Lumpy science from Ken Caldeira

On Twitter, people will say most anything if it aligns with their beliefs and their cause. In this case, climate scientist Ken Caldeira gets called out over some claims about coal and CO2 by our own Willis Eschenbach. It looks like a clear-cut case of confirmation bias.

Willis replies:

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June 21, 2019 12:12 pm

Willis, Willis, Willis, how many times do we have to tell you …The “Woke” do not do math…or logic, or science, or integrity, or honesty, or….Wait…. I need a bigger piece of paper… “42” more pages should do….. : )

June 21, 2019 12:35 pm


Whenever did climate scientists concern themselves with facts?

Reply to  Paul Homewood
June 21, 2019 4:05 pm

When you and Anthony pitched up and presented them. Then they just ignored them.

Thanks guys.

Reply to  Paul Homewood
June 21, 2019 7:00 pm

Hey it’s peer reviewed … Want to buy new peer reviewers 🙂

Does beg the question how long they had to shop around for reviewers?

Reply to  LdB
June 23, 2019 8:56 am

In climate science we use palrewiew. That´s why we have friends.

Andy Pattullo
Reply to  Paul Homewood
June 22, 2019 7:06 am

The CAGW story is a test. For scientists it is a test of integrity versus self-serving career advancement; for politicians, a test of leadership versus opportunism; for environmentalists, sincerity in caring for our planet versus mercenary fear mongering; and for the average citizen, a test as to whether lazy belief in a comfortable mythology is preferable to the hard work of trying to understand what is true. I raise my glass to those who pass the test though it costs them dearly. To those who failed, my sympathies but you are not the people we want making decisions that affect all of humanity and the world on which we live.

Gerard O’Dowd
Reply to  Andy Pattullo
June 26, 2019 6:28 pm

Very well said.

Reply to  Paul Homewood
June 22, 2019 7:43 am

Again, lefties first thing to do is screw up numbers to support their cause. That’s why math has been purposely dumbed down for so many decades — so that few can figure out or care about their deceptions.

dodgy geezer
June 21, 2019 1:09 pm

climate science counting :

Scary big number…

Reply to  dodgy geezer
June 21, 2019 5:07 pm

… or x-axis, one-sixteenth inch per year, … y-axis, one-sixteenth inch per tenth of a degree.

jon jewett
Reply to  dodgy geezer
June 23, 2019 8:04 am

Many years ago George Gamow wrote a book “One, Two, Three, Infinity” (1947). The title came from a tribe in Africa who only had numbers one, two, and three. Beyond that, there were “many”. So, four cows were “many” and 4,000 cows were the same number, i.e. “many”. Or as in our culture “infinite”.

The book is still available with even a Chinese version.

June 21, 2019 1:11 pm

If you entertain a false belief, the belief in a catastrophic greenhouse effect from carbon dioxide, will, over its lifetime in the progression of scientific knowledge, distort gullible minds 100,000 times more than simply entertaining it once.

June 21, 2019 1:14 pm

Totally ignores all of the CO2 sinks that absorb the CO2 guaranteeing it will not last in the atmosphere that long.

June 21, 2019 1:20 pm

A thousand years. That involves so many assumptions, it’s ridiculous.

One of the big errors the alarmists make is to assume that the CO2 uptake by the environment doesn’t change. Also, if the atmospheric CO2 changes, the marginal contribution of any particular ‘lump’ of CO2 also changes.

You could argue ’til you’re blue in the face about CO2 uptake. Pointing out their arithmetic problems is much easier.

Crispin in Waterloo but really in Johor
Reply to  commieBob
June 21, 2019 6:57 pm

There is a missing element of this mathematical error. Of all the heat he claims will be “generated” so to speak, what % of it will be radiated into space?


He may as well have described the total mass of water that would be additionally evaporated from the oceans over 1000 years due to the presumed higher air temperature. So what? Will the atmosphere fill with water or will it fall to earth as rain having (slightly more efficiently) radiated the “extra” energy to space?

Answers on a postcard please.

Robert B
Reply to  commieBob
June 23, 2019 3:06 am

I remember when reading of something that was the beginning of this farce in the 50s was that the rise in CO2 in the 20thC could be due to changes in the land and the weathering of rocks. While human use of fossil fuels was also brought up , its interesting that the author thought that the former was more plausible. Mind you, what chance is there that a 20 ppm rise in global CO2 was measured in the mid 50s.

