2011-02-23 17:50:00Post on CO2-free atmosphere
Chris Colose


*This could conceivably belong in an advanced-rebuttal, but I put it as a standalone

 Chris Colose

The ability for CO2 to warm the surface of a planet through the absorption of infrared radiation is well known.  What is much less appreciated, however, is just how effective of a gas it is in maintaining the greenhouse framework that helps to characterize the modern climate.

To bring this topic to light, one can ask what would happen to Earth's climate if one were to suddenly draw all the CO2 out of the atmosphere. Aside from the obvious impacts on biology by inhibiting photosynthesis, we are interested in the radiative impact and the manifestation of that change on Earth's global temperature. 

This question was brought up recently in a testimony to the subcommittee of the House Science and Technology Committee.   An answer was provided by MIT scientist Dr. Richard Lindzen, who suggested that such a hypothetical removal of all the CO2 in the air would translate into a global cooling of about 2.5 degrees, presumably in Celsius (see here, about 47 minutes into the video).  Dr. Cicerone, who was also on the panel, expressed disagreement although didn't really provide a better answer of his own.

It may be that Lindzen was just giving an estimate off the top of his head in a hearing, but the question is nonetheless interesting to explore further because it provides perspective on how to decompose the greenhouse effect into its individual components and the underlying implications of having a mixture of both condensing (i.e., those that reach saturation values and precipitate from the air) and non-condensing greenhouse gases.  On Earth, water (which is radiatively active as a gas or a cloud) is the only condensable substance, while the "long-lived" greenhouse gases (mostly CO2, CH4, O3, or N2O) do not precipitate from the air under modern temperature or pressure regimes.

One might naively suggest that removing all the CO2 in the atmosphere would produce a similar temperature change as doubling CO2, just in the other direction.  Even without considering the complex nature of feedbacks, this conclusion would be wrong however.  The radiative forcing generated by CO2 change goes as the logarithm of the concentration, and thus removing the whole CO2 inventory would generate a much larger impact than had you doubled it.  In fact, when you get to very small amounts of CO2 (on the order of a few parts per million), the radiative forcing is much faster than logarithmic since you’re opening up new opacity in the central 15 micron band where Earth is strongly emitting (it is for this reason methane changes are commonly cited as being “more powerful than CO2,” which is only true molecule-for-molecule in the modern atmosphere, as methane is starting off at much lower background concentrations.  Methane has no intrinsic properties that make this the case, and when comparing with CO2 side-by-side is even worse of a greenhouse gas).

Even this qualitative reasoning might have led Lindzen to a better ballpark answer than just 2-3 C, which would be even too small if feedbacks were completely neutral.  It’s still qualitative however, and getting a better handle on the question requires radiative transfer modeling and simulations that can adequately handle a greenhouse-free atmosphere without blowing up.  From here, the first question one can ask is how much of the total greenhouse effect is provided by CO2?  This is dependent on the background atmosphere itself, since overlapping absorption with other molecules will give a different number than if that molecule were all by itself, even at the same concentration. When you do these calculations with overlapping absorption, it was found by Schmidt et al (2010) that CO2 contributes to about 20% of the modern greenhouse effect.  The greenhouse effect can be defined energetically as:

where Ts and Te are the surface (288 K) and emission temperature (255 K), respectively. σ is the Stefan-Boltzmann constant.  It follows that CO2 alone provides nearly 30 W/m2 of radiative forcing, much larger than the ~4 W/m2 when you double it in the modern climate.  Assuming the same climate sensitivity, Lindzen’s estimate of a 2.5°C drop for a -30 W/m2 forcing would imply that currently doubling CO2 would warm the planet by only a third of a degree at equilibrium, which is well outside the bounds of IPCC estimates and even very low by most skeptical standards.

At this point, we need to incorporate feedbacks into the problem to get a better feel for how nature really operates.  It is often mentioned as a somewhat routine talking point that “water vapor is the most important greenhouse gas.”  This is true in the sense that it makes up the bulk of the infrared opacity in our atmosphere (~50%) and clouds another 25%, but because it condenses at Earth-like temperatures is very short-lived in the air as it goes through the evaporation, condensation, and precipitation cycle.  Because of the temperature-dependency on the pressure at which water saturates, this makes water vapor a feedback.  Another interpretation would then be that the non-condensing greenhouse gases (chiefly CO2, only about 5% of the greenhouse effect is provided by ozone, methane, N2O, etc) are the “most important,” since they provide enough warming so as to produce the skeleton by which the water vapor greenhouse effect can be strong enough.

