2.3.2. Geostatistical analysis
Geostatistical analysis can help to quantify the spatial characteristics
of SWC for each plot and to determine a potential spatial pattern using
interpolation techniques based on the parameters of the analysis
results. These techniques evaluate the semivariance r (h) for all
possible pairs of nearby-sampled points based on the distance and the
degree of autocorrelation among sampling points (Zhao et al., 2011).
Geostatistical analysis involves two main parts: (1) evaluation of the
degree of autocorrelation among the measured points, (2) interpolation
for similar points not actually sampled, based on the degree of
autocorrelation encountered. The semivariance function r (h) was
calculated using the following formula:
where r (h ) is the semivariance for interval distance classh , h is the sampling interval in each plot,z (xi ) is the measured sample value at
point xi , z (xi+h )
is the sample value at point xi+h , andN (h ) is the total number of sample pairs within the
distance interval h . The shape of the resulting plot ofr (h ) describes the degree of autocorrelation present.
Autocorrelation analysis and kriging interpolation was conducted with
GS+ 7.0 (GeoStatistics for the Environmental Sciences, GS+, Gamma Design
Software, Plainwell, Michigan USA.). Three model parameters are needed
for modeled variograms: (a) the separation distance over which spatial
dependence is apparent (range, A ), (b) the level of randomness
(nugget variance, C 0), and (c) total variation
present (sill, C 0+C ), and then (d)
C/(C+Co) defines the spatial dependence of SWC. C/(C+C°)
> 0.75 indicates a strong spatial dependence relationship,
and value between 0.25 and 0.75 means a moderate spatial dependence,
with still lower values representing a lower degree of auto-correlation
(Zimmermann et al., 2008; Zuo et al., 2008).
The nature of spatial variability in data can be depicted by the four
variogram models including spherical, exponential, linear, and Gaussian
(Isaaks et al., 1989; Webster et al., 1990). To evaluate the performance
of the statistical model, we used RSS (Residual Sums of Squares), a
measure of how well the model fits variogram data. This is one of
sensitive and robust indexes, and RSS is also the parameter for the
variogram model obtained by determining a combination of parameter
values; thus, semivariogram model-fitting was performed based on the
lowest RSS. In addition, regression and coefficient of determination
(r2) were used to indicate how well the model fits the
variogram data.