HYDROLOGICAL PROCESSES
Hydrol. Process. 20, 579– 589 (2006)
Published online 18 October 2005 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/hyp.5925
A modification to the Soil Conservation Service curve
number method for steep slopes in the Loess Plateau
of China
Mingbin Huang,1 Jacques Gallichand,2 * Zhanli Wang1 and Monique Goulet2
1
The State Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau, Institute of Soil and Water Conservation, CAS &
MWR; Northwest Sci-Tech University of Agriculture and Forestry, Yangling, Shaanxi Province 712100, People’s Republic of China
2 Département des Sols et de Génie Agroalimentaire, FSAA, Université Laval, Québec (Qc) G1K 7P4, Canada
Abstract:
The Soil Conservation Service curve number (CN) method is widely used for predicting direct runoff from rainfall.
However, despite the extent of cultivation on hillslope areas, very few attempts have been made to incorporate a slope
factor into the CN method. The objectives of this study were (1) to evaluate existing approaches integrating slope in
the CN method, and (2) to develop an equation incorporating a slope factor into the CN method for application in the
steep slope areas of the Loess Plateau of China. The dataset consisted of 11 years of rainfall and runoff measurements
from two experimental sites with slopes ranging from 14 to 140%. The results indicated that the standard CN method
underestimated large runoff events and overestimated small events. For our experimental conditions, the optimized and
non-optimized forms of the slope-modified CN method of the Erosion Productivity Impact Calculator model improved
runoff prediction for steep slopes, but large runoff events were still underestimated and small ones overpredicted. Based
on relationships between slope and the observed and theoretical CN values, an equation was developed that better
predicted runoff depths with an R2 of 0Ð822 and a linear regression slope of 0Ð807. This slope-adjusted CN equation
appears to be the most appropriate for runoff prediction in the steep areas of the Loess Plateau of China. Copyright
 2005 John Wiley & Sons, Ltd.
KEY WORDS
SCS CN method; slope; runoff; Loess Plateau
INTRODUCTION
The wind-deposited loess soils, in the middle reaches of the Yellow River of China, are among the most
erodible in the world and cover about 620 000 km2 in five provinces. Approximately 280 000 km2 of this
area has annual soil losses averaging 40 to 50 Mg ha1 , with values as high as 100 to 200 Mg ha1 . These
large quantities of eroded sediment are transported to the Yellow River, where they degrade water quality
and rapidly fill reservoirs. This severe erosion problem is caused by the high intensity of summer rainstorms,
steep slopes, and sparse vegetative cover that contribute to increasing the amount of runoff. In particular,
cultivation on land with slopes above 30%, and up to 100%, is considered a major cause of the important soil
loss from this region (Liu et al., 1994). An appropriate method to predict runoff from steep land is, therefore,
essential to delineate sensitive areas to be protected and to develop suitable agricultural practices that will
reduce runoff and soil loss.
The curve number (CN) method, developed by the USDA-Soil Conservation Service (SCS, 1972), for
predicting surface runoff from rainfall, is widely accepted in the world. It is used extensively in various
hydrologic, erosion, and water-quality models, including CREAMS (Knisel, 1980), Erosion Productivity
* Correspondence to: Jacques Gallichand, Département des Sols et de Génie Agroalimentaire, FSAA, Université Laval, Québec (Qc) G1K
7P4, Canada. E-mail: [email protected]
Copyright  2005 John Wiley & Sons, Ltd.
Received 5 May 2004
Accepted 9 February 2005
580
M. HUANG ET AL.
Impact Calculator (EPIC; Sharpley and Williams, 1990), SWRRB (Williams et al., 1985; Arnold et al., 1990),
and AGNPS (Young et al., 1989). The advantages of this method include its simplicity and the use of the single
CN parameter (Ponce and Hawkins, 1996; Bhuyan et al., 2003). CN values have been obtained experimentally
from rainfall and runoff measurements over a wide range of geographic, soil, and land management conditions.
However, the effect of slope is not taken into account in the CN method.
