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DIVISION S-5-PEDOLOGY

Creation and Interpolation of Continuous Soil Layer Classes in the Lower Namoi Valley

^a Australian Cotton Cooperative Research Centre, Dep. of Agricultural Chemistry and Soil Science, Ross Street Building A03, The Univ. of Sydney, NSW Australia 2006
^b Faculty of Environmental Sciences, Griffith Univ., Nathan, Qld 4111, Australia

Corresponding author (johnt{at}acss.usyd.edu.au)

	ABSTRACT

TOP ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
The major errors associated with soil classification and mapping are due to subjective allocation of individuals to classes and incongruities between the classification system and the natural continuous variability of the soil mantle. Fuzzy clustering algorithms can be applied to resolve both errors. In this study we numerically classified 1419 soil horizon samples using fuzzy k-means (FKM) and fuzzy k-means with extragrade (FKME) analysis. Each sample was characterized by 12 chemical and textural attributes that were used for the numerical classification. The fuzzy classes produced were mapped at various depths using a method that considered the unity of class membership and local kriging. The use of a confusion index enabled the representation of the continuous nature of membership between the classes mapped and highlighted areas where the collection of additional information may be appropriate. The resulting classes reflect sensible and practical groupings that are easily related to the natural structure of the landscape. Silt and clay contents were the most distinguishing attributes in identifying the various geological and geomorphic components. Differences in soil-forming process were well highlighted by organic C (Org. C), P, electrical conductivity (EC_1:5), pH, and Cl^- content. We concluded that the fuzzy clustering algorithms and geostatistical techniques provide a worthwhile approach to soil classification and representation of the soil continuum.

Abbreviations: EC_1:5, electrical conductivity • FKM, fuzzy k-means • FKME, fuzzy k-means with extragrade • FPI, fuzziness performance index • NCE, normalized classification entropy • Org. C, organic C

	INTRODUCTION

TOP ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
CONVENTIONAL SOIL CLASSIFICATION systems establish a series of subdivisions that place individual soil profile descriptions into a structured scheme. In soil survey, the surveyor's experience is then used to identify the unknown individual and place it into a recognized class that has similar attributes. The result is a chorochromatic map that shows regions divided into parcels of land, each of a particular soil type (Burgess and Webster, 1984). Thus the soil map produced is a display of spatial distribution of soil classes with soil boundaries constructed by way of mental interpolation between points (Burgess and Webster, 1984). There are many problems inherent with this type of system. First, the precision of any prediction depends on the homogeneity of the mapping units and hence on the within-unit variance (Trangmar et al., 1985). Second, there is the question, "how homogenous with respect to the soil profile is each land unit?" (McBratney and Webster, 1981).

Webster and Burrough (1974) pointed out another difficult task in conventional soil survey related to allocation of individual profiles to the most appropriate class. The classes defined have polythetic memberships (i.e., class membership based on several attributes) applied to the soil that has been influenced by many environmental factors. Further, fragmentary information on which much of a survey is based, as well as human error in sample collection, influence the final classification. Additionally, no matter how small differences in attributes may be, such classification does not account for the gradational nature of the soil continuum, especially at class boundaries.

An alternative to conventional soil classification is a system that accounts for the continuous nature of the soil mantle, both laterally and vertically. One such technique is the method based on fuzzy set theory (Zadeh, 1965), which allows membership of an individual to belong totally, partially, or not at all to a class.

Several studies have demonstrated the use of FKM and FKME, two of the more popular algorithms. For example, Powell et al. (1991) delineated drainage units from pH profiles; Odeh et al. (1992a) applied the algorithms to soil morphological and particle-size data along orthogonal transects; McBratney et al. (1992) identified soil mapping units; McBratney and de Gruijter (1992) delineated common soil profiles using coded morphological horizons; and De Bruin and Stein (1998) represented transition zones in the soil landscape from digital elevation models. The data sets used in most of these studies were relatively small and contained in single transects and small field areas. Moreover, the number of attributes used was limited and they were often only morphological with the soil profile considered as the individual.

