# Thread: [worldbuilding] Greenhouse effect calculation?

1. EDG_:
I tried using the values you used in my equations (even for luminosity and distance) and got an average surface temperature of -18.44°C (254.56 K). And my formulae are based directly on the blackbody temperature calculation.
Ok, I'm not quite sure what that means and I'm no expert on this, but I decided to thoroughly test the programme to see if it is able to accurately predict the surface temperatures of the know planets in our Solar System.

I used mostly Wikipedia as a source for the planetary data, including this page for Bond Albedo http://en.wikipedia.org/wiki/Bond_albedo. (I'll list where I got the figures from specifically, if it doesn't come off Wiki).

Here's a range of Calculations done with the programme for the planets for which I have Albedo figures...

Mercury:
Star - 1 x Sol
Distance - 0.3871 AU
Bond Albedo - 11.9
Greenhouse - 0 X Earth's
Calculated Temperature: 445 K - +172 C
Actual Temperature:---- 452 K - +179 C (http://www.solarviews.com/eng/mercury.htm)
Actual Temperature:---- 443 K - +170 C (http://nssdc.gsfc.nasa.gov/planetary...rcuryfact.html)
Difference between calculated and know Temp = 7 to 2 degrees

I found two different stated mean Temps for Mercury, but either way, the result is very close.

Venus:
Star - 1 x Sol
Distance - 0.7233 AU
Bond Albedo - 75
Greenhouse - 200 X Earth's
Calculated Temperature: 700 K - +457 C
Actual Temperature:---- 735 K - +462 C (http://sse.jpl.nasa.gov/planets/prof...&System=Metric)
Difference between calculated and know Temp = 5 degrees

I've used the figure of 200 times Earth's greenhouse effect for Venus, as is suggested on the calculator site. In order to get it to 462 C you simply need to increase it to 206 times, well within a margin or error.

Earth:
Star - 1 x Sol
Distance - 1.0 AU
Bond Albedo - 29
Greenhouse - 1
Calculated Temperature: 288 K - +15 C
Actual Temperature:---- 287 K - +14 C (http://en.wikipedia.org/wiki/Earth)
Difference between calculated and know Temp = 1 degree

It's pretty much spot on for Earth, within 1 degree.

Mars:
Star - 1 x Sol
Distance - 1.5237 AU
Bond Albedo - 16
Greenhouse - 0
Calculated Temperature: 222 K - -51 C
Actual Temperature:---- 227 K - -46 C (http://en.wikipedia.org/wiki/Mars)
Difference between calculated and know Temp = 5 degrees

Again, within a few degrees of the know value, and if you put Mars' Greenhouse effect to 0.2 of Earth's, then it comes to -46 C. And since Mars does have a small greenhouse effect this seems reasonable.

Pluto:
Star - 1 x Sol
Distance - 39.4817 AU
Bond Albedo - 40
Greenhouse - 0
Calculated Temperature: 40 K - -233 C
Actual Temperature:---- 44 K - -229 C (http://en.wikipedia.org/wiki/Pluto)
Difference between calculated and know Temp = 4 degrees

Very similar to the known value, seems pretty good to me.

So, from this analysis at least, this Calculator seems to be very accurate at predicting surface temperatures to within a few degrees. I don't see how it can be accurate for the planets in our solar system, but not for other hypothetical planets. It even has a function for Star intensity so it should be a very good tool for Worldbuilding.

I don't really understand why you seem to be getting such different figures, have you tried testing you're formula on the know planets, to see if it can accurately predict their temps? Because that's the real test isn't it...

2. Established Member
Join Date
Aug 2004
Posts
122

## That's right

Originally Posted by EDG_
I tried using the values you used in my equations (even for luminosity and distance) and got an average surface temperature of -18.44°C (254.56 K). And my formulae are based directly on the blackbody temperature calculation.
Earth's greenhouse produces about 33 degrees extra of surface temperature. Venus would be -40 C without its greenhouse because the albedo is so high.

