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. 
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