In this talk we introduce the statistical tecnique of
Karhunen-Loève or Proper Orthogonal Decomposition to
investigate into open questions in
solar physics: the dynamics of the photosphere, and its connections
with the helioseismology, and the spatio--temporal features of the
solar activity.
The spatio-temporal dynamics of the solar photosphere is studied by
performing a Proper Orthogonal Decomposition (POD) of line of sight
velocity fields
acquired at Kanzelhohe solar observatory (full disk images) and from
high resolution data coming from the MDI/SOHO instrument.
Using this technique, we are able to identify and characterize the
different dynamical regimes acting in the system. The solar rotaton and
the
supergranulation dominate the most energetic POD modes. Patterns with
larger typical scales of ~10 Mm,
are associated to well known p-modes oscillations at frequencies of
about 3000 microHz
For the first time low frequency oscillations, with frequencies in the
range 20-130 microHz characterized by spatial patterns with typical
scales of about ~3 Mm are observed. These oscillation are the evidence
of the solar global gravity waves and represent a probe to investigate
the interior of the Sun.
We apply the Proper Orthogonal Decomposition (POD) to investigate the
spatio-temporal features of the solar activity. Daily observation in the
period 1949-1996 of the green coronal emission line at 530.3 nm are
used as indicator of the activity behaviour. We show that few POD modes
suffice in describing both the space and time main periodicities. In
particular, being affected by a strongly energetic stochastic behaviour,
daily data are described by five POD modes, while two POD modes are
enough to describe the butterfly diagram in monthly averaged data. Apart
for the basic period T = 11 years, using daily data we found evidences
for inter-cycle temporal periodicities.
The POD represents a powerful tecnique to analize and understand the
spatio-temporal behaviour of the complex systems.
Thus apart of the application to Solar physics we apply the POD in
bio-medical problems.
In details we focus the attention to study the dynamics of the
occurrence of the dengue haemorrhagic fever in the 72 provinces of
Thailand, to describe the evolution of the epidemic during 14 years.