Energy balance

Energy flows on Titan lead to both a greenhouse effect and an anti-greenhouse effect.

To understand how the anti-greenhouse effect impacts a planet or large moon with its host star as an external source of energy, an energy budget can be calculated, similar to how it is done for Earth. For each component in the system, incoming energy needs to equal outgoing energy to uphold the conservation of energy and remain at a constant temperature.^[8] If one energy contributor is larger than the other, there is an energy imbalance and the temperature of an object will change to reestablish a balance. Energy sources across the whole electromagnetic spectrum need to be accounted for when calculating the energy balance. In the case of Earth, for example, a balance is struck between incoming shortwave radiation from the Sun and outgoing longwave radiation from the surface and the atmosphere. After establishing a component's energy balance, a temperature can be derived.

Ideal anti-greenhouse effect

Ideal anti-greenhouse effect energy balance assuming one upper atmosphere layer and a planetary albedo of 0. See text for an explanation of symbols and abbreviations.

In the most extreme case, suppose that a planet's upper atmosphere contained a haze that absorbed all sunlight which was not reflected back to space, but at the same time was nearly transparent to infrared longwave radiation. By Kirchhoff's law, since the haze is not a good absorber of infrared radiation, the haze will also not be a good emitter of infrared radiation and will emit a small amount in this part of the spectrum both out to space and towards the planet's surface. By the Stefan–Boltzmann law, the planet emits energy directly proportional to the fourth power of surface temperature. At the surface, the energy balance is as follows,

${\displaystyle \sigma T_{surf}^{4}=OLR}$

where ${\displaystyle \sigma }$ is the Stefan–Boltzmann constant, ${\displaystyle T_{surf}}$ is the surface temperature, and ${\displaystyle OLR}$ is the outgoing longwave radiation from the haze in the upper atmosphere. Since the haze is not a good absorber of this longwave radiation, it can be assumed to all pass through out to space. The incoming solar energy must be scaled down to account for the amount of energy that is lost by being reflected to space since it is not within the planet-atmosphere system. In the upper atmosphere, the energy balance is as follows,

${\displaystyle {\frac {S}{4}}(1-\alpha )\equiv \sigma T_{e}^{4}=OLR+\sigma T_{surf}^{4}}$

where ${\displaystyle S}$ is the incoming solar energy flux, ${\displaystyle \alpha }$ is planetary albedo (i.e., reflectivity), and ${\displaystyle T_{e}}$ is the effective mean radiating temperature. The incoming solar flux is divided by four to account for time and spatial averaging over the entire planet and the ${\displaystyle 1-\alpha }$ factor is the fraction of the solar energy that is absorbed by the haze. Replacing ${\displaystyle OLR}$ with ${\displaystyle \sigma }$${\displaystyle T_{surf}^{4}}$ in the second equation, we have,

${\displaystyle \sigma T_{e}^{4}=2\sigma T_{surf}^{4}}$

and the ratio ${\displaystyle T_{surf}/T_{e}}$ equals ${\displaystyle \left(0.5\right)^{1/4}}$ or 0.84. This means that the surface temperature is reduced from the effective mean radiating temperature by 16%, which is a potentially significant cooling effect.^[1] This is an ideal case and represents the maximum impact the anti-greenhouse effect can have and will not be the impact for a real planet or large moon.

Outdated concept of anti-greenhouse effect

Earlier discussions in the scientific community pre-dating the current definition established by Dr. Christopher McKay in 1991 referred to the anti-greenhouse effect as a precursor to the Late Precambrian glaciation, describing it more as a carbon sequestration process.^[9] This is no longer the current usage of the term, which emphasizes surface cooling due to high-altitude absorption of solar radiation.

Comparison to negative greenhouse effect

The negative greenhouse effect is a phenomenon that can produce localized, rather than planetary, cooling. Whereas the anti-greenhouse effect involves an overall temperature inversion in the stratosphere, the negative greenhouse effect involves a localized temperature inversion in the troposphere. Both effects increase outgoing thermal emissions—locally in the case of a negative greenhouse effect and globally in the case of the anti-greenhouse effect.^[10][11]

Past

The presence of an organic haze in Earth's Archean atmosphere was first suggested in 1983 and could have been responsible for an anti-greenhouse effect.^[14][15] This hypothesis stems from attempts at resolving the faint young Sun paradox, where a reduced solar output in the past must be reconciled with the existence of liquid water on Earth at that time. In order to explain how water could remain in liquid form, it has been proposed that greenhouse gases helped keep Earth warm enough to prevent water from completely freezing. While one hypothesis suggests that only carbon dioxide was responsible for the additional warmth, another hypothesis includes the presence of both carbon dioxide and methane. One model found that methane in the postbiotic Archean could have existed at a mixing ratio of 1,000 ppm or higher, while the carbon dioxide could be as low as 5,000 ppm to still prevent Earth from freezing over, about 12 times the amount in 2022.^[5][16][17] However, at this 0.2 ratio of methane to carbon dioxide, products deriving from methane photolysis can polymerize to form long-chain molecules that can aggregate into particles, forming the anti-greenhouse organic haze.^[4] The haze is formed when the ratio of methane to carbon dioxide exceeds roughly 0.1.^[14][15] It is posited that the organic haze allowed the creation of a negative feedback loop to stabilize the climate on Archean Earth.^[5] If temperatures increased in Archean Earth, methane production would increase due to methanogens' possible preference for warmer temperatures (see thermophiles).^[5] Increasing temperatures would also increase the carbon dioxide loss through weathering due to an assumed increase in precipitation, leading to decrease carbon dioxide concentrations. This would lead to a higher methane to carbon dioxide ratio and would stimulate the production of the organic haze. This increase in organic haze production would lead to increased opacity of the atmosphere to sunlight, decreased amounts of solar energy reaching the surface, and thus decreases in surface temperature, thus negating the initial increase in surface temperature. One estimation of the anti-greenhouse effect on Archean Earth calculated the impact to be up to about 20 K in surface cooling.^[18]

Present

In the modern state of Earth's atmosphere, there are a few sources of an anti-greenhouse effect. It has been suggested that stratospheric ozone and Earth's thermosphere create a partial anti-greenhouse effect due to their low thermal opacity and high temperatures.^[3] Additionally, ejected dust like that from volcanoes and nuclear fallout after a nuclear war has been suggested to typify an anti-greenhouse effect.^[3][6] Also, the formation of stratospheric sulfur aerosols from volcanic sulfur dioxide emissions has been seen to have a cooling effect on Earth that lasts approximately 1 to 2 years.^[19] All of these sources act to create a temperature structure where a hot upper layer lies above a cold surface, which typifies the anti-greenhouse effect.