More flexible greenhouse model

[lortordermur]

So far SFCalcSheet uses the equation from idealized greenhouse model to calculate a planet’s surface temperature from its effective temperature.

Effective temperature:

T(e) = Effective temperature (K), A = Bond albedo of planet, L = Luminosity of star (W), d = Distance to star (m), σ = Stefan-Boltzmann constant

Surface temperature (greenhouse model):

T(s) = Surface temperature (K), T(e) = Effective temperature (K), ε = Atmospheric absorption (0-1)

The only atmospheric variable in this equation is atmospheric absorption/emissivity, a measure for how much radiation is retained via greenhouse gasses. Basically it only allows for modeling Earth’s atmosphere with varying amounts of greenhouse gasses. An equation that also takes air pressure would be useful for modeling worlds with a different atmosphere or a runaway greenhouse effect.

If you find something that could be adapted for use in SFCalcSheet, let me know here.

[lortordermur]

Here are some resources that may be helpful in modeling a H₂O and CO₂ based greenhouse effect on rocky planets, as well as possible ranges for a circumstellar habitable zone based on atmospheric properties.

Kasting et al.: Habitable zones around main sequence stars
Ramses Mario Ramirez: A more comprehensive habitable zone for finding life on other planets

[jchylik]

Perhaps a good question which greenhouse gasses do you consider.
Although water vapour and carbon dioxide are the main greenhouse gasses in current Earth's atmosphere, there are also other greenhouse gasses that played an important role in the past (methane), and similar could be said for alternative scenario.

For example in a dysoptian sci-fi setting, you can consider a significant greenhouse contribution from nitrous oxides and CFCs (chlorofluorcarbons).

[jchylik]

And some relevant sources on values

Nitrous oxide and Ozone:
https://www.researchgate.net/publication/257864234_Emissivity_of_the_main_greenhouse_gases

CFCs:
https://doi.org/10.1016/0022-4073(77)90116-9

[lortordermur]

Thank you for your effort. I had a look at the sources soon after you posted them and they are really useful in respect to the relative contribution of various greenhouse gasses.

What is still missing for a possible update to the planetary habitability calculator is a simple-ish mathematical relationship between atmospheric density/pressure and overall intensity of the greenhouse effect (preferably as a temperature modificator). It is a very complex topic to research into but I will be able to set aside some time for it very soon and post any useful findings here.

[jchylik]

a simple-ish mathematical relationship between atmospheric density/pressure and overall intensity of the greenhouse effect

That is an interesting idea, but I have to disappoint you, such direct dependence is possible only for some gasses. However the concentration of some of the most important greenhouse gasses, such as water vapour, is very much altitude and temperature dependent.

Not the mention the effect of water vapour when it start condensing, ie. forming clouds.