# CO2 emissions change our atmosphere for centuries

## What the science says...

Individual carbon dioxide molecules have a short life time of around 5 years in the atmosphere. However, when they leave the atmosphere, they're simply swapping places with carbon dioxide in the ocean. The final amount of extra CO2 that remains in the atmosphere stays there on a time scale of centuries.

## Climate Myth...

CO2 has a short residence time

"[T]he overwhelming majority of peer-reviewed studies [find] that CO2 in the atmosphere remained there a short time." (Lawrence Solomon)

The claim goes like this:

(A) Predictions for the Global Warming Potential (GWP) by the IPCC express the warming effect CO2 has over several time scales; 20, 100 and 500 years.

(B) But CO2 has only a 5 year life time in the atmosphere.

(C) Therefore CO2 cannot cause the long term warming predicted by the IPCC.

This claim is false. (A) is true. (B) is also true. But B is irrelevant and misleading so it does not follow that C is therefore true.

The claim hinges on what life time means. To understand this, we have to first understand what a box model is: In an environmental context, systems are often described by simplified box models. A simple example (from school days) of the water cycle would have just 3 boxes: clouds, rivers, and the ocean.

A representation of the carbon cycle (ignore the numbers for now) would look like this one from NASA.

In the IPCC 4th Assessment Report glossary, "lifetime" has several related meanings. The most relevant one is:

“Turnover time (T) (also called global atmospheric lifetime) is the ratio of the mass M of a reservoir (e.g., a gaseous compound in the atmosphere) and the total rate of removal S from the reservoir: T = M / S. For each removal process, separate turnover times can be defined. In soil carbon biology, this is referred to as Mean Residence Time.”

In other words, life time is the average time an individual particle spends in a given box. It is calculated as the size of box (reservoir) divided by the overall rate of flow into (or out of) a box. The IPCC Third Assessment Report 4.1.4 gives more details.

In the carbon cycle diagram above, there are two sets of numbers. The black numbers are the size, in gigatonnes of carbon (GtC), of the box. The purple numbers are the fluxes (or rate of flow) to and from a box in gigatonnes of carbon per year (Gt/y).

A little quick counting shows that about 200 Gt C leaves and enters the atmosphere each year. As a first approximation then, given the reservoir size of 750 Gt, we can work out that the residence time of a given molecule of CO2 is 750 Gt C / 200 Gt C y^{-1} = about 3-4 years. (However, careful counting up of the sources (supply) and sinks (removal) shows that there is a net imbalance; carbon in the atmosphere is increasing by about 3.3 Gt per year).

It is true that an individual molecule of CO2 has a short residence time in the atmosphere. However, in most cases when a molecule of CO2 leaves the atmosphere it is simply swapping places with one in the ocean. Thus, the warming potential of CO2 has very little to do with the residence time of individual CO2 molecules in the atmosphere.

What really governs the warming potential is how long the extra CO2 remains in the atmosphere. CO2 is essentially chemically inert in the atmosphere and is only removed by biological uptake and by dissolving into the ocean. Biological uptake (with the exception of fossil fuel formation) is carbon neutral: Every tree that grows will eventually die and decompose, thereby releasing CO2. (Yes, there are maybe some gains to be made from reforestation but they are probably minor compared to fossil fuel releases).

Dissolution of CO2 into the oceans is fast but the problem is that the top of the ocean is “getting full” and the bottleneck is thus the transfer of carbon from surface waters to the deep ocean. This transfer largely occurs by the slow ocean basin circulation and turn over (*3). This turnover takes 500-1000ish years. Therefore a time scale for CO2 warming potential out as far as 500 years is entirely reasonable (See IPCC 4th Assessment Report Section 2.10).

Intermediate rebuttal written by Doug Mackie

**Update July 2015:**

Here is the relevant lecture-video from Denial101x - Making Sense of Climate Science Denial

