Directory UMM :Data Elmu:jurnal:A:Agricultural Systems:Vol63.Issue2.Feb2000:
Agricultural Systems 63 (2000) 97±110
www.elsevier.com/locate/agsy
Fuzzy class membership approach to soil
erosion modelling
T.R. Nisar Ahamed, K. Gopal Rao, J.S.R. Murthy *
Department of Civil Engineering, Indian Institute of Technology, Powai, Mumbai 400 076, India
Received 4 December 1998; received in revised form 16 May 1999; accepted 22 November 1999
Abstract
To optimize the use of the available land and water resources of a watershed for sustainable
agricultural production, soil erosion assessment and conservation are essential. The Universal
Soil Loss Equation (USLE) is a widely accepted model (Wishmeier and Smith, 1965. Predicting Rainfall Erosion Losses from Cropland (Agricultural Handbook No. 282). USDA.
Washington, D.C.) for assessing soil erosion and to account for the most important factors.
Conventional approaches to classi®cation are designed to assign a given area element (pixel)
to a single erosion class. However, the soil and other physical parameters might vary spatially
within a pixel and it may not correspond entirely to a single erosion class. To determine the
loss of information on the susceptibility to erosion a fuzzy class membership approach was
used to assign partial grades to the erosion classes. In the present studies, a spatially distributed approach was used to consider the in¯uence of the spatial variation in the soil and
other physical parameters in soil erosion assessment in the study area, Kalyanakere subwatershed Karnataka, India, using the USLE model. The emphasis of the studies was laid on
the use of a fuzzy class membership approach in soil erosion classi®cation, and to develop a
criteria table specifying the erosion parameter values related to erosion susceptibility classes
from available literature to apply fuzzy class membership approach for the classi®cation.
Salient features of the approach and the results of the study are presented in this paper.
# 2000 Elsevier Science Ltd. All rights reserved.
Keywords: Soil erosion; USLE; Classi®cation; Fuzzy membership; Spatial variability; GIS
* Corresponding author. Tel.: +91-22-578-2545; fax: +91-22-578-3480.
E-mail address: jsrmty@civil.iitb.ernet.in (J.S.R. Murthy).
0308-521X/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved.
PII: S0308-521X(99)00066-9
98
T.R. Nisar Ahamed et al. / Agricultural Systems 63 (2000) 97±110
1. Introduction
Soil erosion is a two-stage process consisting of the detachment of soil particles
by the impact of raindrops falling on the soil surface and transport by erosive
agents such as running water, which scours the soil surface. The factors that govern
soil erosion are climate, soil characteristics, vegetation and topography. Soil erosion
causes a reduction in the productivity of land due to soil loss and also pollution of
water and the silting of watercourses. Regression models (Chakraborthy, 1993)
or empirical equations (Wishmeier and Smith, 1978) have been used for soil
loss estimation. The widely accepted model to estimate soil loss is the Universal
Soil Loss Equation (USLE) which requires information on soil properties, topography, land use and conservation measures, if any, to control erosion. Many
authors have reported the extensive use of USLE for large basins also (Julien and
Tanago, 1991).
In the present studies, a spatially distributed approach is used to consider the
in¯uence of the spatial variation in soil and other physical parameters in the assessment of susceptibility to soil erosion using the USLE model and a fuzzy class
membership approach is used in classifying the erosion. The details of the approach
and the results of the study are given in the following.
2. The study area
The study area is the Kalyanakere sub-watershed No. 1, Karnataka State, India,
which covers 2250 ha (SOI topographic map No. 57 G/4). It is bounded by latitude 13 80 4000 N to 13 110 4000 N, and longitude 77 70 1200 E to 77 110 3400 E, as shown
in Fig. 1. The drainage of Kalyanakere sub-watershed is sub-dendritic. The area
is mostly undulating with gently sloping pediments and valleys occurring at an
altitude ranging from 820 to 1000 m above mean sea level. There are hillocks
and rock outcrops towards the north-eastern parts of the watershed. A contour
Digital Elevation Model (DEM) was generated (Fig. 2) from the 5-m interval contour map (Fig. 3) of the study area. The contour DEM was used to
generate a grid DEM and a slope map was derived from it. The soil series and
land use information for the area are available at a scale of 1:8000 (Anonymous,
1992). The land use map was compiled for the year 1993. The major land use
categories of the study area are cultivable dry land (72.42%) and cultivable
wet land (11.94%). These maps were digitized with same scale and resolution (14.514.5 m) which resulted in 390 rows (or lines) and 548 columns (or
pixels).
