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Title
International cooperation and technology transfer
Author
Mussio, Luigi

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)
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 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.