Last updated on 5 July 2015 by pattimer. View Archives

Tom Curtisat 01:26 AM on 27 June, 2011Such an interpretation would be a misinterpretation, however, for by 'uptake' Archer and Brovkin mean the process whereby equilibrium is established between the deep ocean and the ocean surface/atmosphere. Because of the slow transfer of CO2 from surface to the deep ocean, the rate at which equilibrium is established with the deep ocean is indeed governed by the cumulative excess above equilibrium levels accumulated by the surface of the ocean, and the atmosphere. (Because the surface and atmosphere equilibriate over a very short time span, Archer and Brovkin, they mention only the atmosphere.) In contrast, establishing equilibrium between ocean surface and the atmosphere is governed annual emissions. On your interpretation of Archer and Brovkin, they flat out contradict themselves within two paragraphs by claiming that Now you may require something more than the fact that on your interpretation of Archer and Brovkin that the ocean surface and atmosphere will equilibrate within a year, but that 'uptake' will "come and fade on a time scale of a few centuries to millennia". That fact should be enough to see that my interpretation of Archer and Brovkin is correct. But to drive home the point, we see in an earlier passage that they definitely use 'uptake' to refer to the slow, centennial scale process of equilibrating between ocean surface/atmosphere and the deep ocean rather than the rapid process of equilibrating between ocean surface and atmosphere:Eric (skeptic)at 13:17 PM on 27 June, 2011KRat 13:39 PM on 27 June, 2011Dikran Marsupialat 17:31 PM on 27 June, 2011Eric (skeptic)at 21:24 PM on 27 June, 2011Dikran Marsupialat 21:47 PM on 27 June, 2011Eric (skeptic)at 23:02 PM on 27 June, 2011Dikran Marsupialat 23:21 PM on 27 June, 2011Response:(DB) Dikran, I was referring to something which came up on Dr Franzen's first post several months ago that, as CO2 level stabilize and then fall, that the oceans will begin to outgas CO2 themselves, going from sink to source & preserving elevated CO2 levels (& temps) at elevated levels compared to preindustrial; look in the comments in that post for the direct discussion (I'd link to it but we're camping out in the bush& I barely have a cellphone signal).[Dikran Marsupial] Cheers DB, I thought it would be something like that. It's swealteringly hot in my office, I wish I were outdoors! ;o)Eric (skeptic)at 23:28 PM on 27 June, 2011KRat 23:35 PM on 27 June, 2011"KR, I must have insinuated something I didn't mean to ("50 year time cycle for full equalization")."You're quite correct, Eric, my apologies. I misread your post, which clearly refers to 50 years as thehalf-life. Sorry about that. That's fairly reasonable - my back of the envelope check on this indicated a half-life of ~40 years assuming absorption rate was proportional to excess over pre-industrial levels. Although, given the 340-350GT we've added to the carbon cycle from sequestered fossil fuels, and themultipleabsorption paths with different equalization times, I don't think it's as simple as a single half-life. The rise in temperature from the added GHG's will mean an equilibrium level of ocean absorbed CO2lowerthan in pre-industrial times, for example. Oops! Reading the past few posts, it appears Dikran has beaten me to these points with much better information...Rob Paintingat 23:37 PM on 27 June, 2011BobCat 03:38 AM on 12 July, 2011Carbon-14page, is that the CO2 adjustment time in the atmosphere is ~10-12 years (stated as a half-life). Compare the plot shown on this page with the theoretical plots (from box models) posted by Dikran Marsupial @ 93. If you want to dispute this, you shouldn’t argue with me about it, but rather the thousands of scientists and engineers (and published papers) that use the well known and tested method of tracer measurement. (Google "tracer" and "measurement" for a huge list -- start anywhere you like.)Response:[Dikran Marsupial] minor edit (as discussed with author)Dikran Marsupialat 17:25 PM on 12 July, 2011Martin Aat 06:31 AM on 17 May, 2012"Individual carbon dioxide molecules have a short life time of around 5 years in the atmosphere. However, when they leave the atmosphere, they're simply swapping places with carbon dioxide in the ocean. The final amount of extra CO2 that remains in the atmosphere stays there on a time scale of centuries."Can you let me have a reference where I can look this up please? When I write down the differential equations for a simple two-box model, with an injected mass of CO2, in addition to an ongoing equilibrium exchange between atmosphere and sink, the result I get does not agree with your explanation. I want to resolve the difference.KRat 07:37 AM on 17 May, 2012(relatively simple)mid-term carbon cycle modeling. Generally speaking, a two-box model will not be sufficient to examine ocean sequestration. The Bern model(not the most complex out there)uses one atmospheric box, four ocean boxes, plus an additional four for the