It was introduced by Matheron (1971) and is now a basic concept in geo- 
statistics. 
The variogram for the terrain surface proves - from theory as well as 
experiments - to be of the form 
Vd) kemdhs s (2) 
where k is the value of V(d) for the distance d = unit (Berry and 
Lewis, 1980), (Frederiksen, Jacobi and Kubik, 1983). 
On a log-log plot the variogram appears as a straight line with the 
slope B. The slope tells about the roughness of the terrain. 
The variogram of a rough surface has a slope close to zero, while a 
very smooth terrain has a steep variogram. 
The variogram serves to quantify the magnitude and extension of the 
various surface fluctuations. The terrain profiles used for the esti- 
mation of the variogram should be sufficiently long to include the 
major surface fluctuations in their full extent. Linear or quadratic 
trends in the data seriously distort the estimate and should be elimi- 
nated from the data before computing the variogram. 
Also discontinuities (break lines) and out lying data have a signifi- 
cant influence on the variogram. These features make the terrain ap- 
pear much rougher than it is in local sections. A method of avoiding 
this impasse is to exclude differences beyond a threshold value from 
the variogram computation. 
Discontinuities which are taken into account in the variogram compu- 
tations, should also be specially treated in the digital elevation 
model to ensure consistency in conclusions concerning accuracy. 
Evaluation of the accuracy of the estimated variogram is rather com- 
plicated. From accuracy studies of variogram estimation (Dixon and 
Maney, 1969), confidence intervals for the mean square differences 
may be deduced. Table 1 gives approximate confidence intervals of 
the computed diffirences for various confidence levels and number 
of difference pairs. 
NS 957 99% 
100 | 20% 25% 
1000 6% 8% 
Table 1. Confidence intervals for mean square differences V(d) in 7 
of their value. 
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