## g. What Determines a Runaway Limit?

(Comparison with the Stratospheric Model)In this section, we will present a discussion on what determines the runaway limit, or the value of the solar constant at which the runaway greenhouse state emerges, in 3D models.

How should the problem be approached ?

Based on our results so far, it was found the meridional contrast of OLR is reduced with increases in solar constant, and the value at the equator reaches a level slightly lower than 400 W/m^{2}. Based on this observation, it may be speculated that the value of OLR approaches 400 W/m^{2}with increases in solar constant, regardless of latitude. If the asymptotic value of OLR is indeed 400 W/m^{2}, then it will provide an explanation for the results of the parameter study that the runaway greenhouse state emerges when solar constant exceeds 1600 W/m^{2}. At solar constant value of 1600 W/m^{2}, global mean incident flux is calculated to be 400 W/m^{2}, and is equal to the asymptotic value OLR. Ultimately, the problem of what determines the runaway limit all comes down to the problem of why the asymptotic value of the OLR is 400 W/m^{2}.

What Determines the Asymptotic Value of OLR ?

Previous studies have discussed outgoing radiation from terrestrial planets using 1D models and have shown that the following two types of constraining conditions exist:

- Constraint on radiation flux passing through the stratosphere:

Outgoing radiation from the top of the atmosphere cannot exceed the upper limit of radiation of the stratospheric model (Komabayashi-Ingersoll limit: 385 W/m^{2}).- Constraint on radiation flux emitted from the troposphere:

The flux of outgoing radiation emitted from the top of the atmosphere must be consistent with that of emitted from the troposphere. Since an upper limit exists in the outgoing radiation emitted from the troposphere, it then follows that there is an upper limit to the outgoing radiation from the top of the atmosphere (350 W/m^{2}) as well.Therefore, we will approach this problem based on the asymptotic value of OLR and these two constraining conditions.

Does the Asymptotic Value of OLR Correspond to the Komabayashi-Ingersoll Limit?

The asymptotic value of OLR, 400 W/m^{2}, is extremely close to the Komabayashi-Ingersoll limit, which is determined from the constraint on radiation flux passing through the stratosphere in a 1D model. However, the value of Komabayashi-Ingersoll limit, 385 W/m^{2}, is the limit for cases in which the tropopause is saturated. The tropopause was not saturated in the results of our 3D calculations and relative humidity at the tropopause for S1570 was approximately 0.5. At a value of relative humidity of 0.5, the upper limit of outgoing radiation that is determined by the constraint on radiation flux passing through the stratosphere will be approximately 450 W/m^{2}. (For more information, see The Komabayashi-Ingersoll Limit When Relative Humidity is Considered.) This implies that the asymptotic value of OLR in the 3D model is not determined by the stratospheric flux constraint. If 3D results correspond to the 1D equilibrium solution, the asymptotic value of OLR and the constraint on the radiation flux emitted from the troposphere should be the determining factors. The feasibility of this hypothesis is examined in the next section.