The land slope is an important factor determining water movement within the landscape. Studies on the
effect of soil slope on runoff have been reported under either simulated or natural rainfall. Under simulated
rainfall, Barros et al. (1999) studied surface runoff and interflow for two shallow soils (sandy loam, silty
clay loam) and two slopes (1 and 3%) in Pennsylvania, USA. Their results indicated that a slope of 3%
increases surface runoff and reduces interflow compared with a slope of 1%. Haggard et al. (2002) performed
an experiment on small plots (1Ð5 m ð 3 m) on a silty loam in northwest Arkansas, USA, with 11 slopes
(from 0 to 28%) and a 1 h rainfall of 70 mm h1 intensity. Their results showed that surface runoff increased
logarithmically with the slope, up to a slope of 15%, at which steeper slopes did not cause more runoff. In
France, Chaplot and Bissonnais (2003) studied the effect of two slopes (4 and 8%), two slope lengths (1 and
5 m) and three rainfall intensities (1Ð5, 8, and 30 mm h1 ) on surface runoff for a silty loam soil. They found
that surface runoff was significantly correlated primarily to soil slope (R D 0Ð51; P < 0Ð0001), and secondarily
to rainfall intensity (R D 0Ð48; P < 0Ð0001). Surface runoff from the 8% slopes was always more abundant
than that from the 4% slopes; and this effect was more pronounced for higher rainfall intensities. Under
natural rainfall conditions, it is generally recognized that surface runoff increases with soil slope (Dodds,
1997). Using five soil slopes ranging from 8 to 30%, El-Hassanin et al. (1993) found that increasing slope
from 8 to 30% increased surface runoff by 160% for several Burundi watersheds. In Pakistan, Shafiq and
Ahmad (2001) used silt loam soil plots of 1, 5 and 10% slope under medium rainfall intensity, and found
that runoff was 11Ð2% of the rainfall amount for the 1% slope, 18Ð1% for the 5% slope, and 26Ð6% for the
10% slope.
An increase in surface runoff due to steeper slopes can be explained by (1) a reduction of the initial
abstraction (Huang, 1995; Fox et al., 1997; Chaplot and Bissonnais, 2003), (2) a decrease in infiltration, and
(3) a reduction of the recession time of overland flow. Reduction of the infiltrating amount on sloping land
was studied by Philip (1991), who showed that infiltration into a 58% sloping homogeneous and isotropic
Yolo clay soil was decreased by 15% compared with a horizontal surface. Using a recession time equation
developed by Woolhiser et al. (1970), based on the kinematic wave approximation, Evett and Dutt (1985)
found that recession time decreased by 59% when the slope was increased from 1 to 15%. The reduced
recession time results in less opportunity for infiltration and in more surface runoff. Few models incorporate
a slope factor to improve prediction of surface runoff volume. Using rainfall-runoff data under simulated
rainfall, Evett and Dutt (1985) developed a nonlinear rainfall-runoff model incorporating slope and length
factors, which accounted for 96% of the runoff variability of the 18 storms studied. However, their model
is site specific and cannot be incorporated into the CN method. Although the effect of the slope on runoff
volume has been clearly established, very few attempts have been made to include a slope factor into the CN
method. One of these is that of Sharpley and Williams (1990), for which a slope-adjusted CN2 , named CN2˛ ,
is obtained by
1
CN2˛ D CN3 CN2 1 2e13Ð86˛ C CN2
1
3
where CN2 and CN3 are the SCS CN for soil moisture conditions 2 (average) and 3 (wet), and ˛ (m m1 ) is
the soil slope. The CN2˛ is then used, instead of CN2 , in the subsequent calculations of the runoff volume.
This method assumes that CN2 obtained from the handbook table (SCS, 1972) corresponds to a slope of 5%.
Surprisingly, Equation (1) does not appear to have been verified in the field.
The objectives of this study were: (1) to evaluate the approach of Sharpley and Williams (1990), which uses
the soil slope, to improve prediction of runoff volume; (2) to develop an equation that would be valid for the
climatic and steep slope conditions observed in the Loess Plateau of China, incorporating the slope into the CN
Copyright  2005 John Wiley & Sons, Ltd.
