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EDG
2009-Feb-24, 07:38 PM
Does anyone know of an accurate equation that would allow me to calculate the greenhouse effect for a planet, given at least the atmospheric composition and surface pressure? I'm looking for something to calculate the factor to multiply the temperature of the planet (the blackbody temperature modified by the albedo) by.

It's odd because greenhouse warming is pretty topical and yet I can't seem to track down any way to calculate how much it should increase the temperature of a planet by.

More specifically, I have a cold mars-like planet with a surface pressure of 1.18 atms (or 0.83 atms), with a 92% CO2/8% N2 atmosphere, albedo 0.22, and that orbits its star in roughly the equivalent orbit to Mars around our own sun today. I'm guessing a greenhouse factor of x1.2 would work here because the atmosphere is much thicker than Mars (that gives an increase of about 40K) but I have no idea if that's remotely accurate or not.

parejkoj
2009-Feb-24, 09:49 PM
Unfortunately, what you are asking for isn't a straightforward calculation. But take a look at these posts for some direction on how to estimate it:

http://www.realclimate.org/index.php/archives/2008/09/simple-question-simple-answer-no/
http://www.realclimate.org/index.php/archives/2006/01/calculating-the-greenhouse-effect/
http://www.realclimate.org/index.php/archives/2007/08/the-co2-problem-in-6-easy-steps/

Murphy
2009-Feb-24, 10:40 PM
There is this nice little calculator programme that I stumbled upon, http://www.astro.indiana.edu/~gsimonel/temperature1.html.

It's relatively simple and I don't know how accurate it is, but I've found it useful.

timb
2009-Feb-24, 10:52 PM
The degree to which a given amount of CO2 warms the Earth is still controversial. See, for example, Warming the early Earth - CO2 reconsidered (http://arxiv.org/pdf/0804.4134v2). Note that the response of the climate to CO2 is far from linear, and beyond a certain amount adding more doesn't make the planet any warmer.

Ronald Brak
2009-Feb-24, 11:02 PM
Generally if the greenhouse due to carbon dioxide equals X, then doubling the CO2 concentration will increase its greenhouse effect to 2X and doubling it again will increase it to 3X. So each percentage point increase in CO2 will have less of a total warming effect then the percentage point before, however you never reach a point where increasing CO2 concentration stops warming the planet.

timb
2009-Feb-24, 11:25 PM
Generally if the greenhouse due to carbon dioxide equals X, then doubling the CO2 concentration will increase its greenhouse effect to 2X and doubling it again will increase it to 3X. So each percentage point increase in CO2 will have less of a total warming effect then the percentage point before, however you never reach a point where increasing CO2 concentration stops warming the planet.

For small changes in CO2 the greenhouse response is approximately logarithmic. I don't think this could be true for large changes; otherwise you could make the surface temperature as large as you please -- say 3000K -- by adding enough CO2. That doesn't sound likely.

Murphy
2009-Feb-24, 11:36 PM
That certainly seems to be what's happening on Venus, doesn't it?

EDG
2009-Feb-24, 11:44 PM
It's not just the CO2 (or CH4 or whatever) concentration though - it's partly down to the thickness of the atmosphere too isn't it? And I suspect that orbital distance is a factor too - if Venus was where Mars is today, would its greenhouse effect be the same?

Ronald Brak
2009-Feb-24, 11:55 PM
The climate senstivity of CO2 is between 2-4.5 degrees with a best estimate around 3 degrees. Assuming for the sake of the argument that is is 3 degrees and that it will stay at 3 degrees as we increase CO2 concentrations. If we start with a CO2 concentration of 380 parts per million then it will take less than 12 doublings of concentration for the earth's entire atmosphere to be carbon dioxide. This would only increase the temperture by under 36 degrees, all else being equal, which seems surprising low and much less than 3,000K.

timb
2009-Feb-25, 01:02 AM
The climate senstivity of CO2 is between 2-4.5 degrees with a best estimate around 3 degrees. Assuming for the sake of the argument that is is 3 degrees and that it will stay at 3 degrees as we increase CO2 concentrations. If we start with a CO2 concentration of 380 parts per million then it will take less than 12 doublings of concentration for the earth's entire atmosphere to be carbon dioxide. This would only increase the temperture by under 36 degrees, all else being equal, which seems surprising low and much less than 3,000K.

