Surface temperature evolution is governed by the balance between incoming fluxs (direct solar insolation, thermal radiation from the atmosphere and the surface itself and turbulent heat fluxs) and thermal conduction in the soil. The parametrization of this last process is often rather crude in terrestrial GCMs where a great part of the surface temperature are either imposed or computed in oceanic models. For a dry planet like Mars, an accurate parametrization of heat conduction is crucial to determine correctly surface temperatures and their response to diurnal, synoptic and seasonal forcing. A new parametrization was therefore developed for the Martian version of the LMD GCM.
The time evolution of the temperature under the surface is given by a classical conduction equation
where the conductive flux is given by
and where and C are the soil conductivity and
specific heat per unit volume, respectively.
In the simple case of a vertically homogeneous soil
(which is assumed here), it can easily be shown that
the model, as far as the time evolution of the surface temperature is
concerned, is only dependent on the soil thermal inertia
.
Although atmospheric GCMs often use
force-restore schemes with one or two layers to simulate the time
evolution of the surface temperature,
it is much more accurate and
straightforward to perform a direct temporal integration of
these equations using a multi-layer difference scheme in the
ground [4, 16]. This was found to
be numerically cheap enough even for a large number of layers
in the soil: with 11 levels, this parametrization only
represents 0.1 of the CPU-time of the Martian GCM.
The soil model is similar to that presented by Warrilow et al. (1981).
The accuracy of the model was checked by computing the phase and
intensity of the surface temperature oscillation forced by a sin varying
surface flux.
For periods in the range from 0.3 to 2000 sols, the model produces errors of less than
1 on the intensity and phase shifts lower than
.