## 1. Introduction

[2] Many different models of the ionosphere have been developed over the last 50 years under the auspices of a wide range of national and international organizations; e.g., the International Telecommunications Union (ITU), the European Cooperation in Science and Technology (COST) program, and the International Union of Radio Science (URSI). These ionospheric models can be broadly classified into three main categories: (1) first principles models based on ionospheric physics and chemistry. They are generally referred to as “physical models”; (2) parametric models which simplify the physical models reducing the number of parameters; (3) empirical models based on observations.

[3] Physical models operate by solving a set of first principles continuity, energy, and momentum equations for the ionospheric plasma [*Schunk*, 1988; *Anderson*, 1993]. Two examples of such models are the Utah State University (USU) Time Dependent Ionospheric Model (TDIM) [*Schunk et al.*, 1986] and the University College London and Sheffield University Coupled Thermosphere-Ionosphere Model (CTIM) [*Fuller-Rowell et al.*, 1987; *Quegan et al.*, 1982]. Unfortunately, physical models require extensive computer resources to provide affordable run times. It should also be noted that physical models (especially ones that are not coupled to neutral atmosphere models) often require inputs derived from empirical models such as the Horizonal Wind Model (HWM) [e.g., *Hedin et al.*, 1996; *Drob et al.*, 2008].

[4] Parametric models simplify the physical models by parameterising them in terms of solar-terrestrial indices and geographical locations. They aim to give a realistic representation of the ionosphere's spatial and temporal structure using a limited number of numerical coefficients. Two examples of parametric models are the Fully Analytical Ionospheric Model (FAIM) [*Anderson et al.*, 1989] and the Parameterised Ionospheric Model (PIM) [*Daniell et al.*, 1993a, 1993b].

[5] Empirical models extract, in general, information on statistical systematic ionospheric variations from past data records. They are often formulated in terms of monthly median parameters; hence they can describe long time average conditions of the ionosphere. This category of models includes the Bent Model [*Bent et al.*, 1972] and the International Reference Ionosphere (IRI) [*Bilitza*, 2001].

### 1.1. Assimilative Models

[6] In the last 15 years, there has been a rapid growth in the development and use of ionospheric “weather” models and other imaging techniques. There exists a wide range of very different approaches, but they can all be generally described as assimilative, since they aim to combine a background model with ionospheric measurements. Background models of assimilative models may range from physical models, through empirical models (e.g., IRI), to the use of closed form orthonormal functions. Assimilation techniques used include Kalman filtering, 3-D variational techniques and Tikhonov Regularisation. An excellent recent review of assimilation models can be found in the work of *Bust and Mitchell* [2008].

### 1.2. Paper Overview

[7] The results in this paper derive from a study initiated by the European Space Agency (ESA)/European Space Operations Centre (ESOC) in Darmstadt, Germany. Part of that study was to undertake comparative testing of four assimilative ionospheric models. The models were all provided with identical input data sets (consisting of ground and space based GPS measurements) and then tested against an independent truth data set considered as truth. The truth data included GPS dual frequency data, dual frequency altimeter data, ionosonde data and Langmuir probe data; however, in this paper we will focus on the results using GPS truth data.

[8] The rest of the paper is structured as follows: Section 2 describes some of the ionospheric modeling efforts undertaken at ESOC in order to set the current study in context. Brief descriptions of the four models under test are also provided. Section 3 provides a description of the input and truth data sets. Section 4 presents the results from the testing which are discussed in section 5. Conclusions are summarized in section 6.