## 1. Introduction

[2] A global model that provides reasonable estimates of cold plasma density is essential for simulating the propagations of plasma waves in the Earth's plasmasphere; for example, the ray tracing of whistler mode waves [e.g., *Bortnik et al.*, 2009; *Santolík and Chum*, 2009]. Diffusive equilibrium models have been widely used to represent the field-aligned density distribution because of their simplicity and flexibility. Recently, however, more realistic density models, such as the global core plasma model (GCPM) [*Gallagher et al.*, 2000], the IMAGE/RPI model [*Huang et al.*, 2004], the global plasmasphere ionosphere density (GPID) [*Webb and Essex*, 2000], and the standard plasmasphere ionosphere model (SIM) [*Gulyaeva et al.*, 2002] have been developed theoretically, semi-empirically, or fully empirically. These recent models enable the simulation of more realistic wave propagations. Among these models, the GCPM has an advantage because it always provides continuous densities in both value and derivative, which is one of the necessary conditions for the simulation of wave propagations. In addition, the computer software of the model is open to the public.

[3] The GCPM is actually a framework to integrate region-specific models for plasma density that have been developed over the years. It provides typical electron densities throughout the ionosphere, plasmasphere, magnetospheric trough, and polar cap under various solar and geomagnetic conditions. Model density in each region is represented by analytical functions that correspond to the plasma distribution features of the region. The model makes it very convenient to obtain a global electron density profile in the inner magnetosphere, but its statistical accuracy has never been examined. As an analysis of the IRI/GCPM error in mid and high latitudes,*Stolle et al.* [2006] showed the bias errors of the estimates of the IRI/GCPM density above Europe and north polar regions between April and November 2001 by comparing measurements from the CHAMP satellite with model density. They proposed a data assimilation technique that improves the model estimates by using GPS TEC data.

[4] In this paper, we discuss the accuracy of the GCPM density, especially in the magnetic equator, through a statistical analysis of the total electron contents (TECs) derived from the GPS data; we then construct an error model for the GCPM. The equatorial density is the most important factor for the GCPM to determine the entire profile in the plasmasphere because field-aligned density is determined by an interpolation of equatorial density and ionospheric density with an exponential function. Long-term global TEC data make it possible to evaluate the accuracy of the global density model.

[5] It should be noted that the GCPM is a model that provides a typical profile under a given condition and is different from models that are used to forecast ionospheric and plasmaspheric states in the near future, for example, a global TEC prediction model [*García-Rigo et al.*, 2011], that is, the GCPM is more similar to a climate model than a weather model. Then, the construction of the error model is based on an estimate of mean bias error of the GCPM-derived TEC for the measured TEC under each condition. In order to estimate the bias error, it is necessary to identify the contributing factors in estimation errors in the GCPM. Constructing a global density model from the GPS-TEC data is much more difficult than constructing such an error compensation model because the number of contributing parameters is much smaller in the error compensation model.