b. Previous Studies on the Runaway Greenhouse State
Previous studies on the runaway greenhouse state have used 1D models. A brief overview of those studies is provided below.
The concept of the runaway greenhouse state began with a qualitative discussion based on the following dynamic scenario: Assume a case in which the incident solar radiation flux applied to a terrestrial planet increases slightly. Since this will increase the planetary surface temperature, water vapor evaporation from the surface would increase as well. The increased amount of water vapor in the atmosphere will then lead to a further increase in surface temperature due to the greenhouse effect. Such positive feedback might result in a cycle in which both the surface temperature and water vapor amount continues to increase (Simpson, 1927; Gold, 1964; Goody and Young, 1989; a review by Goody and Young, 1989). However, as will be described below, previous studies have based most of their discussions on equilibrium models, despite the above dynamical scenario of the runaway greenhouse state.
While the above-mentioned discussions are limited to qualitative "thinking", Komabayashi (1967) and Ingersoll (1969) engaged in the first quantitative discussions on the runaway greenhouse effect by assuming a stratosphere in radiative equilibrium saturated on its lower boundary, and then showing that there is an upper limit of radiation that is emitted from the top of the atmosphere. This has come to be referred to as the Komabayashi-Ingersoll limit. If incident solar radiation flux exceeds this limit, the atmosphere cannot reach an equilibrium state and temperature is expected to keep increasing. Ingersoll (1969) called this "the emergence of the runaway greenhouse state".
Pollack (1971) used a non-gray radiation scheme to calculate the runaway greenhouse state under cloud-present conditions, and confirmed that, even under such conditions, there is an upper limit of radiation emitted from the atmosphere. Additionally, although Abe and Matsui (1988) and Kasting (1988) targets the primitive atmosphere, their results suggest that the runaway greenhouse state will emerge even in cases where radiative processes are elaborately modeled.
Furthermore, since the radiation emissivity of atmospheres of terrestrial planets are determined by the temperature structure and water vapor distribution which are affected by cumulus convections, studies have also been conducted to evaluate how the incorporation of cumulus convection into the model would affect the runaway greenhouse state. Lindzen et al. (1992) suggested the possibility that certain convection models would have suppressing effects on the runaway greenhouse state. It has also been argued that the incident solar radiation flux at which the runaway greenhouse state appears (hereinafter referred to as the runaway limit) is dependent on the cumulus parameterization scheme by Vardavas and Carver (1985) based on 1D equilibrium solution calculations, and by Renno et al. (1994) based on time evolution studies.
All of the above studies have concluded that a critical value of incident solar radiation flux exists, over which atmosphere-ocean equilibrium and coexistence becomes impossible. However, it had yet to be determined whether the Komabayashi-Ingersoll limit and the critical value at which the runaway greenhouse state emerges in Abe and Matsui (1988) are caused by the same mechanism. Their definitions of the runaway state and their respective relationships to the critical values remained unclear, and no standardized definition emerged for the runaway greenhouse state concept. The first clear definition of the runaway greenhouse state was presented by Nakajima et al. (1992), in which the limit value of emitted radiation is investigated using a 1D radiative-convective equilibrium model of a gray atmosphere. The results show that there are several limiting conditions to the emission of radiation by the atmosphere (the existence of an emissivity limit), and that the maximum emission flux from the atmosphere when the amount of dry air and values of specific heat are selected to resemble Earth conditions will be 350 W/m2. It was also found that the point at which the equilibrium solution with ocean ceases to exist in Abe and Matsui (1988) and Kasting (1988) corresponded to the upper limit of radiation determined by the temperature structure of the troposphere.
See the chronology below for a list of major studies on the runaway greenhouse state, and for a summary of discussions on 1D models.
- Chronology of Studies on Runaway Greenhouse State:
Below are some of the past studies on the runaway greenhouse state.
- Summary of results of 1D Models:
Previous studies have established that a upper limits of radiation that are determined by several mechanism exist, which are summarized in the followings. The results are also presented for cases that take relative humidity into consideration. For a relative humidity of 60% and a partial pressure of dry air at the lower boundary of the atmosphere of 105 Pa, the upper limit of radiation obtained by the gray radiation 1D radiative-convective equilibrium model is 390 W/m2.