Guest essay by Leo Goldstein
My new scientific paper Empirical Validation of the Exponential Decay for Surplus CO2 further validates the conclusion that surplus CO2 in the air decays exponentially. The half-life is re-estimated down to 30-35 years. Further, if the CO2 sink rate has changed in the last 100 years, it has increased rather than decreased (i.e., the half-life has decreased). The paper uses pre-1958 concentrations, which were obtained by C.D. Keeling by re-analyzing certain 19th century instrumental measurements and merging them with the ice core measurements.
This pre-1958 data indicates that atmospheric CO2 concentrations steadily increased from 288 ppm in 1860 to 315 ppm in 1958. Thus, the IPCC opinion on atmospheric CO2 concentrations since 1860 is in a good agreement with the empirical data. I do not agree with criticism pointing to some pre-1958 measurements showing significantly higher concentrations. Such high readings were likely caused by local sources of CO2, such as industry, buildings, or even scientists’ own breath. The IPCC’s distortion of the carbon cycle was addressed in a recent article on WUWT.
A summary of the new paper and two relevant graphs appear below.
Surplus CO2 is naturally removed from the atmosphere by natural sinks at a rate proportional to the surplus CO2 concentration, on the multi-decadal scale. This result, analytically derived in (Halperin, Simple Equation of Multi-Decadal Atmospheric Carbon Concentration Change, 2015) is verified here by applying it to the pre-1958 data, which was not used in the original paper. The excellent match confirms the validity of the theoretical result. This paper also presents a more accurate estimate of the half-life of the surplus CO2 concentration: 30-35 years. The correspondent equilibrium concentration is estimated to be in the range of 267-285 ppm (larger equilibrium concentrations correspond to lower half-lives). Also, the paper finds that if the natural sink rate did change in the past 150 years, it increased at least during the period prior to 1958. The paper uses CO2 emissions data, corrected for some inaccuracies, introduced since 1992.
Fig. 1. Comparison of the measured concentration of CO2 in the atmosphere (Keeling curve) to that computed using formula (2) with the same constant half-life from 1860-2013. From Halperin, Empirical Validation of the Exponential Decay for Surplus CO2
Fig. 2. Comparison of the concentrations of CO2 in the atmosphere, based on historic measurements from 1872-1882 (Keeling & From, 1986) and computed using formula (2) with the same constant half-life, from 1860-1957. From Halperin, Empirical Validation of the Exponential Decay for Surplus CO2
Thus, the natural exponential decay of the surplus (over ~280 ppm) CO2 concentration with a half-life of about 30-35 years is established now for a multi-decadal timescale. The significance of this result is that the atmospheric CO2 concentration is unlikely to exceed 550 ppm in the 21st century, despite current exponential growth in the use of the fossil fuels. In the unlikely case that elevated atmospheric CO2 becomes undesirable, it will be possible to lower it significantly by decreasing emissions, although the exponential decay formula should be used in such a case with great caution, because this scenario has not been encountered before.
IMO, even under a business as usual scenario, CO2 is unlikely to settle higher than 600 ppm in the 22nd century. Much higher levels than this would benefit C3 photosynthesizing plants, but continued reliance on fossil fuels probably can’t get us to the ideal 800 to 1300 ppm range maintained in true greenhouses.
For early C02 measurements, can you get them from ice cores?
If so you can calibrate the recent against the historical and get an accurate measurement.
Did they include all the EXTRA tree and plant growth caused by the EXTRA CO2, which, of course, causes there to be less EXTRA CO2 ??
What is not discussed very often in public by alarmists, is why Ari Halperin’s number should matter at all.
Two reasons:
1) ‘Surplus’ CO2 being removed rapidly from the atmosphere, at an increasing rate, means that the hypothetical doubling of CO2 may never occur because we simply don’t have enough fossil fuels to burn or cannot burn them fast enough.
2) If it ever looked like the dire predictions were actually coming true, then we could quickly remedy the situation in the space of a few decades by going full-on nuclear and the CO2 would quickly fall back down.
Two very inconvenient truths for the catastrophists.
For me this piece supports a higher “starting point” of 288 vs 270ppm in calculating a human imprint on CO2 levels and supports a shorter residence period for the “evil substance”. If correct, this information means CO2 will not become a “threat” as it’s concentration will rapidly decline when oil becomes expensive enough to reduce consumption.
It also casts serious doubt on the “scientific” pronouncements of the Leftist and Statists that Government must legislate “fossil fuel” use to prevent catastrophy. Bad science causes much harm. Witness the cholesterol panic, salt panic, the racist belief that genetic differences were/are dispositive in human learning and behavior and a lot of other silliness.
Who gives thanks for the coccolithophores, sedimenting out the life-giving and beneficially warming carbon whaddyacallit?
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I’d have thought that the natural decay rate of CO2 in the atmosphere was evident in the Mauna Loa graph. Just look at that annual sawtooth!
