Runaway greenhouse effect

A runaway greenhouse effect will occur when a planet's atmosphere contains greenhouse gas in an amount sufficient to block thermal radiation from leaving the planet, preventing the planet from cooling and from having liquid water on its surface. A runaway version of the greenhouse effect can be defined by a limit on a planet's outgoing longwave radiation, which is asymptotically reached due to higher surface temperatures evaporating water into the atmosphere, increasing its optical depth. This positive feedback loop means the planet cannot cool down through longwave radiation and continues to heat up until it can radiate outside of the absorption bands of the water vapour.
The runaway greenhouse effect is often formulated with water vapour as the condensable species. The water vapour reaches the stratosphere and escapes into space via hydrodynamic escape, resulting in a desiccated planet. This likely happened in the early history of Venus.
A 2012 study on climate change indicated that "Earth presently absorbs around 240 W m⁻² of solar radiation. Increasing carbon dioxide concentration will make surface warmer with the same outgoing thermal flux. Following this theory, we are not near the threshold of a runaway greenhouse. However, the behaviour of hot, water-vapour-rich atmospheres is poorly understood, and an in-depth study of these is necessary."
However, the authors cautioned that "our understanding of the dynamics, thermodynamics, radiative transfer and cloud physics of hot and steamy atmospheres is weak," and that we "cannot therefore completely rule out the possibility that human actions might cause a transition, if not to full runaway, then at least to a much warmer climate state than the present one."
A runaway greenhouse effect similar to Venus appears to have virtually no chance of being caused by anthropogenic activities. A 2013 article concluded that a runaway greenhouse effect "could in theory be triggered by increased greenhouse forcing," but that "anthropogenic emissions are probably insufficient." Venus-like conditions on Earth require a large long-term forcing that is unlikely to occur until the Sun brightens by some tens of percents, which will take a few billion years. Earth is expected to experience a runaway greenhouse effect "in about 2 billion years as solar luminosity increases".

History

While the term was first 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 in 1927. The physics relevant to what would later be named the 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. That limit is now known as the Komabayashi–Ingersoll limit, to recognize their contributions.

Physics

A runaway greenhouse effect occurs when greenhouse gases accumulate in the atmosphere through a positive feedback cycle to such an extent that they substantially block radiated heat from escaping into space, thus greatly increasing the temperature of the planet.
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 equilibrium, a planet's outgoing longwave radiation must balance the incoming stellar flux.
The Stefan–Boltzmann law is an example of a negative feedback cycle that stabilizes a planet's climate system. If the Earth received more sunlight it would result in a temporary disequilibrium 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 climate change 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 causing further warming is a positive feedback, but not a runaway effect, on Earth. Positive feedback effects are common 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. 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 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,, and the optical depth of water vapor,, 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 equationsWhere the first equation represents the requirement for radiative equilibrium at the tropopause and the second equation represents how much water vapor is present at the tropopause. Taking the outgoing longwave radiation as a free parameter, these equations will intersect only once for a single value of the outgoing longwave radiation, this value is taken as the Komabayashi–Ingersoll limit. At that value the Stefan–Boltzmann feedback breaks down because the tropospheric temperature required to maintain the Komabayashi–Ingersoll OLR value results in a water vapor optical depth that blocks the OLR needed to cool the tropopause.
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.

The moist greenhouse limit

Because the model used to derive the Simpson–Nakajima limit can determine the water concentration as a function of altitude, the model can also be used to determine the surface temperature 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.

Connection to habitability

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 can sustain liquid water. Under this definition, the inner edge of the habitable zone is determined by the outgoing longwave radiation limit beyond which the runaway greenhouse process occurs. 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.
Calculating the inner edge of the habitable zone is strongly dependent on the model used to calculate the Simpson–Nakajima or moist greenhouse limit. The climate models used to calculate these limits have evolved over time, with some models assuming a simple one-dimensional, grey atmosphere, and others using a full radiative transfer solution to model the absorption bands of water and carbon dioxide. These earlier models that used radiative transfer derived the absorption coefficients for water from the HITRAN database, while newer models use the more current and accurate HITEMP database, which has led to different calculated values of thermal radiation limits. More accurate calculations have been done using three-dimensional climate models that take into account effects such as planetary rotation and local water mixing ratios as well as cloud feedbacks. The effect of clouds on calculating thermal radiation limits is still in debate.