[5] The Electron Density Assimilative Model (EDAM) has been developed by QinetiQ [*Angling and Cannon*, 2004; *Angling and Khattatov*, 2006] to assimilate measurements into a background ionospheric model. This background model is provided by IRI2007 [*Bilitza and Reinisch*, 2008], and the majority of the input data are total electron content (TEC) measurements derived from International GPS Service (IGS) stations [*Beutler et al.*, 1999]. Since the international reference ionosphere (IRI) does not include a plasmasphere, a simple exponential electron density profile, matched to the IRI scale height at 2000 km, is used above this height. The assimilation is based on a weighted, damped least mean squares estimation. This is a form of minimum variance optimal estimation (also referred to as Best Linear Unbiased Estimation (BLUE)) that provides an expression for an updated estimation of the state (known as the analysis) that is dependent on an initial estimate of the state (the background model) and the differences between the background model and the observations [*Menke*, 1989; *Twomey*, 1977]. The error covariance matrices of the background model and the observations are also used to control the relative contributions of the background and the observations to the analysis:

where **x**_{a} is the analysis, **x**_{b} is the background model, **K** is the weight matrix, **y** is the observation vector, **B** is the background error covariance matrix, and **R** is the error covariance matrix of the observations [*Rodgers*, 2000]. *H* is the nonlinear observation operator that relates the measurements to the state:

where ɛ is the observation error. The operator is nonlinear because, in EDAM, the background model is composed of the log of the ionospheric electron density. **H** is the Jacobian, whose elements are given by the partial differentials of the observation operator evaluated at the background model; that is,

[6] The use of a nonlinear observation operator requires that, at each assimilation step, the difference between the analysis and background model remains small; that is, it is only acceptable to make small corrections to the background model. Within EDAM, the differences between the analysis and the background model are checked at each assimilation step. If the difference of any element exceeds approximately 5% of the background model's value, the assimilation is rejected.

[7] The assimilation is conducted using a magnetic coordinate system that remains fixed in space with respect to the sun. An assimilation time step of 15 min has been used and the electron density differences between the voxels of the analysis and the background model are propagated from one time step to the next by assuming persistence combined with an exponential decay. The time constant for this decay is set at 4 h. Thus if the data feed is interrupted, the analysis will decay back to the background model.