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    Soil & Water Res., 8, 2013 (1): 1325

    Digital Soil Mapping from ConventionalField Soil Observations

    J BALKOVI 1,2, Z RAMPAEKOV3, V HUTR 4,

    J SOBOCK4and R SKALSK 1,4

    1International Institute for Applied Systems Analysis , Laxenburg, Austria ; 2Department

    of Soil Science, Faculty of Natural Sciences, Comenius University in Bratislava, Slovak

    Republic; 3Department of Geography and Regional Development, Faculty of Natural Sciences,Constantine the Philosopher University in Nitra, Slovak Republic; 4Soil Science

    and Conservation Research Institute, Bratislava, Slovak Republic

    Abstract

    B J., R Z., H V., S J., S R. (2013): Digital soil mapping from conven-tional field soil observations.Soil & Water Res., 8: 1325.

    We tested the performance of a formalized digital soil mapping (DSM) approach comprising fuzzy k-means (FKM)

    classification and regression-kriging to produce soil type maps from a fine-scale soil observation network in Riovce,Slovakia. We examine whether the soil profile descriptions collected merely by field methods fit into the statisticalDSM tools and if they provide pedologically meaningful results for an erosion-affected area. Soil texture, colour,carbonates, stoniness and genetic qualifiers were estimated for a total of 111 soil profiles using conventional fieldmethods. Te data were digitized along semi-quantitative scales in 10-cm depth intervals to express the relativedifferences, and afterwards classified by the FKM method into four classes AD: (i) Luvic Phaeozems (Anthric),(ii) Haplic Phaeozems (Anthric, Calcaric, Pachic), (iii) Calcic Cutanic Luvisols, and (iv) Haplic Regosols (Calcaric). oparameterize regression-kriging, membership values (MVs) to the above AD class centroids were regressed againstPCA-transformed terrain variables using the multiple linear regression method (MLR). MLR yielded significantrelationships withR2ranging from 23% to 47% (P< 0.001) for classes A, B and D, but only marginally significant forLuvisols of class C (R2= 14%,P< 0.05). Given the results, Luvisols were then mapped by ordinary kriging and the

    rest by regression-kriging. A leave-one-out cross-validation was calculated for the output maps yielding R2

    of 33%,56%, 22% and 42% for Luvic Phaeozems, Haplic Phaeozems, Luvisols and also Regosols, respectively (allP< 0.001).Additionally, the pixel-mixture visualization technique was used to draw a synthetic digital soil map. We concludethat the DSM model represents a fully formalized alternative to classical soil mapping at very fine scales, even whensoil profile descriptions were collected merely by field estimation methods. Additionally to conventional soil maps itallows to address the diffuse character in soil cover, both in taxonomic and geographical interpretations.

    Keywords: field soil description; fuzzy k-means; pedometrics; regression-kriging; terrain

    Digital soil mapping (DSM) has become popular

    for producing maps of soil classes and propertiesfrom spatially explicit soil inventories and from

    auxiliary landscape data (MB et al. 2003),

    bridging gaps between discrete soil maps and thecontinuous nature of soil cover (B et

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    al. 1997). DSM integrates many statistical andgeo-information tools and concepts, includingsupervised and unsupervised classifications (DG & MB 1988; B etal. 1997; C & G 2002; H et al.2004b; L 2005; Z et al.2011),geostatistics (W & O 2007), environ-mental correlations and scorpan-based mo dels(MK & R 1999; MB et al.2003). A thorough review of DSM methods andtheir applications in soil science was publishedby MB et al. (2003).

