4. Summary

c. Future Themes and Problems

We have made a step forward in the investigation on the solar constant dependence of atmospheric conditions, including the conditions for the emergence of the runaway greenhouse state. However, the results obtained are for extremely simple systems, and implications for phenomena in the actual world may be limited. There are vast numbers of problems that must be overcome, including those related to the radiation process and cloud effects. Below, we will list some of the challenges and problems with the present study:

• Assessing the general applicability of the results:
  The main conclusion of the present study: "The value of the runaway limit may be represented as the outgoing limit in a 1D model" is attributed to the reduction in meridional contrast in the equilibrium states with increased solar constant. Since the degree of meridional contrast and the magnitude of meridional heat transport can be regarded as being closely connected, a change in the feature of heat transport may force us to change the above conclusions. Based on such perspectives, it would be interesting to perform calculations using conditions where the rotational rate is changed (resulting in a circulation pattern change of the Hadley cell, Williams, 1988a,b) or where the solar flux distribution is changed (when only one side of the planet is heated, the day-night convection becomes dominant).
• Relative humidity distribution:
  The value of the runaway limit is strongly dependent on the relative humidity distribution. Thus, in order to gain a full understanding of the runaway limit, we must first determine how relative humidity is distributed. As the first step, it will be necessary to make a detailed analysis of the water vapor balance in the results we have obtained so far, with taking into consideration the effects of diffusion and advection.
• Wave motion in upper layers:
  In the present study, the vertical filter was introduced in order to eliminate two-grid noise and enable long-time integration. However, the vertical filter prevents us from properly calculating the circulation field in the upper layer. In the future, we must search for a more appropriate technique to eliminate noise by studying the properties of the wave disturbances that are generated in the middle atmosphere with increased solar constant.
• Analysis of Circulation Structure:
  We have barely begun to analyze the changes in the circulation structure that occur with change in solar constant. There are numerous themes of interest associated with circulation structure, including the circulation structure of the middle atmosphere and the generation and sustaining mechanisms of disturbances near the tropical regions. They shall also be among the themes for future research.
• Cloud effects:
  The model employed in the present study is extremely simple and there are numerous points for modification, and/or elements that must be incorporated into it, before we can use it to determine the runaway limit value for an actual planet with some degree of reliability. These include topography (including the distribution of ocean and land), surface conditions (including albedo and the effect of heat transport by the ocean). However, the most important factor that was not considered in our study is cloud effects. For 3D system in which the existence of cloud is considered, the emergence of a runaway greenhouse state can emerge with solar constant large enough to overcome the albedo effect of cloud. Nevertheless, the value of the runaway limit may change dramatically. It is extremely difficult to quantify cloud effects in the condition that the value of solar constant increases. Thus, significant advancements must be made in the remote-sensing observations of the present terrestrial atmosphere, and in theoretical studies using cumulus convection models, before we can even begin to take the cloud effects into consideration.

4.c. Future Themes and Problems