formation of lateral rills (Foster, 1986)
and form in cultivated landscapes as a result of the
concentration of runoff in small valleys. The gullies are
considered ephemeral because they are filled in by
normal tillage practices but frequently recur in the same
* Corresponding author. Tel.: +86 10 62207162;
fax: +86 10 62207162.
E-mail address: [email protected] (H. Cheng).
0167-1987/$ – see front matter # 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.still.2006.06.007
place during the next rainy season (Poesen and Govers,
1990). Ephemeral gully erosion requires a flow energy
that is determined by the flow velocity and quantity of
runoff, which are in turn determined by the slope
gradient and the upslope drainage area. The location
and size of channels is controlled by the generation of
concentrated surface runoff of sufficient magnitude and
duration to initiate and sustain erosion (Vandaele et al.,
1996a). However, in most studies of this phenomenon,
the upslope drainage area has been used as a surrogate
for the volume of runoff because in most cases, no
runoff discharge data are available; moreover, in
landscapes where Hortonian overland flow dominates,
H. Cheng et al. / Soil & Tillage Research 94 (2007) 4–14 5
runoff volume increases proportional to the catchment
area (Leopold et al., 1964). Therefore, the upslope
drainage area and the slope gradient are widely used
parameters in models that determine the location where
channel erosion will develop (Patton and Schumm,
1975; Begin and Schumn, 1979; Nachtergaele et al.,
2001a; Poesen et al., 2003; De Santisteban et al., 2005;
Cheng et al., in press). The following relationship exists
between upslope drainage areas and slope gradient:
SAb > t (1)
where S is the critical slope gradient (m m�1), A the
upslope drainage area (m2 or ha), b (dimensionless) a
parameter corresponding to the relative area, and t is a
threshold value. However, there is considerable varia-
tion in the values of b at threshold t reported in the
literature (Vandaele et al., 1996a).
Predicting or calculating soil losses due to erosion
by ephemeral gullies are important in quantifying the
impact of this form of erosion (Gabriels et al., 1977;
Waston et al., 1986; De Roo, 1998; Woodward, 1999).
Based on field observations of ephemeral gullies on the
Loess Plateau of China, Zhang and Tang (1992)
developed an annual erosion model. The ephemeral
gully erosion model (EGEM; USDA-SCS, 1992) is a
better model in predicting soil losses due to ephemeral
gullies erosion. However, tests of the model in the
Mediterranean showed that it was not capable of
predicting ephemeral gully erosion (Nachtergaele
et al., 2001b) and Zhang and Tang’s model did not
consider rainfall, land use, vegetation cover, and other
factors. At the same time, EGEM is not available on the
Loess Plateau of China. Therefore, it was necessary to
develop a basic model of soil erosion that includes
ephemeral gully erosion and the characteristics of
intensive soil erosion due to ephemeral gullies and
steep slopes in the Loess Plateau of China (Jiang and
Zheng, 2004).
The effect of erosion by ephemeral gullies on hill
slopes has been studied, and an index of the potential
damage has been developed (Chen, 1976; USDA-
NRCS, 1977; Zhang, 1991; Robinson et al., 1998;
Zheng and Gao, 2000). Chen (1976) reported that the
time to produce runoff would increase if the hill slope
has at least one ephemeral gully and that the quantity of
erosion would increase by a factor of 0.8. At the same
time, simulation experiments showed that the quantity
of erosion would increase by 25% due the occurrence of
ephemeral gullies on the Loess Plateau (Zhang, 1991).
The proportion of total erosion accounted for by
ephemeral gullies differed among studies (Spomer and
Hjelmfelt, 1986; Vandaele et al., 1996b; Zheng and
Zhang, 1993); for example, the proportion ranged
between 17 and 83% in southern Portugal (Vandaele
et al., 1996b), and the largest value reported for the
Loess Plateau of China was 70% (Tang et al., 1998).
The Loess Plateau in North China is an area with one
of the highest erosion rates in the world. Ephemeral
gully erosion is a common phenomenon, and the annual
quantity of this form of erosion ranges between 4400
and 7600 t km�2 (Zheng and Zhang, 1993; Zheng and
Gao, 2000). In studies of the morphological parameters
of ephemeral gullies, Chen (1976) and Chen et al.
