Also in this test, scattered point positions are 
derived from real measurement campaigns. 
Figure 4: Test area (B)-Geoid contour lines (m) and 
GPS/leveling points 
The target data set is a 5’x5’ grid in the area 
44.16 <<p <44.83 11.6 < X < 12.3 
when using input gridded 3’x3’ data and a 5’x5’ grid 
in the area 
44.20 <(p <44.62 11.68 <À< 12.3 
when using input scattered data. This reduction of 
the target grid is done to account for the distribution 
of the scattered data which are placed in a quite 
restricted area 
The same testing scheme presented before was 
applied to this test area; the results are summarized 
in Table 3 and Table 4. 
n 
E(m) 
a(m) 
Min(m) 
Max(m) 
AN T 
81 
0.00 
0.01 
0.01 
0.14 
-0.02 
-0.08 
0.02 
0.71 
an r 
81 
0.00 
0.01 
0.01 
0.05 
-0.02 
-0.08 
0.02 
0.30 
AN r 
81 
0.00 
0.01 
0.01 
0.03 
-0.01 
-0.07 
0.01 
0.15 
Table 3: Statistics of the residuals computed with 
gridded input data (bold types for weighted mean 
interpolation) 
n 
E(m) 
a(m) 
Min(m) 
Max(m) 
AN T 
40 
0.01 
0.08 
0.14 
0.13 
-0.43 
-0.14 
0.28 
0.37 
ANr 
40 
0.01 
0.01 
0.06 
0.06 
-0.18 
-0.12 
0.15 
0.17 
AN r 
40 
0.02 
0.02 
0.06 
0.06 
-0.11 
-0.08 
0.18 
0.19 
Table 4: Statistics of the residuals computed with 
scattered input data (bold types for weighted mean 
interpolation) 
As in the previous test, better statistics are obtained 
when using input gridded data and the residual 
geoid values N r . It must be also underlined that, 
contrary to the Alps test area, there are no sharp 
differences between N r and Nr residuals. This is 
expected since no relevant topography is present in 
the test area (B). 
Finally, also for this second test, the results obtained 
with the two interpolation methods are practically the 
same. 
In the end, following a commonly used practice, 
another test was performed. A plane has been fitted 
to the scattered N T data to get the geoid in the area. 
This is usually done in field survey and it is accepted 
as a reliable procedure, at least in flat topography 
areas such as the one under investigation. 
Residuals have been then computed on the 5’x5’ 
restricted target grid; their statistics are listed in 
Table 5. 
n 
E(m) 
a(m) 
Min(m) 
Max(m) 
ANx 
40 
0.04 
0.26 
-0.34 
0.81 
Table 5: Statistics of the residuals computed by 
approximating the geoid with a plane 
Poor results are obtained with respect to weighted 
mean and krigging. It must be concluded that this 
procedure can introduce relevant distorsions in the 
geoid estimate and that it must be avoided. 
3. CONCLUSIONS 
The tests that have been presented proved that the 
interpolation of geoid values should be carried out 
carefully. 
Krigging and weighted mean give nearly the same 
results and can be thus used to get reliable geoid 
estimates. The best results are obtained when 
interpolating the residual geoid N r , applying a 
“remove-restore” procedure. On the other hand, 
fitting the observed geoid data with a plane gives, in 
general, poor geoid estimates , even in flat 
topography areas.