A Classification for a Geostatistical Index of Spatial Dependence

ABSTRACT:

In geostatistical studies, spatial dependence can generally be described by means of the semivariogram or, in complementary form, with a single index followed by its categorization to classify the degree of such dependence. The objective of this study was to construct a categorization for the spatial dependence index (SDI) proposed by Seidel and Oliveira (2014) in order to classify spatial variability in terms of weak, moderate, and strong dependence. Theoretical values were constructed from different degrees of spatial dependence, which served as a basis for calculation of the SDI. In view of the form of distribution and SDI descriptive measures, we developed a categorization for posterior classification of spatial dependence, specific to each semivariogram model. The SDI categorization was based on its median and 3rd quartile, allowing us to classify spatial dependence as weak, moderate, or strong. We established that for the spherical semivariogram: SDI_Spherical (%) ≤ 7 % (weak spatial dependence), 7 % < SDI_Spherical (%) ≤ 15 % (moderate spatial dependence), and SDI_Spherical (%) > 15 % (strong spatial dependence); for the exponential semivariogram: SDI_Exponential (%) ≤ 6 % (weak spatial dependence), 6 % < SDI_Exponential (%) ≤ 13 % (moderate spatial dependence), SDI_Exponential (%) > 13 % (strong spatial dependence); and for the Gaussian semivariogram: SDI_Gaussian (%) ≤ 9 % (weak spatial dependence), 9 % < SDI_Gaussian (%) ≤ 20 % (moderate spatial dependence), and SDI_Gaussian (%) > 20 % (strong spatial dependence). The proposed categorization allows the user to transform the numerical values calculated for SDI into categories of variability of spatial dependence, with adequate power for explanation and comparison.

Keywords: geostatistics; spatial dependence; spatial variability; semivariogram; summary measures