Hydrol. Process. 20, 579– 589 (2006)
MODIFICATION OF SCS CN FOR LOESS PLATEAU, CHINA
581
method. We decided to improve upon the CN method, rather than developing a completely different approach,
because the CN method is widely used, and modifications to that method could be readily implemented in
China. These objectives will be achieved using observed natural rainfall and runoff data obtained from test
plots located in an experimental watershed during an 11 year period at two sites with slopes ranging from 14
to 140%.
THE CN METHOD
The CN method (SCS, 1972) is an empirical equation predicting runoff from rainfall, using a shape parameter
S based on soil, vegetation, land use, and soil moisture prior to a rainfall event:
P 0Ð2S2
for P > 0Ð2S
P C 0Ð8S
QD0
for P 0Ð2S
QD
2
where Q (mm) is surface runoff, P (mm) is rainfall, and S (mm) is the retention parameter. The value of S
is obtained from
25 400
254
3
SD
CN
where CN ranges from 0 to 100. The CN value is determined from land cover and management, and from the
hydrologic soil group using a table from the SCS handbook (SCS, 1972). This CN value (CN2 ) corresponds
to an average soil moisture and is adjusted based on 5-day prior rainfall depth that depends on whether the
crop is in the dormant or growing season.
When experimental rainfall and runoff data are available, values of CN can be obtained from Equation (3)
after S has been back calculated from Equation (2) (Hawkins, 1973):
S D 5[P C 2Q Q4Q C 5P]
4
MATERIALS AND METHODS
Site description
The study was conducted in an experimental watershed of 0Ð87 km2 located at 110° 160 E and 37° 330 N,
4Ð8 km from the city of Xifeng in the Loess Plateau of China (Figure 1). The climate at the experimental site
is semi-arid, with an average annual temperature of 10 ° C and annual precipitation of 562 mm (1957–96),
falling mainly from June to September (67% of annual precipitation). The average annual potential evaporation
is 890 mm and the average frost-free period is 160 days.
From a loess parent mantle, 20 to 50 m deep, the soil cover developed in silty clay loam soil profiles
(FAO-UNESCO, 1988) that do not vary with the position along hill slopes of the experimental watershed
(Li et al., 1985; Liu et al., 1994). Soil particle size distributions and physical characteristics do not change
between the 0–20 cm and 20–40 cm layers, with average values of 8% for sand, 70% for silt, 22% for clay,
0Ð65% for organic matter, 1Ð3 Mg m3 for soil bulk density, and 0Ð10 m3 m3 , 0Ð30 m3 m3 and 0Ð51 m3 m3
for wilting point, field capacity and saturation, respectively.
Field experiments and data collection
The study area occupied about 0Ð25 km2 of the experimental watershed, and consisted of two experimental
setups for a total of nine plots, but no replications. The experimental setups included two types of vegetative
cover: pasture with seven slopes (17, 47, 52, 54, 66, 120 and 140%), and alfalfa with two slopes (14 and
Copyright  2005 John Wiley & Sons, Ltd.
Hydrol. Process. 20, 579– 589 (2006)
582
M. HUANG ET AL.
Figure 1. Location of the experimental site
Table I. Summary of runoff plots characteristics
Vegetation
cover
Plot
no.
Slope
(%)
Length
(m)
Width
(m)
Observation
period
Canopy
cover (%)
Pasture
D1
D2
D3
D4
D5
D6
D7
L1
L2
17
47
52
54
66
119
140
14
18
18Ð0
19Ð5
21Ð0
22Ð0
20Ð0
22Ð0
22Ð5
20Ð0
20Ð0
4Ð5
5Ð0
5Ð0
4Ð5
5Ð0
5Ð5
4Ð0
5Ð0
5Ð0
1964–65
1964–65
1964–65, 1973–78
1964–65
1964–65
1964–65, 1976–78
1964–65
1972–80
1979–80
30–90
20–75
10–90
50–80
50–90
40–70
20–60
20–60
10–60
Alfalfa
18%). The slope length ranged between 18Ð0 and 22Ð5 m, and width was from 4 to 5 m (Table I). The plots
were located in the watershed such that the slope of the soil surface coincided with the desired slope of a
given plot.