    he DSM techniques can represent a formal-ized alternative to the conventional soil mapping,where both the soil classification and mapping arehandled numerically. he soil profiles are classified

    in terms of taxonomic distance or membershipto centroids of soil classes, enabling more soil

    variables to be addressed simultaneously (M-B & D G 1992; Z et al. 2001;C & G 2002). he fuzzy k-means method(FKM, B et al.1984) has recently becomeespecially popular for classification purposes asit enables to represent a continuous characterand uncertainty in mapped soils. Once classified,the soil profile partitions are then interpolatedinto membership maps, which are used instead

    of conventional soil maps. Increased availabilityof remote sensing and GIS data has promotedthe regression-kriging method (O et al.1994,1995) as a generic interpolation tool for the map-ping purposes (H et al.2004b). hat is thereason why we chose regression-kriging and FKMas major components in our DSM model. Someauthors emphasize co-kriging as a superior methodfor mapping undersampled soil properties whenauxiliary covariates are available (K et al.2002; P & B 2006). However, thismethod is more cumbersome and yields only a

    small benefit when soil and auxiliary variables areweakly correlated (A & D M 1987).

    Soil profile surveys have always been the basicstrategy for soil type mapping regardless of whetheror not the maps were produced with the use ofDSM. Although a lot of attention has been paidto coupling of DSM with various soil informationsystems (MB et al. 2003), only few ap-plications used soil profile descriptions gatheredsolely by empirical field obser vation methods(e.g. C & G 2002). his approach in-

    volves several implications compared to measuredanalytical data. Firstly, the horizon properties

    are usually described using various qualitative orsemi-quantitative scales (e.g. S etal. 2002), where the continuous soil variables areranked along discrete empirical categories. hisranking may negatively affect numerical classifica-tion if the attribute space is not correctly designed.Secondly, the resultant numerical partition maynot be fuzzy enough to provide meaningful soil-terrain relationships.

    In this article we add to the above context bytesting the performance of a simple DSM approachto produce soil type maps from a network of com-mon field profile descriptions from the study areain Riovce, Slovakia. We also examine whetherthe standard morphological descriptions compris-ing the qualitative and semi-quantitative horizon

    properties collected in the field fit adequately intothe statistical DSM tools. Additionally, we evaluateif this approach provides pedologically meaning-ful outputs for very fine scales in erosion-affectedlandscape both in taxonomical and geographicalinterpretations.

    MATERIAL AND METHODS

    Model description. he presented DSM model

    (Figure 1) integrates (i) digitizing of soil profileproperties, (ii) unsupervised FKM classificationof soil profiles, (iii) auxiliary terrain data prepara-tion, and (iv) kriging of soil membership maps.

    As concluded by B et al.(1997) andD G et al.(1997), the FKM classificationcan produce meaningful soil typological results.It partitions soil profiles into the given kclasses,where profile properties in the class centre arerepresented by centroids. he centroid membership

    values MV(mij) follow the criteria given by Eq. (1):

    (1)

    where:n total number of profilesk number of classes

    Several authors have suggested hybrid interpola-tions combining kriging and linear regression withterrain variables as powerful methods for mappingsoil classes when soil distribution was closely cor-related with terrain (e.g. O et al. 1994, 1995;G 1999; H et al.2004a). Among

    the hybrid interpolation techniques, regression-kriging (O et al. 1994, 1995) was identified

    k

    jni

    ijijij kjmnimm1 1

    ,...,1,0>;,...,1,1;1.0

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    as the most superior method by K et al.(1995) and B et al.(2000). It couplesMultiple Linear Regression (MLR) with kriging,as given by Eq. (2):

    (2)

    where:mj(s0) MV of classjat a non-sampled locations0ql(s0) l-thpredictor at locations0l parameter of predictor lin MLR

    p number of predictors used for soil classjj(si) MLR residual at a sampled locationsiwi weight of the kriging operator

    he weights, wi, depend on the distances betweenthe observations and the predicted location s

    0

    and spatial relationships between sampled dataaround the predicted location. While geographicdistances are here determined byXand Ycoordi-nates as Euclidean distance, spatial relationshipsare described by the experimental semivariogramfrom values of Eq. (3) as stated in B &W (1980):