In this paper we show how FKM and FKME algorithms can be used to classify a large number of soil layers, using a number of chemical and textural attributes in the lower Namoi valley of New South Wales. We show how contiguous soil classes can be recognized from a large data matrix and be presented continuously across the landscape and at various depths throughout the profile. The resulting classification is compared with the known geology and geomorphic structure of the area, as determined independently (Ward, 1999) and with the results of principal component analysis (PCA).

	THEORY

TOP ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
With conventional or hard classes, the conditions that ensure mutually exclusive, jointly exhaustive and nonempty classes are considered when a set of n individuals (e.g., soil layers) are partitioned into k discontinuous classes where the membership matrix, M = (µ_ic), is equal to one, when an individual i belongs to a class c and µ = 0 otherwise. The following conditions apply

(1)

(2)

(3)

Equation [1] indicates that the memberships of an individual across all classes sum to unity; Eq. [2] means that there is at least one individual with some degree of belongingness to a given class. Equation [3] implies the all-or-nothing membership of the hard classification. Zadeh (1965) relaxed the third condition (Eq. [3]) so that the membership of an individual in any particular class is allowed to be partial and may take any value between 0 and 1. Hence, Eq. [3] becomes

(4)

An individual can be allocated membership in k groups in any number of ways. To determine a best solution, an objective function is first defined, so that the best outcome is the one that minimizes the objective function (Ward et al., 1992)

(5)

where, C = (c_cv) is a k x p matrix of class centers (p denotes the number of variables), c_cv is the value of the center of class c for variable v, x_i = (x_i1,..., x_ip)^T is the vector representing individual i, c_c = (c_c1,..., c_cp)^T is the vector representing the center of class c, and d(x_iv, c_cv) is the square distance between x_i and c_c according to a chosen definition of distance, further denoted by d²_ic for simplicity.

To allow for individuals that lie as bridges between classes, Ruspini (1969) introduced the fuzzification of hard-c functions, an expression generalized by Bezdek (1974) and Dunn (1974)

(6)

where the exponent determines the degree of fuzziness of the final solution. The least meaningful value is = 1 and is equivalent to the hard partition of Eq. [5]. Later, Ohashi (1984) defined a version of J₂(M,C) to reduce the effects of outliers by accommodating them in a special class where they are distributed over larger distances between an individual and the class centers. Further problems arise when differentiating intragrades and extragrades, which apply equally to both types. McBratney and De Gruijter (1992) resolved this problem by making the membership to the extragrade class depend on the distances to the class centers

(7)

with the convention that if both µ_i* and d_ic are zero, the corresponding term in Eq. [7] is zero. Further, the memberships to the extragrade class, µ_i* are not concentrated in a fuzzy hypersphere around a given class center, as with normal classes, but are spread across regions at greater distances from each of the class centers, and the greater the distances, the higher its membership µ_i*.

Minimization of J₃(M,C) is achieved by heuristic Picard iteration of the following equations

(8)

(9)

and

(10)

The FKME algorithms are in accordance with procedures outlined in De Gruijter and McBratney (1988). The Picard iteration is embedded in the following algorithm based on iterative minimization of J₃(M,C)

1. Choose the number of classes k, with 1 < k < n;

2. Choose a value for the fuzziness exponent , with > 1;

3. Choose a definition of distance in the variable-space;

4. Choose a value for the stopping criterion ( = 0.001 gives reasonable convergence);

5. Initialize M = M₀ (e.g., with random memberships or with memberships from a hard k-means partition);

6. At iteration l = 1,2,3, ...,: (re)calculate C = C_l using Eq. [10] and M_l-1;

7. Recalculate M = M_l using Eq. [8] and [9] and C_l;

8. Compare M_l with M_l-1 in a convenient matrix norm. If |M_l - M_l-1| < , then stop; otherwise return to Step 6.

The modification by De Gruijter and McBratney (1988) requires a value of a to be chosen. This determines the mean outlier membership, _i*, defined as

(11)

where _i* is more readily interpretable than a, and therefore it is easier to choose a value for it. This choice would hence be ideally based on prior information about the expected frequency of extragrades in the data set of interest. Where this type of information is unavailable, the same mean membership of the outlier class can be assigned as an average is assigned to the normal classes. This amounts to