Because most rainfall and runoff occurred between May and October of each year, measurements were
taken only during that period. A recording raingauge was located within the study area at a distance not
more than 300 m from any runoff plot. Surface runoff was collected at the downslope end of each plot by a
funnel-type collector and directed into two aluminium containers (0Ð6 m diameter and 1Ð2 m depth) connected
in series such that one-third of the first container overflow was collected by the second container. Rainfall
and runoff volumes were compiled on a per storm basis during the periods from 1964 to 1965, and 1972
to 1980 (Table I). Because of a reduced surface area exposed to rainfall for sloping plots, measured runoff
depths from all plots were standardized to that of an equivalent horizontal plot by
Ro
5
cos where Rc (mm) is corrected runoff depth, Ro (mm) is observed runoff depth, and is the slope (radians).
Rc D
Copyright  2005 John Wiley & Sons, Ltd.
Hydrol. Process. 20, 579– 589 (2006)
583
MODIFICATION OF SCS CN FOR LOESS PLATEAU, CHINA
The theoretical CN2 values were determined for all plots based on vegetation, land use and soil type using
the SCS handbook table (SCS, 1972). These CN2 values ranged between 71 and 86 and were adjusted for
the 5-day prior rainfall (AMC condition) and canopy cover (Table II). During the 11 years of the experiment,
rainfall amount ranged from 0Ð1 to 81Ð7 mm per storm, with the distribution shown in Table III, for a total
number of 547 rainfall events. All rainfall events larger than 20 mm generated runoff in at least one plot.
Data analysis
Runoff depth was analysed using seven independent variables: slope (per cent), rainfall depth (millimetres),
rainfall duration (hours), average rainfall intensity (millimetres per hour), canopy cover (per cent), 5-day prior
rainfall depth (millimetres), and slope length (metres). Several slopes were used for the pasture experiment, and
slope was considered a continuous variable. Conversely, slope was considered a discrete variable for alfalfa
because only two slopes were used. The statistical significance of all variables on runoff depth was performed
with the Procedure REG using a stepwise forward-selection technique (SAS Institute, 1998). Rainfall intensity,
rainfall duration, and runoff depth were log-transformed to ensure normality prior to the regression analyses.
The partial R2 values obtained from the stepwise regressions represent the relative importance of a variable
on runoff variation, with larger values indicating a more important effect.
Parameters for all models were estimated with PEST-ASP (Doherty, 2002) and a least-squares error (LSE)
objective function:
n
LSE D min
Oi Pi 2
6
iD1
where Oi (mm) and Pi (mm) are respectively the observed and predicted runoff depths for the storm event
i and n is the total number of storm events. This objective function was chosen for its ability to produce
stable estimates (McCuen and Synder, 1986). In addition to LSE, model efficiency E (Nash and Sutcliffe,
1970; Risse et al., 1994) was used to evaluate the agreement between observed and predicted runoff. Model
efficiency is defined as
n
Oi Pi 2
ED1
iD1
7
n
Oi O2
iD1
Table II. CN2 values from SCS handbook (SCS, 1972) for hydrologic soil group C for this study
Vegetation cover
Hydrologic condition
Canopy cover (%)
CN2 value
Poor
Fair
Good
Poor
Fair
Good
<50
50–75
>75
<50
50–75
>75
86
79
74
83
76
71
Pasture
Alfalfa
Table III. Rainfall characteristics during the study period
Rainfall depth (mm)
No. of events
No. of events generating runoff
0–10
414
11
Copyright  2005 John Wiley & Sons, Ltd.
10–20
79
20
20–30
28
28
30–40
11
11
40–50
6
6
50–60
4
4
60–70
3
3
70–80
1
1
80–90
1
1
Hydrol. Process. 20, 579– 589 (2006)
584
M. HUANG ET AL.
where E is model efficiency; Oi (mm) and Pi (mm) are respectively the observed and predicted runoff for
storm event i, n is the total number of storm events, and O (mm) is the average of observed runoff for all
storm events.
