OPTIMAL SAMPLE SPACING IN DIGITAL ELEVATION MODELS 
Poul Frederiksen and Ole Jacobi 
Institute of Surveying and Photogrammetry 
The Technical University of Denmark 
Landmálervej 7, DK-2800 Lyngby, Denmark 
and 
Kurt Kubik 
The Ohio State University 
Department of Geodetic Science and Surveying 
1958 Neil Avenue, Columbus, Ohio. 
ABSTRACT 
The paper documents a study specifying the necessary methodology and 
tools for the creation of a digital elevation data base. In particu- 
lar, it documents the required procedures and densities for data cap- 
ture. The choice of the optimal sampling spacing, meeting pregiven ac- 
curacy specifications for the digital elevation model, is based on 
statistical analysis of selected terrain profiles in the projected 
area. The variogram for these terrain profiles is computed and the 
parameters of this variogram are used to enter formulas which relate 
sampling spacing to accuracy of interpolation. The theory and appli- 
cation of this method to actual projects is explained. 
INTRODUCTION 
The purpose of this paper is to demonstrate how the variogram can be 
used for planning the construction of a digital elevation model. 
The elevation model is to be constructed from digitised elevations 
along profiles (or contour lines). The accuracy of this reconstruction 
of the terrain depends mainly on the spacing of the sample points and 
on the surface roughness. A proper spacing of the sample points can 
be selected, if the accuracy requirement for the digital elevation 
model is given. To do so, parameters for the terrain roughness are 
derived from the variogram, and then the required point spacing is 
found from the accuracy specifications. 
Conversely, for a given sample spacing the accuracy of a digital ele- 
vation model can be derived. 
THE VARIOGRAM 
The variogram is defined as the mean Square difference between two 
sample values the distance d apart 
y 
  
v(d) = 1 E(z,- z (1) 
i+d 
  
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