a. Equilibrium State: Meridional Structure of the Troposphere
For the case of S = 1380 W/m2, integration can be
performed over a long time period with L32 simply by including the
Rayleigh friction and Newtonian cooling in the upper-most layer. In
the discussions below, calculation results will be described for the
case in which the time constants of the Rayleigh friction and
Newtonian cooling in the upper-most layer are set to 3 hours and the
time integration is performed for 1000 days. The disadvantages
associated with the inclusion of damping layers and vertical
filtering will be discussed by comparing these results to those from
Experiment S1380 (which includes seven damping layers and
vertical filtering in all layers).
Figure 1(a) shows the meridional distributions of temperature and
mass stream function. The temperature distribution pattern is
similar to that of the Earth's current atmosphere. Nonetheless,
because a gray atmosphere is assumed, the tropopause height
is σ= 0.2, which is low. Although the tropopause is
evident in this figure, vertical temperature gradient is decreased
with implementation of filtering (Figure 1(b)). Regarding the
meridional circulation, the Hadley circulation becomes weak in
response to implementation of filtering. A comparison between
Figures 1(a) and 1(b) reveals that the implementation of filtering
causes the strength of the Hadley circulation to become
approximately half of the original strength. However, the
latitudinal width of the Hadley circulation remains almost the same
between the calculations with and without filtering. It is not yet
well understood why implementation of filtering weakens the strength
of the Hadley circulation. With the filtering, condensation heating
in the equatorial region decreases, which is likely to be one factor
that contributes to the weakening of the Hadley circulation.
(a)  |
(b)  |
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Figure 1: Meridional distributions of temperature (K) and mass stream function (kg/sec). (a) Without filtering and with a single damping layer. (b) Experiment S1380 (filtering included in all layers, seven damping layers).
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Figure 2 shows the water vapor distributions. With the
implementation of filtering, the water vapor content in the upper
portion of the tropical troposphere decreases. The deceased water
vapor content may be explained by the weakening of the Hadley
circulation, which occurs due to the implementation of vertical
filtering.
(a)  |
(b)  |
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Figure 2: Meridional distributions of specific
humidity (kg/kg). (a) Without filtering and with a single damping
layer. (b) Experiment S1380 (filtering included in all layers, seven
damping layers).
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Figure 3 shows meridional distributions of relative humidity. With
filtering, relative humidity decreases in the equatorial
troposphere. As will be described in What
Determines the Runaway Limit?, the runaway limit is highly
dependent on relative humidity. Therefore, determining whether
introducing filtering leads to a relative humidity distribution
different from that obtained without filtering is a matter of
serious concern. In order to determine the runaway limit accurately,
two-grid noise processing, which is a physically sound method, needs
to be applied rather than a makeshift solution such as vertical
filtering.
(a)  |
(b)  |
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Figure 3: Meridional distributions of relative
humidity. (a) Without filtering and with a single damping layer. (b)
Experiment S1380 (filtering included in all layers, seven damping
layers). |
Figure 4 shows meridional distributions of zonal wind. Without
filtering, zonal wind is easterly within the entire equatorial
region, and the structure is similar to that of the actual
Earth. However, with the implementation of filtering, the wind in
the vicinity of σ= 0.6 becomes westerly, although weak.
(a)  |
(b)  |
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Figure 4: Meridional distributions of zonal wind
(m/sec). (a) Without filtering and with a single damping layer. (b)
Experiment S1380 (filtering included in all layers, seven damping
layers).
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