There is a remarkable one man blog which set out to understand the earth’s climate 2 years ago. The author is Kevan Hashemi who is a lecturer at Brandeis University and has worked on the Atlas experiment at CERN. see: https://homeclimateanalysis.blogspot.com/ He seems to have more or less followed the same path as me to understand the greenhouse effect from basic physics and determine by just how much increasing CO2 will change the earth’s temperature. His value of 1.5C warming for a doubling of CO2 levels agrees with mine. He also produced a nice plot of the 350 year HADCET temperature data which I have updated to 2021. This demonstrated that climate change has had a rather small effect on UK temperatures. Of course the slight rise since ~1990 looks a little worse if you plot “anomalies”.

Here is his decadal trend analysis for the full HadCET. Basically he takes a rolling ten year gradient. There is little evidence of any rapid warming since 1850.

However it is his study of the carbon cycle that is particularly interesting because he has correctly explained the CO2 level variations over recent glacial cycles.

The last post on the site summarises his findings which seriously irked some mainstream climate scientists. He replied gallantly but eventually fell silent and this was his last post. Yet I have not seen any carbon cycle model that is able to describe the CO2 response to Ice Age cycles as well as his does.

His model was based on a fixed C14 proportion dispersed in the atmosphere and the deep ocean.

Each year, cosmic rays create 8 kg of carbon-14 in the upper atmosphere. If carbon-14 were a stable atom, all carbon in the Earth’s atmosphere would be carbon-14. But carbon-14 is not stable. One in eight thousand carbon-14 atoms decays each year. The rate at which the Earth’s inventory of carbon-14 decays must be equal to the rate at which it is created. There must be 64,000 kg of carbon-14 on Earth.

The Earth’s atmosphere contains 800 Pg of carbon (1 Pg = 1 Petagram = 10

^{12}kg) bound up in gaseous CO2. Therefore the oceans contain 80,000 Pg.

His argument is that the exchange of CO2 with the deep ocean remains in balance as more CO2 is added to the atmosphere. So to double the CO2 in the atmosphere you need to also double the CO2 contained in the deep oceans. This will take thousands of years of anthropogenic emissions instead of say 100 years. I suspect one possible problem with his logic is that we are constantly adding CO2 to the atmosphere from fossil fuels which are devoid of C14 because they have been buried for millions of years. So the C14 accounting begins to unwind as more of our annual emissions dilute the atmospheric C14 content.

The global carbon cycle is immensely complicated because it depends on life, plate tectonics and volcanism, all working on different timescales. Yet each year ~50% of our annual carbon emissions are absorbed by rapid oceans/biosphere processes and this ratio is unchanged in 50 years.

Today the global net flux of fossil fuel CO2 into the ocean is ~ 2Gtons C per year, amid exchange fluxes of 90 Gtons/year. This implies that if we simply kept emissions stable then the oceans would fairly soon also stabilise CO2 levels in the atmosphere. However there is a complication – the so called buffering or Revelle factor.

“The Revelle factor (buffer factor) is **the ratio of instantaneous change in carbon dioxide (CO****2) to the change in total dissolved inorganic carbon** (DIC), and is a measure of the resistance to atmospheric CO_{2} being absorbed by the ocean surface layer.”

The Revelle effect describes how only a small fraction of pCO

_{2}is present in ocean water when much larger amounts are added to the atmosphere. Depending on the alkalinity of the water, DIC is either present as CO_{3}, HCO_{3}, or CO_{2}. When the pH is high (basic) the Revelle factor is greatest, causing much of the DIC to exist as HCO_{3}or CO_{3}, and not CO_{2}. So, the greater the buffering effect (low Revelle Factor) the more DIC occurs as CO_{3}or HCO_{3}, effectively lowering the pCO_{2}levels in both the atmosphere and ocean.

This statement has taken on mythical proportions and is embedded in carbon cycle models like the BERN model. It implies there is a long tail on carbon levels in the atmosphere

My knowledge of chemistry is pretty minimal but I find it a far more descriptive than quantitive science. Kevan argues that :

“When a gas and liquid are at equilibrium, there is as much gas entering the liquid per unit time as there is leaving it. Because gaseous CO2 has only one species, its probability of absorption into the ocean does not vary with its concentration. ”

This must be true. It is just a question of timescales. David Archer’s book is mostly descriptive with no firm predictions so I suspect we don’t really know how fast the Earth recovers from a sudden release of CO2. The BERN model is basically a parameterised guess.

