Irreversible Climate Change Already?

[Xnn]

Here is a news release from the US Geological Survey.
I've copied some parts of it, but please read the entire release before commenting.

http://www.usgs.gov/newsroom/article_pf.asp?ID=2326

In brief, there are lots of uncertainties and potentials for climate change to impact
the role of the arctic as a CO2 sink and CH4 source. The science isn't there yet
to make much of a prediction and it may be decades before we know for sure.

However, what is interesting are the current CO2 sink and CH4 source numbers.
Although the CH4 source is one eighth the CO2 sink (50 vs 400), since CH4 is 23 times
more powerful as a greenhouse gas, the implication is that the Arctic is
already providing a positive feedback to climate change. It is providing roughly
effectively 3 times more greenhouse gases than it is absorbing. In other
words, even if human CO2 emissions were reduced to near zero, there would
still be a net positive global warming from sources/sinks inherit in the Arctic.

If true, that's a huge statement because unless there are significant changes in the
dynamics of the Arctic, that means climate change is probably irreversible.
By irreversible, I mean even if Humans were to cease all CO2 emissions
(which is highly unlikely), there would still be climate change due to the current
CH4 emissions from the Arctic.

Carbon generally enters the oceans and land masses of the Arctic from the atmosphere and largely accumulates in permafrost, the frozen layer of soil underneath the land’s surface. Unlike active soils, permafrost does not decompose its carbon; thus, the carbon becomes trapped in the frozen soil. Cold conditions at the surface have also slowed the rate of organic matter decomposition, McGuire says, allowing Arctic carbon accumulation to exceed its release.

But recent warming trends could change this balance. Warmer temperatures can accelerate the rate of surface organic matter decomposition, releasing more carbon dioxide into the atmosphere. Of greater concern, says McGuire, is that the permafrost has begun to thaw, exposing previously frozen soil to decomposition and erosion. These changes could reverse the historical role of the Arctic as a sink for carbon dioxide.

“In the short term, warming temperatures could release more Arctic carbon to the atmosphere,” says McGuire. “And with permafrost thawing, there will be more available carbon to release.”

On the scale of a few decades, the thawing permafrost could also result in a more waterlogged Arctic, says McGuire, a situation that could encourage the activity of methane-producing organisms. Currently, the Arctic is a substantial source of methane to the atmosphere: as much as 50 million metric tons of methane are released per year, in comparison to the 400 million metric tons of carbon dioxide the Arctic stores yearly. But methane is a very potent greenhouse gas – about 23 times more effective at trapping heat than carbon dioxide on a 100-year time scale. If the release of Arctic methane accelerates, global warming could increase at much faster rates.

“We don’t understand methane very well, and its releases to the atmosphere are more episodic than the exchanges of carbon dioxide with the atmosphere,” says McGuire. “It’s important to pay attention to methane dynamics because of methane’s substantial potential to accelerate global warming.”

But uncertainties still abound about the response of the Arctic system to climate change. For example, the authors write, global warming may produce longer growing seasons that promote plant photosynthesis, which removes carbon dioxide from the atmosphere. Also, the expansion of shrubs in tundra and the movement of treeline northward could sequester more carbon in vegetation. However, increasingly dry conditions may counteract and overcome these effects. Similarly, dry conditions can lead to increased fire prevalence, releasing even more carbon.

 

[Evo]

The title is not correct, there has never been any "irreversible" climate change recorded on this planet. Where in this link that you quoted do they say "irreversible". And please link to the study that shows it is "irreversible".

Personal opinions and theories are not allowed.

 

[WeatherRusty]

The claim of irreversibility should contain the caveat that this pertains to a time period of from centuries to more than 1,000 years.

http://www.noaanews.noaa.gov/stories2009/20090126_climate.html"

http://www.pnas.org/content/early/2009/01/28/0812721106.full.pdf+html"

 

[Skyhunter]

The title is not correct, there has never been any "irreversible" climate change recorded on this planet. Where in this link that you quoted do they say "irreversible". And please link to the study that shows it is "irreversible".

Personal opinions and theories are not allowed.

He defined what he means by irreversible. And the he also presented it as a question not a statement.