(1988) discussed the critical slope length for the
development of an ephemeral gully, and based on the
extraction of features from aerial photographs, Jiang
et al. (1999) and Zhang (1991) analyzed the develop-
mental parameters for these gullies and reported the
existence of relationships between the critical slope
length, the average distance between ephemeral
gullies, the critical drainage area, and the slope, and
used these parameters to classify erosion intensity.
These relationships were simplistic because they did
not model the physical processes involved in the
development of ephemeral gullies. However, based on
the importance of ephemeral gully erosion, it is
necessary to strengthen models of the underlying
mechanisms.
The present study mainly concentrated on ephem-
eral gully erosion on cultivated hill slopes in a small
catchment and this paper discusses their morphologi-
cal parameters based on measurements with high-
accuracy global positioning system (GPS) receivers,
which have been used successfully in previous
research on soil erosion (Wu and Cheng, 2005). Our
research hypotheses were that the use of GPS
technology would provide more precise and accurate
measurements of the geomorphological parameters
than traditional classification of aerial photographs,
and that the resulting improved data accuracy would
permit the development of useful equations for
predicting the occurrence and severity of gully erosion
based on field measurements. The resulting equations
could provide importance guidance on areas where
mitigation is required to land managers responsible for
preventing erosion.
2. Methods
2.1. The study area
The study area, Qiaogou, is a small catchment
(0.4503 km2) near the City of Suide, in Shaanxi
H. Cheng et al. / Soil & Tillage Research 94 (2007) 4–146
Fig. 2. Measuring the topography of the study area by means of
differential GPS. Receiver 1 is the base station; receiver 2 is the mobile
unit.
Fig. 1. Location of the study area.
Province. It is located on the Loess Plateau of North
China at 378290N, 1108170E (Fig. 1) (Wu and Cheng,
2005). The elevation of the study area ranges from 810
to 960 m. The average temperature in this region is
about 9 8C and annual precipitation ranges from 300 to
500 mm. The rainy season is from June to September.
The Qiaogou catchment was cultivated from 1950 to
2000 and some areas were retired from cultivation in
2001 as a result of a government policy to return
cropland on hill slopes in northwest China to grassland
or woodland to control erosion; as a result, not all of the
area was cultivated in 2002. The main crop was wheat.
The soil is characterstic loess on the Loess Plateau of
North China and there is nearly any management which
leads to the low land product. In this study, we focused
on ephemeral gully erosion in a characteristic hill slope.
The source area is 0.06203 km2 and a small terraced
slope (0.055 km2). Cultivated hill slopes alternating
H. Cheng et al. / Soil & Tillage Research 94 (2007) 4–14 7
Fig. 3. Distribution of measured points in source area of the Qiaogou.
with ephemeral gullies are the main geomorphological
characteristics of the source area.
2.2. Field measurements
We performed a topographic survey of the study area
using a Trimble 4700 RTK GPS, with real-time
differential correction that provided planimetric and
altimetric precision of 1 cm � 2 ppm and 2 cm �2 ppm, respectively. Receiver no. 1 in Fig. 2 is the
base station that served as the benchmark for all
measurements, and receiver no. 2 is a rover that was
used to measure the topography. Measurements were
taken using an approximately 5-m grid. For some areas,
such as the heads and edges of ephemeral gullies, the
gullies themselves, and the edges of terraces, more
intensive measurements were taken. In some cases, the
distance between points was only 0.2 m or less. During
the course of our measurements, we recorded both the
geographical coordinates and the attributes of each
position (including the type of land use and type of
point, such as ‘‘point on the floor of an ephemeral
gully’’). The measurements were taken in May 2002. In
total, we obtained 5187 points in the 0.06203 km2
source area (Fig. 3).
2.3. Data processing
We transformed the collected data using the Trimble
Geomatics software into a format that could be processed
by geographical information system software. We used
the software to calculate the following geomorphological
parameters of the ephemeral gullies: gully length, the
distance between the head of each gully and the
watershed divide, and the average distance between
adjacent gullies. We then created a digital elevation
model (DEM) by interpolation of the measured data
(Fig. 4). The pixel size in the DEM was 2 m � 2 m. With
H. Cheng et al. / Soil & Tillage Research 94 (2007) 4–148
Fig. 4. Digital elevation model of source area.
the help of the grid module of Arcinfo 8.0 (ESRI,
Redlands, CA), we calculated the slope gradient and the
upslope drainage area for each pixel.
