Shukla et al.

Table 1. Semivariogram models and parameters of spatial distribution for soil micronutrients evaluated

Soil Prop/

Nugget

Spatial Dependence

Residual Sum

Sill (Co+C)

Range

Model

Model R 2

Nutrients

(Co)

{C/ (Co+C)}*100

of Square

Zn

0.0076

0.0632

88.00

630

Spherical

0.510

2.32E-03

B

0.0235

0.2856

50.20

629.07

Gaussian

0.673

5.98E-06

Fe

0.334

0.669

49.93

150

Spherical

0.710

1.07E+00

Tableȱ1ȱshowedȱthatȱdecisionȱcoefficientsȱ(R 2 )ȱofȱZn,ȱ rangeȱofȱvariablesȱandȱwasȱrelatedȱtoȱtheȱinteractionȱ

BȱandȱFeȱandȱotherȱsoilȱpropertiesȱrangedȱbetweenȱ betweenȱvariousȱprocessesȱofȱsoilȱproperties,ȱwhichȱ

0.510-0.710.ȱTheȱresultsȱindicatedȱthatȱtheȱtheoreticalȱ areȱ affectedȱ atȱ bothȱ observingȱ andȱ samplingȱ scale.ȱ

modelsȱ chosenȱ preferablyȱ reflectedȱ theȱ spatialȱ Theȱsoilȱmicronutrientsȱhaveȱspatialȱautocorrelationȱ

structureȱcharacters.ȱTheȱgeostatisticalȱdataȱshowedȱ withinȱtheȱrange;ȱotherwiseȱitȱdoesȱnotȱexist.ȱSimilarȱ

thatȱmanyȱofȱtheȱvariablesȱstudiedȱhaveȱtheȱbestȱfitȱtoȱ findingsȱ wereȱ observedȱ byȱ Wangȱ et ȱ al.ȱ (2008).ȱ Theȱ

SphericalȱandȱGaussian.

rangeȱvaluesȱZn,ȱBȱandȱFeȱwereȱalsoȱsmallȱasȱ630,ȱ

629.07ȱandȱ150m,ȱrespectivelyȱ(Table1).ȱTheȱsmallerȱ

TheȱC ₀ ȱinȱTableȱ1ȱisȱnuggetȱvalueȱorȱspatialȱvariabilityȱ

rangeȱ suggestsȱ smallerȱ samplingȱ intervals.ȱ Smallerȱ

arisingȱfromȱtheȱrandomȱcomponents.ȱC ₀ ȱofȱFeȱwasȱ

rangesȱwereȱobtainedȱforȱZn,ȱBȱandȱFeȱcontent.

high,ȱhowever,ȱC _0ȱ ofȱotherȱvariablesȱwereȱquiteȱsmall.ȱ

Itȱwasȱconcludedȱthatȱinȱtheȱcurrentȱscaleȱofȱstudy,ȱ Theȱ valueȱ ofȱ Residualȱ sumȱ ofȱ squaresȱ (RSS)ȱ i.e.,ȱ

theȱvariabilityȱofȱmanyȱsoilȱpropertiesȱresultedȱfromȱ theȱ sumȱ ofȱ squaredȱ errorsȱ (SSE)ȱ ofȱ estimationȱ hasȱ

measurementȱerrorsȱandȱmicro-scaleȱprocessesȱwereȱ beenȱ foundȱ smallȱ showingȱ theȱ observedȱ dataȱ andȱ

high.

estimatedȱvalues.

Nugget/sillȱ ratioȱ (calledȱ alsoȱ nuggetȱ effect)ȱ isȱ Figureȱ2,ȱFigureȱ3ȱandȱFigureȱ4ȱareȱtheȱsemivariogramȱ

usedȱtoȱclassifyȱspatiallyȱstructuredȱvariationȱforȱaȱ modelsȱforȱZn,ȱBȱandȱFe,ȱrespectively.

regionalizedȱ variableȱ asȱ wellȱ asȱ givesȱ goodnessȱ ofȱ

Zn: Isotropic Variogram

prediction.ȱIfȱtheȱratioȱwasȱequalȱorȱlowerȱthanȱ25%,ȱ

variableȱ wasȱ consideredȱ toȱ beȱ stronglyȱ dependent;ȱ

0.276

0.207

ifȱ betweenȱ 25-75%,ȱ thenȱ moderatelyȱ dependent;ȱ

0.138

andȱifȱ>75%,ȱweaklyȱdependent.ȱTheȱstrongȱspatialȱ

0.069

dependencyȱofȱaȱsoilȱpropertyȱcanȱbeȱattributedȱtoȱ

0.000

intrinsicȱ factors,ȱ andȱ weakȱ spatialȱ dependencyȱ toȱ

0.00

2123.28

4246.56

6369.84

Separation Distance (h)

extrinsicȱfactors.ȱItȱwasȱobservedȱthatȱC ₀ /(C ₀ +C)ȱforȱ

Bȱ andȱ Feȱ contentsȱ wereȱ allȱ betweenȱ 25-75%whichȱ

Spherical model (Co = 0.00610; Co + C = 0.05520; Ao = 630.00; r2 = 0.021;

indicatedȱ thatȱ variationȱ ofȱ availableȱ micronutrientȱ

RSS = 0.0641) Figure 2. Variogram Model (Zn)

contentsȱ wereȱ controlledȱ bothȱ byȱ intrinsicȱ andȱ

B: Isotropic Variogram

extrinsicȱ factorsȱ (eg.ȱ fertilization,ȱ Cultivationȱ etc.).ȱ

0.0589

Inȱthisȱstudyȱratioȱwasȱ88%ȱ(>75%)ȱforȱZnȱi.e.,ȱtheseȱ

0.0442

variablesȱwereȱweaklyȱdependentȱandȱitȱalsoȱshowedȱ

0.0295

thatȱsemivariogramȱparametersȱobtainedȱfromȱfittingȱ

0.0147

ofȱ experimentalȱ semivariogramȱ valuesȱ wereȱ fairlyȱ

0.0000

0.00

2123.28

4246.56

6369.84

reasonableȱtoȱdescribeȱtheȱspatialȱvariation.

Separation Distance (h)

Theȱ geostatisticalȱ rangeȱ (calledȱ theȱ largestȱ spatialȱ

Spherical model (Co = 0.00061; Co + C = 0.02022; Ao = 120.00; r2 = 0.000;

RSS = 3.218E-03)

correlationȱ distance)ȱ reflectedȱ theȱ autocorrelationȱ

Figure 3. Variogram Model ( B )

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