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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 kilometer-size convection
is properly incorporated. Current GCMs for the Martian atmosphere
employ a convective adjustment scheme to represent the effects of
unresolvable thermal convection. The convective adjustment scheme
adjusts a convectively unstable temperature gradient to a neutral
state as the result of convective heat transport. This convective
adjustment scheme, and any other parameterization scheme, does not
properly represent wind fluctuations associated with kilometer-size
convection and their contribution to surface stress.
Since the structures of vertical convection in the Martian atmosphere
are not well investigated, we had almost no choice other than to adopt
a convective adjustment scheme for the Martian atmospheric
GCMs. Cumulus convection, which is a dominant process for thermal
transport from the surface to the troposphere in Earth's atmosphere,
is similar to the kilometer-size convection of the Martian
atmosphere. As for terrestrial GCMs, various types of cumulus
convective parameterization schemes have been developed in order to
produce a proper representation of cumulus convection. A simple scheme
is convective adjustment, and more complex schemes incorporate the
distribution of vertical size, entrainment into cumulus clouds, and so
on (e.g., Arakawa and Schubert,
1974). Cumulus convective parameterization is possible due to the
accumulation of real images of cumulus convection and by breakthroughs
of theories. However, what is emphasized in these cumulus
parameterizations is not wind fluctuation but vertical thermal
transport. A convective parameterization scheme that incorporates wind
fluctuations 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, kilometer-size convection. Ground
surface stress in GCMs is calculated from the intensity of winds,
which is explicitly represented in a model parameterized by a
formulation called the bulk formula. In the numerical model used in
the present study, ground surface stress is also calculated via the
bulk formula. Nevertheless, the magnitude of surface stress calculated
in this study is larger than that of GCMs. This is caused by an
explicit calculation of kilometer-size convection.
As is observed in (Figure 5 and
Figure 6), the horizontal mean
surface stress calculated in the present study is not very
large. However, the local values of surface stress are much larger
than the horizontal mean values due to large wind fluctuations
associated with the kilometer-size convection. The values of surface
stress that are represented in the parameterizations of GCMs, even if
the contribution of subgrid-scale turbulence and kilometer-size
convection is incorporated, are averaged for a wide horizontal area of
the GCM grid size. These values correspond to the horizontal mean
stress obtained in the present study, and consequently, should be
smaller than maximum values that appear locally.
Based on the features of the kilometer-size convection revealed by the
present numerical study, a new convective parameterization scheme can
be developed that can estimate wind fluctuation and the maximum value
of surface stress associated with convection. The scheme would
basically consist of a convective adjustment scheme modified with the
addition of the kinetic energy calculations scheme.
By using the potential temperature fluctuation
and depth of the convective layer
 ,
convective kinetic energy is evaluated in the form of Equation
(1).
Assuming the turbulent diffusion coefficient near the surface, for
instance, is the value of the lowest level of the GCM, or given simply
as
= 15 m2 sec-1,
can be evaluated by heat flux
Q
which can be obtained from GCM output as in Section 3.d.
The magnitude of wind fluctuations that are associated with
kilometer-size convection can be estimated by such values. If wind
fluctuation magnitude is estimated in this manner and incorporated
into the calculation of surface stress in
the surface flux parameterization, we expect
dust will be spontaneously lifted from the surface of GCM simulations.
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