No, you can, arithmetically at least, double the amount of CO2 in the atmosphere as long as you like. I didn't say anything about reducing the quantum of other gases. It's the amount of CO2 that matters, not the proportion.

Ronald Brak
2009-Feb-25, 01:48 AM
Well, beyond a certain point CO2 would become surface rather than atmosphere and if you kept adding more eventually it would fuse.

parejkoj
2009-Feb-25, 02:03 AM
Ummm... read the links I posted. It's rather more complicated than either of you are considering, even for relatively small changes in the amount of CO2.

EDG
2009-Feb-25, 02:20 AM
Unfortunately, what you are asking for isn't a straightforward calculation. But take a look at these posts for some direction on how to estimate it:

http://www.realclimate.org/index.php/archives/2008/09/simple-question-simple-answer-no/
http://www.realclimate.org/index.php/archives/2006/01/calculating-the-greenhouse-effect/
http://www.realclimate.org/index.php/archives/2007/08/the-co2-problem-in-6-easy-steps/

Thanks - interesting links, though somewhat depressing :).

So it looks like I can't quantitatively figure this out (not without a handy cluster of parallel processors anyway) - fair enough.

What about qualitatively? I've got a really lousy grasp on this... first we have Venus with an atmosphere of 90+% CO2, at 90 atm surface pressure, and it has an enormous greenhouse effect (GFX) of +(several hundred kelvin).

Then we have Earth with a reasonably dense atmosphere, CO2 concentrations measured in a few hundred ppm, and it has a moderate GFX.

Then we have Mars with a very thin atmosphere of mostly CO2, and it has a small GFX.

So it seems to me that the GFX is strongly proportional to the thickness of the atmosphere (probably clouds reflecting radiation back to the surface, more air molecules to absorb it etc), and also to composition (if Venus' atmosphere was mostly Nitrogen instead of CO2, would it have as a high a GFX? I don't think it would, would it? Or would the thick atmosphere swamp any compositional contribution?).

Can we make any qualitative predictions here for other planets? If Mars had an atmosphere that had the same pressure as Earth, but the composition of modern day Mars, would it have a much higher temperature?

Or am I really just going to have to pull random numbers out of the air for this? ;)

timb
2009-Feb-25, 02:36 AM
Well, beyond a certain point CO2 would become surface rather than atmosphere and if you kept adding more eventually it would fuse.

So there is an upper limit to the amount of warming CO2 can provide, which is what I said earlier and you denied. I'm pretty sure you would reach the limit well before CO2 turned solid.

Ummm... read the links I posted. It's rather more complicated than either of you are considering, even for relatively small changes in the amount of CO2.

Where did I claim it was simple? We are discussing a fantasy planet. For that you want to be in the ballpark of plausibility. The OP's planet has roughly 11 doublings worth of CO2 more than Earth (he was a little unclear about the atmospheric pressure, I used 1 bar), so adding around 11*3=33K to the irradiance adjusted terrestrial temperature probably wont see too many readers throwing the book down in disgust. Maybe you should discount the greenhouse term by the fourth root of the irradiance. Not a huge difference.

Ronald Brak
2009-Feb-25, 02:51 AM
I certainly agree with you, parejkoj, that the situation is much more complex than the simple estimate I did. My rough estimate may definately be wildly off, but I hoped it might be helpful for the kind of world described in the OP.

parejkoj
2009-Feb-25, 03:31 AM
Point taken, timb. Hmmm.... A ballpark guess is probably fine in this case. I guess i missed the forest for the trees.

The problem is, both the fractional content of CO2 and the total amount matter: what is really important is how many IR absorption features are available to help trap heat. But N2 doesn't have much overlap with CO2 in terms of heat-trapping potential (in fact, it doesn't have much in the way of IR absorption features at all), so it can be mostly ignored in this context. So, timb's suggestion is probably the closest: each doubling of CO2 should produce somewhere around 2.5-3ºC of warming (see that first realclimate link for references on this). And it looks like the CO2 absorption on this imaginary planet is far from saturated (see here (http://www.realclimate.org/index.php/archives/2007/06/a-saturated-gassy-argument/) and raypierre's reply here (http://www.realclimate.org/index.php/archives/2007/06/a-saturated-gassy-argument/#comment-35869)), so no worries there.

That in mind, it sounds like it would be a chilly planet.

What's this planet for?

EDG
2009-Feb-25, 03:45 AM
That in mind, it sounds like it would be a chilly planet.