3. Results and discussion
3.1. Characteristics and distribution laws of
ephemeral gullies
We identified a total of 49 ephemeral gullies in the
source area. Table 1 presents their geomorphological
parameters: length, critical slope gradient and upslope
drainage area at the head of the gully, distance between
the head of the gully and the watershed, and the
distance between adjacent gullies. Most of the
ephemeral gullies in the source area were roughly
parallel to each other, but some merged at an acute
angle to form a tree-like branched shape. In addition,
many individual parent gullies divided into two or
more ‘‘child’’ gullies (e.g., nos. 6 and 35; nos. 8, 34,
and 36; nos. 9, 33, and 37; nos. 10, 31, and 39; nos. 32
and 38; nos. 13, 28, and 42; nos. 14, 27, and 42; nos. 15,
26, and 43; nos. 16, 25, and 44; nos. 17, 25, and 44; nos.
19 and 47; nos. 22 and 48; nos. 20 and 49; nos. 21 and
49) and this was the main type of ephemeral gully in
the source area.
The total length of the 49 ephemeral gullies equaled
1196.82 m, and the length density was 192.94 m ha�1
(19.294 km km�2). According to the standard for
classification and gradation of soil erosion released
by China’s Ministry of Water Resources, acute erosion
begins at a length density of 7 km km�2, thus our study
area was considered subject to acute erosion. The
length of an ephemeral gully is a good estimator of its
erosion volume (Nachtergaele et al., 2001b; Cheng
et al., 2006). This suggests that the lengths of
ephemeral gullies can be used to assess their
significance, especially for large-scale surveys of
erosion, because it is easier to measure the length of
an ephemeral gully by means of remote sensing or
H. Cheng et al. / Soil & Tillage Research 94 (2007) 4–14 9
Table 1
The geomorphological parameters of the ephemeral gullies in our study area
Gully no. L (m) D1 D2 A (m2) S (m m�1) AS2 (m2)
1 25.88 122.38 – 164 0.2 6.56
2 14.2 99.49 2.49 108 0.25 6.75
3 17.2 90.4 9.36 313 0.29 26.32
4 71.58 89.12 10.36 1418 0.19 51.19
5 17.59 91.93 17.3 116 0.25 7.25
6 35.74 80.38 9.11 1078 0.21 47.54
7 32.08 74.62 11.8 1180 0.22 57.11
8 33.74 70.51 22.88 1140 0.25 71.25
9 33.73 67.81 16.74 1272 0.26 85.99
10 23.51 67.42 28.97 1317 0.41 221.39
11 19.07 77.46 8.16 850 0.32 87.04
12 12.02 51.34 – 160 0.23 8.46
13 14.77 56.4 5.75 517 0.28 40.53
14 17.69 61.79 14.77 186 0.31 17.87
15 19.08 63.35 18.21 135 0.49 32.41
16 22.15 63.5 21.21 146 0.34 16.88
17 24.13 48.84 12.98 142 0.23 7.51
18 26.42 37.44 20.83 175 0.53 49.16
19 26.72 47.95 – 256 0.35 31.36
20 21.2 62.24 – 226 0.53 63.48
21 24.21 79.44 12.72 816 0.44 157.98
22 29.92 92.88 25.21 1370 0.28 107.41
23 48.75 55.27 51.95 938 0.54 273.52
24 34.03 81.57 28.24 1112 0.37 152.23
25 19.11 83.62 19.18 864 0.5 216.00
26 27.22 83.78 29.18 902 0.41 151.63
27 40.27 81.9 17.48 823 0.46 174.15
28 46.68 74.84 13.29 1312 0.31 126.08
29 32.9 91.11 17.24 917 0.22 44.38
30 26.48 64.15 – 1686 0.35 206.54
31 20.01 94.35 23.36 1720 0.47 379.95
32 17.68 114.46 15.87 65 0.27 4.74
33 22.09 105.9 12.03 2724 0.36 353.03
34 15.79 111.06 18.95 1839 0.25 114.94
35 19.01 126.11 32.02 4041 0.47 892.66
36 22.13 126.36 – 2210 0.26 149.40
37 28.26 128.42 13.06 2178 0.42 384.20
38 17.79 133.04 13.65 208 0.48 47.92
39 27.31 131.67 15.12 3184 0.28 249.63
40 25.94 127.33 20.03 103 0.23 5.45
41 12.42 149.48 29.5 183 0.41 30.76
42 12.4 153.3 6.7 4759 0.42 839.49
43 16.9 151.09 22.22 3140 0.36 406.94
44 16.97 141.01 17.63 3091 0.28 242.33
45 16.18 125.2 10.93 2447 0.39 372.19
46 21.02 120.54 52.66 478 0.47 105.59
47 12.55 131.97 26.9 1912 0.43 353.53
48 12.2 130.24 10.14 2806 0.45 568.22
49 22.1 114.97 10.55 1290 0.39 196.21
Total 1196.82 4629.43
Average 24.42 94.48 18.53 1224.84 0.35 168.23
Minimum 12.02 37.44 2.49 65 0.19 4.74
Maximum 71.58 153.3 52.66 4759 0.54 892.66
L: length; S: critical slope gradient; A: upslope drainage area at the head of the gully; D1: distance between the head of the gully and the watershed;
D2: the distance between adjacent gullies.
