On the Validity of Commonly Used Covariance and Variogram Functions on the Sphere |
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| Authors: | Email author" target="_blank">Chunfeng?HuangEmail author Haimeng?Zhang Scott?M?Robeson |
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| Institution: | 1.Department of Statistics,Indiana University,Bloomington,USA;2.Department of Mathematics and Statistics,Mississippi State University,Mississippi State,USA;3.Departments of Geography and Statistics,Indiana University,Bloomington,USA |
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| Abstract: | Covariance and variogram functions have been extensively studied in Euclidean space. In this article, we investigate the validity
of commonly used covariance and variogram functions on the sphere. In particular, we show that the spherical and exponential
models, as well as power variograms with 0<α≤1, are valid on the sphere. However, two Radon transforms of the exponential model, Cauchy model, the hole-effect model and
power variograms with 1<α≤2 are not valid on the sphere. A table that summarizes the validity of commonly used covariance and variogram functions on
the sphere is provided. |
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