Runaway greenhouse effect

A runaway greenhouse effect is when there is enough of a greenhouse gas in a planet's atmosphere such that the gas blocks thermal radiation from the planet, preventing the planet from cooling and from having liquid water on its surface. The runaway greenhouse effect can be defined by a limit on a planet's outgoing longwave radiation which is asymptotically reached due to higher surface temperatures boiling a condensable species (often water vapor) into the atmosphere, increasing its optical depth. This runaway positive feedback means the planet cannot cool down through longwave radiation (via the Stefan–Boltzmann law) and continues to heat up until it can radiate outside of the absorption bands of the condensable species. The runaway greenhouse effect is often formulated with water vapor as the condensable species. In this case the water vapor reaches the stratosphere and escapes into space via hydrodynamic escape, resulting in a desiccated planet. An example of this is believed to have happened in the early history of Venus. A runaway greenhouse effect is when there is enough of a greenhouse gas in a planet's atmosphere such that the gas blocks thermal radiation from the planet, preventing the planet from cooling and from having liquid water on its surface. The runaway greenhouse effect can be defined by a limit on a planet's outgoing longwave radiation which is asymptotically reached due to higher surface temperatures boiling a condensable species (often water vapor) into the atmosphere, increasing its optical depth. This runaway positive feedback means the planet cannot cool down through longwave radiation (via the Stefan–Boltzmann law) and continues to heat up until it can radiate outside of the absorption bands of the condensable species. The runaway greenhouse effect is often formulated with water vapor as the condensable species. In this case the water vapor reaches the stratosphere and escapes into space via hydrodynamic escape, resulting in a desiccated planet. An example of this is believed to have happened in the early history of Venus. While the term was coined by Caltech scientist Andrew Ingersoll in a paper that described a model of the atmosphere of Venus, the initial idea of a limit on terrestrial outgoing infrared radiation was published by George Simpson (meteorologist) in 1927. The physics relevant to the, later-termed, runaway greenhouse effect was explored by Makoto Komabayashi at Nagoya university. Assuming a water vapor-saturated stratosphere, Komabayashi and Ingersoll independently calculated the limit on outgoing infrared radiation that defines the runaway greenhouse state. The limit is now known as the Komabayashi-Ingersoll limit to recognize their contributions. The runaway greenhouse effect is often formulated in terms of how the surface temperature of a planet changes with differing amounts of received starlight. If the planet is assumed to be in radiative equilibrium, then the runaway greenhouse state is calculated as the equilibrium state at which water cannot exist in liquid form. The water vapor is then lost to space through hydrodynamic escape. In radiative equilbrium, a planet's outgoing longwave radiation (OLR) must balance the incoming stellar flux. Typically a planet's outgoing longwave radiation is equal to the planet's surface temperature to the fourth power due to the Stefan–Boltzmann law, though in a runaway greenhouse state this balance is broken. The Stefan-Boltzmann law is an example of a negative feedback that stabilizes a planet's climate system. If the Earth received more sunlight it would result in a temporary disequilibrium (more energy in than out) and result in warming. However, because the Stefan-Boltzmann response mandates that this hotter planet emits more energy, eventually a new radiation balance can be reached and the temperature will be maintained at its new, higher value. Positive feedbacks amplify changes in the climate system, and can lead to destabilizing effects for the climate. An increase in temperature from greenhouse gases leading to increased water vapor (which is itself a greenhouse gas) causing further warming is a positive feedback, but not a runaway effect, on Earth. Positive feedback effects are common (e.g. ice-albedo feedback) but runaway effects do not necessarily emerge from their presence. Though water plays a major role in the process, the runaway greenhouse effect is not a result of water vapor feedback. The runaway greenhouse effect can be seen as a limit on a planet's outgoing longwave radiation that, when surpassed, results in a state where water cannot exist in its liquid form (hence, the oceans have all 'boiled away'). A planet's outgoing longwave radiation is limited by this evaporated water, which is an effective greenhouse gas and blocks additional infrared radiation as it accumulates in the atmosphere. Assuming radiative equilibrium, runaway greenhouse limits on outgoing longwave radiation correspond to limits on the increase in stellar flux received by a planet to trigger the runaway greenhouse effect. Two limits on a planet's outgoing longwave radiation have been calculated that correspond with the onset of the runaway greenhouse effect: the Komabayashi-Ingersoll limit and the Simpson-Nakajima limit. At these values the runaway greenhouse effect overcomes the Stefan-Boltzmann feedback so an increase in a planet's surface temperature will not increase the outgoing longwave radiation. The Komabayashi-Ingersoll limit was the first to be analytically derived and only considers a grey stratosphere in radiative equilibrium. A grey stratosphere (or atmosphere) is an approach to modeling radiative transfer that does not take into account the frequency-dependence of absorption by a gas. In the case of a grey stratosphere or atmosphere, the Eddington approximation can be used to calculate radiative fluxes. This approach focuses on the balance between the outgoing longwave radiation at the tropopause, F IRtop ↑ { extstyle F_{ ext{IRtop}}^{uparrow }} , and the optical depth of water vapor, τ tp { extstyle au _{ ext{tp}}} , in the tropopause, which is determined by the temperature and pressure at the tropopause according to the saturation vapor pressure. This balance is represented by the following equations The Simpson-Nakajima limit is lower than the Komabayashi-Ingersoll limit, and is thus typically more realistic for the value at which a planet enters a runaway greenhouse state. For example, given the parameters used to determine a Komabayashi-Ingersoll limit of 385 W/m2, the corresponding Simpson-Nakajima limit is only about 293 W/m2. The Simpson-Nakajima limit builds off of the derivation of the Komabayashi-Ingersoll limit by assuming a convective troposphere with a surface temperature and surface pressure that determines the optical depth and outgoing longwave radiation at the tropopause. Because the model used to derive the Simpson-Nakajima limit (a grey stratosphere in radiative equilibrium and a convecting troposphere) can determine the water concentration as a function of altitude, the model can also be used to determine the surface temperature (or conversely, amount of stellar flux) that results in a high water mixing ratio in the stratosphere. While this critical value of outgoing longwave radiation is less than the Simpson-Nakajima limit, it still has dramatic effects on a planet's climate. A high water mixing ratio in the stratosphere would overcome the effects of a cold trap and result in a 'moist' stratosphere, which would result in the photolysis of water in the stratosphere that in turn would destroy the ozone layer and eventually lead to a dramatic loss of water through hydrodynamic escape. This climate state has been dubbed the moist greenhouse effect, as the end-state is a planet without water, though liquid water may exist on the planet's surface during this process. The concept of a habitable zone has been used by planetary scientists and astrobiologists to define an orbital region around a star in which a planet (or moon) can sustain liquid water. Under this definition, the inner edge of the habitable zone (i.e., the closest point to a star that a planet can be until it can no longer sustain liquid water) is determined by the outgoing longwave radiation limit beyond which the runaway greenhouse process occurs (e.g., the Simpson-Nakajima limit). This is because a planet's distance from its host star determines the amount of stellar flux the planet receives, which in turn determines the amount of outgoing longwave radiation the planet radiates back to space. While the inner habitable zone is typically determined by using the Simpson-Nakajima limit, it can also be determined with respect to the moist greenhouse limit, though the difference between the two is often small.