## 1. Introduction

[2] The knowledge of the electron density distribution in the Earth's topside ionosphere and plasmasphere is important from several aspects, such as estimation and correction of propagation delays in the Global Navigation Satellite System (GNSS), ionospheric storm studies, ion composition studies, space-weather effects on telecommunications, etc.

[3] The traditional ground-based vertical incidence sounding (ionosonde) measurements are sufficient for a precise determination of the bottom-side electron density profile. However, the ground-based ionosonde measurements alone are incapable of delivering information about the topside electron profile (above *h*_{m}*f*_{2}). A typical way of “solving” the problem, adopted in the modern digital ionosondes [*Reinisch*, 1996a, 1996b] is to use a Chapman layer [*Banks and Kockarts*, 1973]. A nice feature of this Chapman profiler is that it needs only the peak density and height values to calculate the topside distribution. However, it demonstrates some disadvantages associated first with the use of constant plasma scale height determined from the density distribution around the peak, and second, with the fact that the constructed profile is not tied to any additional measurements.

[4] During the years, the researchers have developed and used other means to gather information on the upper ionosphere and plasmasphere, such as: coherent scatter radar observations of underdense electron density irregularities [*Booker*, 1956; *Greenwald*, 1996], incoherent scatter radar probing [*Bowles*, 1958; *Gordon*, 1958; *Farley*, 1996], observations using topside sounders onboard satellites [*Franklin and Maclean*, 1969; *Reinisch et al.*, 2001], in situ rocket and satellite observations [*Pfaff*, 1996], tomography [*Austen et al.*, 1988; *Leitinger*, 1996b], and occultation measurements [*Phinney and Anderson*, 1973; *Leitinger*, 1996b]. There is no universal method; each type has advantages as well as shortcomings.

[5] The total electron content (TEC) is one of the most important quantitative characteristics of the Earth's ionosphere and plasmasphere. The (vertical) TEC is defined as the integral of the electron density from the ground height up to the ceiling height, i.e., the height of the transmitting satellite or infinity [*Leitinger*, 1996a]. The electron density above approximately 2000 km contributes little (less than 5%) to the integrated electron content and above the mean height of the plasmapause (25,000 km) the contribution is negligible. All modern TEC measuring systems rely on the observation of signal phase differences or on pulse travel time and pulse shape measurements based on geostationary and orbiting satellites. A standard way of measuring TEC is to use ground-based receiver processing signals from: satellites on geostationary orbits, like ATS-6, SIRIO; polar orbiting satellites, like the US Navy Navigation Satellite System (NNSS), the Russian Global Navigation Satellite System (GLONASS) satellites; and the Global Positioning System (GPS) satellites. The development of the GPS has also opened new opportunities to investigate the ionosphere and plasmasphere on a global scale [*Davies and Hartmann*, 1997].

[6] The purpose of this paper is to present a novel approach to the solution of a long-standing problem: the reconstruction of the electron density distribution from the TEC. Proposed is a new technique for reconstructing the topside electron density profile from the three basic types of measurements: ground-based vertical incidence sounding (ionosonde) data, GPS-based TEC measurements, and empirical values of the upper (O^{+}-H^{+}) ion transition height. The aim is to construct a unique height profile of the electron density closely matching the existing conditions at the time of measurements (Figure 1). The ionosonde measurements are important for providing the bottom-side shape of the electron profile including *N*_{m}*F*_{2} and *h*_{m}*F*_{2}. Even if we know the F layer peak density and height, we cannot determine the topside electron distribution because the topside plasma scale height is unknown. The upper transition level (UTL) (if available) is the reference point we need to calculate the plasma scale height. Then, assuming an adequate topside density distribution law the profile can be tied to the F layer peak height and the O^{+}-H^{+} transition height. The fulfillment of the most important quantitative requirement should still be observed, i.e., the calculated TEC (sum total of the integrated bottom side and topside electron density) should equal the measured TEC.

[7] This paper is structured in the following way. First, a general formulation of the problem and overview of the reconstruction method is presented. Second, the most important ionosphere “profilers” (Chapman, exponential, sech-squared, and parabolic) are examined in detail and the corresponding reconstruction formulae are deduced. Third, all required input parameters for this reconstruction are presented: GPS TEC, ionosonde, and O^{+}-H^{+} ion transition height data. Next, important evaluation results are provided in order to determine the most suitable profiler for given geophysical conditions. Evaluations involve satellite in situ observations and theoretical estimations based on calculations using same scale heights and TEC values. In the last part, possible applications of the reconstruction technique are discussed, such as the use of TEC measurements onboard Low Earth-Orbiting (LEO) satellites for profile reconstruction purposes, two- and three-dimensional electron density distribution, and the operational reconstruction on a real-time basis.