The fact that 50% of CO2 emissions have been absorbed by the oceans for the last 70 years needs to be explained first.

The carbon cycle mixes physics, chemistry, biology and geology all up into one complex imbroglio. My gut feeling is that stabilising our carbon emissions must also stabilise CO2 levels within a decade. Of course I could be wrong as could everyone else.

Hello Clive,

MMCC is a political super tanker , it will be hard to turn around , well actually correct for real data. Like many I took the cautious approach but like few ( apparently ) when I see the data I will revise my position because computers ( my feild) have ot be correct or they just don’t work .

I apprciate your work please keep it up and I ‘ll take a look at Kevan Hashemi work.

Thanks

Forbin

Clive,

“My knowledge of chemistry is pretty minimal but I find it a far more descriptive than quantitive science. Kevan argues that :”It could not be more minimal than Kevan’s. One has to admire the thoroughness with which he expounds his scientific reasoning, but the reasoning itself is devoid of understanding of physicl chemistry. The argument that you highlight culminating in

“Therefore the oceans contain 80,000 Pg.”is just juvenile. It assumes the whole ocean is in equilibrium, without any discussion of how long it takes to reach equilibrium. And that timescale is huge.You can see disequilibrium clearly in temperature. In tropical oceans, the surface may be at 25C, but a few hundred metres down it is less than 10C. Heat is not in equilibrium, although it diffuses in much the same way. The diffusivity of heat is much high than that for dissolved substances.

As to

“The fact that 50% of CO2 emissions have been absorbed by the oceans for the last 70 years needs to be explained first.”there is an explanation for the apparent constancy of the factor here. It depends explicitly on the dynamics, and in particular on the fact that the last 70 years has been a period of exponential rise in emission. Whatever the transfer function, it is a property of the exponential that the ratio will be constant. This is embedded in the maths of the Laplace Transform.

“However it is his study of the carbon cycle that is particularly interesting because he has correctly explained the CO2 level variations over recent glacial cycles.”The plot you show is not of his model predictions. It just plots observed Barnola’s CO2 vs Petit’s temperature. AFAICS, he gives no quantitative predictions.

Nick,

You’re right. His model is based on his Eq 3. in the previous post (scroll down)

M(_{A}T_{2}) /M(_{A}T_{1}) = e^{−2300/T2}/ e^{−2300/T1}= e^{2300(1/T1−1/T2)}(Eq. 3)(Eq. 3)

“Our (Eq. 3) predicts a close, positive correlation between temperature and atmospheric CO2 concentration, and it gives us an estimate of the magnitude of the change in CO2 concentration with temperature.

We see close and sustained correlation between CO2 concentration and temperature, even as temperature varies by 12°C. If we assume today’s average global temperature is 14°C = 287 K, the change from ?9°C to +3°C relative to today is a swing from 278 K to 290 K. Our (Eq. 3) predicts an increase in the mass of carbon in the atmosphere by a factor of e2300(1/278?1/290) = 1.41. Because almost all carbon in the atmosphere is bound up in CO2 molecules, the concentration of CO2 in the atmosphere is proportional to the total mass of carbon in the atmosphere, so when the total mass increases by a factor of 1.41, the CO2 concentration should increase by a factor of 1.41 also. Looking at the graph, we see CO2 rising from 190 ppmv to 290 ppmv, which is a factor of 1.52. Given the many uncertainties in our calculations, and in the ice-core measurements themselves, we are well-satisfied with the agreement between our calculations and the magnitude of the CO2 concentration changes in the ice core measurements.”

Stokes is right. Regarding the 50% incorporation: simple if you understand 1D random walk diffusion. ~50% walks deeper and 50% walks back upward and then back to the atmosphere. Very slow to equilibrium since CO2 is difficult to sequester — fat-tail statistics in the diffusion profile, perhaps thousands of years.

Good stuff Clive. Keep it up and let us ‘deniers’ know that there are some unbiased sensible people out there.

Hi Clive,

Just a query about the temperature range during the glacial cycles. The graph you show indicates a range of up to 12C – isn’t that about double the estimated global average? Is it a Vostock proxy? Am I missing something else?!