@ur momisugly John H. Harmon
This is funny! You rant (rightly) about Leftist and Statist junk science, but swallow one of their most fatal canards (namely the bogus claim that there is no such thing as human races and consequently no legitimation for racial discrimination) hook, line and sinker. Selective skepticism?!
If all the oil, gas, and coal reserves shown on IPCC AR5 Figure 6.1 were instantly transferred to atmospheric CO2 at IPCC’s current 57%/43% sink/source rate it would not be enough to meet the ppm concentration needed for IPCC AR5’s RCP 6.0 or 8.5. So IPCC AR5’s two worst case AOGCMs, melting ice sheets, meter sea level rise by 2500, etc. can never be realized.
One of the things that climate science struggles to explain is how each year the increase in atmospheric CO2 is about half of the human emitted total.
But that’s about what you’d expect if the atmospheric CO2 disappears exponentially from a given starting value. Human emitted CO2 has been growing following pretty much an exponential curve. Apply a growing exponential to a system described by a 1st order linear differential equation and the solution is a growing exponential curve growing at the same rate as the input signal.
Set the input signal to zero and the response will then decay to zero at the rate set by the time constant of the system. The fact that the response to a growing exponential input is an exponential with the same exponent as the input signal is just what you’d expect.
It most certainly does not mean that half of the input signal (CO2 level in this case) hangs around forever.
Hello Ari, there is a measurement and an already estimation that the half life of Co2 IN ATMOSPHERE IS AT ~ 5 YEARS.
Are you claiming that your estimation is better than this, if so can you explain if it is based in measurement rather than some fictional thinking like that of IPCC?
There is already many fictional and wishful assessments on that particular point, but there is only one based in real measurement and empirical evidence,,,,,, as far as I can tell, and there is no any real reason or justification in “scientifical” approach to discredited………and as it stand for that measurement the half life of CO2 in atmosphere is at ~5 years, why should I consider that you are even remotely better in that estimation?!
All other estimation based in other than measurement and observation all fit one and the same category and you have to cue yours there and consider that it could be as wrong as any other of that fictional category.
If you have no any good or acceptable reason why should the measurement be “Hand waved” than you are no any better than any one else before or after you claiming something different…it is still and simply another case of obfuscation of reality, regardless of the degree of it….
cheers
1. I don’t think the current growth rate of fossil fuels is best described as exponential. Even if it were, future growth rate will be difficult to maintain a positive sign.
2. unlikely case that elevated atmospheric CO2 becomes undesirable, It most definitely is undesirable to some people.
3. it will be possible to lower [CO2 concentrations] significantly by decreasing emissions. Yes. What should be emphasized is that the rate of reduction in CO2 would likely be much faster than many predict. But it also means significant reductions in CO2 can come only from significant reductions in the use of fossil fuels.
The calculated CO2 looks more believable than the measurements. Neither global average temperature trend nor anthropogenic CO2 emissions were linear so how would atmospheric CO2 be linear?
The joys of trying to model a complex system when several of the significant inputs (CO2 seqestration rate in this case) are not really known. The IPCC models are blowing smoke.
“The excellent match confirms the validity of the theoretical result.”
Mmm, no.
Earth’s carbon cycle contains 45,000 Gt (E15 gr) of stores and reservoirs with a couple hundred Gt/y ebbing and flowing between those reservoirs. (IPCC AR5 Fig 6.1) Mankind’s net contribution to this bubbling, churning caldron of carbon/carbon dioxide is 4 Gt/y. Seems relatively trivial to me.
Mankind’s alleged atmospheric CO2 contribution between 1750 and 2011 added 2 W/m2 of radiative forcing to the earth’s atmosphere. (IPCC AR5 Fig SPM.5) Incoming solar RF is 340 W/m2, albedo RF is 100 W/m2 +/- 30, latent heat RF from the water cycle’s evaporation is 88 W/m2 +/- 8. Mankind’s 2 W/m2 is obviously trivial. The popular GHE theory is a perpetual loop flowing from cold to hot violating two fundamental thermodynamic laws. Physics must be optional for “climate” science. What really counts is the net RF balance at ToA which 7 out of 8 balance models (Trenberth et. al. 2011) show as cooling, not warming.
Every year the pause/hiatus/lull/stasis continues (IPCC AR5 Box TS.3) IPCC’s atmospheric and ocean general circulation models diverge further from reality.
As Carl Sagan observed, we have been bamboozled, hustled, conned by those wishing to steal our money and rob us of our liberties. Hardly a new agenda.