By irreversible, I mean even if Humans were to cease all CO2 emissions
(which is highly unlikely), there would still be climate change due to the current
CH4 emissions from the Arctic.

The paper is cited in the press release from the USGS. The USGS is a valid source within forum guidelines.

Here is the http://www.esajournals.org/toc/emon/79/4"

Here is thehttp://www.esajournals.org/doi/pdf/10.1890/08-2025.1"

 

[vanesch]

One should indeed be clear by what one means by "irreversible". There ARE ways in which climate change can potentially be irreversible, that is when there are several stable states for the same situation (a case of multistability), and a relatively small perturbation flips the climate from one stable state to another one (which could be a snowball earth, or a runaway greenhouse). Taking away the initial "drive" will then not bring climate back to its original stable point. This is a way one could say the change is "irreversible".

If one just means "it's going to take a much longer time to come back, than to drift away", that's strictly speaking not irreversible, but could be considered "irreversible for all practical purposes".

 

[Andre]

...Although the CH₄ source is one eighth the CO₂ sink (50 vs 400), since CH₄ is 23 times more powerful as a greenhouse gas, the implication is that the Arctic is already providing a positive feedback to climate change. It is providing roughly
effectively 3 times more greenhouse gases than it is absorbing.

... I mean even if Humans were to cease all CO₂ emissions
(which is highly unlikely), there would still be climate change due to the current
CH₄ emissions from the Arctic...

There are four elements I think about the role of CH₄ as greenhouse gas. First, the factor 23, second, the residence time of CH₄, third the actual trend of CH₄ in the atmosphere and fourth, the most stunning, the paleoclimatological evidence of the the role of CH₄.

The outcome, in my opinion, is that the role of CH₄ is about 23 times overstated.

So first, what is this factor "23 times more powerful" about? Let's consult http://geoflop.uchicago.edu/forecast/docs/Projects/modtran.html once more.

Let's start to check what doubling either greenhouse gas does on the radiation out. If you hit "submit the calculation" from the defaults, you see in the output:

I_out, W/m² = 287.844

Now double the value for CO₂ (375 -> 750 ppm) and calculate again to get I_out, W/m² = 284.672 hence a difference of ~3.2 W/m²

Now reset CO₂ to 375 and double the CH₄ (1.7 -> 3.4 ppm) and now we get 287.09 W/m² or a difference of only ~0.76 W/m². Compared to 3.2 W/m² not exactly a factor 23, is it?

Let's try a different way seeing what one unit of greenhouse gas does, setting both CO₂ and CH₄ to zero to get a basic I_out of 320.28 W/m². Now If we apply one ppm of CO₂ we get 315.57 ppm (delta ~ 4.7 W/m²) an for one ppm of CH₄ we get an I_out of 319.024 a mere ~1.3 W/m². So at unit level it appears that CO₂ is about 3.75 stronger for greenhouse effect than CH₄

Maybe it helps if we restore the default values (375 and 1.7 ppm) again and see what happens if we increase each with one ppm individually, Unfortunately CO₂ on 376 and 377 gives the same result as 375. Only at 378 ppm we get get I_out, W/m² = 287.812, or a delta of 0.032, which would be ~0.01 W/m² per ppm. If we increase CH₄ to one ppm to 2.7 we get I_out, W/m² = 287.373 or ~0.47 W/m². A whopping 47 times more than the increase of CO₂ from 375 to 376 ppm.

So where is this 23 times coming from? You can draw your own conclusions. But as the last example shows, it’s more like 23 times almost nothing.
Back later, there is plenty more.

 

[vanesch]

I think the 23 more comes from equal QUANTITIES of gas added:

375 ppm CO2 and 1.7 ppm CH4 gives you (MODTRAN) 287.844 W/m2

add 10 ppm CO2: this gives you 287.75 W/m2 or a forcing of 0.094 W/m2 for 10 ppm CO2

add 10 ppm CH4: you get 285.143 W/m2 or a forcing of 2.7 W/m2

so here we find a factor of 28 more forcing for 10 ppm of CH4 added, than for 10 ppm of CO2 added.

Of course this factor changes as a function of the exact delta.

It gives you the comparative effects of releasing 1 Gton of CO2 or 1 Gton of CH4, starting from our current situation, and for small effects.

