HomeMy WebLinkAboutSDP201000054 Legacy Document 2010-08-09 (2)SLOPE GRADIENT EFFECTS ON SOIL LOSS FOR STEEP SLOPES
B. Y. Liu, M. A. Nearing, L. M. Risse
ABSTRACT. Data for assessing the effects of slope gradient on soil erosion for the case of steep slopes are limited. Widely
used relationships are based primarily on data that were collected on slopes up to approximately 25 %. These
relationships show a reasonable degree of uniformity in soil loss estimates on slopes within that range, but are quite
different when extrapolated beyond the range of the measured data. In this study, soil loss data from natural runoff plots
at three locations on the loess plateau in China were used to assess the effect of slope gradient on soil loss for slopes
ranging from 9 to 55% steepness. Plot size at each location was S m wide by 20 m long, and the soils were silt loams or
silty-clay loam. The results indicated that for these plots, soil loss was linearly related to the sine of the slope angle
according to the equation: S = 21.91 sing — 0.96, where 0 is the slope angle and S is the slope steepness factor
normalized to 9 %. This relationship was assessed in terms of the limited existing experimental data for rainfall erosion on
steep gradients and found to be reasonable for data collected on longer plots, but somewhat different than the data from
shorter plot studies. The results of this study would indicate a lesser soil loss at high slopes than does the relationship
used in the Universal Soil Loss Equation, but a greater soil loss than predicted by the Revised Universal Soil Loss
Equation for steep slopes. Keywords. USLE, RUSLE, soil, slopes.
he determination of slope steepness factors is an
integral part of most soil erosion prediction
models. Several scientists have investigated slope
steepness effects on soil loss. McCool et al.
(1987a) discussed data related to the effects of slope
gradient on erosion, as well as the equations that have been
developed and used to evaluate slope gradient effects on
soil loss. Table 1 is a summary of the principle equations
that have been developed to relate soil loss to slope
gradient. The reader is referred to McCool et al. (1987a) or
the primary references for more detail.
The equations in table 1 use one of two independent
variables; either percent of the slope or sine of the slope
angle. They also use one of three different functional
forms: linear, power, or polynomial. All of these equations
were developed using data collected on slopes up to
approximately 25 %; however, some of them were validated
using data collected on steeper slopes. For plots within this
slope range, all of these equations provide calculated slope
factors which are reasonably consistent in value, however,
when the slope is greater than this, the calculated slope
factors from these equations are significantly different
(fig. 1). Renard et al. (1991) reported that computed soil
loss for slopes less than 20 % by Universal Soil Loss
Equation (USLE) and Revised Universal Soil Loss
Equation (RUSLE) are similar. However on steep slopes,
computed soil loss is reduced almost by half with the
RUSLE equation (Renard et al., 1991). When slope
Article was submitted for publication in May 1994; reviewed and
approved for publication by the Soil and Water Div. of ASAE in August
1994.
The authors are Bao Y. Liu, Post - Doctoral Research Associate; Mark
A. Nearing, ASAE Member Engineer, Research Engineer, and L. Mark
Risse, Research Engineer, National Soil Erosion Research Laboratory,
USDA -ARS, West Lafayette, Ind.
steepness is 50 %, the USLE S factor (Wischmeier and
Smith, 1978) is 15.2, while the RUSLE S factor (Renard
et al., 1993) is only 7.0. RUSLE uses the equations
developed and recommended by McCool et al. (1987a).
Some studies have been conducted on steep slopes.
McCool et al. (1987b, 1993) presented the equation:
S — (sin9/0.0869)0•6 (1)
that is based on measured field rill erosion data collected
from more than 2,100 slope segments ranging in slope
from 1.5 to 56 %. These data were collected for conditions
in the Palouse region of the United States where soil loss
was primarily caused by surface flow over thawing soils.
This equation predicts low slope steepness factors
compared to results from equations derived from rainfall
induced erosion experiments. It is used in RUSLE to
predict erosion on thawing soils for slopes greater than or
equal to 9 %.