(12)

which is the preferred starting point, even though _i* is not known a priori. It is therefore appropriate to first find the root of f(a)

(13)

for which De Gruijter and McBratney (1988) suggest the use of a Regula-Falsi procedure and Steffenson's acceleration procedure (Stoer and Bulirsch, 1980) to calculate the solution. In this procedure each iteration consists of two Regula-Falsi steps, yielding a' and a'', followed by an acceleration step in which the next value of a is calculated according to

(14)

where f(a) is evaluated within the main iteration of the fuzzy k-means algorithm, beginning with f(0) = -1/(k + 1) and f(1) = k/(k + 1), with continued iteration until the root is determined to within 1%.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
Study Area
The Namoi Valley, part of the Murray-Darling Basin, lies in northern New South Wales. Edgeroi (Fig. 1) is near the center of the valley 25 km north of Narrabri township. The climate is semiarid. Extensive clearing has left few stands of native forest other than small remnant vegetation, mostly on sandstone ridges. The dominant agricultural pursuits are sheep (Ovis aries) and cattle (Bos taurus) grazing and cereal cropping, particularly wheat (Triticum aestivum L.); irrigated cotton (Gossypium hirsutum L.) production (Fig. 1) has recently become important.

View larger version (48K): [in this window] [in a new window]   Fig. 1. Location of the Edgeroi 1:50000 topographic map sheet with primary grid and site identification number

View larger version (61K): [in this window] [in a new window]   Fig. 2. The geological and geomorphic components of the Edgeroi area (after Ward, 1999). Note that the third and fourth terraced fans are mantled with water sorted clay loess

Data Set
The Edgeroi data set consists of 210 sampling sites arranged in a systematic equilateral triangular grid with an approximate 2.8-km spacing. Figure 1 shows the location of these sites on the Edgeroi 1:50000 map (McGarry et al., 1989). The data set was supplemented with data from the University of Sydney's I.A. Watson Wheat Research Center, which lies at the southern border of the Edgeroi map. This provides an additional 17 profiles. At all sites a core was recovered and sampled for laboratory analysis at depths of 0.0 to 0.1, 0.1 to 0.2, 0.3 to 0.4, 0.7 to 0.8, 1.2 to 1.3, and 2.5 to 2.6 m. The samples were air-dried and ground to pass a 2-mm sieve, with a small subsample passed through a 0.5-mm sieve for total C and CaCO₃ analysis (McGarry et al., 1989). The soil was analyzed for pH; EC_1:5 (mS m^-1); Cl^-1 (mg kg^-1) (Beech and McLeod, 1984); bicarbonate-extractable P (mg kg^-1) (Colwell, 1963); exchangeable cations [mmol(+) kg^-1], based on Tucker (1974), using a mechanical leaching device (Holmgren et al., 1977); CaCO₃ (Loveday and Reeve, 1974); and Org. C (%) (Merry and Spouncer, 1988). Silt and clay (%) were determined by pipette (Coventry and Fett, 1979).

The final raw data matrix was 1419 x 12, (i.e., n = 1419 layers by p = 12 soil chemical and textural attributes (pH, EC_1:5, Org. C, CaCO₃, Cl^-, P, exchangeable Ca, Mg, K, Na, and clay and silt contents). The conventions of McDonald et al. (1984), with minor alterations (McGarry et al., 1989), were used to describe site, vegetation, and soil morphology.

The distributions of EC_1:5, Org. C, CaCO₃, Cl, P, and exchangeable cations were examined. All have slightly to highly skewed distributions. For soil studies, Moore and Russell (1967) suggested that quantitative data should be transformed to give normal distributions. This renders the data dimensionless, moderates the effect of large outliers, and makes arbitrary weighting unnecessary. The variates were therefore transformed to logarithms to normalize the distributions.

Continuous Classification and Principal Component Analysis
The implementation of J₂(M,C) and J₃(M,C) was carried out using MacFUZZY (Ward et al., 1992). The first step involves the choice of distance-dependent matrix. This is required to optimize the performance of the objective functions J₂(M,C) and J₃(M,C). The most commonly used measure of distance is Euclidean, in which variables used for cluster analysis are given equal weight. An alternative is Mahalanobis distance, which is defined by

(15)

where S is the sample variance–covariance matrix of X. In this study, we used Mahalanobis as the distance matrix as it considers differences in variances and correlations among variables are accounted for (Bezdek, 1981).

