Average Temperature of the Earth, and the Greenhouse Effect.

I've often heard it said that there's no 'science' behind greenhouse gasses and no 'proof' that they warm the earth.

As it turns out this is simply untrue.
Assuming that the earth and the sun both radiate as spherical blackbodies.
And assuming that the earth is in thermal equilibrium, then starting from the Stefan - Boltzman law, we can derive the relationship:
\(T_{E} = T_{S}\sqrt{\frac{\sqrt{1-\alpha}R_{S}}{2 D}}\)
Where T_E = the blackbody temperature of the earth, T_S = the (average, surface) temperature of the sun, α = the earths albedo, R_S is the radius of the sun, and D is the distance between the Sun and the earth.

If you substitute the numbers in it turns out that the earth has an effective temperature of -25°C. The exact number varies depending on the Albedo you use, but varies between -32°C and -18°C (0.3-0.4 albedo).

According to this source the average temperature of the earths surface is about 15°C which indicates that something is warming the earth by between 47°C and 33°C.

Physics it would also seem has the answer (again) in Simple Harmonic Motion - there are some molecules which absorb strongly in the infra red, and that absorbed light energy is turned into energy of motion, which is what we measure when we measure the temperature of an object (an object considered as an esnemble of particles before anyone gets cute - temperature is a statisictical property of an ensemble of particles).

This source provides an explanation of the physics behind the 'greenhouse effect' and why our planet is 33-47°C than we might otherwise expect it to be.

The TPF Book has some more useful information in it, and also has these graphs:

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And the Earths Thermal Spectrum which shows just how much infra red energy the earths atmosphere absorbs, and suggests why the surface of our planet is 33-47°C warmer than it otherwise should be.

The relationship between absorbance of infra-red energy and the partial pressure of, or the amount of gas present isn't neccessarily a straight forward one, but, according to wikipedia, currently the atmosphere is about 0.035% CO_2, which corresponds to .00035 atm. According to this

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from this source which deals only with the 4.2-4.25 micron peak of carbon dioxide (not shown in the abover graphs, but visible here from this source. Based on the calibration curve then it would seem that with the current level of carbon dioxide in the atmosphere, the absorbance of infra red radiation by carbon dioxide will respond linearly to the concentration of carbon dioxide in the atmosphere, namely that doubling the amount of carbon dioxide in the atmosphere will double the amount of infra red radiation being absorbed by the arbon dioxide in the atmosphere.

Based on the TPF graph, we can see that at around 14 microns, the earths atmosphere absorbs approximately 2*10^14 Jy of infra red energy (the difference between the red line and the purple line). It should be noted that, ideally, we'd be finding the difference in the area between the purple graph and the red graph to get the total energy absorbed by the atmosphere.

According to NOAA, the mean total mass of the atmosphere is 5.1480*10^18 kg, and according to other sources the specific heat of air is 1.012 kJ/K/kg, so doubling the amount of infra red radiation absorbed at 14 microns over a year, by doubling the amount of carbon dioxide in the atmosphere is sufficient to raise the temperature by 3.8x10^-5 K. This may not seem like much on the face of it, but, bare in mind that it only deals with the energy absorbed by one component of the atmosphere at one specific frequencey, also bare in mind that based on those graphs the total infrared energy absorbed by carbondioxide in the atmosphere is going to be more than the number I used, and therefore the temperature increase must also be more than the number i've calculated.

Bare in mind, that this is essentially all from first principles, hopefully i've managed to demonstrate that there is substantially more physics and actual measurements behind greenhouse gasses and the greenhouse effect than generally seems to be recognized.

Addendum: If you're wondering why i've focused on Carbon Dioxide as a greenhouse gas, it has nothing to do with trying to advocate for carbon credits, it's purely and simply because it's the greenhouse gas the information used in this post is most consistently available for. I should probably also point out the obvious in that in some respects i'm considering only a simplified/ideal system (that is still applicable to the real world).

 

So then based on the above principles, which are well grounded in accepted physics, then one must also accept that altering atmospheric chemistry must alter climate, and the only real debate can be to what extent.

 

The percentage is irrelevant, remember, I provided data that demonstrated that with the amount of CO2 currently in the atmosphere, that the amount of infra red radiation absorbed was linearly proportional to the amount of CO2 in the atmosphere, therefore irrespective of how little there is in the atmosphere, doubling that amount is still going to double the amount of infrared radiation absorbed by CO2 in the atmosphere. While this might, for example, only result in an increase in total abosrbance of IR by the atmosphere from, say 0.1% to 0.2% 0.2% of 10^14 is still a lot of energy.

How much man has contributed is irrelevant, the point is that man has contributed.

Or do you have evidence that suggests that volcanic activity now is higher than it was 150 years ago?

We've already discussed this (to some extent) and you've already agreed that the Milankovich Cycles predict.

And as far as the Oceans go, well, you almost have a point there, almost. Yes, the Oceans are out of synch with teh atmosphere, but AFAIK, the Oceans are on the whole absorbing CO2 from the atmosphere.

