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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.
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