Another two studies on steep and relatively long slopes
(? 4.6 m) were conducted under rainfall simulated on
highway slopes and in the laboratory. Fan (1987)
conducted experiments on highway slopes at 9.4, 16.1,
33.3, and 50.3% slopes on a silty-clay loam soil, and the
calculated slope factors were 1.03, 1.40, 1.22, and 0.88,
respectively. The highest S factor was at 16.1% slope. Fan
(1987) recommended that an equation similar to equation 1
be used for slopes less than 14 degrees, and that a constant
value of 2 be used for slopes greater than 14 degrees for
highway slopes with compacted and cohesive soils. Kilinc
and Richardson (1973) conducted a series of experiments
on a sandy soil at six slope steepnesses ranging from 5.7 to
40 %. The data were collected using a 1.5 -m -wide x 4.6 -m-
long flume under simulated rainfall intensities of 32, 57,
92, and 117 mm /h. The authors did not attempt to provide
an equation for estimating the slope factor, but the data
Transactions of the ASAE
VoL. 37(6):1835 -1840 1994 American Society of Agricultural Engineers 1835
Table 1. Summary of commonly used equations which relate slope gradient to soil loss"
Author Slope Factor Data Source
Zingg (1940)
(s /9)1.4
Simulated Rainfall- to 20%
Smith and Whitt (1947)
0.025 + 0.052 5413
Simulated Rainfall- to 16%
Musgrave (1947)
(s/9)1.35
Composite of Existing Data
Smith and Wischmeier (1957)
0.0065s2 + 0.0453s + 0.065
Natural Runoff Plots 3 -18%
Wischmeier and Smith
65.4sin2A + 4.56sin0 + 0.0654
Natural Runoff Plots 3 -18%
(1978, USLE)
McCool et al. (1987a, RUSLE)
10.8sin6 + 0.03 s < 9%
Simulated Rainfall 0.1 -3%
McCool et al. (1987a, RUSLE)
16.8sin0 - 0.5 s >_ 9%
Natural Runoff Plots 8 -18%
* The slope factor is the soil loss normalized to a 9% slope gradient, s is the percent slope, and 9 is the slope angle.
may be useful for evaluating equations for soil loss on
steep slopes.
For short slopes (< 4.6 m), Singer and Blackard (1982)
reported results of an experiment on interrill erosion using
loam and silty clay loam soils with slopes up to 50 %. They
derived polynomial functions using the sine of the slope
angle to relate soil loss to slope steepness for two soils. The
results of that study showed that the coefficients of the
best -fit equations were different for the two soils, which
indicated that soil type influences the relationship between
soil loss and slope gradient. The loam soil had a greater S
factor than silty-clay loam soil.
Two micro -scale experiments have also been reported.
Foster and Martin (1969) reported results of an experiment
on 33, 50, and 100% slopes. The soil was a clay loam
compacted to four different bulk densities into a very
narrow flume which was 89 cm long. His data showed that
there is an unique slope at which maximum soil loss
occurred for a given bulk density. When slope steepness
was different than that unique slope, soil loss was less.
Gabriels et al. (1975) conducted an experiment on 8, 16,
24, 33, and 44% slopes using 30 -cm -long soil pans. Two
soil layers, the A horizon and the B horizon, of a silt loam
20
O
U 15
d
w
V)
w
z 10
a
w
w
V)
w
G. 5
0
a
- - - Zingg(1940)
.Smith & Whitt(1947)
•-- -- USLE(1978)
- -RUSLE -
Eq. [2] i
10 20 30 40 50 60
SLOPE (%)
Figure 1 -Slope steepness factor, normalized to 9 %, for several slope
steepness relationships from the scientific literature.
soil were used. The slope steepness factor for the two soil
horizons were quite different. These studies also indicate
that soil type influences the relationship between soil loss
and slope gradient.
Data from the loess plateau of north - central China
provides a unique opportunity to evaluate the relationship
between slope gradient and soil loss for steep slopes under
agricultural management. Much of the cultivated farmland
in this area of China lies on slopes ranging from 20 to 40 %,
with some up to 50 %. Because of the homogeneity of the
deep loessial parent material, the soil materials are
relatively uniform in character for different slope gradients
in a particular location under similar management
practices. The primary objective of this study was to
quantify the relationship between soil loss and slope
gradient on steep slopes. This was accomplished using
natural rainfall data from three locations in the loess
plateau of China and existing data from the literature. The
resulting relationships were then compared to the
relationships which others have proposed.
