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Ann. Geophys., 21, 1913-1929, 2003
www.ann-geophys.net/21/1913/2003/
© European Geosciences Union 2003
Combining global and multi-scale features in a description of the solar wind-magnetosphere coupling
A. Y. Ukhorskiy1, M. I. Sitnov2, A. S. Sharma2, and K. Papadopoulos1,2
1Department of Physics, University of Maryland at College Park, USA
2Department of Astronomy, University of Maryland at College Park, USA
Abstract. The solar
wind-magnetosphere coupling during substorms exhibits dynamical features in a
wide range of spatial and temporal scales. The goal of our work is to combine
the global and multi-scale description of magnetospheric dynamics in a unified
data-derived model. For this purpose we use deterministic methods of nonlinear
dynamics, together with a probabilistic approach of statistical physics. In
this paper we discuss the mathematical aspects of such a combined analysis. In
particular we introduce a new method of embedding analysis based on the notion
of a mean-field dimension. For a given level of averaging in the system the
mean-filed dimension determines the minimum dimension of the embedding space in
which the averaged dynamical system approximates the actual dynamics with the
given accuracy. This new technique is first tested on a number of well-known
autonomous and open dynamical systems with and without noise contamination.
Then, the dimension analysis is carried out for the correlated solar
wind-magnetosphere database using vBS time series as the
input and AL index as the output of the system. It is found that the
minimum embedding dimension of vBS - AL time series is
a function of the level of ensemble averaging and the specified accuracy of the
method. To extract the global component from the observed time series the
ensemble averaging is carried out over the range of scales populated by a high
dimensional multi-scale constituent. The wider the range of scales which are
smoothed away, the smaller the mean-field dimension of the system. The method
also yields a probability density function in the reconstructed phase space
which provides the basis for the probabilistic modeling of the multi-scale
dynamical features, and is also used to visualize the global portion of the
solar wind-magnetosphere coupling. The structure of its input-output phase
portrait reveals the existence of two energy levels in the system with
non-equilibrium dynamical features such as hysteresis which are typical for
non-equilibrium phase transitions. Further improvements in space weather
forecasting tools may be achieved by a combination of the dynamical description
for the global component and a statistical approach for the multi-scale
component.
Key words. Magnetospheric physics
(solar wind– magnetosphere interactions; storms and substorms) – Space
plasma physics (nonlinear phenomena)
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