## 1. Introduction

[2] Tomographic imaging or data assimilation for the plasmasphere has been proposed for many years now [e.g., *Hajj et al.*, 2000]. The main limitation to progress has been the fact that for ground based GPS data, the ionospheric content is much larger than the plasmaspheric and, coupled with the limited viewing angles, the information about the plasmasphere is swamped out by the ionospheric signature in the data. Further, many simple iterative tomography algorithms will naturally smear features out along a line of measurement, so that if the wrong algorithm is chosen, mere artifacts could be interpreted wrongly as geophysical signatures. The use and limitations of different approaches were demonstrated in early ionospheric tomography research referenced extensively in the review by *Bust and Mitchell* [2008]. In summary, the more limited the data the worse the artifacts that are created by iterative algorithms. For these reasons it is necessary to develop a method that is specifically suited to the plasmaspheric imaging problem outlined here.

[3] The reconstruction of the time-varying ionospheric electron density distribution from GPS observations is essentially a four-dimensional limited-angle tomographic inverse problem. Dual-frequency GPS receivers provide pseudorange and phase information for which the geometry-free linear combination of the two frequencies provides an estimate of the integrated electron content along a line of sight to within an unknown constant. The accuracy of the pseudorange measurements is limited by errors known as differential code biases at the transmitter and receiver such that absolute TEC can be determined to an accuracy of only a few total electron content (TEC) units. Since this error in the absolute TEC determination is the same order as the plasmaspheric total electron content [*Ciraolo and Spalla*, 1997] the approach developed uses the differential phase observations only. This means that the data are essentially TEC changes along a changing path through the plasmasphere. These are the same GPS data that were used for ground-based GPS ionospheric imaging by *Mitchell and Spencer* [2003].

[4] A new source of data for ionospheric and plasmaspheric science has arisen recently from the COSMIC satellites. *Pedatella and Larson* [2010] have demonstrated the possibility of using COSMIC data for the identification of the plasmapause. In a complementary nature to their work, here we extend the ideas to image the entire plasmaspheric region.

[5] In contrast to ionospheric imaging using ground-based receivers, where many hundreds of receivers are available, plasmaspheric imaging using LEO satellites is problematic owing to the small number of satellites. At present there are six satellites in the COSMIC constellation. The resulting inverse problem is severely underconstrained. One approach, used in the ionospheric imaging community in data assimilation is to regularize the solution using empirical or physical-based models. However, systematic errors in the a priori models can bias the solution and make the interpretation of the results difficult. The method presented here aims to reduce the ambiguity of the inverse problem by mapping to a set of reduced basis functions. The assumption is that the electron distribution in the lower plasmasphere is constant along the Earth’s magnetic field lines which are, to a first approximation, dipole in nature. Parametrically such a field pattern can be represented using two-dimensional Euler potentials [*Wolf et al.*, 2006]. The transform forms a three-dimensional spherical coordinate space to a two-dimensional Euler space and thus reduces the dimensionality of the problem by one. The resulting inverse problem can then be regularized using a local quadratic smoothing in both space and time. This will result in a unique solution using only data and the physics-based mathematical constraint, thus removing the requirement for an empirical model of the plasmasphere to stabilize the solution.

[6] The new method presented in this paper is applied to data obtained from the COSMIC satellites for the months of December 2008 and January 2009. The six satellites in the constellation provide dual-frequency GPS observations every 5 s. Results are presented that show the variation of reconstructed plasmaspheric electron content to changes in the solar-terrestrial environment.