SCHRIFTENREIHE Institut für Pflanzenernährung und Bodenkunde ...

cross-semivariograms (factorial kriging analysis). The LMC is a set of auto- and
cross-semivariogram models in which all its semivariograms are linear
combinations of the same set of elementary structures. A LMC with k = 1, . . ., q
structures may be written as:
g (h)
k
1 1 k k
q q
γ h)
= b g ( h)
+ b g ( h)
+ ⋅⋅
⋅ + b g ( h)
(3)
i , j ( i,
j
i,
j
i,
j
k
b i,
j
where is the partial sill for the i,jth semivariogram for structure k, while
represents the type of semivariogram model (i.e. spherical, exponential,
1
etc.) for structure k. The first structure g ( h)
represents the nugget effect model.
The type of semivariogram model used in Eq. 3 was based on the experimental
semivariograms of the variables (standardized to unit variance and zero mean)
and knowledge of the main geological and anthropogenic factors. Modified
kriging programs in ArcGIS were used to fit the LMC, in which semivariograms
were fitted with appropriate model functions using the maximum likelihood
cross-validation method (Samper and Carrera, 1990).
The scale-dependent correlations between water content and other
properties was determined from the structural correlation coefficients, ρ k i.j
k
bi
, j
k k
i , ib
j , j
k
ρ i,
j =
b
(4)
which are calculated from the partial sill value, , of the
cross-semivariogram model between i and j and the two partial sill values,
k
b j,
j
and , of semivariogram models for i and j, respectively (Casa and
Castrignanò, 2007). Furthermore, constructed variation contributions of each
component to the total variation were calculated based on Eq. 3.
3. Results and discussion
Grazing intensity influenced a range of soil properties listed in Table 1. The
heavily grazed plot (HG) was the most dense, had the least carbon, and the
greatest shear strength. In contrast, the plot protected from grazing for 25 yr (UG
79) was the least dense, had the most carbon and the smallest shear strength.
There appears to be consistent trends between grazing intensity and many of
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k
b i,
j
k
b i,
i