    (3)

    where:(h) semivariance

    h separation lag-distance between locationssiandsi+h

    (si), (si+h) MLR residuals at locationssiandsi+hd(h) number of pairs at any separation distance h

    he semivariogram is a quantitative measureof how the semivariance between the sampledpoints is reduced as separation distance decreases,and it can be modelled by some of the authorisedsemivariogram equations (cf. W & O- 2007). he weighting factors of Eq. (2) areestimated by solving the kriging equations (B- & W 1980). Regression-kriging is apowerful method when the correlation betweensoil and terrain variables is high and the MLRresiduals are spatially correlated (cf. H etal. 2004a). When MVs do not yield any signifi-cant linear relationship with terrain predictors,the regression-kriging interpolation can then be

    Figure 1.Scheme of the digital soil mapping algorithm, including the fuzzy k-mean classification of soil profiles,PCA transformation of terrain predictors and regression-kriging of soil membership maps

    p

    l

    n

    iijilj sswsqsm

    1 11 )()()()( 000

    d

    iii hss

    hdh

    1

    2)()(

    )(2

    1)(

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    replaced by ordinary kriging by omitting the MLRcomponent from Eq. (2).

    Te transformation of terrain predictors by Prin-cipal Component Analysis (PCA) was suggested byH et al. (2004a) to reduce multicollinearity inMLR. Terefore the Principal Components (PCs) arehere considered as complex terrain variables whichare uncorrelated and standardised and can thereforebe used instead of the original terrain predictors(e.g. G et al.2001; H et al. 2004a).

    Study area and soil sampling. he study areacovers approximately 37 ha of arable land in thecadastral area of Riovce in Slovakia (Figure 2).he soils here are mainly Haplic Phaeozems (An-thric, Calcaric), Luvic Phaeozems (Anthric), Calcic,Cutanic Luvisols and Haplic Regosols (Calcaric),

    which are significantly affected by erosion.he soil cover was studied using a grid sampling

    layout composed of parallel downslope transects,trying to ensure that all soil elements are repre-sented in the grid (Figure 2). he between-sampledistances in transects were slightly shorter thandistances between transects: the inter-sampledistance was 70 m on average. A total of 111 soilprofiles were sampled using the hand auger equip-ment. his study was performed by the same re-searchers to minimize the inter-observer variability.

    he following profile properties were estimatedusing the field handbook by S et

    al. (2002): (i) horizon nomenclature, comprisingmaster horizons and other modifiers, and horizonthickness (in cm), (ii) soil matrix colour in themoist state using the Munsell notation, (iii) tex-ture class by the field hand test, ( iv) carbonatesby the effervescence field test, and (v) stoninessin vol. %.All genetic horizons were sampled upto a maximum of 100 cm depth.

    Digitizing of soil profile properties. he soilhorizon data were digitized using the followingrules: (i) Munsell colours were converted into theCIELab coordinates (COLX, COLY, and COLZ)using the method published by M andA (1985), (ii) soil texture estimates wereconverted into central sand and clay contents(SAND, CLAY in %) of the respective texture

    classes of the USDA triangle, (iii) carbonate esti-mates (CARB) were placed along a 1 to 5 ordinalscale; the numbers stand for non-effervescent,

    very sl ightly ef fervescent , sl ightly ef fervescent,strongly effervescent, and violently effervescentsoils, (iv) stoniness remained in the percentage(SKEL), and (v) soil horizons were rated by theintensity of illuvial silica clay accumulation (LUV)and mollic properties (MOL), which are two mainprocesses in the studied soils, using the followingordinals: 1 not applicable; here the layer does

    not constitute a part of either A or B horizon,2 weak; here the layer constitutes a part of A or

    Figure 2. Sketch map of the study area (Riovce, Slovakia) and location of soil profiles of the experiment

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    B horizon, but the horizon does not meet all thecriteria for mollic Am or luvic Bt horizon, and3 intense; here the layer constitutes a part ofthe Am or Bt horizon. he above variables weredigitized by 10-cm depth intervals to gather the

    vertical profile strat if ication. he soil variableswere distinguished by a depth interval and a prop-erty name: e.g. 10_SAND stands for sand contentin the 010 cm layer. As a result, 89 variables wereconstructed for each soil profile (luvic propertieswere omitted for the topmost soil layers). heabove digitizing avoids too many zero values inthe input data, which could cause deviations inthe FKM classification.

