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Ann. Geophys., 25, 971-987, 2007
www.ann-geophys.net/25/971/2007/
© European Geosciences Union 2007
Least-squares gradient calculation from multi-point observations of scalar and vector fields: methodology and applications with Cluster in the plasmasphere
J. De Keyser1, F. Darrouzet1, M. W. Dunlop2, and P. M. E. Décréau3
1Belgian Institute for Space Aeronomy (BIRA-IASB), Ringlaan 3, 1180 Brussels, Belgium
2Rutherford Appleton Laboratory (RAL), Chilton, Didcot, Oxfordshire OX11 0QX, UK
3Laboratoire de Physique et Chimie de l'Environnement (LPCE/CNRS), 3A Avenue de la Recherche Scientifique, 45071 Orléans Cedex 02, France
Abstract. This paper describes a general-purpose algorithm for computing the gradients
in space and time of a scalar field, a vector field, or a divergence-free
vector field, from in situ measurements by one or more spacecraft. The
algorithm provides total error estimates on the computed gradient, including
the effects of measurement errors, the errors due to a lack of
spatio-temporal homogeneity, and errors due to small-scale fluctuations. It
also has the ability to diagnose the conditioning of the problem. Optimal use
is made of the data, in terms of exploiting the maximum amount of information
relative to the uncertainty on the data, by solving the problem in a weighted
least-squares sense. The method is illustrated using Cluster magnetic field
and electron density data to compute various gradients during a traversal of
the inner magnetosphere. In particular, Cluster is shown to cross azimuthal
density structure, and the existence of field-aligned currents in the
plasmasphere is demonstrated.
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