H. Cheng et al. / Soil & Tillage Research 94 (2007) 4–1410
Fig. 6. The distribution curve for the Pearson IV function describing
the mean distance between adjacent ephemeral gullies on hill slopes.
direct measurement than it is to measure the erosion
volume. In addition, the accuracy of the length
measurement is higher. Based on the data in Table 1,
we used TableCurve to analyze the distribution of the
gullies in 5-m length categories and regarded the
central value of each category as the fitted point in
regression analysis. This distribution follows a Pearson
IV function that can be expressed as follows:
y ¼ aþ bð1þ n2Þ�eexp½� f ða tanðnÞ
þ a tanð f=ð2eÞÞÞ�=½1þ f 2=ð4e2Þ��e(2)
where x is the observed ephemeral gully length (m),
n = (x � df/(2e) � c)/d, and the regression coefficients
were a = 1.36, b = 24.39, c = 9.05, d = 4.35, e = 9.89,
f = �136.68, and R2 = 0.95. The high correlation coef-
ficient indicates good agreement between the observed
and predicted gully lengths. The results of this regres-
sion are shown in Fig. 5. Short ephemeral gullies may
have only formed recently, whereas long gullies have
mostly been formed by rapid retreat of the head of the
ephemeral gully over a longer period. Fig. 5 also shows
that the length of the ephemeral gullies in our study area
mostly ranged from 10 to 30 m, with a mean length of
around 24.4 m.
The mean distance between adjacent gullies reflects
the basic distribution of runoff perpendicular to the
slope, and is thus an important characteristic of the
distribution of ephemeral gullies. In our study area, this
distance averaged 18.53 m, with a maximum of
52.66 m, a minimum of 2.49 m, and a range of 10–
30 m for approximately 80% of the gullies. The average
distance between adjacent gullies also followed a
Pearson IV function (Eq. (2)), but with a = �16.82,
Fig. 5. The distribution curve for the Pearson IV function describing
the length of ephemeral gullies on hill slopes.
b = 45.49, c = 13.61, d = 4.34, e = 0.31, f = �0.25, and
R2 = 0.94. The high correlation coefficient indicates
good agreement between the observed and predicted
distances. The regression results are shown in Fig. 6.
Small distances most likely indicate that a new
ephemeral gully formed recently, whereas the longest
distances were mostly located in a southwestern part of
the study area where there is only a small upslope
drainage area and therefore only a small supply of
runoff to create new gullies. Fig. 6 also shows that the
distance between adjacent gullies mostly ranged from
10 to 20 m; in contrast, Zhang et al. (1991) used aerial
photographs to analyze the parameters of ephemeral
gullies and reported a range of 15–20 m for 53.5% of
their gullies. Only 23% of the gullies in the present
study were spaced at a distance of between 15 and 20 m
(Table 2). The reason for this difference may be that
feature extraction using aerial photographs would miss
some of the smaller ephemeral gullies. On the other
hand, the proportion of larger distances between two
neighboring ephemeral gullies in our study was larger
than that in Zhang et al.’s (1991) study because they
mainly discussed ephemeral gullies within the same
distance class, whereas the gullies in our study were
distributed in different classes. In addition, field surveys
Table 2
The frequency distribution for the mean distance between adjacent
ephemeral gullies
Proportion (%) Distance (m)
<10 10–15 15–20 20–25 25–30 >30
Zhang et al. (1991) 3.5 32 53.5 7.5 3.0 0.5
This paper 14 28 23 14 14 7
H. Cheng et al. / Soil & Tillage Research 94 (2007) 4–14 11
are more precise (Vandaele et al., 1996a). Therefore, the
results of our study are more likely to reflect the natural
processes that govern the development of ephemeral
gullies. However, aerial photographs would be more
useful than field surveys to cover longer temporal and
spatial scales, and would thus provide a more
macroscopic understanding of soil erosion.