    Auxiliary terrain variables. he digital eleva-tion model (DEM) was constructed in 5-m resolu-

    tion from detailed altimetry measurements usingthe RBF technique in Geostatistical Analyst forArcGIS software ( J et al. 2001). healtimetry data were measured by Leica AX900GG GNSS receiver with real-time correction forsub-cm precise positioning provided by the SlovakSpace Observing Service. he DEM resolutionreflects both positional accuracy and density ofmeasurements. he following terrain variableswere calculated from DEM: (i) slope steepnessin degrees (SLP), (ii) planar and profile curva-

    ture (PLANCURV, PROFCURV; cf. M et al.1991), (iii) overland flow accumulation in metrescalculated from filled DEM (FLW, 3 3 kernel,cf. M 2002), and (iv) topographic wet-ness index (WI, cf. W & G 2000).Detailed information concerning the above terrain

    variables is presented in able 1.PCA was calculated for the terrain variables in

    SAISICA software (StatSoft Inc. 2003), thusaiming to reduce collinearity and to extract com-posite terrain gradients as mapping predictors.FLW and SLP variables were log-transformed prior

    to PCA. Hereafter, the PCA factor coordinates of

    cases for PC16 were considered as DSM predic-tors (cf. H et al. 2004a).

    Fuzzy k-means classification. he FKM classifi-cation was calculated in FuzME software (M& MB 2002) using diagonal distance,number of classes k= 4, and fuzziness coefficient = 1.5. he fuzziness coefficient was optimizedas suggested by MB and M (1985).he number of classes respects the number ofsoil typological units recognised in the study areaduring the soil survey. Centroids were interpretedaccording to WRB nomenclature (FAO-ISRIC-ISSS 2006).

    In addition, PCA and Detrended CorrespondenceAnalysis (DCA) were calculated for soil profiledata in SAISICA and CANOCO ( B

    & 2002) software to explore inner vari-ability in the profile data matrix.

    Kriging interpolation. he fuzzy MVs wereinterpolated using the regression-kriging Eq. (2).However, ordinary kriging (B & W- 1980) was used when no significant linearrelationships were observed between MVs andterrain predictors. Parameterization of regression-kriging included (i) MLR analysis between MVsand PC16 terrain predictors at sampled loca-tions independently for each soil centroid; where

    coefficients and residuals were calculated,and (ii) semivariance analysis and semivariogrammodel estimation with the residuals. We used5 5 neighbourhood averaging for PC1-6 ras-ters in order to obtain balanced predictor val-ues at the sampled locations, and a conventionalsemivariogram analysis was performed with MVswhen ordinary kriging was used. Kriging weightingfactors for both ordinary and regression krigingwere estimated by solving the kriging equations.All the analyses were calculated in R programme(www.R-project.org) using the following choices:

    Ordinary Least Squares (OLS) for MLR and punc-

    able 1.Descriptive statistics of terrain variables

    Mean Median Min. Max. SD Skewness Kurtosis

    DEM (m) 195 198 160 223 21.5 0.18 1.47

    SLP () 5.02 4.47 0.13 15.03 3.39 0.46 0.73

    PLANCURV (m1) 0.0005 0.0073 1.664 0.785 0.171 1.37 8.15

    PROFCURV (m1) 0.0010 0.0106 1.081 2.277 0.183 2.08 18.06

    FLW (m) 18.7 8.0 0.0 100 27.1 2.10 3.42

    WI 6.44 6.38 4.24 10.14 0.96 0.37 0.01

    SD standard deviation

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    tual technique for kriging. he exponential modelof Eq. (4) was used to calculate the semivariogram(W & O 2007):

    (4)

    where:c0 error (nugget) variancec1 so-called partial sill variancer lag distance

    he DSM algorithms were run over PC1-6 terrainpredictors independently for each soil type to renderthe membership maps with 5m cell resolution. Giventhe averaging-to-the-mean effects of interpolation,the assumption of composite variables given byEq. (1) was violated in the output MV maps. his

    error was corrected by the equalizing variance trans-formation with respect to the original MV matrix,and each voxel of the transformed MV rasters wasafterwards rescaled so that the sum of its MVs wasequal to one.