3. USLE
USLE is a very widely accepted empirical model developed by US Agricultural
Research Service (Wishmeier and Smith, 1965) to predict long-term average soil
T.R. Nisar Ahamed et al. / Agricultural Systems 63 (2000) 97±110
99
losses. The USLE computes the soil loss as a product of six major factors and is
given by:
A RKLSCP;
1
Fig. 1. Location map of study area.
Fig. 2. Contour Digital Elevation Model.
100
T.R. Nisar Ahamed et al. / Agricultural Systems 63 (2000) 97±110
Fig. 3. Contour map (5 m interval).
where A is the long-term average annual soil loss (t/ha/year), R is a rainfall erosivity
factor (t/ha/year), K is the soil erodibility factor, L is the slope length factor, S is the
slope steepness factor, C is the cropping management factor and P is the conservation practice factor.
Wischmeier (1959) found that soil loss is directly proportional to the product of
total kinetic energy of rainfall and maximum rainfall of 30-min duration of a storm.
The rainfall erosivity factor (R) is expressed as:
R 1=100 E I30 ;
2
where E is the total kinetic energy (t/ha/cm) of the rainfall, I30 is the maximum
rainfall of 30-min duration of a storm (cm/h), and E is given by:
E 210:3 89 log10 Ii ;
3
where Ii is the intensity of rainfall (cm/h) in a given duration of time i.
Soil erodibility describes the resistance of the soil to both detachment and transport. It depends on the physical and chemical properties of soils, such as texture,
aggregate stability, shear strength, in®ltration capacity, organic matter content, etc.
The soil erosion factor K is the erosion rate per unit of erosion index (R) for a speci®ed soil in cultivated fallow on a 9% slope, 22.13 m long. Direct measurement of K
from ®eld plots is expensive and time consuming. The following relation is used to
derive K (see the nomograph of Wishmeier and Smith, 1978, for the purpose):
T.R. Nisar Ahamed et al. / Agricultural Systems 63 (2000) 97±110
K 2:1 10ÿ6 12 ÿ OM N1 N21:14 0:0325 S ÿ 2 0:025 P ÿ 3;
101
4
where OM=per cent organic matter, N1=per cent silt+per cent ®ne sand, N2=per
cent silt+per cent ®ne sand+per cent sand, S=soil structure code and P=permeability class of the soil.
The eect of slope length and gradient on the intensity of the erosion process is
collectively known as the `topographic factor, LS'. The slope length is de®ned as the
distance from the point of origin of overland ¯ow to the point where the slope
decreases suciently for deposition to occur or to the point where runo enters a
de®ned channel (Wishmeier and Smith, 1978). The slope length factor L, is a ratio
that gives the soil loss from the actual ®eld slope length to that from a standard ®eld
plot (22.13 m long). The slope steepness factor S, is a ratio that gives the soil loss
from the actual ®eld gradient to that from a standard ®eld plot of 9% slope. The LS
factor (Wishmeier and Smith, 1978) is given by:
2
0:3x0:43
;
LS 1=22:13m 0:043x 6:613
5
where l is the slope length in metres, x is the slope gradient in percentage and m is an
exponent whose value depends on the slope steepness (Wishmeier and Smith, 1978),
as given below:
Slope (%)
m
5
0.5
The cropping management factor, C, is the ratio of soil loss under given conditions to soil loss from cultivated fallow for identical conditions of soil, slope and
rainfall. C factor value varies appreciably from year to year as the crops grown can
be managed in many ways. The conservation practice factor, P, is the ratio of soil
loss with speci®ed conservation practices (contour tillage, strip cropping, terracing,
etc.) to that with up and down the slope cultivation. The eectiveness of the conservation practices in reducing soil loss depends on the steepness of the slope.
Wishmeier and Smith (1978) gave the `C' values for various conditions, and `P'
values for dierent slopes.
4. Fuzzy class membership approach to classi®cation
In the conventional method of classi®cation, the estimated soil loss of each pixel is
assigned to a single class and there is no provision for partial class membership.
Chang and Burrough (1987), Burrough et al. (1992) and Tang and Van Ranst (1992)
applied a fuzzy class membership method to land suitability evaluation. Wang et al.
(1990) showed that the use of fuzzy class membership approach for cropland suitability classi®cation in a GIS environment preserves the complete information.