In deciding a suitable number of classes, many authors (e.g., Roubens, 1982) have proposed validity functionals to assist in the decision making. McBratney and Moore (1985) and Powell et al. (1992) used two of these, the fuzziness performance index (FPI), and the normalized classification entropy (NCE). The FPI is a measure of the degree of fuzziness, while the NCE indicates the degree of disorganization in the classification. The least fuzzy and least disorganized number of classes is considered suitable (i.e., minimum values). To find a suitable number of classes we examined the outcomes for J₂(M,C) when the soil layers were placed in 2 to 15 classes at = 1.15, 1.2, and 1.25. Figure 3 suggests that the best solution probably lies somewhere between 7 to 12 classes since both the FPI and NCE approach minimum values. This is particularly the case for = 1.2 and c =10. However, as Odeh et al. (1992a) suggested, the optimal number of classes is related to the degree of fuzziness and therefore some measure that considers this is required.

View larger version (17K): [in this window] [in a new window]   Fig. 3. The validity functionals, fuzziness performance index (FPI) and normalized classification entropy (NCE), at various fuzziness exponents () plotted against number of soil layer classes (c)

View larger version (24K): [in this window] [in a new window]   Fig. 4. Plot of -[(JE/)c0.5] vs. for 7 to 12 classes (c)

The 10 classes defined were named after land holdings (e.g., Togo, Boolcarrol) or specific land-use areas (e.g., Couradda State Forest) where layers or exemplars (µ = 1) of a particular class were found in large numbers. Italics distinguish these names and the Extragrades and Intragrades throughout the text. Table 1 shows the layer class centroids, arranged in order of decreasing clay content. To understand the relationship among class centroids, individual layers, and attributes and to compare the FKM analysis with another numerical classification, we applied PCA. The object of PCA is to project the distribution of the individuals in character space on a small number of axes that retain the maximum information.

(16)

where t_i is the log-ratio transformed membership µ_i in class i (i = 1,..., j) and is equal to 0.0005, which is one-half of the smallest membership other than zero. They subsequently used ordinary kriging to estimate the transformed membership grades across their study area. In this study, the back-transformed memberships were interpolated using local variograms onto a regular 400-m grid throughout the Edgeroi 1:50000 topographic map sheet. This was done for computational efficiency because 11 variograms and interpolations (i.e., 10 regular and 1 extragrade) had to be calculated for each of the six depths (i.e., 0–0.10, 0.10–0.20,..., 2.50–2.60 m). The results were then back-transformed using

(17)

The union of membership values exceeding 0.5 produced the final composite membership map for each depth. The union of memberships of the 10 regular and one extragrade class to produce a composite map was defined by

(18)

so that the lower limit, z, of maximum membership was set to 0.5. This step in essence is a defuzzification of the FKM classes (Odeh et al., 1992b).

Overlapping Classes and Zones of Confusion
What may be of some additional value is the representation of areas of overlap or uncertainty between classes (i.e., Intragrades). This makes it possible to determine where more information may be appropriate to better understand the nature of the variability or overlap between the two or more classes and where uncertainty about a particular individual's belongingness is not clear. Burrough et al. (1997) derived a confusion index (CI), whereby the confusion of placing an individual site n into one of the two or more fuzzy classes can be determined by

(19)

where µ_maxi is the membership value of the class with the maximum membership for site n and µ_(max-1)i is the second largest membership value for the same site.

The confusion indices for the 210 Edgeroi sites were transformed to normality using the logit transformation

(20)

where t(l) is the transformed CI at a two dimensional spatial location (l), and CI(l) is the confusion index at location l. Punctual ordinary kriging was used for interpolating the t(l) transformed values onto the same 400-m grid as the memberships. Triantafilis et al. (2000) used this approach to interpolate land-suitability memberships in the Edgeroi district. The interpolated values, t(l), were then back-transformed prior to mapping using

(21)

where I(l) is the spatially predicted value of the ln-transformed CI.