June 21, 2019 1:32 pm

The specific heat of air is 1.005 kJ/kg K at 300 K at normal pressure. It does not matter what form the energy is. Until this changes none of the above is relevant.

June 21, 2019 1:34 pm

IOW those of us in cold climates should have burned more coal MANY years ago.

June 21, 2019 1:37 pm

94.7% of facts, aren’t.

Rud Istvan
June 21, 2019 1:49 pm

Good for WE.
Just one detail he left out. His own previous WUWT estimate of the efold bulk CO2 gas concentration atmospheric residency time is about 45-55 years ( efold is a bit more than half life) thanks to biological ocean carbon sinks (calcium carbonate is rather permanent except in deep ocean below ~3800 meters). So the 1000 year forcing is something less than 25-40x. Caldeira is only ‘off’ by four orders of magnitude. And sure as heck does not know about ‘dimensional analysis’ quick computational QC.

June 21, 2019 1:56 pm

I cite

An injection of CO2 into the atmosphere is not quickly absorbed by nature to the extent of 43% remaining

Reply to  Donald L. Klipstein
June 21, 2019 4:20 pm

You seem to have chopped of your post. It makes no sense as written.
Regardless, would you care to support your contention?
Willis did.

Bruce Cobb
June 21, 2019 2:04 pm

Wow, so the CO2 given off by a squawking climate “scientist” will heat the earth 100,000 times over its lifetime over the hot air given off by said “scientist”. Cool.

Reply to  Bruce Cobb
June 21, 2019 6:17 pm

There is a case they should all immediately stop breathing to save us all from there CO2.

June 21, 2019 2:09 pm

I tried my hands at some calculations independently for factchecking this. My calculations are:

One year’s worldwide forcing from increasing atmospheric CO2 from 410 to 411 PPMV is 2.132 E20 joules. (Using 3.77 W/m^2 per 2xCO2 and logarithmic relationship.) If atmospheric CO2 is bumped up from 410 to 411 PPMV and that one extra PPMV decays exponentially with a time constant (tau or e-folding time) of 59 years (see, then after thousands of years the cumulative energy from the forcing is 59 times 2.132 E20 joules or 125.8 E22 joules.

I figure the heat of combustion of 2.123 E12 kg of carbon (the amount of carbon I figure is needed to boost atmospheric CO2 by 1 PPMV) is 6.96 E19 joules. So, as I figure, increasing atmospheric CO2 from 410 to 411 PPMV for one year causes about 3.06 times as much heating as burning the carbon to achieve that does. This figure becomes 3.06*59 or181 times as much heat from the burning of the carbon for 410 PPMV to being quickly bumped up to 411 PPMV and decaying back to 410 PPMV with a time constant of 59 years. It’s even greater but still only in the hundreds in the likely event the Bern model is largely correct instead of exponential decay.

June 21, 2019 2:13 pm

For the record Ken Caldeira, you are full of Schmidt. CO2 in the atmosphere is good , and more CO2 is better.

J Mac
June 21, 2019 2:14 pm

Nice ‘take down’, Willis!

Correlation: I was outside mowing the lawn this morning, here in the Great NorthWet. I just came inside to get a hot cup of coffee and warm up my cold hands! If it will warm things up a bit, please burn train loads of more coal! It’s June 21, the summer solstice, for Pete’s sake!

Reply to  J Mac
June 21, 2019 5:15 pm

Mark Twain once said that the mildest winter he had experienced was a summer on Puget Sound.
I lived for 11 years on Mercer Island. Only one time did summer not quite warm up.

[Other dupes moved to Spam folder. .mod]

June 21, 2019 2:35 pm

Actually, it far less, since the residence time of CO2 in the atmosphere is relatively short and no where near 1000 years. The only carbon atoms that will still be in the atmosphere 1000 years from now will have been recycled by biomass many times over.

David Hood
Reply to  co2isnotevil
June 21, 2019 4:53 pm

HI co2isnotevil, that was what I was mulling over too, but NOT being able to ask with any authority, just WHAT is the residency time of CO2?
I have a chart clearly showing numerous studies which has it at (at a guess of all the studies) around 10 or so years.
The IPCC has theirs at 100yr plus, so, there does seems disconnect there.