In fuzzy class membership approach, to classify each pixel into one of the m classes, a measure of similarity is calculated in terms of the Euclidean distance between
102
T.R. Nisar Ahamed et al. / Agricultural Systems 63 (2000) 97±110
the pixel and the erosion susceptibility class. The Euclidean distance dE between the
pixel vector (x) and class representative vector c is given by,
v
uX
u n
6
dE x; c t xj ÿ cj 2 ;
j1
where j=1 to n are the parameters and c=1 to m are the classes.
The smaller the distance dE ,the more similar is the x, to c. The fuzzy membership
level of the pixel to the erosion class c is de®ned in terms of dE by:
1
dE x c
;
fc x m
P
1
i1 dE x i
7
where fc x is the membership level of pixel x to class c.
For a given pixel, m membership functions exist that indicate the extent to which
the pixel belongs to each of the m classes (EC1, EC2, . . ., EC5). A value of
dE x; c =0 or fc x=1, indicates that the membership of the pixel in class c is unity
and the membership of the other classes is zero which means that the pixel is categorized by class c only.
5. Soil loss estimation and classi®cation
In the present studies the soil loss was estimated using the USLE considering the
in¯uence of the spatial variation of the relevant parameters. Thematic maps compiled on the relevant attributes from various sources and digitized (vide Section 2)
were used in soil loss estimation. Soil loss classi®cation is done by two approaches:
(1) using the USLE only; and (2) using the USLE adapted to a fuzzy class membership approach. The results of the two approaches are compared. The scheme of
soil loss estimation and classi®cation is shown in the ¯ow diagram (Fig. 4).
Based on the seasonal and annual erosion values for 400 stations that represent
the soil climatic zones of India, Raghunath et al. (1982) prepared isopleth maps that
show areas of equal rainfall erosivity and the values of R. Babu et al. (1978) also
prepared similar maps called Iso-erodent maps for the country to estimate R. To
compute R using Eqs. (2) and (3), continuous rainfall data are required. Where
continuous rainfall data are not available, Babu et al. (1978) developed a simple
linear relationship between erosivity index (R) and annual or seasonal rainfall
(June±September) using 43 stations distributed in dierent rainfall zones:
Ra 79 0:363X r 0:83
8
Rs 50 0:389X r 0:88
9
T.R. Nisar Ahamed et al. / Agricultural Systems 63 (2000) 97±110
103
Fig. 4. Approach to soil loss estimation and classi®cation (USLE and fuzzy based). DEM, Digital Elevation Model.
where Ra and Rs are annual and seasonal erosivity index values, respectively, and X
is the average annual or seasonal rainfall (mm) as per the case.
Since the available rainfall information for the study area comes from one rain
gauge, Eq. (8) was used to compute R in the present studies.
The soil of the Kalyanakere sub-watershed is classi®ed into 17 soil series. The Kfactor values for all of the soil series in the study area were computed using Eq. (4)
and the K-factor map was derived. The K values range from 0.13 to 0.30 (Table 1).
Considering l as the pixel length (Hession and Shanholtz, 1988), the LS values
were computed using the slope map and Eq. (5). The LS factor values suggested
(Table 2) by Kok et al. (1995) were adopted in the process to derive the LS map in
the present study.
The land use map was used to derive the C-factor values (Table 3) for the study
area based on the experiments carried out under dierent climatic and physical
104
T.R. Nisar Ahamed et al. / Agricultural Systems 63 (2000) 97±110
Table 1
Soil erodibility factor (K) for dierent soil series
Sl. No.
Soil series type
Area (ha)
Texture
K factor
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
A
B
C
D
E
F
G
H
I
J
K
L
M
N
0
P
Q
311.77
314.89
224.46
25.27
167.44
150.67
91.01
21.45
163.5
135.32
164.77
47.28
46.96
48.35
75.98
25.31
12.825
Sandy loam
Sandy clay loam
Gravelly sandy loam
Sandy loam
Loamy sand
Sandy loam
Loamy sand
Clay loam
Clay
Sandy clay loam
Clay loam
Loamy sand
Sandy clay
Sandy loam
Sandy clay
Clay
Sandy clay
0.136
0.165
0.165
0.15
0.126
0.159
0.165
0.24
0.15
0.236
0.225
0.159
0.236
0.196
0.165
0.184
0.196
conditions (Tejwani et al., 1975; Singh et al., 1985) and a C-factor map was derived.