MATERIALS AND METHODS
Natural rainfall soil loss data from three locations on the
loess plateau of China were used: Tianshui, Ansai, and
Suide experiment stations. Soil texture in the loess plateau
region changes from south to north (Liu, 1966). The
plateau is divided into three zones; clayey loess, loess, and
sandy loess. Each of the erosion stations used in this study
was located in one of the three zones. The region is semi-
arid with annual rainfall ranging from 400 to 600 mm (Li
et al., 1985). Greater than 60% of the precipitation occurs
from June through September. Average annual rainfall was
about 600, 541, and 485 mm for the Tianshui, Ansai, and
Suide locations, respectively. Most of the soil loss were
caused by the storms with maximum intensities ranging
from 18 to 150 mm /h. At the Ansai site, for instance, more
than 90% of the soil loss occurred in July and August. On
the average only eight erosion events occur in a year. The
largest event was 137.6 mm rainfall on 4 August 1988 and
produced 192.6 t /ha of soil loss. This accounted for 80% of
the total soil loss in that year. Two of the soils were silt
loams, and the soil at Tianshui was a silty-clay loam soil
(table 2). Rill erosion on all of these three locations was
obvious. Some scientists estimate that half or more of the
soil loss from these plots is caused by rill erosion. All of
the data were collected under natural rainfall conditions
from plots which were 5 m wide and 20 m long measured
horizontally. Runoff was collected using natural runoff
1836 TRANSACTIONS OF THE ASAE
Table 2. Soil properties of the three sites
Cation
Exchange Organic Field Wilting
Sand Silt Clay Capacity Matter Capacity Point
Location ( %) ( %) ( %) (meq /100g) (%) (mm/mm) (mm/mm)
Snide 32.1 56.2 11.8 9.23 0.47 15.8 3.7
Ansai 19.0 65.2 15.8 11.63 0.63 21.7 4.5
Tianshui 9.0 62.0 29.0 19.55 0.99 23.3 10.7
plots. Soil loss was measured by sampling the sediment
concentration of the runoff which was collected in non-
permeable reservoirs.
The data set used in this study were selected from a
larger database using cropping and tillage factors as
selection criteria. Two sites were cropped plots and one
was fallow. Cropping on these plots was very sparse due to
the slope steepness and the low amounts of available
moisture. Plots were usually tilled by hand before planting
for cropped plots or tilled in spring for fallow plots and
then cultivated by hoe several times during the growing
season. The data from Tianshui consisted of nine years of
observations collected from 1945 through 1953. These
plots were cropped in a three -year four -crop rotation of
winter wheat, buckwheat, corn, and beans, on slopes of 9,
25, 31, and 44 %. Data from Ansai site (Jiang et al., 199 1)
was for five years of fallow conditions on slopes of 9, 18,
27, 36, 47, and 53 %. Four years of data were used from the
Suide site. It was cropped in a four -year rotation of
sorghum, bean, millet, and potatoes on slopes of 15, 26,
and 55 %.
Since the amount of soil loss was different from site to
site, it was normalized so that the data could be pooled
and comparisons between the sites could be made. This
also made it possible to fit a single equation to the soil loss
data from each location. A slope of 25% was selected for
the normalization because each location had plots with
slopes very nearly equal to 25 %, and because this value
was in the mid -range of the measured data. Linear
regression was performed between soil loss and slope
percent for the data at each of the sites for the three slopes
nearest to 25 %. Note that for the Tianshui site, three slope
level were triplicated, thus data from nine plots at that site
were used in the normalization to 25 %. This line fit the
data very well as indicated by the correlation coefficients
of 0.97, 0.99, and 0.94 for the Suide, Ansai, and Tianshui
sites, respectively. The regression was then used to
determine an estimated value of soil loss for a slope of
exactly 25% for each of the three sites. The 25% values
were 17.25, 68.93, and 25.37 t /ha for the Suide, Ansia,
and Tianshui sites, respectively.
Regression analysis was then used to evaluate the fit of
the measured erosion data, normalized to 25 %, using both
sine of slope angle and percent slope as the independent
variable. The best fit equation was selected, and then the
equation was mathematically transformed so that the S
factor calculated was normalized to the usual 9% value
used in the USLE and RUSLE to describe slope gradient
effects on soil loss.
