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. Pre-dicting 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 dis-tributed 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 sub-watershed 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
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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, topo-graphy, 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 assess-ment 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 latit-ude 13804000N to 131104000N, and longitude 77701200E to 771103400 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 inter-val 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 resolu-tion (14.514.5 m) which resulted in 390 rows (or lines) and 548 columns (or pixels).
3. USLE
losses. The USLE computes the soil loss as a product of six major factors and is given by:
ARKLSCP; 1
whereAis the long-term average annual soil loss (t/ha/year),Ris a rainfall erosivity factor (t/ha/year),Kis the soil erodibility factor,Lis the slope length factor,Sis the slope steepness factor, C is the cropping management factor andPis the conserva-tion 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), andEis given by:
E210:389log10Ii; 3
whereIiis the intensity of rainfall (cm/h) in a given duration of timei.
Soil erodibility describes the resistance of the soil to both detachment and trans-port. 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 factorKis the erosion rate per unit of erosion index (R) for a spe-ci®ed soil in cultivated fallow on a 9% slope, 22.13 m long. Direct measurement ofK from ®eld plots is expensive and time consuming. The following relation is used to deriveK(see the nomograph of Wishmeier and Smith, 1978, for the purpose):
K 2:110ÿ6 12ÿOM N1N21:140
:0325 Sÿ2 0:025 Pÿ3; 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=perme-ability 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 factorS, 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:
LS 1=22:13m 0:043x26:6130:3x0:43; 5
where l is the slope length in metres,xis the slope gradient in percentage andmis an exponent whose value depends on the slope steepness (Wishmeier and Smith, 1978), as given below:
Slope (%) <1 1±3 3±5 >5
m 0.2 0.3 0.4 0.5
The cropping management factor, C, is the ratio of soil loss under given condi-tions to soil loss from cultivated fallow for identical condicondi-tions of soil, slope and rainfall.Cfactor 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 con-servation 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 suit-ability classi®cation in a GIS environment preserves the complete information.
the pixel and the erosion susceptibility class. The Euclidean distancedEbetween the
pixel vector (x) and class representative vectorcis given by,
dE x; c
wherej=1 tonare the parameters andc=1 tomare the classes.
The smaller the distancedE,the more similar is thex, toc. The fuzzy membership
level of the pixel to the erosion classcis de®ned in terms ofdEby:
fc x
For a given pixel,mmembership 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 orfc x=1, indicates that the membership of the pixel in classcis unity
and the membership of the other classes is zero which means that the pixel is cat-egorized by classconly.
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 com-piled 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 mem-bership 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:
Ra790:363X r0:83 8
where Ra and Rs are annual and seasonal erosivity index values, respectively, andX 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 computeRin the present studies.
The soil of the Kalyanakere sub-watershed is classi®ed into 17 soil series. The K-factor values for all of the soil series in the study area were computed using Eq. (4) and theK-factor map was derived. TheKvalues 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
conditions (Tejwani et al., 1975; Singh et al., 1985) and aC-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 ofP(Table 4) for the study area (Wishmeier and Smith, 1978) and to derive aP-factor map.
The maps onK, LS,CandP, together with the rainfall factorRcomputed 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, CandP, derived as above (390 rows548 columns) are read into the program row by row. TheR-factor value computed above using Eq. (8), the tabulations of the USLE factor valuesK, LS,C, andP(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 1
Soil erodibility factor (K) for dierent soil series
Sl. No. Soil series type Area (ha) Texture Kfactor
1 A 311.77 Sandy loam 0.136
2 B 314.89 Sandy clay loam 0.165
3 C 224.46 Gravelly sandy loam 0.165
4 D 25.27 Sandy loam 0.15
5 E 167.44 Loamy sand 0.126
6 F 150.67 Sandy loam 0.159
7 G 91.01 Loamy sand 0.165
8 H 21.45 Clay loam 0.24
9 I 163.5 Clay 0.15
10 J 135.32 Sandy clay loam 0.236
11 K 164.77 Clay loam 0.225
12 L 47.28 Loamy sand 0.159
13 M 46.96 Sandy clay 0.236
14 N 48.35 Sandy loam 0.196
15 0 75.98 Sandy clay 0.165
16 P 25.31 Clay 0.184
17 Q 12.825 Sandy clay 0.196
Table 2
LS-factor values corresponding to slope classes
Slope class % 0±5 5±15 15±30 >30
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 correspond-ing 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 3
Cropping factor (C) values for dierent land use classes
Sl No. Land use category C-factor value
1 Finger millet (dry) 0.38
Conservation practice factor (P) on dierent slope gradients
Sl No. Slope % Pfactor
Soil erosion classes and ranges of soil loss
Class EC1 Very slight EC2 Slight EC3 Moderate EC4 Severe EC5 Very severe
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 infor-mation 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 ofKranges 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 withK>0.7 is assigned to EC5, whereas that withK<0.2 is assigned to EC1.
Renard et al. (1991) and Julien and Tanago (1991) noted that the evaluation ofL, S and C remains imprecise and subjective which introduces potential sources of error. Slope categories ranging from 0 to 30% were used to calculate LS, with 0±2% slopes (¯at) assigned to EC1, and slopes exceeding 30% (very steep) assigned to EC5. Information from the available literature (Wishmeier and Smith, 1978; Young et al., 1991; Kok et al., 1995) was used to derive criterion values for slope. Values of Cvary from close to zero for very well protected soil to 1.0 for unprotected bare soil. The values of C for dierent erosion classes that were adopted based on avail-able literature and from runo plot studies at various research organizations in India. The values of the control practice factor (P) are determined in relation to slope (Wishmeier and Smith, 1978).