Thematic maps on land use and slope, and the ®eld information on the conservation
practices were used to adopt the values of P (Table 4) for the study area (Wishmeier
and Smith, 1978) and to derive a P-factor map.
The maps on K, LS, C and P, together with the rainfall factor R computed earlier,
were used in the estimation and classi®cation of soil loss. A computer program in `C'
was developed for the estimation of soil loss by USLE as well as using the fuzzy
class membership approach as per the scheme given in Fig. 4. The raster maps of the
USLE factors K, LS, C and P, derived as above (390 rows548 columns) are read
into the program row by row. The R-factor value computed above using Eq. (8), the
tabulations of the USLE factor values K, LS, C, and P (Tables 1±4), USLE soil loss
class ranges (Table 5) and the fuzzy class membership criteria (Table 6) are also read
into the program. The soil loss is computed pixel by pixel, using: (1) USLE only; and
(2) USLE with fuzzy class membership approach.
5.1. Soil loss classi®cation using the USLE
Permissible soil loss is the maximum soil loss that allows an acceptable level of
crop productivity to be sustained economically and inde®nitely. It is generally
Table 2
LS-factor values corresponding to slope classes
Slope class %
LS factor
0±5
0.5
5±15
3.5
15±30
9.0
>30
16.0
105
T.R. Nisar Ahamed et al. / Agricultural Systems 63 (2000) 97±110
Table 3
Cropping factor (C) values for dierent land use classes
Sl No.
Land use category
C-factor value
1
2
3
4
5
6
7
8
9
10
Finger millet (dry)
Paddy (wet)
Garden
Un®t for agriculture
Waste land
Forest
Settlement
Open (fallow)
Pasture land
Rock outcrop
0.38
0.28
0.001
1.0
1.0
0.05
0.01
0.07
0.09
1.0
Table 4
Conservation practice factor (P) on dierent slope gradients
Sl No.
Slope %
P factor
1
2
3
4
5
6
7
1.0±2.0
3.0±5.0
6.0±8.0
8.0±12.0
13.0±16.0
17.0±20.0
21.0±25.0
0.6
0.5
0.5
0.6
0.7
0.8
0.9
accepted as 12 t/ha/year (Wishmeier and Smith, 1978), but 5 t/ha/year is considered
as the limit for shallow soils. In the present studies ®ve classes of soil erosion (EC1±
EC5) are adopted (Sehgal and Abrol, 1994). The ranges of soil erosion corresponding to these classes are given in Table 5. The soil loss was classi®ed into these ®ve
classes by USLE as per the approach shown in Fig. 4, and an output image is
derived (Fig. 5a).
5.2. Fuzzy membership approach to soil loss classi®cation
In the present studies the principles of fuzzy class membership method as described
under Section 4, are made use of in the soil loss classi®cation using Eqs. (6) and (7).
Fuzzy class membership analysis requires a set of criteria to classify soil loss. Since
there are no standard criteria for classifying soil loss, a set of criteria for classi®cation
Table 5
Soil erosion classes and ranges of soil loss
Class
Range (t/ha/year)
EC1 Very slight
0±5
EC2 Slight
5±10
EC3 Moderate
10±20
EC4 Severe
20±40
EC5 Very severe
>40
106
T.R. Nisar Ahamed et al. / Agricultural Systems 63 (2000) 97±110
Table 6
Criteria for fuzzy approach to erosion classi®cation
Variables
Erosion ratings
Very slight (EC1) Slight (EC2)
Factor (R)
Factor (K)
Factor (LS)
Factor (C)
Factor (P)
90±370
0.90
1.0 (>20.0)
into the ®ve erosion classes (EC1, EC2, . . ., EC5) has been developed in the present
studies based on the ®ve USLE parameters (R, K, LS, C, P) and the limited information from the literature.