Nice argument, but wholly irrelevant. It doesn't disprove that increasesing GHG's will increase temperature - remember, I'm arguing from a foundation built on the laws of physics - Simple Harmonic Motion, and the Stefan-Boltzman distribution.

A nice argument, but again, it's completely irrelevant. Why are you fixated on this point? It doesn't change the physics of Simple Harmonic Motion, and it doesn't change the Stefan-Boltzman Distribution. Remember, the only thing that I've said is that the laws of physics demand that Carbon dioxide, and the other green house gasses absorb IR energy and transform it into kinetic energy (heat energy) and that the proof that this actually happens is also contained in the laws of physics, which, according to the Stefan-Boltzman distribution, and Weins Displacement law demand that Earth should be colder than it is by up to 50 kelvins.

Again that's great, but wholly irrelevant, remember, I included the information for water as well as Methane and CO2, and also explcitily stated that I was simply using CO2 as a specific example, because it was the greenhouse gas that the information was most consistently available for (technically, this argument constitutes a red herring).

That's great, but again, it's wholly irrellevant, remember, I wasn't talking about relative contributions, I was talking about absolute numbers.

See my previous two points.

Remember, all that I've said is that doubling the amount of the CO2 in the atmosphere doubles the amount of infrared radiation absorbed by CO2. Nothing that this paragraph says changes this, nor does this paragraph make any attempt to qualify its assertions.

Right, now compare this to what I did, and that realize that my method would give more reliable, more real data.

I'm not converting percentage concentration into percentage contribution.
I used real data.
I used the a calibration curve to determine whether or not the IR absorbance of CO2 responded linearly at the partial pressure currently in the atmosphere, and found it does.
I then calculated based on the percentage absorbance (a real, measured thing) and the total incoming IR flux (a real, measured thing) how much actual energy the carbon dioxide in the atmosphere was actually absorbing, and then based on the specific heat of air at STP, with 'standard' or 'average' composition (which includes water vapor) calculated how much that extra energy would raise the temperature of the atmosphere by. I also explained that my calculation, for simplicity and brevity, was being done at a single wavelength, then expounded on how this method could be extended to completion.

I argue that my method, lacking further evidence, because you have provided no link, and if the image you embeded was relevant, it's broken, that my method is actually more accurate because it makes NO assumptions other than that the known laws of physics are valid on the earth.

An honest caveat.

Irrelevant - your so focused on the role of water that you've almost entirely missed the point of my post.

I see why your image is broken now.
But, once again, irelevant, for the reasons I've already expounded upon.
Although it occurs to me that there could be good reasons for the DOE leaving water out.

For one thing, the difference in the heights of the bars makes it harder to judge the relative contributions of the other GHG's.

For another thing, water vapour is the most variable component of the atmosphere.

 

Also, stop and take a moment to consider the fact that all i've said is that:
"If there is an anthropogenic change to atmospheric chemistry, then there must be an anthropogenic change to climate".

I've made no real statement about the degree of that influence, and I've freely and explicitly aknoslwedged that there is room for some debate on the degree.

So to try and argue against my comment on the physics, by arguing a point that I myself have already made is at best facile and futile.

 

In your opinion, perhaps.
And your initial question is technically pointless as it's perfectly clear in my original post what I was taking as a baseline measurement.

Did you bother reading it? Or trying to understand it?

And no, it's not alarmist in it's wording, it's simply aknowledging the role that atmospheric composition plays in climate, which, if you had bothered reading the initial post, you would realize that that is what I was addressing - the red herring that the greenhouse effect has no basis in actual science, and making the point that proving that atmospheric composition affects climate is trival.

Red herring, probably an appeal to ridicule as well (as is quite frankly the tone of most of your post).

Did you read my original post? I was talking about increasing the partial pressure of Carbon Dioxide in the atmosphere. Did you bother looking at the calibration curves in my original post?
And no, the Carbon Dioxide does not have to replace another gas to strengthen my argument. Simply putting more CO2 in the atmosphere is sufficient.

Again, I have to ask, did you bother reading my initial post? I thought I was quite clear in it.

Here, seeing as how you apparently didn't read it, let me repeat the bit that's relevant to your attempt at distraction:

So... Apparently my discussion of doubling the amount of carbon dioxide in the air was, quite simply, a matter of practicality and NOTHING ELSE. It is simply the molecule that I was able to find the most information for.

As for my personal opinion, i'll tell you the same thing that i've told Iceaura and Buffalo Roam in my disagreements with them - It's irrelevant to the discussion.

 

I haven't claimed it was, and that wasn't the point that I was making.

I mean, fer crissake, quote me in my original post saying that mans influence on atmospheric chemistry is significant - oh wait, that's right, you can't, because I haven't because I deliberately avoided speculating on issues as to what caused this, and what caused that, and stuck with measured facts.

Feel free to keep your imagined political agenda to yourself.

I explicitly stated that the argument I was addressing was the "There is no hard science behind it all, and there's no proof that greenhouse gasses cause warming".

