4. Summary

 The dependency of the structure of the three-dimensional gray atmosphere on the solar constant and the runaway greenhouse states. 3.i. What Determines a Runaway Limit? (Description with an Equilibrium Solution of 1D Radiative-Convective Model) 4.b. Implications of the Present Study

a. Conclusion

For the problem posed at the beginning of the present paper, the answers we obtained are as follows:

0. What is the feasibility of calculations with large values of solar constant?
In order to perform 3D calculations for cases where the solar constant is increased, the two-grid noise that is most likely attributable to gravity waves must be appropriately suppressed. If this is not done, the amplitude of noise in the upper layer increases and prevents long-time integration. In the present study, a damping layer was added to the upper seven layers and the vertical filters of all layers as a makeshift solution .
1. Are the "runaway state" also realized in 3D?
The runaway greenhouse state appears in our 3D system. The runaway limit obtained in our calculations is S =1600 W/m2.
2. How does the equilibrium state change when the solar constant is changed?
In states with increased solar constant, the meridional temperature contrast decreases. This is due to the increase in the meridional transport of latent heat, which increases condensation heating at high latitude regions. Therefore, the thermal contrast is reduced in the meridional direction, and the meridional OLR distribution flattens. With regards to circulation, the intensity is weakened as the solar constant increases. The width of the Hadley cell remains almost unchanged.
3. What is the atmospheric structure of runaway greenhouse state?
When the runaway greenhouse state emerges, both surface and atmospheric temperature continue to increase, as will water vapor and total atmospheric mass. The solar radiation energy absorbed by the surface is almost completely supplied to the atmosphere from the surface in the form of evaporation flux. Nearly 70% of the evaporated water vapor condenses and heats the atmosphere. Condensation occurs in the equatorial regions and at latitudes near 60°. Extensive condensation occurs at high latitudes as well, and the surrounding atmosphere is heated. Thus, the meridional temperature contrast is decreased significantly.
4. What determines the runaway limit (solar constant at which the runaway greenhouse state emerges)?
Whether a runaway greenhouse state appears in a 3D gray atmosphere depends on the global mean value of incident solar radiation flux, irrelevant to the incident solar radiation flux distribution. In other words, the value at which the runaway greenhouse state emerges, defined as the runaway limit, may be represented by a 1D radiative-convective model that considers relative humidity. In the present calculations, the runaway limit was slightly below 400 W/m2.
4.a. Conclusion The dependency of the structure of the three-dimensional gray atmosphere on the solar constant and the runaway greenhouse states. 3.i. What Determines a Runaway Limit? (Description with an Equilibrium Solution of 1D Radiative-Convective Model) 4.b. Implications of the Present Study