Based on the isoerodent map (Babu et al., 1978) and isopleth map of India
(Raghunath et al., 1982), rainfall factor (R) between 90 and 370 was assigned to
EC1, while a value above 1063 was assigned to EC5. The value of K ranges typically
from 0.1 to 0.45 with smaller values for large sand and large clay content soils
whereas larger values for larger silt content soils (Renard et al., 1991). Zachar (1982)
found that K varies for dierent types of soil for critical slopes from 0.03 (slight
erosion class) for the most resistant soil types to 0.69 (severe erosion class) for the
most susceptible soil types. For the study area, soil with K>0.7 is assigned to EC5,
whereas that with K
www.elsevier.com/locate/agsy
Fuzzy class membership approach to soil
erosion modelling
T.R. Nisar Ahamed, K. Gopal Rao, J.S.R. Murthy *
Department of Civil Engineering, Indian Institute of Technology, Powai, Mumbai 400 076, India
Received 4 December 1998; received in revised form 16 May 1999; accepted 22 November 1999
Abstract
To optimize the use of the available land and water resources of a watershed for sustainable
agricultural production, soil erosion assessment and conservation are essential. The Universal
Soil Loss Equation (USLE) is a widely accepted model (Wishmeier and Smith, 1965. Predicting Rainfall Erosion Losses from Cropland (Agricultural Handbook No. 282). USDA.
Washington, D.C.) for assessing soil erosion and to account for the most important factors.
Conventional approaches to classi®cation are designed to assign a given area element (pixel)
to a single erosion class. However, the soil and other physical parameters might vary spatially
within a pixel and it may not correspond entirely to a single erosion class. To determine the
loss of information on the susceptibility to erosion a fuzzy class membership approach was
used to assign partial grades to the erosion classes. In the present studies, a spatially distributed approach was used to consider the in¯uence of the spatial variation in the soil and
other physical parameters in soil erosion assessment in the study area, Kalyanakere subwatershed Karnataka, India, using the USLE model. The emphasis of the studies was laid on
the use of a fuzzy class membership approach in soil erosion classi®cation, and to develop a
criteria table specifying the erosion parameter values related to erosion susceptibility classes
from available literature to apply fuzzy class membership approach for the classi®cation.
Salient features of the approach and the results of the study are presented in this paper.
# 2000 Elsevier Science Ltd. All rights reserved.
Keywords: Soil erosion; USLE; Classi®cation; Fuzzy membership; Spatial variability; GIS
* Corresponding author. Tel.: +91-22-578-2545; fax: +91-22-578-3480.
E-mail address: jsrmty@civil.iitb.ernet.in (J.S.R. Murthy).
0308-521X/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved.
PII: S0308-521X(99)00066-9
98
T.R. Nisar Ahamed et al. / Agricultural Systems 63 (2000) 97±110
1. Introduction
Soil erosion is a two-stage process consisting of the detachment of soil particles
by the impact of raindrops falling on the soil surface and transport by erosive
agents such as running water, which scours the soil surface. The factors that govern
soil erosion are climate, soil characteristics, vegetation and topography. Soil erosion
causes a reduction in the productivity of land due to soil loss and also pollution of
water and the silting of watercourses. Regression models (Chakraborthy, 1993)
or empirical equations (Wishmeier and Smith, 1978) have been used for soil
loss estimation. The widely accepted model to estimate soil loss is the Universal
Soil Loss Equation (USLE) which requires information on soil properties, topography, land use and conservation measures, if any, to control erosion. Many
authors have reported the extensive use of USLE for large basins also (Julien and
Tanago, 1991).
In the present studies, a spatially distributed approach is used to consider the
in¯uence of the spatial variation in soil and other physical parameters in the assessment of susceptibility to soil erosion using the USLE model and a fuzzy class
membership approach is used in classifying the erosion. The details of the approach
and the results of the study are given in the following.
2. The study area
The study area is the Kalyanakere sub-watershed No. 1, Karnataka State, India,
which covers 2250 ha (SOI topographic map No. 57 G/4). It is bounded by latitude 13 80 4000 N to 13 110 4000 N, and longitude 77 70 1200 E to 77 110 3400 E, as shown
in Fig. 1. The drainage of Kalyanakere sub-watershed is sub-dendritic. The area
is mostly undulating with gently sloping pediments and valleys occurring at an
altitude ranging from 820 to 1000 m above mean sea level. There are hillocks
and rock outcrops towards the north-eastern parts of the watershed. A contour
Digital Elevation Model (DEM) was generated (Fig. 2) from the 5-m interval contour map (Fig. 3) of the study area. The contour DEM was used to
generate a grid DEM and a slope map was derived from it. The soil series and
land use information for the area are available at a scale of 1:8000 (Anonymous,
1992). The land use map was compiled for the year 1993. The major land use
categories of the study area are cultivable dry land (72.42%) and cultivable
wet land (11.94%). These maps were digitized with same scale and resolution (14.514.5 m) which resulted in 390 rows (or lines) and 548 columns (or
pixels).