Funny coincidence – I haven’t seen Kevan for 25 years but was at Uni’ with his sister and knew him and his family well.

Yes these are changes in temperature (anomalies) as deduced from the Vostok Ice Core.

We don’t know how representative that is compared to global temperatures.

You can probably get in touch with Kevan by leaving a comment on his blog !

Interesting to see the climate enforcers’ persistence in trying to silence him. Their air of omniscient authority would be amusing if they were not really trying to shut down dissent

“Of course I could be wrong as could everyone else.”

Or… one could recognize that hundreds of smart people have been studying this field for decades. The mathematical basis of global scale analyses were set out in 1979 by Rodhe & Bjorkstrom (https://www.tandfonline.com/doi/pdf/10.3402/tellusa.v31i3.10434?needAccess=true). But 40 years of science means that the field has moved far past simple global box-model analysis. For example, https://journals.ametsoc.org/view/journals/clim/26/18/jcli-d-12-00417.1.xml does model/observation comparisons taking into account seasonal cycles and geographic variations of CO2 fluxes.

Moreover, the idea that carbon cycle modelers have ignored C14 is ridiculous. It is not only included, but again, state of the art models not only can model atmospheric vs. oceanic C14, but also capture geographic resolution – e.g., https://cp.copernicus.org/preprints/cp-2019-159/cp-2019-159.pdf

“The large-scale distribution of modelled ?14C broadly resembles the observed pattern in the Global Ocean Data Analysis Project (GLODAP; Key et al., 2004)”

Do state-of-the-art carbon cycle models perfectly match observations? Of course not. But if there were any major biogeochemical assumptions that were totally off-base (like the claims that Keven is making), this would have showed up long ago.

Marcus,

Yes I have read quite a lot about the carbon cycle and realise that there are various processes including, biosphere exchange and geological weathering and plate tectonics that run on thousand year time spans. However the fastest absorption is with the mixed layer in the oceans covering 2/3 of the world’s surface and this is where the most of that half of our emissions are absorbed each year.

If I attach a CO2 cylinder to a soda stream of tap water, then I can saturate the water with dissolved CO2. Can you or Nick explain why if we were to stop emissions tomorrow the excess CO2 would not disappear into the Oceans over the next ~30 years. The other sinks would then readjust over longer timespans as the mixed layer CO2 exchanged with the deep oceans. Are you saying the surface layer saturates before atmospheric CO2 levels return to normal because that is the only way that long tail CO2 levels can be explained ?

You mentioned the Revelle factor in your top post, but seem to dismiss it: it is, however, key to this problem. See Figure 3 of Sabine et al., 2004 (https://www.pmel.noaa.gov/pubs/outstand/sabi2683/sabi2683.shtml): Revelle factors range from 8 to 16 depending on location.

Lets assume conservatively that the global factor is 10, and that Kevan’s numbers of 800 gigatons of C in the atmosphere and 80,000 in the oceans are correct. Let’s also assume that the ocean mixes instantly. Then, if we add 100 gigatons of C to the atmosphere and let everything run to equilibrium, with a Revelle factor of 10 we’d see about 9 gigatons of C remain in the atmosphere indefinitely (e.g., 9 GtC is a 1.1 percent increase in atmospheric carbon, whereas 91 GtC is a 0.11 percent increase in oceanic carbon). So that’s a 9 percent very long tail. (eventually you get deep ocean sediment burial which would deal with that long tail, but that is a 1000s of year process)

Now, if we correct Kevan’s ocean number which is off by a factor of 2 (there’s only 40,000 GtC in the oceans), then we get a 20 percent very long tail… which is about where Archer et al. and most of the carbon cycle models end up.

And that’s before we take into account the slow mixing of the upper ocean and the deep ocean… so the 20 percent number is for hundreds of years from now. So 30 years from now, a substantially larger percent of the additional carbon released would still be in the atmosphere.

Another paper that might be of interest – Gruber et al. have a method for calculating anthropogenic carbon from oceanic observations – check out Figure 1 of https://www.aoml.noaa.gov/wp-content/uploads/2019/03/1193.full-1.pdf. This is the kind of data that the carbon cycle models (Archer, Bern, etc.) are checked against*. If there was something substantively off about the oceanic chemistry assumptions that underly the Revelle factor, this would show up in large model/obs discrepancies.

