successful in providing high‐latitude electric fields required to model the IT response to magnetospheric energy input. While W05 can be used to specify the Joule heat as a standalone model, the major application of the code is in providing the high‐latitude electric field required by the General Circulation Models (GCMs), which will be discussed below.
The main drawback to W05 is the lack of dynamical behavior inherent during periods of magnetic activity. Empirical models cannot capture the highly fluctuating magnetospheric energy input during storms. This is evident in a comparison of Poynting flux measured along the DMSP orbit with predicted values from the model, as shown in Figure 1.4, reproduced from Figure 10 of Huang et al. (2017a). On the left are shown the estimated values of Poynting flux from the DMSP measurements of cross‐track horizontal velocity and FACs during a magnetic storm, which occurred on 5–6 August 2011. The Northern Hemisphere (NH) is shown above, the Southern Hemisphere (SH) below. Measured values along the orbit track are shown as overplots with the highest value plotted last. On the right are the model predictions of W05 along the same orbital tracks as DMSP plotted in the same way. The highest value of Poynting flux in each panel is indicated at the bottom left of the panel, together with the magnetic latitude (MLat) and magnetic local time (MLT) of the location where that value of Poynting flux occurred.
Figure 1.4 Comparison between observed Poynting flux from DMSP (a)–(c) with the W05 model predictions along the DMSP orbit (b)–(d) for the 5 August 2011 storm. Northern Hemisphere values are shown in (a) and (b); Southern Hemisphere results are shown in (c)–(d)
(figure reproduced from Fig. 10 by Huang et al., 2017a. Reproduced with permission of Elsevier).
The discrepancies in the values and spatial distribution of Poynting flux between observations and W05 in this case are clear. The model captures the average distribution and magnitude of EM energy entering the ionosphere, but dynamic variations, which characterize the storm, are missed. In different events, the discrepancies can be similar or different. This is not intended as a criticism of the model, merely to point out the limited ability of empirical models to represent dynamic processes such as magnetic storms.
1.2.3 The Cosgrove Model
A newer empirical model of EM input has been developed by Cosgrove et al. (2014) (hereafter referred to as Cosgrove14) based on data from the FAST satellite. At the outset, the paper states that one goal of the model is to provide the high‐latitude electric field driver for GCMs. A major difference between the Weimer and Cosgrove models lies in the way Poynting flux is calculated. In W05, the EM energy is estimated from the average electric field <E> and the average magnetic perturbation <δB> as S = <E> x <δB > /μ0 In Cosgrove14, the vector product, S = E x δB/μ0, is calculated before any averaging or functional fits are applied. In this way, perturbations in the measured E and B are captured more accurately. As pointed out in past studies, variability in the electric field can contribute to the total Joule heat (Codrescu et al. 1995; Cosgrove & Codrescu, 2009). In the standard formulation employed in W05, Joule heat is computed as the mean of <E 2>. However, if there is a high level of fluctuation about the mean of E (i.e., if <|E − < E>|2> is large), then the contribution to Joule heat from the variability is missing if it is assumed that <|E|> represents the total electric field. Codrescu et al. (2000) used radar measurements to calculate the <|E − < E>|2> term, and found that the variability was comparable with the mean value of E. In Cosgrove14, the direct estimate of Joule heat from the measured E attempts to avoid this problem.
Possibly as the result of the methodology, or because the data from which this model is derived is more comprehensive, the model predictions of Poynting flux in the cusp is significantly larger than that forecast by W05. Figure 1.5 (reproduced from Figure 5 in Cosgrove et al., 2014) illustrates the cusp feature for northward IMF, for high (top) and low (bottom) magnetic activity. In this model, the pattern of Poynting flux for high magnetic activity is generally similar to the upper panel of Figure 1.5, regardless of IMF orientation.
Figure 1.5 Cosgrove14 output for high and low magnetic activity for northward IMF. The upper and lower panels have different color bars to prevent saturation. The AL index is shown at center above each panel. The integrated Poynting flux is shown at left above each panel. The Poynting flux for high magnetic activity is similar to that for southward IMF, regardless of actual IMF. IMF clock angle is 0°, magnetic dipole tile angle is 0°, solar wind velocity is 450 km s‐1, solar wind number density is 4 cm‐3, and IMF strength in the GSM y‐z plane is 5 nT
(figure and caption reproduced from Cosgrove et al., 2014. Reproduced with permission of John Wiley & Sons).
However the basis of Cosgrove14 is a representation of the high‐latitude Poynting flux by spherical harmonical fits to averages of the measurements. This arrives at the same problem with W05, namely that the model predictions cannot reproduce the highly variable energy input into the IT system characteristic of high magnetic activity. As stated in the paper (Cosgrove et al., 2014), “averaging over a large number of events, as is done to produce this model, will result in significant smearing. Because of this, the model output is not representative of an instant of time, but rather reflects an expected value for each UT, MLT, MLAT, and set of geophysical parameter values.” The Cosgrove14 model, which is relatively new, has yet to undergo the testing and validation that occurred with W05 and previous version of the Weimer models.
1.2.4 Assimilative Modeling of Ionospheric Electrodynamics (AMIE)
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, JP, 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, JP, 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