Nice piece of work Ari. I argued not long ago in a comment on CO2 and the greening of the planet, that the sequestration rate in the biosphere is increasing exponentially with a simple thought experiment:
We have a growth of a fringe of new green plants around arid regions. This fringe causes some increase in soil moisture along the fringe zone and seeds from it are sown in a new, inner, concentric fringe zone, etc (perhaps until the Sahara greens over again). Meanwhile the plants of the first “fringe” are also growing larger and sequestering more CO2, along with the new fringes going moving inward into the arid zone. Note that this accelerated removal of CO2 is also going on in the Oceans. This means that with a relatively steady increase in fossil fuel emissions, an accelerating sequestration rate will mean the atmospheric content will level off perhaps more quickly. Your work and possibly a higher exponential rate of reduction of CO2 from the atmosphere than you calculate will certainly give CAGW a decent burial.
This negates hundreds of models predicated on steady decay. It also is an interesting addition to the idea that CO2 radiation absorption is saturated.
There is no “surplus” CO2 in the atmosphere. The 14C bomb tests pre-1963 added a known amount of CO2 to the atmosphere, mostly over the far north from many russian atomic bomb tests.
That 14CO2 mixed with the existing bulk of total atmosphere CO2. It took about a year for the northern 14CO2 to mix throughout the southern hemisphere atmosphere. The 14CO2 is then measured with time.
The observed (measured) 14CO2 declined after 1963 (1964 in the SH).
The measured 14CO2 ten years later had dropped to 1/2 the peak in 1963/4 toward the long term base line.
Therefore tracer 14C was removed from the atmosphere at an exponential rate with a t1/2 of 10 years.
The physics of the 14CO2 is exactly the same as “natural” CO2, therefore natural CO2 declines at exactly the same rate as the tracer.
There are claims that the 14CO2 added to the atmosphere does not represent the total CO2. Those arguments are simply false. The observed drop of atmosphere CO2 into long-term sinks is proof that the CO2 biogeochemical cycle is very fast, about 5 to 7 percent of all atmosphere CO2 is lost to very long term sinks of multi-century to millenial time scales. The deep sources, geological and oceanic, are very much larger than claimed by IPCC and the Bern model. The OCO-2 data support the huge natural turnover of CO2 on a global basis.
The claim that any CO2 remains “permanently” in Earth’s atmosphere shows a gross mis-representation of the observed facts.
Another look at this issue
http://wattsupwiththat.com/2013/07/01/the-bombtest-curve-and-its-implications-for-atmospheric-carbon-dioxide-residency-time/#comment-1352246
gives a more info on this subject.
Eric, thank you for this interesting post. While what you have done is certainly valid work, I fear that it has not proven what you think it has proven.
You say that the decay of a pulse of atmospheric CO2 can be accurately modeled using a single exponential decay time constant tau in the range of 35-40 years or so. I agree, as does Mark Jacobson here.
The IPCC says that the decay of CO2 is long-tailed, and as such it is better modeled by using three different time constants tau1, tau2, and tau3 of 2.6, 18, and 171 years, acting respectively on fractions f1, f2, and f3 of 32%, 28%, and 25% of the CO2 respectively, with an additional fraction f0 of 15% of the CO2 which never decays.
Now to me, that seem highly unlikely. IF every time a pulse of CO2 were added to the atmosphere fifteen percent of it never decayed … it wouldn’t take long (geologically) for volcanic eruptions to fill the atmosphere with CO2.
However, that’s not the current problem. The current problem is that we simply don’t have enough data to reliably distinguish between the two different explanations. The two calculated results are very similar over the early part of the record, and they won’t start to diverge significantly until something like 2025 or so.
Let me recommend that you use the values above for tau 1 to 3, and fractions f0 to f3, to replicate the IPCC method and compare it to your own calculations. You may be surprised by what you find. Here’s what I found:
You can see the problem … I used ice core data for 1850-1959, and I used fossil emissions, concrete production emissions, and land-use change data for total anthropogenic emissions.
Best regards, I look forwards to seeing your figures.
w.
If somebody claims that the decay rate of 14C is applicable to the the total CO2 decay rate or the decay rates of anthropogenic and the total CO2 are the same, then he/she does not understand the effects of the recycling system of the atmosphere, the ocean and the biosphere.
Mike M. (period) : The Bern model can and is likely the simplest model that can fit all the data.
Thank you for that post. I looked up “Bern Model” on wikipedia and there is no entry. What is a good reference?
Open Question:
Since plants have a preference for 12C over 13C, the selectivity is undoubtedly even greater for 14C. It would seem to me that 12C should have a shorter residence time than 14C. If estimates on the rate of decline for 14C based on sequestration are correct, what correction would need to be applied for the rate of decline for the 13C/12C mix that constitutes the CO2 in the atmosphere?
OK, long + interesting thread:
Guest essay by Ari Halperin
My new scientific paper Empirical Validation of the Exponential Decay for Surplus CO2 further validates the conclusion that surplus CO2 in the air decays exponentially.
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But zero response to Ari Halperin
– surplus CO2 decays exponentially.
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