There have been a number of studies which examine the evolution of the climate system with no CO2 in the atmosphere.  Such experiments are described for example in Pierrehumbert et al (2007) , or by Voigt and Marotzke (2009)From these papers, one can trigger a full snowball Earth with a sufficient reduction in atmospheric CO2.  A substantial reduction in water vapor (shown below, from Lacis et al (2010) as well as increase in the surface albedo are important feedbacks here, showing that removing the non-condensing greenhouse gases (mostly CO2) in the atmosphere can collapse nearly the entire terrestrial greenhouse effect.  What’s more, since the albedo increases substantially, the total greenhouse effect can be thought of as providing even more than 33 K of warming relative to Earth’s blackbody emission temperature. In the Lacis et al experiments, removing the CO2 from the atmosphere generates a cooling of around 30 C, an order of magnitude difference from Lindzen's answer.

Figure 1: Time evolution of global surface temperature, TOA net flux, column water vapor, planetary albedo, sea ice cover, and cloud cover, after zeroing out all of the noncondensing GHG’s.  From Lacis et al (2010)

Why might we care about such a hypothetical situation anyway? Aside from Lindzen, there are a number of interesting applications to low solar or low CO2 cases.  A concern with “large” climate changes (i.e., on the scale of snowball Earths or runaway greenhouses) is that there’s bifurcation (loosely, tipping points) in the system.  This is to say that one can conceivably draw down CO2 from the atmosphere and trigger a snowball, although it would take extremely high values of CO2 (much higher than the original amount) to get back out of this glaciated state.  In case skeptics bring it up, this is at least one way to have an ice-covered planet with very high CO2 levels.  Indeed, precisely how to escape a full-blown snowball is one of the grand unresolved questions in climate science. Once you're out of a snowball however, you're left with a very hot climate until weathering can draw down CO2 to moderate values. Shown below (from Pierrehumbert et al., 2011, accepted) is a bifurcation sketch of the temperature as a function of the CO2 content in the atmosphere, with a lower solar insolation than today (the paper is a review article on the Neoproterozoic climate).  One can do a similar type of diagram against the incoming shortwave radiation, but in any case the presence of an albedo feedback makes multiple temperature solutions possible, even for the same incoming stellar radiation and greenhouse effect.  For example, if the Earth were magically ice-covered today, this would be a completely stable situation and there would be no tendency to escape that state unless the greenhouse effect was substantially enhanced or the sun got brighter.  This is a big problem in planetary habitability studies, especially if a planet succumbs to a snowball fate early in its history when the sun is faint. Once you begin to melt ice however, the temperature jumps rapidly to a very hot solution.

This is germane to a recent paper by Rosing et al (2010) which purported to show that the "faint sun" paradox can be resolved through a lower albedo rather than through a substantially enhanced greenhouse effect.  This paper is interesting, and an example of good scientific skepticism, in the sense that the authors are proposing a new idea for a subject still open for research.  The idea is problematic however, since even for Neoproterozoic insolation, you kick over into a snowball at about 3x present CO2, and the situation is even worse for early Earth insolation, which is some 20-25% lower than today.  There is no mechanism to adjust the albedo in such a way as to offset temperature changes, whereas the long-term silicate weathering thermostat acts as a negative feedback between CO2 concentations and temperature over geologic time.




Figure 2: Bifurcation diagram for a zero-dimensional energy balance model. Calculations performed with L = 1,285Wm−2. For CO2 inventories up to approximately 1,000 Pa, the inventory can be converted to a mixing ratio in parts per million by volume (ppmv) by multiplying by 6.6. The CO2 concentrations on the upper horizontal axis are stated as fractions (e.g., 0.0065 corresponds to6,500 ppmv). The vertical dashed lines marked “Left” and “Right” indicate the left and right boundaries of the hysteresis loop for the case with ice albedo equal to 55%.  Adopted From Pierrehumbert et al., 2011, accepted

Lindzen has argued for a relatively insensitive climate system in the past, in which case it would be difficult  to explain the magnitude of large climate changes in the past, ranging from snowballs, the PETM, glacial-interglacial cycles, etc.  However, arguing that the climate would cool only be 2.5 degrees when you remove all the CO2 in the atmosphere is really just a made up number and ignored several articles on the subject that show otherwise.  Just the opposite, evidence shows that CO2 provides the building block for the terrestrial greenhouse effect, both because it absorbs strongly near the peak emission for Earth, and because it allows Earth to be warm enough to sustain a powerful water vapor greenhouse effect. 

2011-02-24 00:57:13Feedback
Daniel Bailey
Daniel Bailey

Thanks for the thorough post.  The maths you use are beyond me, which is a reflection on my shortcomings rather than an indictment of your communication abilities (which are splendid, as I've enjoyed many a post of yours over time).  So I won't comment on those.

As for the formula's you might try QuickLatex: http://quicklatex.com/

Your links are broken; the SkS WYSIWYG editor sometimes introduces  a short text string to the start of links when you paste them in (I don't know why).  If you have SkS hosting this preliminary blog post & put in a link, I or one of the others can help you in the editing of it.  Your call.

Nice post. 

Thanks for all your previous work; it's taught me a lot!