I explicitly stated that if we accept the Stefan Boltzman distribution, and we accept Simple Harmonic Motion, then we must accept that atmospheric composition must influence climate (because atmospheric composition influences heat capacity), and therefore the only point of debate can be to what extent.

And now you, and Buffalo roam are forwarding aguments of extent as if they somehow negate the physics of the matter.

The topic, and the original post aren't about anthropogenic climate change, they're about the greenhouse effect, which I have seen called imaginary.

Your contention that I'm "trying to scientifically justify a political issue by analyzing a trivial and uncontested issue" is patently false - unless you're trying to argue that because some idiot made a film about some drowning polar bears somehow invalidates Weins Displacement Law, Simple Harmonic Motion and the Stefan Boltzman Distribution? If it's that easy to debunk mainstream science then wow.

Oh, and I thought of something in relation to your earlier post, I had a thought after I logged off, which made me laugh.

You said " You would have a stronger point if you had said that the increased CO2, replacing some other gas which absorbs less IR radiation (like oxygen), would result in a net increase in total IR absorption." But tell me (and yes, i'm addressing specific sources of carbon dioxide here - combustion, but making no comment on the cause of the combustion, because after all, there is naturally occuring combustion as well) when wood is burned, and carbon is converted into carbon dioxide, if not the atmosphere, where do you suppose the 'oxide' component comes from?

 

Interesting, but wholly irrelevant rhetoric.

 

This would be the same emissivity that includes atmospheric contributions?
I can only imagine you're referring to treating the earth as a grey body, perhaps you'd care to post a link or two to back up your assertions?

 

I wasn't sure, and was genuinely curiose, perhaps I could have worded my previous post a little better.

And yeah, that was kinda part of the point that I was trying to make - I was trying to avoid the politics of the issue, and get back to the grass roots of the science, the measured facts and variables. The knowns, rather than the speculations.

 

I would also like to point something else out.

It's been stated in this thread, and elsewhere, that the Greenhouse Effect is a political issue with no basis in science, that's part of what I'm trying to address - the Greenhouse Effect is firmly entrenched in classical science.

There's something else I would like to point out - that it's actually the other way around, the greenhouse effect is a scientific entity that has been made into a political issue.

The Greenhouse effect was first discovered in 1824 by Joseph Fourier. It was also first experimented on by John Tyndall in 1858, and first qualitatively reported on by Svante Arrhenius in 1896, and so well and truely predates the modern political issue.

After Arrhenius the greenhouse effect was considered something of a curiosity, and unlikely to ever be an issue (the logic had something to do with overlapping spectral bands, but was based on inaccurate information). This began to change in the 1950-1960's. Why? Because of the Cold War - what happens in the Ocean and the Atmosphere became of interest to the Military, and so more funding was available for it's study. It was around then that it was discovered, because of improved technology, and improved physics, that the absorption bands had fine structure, and the logic that up until then had been accepted was erroneous.

The Hypothesis that low CO2 caused Ice Ages had been accepted since it was first proposed by Tyndall in 1858, again, the only thing that has been debated since Arrehnius proposed it in 1896 (he suggested that at (then) current rates of burning coal, we might see some effect from increasing carbondioxide in about 3000 years) is to what degree human contributions would effect the climate. It was then put forward again by Callendar in 1938 that Atmospheric CO2 was climbing and temperature was rising with it.

First it was argued it was impossible for us to burn enough coal, then as industry burn it was argued (by scientests) that the overlap between the water bands and the CO2 bands would protect us, then when the fine structure was discovered, it was argued that the oceans could absorb all the CO2 we can produce at the rate we produce it - what was discovered in the late 50's early 60's was that the Oceans were absorbing CO2 more slowly than had been believed - so arguably it was at this point, 55-65 years after Arrehnius' original comment that it began to be accepted by the mainstream as a possibility.

It wasn't until Richard Nixon in 1969 that the Greenhouse effect and Global warming became a political issue.

So, to summarize, and perhaps clarify.
That the greenhouse effect existed was discovered in 1824, 145 years before Richard Nixon made it a political issue in 1969.
That changing the levels of CO2 in the atmosphere might change the mean global temperature was first poposed in 1858, 111 before Richard Nixon made it a political issue in 1969.
That Humans might affect the temperature of the planet through CO2 emissions was first proposed in 1896, 73 years before Richard Nixon made it a political issue in 1969.
That Human Beings were currently warming the environment through rising CO2 emissions was first proposed in 1938, 31 years before Richard Nixon made it a political issue in 1969.
That Human beings were currently warming the environment through rising CO2 emissions was accepted into the mainstream of science in 1960, 9 years before Richard Nixon made it a political issue.

I'm not tryting to scientifically justify a political issue by making a simplistic comparison.
I'm trying to put the science into a scientific phenomenom that has become overly politicsized.

 

No it isn't, the IR absorbance of a gas is proportional to the partial pressure of that gas.

Increasing the total mass of a particular gas in the atmosphere without removing another will increase the partial pressure of that gas.

Thankyou.