 

[Andre]

Note that I did the same for one ppm for each with the 47 times result in my previous post.

Anyway the second factor was resident time of CH4 in the amosphere. That's estimated to be about a decade. This simply implies that CH4 would disappear rather quickly as it is oxydized in the atmosphere, so you'd need a big continuous source to keep the levels up whereas there must be limits to the stored amounts in the Arctic.

Third factor was the actual CH4 levels of the last few years which can be seen to be stabilizing http://www.mfe.govt.nz/environmental-reporting/atmosphere/greenhouse-gases/atmospheric-levels.html at Barring Head for instance:

http://www.mfe.govt.nz/environmental-reporting/atmosphere/greenhouse-gases/images/ch4-baring.jpg

... giving no support for an additonal large CH4 source so far.

Fourth factor is worth a separate thread I think, back for that later.

 

[vanesch]

Note that I did the same for one ppm for each with the 47 times result in my previous post.

Yes, I saw that, but given the very small difference in power, we might have numerical roundoff errors (although, on the other hand, 10 ppm is not a "small change" for the CH4, I agree).

Anyway the second factor was resident time of CH4 in the amosphere. That's estimated to be about a decade. This simply implies that CH4 would disappear rather quickly as it is oxydized in the atmosphere, so you'd need a big continuous source to keep the levels up whereas there must be limits to the stored amounts in the Arctic.

I didn't know this. Then indeed, there isn't any reason to consider this as an important greenhouse gas, so I wonder why people DO consider it important.

About the evolution of the CH4 concentration, what happened around 1999 that made for the kink ?

 

[Skyhunter]

You also must consider the fact that when CH₄ decays in the atmosphere it recombines with oxygen, the end result is one CO₂ molecule and four H₂O molecules. Since this process usually takes place in the stratosphere where UV energies are higher, methane is the primary source of water vapor above the tropopause.

 

[Andre]

Yes, I saw that, but given the very small difference in power, we might have numerical roundoff errors (although, on the other hand, 10 ppm is not a "small change" for the CH4, I agree).

Apart from that it's not a linear effect so the effect of 1 ppm is not the same as 1/10 of 10 ppm.

Then indeed, there isn't any reason to consider this as an important greenhouse gas, so I wonder why people DO consider it important.

Because that's how it appeared in the Greenland Ice cores. I'll try and start a thread on that in a while.

About the evolution of the CH4 concentration, what happened around 1999 that made for the kink ?

The answer has not risen beyond any speculation. It's simply unknown.

 

[Andre]

You also must consider the fact that when CH₄ decays in the atmosphere it recombines with oxygen, the end result is one CO₂ molecule and four H₂O molecules. Since this process usually takes place in the stratosphere where UV energies are higher, methane is the primary source of water vapor above the tropopause.

True, but per 1 ppm CH4 on 1.7 ppm, is a whole lot different than 1 ppm CO2 on -say- 385 ppm. Furthermore the greenhouse effect of the stratosphere is supposed to be cooling, not warming.

 

[Xnn]

Evo; Please notice that I posed question.

WeatherRusty; Thanks for the links. It looks like the "reversible" question has been answered already for human causes. My question/surprise was that the Arctic Ecosystem itself was becoming a climate driver all by itself.

Skyhunter; Thanks for coming to my defense by injecting some reason.

Andre; is vanesch correct about the number 23? I think he is.

However, your point about what happened to CH4 atmospheric concentrations since 1999 is relevant. Not clear if the USGS factored that in with their emission numbers.
I haven't seen much of an timeline accounting for the changes in CH4 emissions and sinks (if that is what we call them). Something seems to have changed for the better, but what?

One of the things about the press releases is that it appears to form the basis for grant request as much as anything.

 

[Skyhunter]

Furthermore the greenhouse effect of the stratosphere is supposed to be cooling, not warming.

Not the greenhouse effect in general but CO₂ specifically. CO₂, because of it's quantum shape will radiate more energy in the stratosphere than is available there for absorption. Water vapor in the stratosphere will lead to stratospheric warming.

I don't know the net result, just pointing out that there is more to CH₄ emission forcing than it's absorption spectra.