2011-02-24 01:28:00


very interesting post. The part on stability is not commonly debated in blogs and probably needs some clarification on what's the meaning of bifurcation and what is shown in fig.2. The caption of fig. 2 should explicitly say what the symbols mean.

If you know latex, the best way to write equation is to use this online equation editor and import them as images. Your equation, for example, is here.
Alternatively, in html you can write greek letters as &letter; where "letter" may be alpha, beta,etc.. Your equation would thus be GHE = σTs4 − σTe4.

P.S. please alert us when Pierrehumbert et al paper will get published, I suspect it will be particularly interesting.

2011-02-24 03:46:03
Mark Richardson

Definitely LaTeX up your equations. It makes them look so much better!


And it's easy to learn! A quick google will point you to the basic commands, e.g. \Delta for Δ and \delta for δ

2011-02-24 05:39:26
Chris Colose


I updated the post with a bit of new material and fixed up the equations.  Being a "Skeptical science" website I also wanted to give an example of a paper which is good in expressing a new point of view (properly, rather than being denier hogwash), but one I think is wrong nonetheless.  There is a Nature comment coming out about the Rosing paper I think soon.  The Pierrehumbert paper should be up on Ray's site soon as a pre-print...I know it is accepted thus far but not sure when it will be formally published.  Ray sent me a copy which is why I have it.

 I'll fix the links briefly...


2011-02-24 08:31:09
Glenn Tamblyn




Sometime ago I started working on a post on a similar theme based on 'unpacking Kiehl Fusullo & Trenberth's Energy Budget paper but have had to put it on the back burner due to work commitments

Take a look


2011-02-24 16:04:17
Chris Colose


Okay links fixed.  I just removed some of the symbology from the caption, which I originally copied from the original paper.  They were just paramters Ray used in his simple energy balance model, and not really important for this post.


Glenn I just skimmed over it without checking numbers/equations.  Your outline seems OK.  I think people might have trouble wading through it (and as you mention some of it is unphysical, diagnosing how things change when you add/remove something else is not trivial). 

2011-02-24 20:59:48Chris, thanks for writing this
John Cook

Would anyone know of online examples of Lindzen's argument (which I presume would be something like "removing all CO2 from the atmosphere would make little difference").

Chris, should be fun when one of us convert your advanced rebuttal into easier versions.

2011-02-25 06:04:58Further Reading
John Hartz
John Hartz

Recommend that you reference/link the seven-part series, "Understanding Atmospheric Radiation and the 'Greenhouse' Effect" posted on the Science of Doom website in a "Further Reading" tab to your article.


2011-02-25 17:17:23
Chris Colose


If anyone wants to do other versions of this, that's fine.  I can them too if no one is interested. 

 John-- I've seen claims like this but I can't remember where.  Presumably this would be one implication drawn from those who think the greenhouse effect isn't real, like G&T.  This could also be a standalone too if no one finds anything worthwhile to respond to aside from Lindzen's quote.   Let me know.

2011-03-01 16:45:33
Chris Colose


If one of the mods can please update me that would be great, I don't think I have the ability to put this up on my own.  I seen another option to create a rebittal but I don't know if this falls neatly into any of the categories.  I guess I can do one to on "why CO2 levels were high during snowball Earth" which follows up on some of these lines

2011-03-01 18:47:24Added the new argument to the database
John Cook


I've added the new argument to the database for you to preview:


I can't find any examples of it online though - is the only recourse to create a transcript of Lindzen's testimony?

Or is "Removing all CO2 would make little difference" not quite the argument you want to hit? You can edit the final rebuttal via:


If you're happy with it as is, let me know and I'll publish it as a blog post also.

2011-03-01 19:04:43


If Chris himself will write a shorter version it would be best, of course. If he won't, I'll do it after I'm done with the PDO rebuttal.

2011-03-04 04:56:53
Chris Colose


I think it would be best as a stand-alone blog post rather than a "rebuttal" but it's your call.  I haven't seen the argument phrased in the way Lindzen did, although there are certainly arguments that the greenhouse effect isn't real, CO2 is only a tiny constituent in the atmosphere, etc which are meant to give similar impressions, but my intention was educational anyway rather than baking up a refutation.  I could do a post on high CO2 levels during a snowball (which Monckton usually throws around) too. 

Riccardo-- I can do a shorter post, but I'm not sure if you need one if this ends up being a standalone (do you only do that for rebuttals?)

2011-03-09 16:32:54
Chris Colose


Thanks for adding this to the ready-to-post list.  I've made some last minute changes, especially toward the beginning for some further clarity.

2011-03-10 17:26:17Ready to post
John Cook


Chris, I've set up the blog post which is ready to go tomorrow morning:

What would a CO2-free atmosphere look like?

Sorry about the delay in getting this live. Next time, things will move much quicker!

BTW, you can add blog posts directly into the system yourself via the Author Admin (more details in this thread)

I think I agree, this works better as an educational blog post than a rebuttal as it's not really an argument that has ever been made apart from that throwaway comment by Lindzen.