	RESULTS AND DISCUSSION

TOP ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
Fuzzy k-Means and Principal Component Analysis
The biplots for the PCA are shown in Fig. 5a . The eigenvalues computed for the correlation matrix of n x p data is shown in Table 2. The first and second components accounted for 44 and 20% of the total variance, respectively. The contribution of each of the attributes to the first two components is shown in Fig. 5b. By projecting vectors onto the component axes individual contributions to the vector can be found. Magnesium, pH, clay (to a lesser extent), and Ca contributed largely to the first component (Fig. 5b), while Org. C contributed most to the second component. No clear separation of the 1419 soil layers was obviously achieved using this approach.

View larger version (32K): [in this window] [in a new window]   Fig. 5. Biplot showing (a) distribution of 1419 soil layers and (b) rays of the 12 attributes shown as lines, on the first two principal components

View larger version (21K): [in this window] [in a new window]   Fig. 6. Biplot showing the position of the 10 layer centroids and 95% density ellipses for (a) Couradda, Moema, and Wewak, (b) Mayfield, Bald Knob, and Togo, and (c) Noelurma, Moplain, Nundi, and Boolcarrol classes along the first two principal components

The 95% density ellipse for the Extragrades (Fig. 5a) indicates that these individuals were generally located across the multivariate plane, although most were located below 0 along Principal Component 1 and in areas of the plane adjacent to the Couradda layers. With respect to the Intragrades these were spread fairly evenly throughout the multidimensional plane.

Fuzzy Layer Classes
Two classes, Togo and Boolcarrol, define the low-lying heavy-clay plains, the landforms including aeolian and water-sorted aeolian clays lying on the fourth alluvial terrace (Fig. 7a and 7b) . In periods of general rain, water covers large areas to leave fine sediment in low places especially in the western part of the district. The Boolcarrol layers, which characterize the B horizon, contain greater accumulations of salts and gypsum than the Togo layers, which are mostly located at the ground surface (Table 3). Layer differentiation is probably due to drainage and weathering. Powell et al. (1991) also found that class memberships on soil transects coincided with drainage status and position in the landscape.

View larger version (132K): [in this window] [in a new window]   Fig. 7. Location of exemplars (square) and members of layer class: (a) Togo, (b) Boolcarrol, (c) Bald Knob, (d) Moplain, (e) Mayfield, (f) Nundi, (g) Wewak, (h) Noelurma, (i) Moema, (j) Couradda, (k) Extragrade, and (l) Intragrade soil layers, as shown in relation to Edgeroi geology and geomorphology. Note that exemplars µi = 1

The pedologic horizons and landscapes are well reflected by the FKME analysis even though the data set analyzed contained no depth weighting or landform data. We attribute this to the variety of attributes that were used.

Extragrades and Intragrades
The fuzzy analysis does not properly resolve the various sandy soil layers of the foothills. Many coarse-textured layers are classed as Extragrades as a result (123 samples from 54 profiles). Most are associated with the Tertiary and Pilliga sandstones (Fig. 7k), probably due to variation of landscape processes. Two hundred-eleven soil layers with memberships of <0.5 in all 10 classes define the Intragrades. These samples are located in 117 profiles in varied localities and suggest that the scoring feature of fuzzy analysis is able to handle transitions between classes satisfactorily. The location of these Intragrade layers and their spatial distribution with respect to the 10 recognized layer classes is shown in Fig. 7l.

Composite Fuzzy Class Maps
The purpose of conventional soil classification is to define relatively homogenous areas of soil, which can be managed or used in the same way. Composite fuzzy class maps (using Eq. [16]–[ 18]) were generated at each depth (i.e., 0–0.10, ..., 2.50–2.60 m) in order to show how the results shown in Fig. 7 can be used for this purpose. From Fig. 8a it is obvious Wewak and Togo layers characterize the topsoil of the central and western areas of the Edgeroi district, respectively. This has implications for soil management and land use. The Wewak layers are known to be prone to dispersion, particularly after heavy rainfall events, whereas the Togo layers are renowned for their shrink–swell behavior (Triantafilis, 1996). As a result the areas where irrigated cotton extends is confined to the location of the Togo layers. Further, the most suitable area of expansion for irrigated cotton production is to the north of the existing irrigated farms.