Reply to  David Hood
June 21, 2019 8:32 pm


Well, lets say it’s been about 150 years since man starting burning fossil fuels. If you add up all the man made CO2 based on the amount of fuel burned, cement and aluminum ever produced, about half of it is missing. Instead of increasing from 280 to 400, it would be about 520 ppm if all that CO2 was still present, most of which is expected to have been dissolved in static CO2 sinks like the oceans. Without the effects of biology, this sets the half life residence time to about 150 years.

On a yearly basis, the average CO2 seasonally varies by about 6-7 ppm, mostly as the net response to biology consuming CO2 to produce biomass which is subsequently decomposed where the N hemisphere has more biomass than the S. Otherwise, the hemispheres would cancel and there would be no ‘sawtooth’ variability in the Moana Loa CO2 record whose peaks coincide with maximum decomposition of N hemisphere biomass. The biomass of each hemisphere must consume and decompose many times more than 6-7 ppm in a season and is more like about the equivalent of about 30 ppm per hemisphere where the N consumes and decomposes 6-7 ppm more.

At a 30 ppm recycling rate by biology, it would only take about 7 years to recycle the 120 ppm NET man made component of atmospheric CO2 and about 13 years to recycle all 400 ppm in the atmosphere.

Even if you assume that CO2 is not well mixed enough for the consumption/decomposition rates to mostly cancel between hemispheres and biology is only consuming/decomposing 6 ppm per year, it would still only take less than 70 years for biology to cycle through all 400 ppm, which represents the maximum upper case ‘half life’ for the CO2 residence time.

In any event, it’s far less than 1000 years no matter how you calculate it.

Reply to  co2isnotevil
June 22, 2019 3:05 am

Would you please write a paper and publish that.

June 21, 2019 2:45 pm

“If you burn a lump of coal, the greenhouse effect from the carbon dioxide released from burning that coal will, over its lifetime in the atmosphere, heat the Earth about 100,000 times more than the thermal energy released from burning that coal.”

This is an utterly meaningless statistic, even if true. The heating effect on the entire planet of burning a single lump of coal is so insignificant that it can be ignored as utterly irrelevant. What does it matter that this effect, which is so vanishingly small as to have absolutely no impact on any one or any thing during any interval for which the CO2 is in the air, lasts so long that the sum of the energy retained by the CO2 vastly outstrips the energy used by burning the coal? All you’re doing is measuring the total duration of a meaningless effect. It tells you nothing about whether the benefit you get from burning coal is worth the increase in temperature caused by doing so.

The post portrays this as a demonstration of confirmation bias. That may be true, but I think it would be more apt to say that it shows a clear lack of critical reasoning skills on the part of the person tweeting the statistic. Unfortunately, I think this is par for the course among climate “scientists.”

Jeff Alberts
Reply to  Kurt
June 21, 2019 6:43 pm

“The post portrays this as a demonstration of confirmation bias. That may be true, but I think it would be more apt to say that it shows a clear lack of critical reasoning skills on the part of the person tweeting the statistic. Unfortunately, I think this is par for the course among climate “scientists.””

I don’t think you can call it a lack of reasoning skills, but a lack of honesty. Any “lack of reasoning” has to be willful.

Reply to  Jeff Alberts
June 21, 2019 10:47 pm

Critical reasoning refers to the ability to sift through what is relevant and what is not relevant. Setting aside whether the authors of the GRS paper got their math right, one of those authors tweeted the statistic as if it is something meaningful. It is not. I don’t see any basis to chalk this up to dishonesty.

Here’s another quote from this coauthor: “If you’re talking about mugging little old ladies, you don’t say, ‘What’s our target for the rate of mugging little old ladies?’ You say, ‘Mugging little old ladies is bad, and we’re going to try to eliminate it.’ You recognize you might not be a hundred per cent successful, but your goal is to eliminate the mugging of little old ladies. And I think we need to eventually come around to looking at carbon dioxide emissions the same way.”