RESULTS AND DISCUSSION
Average annual soil loss measured from each of the
plots are presented in table 3. When the normalized values
of soil loss were plotted for all of the locations, it was
apparent that a single equation could be used to fit all of
the data (fig. 2). There is some question in the scientific
literature as to whether percent slope or the sine of the
slope angle is more appropriate for characterizing slope
gradient effects on soil loss (Mclsaac et al., 1987; McCool
et al., 1987a). McCool et al. (1987a) presented conceptual
reasoning for why the sine of the slope angle is preferable
to use in place of slope percent. The sine term is consistent
with the relationship for calculating average flow shear
stress of runoff water, and thus it was suggested that the
sine of the slope angle should be more physically
representative of erosion processes on slopes. Mclsaac
et al. (1987), however, analyzed several data sets and found
that percent slope as an independent variable tended to
have a better fit to the data, but that the differences were
not significant. Table 4 shows a comparison of regressions
between the soil loss data from this study and both the
percent slope and the sine of the slope angle. For two of the
three locations the sine of the slope angle produced greater
coefficients of determination than did use of the slope
percent term. Because of the better fit at two of the three
sites, the sine of the slope angle was used to describe the
slope gradient relationship.
The relationship between soil loss and slope angle
derived from this data is:
S = 21.91 sinO - 0.96 (2)
Table 3. Average annual soil loss in t/ha and normalized to 25% slope
VOL. 37(6):1835 -1840 1837
Slope
Annual
Annual Soil Loss
Plot
Runoff
(Normalized
Number
(degree)
( %)
(mm)
(t/ha)
to 25 %)
Suide Site
32
8.6
15.1
20.8
5.80
0.336
18
14.7
26.2
20.0
2193
1.271
11
28.7
54.7
17.8
42.71
2.476
Ansai Site
1
5
8.7
45.1
15.32
0.222
2
10
17.6
52.0
4421
0.641
3
15
26.8
52.8
77.52
1.124
4
20
36.4
55.3
103.26
1.497
5
25
46.6
55.2
139.87
2.027
6
28
53.2
55.5
140.70
2.039
Tianshui Site
15
5.4
9.4
9.3
8.01
0.316
16
5.1
8.9
16.8
7.80
0.307
17
4.7
8.3
13.4
13.51
0.533
7
14.2
25.3
10.7
24.45
0.964
8
14.1
25.2
14.0
25.28
0.996
9
13.9
24.8
125
23.95
0.944
12
17.4
31.3
12.3
30.87
1.217
13
17.7
31.8
15.7
36.25
1.429
14
17.5
31.4
9.9
30.23
1.192
18
23.7
43.9
16.1
65.19
2.570
VOL. 37(6):1835 -1840 1837
18
15
O
E�
W 12
N
W
d
9
O
Z
In 6
O
a
3
O
• Tianshui
■ Ansai
• Suide
—Eq. [2]
••••• USLE
--- RUSLE(long slopes)
0` '
0 10
20 30 40 50 60
SLOPE ( %)
Figure 2–Soil loss, normalized to 9% slope, from the natural rainfall
plot data used in this study.
where S is the average annual soil loss relative to a 9%
slope. An analysis of variance showed that the regression
coefficient in equation 2 was significantly (0 — 0.01)
greater than zero indicating a linear relationship. Since this
equation was derived from data using slope lengths of 20 m
under conditions similar to those under which USLE
parameters were developed, it can be considered applicable
to hillslope scale erosion on steep slopes. The coefficient in
this equation is greater than the one used in RUSLE
(McCool et al., 1987a, equation, table 1), and thus gives
greater values for the slope factor. On the other hand,
equation 2 gives a lower slope factor at high slopes than
the one which was used in the USLE (fig. 1).
Equation 2 predicted lower S factor than were indicated
from Kilinc and Richardson's (1973) soil loss data from
three higher rainfall intensities, but higher than the soil loss
data from one low rainfall intensity (fig. 3). However, it
produced higher S factors than those suggested by the soil
loss data of Fan (1987). The Kilinc and Richardson study
was conducted using a noncohesive sandy soil while Fan's
study was conducted on a cohesive silty-clay loam soil on
which very little rill erosion occurred. It is interesting to
note that for the three higher rainfall intensities in Kilinc
and Richardson's study (1973), there was a greater increase
in soil loss with slope gradient than for the lowest intensity,
which appeared to approach a constant value. Fan's study
Table 4. Coeffcients of determination
of linear regressions in slope
steepnees -soil loss
relationships
Data Source % Slope sin (0)
Suide 0.97 0.98
Ansai 0.98 0.99
Tianshu 0.87 0.85
12
b\
10
O
E-
Q 8
W
N
..a
6
O
z
4
O
a
a 2
O
Rainfall intensity
(mm /h)
• 32 ■ 57 ■
• 93 • 117
Eq. [2]
Fan(1978) ■
u,
0 5 10 15 20 25 30
SLOPE (%)
35 40 45
Figure 3–Data from the study of Kilinc and Richardson (1973),
measured in the laboratory of 4.6 -m -long beds using a rainfall
simulator and normalized to a 9% slope. Equation 2 was derived
from the natural rainfall data presented in this study.
also appeared to approach a constant value. The fact that
some data indicates that the S factor approaches a constant
value may be related to transport processes for lower
rainfall intensities or areas dominated by interrill erosion.
