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formation corresponds to the hurricane origin. Calculation of the hurricane origin
probability depends on the dynamics of cluster space structure.
To formalize the detection procedure for the beginning of a hurricane we
introduce the algorithm for the assessment of the ocean-atmosphere system insta-
bility I
m
(t) (Soldatov et al. 2008; Krapivin et al. 2007a; Sukov et al. 2008a):
X
X
m
N
s
i
¼
1
b
i
a
i
ð
t
j
Þ
1
s
ð
m
N
Þ
I
m
ð
k
Þ¼
ð
k
¼
1
;
2
;
3
; ...;
K
Þ
ð
7
:
3
Þ
j
¼
1
where N is the length of the quasi-stationary period of observations to calculate
average values of the ocean-atmosphere system characteristics; m is the length of
time interval on which indicator I
m
(k) is assessed; s is the number of registered
parameters of the ocean-atmosphere system;
cient for the i-th
characteristic; k is the number of the time interval for the I
m
(k) assessment;
ʲ
i
is the weight coef
D
ðÞD
x
i
j
þ
1
ð
Þ
0
;
1 when
x
i
a
i
ðÞ¼
ð
7
:
4
Þ
D
ðÞD
x
i
j
þ
1
ð
Þ
[
0 when
x
i
0
where
mk
1
ð
X
Þ
j
þ
N
1
1
N
D
x
i
ðÞ¼
x
i
ðÞ
x
i
mk
1
ð
ð
Þþ
j
þ
N
Þ;
l
¼
mk
1
ð
Þ
j
mk
1
ð
Þ
j
þ
N
X
1
N
D
x
i
j
þ
1
ð
Þ¼
x
i
ðÞ
x
i
mk
1
ð
ð
Þþ
j
þ
N
þ
1
Þ
l
¼
mk
1
ð
Þ
j
þ
1
ned by the
Eqs. (
7.3
) and (
7.4
) characterizes the changeability of the current average value of the
vector {x
i
}. Figure
7.16
explains the calculation procedure for the ocean-atmosphere
system instability indicator. As it is seen, it is necessary to assess the quasi-stationary
time interval in order to use traditional statistics for the meteorological data pro-
cessing. Analysis of the one-dimensional distributions for selected meteorological
parameters measured by TAO/TRITON&PIRATA showed that this interval is 7 h.
Figure
7.17
gives an example of the calculation of I
m
(t) for the case of hurricane
Katrina. One can ascertain that the approach of the hurricane origin is accompanied
by the increase of I
m
(t). In this connection three regions of I
m
(t) take place:
Indicator represented in Fig.
7.17
was calculated with the following parameters:
s = 17 (see Table
7.8
). All environmental parameters take into consideration,
An indicator of the ocean-atmosphere system instability I
m
(t)de
ʲ
i
=1
…
(i=1
cients of environmental parameters are assumed equal),
m=24 h (time period for the instability indicator calculation equals one day), N =7
(quasi-stationary time interval for environmental data), K=31 days (a time period
for the calculation of instability indicator). All parameters were estimated by
numerical experiments to have high reliability within the calculation results.
17; weight coef
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