 

[WeatherRusty]

Andre,

From Post#6:

So where is this 23 times coming from? You can draw your own conclusions. But as the last example shows, it’s more like 23 times almost nothing.

Global Warming Potential (GWP) adds one more factor into the consideration of the relative importance or "effectiveness" of the various GHGs. Some gases linger in the atmosphere far longer than others before natural processes remove them. In the case of a GHG, the Global Warming Potential (GWP) takes into account the fact that a GHG that lingers longer has a greater cumulative contribution to the greenhouse effect over its "lifetime" than does a gas that is quickly removed. Recall that water vapor tends to cycle out of the atmosphere in a matter of days; water vapor, therefore, has a negligibly small GWP. Methane takes, on average, about 12 years to disappear from the atmosphere. Carbon dioxide takes centuries. Some gases take even longer periods of time! GWP is stated in terms of a given time interval, such as "the GWP for a 20 year time horizon" or "the GWP for a 100 year time horizon"; this latter is the most commonly stated time period for GWP. Carbon dioxide is used as the reference gas, and therefore, by definition, has a GWP of precisely 1. A definition of GWP could be stated something like: the total radiative forcing produced by a given amount (such as one kilogram) of a particular GHG over the entire course of a specified time period (most commonly a century) as compared with the same amount of carbon dioxide. Methane, which is "pound-for-pound" a much more "potent" GHG than CO2 has a GWP of 62 over a 20 year period. Over a 100 year period, the GWP of methane is a much-reduced 23; though methane is more "potent" than carbon dioxide, it is also "shorter-lived", which tends to offset its total contribution to the greenhouse effect. Nitrous oxide, which is both a very "potent" GHG and a long-lived one (atmospheric lifetime of 114 years), has a GWP of 296 on a 100 year scale. Some fluorocarbons have GWP values of more than 1,000 or even more than 10,000; we would have some really big problems if we released large quantities of them into the atmosphere!

http://www.windows.ucar.edu/tour/link=/earth/climate/greenhouse_effect_gases.html"

More near the end of this EPA article including tables of GWP:

http://www.epa.gov/climate/climatechange/emissions/downloads/ghg_gwp.pdf"

 

[Xnn]

So, this is interesting.

According to the EPA document, the 100 year Global Warming Potential of Methane (CH4) is 25 times that of CO2.

In the SAR it was 21
In the TAR is was 23
In AR4 it is 25.

So, the USGS quoted an out of date value or is using a different time horizon.

100 years is the conventional metric used by most countries.

 

[Xnn]

The IPCC has estimated that slightly more than half of the current CH4 flux to the atmosphere is anthropogenic, from human activities such as agriculture, fossil fuel use, and waste disposal (IPCC 2007).

More from the EPA/IPCC.

In other words, almost half the CH4 flux are from "natural" sources, which presumably would be things like the Arctic regions reaction to warming already in place.

 

[Xnn]

Some scientists hypothesize that severe droughts in certain regions have reduced methane emissions from wetlands in the last few years, though this claim is far from proven.

From the UCAR link... droughts are good for mitigating methane releases. But the long term predictions of global warming are for globally higher precipition levels.

 

[mheslep]

The paper is cited in the press release from the USGS. The USGS is a valid source within forum guidelines.

?? The paper referenced by USGS in EM is within the guidelines, not every statement made by the USGS - per my understanding.

Title, authors:
Sensitivity of the Carbon Cycle in the Arctic to Climate Change
A. David McGuire, Leif G. Anderson, Torben R. Christensen, Scott Dallimore, Laodong Guo, Daniel J. Hayes, Martin Heimann, Thomas D. Lorenson, Robie W. Macdonald, Nigel Roulet
http://www.esajournals.org/toc/emon/79/4

 

[mheslep]

IPCC AR4's list of forcings below. CH4 is 1/3 that of CO2, slightly more than ozone. Perhaps that's due simply to CH4's small concentration in the atmosphere relative to CO2, or some other factor discussed above. For whatever reason, it's a distant second to CO2 in forcing, and thus I think it can't lead irreversibility arguments.

http://www.jaxa.jp/article/special/eco/img/kimura_photo04_be.jpg

 

[vanesch]

Andre,

From Post#6:




Global Warming Potential (GWP) adds one more factor into the consideration of the relative importance or "effectiveness" of the various GHGs. Some gases linger in the atmosphere far longer than others before natural processes remove them. In the case of a GHG, the Global Warming Potential (GWP) takes into account the fact that a GHG that lingers longer has a greater cumulative contribution to the greenhouse effect over its "lifetime" than does a gas that is quickly removed.

