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5.b. Treatment of convection in a GCM
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Our simulation results suggest that GCMs could simulate
dust injection into the atmosphere from a dust-free initial
condition if a small-scale wind fluctuation
associated with the km-size convection would be
properly incorporated.
Current GCMs for the Martian atmosphere
employ the convective adjustment schemle
to represent the effects of unresolvable thermal convection.
The convective adjustment scheme adjusts convectivly
unstable temperature gradient to the neutral one as the result
of convective heat transport;
The convective adjustment scheme and any other parameterization schemes
do not represent wind fluctuations associated with the
km-size convection and its contribution
to the surface stress are available.
Since the knowledge on the structures of vertical convection in
the Marian atmosphere has been quite limited, we have had
almost no choice other than adopting the convective adjust
scheme for Martian atmospheric GCMs.
The phenomenon in the Earth's atmosphere
that corresponds to the km-size convection in the Martian atmosphere
which is a dominant process of thermal transport from the
ground surface to the entire troposphere
is cumulus convection,
As for terrestrial GCMs, various kinds of
cumulus convective parameterization
schemes have been developed in order to have
a proper representation of cumulus convection.
The simplest one among them is the convective adjustment,
and more complex ones incorporate distribution of
vertical size of cumulus, entrainment into cumulus, and so on.
(e.g., Arakawa and Schubert, 1974).
The reason why the development of
cumulus convective parameterization has been possible is that
we have been accumulating real images of cumulus convection
to a certain extent through both of observations and theories.
However, what has been emphasized in those cumulus parameterizations
is not wind fluctuation but vertical thermal transport.
A convective parameterization scheme which incorporates
fluctuations of wind has not been considered in the
development of terrestrial GCMs.
The present study reveals several features of vertical convection
in the Martian atmosphere; that is the km-size conveticon.
Ground surface stress in GCMs
is calculated from the intensity of winds explicitly represented
in the model parameterized by the formulation called the bulk formula.
In the numerical model used in the present study
ground surface stress is also calculated by the bulk formula.
Nevertheless, the magnitude of ground surface stress calculated
in this study is larger than those of GCMs.
This is caused by the explicit calculation of the km-size convection.
As is observed in Figure
5, Figure 6,
the horizontal mean value of ground surface stress
calculated in the present study is also not very large.
However, the local values of ground surface stress can be much larger
than the horizontal mean value because of the large amount of wind
fluctuation associated with the km-size convection.
The ground surface stress represented in the parameterizations of GCMs,
where the contribution of subgrid scale turbulence including
km-size convection might be incorporated,
is the value representing an average
over a wide horizontal area of the scale of the GCM grid size.
Those values correspond to the horizontal mean stress obtained
in the present study, and consequently should be smaller than
the maximum values appearing locally.
Based on the features of the km-size convection revealed by the
present numerical study, we can develop a new convective
parameterization scheme which can estimate wind fluctuation
and maximum value of ground surface stress associated
with the convection.
The brief idea is to
evaluate convective kinetic energy
added on to the convective adjustment scheme.
By the use of potential temperature fluctuation 
and the depth of convecitve layer  ,
convective kinetic energy is evaluated roughly in the form
like (1).
Assuming the valude of turbulent diffusion coefficient near
the surface, for instance,
given by the value of the lowest level of the GCM
or given simply as
 = 15
m2sec-1,
from the discussed in Section 3.d.,
can be evaluated by the heat flux
obtained from the output of GCM.
The magnitude of wind fluctuation associated with the km-size convection
can be estimated by those values.
If the magnitude of wind fluctuations estimated in those manners
is incorporated into the calculation of surface stress
in Surface flux parameterization,
we expect dust can be spontaneously ejected from the surface
of GCM simulations.
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