For a typical slope, the distance between the head of
the ephemeral gully and the watershed is a characteristic
value to represent the distribution law of ephemeral
gullies along the slope direction. The maximum was
153.3 m, while the minimum is 37.74 m. The average
distance of ephemeral gullies is 94.48 m. The average
distance of ephemeral gullies is relative large due to the
effect of the small terrace, in our study area it cannot be
used to reflect the distribution law. However, most of
them the average distance of ephemeral gullies are 60–
120 m. Therefore, at a certain extent, the distance
between the head of the ephemeral gully and the
watershed can reflect the distribution law of the head of
ephemeral gullies along the typical slope surface on the
Loess Plateau of China. Of course, for other regions,
because of some influences, such as topography,
vegetation, flow hydraulics, soil and land use, the
distance would be great difference.
The results of our study also permit a qualitative
discussion of the results at a micro level. For example,
soil loss is obvious if you compare point 1 in Fig. 7 with
points 2 and 3, and the mean height different in the
ephemeral gully is almost 2 m (1.93 m between points 1
and 2 versus 2.12 m between points 1 and 3). Because
the original slope (the slope at points 2 and 3) should be
relatively smooth, it is obvious that the soil loss due to
ephemeral gullies is serious. In future research, we plan
Fig. 7. A sketch map of intense soil loss due to ephemeral gullies.
to study the process in detail by developing a
mathematical model of the process. Ephemeral gullies
are distributed widely throughout the hilly cropland of
the Loess Plateau. Successive cultivation and irrational
land use leads to the occurrence and development of
ephemeral gullies and thus, to erosion. However, small
changes in topography (e.g., between starting terrace
and unknotting land), land cover (e.g., woodland versus
grassland), planting style (down the slope versus across
the slope), and other factors all influence the occurrence
and development of ephemeral gullies (Liu and Wu,
1993). These changes in topography could reduce soil
loss, but may not change the path of existing gullies. For
example, point 1 in Fig. 7 represents part of an
ephemeral gully whose upper end vanished in the 1960s
when the terraces were built, but some obvious marks of
that upper part of the ephemeral gully remain after
nearly 50 years (point 4 in Fig. 7). The edge that
represents a change in topography (point 5 in Fig. 7) is
also an area of intense soil loss. There are several hole-
ephemeral gullies (Cheng et al., in press) along the edge
that represents a change in topography along the slope.
In recent years, the policy of returning cropland on hill
slopes in northwest China to grassland or woodland
would therefore help to reduce soil loss. We will
continue to monitor the development of the ephemeral
gullies in our study area and the effect of the methods.
3.2. S–A relationship
Table 1 presents the critical slope gradient (S), the
upslope drainage area (A), and their product (AS2). The
critical slope gradient ranged between 0.19 and
0.54 m m�1, with an average of 0.35 m m�1, and the
upslope drainage area ranged from 65 to 4759 m2, with
an average of 1224.84 m2. The wide range of upslope
drainage areas suggests that some new, small ephemeral
gullies formed from very small upslope drainage areas,
whereas other, older gullies may have formed over
longer periods of time from larger upslope drainage
areas. The slopes tend to be very gentle at the top of hill
slopes, and surface and rill erosion often occur at those
locations. However, the slope gradient tends to increase
further down the slope, and ephemeral gully erosion
begins at those locations. Therefore, there should be
some critical slope gradient at which surface and rill
erosion begin to transform into ephemeral gully erosion,
and recognizing this point will have great significance
for determining how to control soil erosion. Based on
the data in Table 1, the slope gradients where ephemeral
gully erosion began ranged from 10.758 to 28.378, with
a mean value of 19.098. These minimum and maximum
H. Cheng et al. / Soil & Tillage Research 94 (2007) 4–1412
Fig. 8. The relationship between slope gradient at the head of
ephemeral gullies (S) and the upslope drainage area (A).