3. USLE
USLE is a very widely accepted empirical model developed by US Agricultural
Research Service (Wishmeier and Smith, 1965) to predict long-term average soil
T.R. Nisar Ahamed et al. / Agricultural Systems 63 (2000) 97±110
99
losses. The USLE computes the soil loss as a product of six major factors and is
given by:
A RKLSCP;
1
Fig. 1. Location map of study area.
Fig. 2. Contour Digital Elevation Model.
100
T.R. Nisar Ahamed et al. / Agricultural Systems 63 (2000) 97±110
Fig. 3. Contour map (5 m interval).
where A is the long-term average annual soil loss (t/ha/year), R is a rainfall erosivity
factor (t/ha/year), K is the soil erodibility factor, L is the slope length factor, S is the
slope steepness factor, C is the cropping management factor and P is the conservation practice factor.
Wischmeier (1959) found that soil loss is directly proportional to the product of
total kinetic energy of rainfall and maximum rainfall of 30-min duration of a storm.
The rainfall erosivity factor (R) is expressed as:
R 1=100 E I30 ;
2
where E is the total kinetic energy (t/ha/cm) of the rainfall, I30 is the maximum
rainfall of 30-min duration of a storm (cm/h), and E is given by:
E 210:3 89 log10 Ii ;
3
where Ii is the intensity of rainfall (cm/h) in a given duration of time i.
Soil erodibility describes the resistance of the soil to both detachment and transport. It depends on the physical and chemical properties of soils, such as texture,
aggregate stability, shear strength, in®ltration capacity, organic matter content, etc.
The soil erosion factor K is the erosion rate per unit of erosion index (R) for a speci®ed soil in cultivated fallow on a 9% slope, 22.13 m long. Direct measurement of K
from ®eld plots is expensive and time consuming. The following relation is used to
derive K (see the nomograph of Wishmeier and Smith, 1978, for the purpose):
T.R. Nisar Ahamed et al. / Agricultural Systems 63 (2000) 97±110
K 2:1 10ÿ6 12 ÿ OM N1 N21:14 0:0325 S ÿ 2 0:025 P ÿ 3;
101
4
where OM=per cent organic matter, N1=per cent silt+per cent ®ne sand, N2=per
cent silt+per cent ®ne sand+per cent sand, S=soil structure code and P=permeability class of the soil.
The eect of slope length and gradient on the intensity of the erosion process is
collectively known as the `topographic factor, LS'. The slope length is de®ned as the
distance from the point of origin of overland ¯ow to the point where the slope
decreases suciently for deposition to occur or to the point where runo enters a
de®ned channel (Wishmeier and Smith, 1978). The slope length factor L, is a ratio
that gives the soil loss from the actual ®eld slope length to that from a standard ®eld
plot (22.13 m long). The slope steepness factor S, is a ratio that gives the soil loss
from the actual ®eld gradient to that from a standard ®eld plot of 9% slope. The LS
factor (Wishmeier and Smith, 1978) is given by:
2
0:3x0:43
;
LS 1=22:13m 0:043x 6:613
5
where l is the slope length in metres, x is the slope gradient in percentage and m is an
exponent whose value depends on the slope steepness (Wishmeier and Smith, 1978),
as given below:
Slope (%)
m
5
0.5
The cropping management factor, C, is the ratio of soil loss under given conditions to soil loss from cultivated fallow for identical conditions of soil, slope and
rainfall. C factor value varies appreciably from year to year as the crops grown can
be managed in many ways. The conservation practice factor, P, is the ratio of soil
loss with speci®ed conservation practices (contour tillage, strip cropping, terracing,
etc.) to that with up and down the slope cultivation. The eectiveness of the conservation practices in reducing soil loss depends on the steepness of the slope.
Wishmeier and Smith (1978) gave the `C' values for various conditions, and `P'
values for dierent slopes.
4. Fuzzy class membership approach to classi®cation
In the conventional method of classi®cation, the estimated soil loss of each pixel is
assigned to a single class and there is no provision for partial class membership.
Chang and Burrough (1987), Burrough et al. (1992) and Tang and Van Ranst (1992)
applied a fuzzy class membership method to land suitability evaluation. Wang et al.
(1990) showed that the use of fuzzy class membership approach for cropland suitability classi®cation in a GIS environment preserves the complete information.
