Readers may recall claims of 1000 year residence times for CO2. This essay suggests a much shorter interval. -Anthony
Guest essay by Leo Goldstein
Surplus CO2 is removed from the atmosphere by natural sinks at a rate proportional to the surplus CO2 concentration. The half-life of the surplus CO2 concentration is approximately 40 years. This is the conclusion of my research paper, published on defyccc.com today.
I am grateful to Prof. Fred Singer and Prof. William Happer for their help in writing this paper.
The correct (although approximate) formula for CO2 concentration leads to a number of conclusions of public interest:
- CO2 concentration in the atmosphere will increase much slower than has been claimed by the IPCC.
- A relatively small part of the anthropogenic CO2 in the atmosphere has been released by the US; a relatively large part of the anthropogenic CO2 has been released by China.
- If stabilizing or decreasing atmospheric CO2 content becomes desirable at some point in the future, that can be achieved by decreasing anthropogenic CO2 release at that time; no premature action is needed.
- The warming effect of anthropogenic CO2 is less than the warming effect of other gases and aerosols (according to IPCC calculations) in both the short and long term, so what are the motives behind this laser focus on CO2?
The topic of the CO2 removal rate has been discussed a number of times on WUWT (by Christopher Monckton of Brenchley, Docmartyn in comments on Dr. Lindzen’s article, Anthony Watts and others), and various opinions were expressed. Estimates of the half-life varied.
For some time, the subject was surrounded by confusion, created by sloppy definitions and evasive statements in IPCC assessment reports. There was a mix-up between the residence time of a CO2 molecule in the atmosphere and the rate of change of the surplus CO2 concentration. The residence time (~5 years) is of little interest, except as an indication of quick carbon turnaround. The true subject of interest is the rate of change of the surplus carbon concentration in the atmosphere. Another issue was the link between CO2 concentration and temperature. On the geological timescale, the rise in CO2 concentration tends to follow the temperature rise, concurring with a hypothesis that the latter causes the former. Nevertheless, such an effect is not significant on the multi-decadal scale. CO2 concentration in the atmosphere grows mostly because of anthropogenic release of CO2 through fossil fuels combustion and land use changes.
The paper’s full title is Simple Equation of Multi-Decadal Atmospheric Carbon Concentration Change. It is article-length (~5,000 words, not counting references), citable, and discoverable by search engines, including the Climate Sanity and Freedom Search. In a slight departure from a widely-used academic format, the paper contains a Summary (for busy readers). The abstract is as follows.
Surplus CO2 is removed from the atmosphere by natural sinks at rate, proportional to the surplus CO2 concentration. In other words, it undergoes exponential decay with a single decay constant. This conclusion is rigorously proven, using first principles and relatively recent observations of oceans. Historical data for CO2 concentrations and emissions from 1958–2013 are then used to calculate the half-life of the surplus concentration. This theoretically derived formula is found to be an excellent match to the historical CO2 concentrations over the measurement period. Furthermore, the “initial” CO2 concentration in the formula came out to be very close to the likely “pre-industrial” CO2 concentration. Based on the used datasets, the half-life of the surplus concentration of CO2 in the atmosphere is found to be approximately 40 years.
So Ari, what’s the implication for your research for IPCC emission scenarios? Does the shorter half life of CO2 mean atmospheric CO2 builds up less rapidly than the scenarios project? Or is it just that atmospheric concentrations do not remain as high as long once global emissions peak and start to decline?
The implication for IPCC scenarios are devastating. 1) The CO2 concentrations will not grow as high as IPCC projects; 2) It will be possible to quickly stabilize or even decrease CO2 concentrations in the future, if desirable; 3) All IPCC models belong in the garbage bin, because they use incorrect model for CO2
BTW, 40 years is a half life of surplus CO2 concentration, not what is said in the title
This is bad news, if true. The impending glacial period is the only climate threat to civilization, and I was sort of hoping some aspects of the pseudo-science from the climate cult was true, e.g. CO2 cancelling the ice age.
First, Ari Halperin, thanks for an interesting article. However, I fear that your linked paper is far from proving your point. While there is widespread agreement that the decay in airborne CO2 is exponential, we can’t yet say which exponential decay is correct.
?w=450
The problem is that in the early years (say the first 150 years or so) of increasing CO2, there is very, very little difference between a straight single-exponent exponential decay model such as you discuss, and the multi-exponent exponential decay “Bern Model” favored by the IPCC. This graphic shows the difference in the expected airborne fraction under the two models compared with the actual observed airborne fraction. I’ve used the Law Dome data for the pre-1959 CO2 levels, and the Mauna Loa data after that.
I’m sure you can see the challenge. At present the models give almost identical answers.
So while sometime around 2030 or so we will eventually be able to determine which of the two is correct, at present we simply don’t have the data to draw any conclusions as to which model is the better one.
Given that, I agree with you that a single-exponent decay is best fit with an e-folding time of around forty years. This is also the conclusion given in a paper by Mark Jacobson, the one modeler I pay attention to.
