The two models described above have been coupled together using the methodology shown in the figure below. This figure shows which fields are passed between the models and how these fields are used in the models.

As described above, the MHD model has a time step of 0.01 - 0.1 seconds, depending on the grid and the Boris factor used. The ionospheric boundary condition is considered to be electrostatic and is only calculated every 100th time step (i.e. every 1 to 10 seconds). The TIEGCM, on the other hand, has a typical time step of 60-300 seconds. Therefore, coupling between the models need only occur every 6th to 300th time that the ionospheric boundary condition is calculated.

When the coupling occurs, the ionospheric potential pattern (from the previous ionospheric potential calculation) and electron precipitation pattern (from the current time step) are fed into the TIEGCM. The electron precipitation is used to determine the nightside ionization in calculating the electron density. The electron density, combined with the densities of different neutral constituents, is subsequently used to determine the densities of different ion species. Collision rates between ions and neutrals are then calculated. These collision rates specify the acceleration of the neutral wind and the different conductivities.

The potential pattern is used to specify the high latitude motion of the ions. At this time, the TIEGCM has a sophisticated low-latitude dynamo solver. This solver determines the electric potential of the middle and lower latitude regions, while the high latitude region is specified by an external model (typically the Heelis or AMIE models). A transition region between the high latitude and midlatitude allows a the discontinuity in the modeling techniques to be spread over an approximately 10° latitude span. This latitudinal placement of this transition region is flexible and is changed for varying conditions.

For the low- and mid-latitude region, the neutral winds drive the dynamo calculation. This is done by taking a field-line integral of the neutral wind velocity multiplied by the conductivity. The divergence of this quantity is considered to be a quasi-neutral wind field aligned current, and is used for the calculation of the low- and mid-latitude dynamo in the TIEGCM. This quantity is also fed back into the MHD potential solver, where is is subtracted from the magnetospheric FACs.

The conductances are not consistent between the two models. In the MHD ionospheric model, the dayside conductances are calculated using an empirical relationship between F10.7, solar zenith angle and the Hall and Pedersen conductances. The effects of electron precipitation are included by the use of the Robinson 1987 formulation, which relates the electron precipitation to the Hall and Pedersen conductances.

The TIEGCM, on the other hand, calculates the electron density due to solar illumination, particle precipitation, advection, and other secondary sources. The electron densities, temperatures, and neutral densities are used to calculate collision rates between the different species, which are directly related to the Hall and Pedersen conductivities. Once this is done, the conductivities can be height integrated to give the conductances.

The reasoning for not using the TIEGCM calculated conductances in the MHD model is that the grid size in the TIEGCM (5° latitude by 5° longitude) is too large. The auroral zone is ill represented by the TIEGCM. Because the particle precipitation is calculated by the MHD model, and the conductances derived from the Robinson [1987] closely match those derived by models such as the TIEGCM, it was decided that it would be better to use the high resolution conductances from the MHD model than the low resolution conductances from the TIEGCM. Once the resolution of the TIEGCM is increased, a more self-consistent coupling can occur.

Figure 1 - MHD to TGCM

Figure 2- TGCM to MHD

For more information on the MHD model, visit the MHD Website.

For information on the TGCM models, visit the TGCM website.