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Novel Higher-Order Statistical Method for Extracting Dependencies in Multivariate Geospace Data Sets
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| Understanding magnetospheric dynamics and
the relationship between the solar wind driver and the magnetospheric
response is of great practical interest because it could potentially
help to avert catastrophic loss of power and communications. In order
to build good predictive models it is necessary to understand the most
critical nonlinear dependencies among observed plasma and
electromagnetic field variables in the coupled solar
wind/magnetosphere system. We propose to develop and apply a novel
cumulant-based information-dynamical measure in conjunction with other
nonlinear techniques to magnetospheric data to characterize: (1) the
underlying dynamics, (2) the nonlinear behavior of the geospace
systems, (3) the solar cycle dependence of these properties, and (4)
the predictability of the systems. Because this nonparametric,
statistical approach assumes no intrinsic underlying dynamics, it is
possible to avoid some of the pitfalls involved in parametric modeling
and/or physics based models. Moreover, the information gained from the
cumulant-based information flow could be used to guide the development
of predictive models.
To illustrate the power of our method, we will examine the nonlinear
cross dependencies in a large database of geospace variables. We will
evaluate the underlying dynamics of the magnetosphere by examining the
time evolution of geomagnetic indices, Kp, Dst, and AE, as well as
more direct measures of the magnetospheric state, energetic electron
flux, tail stretching, and energetic electron precipitation. From
this data we will be able to estimate a predictability horizon which
will indicate the maximum ``look ahead'' for which the space climate
can be predicted. We will also use the information-dynamical measures
to identify variables derived from solar wind data that maximize the
information content about the magnetospheric response.
This work should have a significant impact on
space science, space/mathematical science education, and society at
large. First, we have developed a new technique for analyzing
nonlinear dependencies in large data set using cumulant-based
significance measures. Because the methods and techniques do not
presuppose an underlying dynamics, they are transportable across a
wide range of complex nonlinear systems which can broadly impact
fields ranging from geoscience to bioscience. Second, detection of
the most important nonlinear interactions in the systems could be used
to identify the most important physical processes that will aid
development of physical models and predictive capabilities for
understanding severe space weather. Third, we will submit an E/PO
proposal where we will develop web-based outreach
tools to teach high school students basic concepts in nonlinear
dynamics with applications to space science. Finally, the
results will be widely disseminated in mathematical and geospace
journals and presented at meetings and workshops. |
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