This is an absurdly unhelpful comparison. “Mugging little old ladies” is in no way analogous to burning fossil fuels to say, heat your home so you and your family don’t freeze to death in a Minnesota winter, or to drive to work so you can earn the money needed to provide the food and shelter you need to survive. There is no balancing of interests associated with “mugging little old ladies.” Conversely, virtually every use of fossil fuels not only provides a benefit to society, but the incremental benefit to burning those fossil fuels vastly exceeds any harm done via the greenhouse effect.

That a supposed scientist would make such a silly argument doesn’t demonstrate dishonesty, it demonstrates stupidity.

Jeff Alberts
Reply to  Kurt
June 22, 2019 4:36 pm

There’s no reason it can’t demonstrate dishonesty AND stupidity.

Reply to  Kurt
June 22, 2019 2:24 am

My thought exactly. I just cannot udnerstand what I’m supposed to worry about with this comparison? For one thing, everything is a trade off. If say burning the coal saves 100 lives, then you have to show that not burning the coal saves 101 lives. This is not just motivated reasoning, it is Begging the Question, assuming the conclusion to prove your conlcusion.

After all, we don’t burn coal for fun, we burn it because it produces benefits. So prove the disbenefits outweigh those benefits, not just Tweet stupid claims.

June 21, 2019 2:45 pm

With a residence time of ~50 years the radiation forcing would be ~65 times the combustion heat.

Reply to  Teerhuis
June 24, 2019 10:42 am

One major issue here is that radiant forcing from the Sun and combustion are both adding new Joules (heat) to the system, while recycling surface emissions absorbed by atmospheric GHG’s is only moving existing heat around the system.


The true radiant forcing effect from GHG’s is zero. Only the Sun is a source of radiant forcing. We can consider changes to the system, for example doubling CO2, as being equivalent to additional W/m^2 of solar forcing while keeping the system (CO2 concentrations) constant, but in no way shape or form do atmospheric GHG’s add new energy to the system and adding new energy to the system is the salient characteristic of radiant forcing.

Michael Jankowski
June 21, 2019 2:57 pm

“… Integrating the radiative forcing from zero to infinity yields about 4.5 × 1010 J of global warming per mol CO2 released to the atmosphere. Combusting one mole of reduced carbon yields about 393.51 kJ/mol (standard enthalpies of formation) [Oxtoby et al., 2011]. Therefore, on a molar basis, the time‐integrated radiative forcing from CO2 released from burning carbon, over its lifetime in the atmosphere, exceeds the thermal energy released by that burning by a factor of about 100,000…”

According to , coal has an energy content of 39.3 kJ/g and releases 2.0 moles of CO2 per 10^3 kJ.

If I accept the “4.5 × 1010 J of global warming per mol CO2 released” figure, I get 434 as the ratio of J of global warming per mole of coal burned. Authors want to make it on a moles of C basis…still doesn’t get you near 100,000. I can get 90,000 as the ratio of J of global warming per gram of coal burned, but that’s not the claim.

June 21, 2019 3:09 pm

In my figure of 65x the 43% reduction should not be used. Without that factor the forcing results in 150x.

Terry Haskew
June 21, 2019 3:42 pm

There is NO greenhouse effect. Co2 has no measurable effect on temperature. There problem solved. If you want to dispute that provide a model with workings using robust science that shows how its possible for the composition of the atmosphere can warm the surface. Such a model must apply to at least mars and venus as well as the earth.

Nicholas McGinley
June 21, 2019 3:46 pm

Wait a second!
When was the ECS declared to be a known quantity?
Or any warming proven to be from any particular cause?
AFAICT, the jury is still very much out on several critic details.
Let us not forget how much of the “evidence” consists of data that was never actually measured, but arrived at by guesswork and outright chicanery.

June 21, 2019 3:48 pm

The root cause of this nonsense lies in the IPCC. definition of Radiative Forcing which defines the FORCE ; but assigns an energy flux value to it. (Watts/sq.m).
Force has units of Lbs (Kg)mass; but for an energy flux it is FtLbs(joules)A huge difference.
This flux could only have been calculated by defining accurately the state of the climate at a particular time.
It is therefore nonsense to use this figure in a changing climate situation; as for each state of the climate the value needs to be calculated which is essentially a circular logic situation.