With that said, however, here in 2015 we simply don’t have enough data conclude that the single-exponent model is preferable to the Bern Model.
My best to you, thanks for the work,
w.
For folks interested in further reading, I’ve written about the Bern Model in the past …
My post was responded to in an interesting post by Joe Born entitled “Is The Bern Model Non-Physical?”
Regards to all,
w.
Note also that the IPCC has used several different versions of the Bern Model in succeeding Assessment Reports, with different numbers of parameters and different values for the parameters. They are all similar, however, in predicting a very long-tailed exponential decay of the levels of airborne CO2.
w.
Willis, the trouble with the “Bern model ” is just that; it is a model.
Nobody has done any experiment to take the atmospheric CO2 down below the 315 ppm level of the 1957/58 IGY ML amount, and observed any long time constant tail suddenly kick in to slow the decay.
Something in the vicinity of the Hawaiian islands and its surroundings, is capable of removing 6 ppm of CO2 from the atmosphere in five months. In the arctic ocean processes remove 18-20 ppm in that same time (and at that same time).
The ocean surface, and the atmosphere do not just come to some Henry’s law balance and then just stay there.
The tropical oceans generally have a temperature gradient that gets colder with depth, at least for some distance.
That means that the Henry’s law equilibrium concentration of CO2 is lower at depth than is the surface which is in contact with the atmosphere.
So CO2 can preferentially diffuse from the surface to colder depths, driven by that CO2 concentration gradient.
So the tropical ocean near surface temperature gradient is a pumping system for continuously depleting the surface layer of CO2 and driving it deeper, and then Henry’s law replenishes the surface from the atmosphere.
So I don’t see any experimental data for the prompt removal process shutting down and some longer time constant process that nobody has made any observations of, take over.
I’ve still not heard any good explanation for the 18-20 ppm removal rate over all of the arctic ocean where nothing is growing; except for plankton. I have my own idea on that. Namely the segregation coefficient of CO2 at the ice/water interface, when the sea ice melts.
g
george e. smith November 25, 2015 at 1:56 pm
ANY mathematical description of the process is a model. Your objection would remove all math.
Here’s how I got involved in this question some years ago, from the reverse side as usual. I looked at the data before I looked at the literature. I got to thinking about how we have reasonably good data for both emissions and atmospheric CO2 levels since maybe 1875 or so. I got the emissions data (including estimates of land-use change) and the CO2 levels, and I used “Solver” in Excel to estimate the time constant. This best fit gives a value of about 40 years for the e-folding time.
So yes, that is the experimental data, as best as we can measure it. And when I estimated the time constant I got the longer time span of around 40 years. If you have a problem with that process, I suggest that you try it yourself. Please report back with your results, I’d be interested.
While this is true, it is a result of variations in the largest single variable regarding the short-term (less than one year) changes in CO2 levels—the biosphere. When the myriad of green things on land and in the ocean are growing in the spring and summer, they are pulling CO2 out of the atmosphere at a rate of knots, and converting it to leaves and grass and phytoplankton and such. In the fall and winter, things die off and rot, and the rotting releases CO2 and methane (which rapidly converts to CO2).
And indeed, as you point out, the swing is larger nearer the poles. This is because there is more difference between the summer and winter conditions of the biosphere.
But this summer-winter fluctuation is net-zero or thereabouts as regards CO2. On average, the CO2 that is fixed by the biosphere in one half of the year equals the CO2 emitted by the biosphere in the other half. As a result, it has little effect on what we are discussing, the longer term evolution of the CO2 levels.
You could think of it as the biosphere breathing in CO2 over half the year and then exhaling it during the other half. Yes, as you point out there is a lot of CO2 first inhaled and then exhaled over the course of a year. But no matter how deep the breathing is, that doesn’t affect the CO2 levels …
My regards to you,
w.
@ur momisugly george e. smith says:
The Hawaiian islands have absolutely nothing whatsoever to do with the average 6 ppm bi-yearly (6 months) cycling of atmospheric CO2.
Measurements of atmospheric CO2 are conducted at Mauna Loa, Hawaii, which is located in the Northern Hemisphere @ur momisugly 19.4795° N latitude.
The temperature of the ocean waters in the Southern Hemisphere, …. which has the greatest surface area, ….. is the “driver” of the aforesaid average 6 ppm bi-yearly (6 months) “steady & consistent” cycling (ingassing/outgassing) of atmospheric CO2.
And ps: The only thing in the natural world that is “steady & consistent” is the seasonal cycling of the equinoxes. To wit:
http://i1019.photobucket.com/albums/af315/SamC_40/keelingcurve.gif
Willis,
Did you read my paper beyond the title? I have not assumed exponential decay. I have derived the CO2 concentration change law from the physics of oceans and biota. Then I used the empirical data from 1958 to verify it and to calculate the half-life. I did not use pre-1958 data because it is disputed.
As to the Bern model, it is physical nonsense, and I agree with you.
