Spatial Dependence Measures

Sen Z.

SPATIAL MODELING PRINCIPLES IN EARTH SCIENCES, 2ND EDITION, pp.177-252, 2016 (Peer-Reviewed Journal) identifier


Rather than geometrical weighting functions as in Chap. 2, it is preferable to obtain spatial dependence function from a set of measurement points. Prior to such a functional derivation, it is necessary to examine the isotropy and homogeneity of the spatial data directionally and pointwise features of the regionalized variable (ReV). The basics of semivariogram (SV) with its different components such as sill, nugget, and radius of influence are presented in descriptive and application manners. Similar to SV, cumulative SV (CSV) and point CSV (PCSV) concepts are explained with applications to groundwater quality data. It is emphasized that PCSV helps to depict the spatial behavior features around any sampling point by taking into consideration the contribution from the surrounding measurement points. It is shown that for each location of measurement, it is possible to obtain the radius of influence, if necessary along any direction, and their regional contour maps provide the radius of influence at non-measurement locations. Once the radius of influence is known, then it is possible to depict which nearby measurement locations should be taken into consideration in the calculation of unknown data value. The validity of any method can be decided on the basis of cross-validation error minimization. A new concept of spatial dependence function (SDF) is developed without need that the regional data has normal (Gaussian) probability distribution. The application of SDF is presented for earthquake and precipitation data from Turkey.