The sophistication of modern carbon cycle work is what makes it particularly frustrating when the Kevan’s and Essenhigh’s and Salby’s come in with a simplified global analysis that they claim completely overturns the standard model, but haven’t done even basic homework on the state of the science and act like they are the first ones to think about using radiocarbon isotopes (Kevan, Essenhigh) or addressing the annual ENSO cycle (Salby).

*There was a 1996 paper by Gruber et al. that not only did the observational calculations but also included the carbon cycle model comparison. The kind of discrepancies identified: too little anthropogenic CO2 in the model at 200m to 500m depth between 40 degrees and 50 degrees north, because of a known issue where the models had too much upwelling of deep water on the landward side of the gulf stream because of the horizontal mixing scheme used. And that was 25 years ago. Unfortunately, the paper is paywalled.

Great !

Using a linear regression–based method, we find a global increase in the anthropogenic CO2 inventory of 34 ± 4 petagrams

of carbon (Pg C) between 1994 and 2007. This is equivalent to an average uptake rate

of 2.6 ± 0.3 Pg C year?1 and represents 31 ± 4% of the global anthropogenic CO2 emissions

over this period.

Is it possible that another 20% has been taken up by the Biosphere through the CO2 fertilisation effect?

This would then produce the observed 50% airborne fraction for annual emissions ?

Thanks. This is very informative. So the real problem is the buffering effect of ocean chemistry. So if we end up finally doubling CO2 levels to 600ppm then after a century or so it only reduces to ~ 360ppm (330 for Kevan).

1) See figure SPM.7 from the AR6 WGI report which shows how carbon is divided between the atmosphere, ocean, and land systems at the end of the century under different emission scenarios.

2) We have emitted 2400 GtCO2 to date (650 GtC). Using the 20 percent assumption, that means that if we we to drop emissions to zero tomorrow, we’d still have added 130 GtC permanently to the atmosphere. 130 GtC is about 60 ppm (using a 2.1 factor for GtC to ppm). So cutting emissions to zero tomorrow would see us decline to 340 ppm. Annual emissions of 40 GtCO2 (10 GtC) means 2 GtC permanently added or about 1 additional permanent ppm per year.

(your thought experiment of 600 ppm only works if you go from pre-industrial to 600 instantly, and then let it relax back over a couple centuries. If we get to 600 ppm more slowly, then we’d already have used up a lot of the ocean buffer, so it would drop much less)

thanks,

OK I get it.

The only positive is that we may have inadvertently avoided another Ice Age, or at least delayed it by a few 10s of thousand years.

My recollection is that the last chapter of David Archer’s “The Long Thaw” addresses exactly that thesis – that we have already ensured that we will entirely skip the next glacial period.

I keep seeing this same claim “His value of 1.5C warming for a doubling of CO2 levels agrees with mine”

But if 100% of radiated heat is already being absorbed by so called green house gases, mainly water vapour and Co² how is increasing the amount of Co² going to result in the capture of any more heat? I understand that the Co² may act to delay the transfer of heat into space but it cannot absorb more heat than exists! What am I missing?

All that happens is the height of the tropopause increases slightly while the lapse rate remains the same. Hence surface temperature increases.

Given the majority of the heat absorbed by Co² takes place in the first 10m of the atmosphere and I think over 99% of heat Co² is capable of absorbing is done so by 100m. How does a slight increase in the tropopause have any significant warming affect?

because the earth can only cool by radiating IR to space. IR photons in the 15 micron band are reabsorbed lower in the atmosphere and can only escape above a certain height. This drives convection. The tropopause is where convection stops and radiation dominates. It is a mix of net H2O O3, CH4 and CO2 effects.

Hi, If I understand this blog it appears that it treats the ocean as totally available to reach an equilibrium with atmospheric CO2.. The author of the original blog appears to believe that the dynamics of the Carbon Cycle are understood and can be modeled.

Is this correct? How long will it actually take for the deep ocean to reflect the atmospheric carbon dioxide, if it does what is the lag period? Hundreds of years? Thousands of years?

I suspect the latter.