An important difference between E and R2 is that E compares predicted and observed values with the 1 : 1
line rather than with the best linear regression line. Model efficiency will always be less than the coefficient
of determination, and decreasing E values indicate larger differences between predicted and observed values.
RESULTS AND DISCUSSION
Effect of slope on runoff
A summary of runoff data obtained during the measurement period is showed in Table IV. Except for
the minimum depth of runoff, all other runoff-related variables (i.e. number of runoff events, mean runoff
depth, and mean CN value calculated by Equations (3) and (4)) increase with slope. Results of the stepwise
regression analyses are presented in Table V. For pasture, 54Ð4% of the runoff depth variation is explained by
three variables: rainfall depth (28Ð2%), average rainfall intensity (16Ð7%) and slope (9Ð5%). For alfalfa, 56Ð6%
of the runoff depth variation is due to three variables, two of which are the same as for pasture: slope (22Ð8%),
rainfall duration (22Ð0%), and average rainfall intensity (11Ð9%). The smaller effect of slope on runoff for
pasture compared with alfalfa (partial R2 of 9Ð5 versus 22Ð8%) is caused by the smaller number of slopes (two
versus seven); fewer slope levels increases the importance of this parameter on runoff depth for the same
climatic conditions and resulting rainfall events. Moreover, Table V shows positive regression coefficients for
slope (2Ð30 for pasture and 2Ð65 for alfalfa), which means that runoff depth significantly increases with slope.
Standard CN method
Theoretical runoff depths were calculated from the CN values of the SCS handbook (SCS, 1972) for each
plot-runoff event, based on hydrologic and antecedent moisture conditions, and were compared with the
corresponding observed runoff depths. Figure 2a shows that the standard CN method underestimates large
runoff events, but overestimates some of the small events. Table VI shows that, for all data (pasture and
alfalfa), the standard CN method yielded a slope of the regression line of 0Ð583 and an intercept of 0Ð193,
which confirms the underprediction observed in Figure 2a. A similar underestimation of the CN value, based
on the SCS handbook table (SCS, 1972), has also been reported by Van Mullen (1991) for rangeland and
cropland in Montana and Wyoming, and by King et al. (1999) in Mississippi.
For all plot-runoff events, the E value of the standard CN method is 0Ð698. However, calculations for each
slope category showed that E decreases gradually with steeper slopes. For pasture plots, the E value decreases
Table IV. Statistical characteristics of runoff and CN for all plots
Vegetation
cover
Pasture
Alfalfa
Plot
D1
D2
D3
D4
D5
D6
D7
L1
L2
Slope
(%)
17
47
52
54
66
119
140
14
18
Average no.
runoff events
per year
7Ð5
8Ð5
9Ð2
9Ð0
9Ð5
10Ð5
12Ð5
6Ð6
7Ð0
Copyright  2005 John Wiley & Sons, Ltd.