    A cross-validation leave-one-out approach wasused to validate the DSM model. It uses a loopfunction over observation data leaving a profileout of the mapping analysis when a prediction iscalculated for that particular profile. Pearsons cor-relation coefficients (r) and the linear regressionmodel withR2andF-testPvalues were used to testthe significance of such predictions.

    We used the pixel-mixture technique (DG et al.1997) to visualize the soil typedistribution using the algorithm published forR programme at http://spatial-analyst.net/wiki/index.php?title=Uncertainty_visualization.

    RESULTS AND DISCUSSION

    Fuzzy k-means classification

    Te ordinations of soil profiles (n= 111) and theirproperties (m= 89) in attribute space were analysedusing PCA (Figure 3). An attribute space of linearordinations is appropriately configured when profileattributes are linearly related to principal components.

    We examined this assumption by DCA as introducedby B and (2002), who suggestedthe maximum length of gradient expressed in SD ofthe attribute turnover along the ordination axis to bea measure of data heterogeneity. Given this measure,an input data matrix is suitable for linear ordinationswhen the DCA gradient length is less than 4 SD.Te value of 0.95 SD in our analysis indicates thatthe input matrix is properly shaped for both PCAand FKM analyses. Additionally, we do not expectany severe deviations in PCA and FKM calculationscaused by too many zero values in the input matrixsince this was avoided with data digitizing.

    )/3exp(1)( 10 rhcch

    Figure 3. Principal Component Analysis (PCA) scatter plot of the soil profile data projected at the first two prin-cipal components (40.4% of the total eigenvalue): (a) factor coordinates of attributes, and (b) factor coordinates of

    profiles; shaded areas outline where the fuzzy k-means (FKM) class maxima are plotted; PCA analysis was basedon correlation; notation of soil variables: Depth_property

    (a)

    PC 1: 26.24% PC 1: 26.24%

    PC2:14.18%

    1.0 0.5 0.0 0.5 1.0 15 10 5 0 5 10 15

    1.0

    0.5

    0.0

    0.5

    1.0

    15

    10

    5

    0

    5

    10

    15

    (b)

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    Following the resultant ordination in the PC1-2quadrate (Figure 3) we judge that semi-quantitativeand ordinal profile data demonstrate quite a con-tinuous ordination pattern which conditions properFKM classification. Shaded areas in Figure 3boutline profiles which have their MV maxima inthe particular FKM classes. It is quite clear that

    profiles with their MV maxima in class A consti-tute the most homogeneous sample, whereas theother classes, and especially classes C and D, areinternally more heterogeneous.

    he FKM analysis yields four class centroids(AD), which were interpreted as Luvic Phaeo-zems (Anthric), Haplic Phaeozems (Anthric, Cal-

    Figure 4. Class centroid details; carbonate content (CARB): 1 non-effervescent, 2 very slightly effervescent,3 slightly effervescent, 4 strongly effervescent, 5 violently effervescent; mollic horizon features (MOL):1 without, 2 weak (A, not Am), 3 intense (Am); luvic horizon features (LUV): 1 without, 2 weak (B(t), not Bt),

    3 intense (Bt); clay content estimate from textural class (CLAY) in %; sand content estimate from textural class(SAND) in %; stoniness estimate (SKEL) in %

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    caric, Pachic), Calcic Cutanic Luvisols, and Haplic

    Regosols (Calcaric), respectively. Additional infor-mation needed to support the classification wasprovided by the Soil Science and ConservationResearch Institute in Bratislava, Slovakia, fromauxiliary data sources. Vertical distributions of thestudied profile properties in particular centroidsare illustrated in Figure 4. Whereas class A and Ccentroids represent more or less climax soils, theclass B centroid depicts colluvic soils with topsoilmaterial accumulated via tillage-induced erosion,and the class D centroid comprises strongly erodedsoils with only shallow remnants of mollic andluvic horizons. Apparently, the soil erosion andaccumulation are fundamental forces affectingthe taxonomical variety of soils in this study area.