The resulting erosion susceptibility values, therefore, were represented as a 2-D matrix of ®ve classes (EC1±EC5) and the corresponding ranges of values of the ®ve parameters (R,K, LS,C P) are shown in the criterion table (Table 6). Maps of the USLE parameters and the criteria as above were used for the soil loss classi®cation adopting fuzzy class membership approach shown in the ¯ow chart (Fig. 4). Five fuzzy class membership images were derived corresponding to the ®ve erosion clas-ses (EC1±EC5). The information of the ®ve membership class images was combined and that of the highest membership grade for the ®ve erosion classes was derived (Fig. 5b). This image also shows the per cent area coverage of the ®ve classes.
Table 6
Criteria for fuzzy approach to erosion classi®cation
Variables Erosion ratings
Very slight (EC1) Slight (EC2) Moderate (EC3) Severe (EC4) Very severe (EC5)
Factor (R) 90±370 370±614 614±700 700±1063 >1063
6. Results and discussion
In the USLE method, the factorsR,Kand LS are controlled by natural processes and usually remain constant for an area. Since the crops grown can be managed in many ways,Cmay vary appreciably from year to year. Once the GIS data base for the USLE layers is established, periodic re-evaluation of soil losses can be examined by determining the changes in the values of factors Cand P. The cropping man-agement practices and/or the conservation practices may be changed appropriately to reduce soil loss and maintain the productivity.
The results of the two approaches using USLE (1) without, and (2) with the fuzzy class membership approach are summarized in Table 7. It can be seen from the table that 50±60% of the area experiences very slight erosion, with an estimated soil loss ranging from 0 to 5 t/ha/year which is within the permissible range. Land parcels with slopes of 1±3% and with soils of low erodibility belong to this class, and the erosion is limited to only sheet erosion. The land use classes in this category are wet lands, forest, plantation and low-lying areas. At the other extreme, an area of 3±6% experiences very severe erosion. These areas are on the north-eastern hillocks and ridges and the erosion is associated with soil having large value of K. The topo-graphic conditions also promoted narrow and deep gullies, barren land without vegetative cover, etc. The areas of moderate erosion class occupy about 7±15% of the study area and are mainly on cultivated dry lands, which have moderately undulating slopes up to 10%.
The fuzzy membership approach (Wang et al., 1990) was developed for cropland suitability rating. However, in the present case the principles of this method are used to classify soil loss while preserving the partial membership information. To under-stand the impact of the loss of information on erosion susceptibility spatially, the fuzzy class membership approach prescribes partial grades to erosion classes in a GIS environment. To apply the fuzzy class membership analysis a criteria table that speci®es the erosion parameter values related to erosion susceptibility classes is derived.
the percentage area of the erosion classes from the two methods is not substantial, there is considerable spatial variation among the classes. Using cross-tabulation classi®cation of the two images from the USLE and fuzzy method, it is possible to assess the spatial dierences in the classes. The cross-classi®cation image (Fig. 5c) shows that 45.19% of the class EC1 is unchanged in the two methods. There is substantial dierence in the areas of the classes EC2 (5.3%), EC3 (4.8%) and EC5 (1.8%).
Since the computations are made pixel wise it is feasible to identify speci®c loca-tions liable to severe erosion and quantify critical areas by this approach. This can be used to prioritize soil and water conservation measures.
7. Conclusions
The following conclusions can be drawn from the present studies.
1. The fuzzy class membership approach is suited for delineating areas of various soil loss ratings appropriately. This allows partial membership of classes com-bined with the merits of GIS approach that allows spatial variation of relevant terrain and other parameters to be considered.
2. The study shows that more than half of the watershed area is susceptible to slight erosion, class EC1, and the rate of erosion is well within the permissible limits. An area of about 4±9% comprising classes EC4 and EC5 experiences severe erosion, which needs suitable conservation measures to be adopted on a priority.
3. In comparison with the results from the USLE method, the fuzzy set approach has shown that, although the total area susceptible to erosion remains more or less the same, there is substantial spatial variation within the erosion classes. Preserving the complete information in fuzzy class membership highlights the spatial variation in the severe erosion classes. In other words assigning one pixel to one class in conventional erosion analysis by USLE method leads to an erroneous areal distribution of the higher erosion classes. It should be noted that for both the methods, the parameters are those of the USLE equation. This analysis indicates the need for further studies to understand the erosion classi®cation process.
Table 7
Comparison of classi®cation of erosion by USLE and fuzzy approach
Sl No. Erosion int. class Fuzzy based (%) USLE based (%)
1 EC1 (Very slight) 56.45 61.64
2 EC2 (Slight) 24.30 21.42
3 EC3 (Moderate) 15.8 7.58
4 EC4 (Severe) 0.26 3.50
4. The criterion developed for the fuzzy membership classi®cation needs to be re®ned, based on the availability of more experimental data from soil con-servation research and incorporating all relevant parameters.
5. The factorCis the most important one in the USLE that can be controlled to reduce erosion. This is achieved by proper management of the crops grown in the area from year to year.
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