Semivariance

In spatial statistics, the empirical semivariance is described bysemivariance, γ ( h ) = 1 2 n ( h ) ∑ i = 1 n ( h ) [ z ( x i + h ) − z ( x i ) ] 2 {displaystyle gamma (h)={dfrac {1}{2n(h)}}sum _{i=1}^{n(h)}^{2}} where z is the attribute value In spatial statistics, the empirical semivariance is described bysemivariance, γ ( h ) = 1 2 n ( h ) ∑ i = 1 n ( h ) [ z ( x i + h ) − z ( x i ) ] 2 {displaystyle gamma (h)={dfrac {1}{2n(h)}}sum _{i=1}^{n(h)}^{2}} where z is the attribute value where z is a datum at a particular location, h is the distance between ordered data, and n(h) is the number of paired data at a distance of h. The semivariance is half the variance of the increments z ( x i + h ) − z ( x i ) {displaystyle z(x_{i}+h)-z(x_{i})} , but the whole variance of z-values at given separation distance h (Bachmaier and Backes, 2008). A plot of semivariances versus distances between ordered data in a graph is known as a semivariogram rather than a variogram. Many authors call 2 γ ^ ( h ) {displaystyle 2{hat {gamma }}(h)} a variogram, others use the terms variogram and semivariogram synonymously. However, Bachmaier and Backes (2008), who discussed this confusion, have shown that γ ^ ( h ) {displaystyle {hat {gamma }}(h)} should be called a variogram, terms like semivariogram or semivariance should be avoided.