Environmental Engineering Reference
In-Depth Information
Observed scatter ratios often deviate significantly from idealized ratios, which is to be
expected since the simplified model treats several variable parameters as constants (
e
.
g
.,
ground reflection). We can estimate the effect of non-ideal field conditions by a statistical
probability of exceedance
model derived from the results of the cases in Table 9-1. This
useful parameter is the probability that the observed signal scatter ratio will exceed the
idealized ratio by a given amount, or
Y
(D
Z
O
> D
Z
) =
Y
E
(D
Z
)
(9-27a)
D
O
=
Z
O
-
Z
I
(9-27b)
where
Y
( ) = probability of ( ); 0 £
Y
£
1
Y
e
( ) = probability of exceeding ( )
D
Z
O
,
D
Z
=
observed and selected deviations in the signal scatter ratio (dB)
Figure 9-16 shows the probability of exceedance as a function of the deviations for the 75
cases in Table 9-1. A linear fit to the central portion of this distribution is
Y
E
(D
Z
) = 0.39 - 0.11D
Z
- 5.5 £ D
Z
£ 3.5
(9-28a)
from which
Z
=
Z
I
+ 3.5 - 9.0
Y
E
(9-28b)
where all quantities are in dB units. In ratio form,
Z
=
F
E
Z
I
log
F
E
= 0.35 - 0.090
Y
E
(9-28c)
where
F
E
= empirical exceedance factor
Figure 9-16. Probability analysis of deviations between observed and idealized signal
scatter ratios.
Data points are the cases listed in Table 9-1. [Spera and Sengupta 1994]
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