Mark Bullock did extensive modelling of Venus's atmosphere for his PhD thesis - which is available online - and he found that above about 925 K the emitted frequencies of the surface become too high for the opacity of a CO2 atmosphere to keep it in. Venus, thus, has a 'thermostat' which prevents it from getting warmer even with 1000 bars of CO2 available. Conversely if the place cooled a bit the atmosphere would start reacting with any metal oxides on the surface and form carbonates, cooling things down further. Of course that takes millions of years naturally, but it's quite rapid in geological terms. In less than a 100 million years, if enough oxides are available, the pressure drops to 43 bar and the temperature is just 400 K.

So real atmospheres aren't easily described by a single formula. But decent estimates can be made using a formula that Martyn Fogg used in several of his planet-modelling studies in the early 1980s (you thought such modelling hasn't been done before? Of course it has!) Unfortunately my copy of his paper is buried in my files so I might only dig it up if you're really interested.

3. Order of Kilopi
Join Date
Jun 2006
Posts
7,157
Mr Kotter, on behalf of my fellow sweathogs, may I humbly prevail upon you to provide a definition of "important?" For what is important may vary from person to person. I don't know whether to answer with the greenhouse gas that has the most effect or the one we should be most concerned about.

4. Originally Posted by EDG_
Radiative Forcing has something to do with this, right?

Yes. CO2 is a radiative forcing. H20 vapor (and associated phases of water in the atmosphere) is a source of (mostly) positive feedback. In fact it is the fact that water is able to exhibit all 3 phases that limits its time scale in the atmosphere, moving it from the radiative forcing column into the feedback column. Positive radiative forcings act to increase the temperature by affecting the way that energy is transported via radiation through the Earth system (net in vs. net out), negative ones act to decrease. Increasing the temperature drives up the water vapor content in the atmosphere (due to the exponential behavior of the equilibrium vapor pressure), maintaining roughly constant relative humidity. Once in the atmosphere, however, CO2 remains for 100s of years, cycled through by various sinks (photosynthetic life, oceans, erosion/carbon-silicate cycle, etc). Of course, forcings can also act as feedback. That link I gave above will fill in some of the details.

I am not sure what ngc3314 (aka 'Mr. Kotter') had in mind with his question. Maybe he'll fill us in.

5. Originally Posted by Spaceman Spiff
To the first point: you betcha; inquire with Venus. To the second point: if the CO2 mass becomes that significant, then the temperature must rise at all levels to generate sufficient pressure (gradient) to maintain hydrostatic equilibrium as well as thermal equilibrium. There is no free lunch.
Insofar as that makes sense to me it seems wrong. Massive bodies aren't obliged to be hot.

Originally Posted by Spaceman Spiff
But I suppose this discussion is a bit off target from the OP.
True.

6. Originally Posted by Murphy
Ok, I'm not quite sure what that means and I'm no expert on this, but I decided to thoroughly test the programme to see if it is able to accurately predict the surface temperatures of the know planets in our Solar System.
Well, forget about albedo and greenhouse effect for now - you should at least be getting the same blackbody temperatures that I calculate, which are listed below:

Mercury (0.3871 AU): 447.88 K
Venus (0.7233 AU): 327.66 K
Earth (1 AU): 278.66 K
Mars (1.5237 AU): 225.75

I'm using:

T = (L/(16.pi.sigma.a²))^(0.25)

to calculate the blackbody temperature.

where L = Luminosity of star in watts, sigma = stefan-boltzmann constant, and a = semimajor axis in metres.

That formula *should* be correct, but if it isn't then I want to know about it!!

7. Originally Posted by timb
Insofar as that makes sense to me it seems wrong. Massive bodies aren't obliged to be hot.
No, they are not. That is correct. However, planets that are not in thermal equilibrium will move toward one. Unless the planet has significant internal energy source (unlike present-day Earth), the net energy 'in' comes from photons emitted by the host star and absorbed by the planet (surface, atmosphere, etc). The net energy 'out' is also via radiation that escapes the Earth into the cold near-vacuum of space. If the two are in balance (at least on average over timescales of interest), an equilibrium temperature is established. Otherwise the planet will heat up (if heating rate > cooling rate) or cool down (if cooling rate > heating rate) until equilibrium is attained. Introducing or increasing a radiative forcing agent moves the system away from equilibrium.

Depending on how far things are moved away from some previous equilibrium, there may be changes that occur in the system that themselves alter the in/out balance, either dampening further changes or accelerating them. This is the "feedback" mechanism.