Runoff depth (mm)
Mean
(mm)
Standard
deviation (mm)
Minimum
(mm)
Maximum
(mm)
0Ð37
0Ð28
0Ð70
0Ð95
1Ð79
2Ð36
4Ð02
1Ð86
5Ð93
1Ð53
1Ð60
2Ð12
3Ð12
4Ð00
4Ð88
9Ð05
3Ð86
4Ð50
0Ð03
0Ð01
0Ð02
0Ð02
0Ð05
0Ð07
0Ð02
0Ð00
0Ð08
6Ð38
7Ð12
8Ð20
10Ð68
13Ð16
17Ð08
27Ð86
26Ð12
32Ð28
Mean
CN
CN standard
deviation
71Ð1
78Ð6
78Ð3
83Ð1
79Ð2
79Ð4
87Ð8
72Ð1
78Ð5
7Ð2
13Ð9
11Ð2
13Ð0
11Ð1
8Ð1
6Ð1
9Ð5
9Ð8
Hydrol. Process. 20, 579– 589 (2006)
585
MODIFICATION OF SCS CN FOR LOESS PLATEAU, CHINA
Table V. Stepwise regressions for variables affecting runoff in pasture and alfalfa plots
Vegetative
cover
Pasture
Alfalfa
a
Variablea
Regression
coefficient
Partial
R2
Model R2
F value
P > Fc
Intercept
Rainfall depth (mm)
ln(ARI) (ln(mm h1 ))
Slope (m m1 )
Slope length (m)
Canopy cover (%)
ln(RD) (ln(h))
PRD (mm)
Intercept
Slope (m m1 )
ln(RD) (ln(h))
ln(ARI) (ln(mm h1 ))
PRD (mm)
Canopy cover (%)
Rainfall depth (mm)
0Ð7827
0Ð0411
0Ð5790
2Ð3036
0Ð1824
0Ð0033
0Ð2171
0Ð0012
9Ð8659
2Ð6504
1Ð1343
2Ð1726
0Ð0382
0Ð0345
0Ð0218
—b
0Ð2823
0Ð1667
0Ð0950
0Ð0051
0Ð0013
0Ð0011
0Ð0001
—
0Ð2275
0Ð2202
0Ð1185
0Ð0573
0Ð0318
0Ð0074
—
0Ð2823
0Ð4490
0Ð5440
0Ð5491
0Ð5504
0Ð5515
0Ð5516
—
0Ð2275
0Ð4477
0Ð5662
0Ð6235
0Ð6554
0Ð6628
—
78Ð6831
60Ð2271
41Ð2577
2Ð2453
0Ð5859
0Ð4669
0Ð0547
—
20Ð9121
35Ð0256
12Ð6870
10Ð3515
6Ð1849
1Ð4500
—
0Ð0001ŁŁ
0Ð0001ŁŁ
0Ð0001ŁŁ
0Ð1356ns
0Ð4449ns
0Ð4952ns
0Ð8154ns
—
0Ð0001ŁŁ
0Ð0001ŁŁ
0Ð0007ŁŁ
0Ð0020ŁŁ
0Ð0154Ł
0Ð2327ns
ARI: average rainfall intensity; RD: rainfall duration; PRD: the 5-day prior rainfall depth.
b Not applicable.
c Significance: ŁŁ
, at 0.01 level; Ł , at 0.05 level; ns, not significant.
from 0Ð665 for the 17% slope (with a number of events n D 15) to 0Ð355 for the 140% slope (n D 25). For
alfalfa, the E value decreases from 0Ð892 for the 14% slope (n D 59) to 0Ð816 for the 18% slope (n D 14).
This reduction of E, caused by an increase in slope, indicates that runoff prediction by the standard CN model
could be improved by the addition of soil slope.
The Sharpley and Williams (1990) approach
Sharpley and Williams (1990) presented Equation (1), which adjusts for the slope the CN2 values obtained
by the CN method. Runoff calculated with these adjusted CN2 values is compared with the observed runoff
in Figure 2b, which shows improvements over Figure 2a for large runoff events. However, data points are
more scattered for low runoff values. These observations are reflected in Table VI, which shows that, for all
data (pasture and alfalfa), the slope of the regression line is closer to 1Ð0 (0Ð749), but the intercept is 0Ð517,
which means an overprediction of small runoff events. Considering all data, the Sharpley and Williams (1990)
CN method increased E to 0Ð722, compared with 0Ð698 for the standard CN method, but tends to increase
overprediction of small runoff events.
The equation of Sharpley and Williams (1990) has three empirical parameters: a, b, and c, which have the
values of 1/3, 2, and 13Ð86 respectively. The generalized form of Equation (1) is therefore
CN2˛ D aCN3 CN2 1 bec˛ C CN2
8
The hypothesis of Sharpley and Williams (1990) is that the CN2 value is for a slope of 5%. For CN2˛ to
be equal to CN2 at a 5% slope requires the first term of the right-hand side of Equation (8) to be zero. This
occurs if
1
1
c D ln
9
˛
b
where ˛ (m m1 ) is the slope. Keeping the hypothesis that SCS CN2 values are for a 5% slope,
we might still improve the predictive capability of the Sharpley and Williams (1990) approach by
Copyright  2005 John Wiley & Sons, Ltd.