In fuzzy class membership approach, to classify each pixel into one of the m classes, a measure of similarity is calculated in terms of the Euclidean distance between
102
T.R. Nisar Ahamed et al. / Agricultural Systems 63 (2000) 97±110
the pixel and the erosion susceptibility class. The Euclidean distance dE between the
pixel vector (x) and class representative vector c is given by,
v
uX
u n
6
dE x; c t xj ÿ cj 2 ;
j1
where j=1 to n are the parameters and c=1 to m are the classes.
The smaller the distance dE ,the more similar is the x, to c. The fuzzy membership
level of the pixel to the erosion class c is de®ned in terms of dE by:
1
dE x c
;
fc x m
P
1
i1 dE x i
7
where fc x is the membership level of pixel x to class c.
For a given pixel, m membership functions exist that indicate the extent to which
the pixel belongs to each of the m classes (EC1, EC2, . . ., EC5). A value of
dE x; c =0 or fc x=1, indicates that the membership of the pixel in class c is unity
and the membership of the other classes is zero which means that the pixel is categorized by class c only.
5. Soil loss estimation and classi®cation
In the present studies the soil loss was estimated using the USLE considering the
in¯uence of the spatial variation of the relevant parameters. Thematic maps compiled on the relevant attributes from various sources and digitized (vide Section 2)
were used in soil loss estimation. Soil loss classi®cation is done by two approaches:
(1) using the USLE only; and (2) using the USLE adapted to a fuzzy class membership approach. The results of the two approaches are compared. The scheme of
soil loss estimation and classi®cation is shown in the ¯ow diagram (Fig. 4).
Based on the seasonal and annual erosion values for 400 stations that represent
the soil climatic zones of India, Raghunath et al. (1982) prepared isopleth maps that
show areas of equal rainfall erosivity and the values of R. Babu et al. (1978) also
prepared similar maps called Iso-erodent maps for the country to estimate R. To
compute R using Eqs. (2) and (3), continuous rainfall data are required. Where
continuous rainfall data are not available, Babu et al. (1978) developed a simple
linear relationship between erosivity index (R) and annual or seasonal rainfall
(June±September) using 43 stations distributed in dierent rainfall zones:
Ra 79 0:363X r 0:83
8
Rs 50 0:389X r 0:88
9
T.R. Nisar Ahamed et al. / Agricultural Systems 63 (2000) 97±110
103
Fig. 4. Approach to soil loss estimation and classi®cation (USLE and fuzzy based). DEM, Digital Elevation Model.
where Ra and Rs are annual and seasonal erosivity index values, respectively, and X
is the average annual or seasonal rainfall (mm) as per the case.
Since the available rainfall information for the study area comes from one rain
gauge, Eq. (8) was used to compute R in the present studies.
The soil of the Kalyanakere sub-watershed is classi®ed into 17 soil series. The Kfactor values for all of the soil series in the study area were computed using Eq. (4)
and the K-factor map was derived. The K values range from 0.13 to 0.30 (Table 1).
Considering l as the pixel length (Hession and Shanholtz, 1988), the LS values
were computed using the slope map and Eq. (5). The LS factor values suggested
(Table 2) by Kok et al. (1995) were adopted in the process to derive the LS map in
the present study.
The land use map was used to derive the C-factor values (Table 3) for the study
area based on the experiments carried out under dierent climatic and physical
104
T.R. Nisar Ahamed et al. / Agricultural Systems 63 (2000) 97±110
Table 1
Soil erodibility factor (K) for dierent soil series
Sl. No.
Soil series type
Area (ha)
Texture
K factor
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
A
B
C
D
E
F
G
H
I
J
K
L
M
N
0
P
Q
311.77
314.89
224.46
25.27
167.44
150.67
91.01
21.45
163.5
135.32
164.77
47.28
46.96
48.35
75.98
25.31
12.825
Sandy loam
Sandy clay loam
Gravelly sandy loam
Sandy loam
Loamy sand
Sandy loam
Loamy sand
Clay loam
Clay
Sandy clay loam
Clay loam
Loamy sand
Sandy clay
Sandy loam
Sandy clay
Clay
Sandy clay
0.136
0.165
0.165
0.15
0.126
0.159
0.165
0.24
0.15
0.236
0.225
0.159
0.236
0.196
0.165
0.184
0.196
conditions (Tejwani et al., 1975; Singh et al., 1985) and a C-factor map was derived.