Water, of course, is the joker in the pack as much depends on the RATE of evaporation at the time.
Assigning a variable as a constant is a no no. Particularly if you do not know how the constant was derived.

michael hart
June 21, 2019 3:54 pm

Some calculations are pointless and should never be done at all.

Reply to  michael hart
June 21, 2019 7:01 pm

That 🙂

June 21, 2019 3:55 pm

Ken was approximately 99.9986754985352% wrong.

Reply to  toorightmate
June 23, 2019 2:17 am

About 1/1064 right?

June 21, 2019 3:55 pm

Wilis, I am a bit confused, which at 92 is to be expected. But this effect of
CO2, I understood that it was logerthermic, that it became less and less of
an effect as the pip in the atmosphere increased.


June 21, 2019 4:08 pm

“On Twitter, people will say most anything…”
Well, as the tweet says, it’s actually said in a paper in JGR. In fact, WUWT wrote about it here. He actually goes through a calculation process similar to here, with similar results, as shown in the graph featured in the WUWT post (which on my page is shown just above the “Related Posts” part here). The difference seems to be that he, as he expresses, “integrates to infinity”. IOW he allows for a lifetime of many millennia, even with decay. I don’t know how meaningful that is, but it seems to be what he does.

Michael Jankowski
Reply to  Nick Stokes
June 21, 2019 5:25 pm

Great contribution. I was just about to check-out the local bridges to see if I could find a troll, but now I don’t have to.

David Yaussy
Reply to  Michael Jankowski
June 22, 2019 5:16 am

Nick was just offering a rational observation. That’s not trolling. If he’s wrong, explain why so we can all benefit.

Michael Jankowski
Reply to  David Yaussy
June 22, 2019 5:13 pm

There was nothing of substance in his post to address. His “rational observation” was clearly taking digs at the post author and possibly other WUWT participants.

Reply to  Nick Stokes
June 22, 2019 7:54 am

For integration to infinity to be meaningful the amount of CO2 in the atmosphere can ever only increase, never decrease. You know very well that is not true, Nick.

Reply to  tty
June 22, 2019 6:24 pm

“can ever only increase, never decrease”

Not at all. In fact, their Fig 1 shows the decay curve of a pulse. The issue is that they assume the decay is, after a while, very slow, and so has a large integral over all time. But it is decreasing.

June 21, 2019 4:25 pm

People have missed the most important “fact” about heating the Earth.

The Earth is in a daily chaotic temperature equilibrium. Every day it warms by about 10 degrees Celsius over land, and every night it cools by about 10 degrees Celsius over land.

The Stefan–Boltzmann law states that the total energy radiated per unit surface area of a black body across all wavelengths per unit time is directly proportional to the fourth power of the black body’s thermodynamic temperature T.

If the Earth warms to more than the equilibrium temperature at any time, the Stefan-Boltzmann law ensures that the Earth will radiate more energy, and move the Earth nearer to the equilibrium temperature. For example, after summer (which has a lot more energy than a lump of coal), a hemisphere returns to winter (often 20 to 30 degrees Celsius colder than summer).

The CO2 liberated by a lump of coal may affect the equilibrium temperature of the Earth by a tiny amount. But it doesn’t keep warming the Earth forever. What effect would a forest fire have on the Earths long-term temperature? That would generate millions of times more CO2 than a lump of coal. Does the Earth get permanently warmer after every forest fire?

Alarmists should learn to keep their mouths shut, until after they put their brain into gear. Because loose mouths generate heat.

Reply to  Sheldon Walker
June 22, 2019 7:56 pm

Instead of the “lump of coal” I’d like to see the calculations for “winning WWII” as a much more useful example.
Calculate how much coal, diesel, gasoline, food, ammunition etc. that was consumed by the Allies from Sept. 1 1939 to Sept. 2 1945. Then express how many billions and billions of years this amounts to in the climate scientists mind.
Answer can be in “hiroshimas” if needed…

Right-Handed Shark
June 21, 2019 5:34 pm

Frankly, I don’t get this idea that CO2 resides in the atmosphere for any fixed period of time, whether it’s years, decades or centuries. When I went to school, I remember being told that CO2 bonds with water on contact, and I remember performing a simple experiment in the chemistry lab that proved it. The same fact came up in biology too, I distinctly remember being told that rainwater is always a mild solution of carbonic acid, an important part of the carbon cycle. Therefore, if it’s raining out, I can easily imagine a molecule of CO2 emerging from the factory chimney and being absorbed by a raindrop within seconds of being released. Where does this idea of “residence” come from?

