i. What Determines a Runaway Limit?
(Description with an Equilibrium Solution of 1D Radiative-Convective Model)
Based on the results shown in previous sections, we will now compare
the 1D radiative-convective equilibrium solution and the results of
3D model calculation. It should be noted that relative humidity of
the results obtained by 3D numerical calculations is not 100 %. In
Nakajima et al. (1992), the all 1D equilibrium solutions
assume a value of relative humidity of 100% in the
troposphere. Here, we did not attempt to adjust the relative
humidity to 100 %, but instead examined the equilibrium solutions in
the 1D radiative-convective model with relative humidity fixed at 60
%, which is the value obtained in the 3D calculations. Figure 1
shows the 3D calculation results superimposed on the vertical
temperature structure of the 1D equilibrium solution. It can be seen
that the temperature structure near the level at
which τ = 1 is determined by the moist
adiabatic temperature gradient. Furthermore, the upper limit of OLR
calculated from the 1D equilibrium solution with relative humidity
fixed at 60 % is around 390 W/m2 (Figure 2), and is
nearly equivalent to the value of the runaway limit in the 3D
model. The upper limit of OLR exists in 1D calculations because the
temperature near the τ = 1 level is
determined by adiabatic lapse rate and imposes an upper limit in
radiation flux at the top of the troposphere. This ultimately
implies that the runaway limit in the
3D system is determined by the constraint on radiation flux emitted
from the troposphere with considering relative humidity.
Figure 1: The vertical distribution of global
mean temperature (red) and that obtained by 1D radiative
convective equilibrium model (aqua).
|
Figure 2: The OLR profile (W/m2) as
a function of surface temperature (K) obtained by the 1D
radiative convective equilibrium model given various relative
humidity values: The red line shows 100 %, the yellow line shows
80 %, the green line shows 60 %, and the blue line shows 40
%. Aqua and purple circles show the relationship between global
mean surface temperature and OLR calculated by GCM: The aqua
circles represent equilibrium states, and the purple circles are
in the runaway greenhouse states at Day 1000 or 2000.
|
Based on the above discussions, it is strongly suggested that an
upper limit of outgoing radiation also exist in 3D models based on
the equilibrium solution. Therefore, it may be concluded that the
present study has successfully established that the thermal runaway
state obtained in our 3D numerical calculations corresponds to the
runaway greenhouse state , that is, the case where the incident
solar radiation flux exceeded the upper limit of outgoing radiation
that was determined by equilibrium solutions of Nakajima et
al. (1992). Based on this reason, it has also been confirmed
that the thermal runaway state obtained for cases
of S ≥ 1600 W/m2 can be
rightfully referred to as the runaway greenhouse state.
