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5.b. Convective parameterization in GCM
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Our simulation results suggest that dust injection into the atmosphere
can be self-consistently simulated by using GCM with dust-free initial
condition if a small-scale wind fluctuation associated with the
km-size thermal convection is considered.
In order to represent the effects of the unresolvable thermal convection,
current Mars GCMs employ the convective adjustment.
However, the convective adjustment scheme only "adjusts" convectivly
unstable temperature gradient to the neutral one, without
considering kinetic energy budget at all.
Therefore, no information on wind fluctuation associated with the
km-size thermal convection and its contribution to the surface are
available.
Another convective parameterization scheme which can consider kinetic
energy of the thermal convection have not be developed because
dynamical structure of the thermal convection, for example, the
circulation pattern of convection and the magnitude of convective
wind were not revealed.
The cumulus convection, which is dominant process to transport thermal
energy from the surface to the whole of troposphere in the
terrestrial atmosphere, is corresponding phenomenon to the km-size
thermal convection in the Martian lower atmosphere.
Various convective parameterization schemes which represent vertical
heat transport associated with the unresolved cumulus convection in
terrestrial GCM have be developed, because the thermal and
dynamical structure of cumulus convection are revealed by many
obsrvation and theoritical studies.
The convective adjustment is the simplest one.
In more complex schemes, the vertical size distribution and
entrainment of cumulus cloud are considered as parameters (c.f., Arakawa and Schubert, 1974).
However, the cumulus parameterization focuses on not wind fluctuation
but vertical heat transport associated with the cumulus convection.
The convective parameterization which can estimate wind fluctuation
associated with the cumulus convection neither have be considered
nor be required to terrestrial GCMs.
This numerical study reveals that the thermal convection in the
Martian lower atmosphere is km-size convection.
The surface stress associated with the km-size convective wind is
calculated from the lowest level horizontal wind velocity by using
the bulk formula which is used in GCMs.
In spite of using the same bulk formula, the instantaneous value of
surface stress simulated by our 2D numerical model is much larger
than that by GCM because of explicit calculation of the
km-size convection.
The order of magnitude of horizontal mean surface stress simulated by
our 2D numerical model (Figure
5, Figure 6) is equal to
that by GCM.
However, the instantaneous values of surface stress is much larger
than the horizontal mean value because of existence of the wind
fluctuation associated with the km-size convection.
The surface stress represented in GCM is averaged over the horizontal
scale of GCM grid which is larger than that of the km-size
convection.
Therefore, the value of surface stress simulated by GCM corresponds to
that of horizontal mean surface stress simulated by our 2D
numerical model, and is smaller than the instantaneous maximum value.
Based on the feature of km-size thermal convection revealed by this
numerical study, we can develop a new convective parameterization
scheme which can be estimate wind fluctuation and instantaneous
maximum value of surface stress associated with the km-size thermal
convection, which is a convective adjustment including kinetic
energy calculation scheme.
The kinetic energy, or, wind fluctuation of the thermal convection can
be estimated from temperature fluctuation  and
depth of convection layer  by using
equation (1).
can be estimated from heat flux  which should be transported by the thermal
convection and turbulent diffusion coefficient K near the
surface by using estimation scheme discussed in Section 3.d.: and  can be obtained from output data of GCM.
If the wind fluctuations estimated by following the manner mentioned
above are considered in the calculation of surface stress, dust can
be raised from the surface under dust-free condition in GCM
simulations.
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