Ah, so what is compared is not the power (the forcing), but the total amount of heat (the time integral of the power) over their atmospheric life time, given a delta-function "injection", is that it ?

 

[WeatherRusty]

Ah, so what is compared is not the power (the forcing), but the total amount of heat (the time integral of the power) over their atmospheric life time, given a delta-function "injection", is that it ?

A definition of GWP could be stated something like: the total radiative forcing produced by a given amount (such as one kilogram) of a particular GHG over the entire course of a specified time period (most commonly a century) as compared with the same amount of carbon dioxide.

RF is typically given as Watts/meter^2.

Global warming potential (GWP) is an estimate of how much a given greenhouse gas contributes to Earth’s radiative forcing. Carbon dioxide (CO2) has a GWP of 1, by definition, so a gas with a GWP of 23 would increase radiative forcing by 23 times as much as the same amount (mass) of CO2. A GWP value is defined over a specific time interval, so the length of this time interval must be stated to make the value meaningful, typically 100 years.

So 1 kilogram of introduced CH4 produces 23 times more radiative forcing over the course of 100 years than does 1 kilogram of CO2.

1 kilogram of introduced CH4 produces 62 time more radiative forcing over the course of 20 years than does 1 kilogram of CO2.

2001 IPCC TAR values given.

The GWP depends on the following factors:

* the absorption of infrared radiation by a given species
* the spectral location of its absorbing wavelengths
* the atmospheric lifetime of the species

 

[Skyhunter]

?? The paper referenced by USGS in EM is within the guidelines, not every statement made by the USGS - per my understanding.

Title, authors:
Sensitivity of the Carbon Cycle in the Arctic to Climate Change
A. David McGuire, Leif G. Anderson, Torben R. Christensen, Scott Dallimore, Laodong Guo, Daniel J. Hayes, Martin Heimann, Thomas D. Lorenson, Robie W. Macdonald, Nigel Roulet
http://www.esajournals.org/toc/emon/79/4

Not every statement may be accurate, nor every study robust, but the USGS is a valid scientific body and therefore a valid source for this forum.

 

[mheslep]

Not every statement may be accurate, nor every study robust, but the USGS is a valid scientific body and therefore a valid source for this forum.

Respectable certainly. But valid according to who? I say the opinions Christy and Spencer are valid, but I refrain from posting excerpts from their websites here. I thought the rule for asserting scientific data/principals in Earth is peer reviewed sources, end of story? Otherwise we're back to what is valid and not. Note I don't have any problem with general website references in this case as it by way of introducing a question as you pointed out.

 

[Ivan Seeking]

Does irreversible [as defined earlier] include geoengineering?

For example, some schemes, such as the dispersion of bright white [light-reflecting] particulates at high atltitudes, could reduce the incident radiation by as much as 2%.

 

[mheslep]

Does irreversible [as defined earlier] include geoengineering?

For example, some schemes, such as the dispersion of bright white [light-reflecting] particulates, at high atltitudes, could reduce the incident radiation by as much as 2%.

Good question. If reality is bistable as Vanesch posited, then geoengineering would probably be required to reduce temperatures below present ones to flip the state back again. I've been avoiding digging into the McGuire et al paper, I expect that's required for an answer.
http://www.esajournals.org/doi/pdf/10.1890/08-2025.1

 

[Skyhunter]

https://www.physicsforums.com/showpost.php?p=2007697&postcount=1

Controversial claims must be supported by evidence that comes from a scientific, peer-reviewed journal or a similarly reliable source, i.e., unsubstantiated claims are not allowed.