If the transport capacity of flow is limited due to lower
rainfall intensities, a lack of rills, or a very cohesive soil
which limits sediment supply, then total soil loss would
approach a constant maximum value. Both the formation of
rills and the use of noncohesive soils would tend to
increase the S factors. While the data displayed
considerable variability, the slope factors produced by
equation 2 fell within the range of measured values for
these two studies.
On short slopes there is less opportunity for rill erosion
to occur and the slope steepness factor relationships of the
USLE, which are based on unit plot scale data, are not
reliable (Foster et al., 1981). Foster (1982) developed a
different relationship for short slopes which was based on
the study by Lattanzi et al. (1974). This. relationship was
subsequently used in RUSLE (Renard et al., 1993, McCool
et al., 1987a). As for the case of long slopes, the slope
steepness relationship for steep slopes may be different
than the ones derived with data from slopes under 20 %.
Singer and Blackard's (1982) data were useful for deriving
a relationship for steep slopes with short lengths. A power
function normalized to 9% of the form:
S — 12.14(sin0)0•97 — 0.81 (3a)
S — 4.87(sin0)0.69 + 0.08 (3b)
fit the Singer and Blackard data quite well (fig. 4) for the
loam and silty -clay loam soils, respectively. Comparison of
equations 3a and 3b with the corresponding equation used
in RUSLE shows that, as is true for the case of long slopes,
1838 TRANSACTIONS OF THE ASAE
10
0 8
E~
Q
w
N 6
a
x
0
z 4
to
0
a
.� 2
O
A
Singer & Blackard Data(1982)
• Loam
A Silty Clay Loam
—Eq. [2]
----- RUSLE(short slopes)
. .s•.
• . • ' E4 `gbh
•'
i
0 10
20 30 40 50
SLOPE (%)
Figure 4- Interrfl1 erosion data from the study of Singer and Blackard
(1982) compared to the results of this study for 20-m -long plots and
the RUSLE relationship for short slopes.
the RUSLE relationships may be underpredicting the
effects of slope gradient on erosion for steep slopes (fig. 4),
particularly relative to the loam soil data. Studies
conducted by both Gabriels et al. (1975) and Foster and
Martin (1969) have also indicated the importance of soil
properties in defining the relationship between slope
steepness and soil loss on short slopes. Foster and Martin
found that there was a unique slope from which maximum
erosion would occur for soils with varying bulk densities
while Gabriels et al. (1975) found that soils with different
aggregate sizes displayed different relationships between
soil loss and slope steepness. However, most of the data
from these studies also indicate that the RUSLE equation
may underestimate the S factor on short steep slopes.
Comparing the case of short slopes to long slopes, i.e., in
comparing the Singer and Blackard data to equation 2 as
shown in figure 4, we find that the slope gradient effect is
greater for the long slopes (i.e., for equation 2). This is
consistent with what we would expect in terms of the
relative amounts of rill versus interrill erosion which
occurs on the short and long slopes.
CONCLUSIONS
• This study reports some of the few existing soil loss
data from natural runoff plots at slopes up to 50 %.
The data from 20 -m -long natural runoff plots from
three sites on the loess plateau of China showed that
for slopes between 9 and approximately 50 %, soil
loss was linearly related to the sine of the slope angle
according to the relationship given in equation 2. The
form of equation 2 is similar to the one used in
RUSLE, but produces greater slope steepness factors
than does RUSLE, particularly at slopes greater than
25% where measured data are extremely rare.
The data in the scientific literature for assessing the
effect of slope gradient at slopes greater than 25% is
limited, however, for the data which do exist for
longer slopes (4.6 m), equation 2 falls within the
range of the measured data. The existing data for
shorter slopes would indicate a lesser slope gradient
effect for short-steep slopes than for long -steep
slopes.
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1840 DtANSAMONS OF THE ASAE