Atmosphere and Greenhouse on Rocky Planets

[Sesquitone]

After playing around with setting up some solar systems with rocky planets, I wanted some insight on how non-Earth atmospheres are simulated. I'm putting it in discussion because I do not know enough to say if what I'm encountering is a bug or simply the consequence of a series of features.

I noticed that while adjusting the atmospheric mass of rocky planets, there is a point where the greenhouse effect transitions from being based on the IR Emissivity to being based on atmospheric pressure or mass. The specific point depends on other properties in a way I don't yet understand, but testing on random rocky planets places it somewhere in the 10-100 kPa order of magnitude. For IR Emissivity values significantly greater than 0, the transition between these two regimes when changing the atmosphere's mass is quite rough.

I'd like to learn more about the basis of this, mainly to see if it's intentional, and how and why it is calculated in this way. Gratuitous physics explanations are welcome!

[Arian]

Scale Height is playing a big role once the atmosphere passes a certain mass relative to the planet's mass.
The atmosphere layer's thickness.
The more massive a planet is the more atmosphere it takes to get the atmosphere reach higher above the surface, because of gravity. For the same reason the pressure will go up with more atmosphere mass.
Pressure and gravity are working against each other and it's only at and above a certain M_atmosphere / M_planet ratio that gravity gets the upper hand. Below that ratio, gases would simply escape.

Infrared Emissivity mostly refers to your planet cooling down and not so much to reflecting light of IR wavelength. With a thick layer of atmosphere containing reflective stuff the IR light of both sources will hit the surface more often, bouncing between surface and greenhouse contributors. Also while (visible) light is escaping the planet it's wavelength slightly shifts towards red and eventually infrared, contributing to the effect because visible light is also reflected and hence bounces as well, shifting a little towards red each time it goes "up".

[Sesquitone]

Thank you for the information. What you said makes sense in regards to reality and physical models. My question relates to reconciling what I see in the game with reality. In particular, the changes in atmospheric mass around that critical ratio can cause dramatic shifts in the temperature rise due to the greenhouse effect (or at least what is called such in the program). Depending on the parameters for albedo and IR emissivity, I've seen shifts in the greenhouse effect as large as starting at +50 K and crash to near 0 K when crossing over that point (~1% increase) in atmospheric mass. The more predictable rise with significantly more mass makes sense, but that already sits well with me. I have doubts that such a dramatic shift around that transition really fits well with reality and expectations of game mechanics.

I guess my question boils down to what the mathematical model of the surface temperature is right now. It clearly implements some aspects like the Stefan–Boltzmann law and non-ideal body properties for absorbance and emission, but some of the numerical results like those dramatic shifts don't make much sense to me.

[Naomi]

In answer to the question, you have indeed observed a discontinuity in the way we calculate temperature for very thick atmospheres. Usually for rocky planets we use a single layer atmosphere with an infrared emissivity, as referred to in the third item of the FAQ: http://universesandbox.com/blog/2014/10/climate/#FAQ. The trouble is that this conceptualization does not work for very thick atmospheres like Venus. You would need an infrared emissivity much greater than 1, which doesn't really make sense. So we use an equation for an optically-thick dry troposphere runaway greenhouse limit, which depends on other parameters and is calibrated for Venus. So any time you add a random rocky planet, when it crosses an arbitrary atmosphere mass threshold it will stop paying attention to the Infrared Emissivity value, and start behaving more like Venus. We will probably change this at some point to more realistically cover the in-between states and expose what's going on. Thanks for noticing and for your question!