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point the elevation difference, Ah,,, =h, —h has been
PIL?
calculated.
The points located within the lakes of Lombardy and Piedmont
are characterized by a constant Ah: for example points
belonging to the Lago Maggiore in Piedmont are characterized
by a constant Ah equal to 1 meter and points belonging to the
Lago di Livigno in Lombardy has a constant Ah of 15 m. To
avoid that these blunders influence the final statistics they have
been removed from the datasets. The analyses on the height
differences have been done following this schema:
e statistical analysis,
e subdivision of the differences into classes and computation
of the percentage of points belonging to each class,
e spatial analysis of the distribution of differences.
3.1.1 Results and statistics of the comparison between
Switzerland and Lombardy DTMs: The CH DTM has been
interpolated directly on the comparison points (which are in
ETRF89). Since the Lombardy DTM is in R40-GB
(cartographic coordinates), the comparison points have been
transformed from ETRF89 to R40-GB before doing the
interpolation, by adopting the afore mentioned GK2CNV
routine.
The sample has been considered from a statistical point of view:
* number of points = 256737
e mean g(Ahj) = -0.1 m
* variance: o (Ahi) = 357 m?
eo std. c(Ah; ) = t189m
* max max(Ah; ) = 352 m
* min: min(Ah; ) = -257 m
The sample has mean almost equal to zero and standard
deviation greater but comparable with the altimetric accuracies
of the two DTMs.
The sample has been classified by absolute values. The result of
this operation has been summarized in Table 3 : more than 80%
of the points present differences smaller than 20 meters. On this
regard the results are satisfactory. On the other hand, several
(964) outliers (IAhl » 100m) are present.
Class | Limits Percentage
1 0 m x IAhl « 10m 60.6896
2 10 m € I^hl « 20 m 23.4790
3 20 m € IAhl « 50 m 13.3196
4 50 m € IAhl « 100 m 2.17%
5 100 m € IAhl « 150 m 0.28%
6 IAhl 2 150 m 0.10%
Table 3. Classes of elevation differences between Switzerland
and Lombardy and their percentages
As concerns the distribution of the sample, Figure 2 shows the
frequency curve of the height differences, compared to a
Gaussian with the same mean and standard deviation of the
sample and computed in the interval -30=+36. There is no
correspondence between them, in particular in the neighborhood
of +6, where the sample tends to differ from the theoretical
distribution. This is confirmed by the classical chi square
adapting test.
Figure 3 shows the spatial distribution of the differences. Note
that the overlapping region between the two DTMs is in
Lombardy, because the CH DTM covers part of the Italian
region, while the viceversa does not happen. The figure shows
that the biggest differences are concentrated in some specific
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B4, 2012
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia
areas, that do not correspond to the most mountainous areas. For
example, the North-East. part has higher mountains than the
central one where more outliers are present. The correlations
between the differences and both the heights and the local
slopes have been computed: none of them is significant (both
the values are smaller than 0.05). This phenomenon is probably
due to some problem during the realization of the DTMs (i.e.
errors in the digitization of the cartography to obtain the
DTMs): specific analyses have been started and will be reported
in a following paper.
x19 Adjustment of the sample to a gaussian (u=-0.06 m, c=19m)
— sample distribution |
| 7*7: normal distribution |
2 A
f 1
{MA
à
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Figure 2. Adjustment of the height differences (Switzerland-
Lombardy DTMs) sample to a Gaussian distribution
3.1.2 Results and statistics of the comparison between
Switzerland and Piedmont DTMs: In this case the two DTMs
are in the same reference frame (ETRF89). The statistics of the
differences are reported below:
e number of points = 824057
e mean: g(Ahp) = 1.3m
* variance: c (Ahp) = 666 m?
e std: c(Ahp) = +25.8m
* max: max(Ahp) = 318m
® min: min(Ahp) = -265 m
The mean of the differences is greater than 1 meter. This value
is not significant if compared to the nominal accuracy of the
datasets. However, a bias in the Piedmont DTM seems
confirmed by its comparison with the Lombardy DTM (here not
discussed for space reasons). Also in this case deeper analyses
are needed.
In this case, the standard deviation of the differences is
significantly bigger than the nominal accuracies of the two
DTMs under consideration.
As in the Lombardy case, the sample distribution does not fit a
Gaussian distribution with the same mean and standard
deviation of the sample.
After the computation of the elevation differences Ahp, the
sample has been divided into the six classes used already for
Lombardy (Table 4). In this case the differences smaller than 20
meters are less than 70 96 and more outliers are present (4637).
Figure 4 shows the spatial distribution of elevation differences
over the overlapping area of the two DTMs. Differently from
the previous case, there aren't areas characterized by particular
anomalies and the Ahp change gradually from class 1 to 6.
These considerations allow to exclude the presence of some
systematic behavior in the realization of the DTMs. The
correlations between the differences and both the heights and
the local slopes are not significant (both the values are smaller
than 0.05).