    Te MVs contain a significant portion of fuzzi-ness and the overall confusion index (B etal.1997) averaged 0.62. When aggregated by classmaxima, the average confusion index values were 0.66,0.47, 0.79 and 0.62 for A to D classes, respectively.

    Te highest confusion was calculated for Luvisols,

    which represent a minority soil type in the studyarea since only 14 out of 111 soil profiles were clas-sified as Luvisols during the field survey. In contrast,Phaeozems of class B are clearly determined by itscentroid as they show the lowest confusion index.

    Composite terrain gradients

    o a certain extent, the terrain gradients werecollinear since they were all derived from DEM.In particular, DEM yi elds significant Pearsonscorrelations with FLW, PROFCURV, SLP and WI(r = 0.08, 0.30, 0.11 and 0.07, respectively, all

    P< 0.01). he overland flow accumulation (FLW)significantly correlates with all the other variables:r = 0.32, 0.18, 0.28 and 0.30 for PLANCURV,PROFCURV, SLP and WI, respectively. Finally,PLANCURV significantly correlates with PROF-CURV (r= 0.28) and WI (r= 0.41), and WI

    able 3.Results of multiple linear regression method (MLR) between PC1-6 terrain predictors and log-transfor-

    med MVs of classes A to DRegressioncoefficient

    Class A P Class B P Class C P Class D P

    0(intercept) 1.441 < 0.001 2.109 < 0.001 1.836 < 0.001 1.890 < 0.001

    1(PC1) 0.071 < 0.172 0.365 < 0.001 0.127 < 0.015 0.375 < 0.001

    2(PC2) 0.243 < 0.001 0.201 < 0.017 0.088 < 0.159 0.164 < 0.017

    3(PC3) 0.019 < 0.805 0.472 < 0.001 0.144 < 0.057 0.229 < 0.006

    4(PC4) 0.149 < 0.170 0.052 < 0.717 0.063 < 0.554 0.118 < 0.307

    5(PC5) 0.148 < 0.164 0.559 < 0.001 0.118 < 0.264 0.373 < 0.001

    6(PC6) 0.364 < 0.255 0.568 < 0.182 0.030 < 0.925 0.176 < 0.606

    R2 0.233 < 0.001 0.466 < 0.001 0.136

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    yields significant correlat ions with PROFCURVat r= 0.23 and SLP at r= 0.63.

    Because of the established collinearity, PCA wasused to calculate new, uncorrelated terrain vari-ables. he factor coordinates for PC1 to 6, whichare linear combinations of the original terrain

    variables (able 2), are considered new compositeand uncorrelated terrain variables inputting theDSM model. A contribution of PC1-6 to the totalPCA matrix eigenvalue is also shown in able 2.

    Kriging of membership maps

    he coefficients and residuals of MLR be-tween log-transformed MVs and PC1-6 predictors

    of Eq. (2) were calculated using the OLS method.All the MLR models were statistically significant at

    P< 0.05 (able 3), however, the explained variancestrongly varied with soil classes: R2was between14% and 47%. Haplic Phaeozems of class B andHaplic Regosols of class D, which are essentiallyaffected by erosion and accumulation processes,respond to terrain variables better than the others(R2= 0.47 and 0.46 for class B and D, respective-ly). In contrast, Cutanic Luvisols of class C showonly a weak, although still significant response(R2= 0.14). he spatial distribution of Luvisols isexplained rather by local outcrops of clay sedimentsthan by terrain forces in the study area.

    he class AD residuals had almost normaldistributions , although they were not all perfectly

    Figure 5. Exponential semivariogram models of MV (solid line) and their residuals (dashed line): (a) class A Lu-vic Phaeozems, (b) class B Haplic Phaeozems, (c) class C Cutanic Luvisols, and (d) class D Haplic Regosols