Hydrol. Process. 20, 579– 589 (2006)
586
M. HUANG ET AL.
35
25
20
15
10
5
Eq. (2)
5
10
15
20
25
30
20
15
10
5
Eq. (1)
0
35
5
10
15
20
25
30
35
OBSERVED RUNOFF (mm)
OBSERVED RUNOFF (mm)
35
25
20
15
10
5
0
5
10
15
20
25
30
1
25
20
15
10
5
Eq. (14)
Eq.(10)
0
d
30
1:
1:
30
1
c
ESTIMATED RUNOFF (mm)
35
ESTIMATED RUNOFF (mm)
1
25
0
0
0
b
30
1:
ESTIMATED RUNOFF (mm)
30
1
a
1:
ESTIMATED RUNOFF (mm)
35
0
35
0
OBSERVED RUNOFF (mm)
5
10
15
20
25
30
35
OBSERVED RUNOFF (mm)
Figure 2. Observed versus predicted runoff depth by (a) standard CN method, (b) Sharpley and Williams (1990), (c) optimized Sharpley
and Williams (1990), and (d) equation developed for the steep slopes of the Loess Plateau
optimizing parameters a and b, parameter c being completely determined by Equation (9). The optimization
yielded
10
CN2˛ D 0Ð8794CN3 CN2 1 1Ð0311e0Ð6116˛ C CN2
Compared with Equation (1), Equation (10) only marginally improved runoff prediction (Figure 2c).
Table VI shows that the E resulting from Equation (10) is 0Ð788 compared with 0Ð722 for Equation (1),
when using all runoff data. The optimized equation still underpredicts runoff for the large storm events, with
a regression slope of 0Ð730. For pasture in particular, the slope of the regression line is only 0Ð664. For the
experimental conditions of this study, the approach of Sharpley and Williams (1990) has limited applications.
It appears that another approach must be developed to adjust CN2 values for conditions of the steep slopes
found in the Loess Plateau of China.
An equation for steep slopes in the Loess Plateau
Based on observed rainfall and runoff data, observed values of CN (CNo ) were calculated using
Equations (4) and (3), and corrected for antecedent moisture conditions to obtain a set of 275 observed
CN2o values. Figure 3 shows that the ratio of observed to tabulated CN values (CN2o /CN2 ) increases with
slope. Therefore, a value of CN2 for a given slope (CN2˛ ) can be determined by multiplying the SCS handbook
CN2 value by a correction factor based on a slope function:
CN2˛ D CN2 f˛
Copyright  2005 John Wiley & Sons, Ltd.
11
Hydrol. Process. 20, 579– 589 (2006)
587
MODIFICATION OF SCS CN FOR LOESS PLATEAU, CHINA
Table VI. Runoff depth predicted by the CN method with and without adjustment for slope
Plot
No. of events
Linear regression statistic
Intercept
Equation
Total
Pasture
Alfalfa
Equation
Total
Pasture
Alfalfa
Equation
Total
Pasture
Alfalfa
Equation
Total
Pasture
Alfalfa
(2), standard CN method (SCS, 1972)
275
0Ð193
202
0Ð352
73
0Ð003
(1), Sharpley and Williams (1990)
275
0Ð517
202
0Ð693
73
0Ð273
(10), optimized Sharpley and Williams (1990)
275
0Ð361
202
0Ð520
73
0Ð069
(14), for steep slopes in the Loess Plateau
275
0Ð337
202
0Ð410
73
0Ð109
Model
efficiency E
Slope
R2
0Ð583
0Ð405
0Ð779
0Ð741
0Ð632
0Ð894
0Ð698
0Ð539
0Ð868
0Ð749
0Ð588
0Ð899
0Ð725
0Ð570
0Ð894
0Ð722
0Ð567
0Ð894
0Ð730
0Ð664
0Ð811
0Ð784
0Ð687
0Ð898
0Ð788
0Ð686
0Ð882
0Ð804
0Ð813
0Ð801
0Ð827
0Ð773
0Ð903
0Ð826
0Ð768
0Ð888
Figure 3. Relationship between the observed and theoretical CN ratio, and soil slope
Similar to Sharpley and Williams (1990), we assumed that the SCS CN2 is for 5% slopes. After several
trials, we determined a two-parameter (a1 and a2 ) slope function, resulting in the following expression for
CN2˛ :
a1 C a2 ˛ 0Ð05
CN2˛ D CN2
12
˛ 0Ð05 C a1
Using all rainfall and runoff data, parameters a1 and a2 were optimized, resulting in
CN2˛ D CN2
323Ð57 C 15Ð63˛ 0Ð05
˛ 0Ð05 C 323Ð57
13
322Ð79 C 15Ð63˛
˛ C 323Ð52
14
Equation (13), after simplification, yields
CN2˛ D CN2
Copyright  2005 John Wiley & Sons, Ltd.