8. Originally Posted by qraal
Earth's greenhouse produces about 33 degrees extra of surface temperature. Venus would be -40 C without its greenhouse because the albedo is so high.

Mark Bullock did extensive modelling of Venus's atmosphere for his PhD thesis - which is available online - and he found that above about 925 K the emitted frequencies of the surface become too high for the opacity of a CO2 atmosphere to keep it in. Venus, thus, has a 'thermostat' which prevents it from getting warmer even with 1000 bars of CO2 available. Conversely if the place cooled a bit the atmosphere would start reacting with any metal oxides on the surface and form carbonates, cooling things down further. Of course that takes millions of years naturally, but it's quite rapid in geological terms. In less than a 100 million years, if enough oxides are available, the pressure drops to 43 bar and the temperature is just 400 K.
That's all very interesting. Thanks!

9. Originally Posted by EDG_
Well, forget about albedo and greenhouse effect for now - you should at least be getting the same blackbody temperatures that I calculate, which are listed below:

Mercury (0.3871 AU): 447.88 K
Venus (0.7233 AU): 327.66 K
Earth (1 AU): 278.66 K
Mars (1.5237 AU): 225.75

I'm using:

T = (L/(16.pi.sigma.a²))^(0.25)

to calculate the blackbody temperature.

where L = Luminosity of star in watts, sigma = stefan-boltzmann constant, and a = semimajor axis in metres.

That formula *should* be correct, but if it isn't then I want to know about it!!
Ok, by Black body temperature you mean a scenario with just the star at a certain distance and assume the planet's Albedo is 0 (i.e. absorbs everything), right?
Well you can put that scenario into the calculator programme, by having all Albedo values to 0 and no greenhouse effects...

Mercury:
Distance - 0.3871 AU - Temperature: 460 K - +187 C
Venus:
Distance - 0.7233 AU - Temperature: 336 K - +63 C
Earth:
Distance - 1.0000 AU - Temperature: 286 K - +13 C
Mars:
Distance - 1.5237 AU - Temperature: 232 K - -41 C
Pluto:
Distance - 39.4817 AU - Temperature: 46 K - -227 C

Somewhat different from your figures, but still within the same range. It could be that the programme simply uses a different formula for calculating Black body temp, or that they have additional formulas worked in that they think will make it more accurate, or something like that.

This page http://www.astro.indiana.edu/~gsimonel/, lists the people who created the "Planet Temperature Calculator"...
"The program was developed by Glenn Simonelli and Richard Durisen, in consultation with Frank ("Buddy") Morris, Jiangmei Wu, and David Goodrum of the Teaching & Learning Technologies Centers at Indiana University".

Their E-mail addresses are given as links, maybe you could contact them and ask them how their programme works? Or the formulas they used at least.

10. Yeah, looks like it's similar enough, but I guess they're making estimations somewhere along the way.

The way I figure out the final temperature is to multiply the BB Temp by (Albedo^0.25), and then multiply the result directly by the GFX Factor (which starts at 1.00 for no atm, and can go up to 2.50 or so).

Incidentally, IIRC there's is a specific name for the BB temp with just the Albedo factored into it (without GFX), but I've forgotten what it is - does anyone else recall it?

11. Originally Posted by Spaceman Spiff
No, they are not. That is correct. However, planets that are not in thermal equilibrium will move toward one. Unless the planet has significant internal energy source (unlike present-day Earth), the net energy 'in' comes from photons emitted by the host star and absorbed by the planet (surface, atmosphere, etc). The net energy 'out' is also via radiation that escapes the Earth into the cold near-vacuum of space. If the two are in balance (at least on average over timescales of interest), an equilibrium temperature is established. Otherwise the planet will heat up (if heating rate > cooling rate) or cool down (if cooling rate > heating rate) until equilibrium is attained. Introducing or increasing a radiative forcing agent moves the system away from equilibrium.

Depending on how far things are moved away from some previous equilibrium, there may be changes that occur in the system that themselves alter the in/out balance, either dampening further changes or accelerating them. This is the "feedback" mechanism.
Now you seem to have retreated from your previous position, that the temperature of a planet could be increased without limit by adding CO2. I asserted that adding CO2 to an Earthlike planet could only increase its temperature so much, and could, for example, never increase it to such a temperature as 3000K. You told me this was a "fallacy". About how much CO2 would be required to increase the "surface" temperature of Earth to 3000K? If you apply the logarithmic relation the mass of the final object is far greater than that allowed for a planet (considerably greater than the observable universe, actually), so I think may claim is safe.