I would consider the US Geological Survey to be a reliable source and I suspect the moderators and administrators here would agree.

http://www.usgs.gov/

 

[mheslep]

https://www.physicsforums.com/showpost.php?p=2007697&postcount=1



I would consider the US Geological Survey to be a reliable source and I suspect the moderators and administrators here would agree.

http://www.usgs.gov/

So would I for the contents of their 'Maps, Imagery, Publications' area and similar, but not in the dashed off material in 'New Releases'
http://www.usgs.gov/pubprod/

Otherwise the general writings of published scientists like Spencer should be considered as reliable.
http://www.drroyspencer.com/

Moderator opinion?

 

[Ivan Seeking]

So would I for the contents of their 'Maps, Imagery, Publications' area and similar, but not in the dashed off material in 'New Releases'
http://www.usgs.gov/pubprod/

Otherwise the general writings of published scientists like Spencer should be considered as reliable.
http://www.drroyspencer.com/

Moderator opinion?

Any controversial claim would require a paper or an official reference. No blogs are acceptable for debated topics as a reference.

 

[Skyhunter]

Any controversial claim would require a paper or an official reference. No blogs are acceptable for debated topics as a reference.

Which is wht Roy Spencer only makes his controversial claims on his website instead of the papers he submits for peer review.

 

[vanesch]

Does irreversible [as defined earlier] include geoengineering?

Ah, that's another use of the word "irreversible" ("no matter what we do, we can't repair it").

I would call "irreversible" anything that is caused by a (small) drive, and doesn't disappear after some time when the drive is taken away. Most more or less stable systems are reversible for small enough drives.

 

[mheslep]

Any controversial claim would require a paper or an official reference. No blogs are acceptable for debated topics as a reference.

Sounds good, but what's official? Any US government science office website? Including news releases? Any university science dept website? Chinese government websites?

 

[Ivan Seeking]

Sounds good, but what's official? Any US government science office website? Including news releases? Any university science dept website? Chinese government websites?

If an agency is a government agency, such as the USGS, NOAA, or the EPA, offering a page that discusses the state of the climate, then I would expect it to be acceptable. As soon as we get into statements made by individuals, such as a blog as the USGS, then I think it would not qualify.

When I said official, I meant a *.gov site. As for China, why not? If the page represents the peer-reviewed work of mainstream scientists, such as a NOAA page, then it should be okay.

In any event, applicable peer review is the key constraint to consider.

 

[zankaon]

I think the 23 more comes from equal QUANTITIES of gas added:

375 ppm CO2 and 1.7 ppm CH4 gives you (MODTRAN) 287.844 W/m2

add 10 ppm CO2: this gives you 287.75 W/m2 or a forcing of 0.094 W/m2 for 10 ppm CO2

add 10 ppm CH4: you get 285.143 W/m2 or a forcing of 2.7 W/m2

so here we find a factor of 28 more forcing for 10 ppm of CH4 added, than for 10 ppm of CO2 added.

Of course this factor changes as a function of the exact delta.

It gives you the comparative effects of releasing 1 Gton of CO2 or 1 Gton of CH4, starting from our current situation, and for small effects.

One might keep in mind that equal quantities might be best considered in terms of effect of equal number of molecules; that is 1 mole. The respective gram molecular weights are 44 gm for CO2 and 16 gm for methane, giving the same number of molecules i.e. Avogadro number of ~6 x 10^23, even though the wt difference would be 44/16 = 2.75. http://en.wikipedia.org/wiki/Avagadro%27s_number"

addendum: If CO2 and methane absorb infrared radiation (via molecular rotation change, if i recall) given off by Earth etc., why then wouldn't these same molecules absorb incoming solar radiation? Might it relate to quantity of infrared radiation re-radiated especially at night?

 

[sylas]

One might keep in mind that equal quantities might be best considered in terms of effect of equal number of molecules; that is 1 mole. The respective gram molecular weights are 44 gm for CO2 and 16 gm for methane, giving the same number of molecules i.e. Avogadro number of ~6 x 10^23, even though the wt difference would be 44/16 = 2.75. http://en.wikipedia.org/wiki/Avagadro%27s_number"

Quite right. The factor 23 difference is per additional molecule, not per equal mass unit.

I think the 23 more comes from equal QUANTITIES of gas added:

375 ppm CO2 and 1.7 ppm CH4 gives you (MODTRAN) 287.844 W/m2

add 10 ppm CO2: this gives you 287.75 W/m2 or a forcing of 0.094 W/m2 for 10 ppm CO2

add 10 ppm CH4: you get 285.143 W/m2 or a forcing of 2.7 W/m2

so here we find a factor of 28 more forcing for 10 ppm of CH4 added, than for 10 ppm of CO2 added.

