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Title
International cooperation and technology transfer
Author
Mussio, Luigi

243
5. DISPLACED VOLUME ESTIMATION
The volumes are computed through the comparison
between the two DEMs, post and ante-event; for volume
it is intended that one of prismatic solid inclusive
between two surfaces having same area and same grid
step. Volumes are calculated using the following three
methods:
Trapezoidal Rule
it is a generalization of the method of the trapezes used
for integrating the functions of a variable, in which the
area subtended by the curve is equal to the sum of the
areas of the trapezes that are obtained from an assigned
partition of the interval of integration.
Simpson's Rule
it is also derived by the analogous procedure used for the
functions of a variable in which a function (polynomial of
second degree) passing for the gives points is introduced.
Simpson's 3/8 Rule
it is a variation to the preceding method.
In table 8 a summary of the calculated volumes is carried
as to the sum of positive (cuts) and negative (fills)
volumes.
The cut volume concerns the material in those places
where the upper surface is above the lower surface (zones
where the accumulation has been verified) while the fill
one is the volume of material in those places where the
lower surface is above the upper surface (zones interested
from remove of material).
The values of cut and fill volumes carried over are
referred to the trapezoidal method and in table they are
brought in absolute value
SA20
ID.
KR.
M.C.
TR.
Trapezoidal Rule
[m 3 ]
-11.292.400
-9.528.890
33.056.200
3.249.320
Simpson's Rule
[m 3 ]
-11.299.200
-9.529.190
33.054.800 |
3.250.530
Simpson's 3/8 Rule
[m 3 l
-11.297.000
-9.526.440
33.056.200
3.249.220
Negative Volumes (Fill)
[m 3 ]
12.515.800
10.965.700
10.525.000
1.324.340
Positive Volumes (Cut)
¡m 3 l
1.223.400 |
1.436.810
43.581.200
4.573.660
Table 8 - Volumes computation
From the table it is noticed that the differences among
the volumes calculated with the three integration
methods are very modest. Vice versa, there are great
differences among the values relative to the four
interpolators, above all as far as it concerns the method
M.C. (maximum values) and the TR. (least values),
that differ between them of a factor 10.
You note besides like the cut volumes are very
different from the fill ones; that is also because in the
areas to valley the detritic material has been partially
removed in the following days immediately the events.
Either for the entity of the values obtained and for the
difference between the various methods strong doubts
fed on the reliability of the aforesaid values. This
induces besides to think that the DEMs (ante and post
event) can not be entirely homogeneous among them
because of different references of height.
6. CONCLUSIVE REMARKS
The different spatial disposition of the points causes a
different behaviour of the same algorithm.
Summarising the results of the tests turned to a
comparison of the most common methods of data
interpolation, effected on the base of the evaluation of
the residuals as well as the visual analysis of the
relative contour line maps, the methods: Inverse
Distance to Power, Kriging, Minimum Curvature and
Triangulation with Linear Interpolation, can be
considered reliable with the set of data at disposal.
References
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