**AAS 198th Meeting, June 2001**

*Session 3. Analysis, Data and Distances*

Display, Monday, June 4, 2001, 9:20am-6:30pm, Exhibit Hall
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## [3.03] The Physical Content of the Leading Orders of Principle Component Analysis of Spectral Profiles

*A. Skumanich, A. Lopez Ariste (High Alt. Obs-NCAR)*

We consider the PCA (Principle Component Analysis) method of
profile analysis introduced by Ref (1). In this method one
constructs a covariance matrix C_{ij} given by the product
of the profile amplitudes at wavelengths \lambda_{i} and
\lambda_{j} averaged over all profile samples (either over
space or time). The matrix is 'diagonalized' and ordered by
Singular Value Decomposition. The resulting orthonormal
eigenfunctions over wavelength space are then used as a
basis for the expansion of the observed profiles at each
space(time) point. The eigenvalue ordering is by magnitude
of the mean square over space(time) of the expansion
coefficients and is given by the product of the frequency of
occurrence of the particular eigenfunction and its intrinsic
mean square amplitude. An error based truncation scheme
yields a coefficient set which is a compression of the
original data set.

We have applied the PCA method to the 40,000 profiles for
each Stokes component for a Solar active region. In the case
of the intensity profile we find that the expansion appears
to be similar to a Taylor series with the 0th efunction
being the zero order term, the 1st efunction as the first
derivative of the zero term and the 2nd efunction as the
second derivative term. Thus we derive a line-of-sight
velocity from the coefficients of the first derivative term
and a magnetic signature, using the weak field
Milne-Eddington approximation, from the second. A comparison
with a Stokes profile inversion shows that the thus
estimated velocity and magnetic parameters are in good
agreement with the more time consuming profile fitting
values but do show a "roll-off" for sufficiently large
values. One also finds that the bright 'quiet' Sun points
have an upflow while the dark have a downflow similar to
that derived by other analysis.

1) Rees, D., López Ariste, A., Thatcher, J. & Semel, M.
2000, A & A, 355, 759

The National Center for Atmospheric Research is sponsored by
the National Science Foundation.

The author(s) of this abstract have provided an email address
for comments about the abstract:
sku@hao.ucar.edu

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