    Distance (m)

    Semivariance

    Semivarian

    ce

    Distance (m)

    0 50 150 250 350 450

    0.055

    0.050

    0.045

    0.040

    0.035

    0.030

    0.025

    0.020

    0.015

    0.010

    0.005

    0.0

    0 50 150 250 350 450

    0 50 150 250 350 4500 50 150 250 350 450

    0.030

    0.025

    0.020

    0.015

    0.010

    0.005

    0.0

    0.09

    0.08

    0.07

    0.06

    0.05

    0.04

    0.03

    0.02

    0.01

    0.0

    0.07

    0.06

    0.05

    0.04

    0.03

    0.02

    0.01

    0.0

    (a) (b)

    (c) (d)

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    Gaussian. he Kolmogorov-Smirnov Dtest was0.127 (P< 0.15), 0.222 (P< 0.01), 0.101 (P< 0.2)and 0.204 (P< 0.01) for classes A to D respectively.Spatial distribution of MVs and their MLR residualswas analysed using semivariograms and exponentialsemivariogram models of Eq. (4). All the studiedsoil classes demonstrate a slightly different spatialdistribution. Firstly, the B class MVs (black circlesin Figure 5b) yield an almost unbounded semi-

    variogram indicating a spatial trend, which waseffectively removed when terrain variables wereincluded as indicated by the residual semivari-ogram (empty circles in Figure 5b). Both partialsill (c1) and range (r) values decreased when theresiduals alone were analysed. Secondly, althoughthe D class MVs correspond quite closely with the

    terrain variables, they show only a very short rangeof spatial autocorrelation, which is also visible inits residuals (Figure 5d). his is because Regosolscreate only small and scattered patches ratherthan solid soilsc apes. hirdly, the A cla ss MVs

    yield an obvious semivariogram (Figure 5a, solid

    line), which again has a shorter range and lowersill when residuals alone were analysed (Figure 5a,dashed line). Luvic Phaeozems, as typical climaxsoils in this region, create wider zones where soilprofiles were strongly autocorrelated, but were lessbounded by terrain dynamics. Finally, the C classMVs demonstrate a semivariogram similar to thelatter one. However, there is no significant differ-ence between MVs and their residuals (Figure 5c)since the terrain variables do not capture enoughof the MV spatial variation. his is also why weused ordinary kriging instead of regression-krigingfor C class MV mapping.

    he classes AD were interpolated into griddedmembership maps with 5-m cell size. he fourmembership maps (Figures 6ad) were rescaled

    as described in the methodology section to re-store the assumption of composite variables. heresultant pictures concur with f ield experiences.Luvic Phaeozems (class A) and Cutanic Luvisols(class C) occur especially at plateau parts of thestudy area where they represent the remnants of

    Figure 6. Digital membership maps of fuzzy k-means(FKM) classes: (a) class A Luvic Phaeozems (Anthric),(b) class B Haplic Phaeozems (Anthric, Calcaric,Pachic), (c) class C Calcic Cutanic Luvisols, (d) class

    D Haplic Regosols (Calcaric), (e) synthetic digital soilmap constructed by a pixel-mixture technique

    Membershipval ues

    Membershipval ues

    Membershipvalues

    Membershipvalues

    Membershipval ues

    0.000.100.110.190.200.290.300.380.390.48

    0.490.58> 0.58

    0.000.170.180.260.270.330.340.420.430.510.520.60> 0.60

    0.000.050.060.160.170.270.280.380.390.50

    0.510.64> 0.64

    0.000.090.100.140.150.210.220.270.280.350.360.45> 0.45

    class Aclass Bclass Cclass D

    (a) (b)

    (c) (d)

    (e)

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    a climax soil cover. Haplic Phaeozems of class Brepresent colluvial soils spreading along valleys,whereas Haplic Regosols of class D comprise erosiveremnants of the former class A or C soils. Diffuse

    transitions between the four soil classes are visual-ized via the pixel-mixture method highlighted inFigure 6e. his kind of synthetic map can substi-tute for conventional soil maps and, moreover, itprovides an intuitive picture of diffuse soil cover.

    he four class membership maps were validatedagainst the original MVs using the cross-validationapproach (able 4). he DSM model performedmost effectively with class B and D MVs (R2= 56%and 42%, respectively, both P< 0.001). It per-formed less effectively, although still significantly

    with class A and C MVs (with R

    2

    = 33% and 22%,respectively, bothP< 0.001).