biosphere.Tom Curtisat 08:49 AM on 17 May, 2012Dikran Marsupialat 17:14 PM on 17 May, 2012Martin Aat 05:29 AM on 18 May, 2012KR:Thank you for the Bolin and Eriksson 1958 reference. The link does not lead to the paper itself and I did not manage to locate the paper. (I don't have access to library facilities.) I am aware of the Bern model but my query is related to understanding the fundamentals, not the details of the results used by the IPCC and predicted by the Bern model.Tom Curtis:I have not considered volcanic CO2. But, as I said above, at present I am trying to understand the basic principles, I am not attempting to produce realistic results.Dikran Marsupial:Thank you for the link to the abstract of your paper. I read the words which seem to reiterate the statement at the head of this page but, as I said before, my calculations seem to differ from this and I am trying to resolve the discrepancy. The SkS comment is:"Individual carbon dioxide molecules have a short life time of around 5 years in the atmosphere. However, when they leave the atmosphere, they're simply swapping places with carbon dioxide in the ocean."My understanding is that this means that it takes much longer for the system to reach equilibrium than the residencetime of molecule. My calculations give the same average lifetime in the atmosphere for a CO2 molecule in an injected mass of CO2 as the average time for atmospheric CO2 to reach its new equilibrium following the injection. This differs from the SkS statement, if I have correctly understood the latter. Here is what I have done. I have taken a very simple case but I am simply trying to understand the basics, not produce realistic results. I have considered a case of two finite boxes, atmosphere and ocean (let's say). I have made assumptions as follows: 1. The rate of diffusion from atmosphere to ocean (Gt/yr) is proportional to the mass of CO2 (Gt) in the atmosphere and is independent of the mass of CO2 in the ocean. 2. The rate of diffusion from to ocean to atmosphere (Gt/yr) is proportional to the mass of CO2 (Gt) in the ocean and is independent of the mass of CO2 (Gt) in the atmosphere. Note: Assumptions 1 and 2 imply that the system is linear. 3. The system is initially in equilibrium, so that, initially, the rate of diffusion from atmosphere to ocean equals the rate of diffusion from ocean to atmosphere. 4. I assumed a significant total mass of CO2 (in ocean and atmosphere) and calculated the equilibrium mass of CO2 in atmosphere from the diffusion rate coefficients. 5. I then assumed that an additional mass M (Gt) of CO2 is injected into the atmosphere. I calculated: - the equilibrium mass in the atmosphere and in the ocean when the system once again reaches equilibrium, with the additional M Gt in the system. The equilibrium levels will have changed because I have not assumed the ocean is infinite. - I solved the 1st order differential equation giving the atmospheric CO2 as a function of time, to find the time constant with which the atmospheric CO2 reaches the new equilibrium in the presence of the ongoing equilibrium exchange. Then I repeated the calculation, but this time assuming that initially there waszeroCO2 in the atmosphere and zero in the ocean. So, physically, the injected molecules of CO2 leaving the atmosphere cannot be being replaced by CO2 from the ocean - there was none in there. I solved the differential equation to find the average time for an injected mass of CO2 to reach the new equilibrium (for a system containing no other CO2), and it was the same as for the initial calculation of the average time to reach equilibrium (for a system with CO2 present in atmosphere and ocean much greater in mass than the injected CO2). This was not unexpected, as the differential equation is linear, so the response to an input (the injected mass) should be independent of the response to other inputs (such as the ongoing equilibrium interchange)simultaneously present. I hope the foregoing makes sense. What I am still hoping to find, is a paper that explains (using mathematics, rather than verbal reasoning) how it is that the average lifetime of an injected CO2 molecule differs greatly (or differs at all) from the average time it takes for the system overall to reach equilibrium following the injection of a mass of CO2. Thank you for any help you can give me.Response:[DB] KR's link itself had a further link to Bolin and Eriksson 1958.Tom Curtisat 08:43 AM on 18 May, 2012learn from other peoples mistakes, for you will not live long enough to make them all yourself. To that end, I recommend purchasing "Global Warming: understanding the forecast" which is the best general introduction to the science of the green house effect and carbon cycles available. It is doubly useful because it has an associated, free online course with associated video lectures and models. The model which will most interest you is the Geocarb model, described as "an on-line zero-dimensional descendent of the Berner & Kothavala (2001) GEOCARB III model".Dikran