Environmental Engineering Reference
In-Depth Information
6 15 2010
6 16 2010
6
5
4
3
2
1
0
0:00
6:00
12:00
18:00
0:00
6:00
12:00
t
hours
(a)
50
40
30
20
10
0
1 1 2010
2 15 2010
4 1 2010
5 15 2010
t
days
(b)
Figure 2.10. Rainfall time sequence recorded in Torino (Italy) with (a) 10-min and
(b) daily aggregation windows.
representation of the random forcing. Apart from rainfall, several other intermittent
stochastic processes in the biogeosciences can be modeled as WSN processes. For
example, the effect of fires in vegetation dynamics, the dynamics of epidemics in
ecological models, the occurrence of landslides in models of landform evolution, or
the dynamics of earthquakes can be represented as WSN, as discussed in Chapter 4.
2.3.4 Stochastic process driven by white shot noise
Consider the stochastic equation
d
d
t
ξ
sn
(
t
)
=
φ
+
φ
,
f
(
)
g
(
)
(2.57)
driven by a WSN with zero average. Because the noise is white (i.e., nonautocorre-
lated), a problem of interpretation of Eq. (
2.57
) arises: If
g
(
(i.e.,
if the noise is multiplicative), Eq. (
2.57
) is meaningless (
van Kampen
,
1981
) unless
an interpretation rule is specified.
φ
) does depend on
φ
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