That's what I'm figuring... it's going to be around 10°C at the equator during the summer, and around -20°C there in the winter.

What's this planet for?

Hopefully, eventual release in an SF RPG supplement :). (I'll be adding a credit to BAUTForum too).

Spaceman Spiff
2009-Feb-25, 03:57 AM
The degree to which a given amount of CO2 warms the Earth is still controversial. See, for example, Warming the early Earth - CO2 reconsidered (http://arxiv.org/pdf/0804.4134v2). Note that the response of the climate to CO2 is far from linear, and beyond a certain amount adding more doesn't make the planet any warmer.

hmmm....I wonder when this occurs? (hint: Venus has ~90 atmospheres of CO2; Earth currently sports 386 ppm CO2 of a single atmosphere of pressure.) This is a fallacy. Here (http://www.realclimate.org/index.php/archives/2008/03/venus-unveiled/) is all you might want to know about the atmosphere of Venus (you can skip down to "Peeking at the surface" with regards to the question at hand), and this (http://www.realclimate.org/index.php/archives/2007/06/a-saturated-gassy-argument/) and especially this (http://www.realclimate.org/index.php/archives/2007/06/a-saturated-gassy-argument-part-ii) explain one of the reasons why the above statement is a fallacy.

We see that for the pre-industrial CO2 concentration, it is only the wavelength range between about 13.5 and 17 microns (millionths of a meter) that can be considered to be saturated. Within this range, it is indeed true that adding more CO2 would not significantly increase the amount of absorption. All the red M&M's are already eaten. But waiting in the wings, outside this wavelength region, there's more goodies to be had. In fact, noting that the graph is on a logarithmic axis, the atmosphere still wouldn't be saturated even if we increased the CO2 to ten thousand times the present level.As a matter of fact carbon dioxide never stops absorbing, albeit the "greenhouse" effects will certainly be non-linear (logarithmic) with respect to its concentration except at low concentrations.

The other reason is mentioned in the first article (http://www.realclimate.org/index.php/archives/2007/06/a-saturated-gassy-argument/). It's because what matters is the temperature of the effective emitting layer (i.e., the photosphere), which lies somewhere high in the atmosphere. Piling on more CO2 not only increases the atmosphere's overall opacity, it increases the altitude of the layer that is the planet's effective photosphere, where T is lower and thus the thermal emission is lower. So the whole danged atmosphere (and the surface) must increase their temperatures to put the planet back into thermal equilibrium.

It's just an argument of the conservation of energy.

timb
2009-Feb-25, 04:28 AM
hmmm....I wonder when this occurs? (hint: Venus has ~90 atmospheres of CO2; Earth currently sports 386 ppm CO2 of a single atmosphere of pressure.) This is a fallacy. Here (http://www.realclimate.org/index.php/archives/2008/03/venus-unveiled/) is all you might want to know about the atmosphere of Venus (you can skip down to "Peeking at the surface" with regards to the question at hand), and this (http://www.realclimate.org/index.php/archives/2007/06/a-saturated-gassy-argument/) and especially this (http://www.realclimate.org/index.php/archives/2007/06/a-saturated-gassy-argument-part-ii) explain one of the reasons why the above statement is a fallacy.

As a matter of fact carbon dioxide never stops absorbing, albeit the "greenhouse" effects will certainly be non-linear (logarithmic) with respect to its concentration except at low concentrations.

The other reason is mentioned in the first article (http://www.realclimate.org/index.php/archives/2007/06/a-saturated-gassy-argument/). It's because what matters is the temperature of the effective emitting layer (i.e., the photosphere), which lies somewhere high in the atmosphere. Piling on more CO2 not only increases the atmosphere's overall opacity, it increases the altitude of the layer that is the planet's effective photosphere, where T is lower and thus the thermal emission is lower. So the whole danged atmosphere (and the surface) must increase their temperatures to put the planet back into thermal equilibrium.

It's just an argument of the conservation of energy.

At some point the CO2 becomes the surface (CO2-III) and adding more just increases the gravity, which makes the photosphere lower.

timb
2009-Feb-25, 04:37 AM
That's what I'm figuring... it's going to be around 10°C at the equator during the summer, and around -20°C there in the winter.

Your equator has a distinct summer? it must be a high obliquity planet, or in an eccentric orbit. If the average temperature is less than 0°C your planet will likely suffer a global snowball (if watery) and the CO2 could even freeze out. I've read contradictory reports as to whether CO2 can keep a Mars-like planet warm indefinitely.

