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Annales Geophysicae An interactive open-access journal of the European Geosciences Union
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Volume 25, issue 4
Ann. Geophys., 25, 971-987, 2007
https://doi.org/10.5194/angeo-25-971-2007
© Author(s) 2007. This work is distributed under
the Creative Commons Attribution 3.0 License.
Ann. Geophys., 25, 971-987, 2007
https://doi.org/10.5194/angeo-25-971-2007
© Author(s) 2007. This work is distributed under
the Creative Commons Attribution 3.0 License.

  08 May 2007

08 May 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 J. De Keyser et al.
  • 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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