12. I never said anything about T increasing without limit. All I was saying was that, as you've just now noted, for all practical purposes adding CO2 to Earth's atmosphere will result in continued increases in T. This was to counter the fallacious claims that the absorption by CO2 in Earth's atmosphere is already "saturated", and so adding more won't change the energy budget significantly.

The last bit I wrote was just to make the point that systems do not behave as they always did for arbitrary changes in their state variables. Changes in phase of the matter (e.g., formation of droplets or aerosols), in the (photo)chemical reactions that determine molecular distribution, in the state of ionization, in the equation of state, in the pressure broadening of the molecular transitions and collision-induced transitions with increasing pressures (all of which change the atmosphere's wavelength dependent opacity), in the radiation field spectral distribution, in the surface composition (for planets with true surfaces), etc, will ultimately change the energy budget.

Take Venus as an example. You don't make the Earth into Venus merely by, "poof", adding ~90 atmospheres of CO2 to it (although it would certainly be awfully hot down here). Somewhere along the way, most of the water it had went into the vapor state. Over time this vapor was in large part dissociated, so that today water vapor is a minor constituent to its atmosphere (although still comparable in mass to that in Earth's atmosphere). Amongst other things, this would have changed the nature of the composition of its clouds. In fact Venus is still losing water at present. And of course, there are other differences.

And if you're going to make a gas giant, what I meant there is that for Jovians of the same age, more massive 'Jovians' are hotter than the less massive ones.

Here are two interesting quotes from the comments section of the article on Venus' atmosphere I linked to above:

I’m not sure I see your point. The atmospheric pressure on the surface of Venus is 92 times that of Earth at sea level. C02 represents 96.5% of the Venusian atmosphere - that’s 965000 ppm compared to 380 ppm on Earth. Even allowing that Venus is a little smaller than Earth there must be around 200,000 times as much CO2 in the Venusian atmosphere. Unless my “back of the envelope” calculations are way out…

[Response: But the point was that 200,000 is only 18 doublings, so if you use a logarithmic law you don’t appear to get enough greenhouse effect to account for the temperature of Venus. The answer to that is that in fact the log law only holds up to about 0.2 bars of CO2, and after that the effect starts to get stronger — even more so once you get enough surface pressure that the self-broadening takes off. –raypierre]
and

This was fascinating though, and I was suprised to learn that there is still water vapor there. I was curious as to what kind of climate implications there might have been (or that extended to the present day) from the global resurfacing of the planet?

[Response: It’s just in traces, but it’s there. And it’s still escaping from the planet. An exciting question is the extent to which the Venusian mantle is still hydrated. Are we seeing the last gasp of water vapor, or is there still a bit coming out through episodic volcanism? The catastrophic resurfacing theories do various things to climate depending on the composition of outgassing — water vapor vs SO2. With a lot of SO2 you can cool things down by making clouds, which gradually dissipate and give warming. At the end of the cloud cycle you get really hot surface temperatures, maybe 100C warmer than at present. If there’s a lot of H2O outgassing as well, then you can get an additional pulse of heat through the added H2O greenhouse effect. This, by the way, shows the importance of the “thinning and cooling” effect we highlighted in the “Saturated Gassy Argument” post on Angstrom vs. Arrhenius: no matter how optically thick a planet’s atmosphere becomes, you can always make it hotter by adding more greenhouse gas, because the “new” greenhouse effect is added near the top of the atmosphere where thing are thin and cold and the existing opacity is weak. –raypierre]

13. Newbie
Join Date
Feb 2021
Posts
5
To make things easier to calculate... I just want to know that would be the greenhouse temperature if Earth had the same atmospheric composition and percentage of gases but if the air pressure was 3 times higher. Just multiply the greenhouse value by 3? If the greenhouse is about 30oC on Earth, it would be 90oC if the air was 3 times more pressurized? I don't think that would be the case though. Maybe by multiplying by 1,3x instead of 3x? And if the Earth had the same atmosphere, but just 10 times it's actual pressure?