Classical Spatial Variation Models

Sen Z.

SPATIAL MODELING PRINCIPLES IN EARTH SCIENCES, 2ND EDITION, pp.129-176, 2016 (Peer-Reviewed Journal) identifier


Men have tried to model spatial behavior of the natural phenomena since a long time with initiative simple models such as the weighting functions, which are supposed to represent regional dependence structure of the phenomenon concerned. Unfortunately, commonly employed weighting functions are not actual data dependent, and hence they are applicable invariably in each spatial prediction, which is not convenient since each spatial phenomenon will have its own spatial dependence function. Spatial data distribution can be uniform, randomly uniform, homogeneous, isotropic, clustering, etc. which should be tested by a convenient test as described in the text. Besides, statistically it is also possible to depict the spatial variation through trend surface fit methods by using least squares technique. Finally in this chapter, adaptive least squares techniques are suggested in the form of Kalman filter for spatial estimation.