View larger version (60K): [in this window] [in a new window]   Fig. 8. Composite map showing layer class mapping units at depths of (a) 0 to 0.10, (b) 0.10 to 0.20, (c) 0.30 to 0.40, (d) 0.70 to 0.80, (e) 1.20 to 1.30, and (f) 2.50 to 2.60 m

At all depths, it is also apparent that the Extragrades form readily mappable units. In the topsoil (Fig. 8a and 8b), these units coincide with the areas defined by the Pilliga Sandstone. Apart from this class, however, and with respect to the eastern areas of the district, few layer class units are discernable. This appears to be a function of the more variable nature of the geology and geomorphology on the footslopes of the Nandewar Range (Ward, 1999; McBratney et al., 1991).

Maps of Confusion Index
The increased variability, as described above, is not an indication of increased uncertainty or confusion. This is because the FKME classified membership grades to layers, which in most cases µ_i > 0.5. This is confirmed by the maps of CI shown in Fig. 9a through 9f . In each map, the nonshaded areas indicate where membership to a particular class is high (i.e., µ_i 1) and no confusion exists with its classification (i.e., CI 0.2). Conversely, the increasingly dark shaded areas suggest where membership to two or more classes may be similar and so allocation of the individual to a given class is ambiguous (i.e., CI 0.8), so that in the eastern areas, although there are generally fewer discernible mapping units, there is little confusion about the membership to a particular class.

View larger version (47K): [in this window] [in a new window]   Fig. 9. Maps of confusion index (CI) at depths of (a) 0 to 0.10, (b) 0.10 to 0.20, (c) 0.30 to 0.40, (d) 0.70 to 0.80, (e) 1.20 to 1.30, and (f) 2.50 to 2.60 m

This uncertainty is attributable to the soil forming processes acting in a complicated manner, particularly on the alluvial plains. At the 0- to 0.10-m depth (Fig. 9a) the confusion index is large near the floodplain as it is where three readily identifiable mapping units essentially intersect and include Togo, Wewak, and Mayfield (Fig. 8a). This is similarly the case at 0.70- to 0.80-m depth where the greatest confusion (Fig. 9d) occurs between the four major mapping units, including Togo, Boolcarrol, Nundi, and Moplain, the latter three being essentially subsoil classes (Fig. 8d).

	CONCLUSIONS

TOP ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
This paper provides a step by step account of how the FKM algorithm can be implemented to classify soil information. The use of indices such as FPI and NCE and the derivative J₂(M,C) with respect to the degree of provided objective methods for choosing a suitable number of classes and the degree of overlap between them. The approach therefore removes some of the subjectivity of conventional soil classifications in deciding how many classes exist and how individuals are allocated to them.

The FKME classification of soil layers (i.e., n = 1419) in the Edgeroi district also yielded sensible groupings and supported soil landscape interpretations. The results achieved also reflected current land use patterns and assisted in making rational distinctions where subtle differences occur. The success achieved is attributable to the wide variety of quantitative soil attributes determined (i.e., p = 12; e.g., clay, silt, pH, EC_1:5, Org. C, CaCO₃, Cl, P) in the Edgeroi study area. The use of these attributes allowed distinctions between topsoil and subsoil layers.

Topsoil layers necessarily contain larger amounts of P and Org. C than subsoil horizons (e.g., Wewak and Moema), and subsoil layers in semiarid regions mostly contain larger amounts of soluble salts (e.g., Boolcarrol and Nundi). Moreover, the quantitative textural data allowed for the various sediments of the landscape to be distinguished and emphasized the relation of soil to site, especially on the heavy-clay plains (e.g., Togo and Boolcarrol) and medium clays subject to intermittent and ephemeral runoff (e.g., Wewak and Mayfield).

The FKME classification also provided secondary information (i.e., matrix of n into k = 11 fuzzy classes), which can be used to better represent the soil continuum across the surface and in a soil horizon sense down the profile. Here, transformed memberships to each fuzzy class were interpolated using local kriging at various depths. The final maps produced, which considered only memberships above 0.5, allow the maximum amount of information to be displayed. Use of the confusion index identified areas where more detailed sampling is required to better (i) elucidate mappable units (i.e., eastern half of the Edgeroi district) and (ii) characterize the transitional areas of the landscape (i.e., southwest corner of the Edgeroi area near the Namoi flood plain).

