Geoscience Reference
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change. Identi
cation of the expectation time
˄
can be changed by accidental value
of
˄
using the procedure of sequential analysis where I
Ω
is compared to thresholds.
7.5 Percolation Procedure
N
d
¼ N
i
1
;...;
i
d
of dimension d with side h in the
phase space of the meteorological parameters enumerated in Table
7.8
. Data
Let us consider the cubic grid
ow
from the system TAO/TRITON&PIRATA is not restricted in time and is charac-
terized by data entry
fl
f g
regularly at hourly intervals. A limited
time interval, T, is chosen with the successive times {t
j
; j =1,
x
¼
x
i
;
i
¼
1
; ...;
10
, N} when data on
the meteorological situation in the previously surveyed site of the ocean-atmosphere
system are delivered. In the course of time the cells
…
N
i
1
;...;
i
d
in which a point
is hit are colored. Here the value xi
i
ð
t
j
Þ
is the observed value of
the ith parameter in the time t
j
∈
x
1
ð
t
j
Þ; ...;
x
d
ð
t
j
Þ
T. Following percolation procedure (Soldatov
2006, 2007, 2009c; Sukov and Soldatov 2007; Sukov et al. 2008b) we form clusters
by combining the interfacing of colored cells into a unique chain. Parameter
ʻ
denotes the fraction of the total number of cells that are colored and
is the relative
volume of the cluster space; the distribution of the clusters by their size is assessed.
The cluster space structure depends on the interval T, the choice of which is
determined by the speci
ʼ
c character of the given task. As it follows from the data
and
l
when
the observations are gathered over a long time. Under this consideration the
character of such a transition between different phase states of the ocean-atmo-
sphere system re
processing, parameters
ʻ
and
ʼ
can achieve their asymptotic levels
k
ects the objective laws of the start of a hurricane. Consequently, a
calculation of percolation cluster parameters for different environmental conditions
of the ocean-atmosphere system functioning gives the possibility of constructing a
decision making rule to assess the moment at which the phase transition in the
ocean-atmosphere system dynamics occurs.
An average cluster size S (number of colored cells) and correlation length
fl
ʾ
(linear size of the cluster) are approximated by the following functions
j
c
; nðkÞ k k
j
v
S
ðkÞ k k
j
j
;
ð
7
:
2
Þ
where the parameters
depend on the cluster space dimension d and in a
particular case are determined empirically. Functions S and
ʳ
and
ʽ
ʾ
de
ned in the for-
mulae (
7.2
) increase sharply at the start of a hurricane. By de
nition (Essam 1980)
an average number N
t
of colored sites in the percolation cluster after numerous steps
t of the walking of point A and under the absence of a critical transitions equals:
N
t
[
¼
t
2
;
\
where parameter
ʸ ∈
[1.29
2.84] is evaluated in each case by means of a modeling
-
procedure.
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