Table 3
The frequency distribution for slope gradient of the occurrence of
ephemeral gully erosion
Slope gradient (8)
<18 18–22 22–25 25–28 28–31 >31
Zhang et al. (1991) 0 15 23 28 24 10
This paper 47 17 18 16 2 0
values are less than those that have been previously
reported (e.g., 188 and 358; Zhang et al., 1991) and the
frequency of occurrence at different slope gradients also
differed (Table 3). The frequency of slope gradient less
than 188 was 47% in our study, versus 0% in Zhang
et al.’s study. This may have resulted from the use of
feature extraction from aerial photographs in the
previous study, an approach that could not discern
relatively small ephemeral gullies or precisely locate
the head of ephemeral gullies on gentle slopes; in
contrast, the slope gradients in the present study were
calculated from a DEM with a 2 m � 2 m grid and the
head location was identified by means of GPS with high
accuracy. Based on the distribution of slopes in the
upland regions of the Loess Plateau of China, the
average slope gradient should exceed that reported by
Zhang et al. (1991), who mainly discussed ephemeral
gullies in the slope class where ephemeral gullies first
begin to occur, whereas ephemeral gullies in the present
paper are distributed in a range of classes. Therefore,
although the pixel size used in the DEM will affect the
accuracy of the slope calculations, our results should
still be more accurate than those of Zhang et al. (1991).
Once again, this does not mean that the latter study is
not valuable; on the contrary, interpretation of aerial
photographs remains essential for studies at long
temporal and large spatial scales.
Montgomery and Dietrich (1988, 1992) thought that
AS2 values between 500 and 4000 m2 are not affected by
other factors such as soil properties, climate, and soil
use because they obtained similar results for three
regions of the United States with different soil
properties, climate, soil, land use, and slope gradients:
Oregon, with annual rainfall of 1500 mm, sandstone-
derived soil, logged forest as the main land use, and
slopes of 9–100%; the southern Sierra Nevada, with
annual rainfall of 260 mm, soil derived from deeply
weathered granitic rocks, open oak woodland and
grasslands as the primary land use, and slopes of
9–100%; California, with annual rainfall of 760 mm,
greywacke-derived soil, coastal prairie land use, and
slopes of 9–100%. Therefore, they regarded AS2 as a
key index of the head position of erosion channels.
However, the AS2 values for the 49 ephemeral gullies in
the present paper ranged from 4.74 to 892.66 m2
(Table 1), with a mean value of 168.23 m2. Although
this is consistent with the values previously reported for
gullies in the Loess Plateau of China (41–814 m2; Wu
and Cheng, 2005), our values were clearly lower than
those reported by Montgomery and Dietrich (1992).
Our paper agrees with the results reported by Wu and
Cheng (2005), which suggests that AS2 does vary among
regions.
The erosion system (e.g., rill erosion, ephemeral
gully erosion, gully erosion, and large-channel erosion)
appears to have a strong effect on AS2. Montgomery and
Dietrich (1992) focused on large channels in their
catchment, whereas our study focused on ephemeral
gullies. Grid size is also a key factor. The pixel size in
our DEM was 2 m � 2 m (i.e., 4 m2), versus 20 m2 for
Montgomery and Dietrich. Grid size will affect the
accuracy of the slope calculations, and this may also
explain the different results. Despite these differences in
the reported AS2 values, AS2 is still a key indicator of the
location where the channel head should appear in a
DEM. Therefore, we suggest that our AS2 values (from
4.74 to 892.66 m2) should be used for characteristic hill
slopes in the Loess Plateau of China as an indicator for
determining the position of gully heads from DEM with
a 2 m � 2 m grid size. On the other hand, previous
results suggested that the relationship between the
critical slope gradient and the critical upslope drainage
area could be expressed as follows:
S ¼ aA�b (3)
where a and b are regression parameters. In this paper, we
have plotted this as a log–log relationship and have drawn
H. Cheng et al. / Soil & Tillage Research 94 (2007) 4–14 13
Fig. 9. Predicted vs. measured length of ephemeral gullies as a
function of the flow energy.
a straight line passing through the lowest values in our
data to define the boundary conditions (Fig. 8). The
critical relationship (S = 0.058A�0.3) derived from this
data is consistent with previous results, in which the value
of b was between 0.25 and 0.60, most values were
concentrated around 0.40, and a ranged from 0.0035 to
0.350 (Vandaele et al., 1996a). The critical relationship
can thus provide a simple model of channel initiation by
overland flow that has been tested successfully using field
data. Therefore, this relationship may also be a useful
indicator for determining the position of ephemeral gully
heads in small watersheds in the Loess Plateau of China.