Thematic maps on land use and slope, and the ®eld information on the conservation
practices were used to adopt the values of P (Table 4) for the study area (Wishmeier
and Smith, 1978) and to derive a P-factor map.
The maps on K, LS, C and P, together with the rainfall factor R computed earlier,
were used in the estimation and classi®cation of soil loss. A computer program in `C'
was developed for the estimation of soil loss by USLE as well as using the fuzzy
class membership approach as per the scheme given in Fig. 4. The raster maps of the
USLE factors K, LS, C and P, derived as above (390 rows548 columns) are read
into the program row by row. The R-factor value computed above using Eq. (8), the
tabulations of the USLE factor values K, LS, C, and P (Tables 1±4), USLE soil loss
class ranges (Table 5) and the fuzzy class membership criteria (Table 6) are also read
into the program. The soil loss is computed pixel by pixel, using: (1) USLE only; and
(2) USLE with fuzzy class membership approach.
5.1. Soil loss classi®cation using the USLE
Permissible soil loss is the maximum soil loss that allows an acceptable level of
crop productivity to be sustained economically and inde®nitely. It is generally
Table 2
LS-factor values corresponding to slope classes
Slope class %
LS factor
0±5
0.5
5±15
3.5
15±30
9.0
>30
16.0
105
T.R. Nisar Ahamed et al. / Agricultural Systems 63 (2000) 97±110
Table 3
Cropping factor (C) values for dierent land use classes
Sl No.
Land use category
C-factor value
1
2
3
4
5
6
7
8
9
10
Finger millet (dry)
Paddy (wet)
Garden
Un®t for agriculture
Waste land
Forest
Settlement
Open (fallow)
Pasture land
Rock outcrop
0.38
0.28
0.001
1.0
1.0
0.05
0.01
0.07
0.09
1.0
Table 4
Conservation practice factor (P) on dierent slope gradients
Sl No.
Slope %
P factor
1
2
3
4
5
6
7
1.0±2.0
3.0±5.0
6.0±8.0
8.0±12.0
13.0±16.0
17.0±20.0
21.0±25.0
0.6
0.5
0.5
0.6
0.7
0.8
0.9
accepted as 12 t/ha/year (Wishmeier and Smith, 1978), but 5 t/ha/year is considered
as the limit for shallow soils. In the present studies ®ve classes of soil erosion (EC1±
EC5) are adopted (Sehgal and Abrol, 1994). The ranges of soil erosion corresponding to these classes are given in Table 5. The soil loss was classi®ed into these ®ve
classes by USLE as per the approach shown in Fig. 4, and an output image is
derived (Fig. 5a).
5.2. Fuzzy membership approach to soil loss classi®cation
In the present studies the principles of fuzzy class membership method as described
under Section 4, are made use of in the soil loss classi®cation using Eqs. (6) and (7).
Fuzzy class membership analysis requires a set of criteria to classify soil loss. Since
there are no standard criteria for classifying soil loss, a set of criteria for classi®cation
Table 5
Soil erosion classes and ranges of soil loss
Class
Range (t/ha/year)
EC1 Very slight
0±5
EC2 Slight
5±10
EC3 Moderate
10±20
EC4 Severe
20±40
EC5 Very severe
>40
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T.R. Nisar Ahamed et al. / Agricultural Systems 63 (2000) 97±110
Table 6
Criteria for fuzzy approach to erosion classi®cation
Variables
Erosion ratings
Very slight (EC1) Slight (EC2)
Factor (R)
Factor (K)
Factor (LS)
Factor (C)
Factor (P)
90±370
0.90
1.0 (>20.0)
into the ®ve erosion classes (EC1, EC2, . . ., EC5) has been developed in the present
studies based on the ®ve USLE parameters (R, K, LS, C, P) and the limited information from the literature.
Based on the isoerodent map (Babu et al., 1978) and isopleth map of India
(Raghunath et al., 1982), rainfall factor (R) between 90 and 370 was assigned to
EC1, while a value above 1063 was assigned to EC5. The value of K ranges typically
from 0.1 to 0.45 with smaller values for large sand and large clay content soils
whereas larger values for larger silt content soils (Renard et al., 1991). Zachar (1982)
found that K varies for dierent types of soil for critical slopes from 0.03 (slight
erosion class) for the most resistant soil types to 0.69 (severe erosion class) for the
most susceptible soil types. For the study area, soil with K>0.7 is assigned to EC5,
whereas that with K