So, the average number of samples in a profile must be well beyond 
100 to obtain a significant slope 8 of the variogram. 
In order to express the spatial properties of the terrain, variograms 
are computed for different profiles in different directions. In parti- 
cular the directions of the strike and drainage and the directions ortho- 
gonal to these should be investigated. Mean variogram are computed from 
the variograms of approximately parallel profiles within homogenous re- 
gions. If no significant difference exists between the variograms for 
different directions, an average is computed for these as well. The mean 
variogram is plotted on double logarithmic paper and the slope of the 
curve is estimated. 
PLANNING PARAMETERS 
In order to plan the sample spacing and estimate the accuracy of a di- 
gital elevation model, the terrain is described by its variogram as 
outlined before. Using the model of the variogram in equation (2) the 
unit of d is most conveniently chosen to be the sample spacing used 
for the estimation of the variogram. 
The required accuracy c (mean square error or standard deviation) of 
the elevation model must also be given. The parameter c may either 
denote the average standard deviation omean Of elevations extracted 
from the model or it may refer to the maximum standard deviation omax- 
The final accuracy of the digital elevation model is composed of the 
accuracy of data acquisition and the accuracy of interpolation: 
2 = 2 2 
Oe T ag interpol.* 9 sample points (3) 
The inaccuracy of data capture may be due to the process of measure- 
ments (i.e. photogrammetric height measurements), or it may be due 
to the uncertainties in the measured phenomenon (i.e. uncertainties 
of a contour line to be digitised, or uncertain definition of the 
terrain surface when measured photogrammetrically). 
We relate the sample spacing to 9interpol,» and thus the accuracy 
specification must be reduced by the sample variance 
2 
a hl - -2 
9 interpol. 9 g (4) 
sample points 
  
INTERPOLATION ACCURACY AND SAMPLE SPACING 
We limit ourselves to the study of interpolation in profiles and in 
grids of sample points. When a set of surface heights Zi 7 Z(Xssy4) 
is given, various interpolation procedures may be applied to 
compute an approximation z* to z at a required location (x,y). 
  
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