distribution of measured GPS/leveling data is 
shown. 
10.5 11.0 11.5 12.0 
Figure 3: Test area (A)-Geoid contour lines (m) and 
GPS/leveling points 
Since this area is in the Alps, geoid has strongly 
varying features, as the area is characterized by 
high mountain peaks and deep valleys. 
As explained before, two input data sets where 
computed. 
Gridded data were evaluated on a regular 3’x3’ grid, 
covering the whole area. 
As mentioned before, scattered data positions 
where assumed to coincide with real data 
campaigns performed in this area; in this way a data 
base of 102 scattered geoid values has been 
considered. 
The target data base is formed by geoid undulations 
on a 5’x5’ regular grid in the area 
45.6 <(p <46.8 10.4 <*.<11.5 
Two widely used interpolation methods were applied 
to get the estimates; they are krigging and weighted 
mean. When using the weigthed mean estimator, 
the weight was set equal to the inverse of the 
distance between prediction and measure point to 
the power of two. 
Interpolation were carried out using as input data 
the whole geoid signal and the two residuals listed 
above in b) and c), both for the regular 3x3’ grid 
and the scattered data case. 
Differences were then computed, component by 
component, between estimated and target values on 
the regular 5’x5’ grid. 
The statistic of the differences are listed in Table 1 
for regularly distributed input data and in Table 2 for 
scattered input data. 
n 
E(m) 
Min(m) 
Max(m) 
AN T 
225 
0.00 
0.00 
0.02 
0.05 
-0.06 
-0.11 
0.08 
0.16 
ANr 
225 
0.00 
0.00 
0.03 
0.05 
-0.09 
-0.13 
0.12 
0.14 
AN r 
225 
0.00 
0.00 
0.01 
0.01 
-0.03 
-0.04 
0.02 
0.04 
Table 1: Statistics of the residuals computed with 
gridded input data (bold types for weighted mean 
interpolation) 
n 
E(m) 
<r(m) 
Min(m) 
Max(m) 
AN T 
225 
0.10 
0.11 
0.50 
0.63 
-2.27 
-2.60 
0.97 
1.34 
an r 
225 
0.20 
0.30 
0.32 
0.34 
-1.23 
-0.63 
1.15 
1.15 
AN r 
225 
0.00 
0.04 
0.08 
0.12 
-0.59 
-0.21 
0.12 
0.36 
Table 2: Statistics of the residuals computed with 
scattered input data (bold types for weighted mean 
interpolation) 
As it is expected, the residuals computed with 
gridded data are better then the ones obtained with 
scattered data points, which are not uniformly 
distributed in the computation area. 
Furthermore, interpolations based on the residual 
signal N r are always better than the ones based on 
global geoid and N R , particularly with scattered 
data. 
So, when using real data, it is etremely important to 
remove the model and the RTC components to get 
reliable interpolations. 
No sharp differences are on the contrary evident 
with respect to the interpolation method used; both 
krigging and weighted mean lead nearly to the same 
results. 
2.2 Test area (B) 
A second area has been then selected in a flat area 
along the Adriatic Sea. This zone is centered on 
Ravenna and it has the following boundaries: 
44 < cp <45 11.5 <X< 12.5. 
Following the same scheme presented in the test 
area (A), gridded data were computed on a regular 
3’x3’ grid and on a set of 96 scattered points shown 
in Figure 4.