Murphy
2009-Feb-25, 05:16 AM
Going back to the original post, using the simple Planet Temp calculator I mentioned earlier (http://www.astro.indiana.edu/~gsimonel/temperature1.html), and plugging in the figures EDG provided (the Star's output wasn't mentioned, so I've just used the Sun)...

Star = 1 x Sol
Distance = 1.524 AU
Bond Albedo = 22
Greenhouse Effect = 1.2 x Earth's

I get an average surface temperature of -31 degrees C.

In order to get the +10 degrees C temp you mentioned, the planet would have to have a greenhouse effect 4.2 times stronger than Earth's.

Now I don't know how accurate that is, or how it converts into atmospheric composition and pressure, but I think it give a fair estimate of what you'd need.

EDG
2009-Feb-25, 05:44 AM
Your equator has a distinct summer? it must be a high obliquity planet, or in an eccentric orbit.

It's an eccentric orbit.

EDG
2009-Feb-25, 05:50 AM
Now I don't know how accurate that is, or how it converts into atmospheric composition and pressure, but I think it give a fair estimate of what you'd need.

It doesn't seem to be that accurate to me. Using its semimajor axis distance, the planet should have a blackbody temperature of 225K, and when you factor in the albedo of 0.22 that should drop to 212K. The GFX factor I'm using is 1.2, so the final temperature is 254K.

Murphy
2009-Feb-25, 06:40 AM
Well I don't know, I've tried testing it out with some know planets in the solar system, and the programme seems to get it right most of the time, to within a few degrees of the actual values. It seems to get it right for Mars for instance. So, I don't know, try it out your self.

EDG
2009-Feb-25, 06:46 AM
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.

Spaceman Spiff
2009-Feb-25, 03:27 PM
At some point the CO2 becomes the surface (CO2-III) and adding more just increases the gravity, which makes the photosphere lower.

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.

But I suppose this discussion is a bit off target from the OP.

ngc3314
2009-Feb-25, 03:38 PM
And at the risk of going farther OT, but relevant to the whole worldbuilding thing and definitely worth knowing - in the case of the Earth, by far the most important greenhouse gas is _________?

(Let's not just have the same people with their hands up, please!)

parejkoj
2009-Feb-25, 03:48 PM
Oh... Oh... Teacher, Teacher! I know! I know! Call on me!

;-)

Spaceman Spiff
2009-Feb-25, 04:45 PM
"Oooh! Oooh! Mr. Kotter! Mr. Kotter! Call on me! -- Is this a 'trick' question?"

Either way, an informed discussion of this issue, at least as it concerns our Earth, can be found here (http://www.realclimate.org/index.php/archives/2005/04/water-vapour-feedback-or-forcing/).

EDG
2009-Feb-25, 05:42 PM
Radiative Forcing has something to do with this, right?

http://en.wikipedia.org/wiki/Radiative_forcing

Murphy
2009-Feb-25, 11:03 PM
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/factsheet/mercuryfact.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/profile.cfm?Object=Venus&Display=Facts&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...

qraal
2009-Feb-25, 11:43 PM
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.

Ronald Brak
2009-Feb-26, 01:57 AM
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.

Spaceman Spiff
2009-Feb-26, 02:44 AM
Radiative Forcing has something to do with this, right?

http://en.wikipedia.org/wiki/Radiative_forcing

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 (http://www.realclimate.org/index.php/archives/2005/04/water-vapour-feedback-or-forcing/) 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.

timb
2009-Feb-26, 06:54 AM
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.

But I suppose this discussion is a bit off target from the OP.

True.

EDG
2009-Feb-26, 06:58 AM
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!!

Spaceman Spiff
2009-Feb-26, 03:50 PM
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.

Spaceman Spiff
2009-Feb-26, 03:56 PM
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!

Murphy
2009-Feb-26, 05:39 PM
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.

EDG
2009-Feb-26, 07:01 PM
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?

timb
2009-Feb-26, 11:06 PM
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.

Spaceman Spiff
2009-Feb-27, 03:37 AM
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 (http://www.realclimate.org/index.php/archives/2008/03/venus-unveiled/):

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 (http://www.realclimate.org/index.php/archives/2007/06/a-saturated-gassy-argument/)” post on Angstrom vs. Arrhenius (http://www.realclimate.org/index.php/archives/2007/06/a-saturated-gassy-argument-part-ii): 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]