Ari Halperin November 25, 2015 at 2:32 pm Edit
Thanks, Ari, indeed I did read it. My puzzle is what you think that I disagreed with. This is the reason I always ask people to QUOTE MY EXACT WORDS YOU OBJECT TO. For example, I didn’t say you “assumed exponential decay” as you seem to think, so I fear I can’t answer that objection.
Setting that confusion aside, I greatly doubt that you have “rigorously proven, using first principles and relatively recent observations of oceans”, that CO2 “undergoes exponential decay with a single decay constant”.
First, it is rarely possible to prove anything in science other than pure math.
Second, as my graph above shows, we simply don’t have a long enough time-series to distinguish between single-constant and multiple-constant exponential decay.
All the best,
w.
I would like to briefly comment on the ‘decay time(s)’. If we look at, for example, the half-life of C14 in the atmosphere, it only shows us how fast this is taken out of the atmosphere by the carbon sinks. But there are different sinks: Some of it will never return (and I don’t mean on geological timescales here) as it may become ocean sediments, for example. If it is taken up by the ocean, small (maybe undetectable amounts) will eventually return to the atmosphere, the same for the biomass on the surface.
Most of it will dilute into the total carbon pool. BUT: the absorbed C14 will be ‘replaced’ by C12 from decaying biomass. So there is always a large amount of carbon that is recycled. We cannot take the C14 decay time to predict how fast CO2 concentration will drop if we would stop venting CO2 exhaust into the atmosphere. These are two different time constants! I see that a lot of discussions are not clear about this.
Then regarding the different time constants from various absorption processes, one has to also know their dynamics. It has been pointed out that the shortest time constant is the dominant (1/T = 1/T1 + 1/T2 + …) but it may also be the one that gets saturated the fastest, then the absorption would suddenly follow the next shortest absorption rate and so on. I know of similar but opposite decay processes in phosphorescence, it may have a slow and a fast component. So there the decay is first governed by the fast decay, after that component is exhausted, it follows with the long decay tail.
Stephan
The point of the article is that on the only relevant timescale – a multi-decadal one – there is a single time constant, and it is ~40 years.
richard verney November 25, 2015 at 2:04 am
An interesting question, Richard. Here’s the difficulty. A mature forest is not a carbon sink as you claim. A mature forest is carbon-neutral. Once a forest reaches a certain age, it is dying as fast as it grows, and the rate of decay is equal to the rate of CO2 absorption.
Best regards,
w.
Willis,
Just a question:
Have you considered coal seam fires? Many of them have been burning for decades, and some have burned for hundreds of years. They cannot be extinguished.
I know they don’t contribute a big percentage of CO2 to the atmosphere (but who really knows?) However, the CO2 they constantly emit can’t be considerd ‘carbon-neutral’ since it’s from coal that has been underground for many millions of years.
Thanks, db. There are a variety of natural sources of CO2 additions to the atmosphere, including coal seam fires. My point is that the aggregate of all of them doesn’t seem to change much year over year, or we’d see it in the CO2 records.
w.
Interesting. Only the first citation claims that a mature forest is still accumulating carbon, albeit at a quite slow rate.
I was sorry that it was paywalled. I can’t even begin to say whether it is valid without having the study in hand.
In any case, let me amend my statement to say “A mature forest is only a small carbon sink”
Thanks for schooling me on the question, always more to learn.
w.
@ur momisugly Willis Eschenbach – November 25, 2015 at 1:22 pm
Willis, they say “seeing is believing” …… so why don’t you take a “look-see” at the following picture and then tell me which one(s) of those yearly “growth rings” most probably contains the greatest quantity of sequestered CO2. The “growth rings” at the center of the tree or the “growth rings” toward the outside diameter of the tree?
And don’t be fergettin the fact that the “outer” growth ring extends from the base of the trunk all the way up to the tippity-top of each limb …. and the other growth rings extend upward in accordance with their “year of growth”.
http://cdn.phys.org/newman/gfx/news/hires/2013/2-monsoonfailu.jpg
Not even close. Its half-life in the atmosphere is 12 years, based on the annual Northern Hemisphere leaf change record imbedded in the Keeling curve. A similar figure comes from decay of atmospheric carbon-14 after the suspension of atmospheric nuclear tests. in the sixties.
This is what I struggle with. There appears to be no definitive answer. Albeit, answers leaning towards the ~12yr time span. When will “climate scientists” stand up and say “we don’t know”?
Janice Moore quotes Richard Feynman as saying: “The key to science: on finding a new physical law: First, we guess. Then, we perform a calculation to see what are the implications of the guess. And then we compare the result with direct observations. If it disagrees, it’s wrong.” In the language of global warming climatology is Prof. Feynman’s “guess” a “prediction” or is it a “projection”?
When a distinction is made between a “prediction” and a “projection” in this language, the former is a kind of proposition but the latter is not. A global warming model that makes “predictions” is falsifiable; a global warming model that makes “projections” is not. A model that makes “predictions” conveys information to a policy maker about the outcomes from his/her policy decisions; a model that makes “projections” does not. A model that makes “predictions” supports attempts at controlling Earth’s climate”; a model that makes “projections” does not.
The IPCC climate models make “projections.” So does the model under review.