Hydrol. Process. 20, 579– 589 (2006)
588
M. HUANG ET AL.
where the slope ˛ (m m1 ) should be between 0Ð14 and 1Ð4 to stay within the bounds of the experimental
values. Values of CN2˛ should never be above 100. In the handbook table (SCS, 1972), CN2 values range
from 6 to 94 depending on the hydrological soil group and land use, whereas the corresponding CN2˛ values
corrected with Equation (14) vary from 6Ð4 to 99Ð7 for a slope of 140%.
Comparing Figure 2a–c with Figure 2d shows that runoff predicted by Equation (14) is in better agreement
with experimental runoff values. From Table VI we can see that, for all runoff data, the slope of the regression
line has increased to 0Ð804, compared with 0Ð583, 0Ð749, and 0Ð730 for Equations (2), (1) and (10) respectively.
Use of Equation (14) improved E to 0Ð826, compared with 0Ð788 and 0Ð722 respectively for the optimized and
non-optimized Sharpley and Williams (1990) approaches. Moreover, compared with Equations (1), (2) and
(10), Equation (14) separately improved pasture and alfalfa performance parameters. However, Equation (14)
still results in overprediction for small events (intercept is 0Ð337), which might be inherent to the SCS method
of defining the rainfall versus runoff relationship. For small storm events, Hawkins (1975), Bondelid et al.
(1982) and Ponce (1989) found the CN method to be highly sensitive to the antecedent moisture condition;
this parameter is not clearly defined, and so the present computation method might not be appropriate for the
climatic conditions prevailing in the Loess Plateau.
CONCLUSIONS
An 11-year experiment, consisting of seven pasture plots and two alfalfa plots, with slopes ranging from 14 to
140%, was conducted to develop an equation incorporating a slope parameter into the CN method to predict
surface runoff from steep slopes in the Loess Plateau of China. The following conclusions can be drawn from
this study:
1. Runoff increased significantly with slope; slope explained about 10% of runoff depth variation in pasture,
and 23% in alfalfa.
2. The standard CN method underpredicted large runoff events and overpredicted small ones; the discrepancy
between observed and predicted runoff depth increased with slope.
3. A slope-adjustment CN method, used in EPIC, was tested in both its original and optimized forms; in both
cases the runoff prediction was improved for steep slopes, but large runoff events were underpredicted and
small ones overpredicted.
4. A CN slope-adjusted equation was developed based on the relationship between observed and theoretical
CN values and slope; this equation yielded the best predicted runoff depth values, with an R2 of 0Ð827 and
a linear regression slope of 0Ð804.
5. The CN slope-adjusted equation appears to be the most appropriate for runoff prediction in the steep areas
of the Loess Plateau, but it needs to be validated and possibly improved for other sites.
ACKNOWLEDGEMENTS
This work was financed by the Important Direction Project of Innovation of CAS (KZCX3-SW-442), the
Chinese National Natural Science Foundations (No. 40471062), and the Innovation Project of the Institute of
Soil and Water Conservation, CAS & MWR.
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Copyright  2005 John Wiley & Sons, Ltd.
Hydrol. Process. 20, 579– 589 (2006)