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.