therefore be interpolated to equispaced data. It must be studied still 
under which conditions a sufficient spectrum is obtained this way. 
The r.m.s.e. given in table 1 (and their estimates given in table 2) 
reflect ideal data collection, i.e., sampling without measuring error. A 
random measuring error in ES just adds a component to the overall DEM 
error (see page 2). For bilinear interpolation in the DEM, it holds 
/11/: 
2. 2 42 
ey” ok 
In PS, a random measuring error also affects the sampling density. 
Sampling with a measuring error basically increases the number of 
measured points; the larger the standard deviation © the more points 
M? 
to be measured. Experiments have shown, however, that the model 
2 i 2 272 
TpEM ^ Os * (2/3) OM 
is also valid for PS (and linear interpolation) if the threshold value 
is chosen properly and the sampling density is not significantly in- 
fluenced by the measuring error. 
Accuracy prediction for the purpose of specifying the parameters of PS 
can utilize the tools described above. Given accuracy specifications in 
terms of an r.m.s.e., the procedure includes equispaced sampling with 
sufficient density of one or two representative profiles for computing 
the power spectrum, generating the composed transfer function for dif- 
ferent grid spacings and threshold values, and computing the 
corresponding estimates Gg Taking accuracy specifications and expected 
measuring error into account allows selecting of proper values for grid 
spacing and threshold. A rule of thumb for PS parameter specification 
was found empirically: Minimum grid spacing should not be larger than 
the sampling interval of ES leading to 9s & 30/5, if co is the required 
DEM accuracy. 9g of ES can easily be estimated for different sampling 
intervals from transfer function H(u) and the power spectrum of a 
sampled profile (see page 2). The threshold value should not be larger 
than 3 co and not smaller than 2.5 OM: Applying this rule to the test 
sites Tl, T5, T6 (see table 1), assuming a required DEM accuracy of 
30 = 10 (e.g., for 10 m contouring), leads to a minimum grid spacing of 
125 m for Tl, 6062.5 m for T5, 31.25 m for T6. Using a threshold value 
T = 10 m results in DEM errors conditional on sampling and linear inter- 
polation of 2 m, 2.8 m, 2.8 m, respectively. A random measuring error 
with TTR, lm (corresponding to 0.1%. of the flying height) would add 
0.44 to the overall m.s.e. of the DEM. 
Even if DEM specifications were more differentiated, e.g., by stating 
the required resolution and corresponding fidelity instead of a global 
r.m.s.e., the spectral approach to quality assessment of DEMs would be 
very promising. 
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