Marsupialat 22:34 PM on 18 May, 2012Martin Aat 23:26 PM on 18 May, 2012DBThank you for the link. I've downloaded the Bolin and Eriksson paper and I'm now reading it. It's often the earliest papers that give the deepest insight, perhaps because they had to sort things out from basics.Tom CurtisThank you for the Archer recommendation. I have sent for a copy. From a quick peek via Amazon, if seems to be a descriptive introduction, avoiding the use of mathematics. It's quite true that life is to short to do everything but I'm determined to get to the bottom of the point I'm trying to understand in this case. So far as I can see, injecting a mass of CO2 into the atmosphere results in an exponential approach to a new equilibrium with a time constant equal to the avererage atmospheric residence time of a CO2 molecule. This seems to conflict with what I've seen in several places, including the statement at the top of this page.Dikran MarsupialThank you. "the adjustment time is essentially independent of the residence time" This is the key point that I believe this SkS page makes, and which I have not been able to reconcile with my own intuition nor with my calculations of a simple model. I believe I have correctly formulated the differential equation, for my simplified case where there are zero emissions other than a one-off injection. [dx/dt = rate CO2 exits ocean - rate CO2 exits atmosphere, where x = CO2 in atmosphere]. I've emailed you a request for a reprint of your paper and maybe it will help me pin down the discrepancy between my understanding and what I've seen stated here and elsewhere.KRat 01:46 AM on 19 May, 2012total concentration(not individual molecular identities)changes. If you(from your intuitions)get this point wrong, you're going to obtain wildly wrong answers. As a rather brain-dead computation(an example - please do not consider this authoritative, as it skips: Currently oceans and the biosphere are absorbing ~2ppm of our slightly greater than 4ppm emissions. If the equilibrium for oceans and atmospheric CO2 is 285 ppm, we're currently at 395, and absorption rates are scaled by the imbalance from equilibrium, then 2/110 =somany factors)~1.8% of the imbalance is absorbed every year. That's thedifferencebetween ocean absorption and ocean emission via CO2 exchange. If we were to stop emitting right now, with that simple 1.8% decrease per year, we're looking at ane-fold. Not 5. Again - the residence time is not directly related to the sum flow into and out of climate compartments, the adjustment time. That comes from the(1/e)decay time of about 55 yearsdifferencesbetween flow rates.Martin Aat 03:49 AM on 19 May, 2012KR"The important thing to remember is that regardless of residence time, the vast majority of CO2 molecules entering the ocean are simply swapped with another molecule."Yes, completely agree. And if the system were in equlibrium, 100% of entering molecules would be swapped for an exiting molecule."The rate of importance is how fast total concentration (not individual molecular identities) changes."Completely agree with this too. (...) At present I'm trying to understand simple idealised cases - I'm avoiding realistic situations as there are too many extra things to cause confusion. I'm working through DM's paper at the moment."Again - the residence time is not directly related to the sum flow into and out of climate compartments, the adjustment time. That comes from the differences between flow rates."Again, I agree. Yet something does not add up for me and I reach a different final conclusion. I'm going to track it down - I promise.IanCat 04:48 AM on 19 May, 2012provided that you interpret the results with care. Using X for atmospheric CO2, and Y for ocean CO2. The differential equations are dX/dt= -F(X) + G(Y) dY/dt= F(X) - G(Y) With F(X) and G(Y) being fluxes out of the atmos and ocean respectively. In your scenario, you initially assumed that the system is in equilibrium and then perturb X to determine the response. Suppose the system is initially in equalibrium (X*,Y*), i.e. F(X*)=G(Y*). Linearising the above system I'll get d(X-X*)/dt= -F'(X*)(X-X*) + G'(Y*)(Y-Y*) d(Y-Y*)/dt= F'(X*)(X-X*) - G'(Y*)(Y-Y*) The implication is if you want to treat the problem as a linear one, the time constants are actually given by derivatives of the fluxes with respect to concentration, i.e. how sensitive the fluxes are to a change in CO2.The equilibration time scale is given by 1/F'(X*).On the other hand, the residence time or lifetime is defined as as capacity divided by the flow rate, in our case at equilibrium is given by X*/F(X*). Intuitively this is sensible: if we have 100 tons of CO2 in the atmosphere, and it is entering the ocean at a rate of 100tons/day, it'll take about a day to clear the atmosphere of CO2. Now if the flux F(X) is linear in X as in your model, the residence time and equilibration time is exactly the same! The fact that you can't get a separation between the two timescales is due to your choice of F(X) and G(Y).IanCat 04:56 AM on 19 May, 2012