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This model relies on inversion of observations, initially of perturbations in the magnetic field measured by ground magnetometers (Richmond & Kamide, 1988, and references therein; Richmond, 1992), to infer the electrodynamic state of the ionosphere. In addition to currents measured at the ground, the model was expanded to include measurements of electric fields by radar and satellite, and magnetic perturbations from satellite. However, given the wide distribution of ground magnetometer sites and the relative sparsity of other forms of data AMIE ingests, the model is mostly driven by ground‐based magnetic field perturbations.

For a full description of the methodology used in the model, the reader is referred to the paper by Richmond and Kamide (1988). Briefly, the model uses as basis functions, the electrostatic potential, Ф, the electric field, E, the field‐aligned current density, J_P, the height‐integrated horizontal ionospheric electric current density, I, and magnetic perturbations δB. The basis functions for the potential, ϕ, are assumed to be complete, while the other basis functions, E, I, J_P, can be derived from ϕ, assuming knowledge of the conductance tensor, ∑. Using Gauss‐Markoff optimization of the linear expansion of the basis terms in magnetic latitude and longitude, the model derives the best fit of the coefficients in the expansion to the observations, which are assimilated.

In general, the model has been successful in reproducing electrodynamics in the high‐latitude ionosphere (Lu et al., 1995; Ridley et al., 1997, and many others). As in the case of the W05 and Cosgrove14 models, AMIE has been used widely as input to the GCMs. Unlike the empirical models, AMIE captures near‐real‐time variations in high‐latitude electrodynamics, with some smoothing in the assimilation scheme. Temporal and spatial resolution depend on the data to be assimilated.

However, there at two caveats. The assumption that the currents in the ionosphere can be represented by equivalent currents on the ground needs to be applied with caution. The assumption is valid in the case of Hall currents, which are detected by ground magnetometers. Comparisons of satellite‐based measurements from CHAMP and ground detections of currents from the IMAGE network have validated the equivalent current assumption (Ritter et al., 2004). However, ground‐detection of Pedersen current is inhibited by the shielding effect of FACs (Araki et al., 1989). As a result, correlation of ground‐ and space‐based observations of Pedersen currents is poor (Ritter et al., 2004). In practice, AMIE uses an empirical model to relate the measured Hall current to Pedersen current (Ahn et al., 1983a). But the empirical models are frequently based on observations limited to the auroral regions. Application of the results to subauroral or polar latitudes is questionable.

The only region at high latitudes in which Hall current dominates is the auroral zone in which energetic particle precipitation is the norm (Newell et al., 2005, and references therein). At latitudes poleward and equatorward of the auroral zone, or Boundary Plasma Sheet as described by Newell et al. (1991), which are characterized by soft electron precipitation, the use of empirical models to estimate Pedersen conductivity may distort the true picture. The lack of ground signature of ionospheric electrodynamics was illustrated in a study of a superstorm on 6 April 2000 by Huang and Burke (2004). During the storm, four DMSP spacecraft detected intense FACs, with ΔB between 1,000 and 1,400 nT at 840 km altitude, at latitudes equatorward of 60° MLat. At the conjugate location on the ground, the maximum magnetic perturbation was under 50 nT.

The second cautionary note on application of AMIE is related to the first, and derives from the conductance that is required for the synthesis of observations. The standard model referenced for use with AMIE is by Ahn et al. (1983a). The estimate of conductivity in this model assumes energetic electron precipitation leading to Hall current at altitudes between 100 and 125 km. Pedersen conductivity is estimated from Hall conductivity as a ratio derived empirically. Robinson et al. (1987) give a similar relationship. However, these empirical ratios are derived for auroral precipitation in which electron energies are generally assumed to be ≥1 keV. Huang and Burke (2004) estimated the Pedersen conductance using measured magnetic deflections and precipitating electron fluxes from DMSP F13 and F15 satellites for the superstorm on 6 April 2000. The relation between conductance, magnetic field, and electric field is simply Ohm’s law, J = ∑ x E, where J and E are the height‐integrated current density and electric field, respectively. Figure 1.6 compares the values obtained from the DMSP data with the Robinson et al. (1987) formulas for Pedersen and Hall conductances. The horizontal bars indicate the time intervals when Pedersen conductance can be estimated directly. It is clear that the empirical results (Ahn et al., 1983a; Robinson et al., 1987) do not represent the conductance well in regions where keV electrons are not dominant.

Figure 1.6 (a)–(b) Values of Pedersen (∑_P) and (c)–(d) Hall (∑_H) conductance estimated from energetic electron fluxes measured by (a) and (c) DMSP F15 and (b) and (d) F13 using the formula by Robinson et al. (1987) during a superstorm on 6 April 2000. F15 is located at ‐52° MLat, 221 MLT. F13 is located at 59.9° MLat, 6.7 MLT. Heavy horizontal lines indicate values of ∑_P estimated from measured δB_z and E_Y variations

(figure and caption based on Huang & Burke, 2004. Reproduced with permission of John Wiley & Sons).

Given our understanding that EM energy dominates the energy budget, the assumptions underlying the model should be examined for relevance. In particular, the role of the auroral zone as the locus of all energy input has been questioned (Huang et al., 2014) based on the total energy budget during a magnetic storm. This may be addressed by AMIENextGen, an updated version of AMIE, which is being developed (Matsuo et al., 2015; Cousins et al., 2015; McGranaghan et al., 2016). In AMIENextGen, many of the data sources are based on satellite observations, which may avoid some of the difficulties with AMIE.