240
The analysis of the contour maps reveals the unreliability
of some algorithms, for the following reasons:
the method N.N. produces contour lines with a
course to irregular grid, with lines of discontinuity
conformed in real precipices, absolutely not
correspondents to the real morphology of the ground;
the method P.R., being a method of global
interpolation, confirms its unsuitable to represent the
physical surface of the ground, also with the use of a
polynomial of degree 10;
the R.B.F. and the SH.’s method produce graphics
with numerous anomalous peaks (bull's eyes); the R.B.F.
especially in the low part of the landslide, the SH. in all
its extension.
The remainders four methods elaborate DEMs that
produce contour line graphics without apparent
anomalies.
For the most meaningful methods and for which was
possible, the options of default have been varied to verify
the behaviour of the algorithms and to choose the best
options to interpolate the set of data. The tests have been
performed only on SA20.
To varying the disposition of the data (simple, quadrant,
octant and all data) the values of the residuals and their
statistic parameters didn't change significantly; therefore
the options of default have been maintained and some
other free parameters have been varied.
In the following the fulfilled tests are described.
- Inverse Distance to a Power
Power from 1 to 5 has been tested while the default
option is equal to 2.
In table 3 you can note that values of the parameters are
slightly dependent from the power, sort exception for the
interpolation of power 1 that furnishes minimum,
maximum and standard deviation values of residual very
high. From 3 r power on the differences are very small.
Kriging
The performed tests have concerned the statement of
different functions of variogram. Changing the options,
the standard deviation values and the residual maximum
and minimum stay substantially unchanged.
Minimum Curvature
The only option of the method concerns the maximum
value of the residual and the number of the iterations.
Varying these values the residuals increase notably, as the
average and the standard deviation.
Radial Basis Functions
Changing type of function in comparison to that of
default (Multiquadric) it doesn't change so much in terms
of residuals and statistic parameters.
Value of the default smoothing parameter R 2 is equal to
139; in table 4 you can note that setting the value equal to
zero, the parameters of interest worsen notably while an
intermediate value in comparison to that of default
doesn't produce significant variations.
- Shepard's Method
Changing the value of the smoothing parameter with
respect to that of default (equal to zero), the results
worsen notably and they become unacceptable, as it is
visible in table 5.
SA20
Average
St. Dev.
; Minimum
Maximum
l.D.
[cm]
Power 1
5.9
186.4
-1039.5
794.2
ID.
[cm]
Power 2
0.5
37.9
-343.2
231.8
l.D.
[cm]
Power 3
0.4
23.3
-250.7
191.3
l.D.
[cm]
Power 4
0.4
21.1
-251.5
173.3
l.D.
[cm]
Power 5
0.4
20.4
I -253.8
156.1
Table 3 - SA20 landslide. Test with Inverse Distance to a Power method.
SA20
Average
St. Dev.
Minimum
Maximum
R.B.F.
[cm]
R 2 = 139
-1.2
8.9
-67.7
74.5
R.B.F.
[cm]
R 2 = 70
-1.1
8.2
-65.0
79.2
R.B.F.
[cm]
r 2 = o
-0.4
35.3
-226.6
289.6
Table 4 - SA20 landslide. Test with Radial Basis Functions method.
SA20
Average
St. Dev.
Minimum
Maximum
SH.
[cm] \ Smooth = 0
-6.9
54.4
-444.0
249.6
SH.
[cm] \ Smooth = 1
-568.6
1498.3
-11642.8
5354.4
SH.
[cm] : Smooth = 2
-590.8
1602.2
-14394.9
5950.9
Table 5 - SA20 landslide. Test with Shepard’s method