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Fig. 7.20 A dynamics of the Instability Indicator for the ocean-atmosphere system during season
of tropical hurricanes 2008 calculated by the data of meteorological stations located in the
Caribbean Basin and Gulf of Mexico. Parameters of I
m
(k) were equaled to s = 17, m =24h,N =7,
K = 62 days
Furthermore, in this
, t) corresponds to the OAS phase
state and illustrates the trend of the cyclone evolution. Therefore, using one of the
prediction algorithms, it is possible to evaluate the probability when stochastic
process I
T
(
figure the value of IT(φ,
T
(
ˆ
,
ʻ
, t) intersects some threshold. In fact, this task comes to the random
walk control on the plane (IT,
T
,t). The solution to this task can be achieved with the
employment of evolutionary method (Krapivin and Shutko 2012; Krapivin and
Varotsos 2007) or the sequential analysis algorithm (Krapivin and Varotsos 2008;
Soldatov 2009a).
The evolutionary method consists of the building of a model that is suitable for a
stochastic process IT(φ,
T
(
ˆ
,
ʻ
, t) under the conditions where the currently available
knowledge does not allow for the development of a mathematical model capable to
describe this process. The sequential analysis algorithm in contradiction to the
Neyman-Pearson criterion does not separate the stages of the data processing, rather
it alternates these stages. This algorithm provides the possibility for a decision
making after each realization of a random process {IT(φ,
T
(
ˆ
,
ʻ
, t
i
}.
Figure
7.23
demonstrates this possibility for the case of the hurricane Irene in
2011. Inspection of this figure shows that the instability indicator responds to the
OAS phase transitions with some probability, which depends on the weather station
ˆ
,
ʻ
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