An Empirical Soil Loss Equation
An Empirical Soil Loss Equation
An Empirical Soil Loss Equation
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Department of Resources and Environmental Sciences, Beijing Normal University, Key Laboratory of
Environmental Change and Natural Disaster, the Ministry of Education of China,
Beijing 100875, PR China
Abstract: A model was developed for estimating average annual soil loss by water on
hillslope for cropland, which is called Chines Soil Loss Equation (CSLE). Six factors
causing soil loss were evaluated based on soil loss data collected from experiment stations
covering most regions of China and modified to the scale of Chinese unit plot defined. The
model uses an empirical multiplicative equation, A=RKLSBET, for predicting interrill
erosion from farmland under different soil conservation practices. Rainfall erosivity (R)
was the product of rainfall amount and maximum intensity of 10min, and also was estimated
by using daily rainfall data. The value of soil erodibility (K), the average soil loss of unit
plot per rainfall erosivity, for 6 main soil types was calculated based on the data measured
from unit plots and other data modified to the unit plot level. The method of calculating K
from soil survey data for regions without measured data was given. The slope length and
steepness factors was calculated by using the equations in USLE if slope steepness is less
than 11 degree, otherwise the steepness factor was evaluated by using a new seep slope
equation based on the analysis of measured soil loss data from steep slope plots within China.
According to the soil and water conservation practices in China, the values of bio-control,
engineering-control, and tillage factors were estimated.
Keywords: Chines soil loss equation, soil loss, unit plot
1 Introduction
Soil loss equation is to predict soil loss by using mathematical methods to evaluate factors
causing soil erosion. It is an effective tool for assessing soil conservation measures and making land
use plans. Universal soil loss equation is an empirical equation developed during 1950’s that had
been applied for natural resources inventory successfully in the US and revised in 1990’s. From
1980’s the process-based models for prediction of soil loss have been studied though the world, such
as WEPP (Water Erosion Predict Project, Nearing et al., 1989), GUEST (Griffith University Erosion
System Template, Misra and Rose, 1996), EUROSEM (the European Soil Erosion Model Morgan et
al., 1998) and LISEM (Limburg Soil Erosion Model, De Roo and Wesseling, 1996). There have been
many studies on soil erosion models and related experiments since 1940's, but the models were limited
in local levels and difficult to expand to broad regions due to data collected without universal standard.
So far there is not any soil loss equations that could be applied through China with minor errors. The
objective of this study is to develop a soil loss equation used within China based on measured data
from Chinese unit plots and data from many plots modified to Chinese unit plot, which is called
Chinese soil loss equation (CSLE).
2 Model description
Soil loss is a process of soil particle detachment by raindrops and then transported by runoff from
the rainfall. Many factors like soil physical characteristics slope features, land surface cover etc. will
influence soil loss amount, but they have interactions. It is necessary to distinct their effects on soil
loss mathematically and to evaluate them on the same scale in order to improve the accuracy of the
model. Unit plot is such a good method to solve the problem. The normalized data covering the
China by modified to unit plot supported the development of Chines soil loss equation. In addition,
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two features of soil erosion in China are distinctive and should be considered in the equation. One is
soil erosion with steep slope, and the other is the systematical practices for soil conservation during the
long history of combating soil erosion, which could be classified as biological-control,
engineering-control and tillage measures. So the Chinese soil loss equation was express as follows
after the analysis of data collected from most regions of China
A = RKSLBET (1)
where A is annual average soil loss (t/ha), R is rainfall erosivity (MJ mm/(h ha y)), K is soil
erosibility (t ha h/(ha MJ mm y)), S and L are dimensionless slope steepness and slope length
factors, B, E, and T are dimensionless factors of biological-control, engineering-control, and tillage
practices respectively. The dimensionless factors of slope and soil conservation measures were
defined as the ratio of soil loss from unit plot to actual plot with aimed factor changed but the same
sizes of other factors as unit plot. Chinese soil loss equation is to predict annual average soil loss
from slope cropland under different soil conservation practices.
To evaluated factors in the equation, about 1841 plot-year data were analyzed. Of these, 214
plot-year data from 12 plots and 1143 rainfall events from 14 weather stations were used to evaluate
rainfall erosivity. The Chinese unit plot was determined by analyzing 384 plot size data, and about
200 plot-year data from 12 plots modified to unit plot were used to evaluate erodibility for 6 types of
soil. About 30 plot-year data from steep plots modified to unit plot was used to establish the steep
slope factor equation. Other plot data was used to calculate the values of biological-control,
engineering-control and tillage factors.