    CONCLUSIONS

    he presented DSM model comprises FKM clas-sification and kriging of membership maps withthe use of terrain predictors. he FKM methodrepresents a formalized approach to soil classifica-tion which addresses the continuous character ofsoil objects. As shown above, the digitization of

    soil horizon properties gathered by way of con-ventional field observations provided reliable soi lclasses and MVs continuous enough to be spatiallyinterpolated into membership maps. Resultantdigital soil maps demonstrate a rational pictureof the soil type distribution, which concur withexpert field experience.

    he DSM method was especially powerful forerosion-affected soil B and D classes where terrain

    variables significantly improved mapping perfor-mance. With a decreasing correlation between

    MVs and terrain variables, there was accompa-nying deterioration in DSM model performance.

    he kriging component became more importantfor the spatial mapping of classes A and C, whichwere here located at plateau landscapes . Moreover,Cutanic Luvisols of class C are locally conditioned

    by the presence of clay stratum rather than theterrain alone, which was not considered by theDSM model. his is why the regression-kriginginterpolation performed no better than the ordi-nary kriging method in this case.

    Although the DSM model validity between 22 and56% (P< 0.001) is not too high, it is worth notingthat this study area is extremely heterogeneousdue to the changes in erosion and accumulationprocesses over small distances. his is not fullycaptured even by this fine-scale sampling.

    he spatial interpolation of MVs violates thecompositional character of the fuzzy partitionassumed by Eq. (1). Although this condition wasformally restored by two-step rescaling of the re-sultant membership maps, this remains a methodi-cally suboptimal solution which could potentiallybenefit from the compositional kriging componentintroduced by W and D G (2001),once it is implemented to regression-kriging.

    We conclude that the DSM model represents acompletely formalized alternative to classical soilmapping at very small scales, even when the soil

    profile descriptions were collected merely by fieldestimation methods. Additionally to conventionalsoil maps, this model enables us to address thediffuse characteristics in soil cover, both in thetaxonomic and geographical meanings. Here wemust stress that the fine-scale soil inventoriesquickly emerge as a result of precise farming sup-port or environmental assessments at a municipallevel. Increasing demands for soil information canbe satisfied by local soil inventories supplying asignificant and ever growing pool of soil informa-

    tion. Given that perspective, the coupling of suchfield surveys with remote sensing and GIS infor-

    able 4.Cross-validation results; the relationships between original and modelled MVs were tested using linearregression (N = 111)

    Class SU Model r R2 P

    A Luvic Phaeozems (Anthric) Regression-Kriging 0.58 0.33 < 0.001

    B Haplic Phaeozems (Anthric, Calcaric, Pachic) Regression-Kriging 0.75 0.56 < 0.001

    C Calcic Cutanic Luvisols Ordinary Kriging 0.46 0.22 < 0.001

    D Haplic Regosols (Calcaric) Regression-Kriging 0.65 0.42 < 0.001

    R2 coefficient of determination;P probability forF-test value; r Pearsons correlation coefficient

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    mation at fine scales will support the generationof important soil maps for farmers and executives.

    Acknowledgements.Tis paper was financially supported

    by Ministry of Agriculture and Rural Development of the

    Slovak Republic in the Research Plan of the Soil Science and

    Conservation Research Institute (2011). We are very grateful

    to Ray Marshall for improving the English.

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    Received for publication August 14, 2012

    Accepted after corrections November 12, 2012

    Corresponding author

    RNDr. J B, PhD., International Institute for Applied Systems Analysis,

    Schlossplatz 1, A-2361 Laxenburg, Austria

    e-mail: [email protected]