3.3. L–E relationship
Thelengthofephemeralgullies isa requiredparameter
for EGEM and has turned out to be a key parameter in
determining the volume of ephemeral gullies (Nachter-
gaele et al., 2001b). As mentioned above, there is a strong
correlation between the length and erosion volume of
ephemeralgullies.This suggests thatgully lengthwillbea
significantanduseful indexoferosion,especially in large-
scale surveys of erosion, because it is easier to measure
gully length (by means of remote sensing or direct
measurement) than it is to obtain erosionvolumes, and the
accuracy of length measurement will also be higher. On
the other hand, gully length is determined by flow energy,
which in turn is determined by the combination of flow
velocity and flow quantity; flow velocity and quantity are
determined by the slope gradient and upslope drainage
area, respectively. The location and size of runoff
channels is essentially controlled by the generation of
concentrated surface runoff of sufficient magnitude and
duration to initiate and sustain erosion (Vandaele et al.,
1996a). However, in most studies of this relationship,
upslope drainage area was used as a surrogate for the
runoff volume because no runoff discharge data were
available. Therefore, flow energy can be expressed by the
relationship between slope gradient and upslope drainage
area. In the present paper, we defined flow energy (E) as
the difference between the AS2 values at the head and the
tail of ephemeral gullies, and analyzed the relationship
between the two parameters based on our data. No
research on this relationship appears to have been
previously published in the literature.
We fitted our length data against the calculated flow
energy and obtained the best fit for the following
equation:
L ¼ aE þ b (4)
where a = 0.0305, b = 18.185, and the correlation coef-
ficient was R2 = 0.71. Fig. 9 shows that the length of
ephemeral gullies predicted using this equation pro-
vides a good match with the actual length. This equation
represents only a first attempt to define the relationship
and requires additional research to improve its useful-
ness. Nonetheless, our results demonstrate that the
critical slope gradient and the upslope drainage areas
determine the location where ephemeral gullies will
occur, and that their length is a key parameter in
deciding their volume. Therefore, it should be possible
to express the volume of ephemeral gullies as a function
of the critical slope gradient and critical upslope drai-
nage area. In other words, the critical slope gradient and
critical upslope drainage area at the head of an ephem-
eral gully will determine the quantity of erosion.
4. Conclusion
We surveyed 49 ephemeral gullies on hill slopes in
the source area. The total length of these gullies equaled
1196.82 m, and the length density was 192.94 m ha�1.
The average distance between adjacent gullies was
18.53 m, with a maximum of 52.66 m and a minimum
of 2.49 m. The length and average distance between
gullies both followed a Pearson IV distribution function.
The value of AS2 ranged from 4.74 to 892.66 m2 and
should be used as an indicator for determining the
position of the gully head in the Loess Plateau of China
based on a DEM with a 2 m � 2 m grid size. The
relationship between the upslope drainage area and the
critical slope gradient was expressed as S = 0.058A�0.3,
and may provide another indicator for determining the
position of the gully head in small watersheds. For the
first time in the literature, we established a relationship
between gully length and flow energy (expressed as the
H. Cheng et al. / Soil & Tillage Research 94 (2007) 4–1414
difference between AS2 values at the head and tail of the
gully): L = 0.0305E + 18.185 (R2 = 0.71). In addition,
although changes in topography influence the occur-
rence and development of ephemeral gullies, once an
ephemeral gully became established, changes in
topography did not alter its location.
Acknowledgements
This study was supported by the National Nature
Science Foundation of China for Key Projects (Grant
no. 10532030), the Key Technologies Research and
Development Program of the Tenth Five-year Plan of
China (Grant No. 2005BA517A06), and the National
Nature Science Foundation of China (Grant Nos.
40301025 and 40071080).
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