This study confirms the view of Grigal and Arneman (1969) that the potential of numerical methods, such as FKME analysis, lies in their ability to summarize large amounts of data. The results are also consistent with the ability of numerical methods to account for the polythetic nature of soil information.

	ACKNOWLEDGMENTS

 
The authors are grateful to the Australian Cotton Research and Development Corporation for providing the senior author with a post-graduate scholarship and the provision of research monies to carry out this work. Particular thanks are due to the journal's referees who materially improved this paper.

Received for publication April 23, 1999.

	REFERENCES

TOP ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 

• Aitchison, J. 1986. The statistical analysis of compositional data. Chapman Hall, London.
• Beech, T.A., and S. McLeod. 1984. An autoanalyser method for the determination of chloride in soil extracts. Proc. of the Nat. Soils Conf. of the Aust. Soc. of Soil Sci. Inc. Brisbane, Australia.
• Bezdek, J.C. 1974. Numerical taxonomy with fuzzy sets. J. Math. Biol. 1:57–71.
• Bezdek, J.C. 1981. Pattern recognition with fuzzy objective function algorithms. Plenum Press, New York.
• Burgess, T.M., and R. Webster. 1984. Optimal sampling strategies for mapping soil types. I. Distribution of boundary spacings. J. Soil Sci. 34:641–654.
• Burrough, P.A., P.F.M. Van Gaans, and R. Hootsmans. 1997. Continuous classification in soil survey: Spatial correlation, confusion and boundaries. Geoderma 77:115–135.[ISI]
• Colwell, J.D. 1963. The estimation of the phosphorus fertilizer requirements of wheat in southern New South Wales by soil analysis. Aust. J. Exp. Agric. Anim. Husb. 3:190–197.
• Coventry, R.J., and D.E.R. Fett. 1979. A pipette and sieve method of particle size analysis and some observations on its efficacy. CSIRO Australia Div. of Soils, Div. Rep. 38. CSIRO Australia, Canberra.
• De Bruin, S., and A. Stein. 1998. Soil–landscape modelling using fuzzy c-means clustering of attribute data derived from a Digital Elevation Model (DEM). Geoderma 83:17–33.[ISI]
• De Gruijter, J.J., and A.B. McBratney. 1988. A modified fuzzy k-means method for predictive classification. p. 97–104. In H.H. Bock (ed.) Classification and related methods of data analysis. Elsevier, Amsterdam.
• Dunn, J.C. 1974. A fuzzy relative of the isodata process and its use in detecting compact, well seperated clusters. J. Cybernetics 3:22–57.
• Grigal, D.F., and H.F. Arneman. 1969. Numerical classification of some forested Minnesota Soils. Soil Sci. Soc. Am. Proc. 33:431–438.
• Holmgren, G.G.S., R.L. Juve, and R.C. Geschwender. 1977. A mechanically controlled variable rate leaching device. Soil Sci. Soc. Am. J. 41:1207–1208.[Abstract/Free Full Text]
• Loveday, J., and R. Reeve. 1974. Carbonate determination. Methods for analysis of irrigated soils. p. 131–134. In J. Loveday (ed.) CAB Technical Communication 54. CAB International, Wallingford, UK.
• McBratney, A.B., and J.J. De Gruijter. 1992. A continuum approach to soil classification and mapping: Classification by modified fuzzy k-means with extragrades. J. Soil Sci. 43:159–175.
• McBratney, A.B., J.J. De Gruijter, and D.J. Brus. 1992. Spatial prediction and mapping of continuous soil classes. Geoderma 54:39–64.
• McBratney, A.B., G.A. Hart, and D. McGarry. 1991. The use of region partitioning to improve the representation of geostatistically mapped soil attribute. J. Soil Sci. 42:249–263.
