Precision Agric (2008) 9:173–175 DOI 10.1007/s11119-008-9056-2 SHORT D ISCUSSION Variogram or semivariogram? Understanding the variances in a variogram Martin Bachmaier Æ Matthias Backes Published online: 24 February 2008 Springer Science+Business Media, LLC 2008 The theoretical variogram and the confusion in the literature The deﬁnition of the theoretical variogram, c, is based on regionalized random variables ~ ~ ~ Zð~ xÞ and Zð~ x þ hÞ where ~ x and ~ x þ h represent the spatial positions separated by a vector h: hi hi 1 1 ~ ~ ~ cðhÞ¼ E ½Zð~ x þ hÞ Zð~ xÞ ¼ Var Zð~ x þ hÞ Zð~ xÞ : ð1Þ 2 2 The Zð~ xÞ and Zð~ x þ hÞ denote random variables. According to the intrinsic hypothesis, ~ ~ cðhÞ is assumed to depend only on the separation vector, the lag h; but not on the location ~ ~ ~ x: Further, the increments Zð~ x þ hÞ Zð~ xÞ are assumed to have no drift: E½Zð~ x þ hÞ Zð~ xÞ ¼ 0 for all h and all ~ x; otherwise the last identity in Eq. 1 would not hold. Concerning the terminology, there is great confusion in the geostatistical
Precision Agriculture – Springer Journals
Published: Feb 24, 2008
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