A threshold for erosive rainfall of 12mm was estimated, close to that suggested by Wischmeier
and Smith (1978), 12.7mm. After comprehensive considering the accuracy of rainfall erosivity, the
data availability and calculation simplicity, the rainfall index of a rainfall event for Chinese soil loss
erosion was defined. It is the product of rainfall amount (P) and its maximum 10-min intensity (I10),
and the relationship between PI10 and the universal rainfall index EI30 was also estimated as follows:
where E is the total energy for a rainfall event (MJ/ha), I30 and I10 are the rainfall maximum 30min and
10min intensities respectively (mm/hr), P is the rainfall amount (mm). The annual rainfall erosivity
is the sum of PI10 for total rainfalls through the year. Actually, it is also difficult to get the rainfall
event data. To apply the weather data from weather stations covering the China, an equation function
for estimating half-month rainfall erosivity by using daily rainfall data was developed.
n
Rhm = 0.184∑ ( Pd I10 d ) R2 0.973 (3)
i
i =1
where Rhm is the rainfall erosivity for half-month (MJ mm/h ha), Pd is the daily rainfall amount (mm)
and I10d is the daily maximum 10min rainfall intensivity (mm/h). I=1, …, n is the rainfall days within
a half-month. If there is no I10d available, Rhm was also calculated by using only daily rainfall
amount.
n
Rhm = α ∑ ( Pd )i
β
(4)
i =1
where α and β are fitted coefficients and other variables had the same meaning as above.
Seasonal rainfall erosivity distribution could be estimated by the sum of Rhm. To plot Chinese
isoerodent map for estimation or interpolation of local values of average annual rainfall erosivity in
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any place, the empirical relationships by using different rainfall available data were estimated (not
listed). Users can choose different equations to calculate average annual rainfall erosivity according
to the data availability.
Soil erodibility is defined as soil loss from unit plot with 22.1m long and 9% slope degree per
rainfall erosion index unit (Olson and Wischmeier, 1963). Different from the US, much of soil loss
was from steep slope in China. So the Chinese unit plot was defined as a 20m long, 5m wide and 15°
degree slope plot with continuously in a clean-tilled fallow condition and tillage performed upslope
and downslope. The suggestion of Chinese unit plot made data measured be used to evaluate K
values as much as possible without large errors. Because 15° is the middle values for most plots in
China. Modified data measured from both plots of less than 15° and larger than 15° to a unit plot had
the relative minimum errors.
Based on the K defination and Chines unit plot, soil erodibility for 6 main soil types in China was
estimated. For example, the values of K for loess were 0.61, 0.33, and 0.44 t ha h/(ha MJ mm) in
Zizhou, Ansai, and Lishi in Loess Plateau of China.
λ
m
L= (5)
22.13
steeper than 5° than that from slopes less than 5°, and he recommended two different slope steepness
factor equations for different ranges of slopes:
So in Chinese soil loss equation, slope steepness factor could be estimated by using equation (6-1)
to (6-3) under different slope conditions
During the development of the historical agriculture traditions in China, the systematical practices
for soil and water conservation formed. They could be divided into three categories:
biological-control, Engineering-control and tillage measures. Biological-control practices include the
forest or grass plantation for reducing runoff and soil loss. Engineering-control practices refer to the
changes of topography to reduce runoff and soil loss by engineering construction like terrace,
check-dams. Tillage practices are the measures taken by farmland equipment. The difference
between engineering and tillage is that the latter does not change the topography and is only applied on
the farmland.
Sophora Korshinsk Seabuckthorn Seabuckthorn Seabuckthorn Erect Sainfoin Alfalfa First year Second year
& Poplar & Chinese Pine
Peashrub Milkvetch Sweetclover Sweetclover
0.004 0.054 0.083 0.144 0.164 0.067 0.160 0.256 0.377 0.083
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Many studies gave the B values for different biologic measures in China, but they were not from
the universal calculated methods and could not be used directly in soil loss equation. Based on the
defination of B values, the ratio of soil loss from plots with some biological-control practice to that
from unit plot, we calculated B values for some types of biological-control practices (Table 1). Some
values for typical engineering-control and tillage measures in China were summarized (not listed).
References
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for USDA-water erosion prediction project technology. Transactions of The ASAE, 1989,
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