• McBratney, A.B., and A.W. Moore. 1985. Application of fuzzy sets to climatic classification. Agric. For. Meteorol. 35:165–185.
• McBratney, A.B., and R. Webster. 1981. Spatial dependence and classification of soil along a transect in northeast Scotland. Geoderma 26:63–82.
• McDonald, R.C., R.F. Isbell, J.G. Speight, J. Walker, and M.S. Hopkins. 1984. Australian soil and land survey field handbook. Inkata Press, Melbourne.
• McGarry, D., W.T. Ward, and A.B. McBratney. 1989. Soil studies in the Lower Namoi Valley-Methods and data 1: The Edgeroi data set. Division of Soils, CSIRO Australia, Canberra.
• Merry, R.H., and L.R. Spouncer. 1988. The measurement of carbon in soils using a microprocessor-controlled resistance furnace. Comm. Soil Plant Anal. 19:707–720.
• Moore, A.W., and J.S. Russell 1967. Comparison of coefficients and grouping procedures in numerical analysis of soil trace element data. Geoderma 1:139–157.
• Odeh, I.O.A., A.B. McBratney, and D.J. Chittleborough. 1992a. Soil pattern recognition with fuzzy c-means: Application to classification and soil landform interrelationships. Soil Sci. Soc. Am. J. 56:505–516.[Abstract/Free Full Text]
• Odeh, I.O.A., A.B. McBratney, and D.J. Chittleborough. 1992b. Fuzzy c-means and kriging for mapping soil as a continuous system. Soil Sci. Soc. Am. J. 56:1848–1854.[Abstract/Free Full Text]
• Ohashi, Y. 1984. Fuzzy clustering and robust estimation. p. 18–21. In 9th meeting SAS Users Group International. Hollywood Beach, FL.
• Powell, B., A.B. McBratney, and D.A. McLeod. 1991. The application of fuzzy classification to soil pH profiles in the Lockyer valley, Queensland, Australia. Catena 18:409–420.
• Powell, B., A.B. McBratney, and D.A. McLeod. 1992. Fuzzy classification of soil profiles and horizons from the Lockyer valley, Queensland, Australia. Geoderma 52:173–197.
• Prescott, J.A. 1944. A soil map of Australia. CSIRO, Australia, Bull. 177. CSIRO Australia, Canberra.
• Roubens, M. 1982. Fuzzy clustering algorithms and their validity. Eur. J. Oper. Res. 10:294–301.
• Ruspini, E.H. 1969. A new approach to clustering. Inf. Control 15: 22–32.
• Stannard, M.E., and I.D. Kelly. 1977. The irrigation potential of the lower Namoi valley. Water Resources Commission, New South Wales, Australia.
• Stoer, J., and R. Bulirsch. 1980. Introduction to numerical analysis. Springer-Verlag, New York.
• Trangmar, B.B., R.S. Yost, and G. Uehara. 1985. Applications of geostatistics to spatial studies of soil properties. Adv. Agron. 38: 45–94.
• Triantafilis, J. 1996. Quantitative assessment of soil salinity in the lower Namoi valley. Ph.D. diss. Univ. of Sydney, New South Wales, Australia.
• Triantafilis, J., W.T. Ward, and A.B. McBratney. 2000. Continuous land suitability assessment in the lower Namoi valley. Aust. J. Soil Res. 39:273–289.
• Tucker, B.M. 1974. Laboratory procedure for cation exchange measurements in soils. CSIRO Division of Soils, Technical Paper 23. CSIRO Australia, Canberra.
• Ward, W.T. 1999. Soils and landscapes near Narrabri and Edgeroi, New South Wales, with data analysis using fuzzy k-means. CSIRO Div. of Soils Div. Report, Melbourne.
• Ward, A.W., W.T. Ward, A.B. McBratney, and J.J. de Gruijter. 1992. MacFUZZY-A user friendly program for data analysis by generalized fuzzy k-means on the Macintosh. CSIRO Div. of Soils, Div. Rep. 116. CSIRO Australia, Canberra.
• Webster, R., and P.A. Burrough. 1974. Multiple discriminant analysis in soil survey. J. Soil Sci. 25:120–136.
• Zadeh, L.A. 1965. Fuzzy sets. Inf. Control 8:338–353.

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