Your value of 28 is actually more accurate for current conditions than the 23 quoted previously. But we can improve it further. The modtran calculator is a useful but simple tool intended for student use; and it doesn't actually work all that well for calculating forcings accurately. (See email from the author David Archer in [post=2324953]msg#26[/post] of thread "Rising Carbon Dioxide Levels Don’t Increase Earth’s Temperature", in response to some issues you uncovered earlier.)

A more accurate approach would be to use formulae for estimating forcings, and take derivatives. The equations in http://www.grida.no/publications/other/ipcc_tar/?src=/climate/ipcc_tar/wg1/212.htm of the third IPCC assessment report continue to be a good guide and are still applied in the more recent fourth assessment. Note that the methane forcing has a correction for N₂O, due to overlap in the absorption bands.

Here is a transcription of those formulae, followed by some algebraic manipulations to get the forcing per unit concentration. A "forcing" is a change in energy balance, measured in W/m², arising from a change (in this case) in concentrations of gases.

Variables used:

$$\begin{array}{ll} M_0, M & \text{Methane concentrations (ppbv) initial and final} \\ N_0, N & N_2O \text{ concentrations (ppbv) initial and final} \\ C_0, C & CO_2 \text{ concentrations (ppmv) initial and final} \\ \Delta F_M, \Delta F_N, \Delta F_C & \text{Associated forcings} \end{array}$$​

Formulae:

$$\begin{align*} \Delta F_C & = 5.35 \times \log_e \left[ C / C_0 \right] \\ f(M, N) &= 0.47 \times \log_e \left[ 1 + 2.01 \times 10^{-5} (MN)^{0.75} + 5.31 \times 10^{-15} M(MN)^{1.52} \right] \\ \Delta F_M & = 0.036 ( \sqrt{M} - \sqrt{M_0} ) - ( f(M, N_0) - f(M_0, N_0) ) \\ \Delta F_N & = 0.12 ( \sqrt{N} - \sqrt{N_0} ) - ( f(M_0, N) - f(M_0, N_0) ) \\ \intertext{Now get rates of change for forcing, per change concentrations} \frac{dF}{dC} &= \frac{5.35}{C} \\ \frac{\partial f}{\partial M} & = 0.47 \frac{2.01 \times 10^{-5} \times 0.75 \times N^{0.75}M^{-0.25} + 5.31 \times 10^{-15} \times 2.52 \times (MN)^{1.52}}{1 + 2.01 \times 10^{-5} (MN)^{0.75} + 5.31 \times 10^{-15} M(MN)^{1.52}} \\ \frac{dF}{dM} &= \frac{0.018}{\sqrt{M}} - \frac{\partial f}{\partial M}[M,N_0] \end{align*}$$​

As we should expect, the rate of change of forcing is independent of initial values; although methane results depend on N₂O concentrations. Current values (accessed July 2009) are at Recent Greenhouse Gas Concentrations, CDIAC. Note that methane varies significantly over the course of a year, so a range is given.

Values: C = 383.8 ppm. N = 320 .. 321 ppb. M = 1735 .. 1857 ppb.
Substituting in the formulae, and scaling the methane rate by 1000 to convert from ppb to ppm, gives:

$$\begin{align*} \frac{dF}{dC} &= 0.014 \\ 1000 \times \frac{dF}{dM} &= 0.36 \text{ to } 0.37 \\ \text{ratio efficacy methane to } CO_2 &= 25.7 \text{ to } 26.6 \end{align*}$$​

Methane is currently about 26 times more potent in the forcing impact, molecule for molecule. The main reason for this is not because the molecules themselves are any better at thermal absorption, but because concentrations are so much lower, which means small additional changes have a larger effect.

After doing this calculation, I found that the results are available in the fourth assessment report, table 2.14, as "radiative efficiency" given in W m^-2 ppb^-1. Scaling by 1000, they are 0.014 for CO₂ and 0.37 for methane; as obtained in the calculations shown here.

Cheers -- sylas