Humanity is creating a huge distortion in the natural carbon cycle, this has consequences. Twice I have run into Piers Corbyn, on each occasion I try and listen to the science, but am defeated by the spittle and the realization that he is on a crusade. I want to live on an ecologically stable planet, listen to alternative views, but at the same time clearly adopt the precautionary principle.

Sounds like you have a good grasp of the situation.

I have also met Piers a couple of times as well. I remember at the Royal Society meeting to discuss the AR5 report he stood up and told all the scientists present that they were totally wrong about everything. This did not go down too well but it shows you what thick skin he has. He was making weather forecasts at the time based on solar activity which you had to pay for. It seems he had quite a large number of subscribers. So he claims any change in global temperatures is caused by the solar activity.

However the world would be a boring place without eccentrics like him !

“The only positive is that we may have inadvertently avoided another Ice Age, or at least delayed it by a few 10s of thousand years.”Between entering a period of substantial ice cover of the earth or a warming of the average temperature on the earth by 1°C to 2°C which do you believe would cause the least loss of human life?

I really appreciate the posts by Marcus above, explaining the long residence times for carbon in the atmosphere, and also take note of his point about frustration with those who have not checked out all the work already done many years ago. But I still remain totally confused about the actual effects of that carbon remaining in the atmosphere, having read the recent paper by Lightfoot (ref. below). To an amateur this paper looks pretty sound as it is based on real measurements of temperature and humidity over a wide range of latitudes and geographic regions. For brevity I just quote/copy the final conclusions:

—-

5. Warming by water vapor overwhelms that of CO2 and the other non-condensing GHGs and renders their warming ineffective.

6. For practical purposes, the level of carbon dioxide in the atmosphere is at its upper limit for warming the air of the Earth. No additional amount of CO2 can affect the air temperature.

—-

So is Lightfoot correct ? – and if not why not ? Could it be that his theory about temperature and humidity is incorrect ?

http://thelightfootinstitute.ca/imglib/Earth_temp_paper.pdf

Hi Bob,

Water vapour is a powerful greenhouse gas but it also condenses as clouds especially in the tropics which “cools” the surface through increased albedo. So the standard IPCC position is that H2O acts as a feedback to CO2 forcing. In other words CO2 greenhouse effect results in a warmer oceans which evaporate more H2O. This assumes that net atmospheric water vapour content would remain constant without manmade CO2 increases. The playoff between enhanced H2O greenhouse effect (warming) and increased cloud albedo (cooling) is not fully clear, although most climate models predict a positive feedback. That is why their ECS values are so high compared to ~1.6C for CO2 alone. I think it is still pretty uncertain how clouds change the picture. It is remarkable though just how stable the climate has been over millions of years. This implies H2O regulates climate.

So his point 5. for “radiative warming” may be correct but it is still driven by increased CO2.

His point 6. is not completely true as CO2 forcing is logarithmic. This is what I got from CO2 forcing alone

So we can still get about another 0.6c of warming by the time CO2 levels have doubled.

I’ll also note that CO2 is only logarithmic around current day concentrations. At very low concentrations, CO2 forcing would be linear. At much higher concentrations than today, it will depend on what absorption lines are dominating.

The relationship of forcing with concentration for any GHG always starts linear at very low concentrations, then tends to become sub-linear (square root or logarithmic) with increasing concentration as the key absorption line saturates and increasing forcing is happening mostly because of line-broadening, but if there’s a secondary absorption line that line can eventually become dominant (at higher concentrations) and briefly return the relationship to near-linear.

Also, “stable” is in the eye of the beholder – the climate has oscillated between glacials and interglacials for a couple million years. Those are pretty big climate swings, indicating that there is some amount of instability in the system that can be triggered by orbital variations. The increased forcing from doubling CO2 could certainly be considered of similar magnitude to the orbital variation changes (the orbital variation changes will be of a different nature though: possibly less than CO2 doubling in terms of total globally averaged forcing, but more than CO2 doubling in terms of seasonal/hemispheric changes).

I have plotted the HadCET data (after applying a 15 years rolling average) and they overlap quite well with the GISTEMP global temperatures, with an evident increase after 1900: https://drive.google.com/uc?export=download&id=1lnrRY8zp4JPz7sUSScPJpXaQBAQbfFaw

define first what is “Bias” (9.5) ?

and what is meant by “Lowess” ?

and how do you get “yearly”?