Jan E Christoffersen
Reply to  Right-Handed Shark
June 21, 2019 7:23 pm


Good point. I hope someone can offer an explanation.

Reply to  Right-Handed Shark
June 21, 2019 9:42 pm

You are assuming that CO2 + H2O only goes to making carbonic acid. As anyone who has spilled a soda bottle will tell you, the reaction can go in the other direction, too. In real life, we have CO2 being released (okay, being “restored”) to the atmosphere, then dissolved in cold ocean water (cold, liquid water hangs on to CO2, except when it doesn’t).

Cold sea water can take up a lot of of C02. Warming sea water can release all that CO2. Residence time is an odd amalgam of CO2 absorption, release, and dissolution in the atmosphere. All those add up to sequestering or releasing CO2 that has taken up residence in our atmosphere

Right-Handed Shark
Reply to  Ric Werme
June 22, 2019 3:34 am

Okay, but in the soda bottle the CO2 is around 3-4 times atmospheric pressure, and when that pressure is released the excess CO2 escapes. Not so with the raindrop. The rainwater runs off into the river and on to the sea where the CO2 can be absorbed by algae, and on into the carbon cycle. Or that same molecule may indeed be released into the atmosphere, where it may meet another raindrop. But I still cannot accept that CO2 can remain in the atmosphere unchanged for decades, centuries, or as Mickey Mann claimed recently in a BBC interview, millenia.

John Andrews
June 21, 2019 8:51 pm

I would like to see the error terms associated with some of these “calculations.”

June 22, 2019 1:23 am

The heat produced by burning some coal will go in the end upward by convection and then will be lost into space by radiative transfer (thanks to active gases in the infrared spectrum, as CO2 or WV is …) so that the net energy accumulated in the atmosphere will be ZERO point ZERO.

You can multiply ZERO point ZERO by any dummy number you want Mr Caldeira, the result will be always ZERO point ZERO.

Try to think about thousands of volcanoes emitting heat during billions of years … and despite that, we are in a glaciation epoch, so : where did all this heat went ? In the bottom of the Oceans ?

Seems that the Climate Clownery is knocking down new bounds every each day.

Reply to  Petit_Barde
June 30, 2019 5:32 pm

Negative feedbacks reduce heating effects, Petit_Barde, but not to “zero point zero.”

The direct heating effect on the whole Earth of burning coal is, indeed, small. But it’s not “zero point zero.”

The indirect warming effect from elevated CO2 levels is larger than that, but still modest. It’s not “zero point zero,” either.

The Precious Air Fertilizer (CO2) acts as a dye in the atmosphere, which “colors” the atmosphere in the far infrared, esp. around 15 µm, which, significantly, happens to be close to the peak of the Earth’s emission spectrum. In graph of the Earth’s emission spectrum (measured from orbit above the tropical western Pacific), the big green notch is the effect of CO2:

comment image

Since nearly all of the emissions from the Earth are in the far infrared, but over half of the incoming energy (from the Sun) is at shorter wavelengths, tinting the atmosphere in the far infrared has a differential effect. Since there’s more outgoing than incoming far infrared, GHGs absorb mostly outgoing radiation, preventing it from escaping into space. That causes warming. (It’s not how actual greenhouses work, but it’s still a real effect.)”

That big green notch in the graph is the effect of CO2 in the atmosphere, on the Earth’s emission spectrum. At the bottom of the notch, the emissions which make it to space (to be measured by the satellite) are only about 1/3 the intensity of the emissions at those same wavelengths which left the surface.

That’s why CO2 warms the Earth.

BTW, look at the very center of that green notch. Do you see the narrow spike?

That’s CO2 radiating, from the upper stratosphere.

Of course, there’s not much of it, way up there, where the pressure is only a few millibars. And, of course, there’s very little pressure broadening, so the spike is very narrow. But it is clearly visible.

June 30, 2019 4:19 pm

Ken Caldeira and I argued about this on Twitter, here:

He thinks the average residence time for added CO2 is nearly 10,000 years. It’s actually about fifty years.

This is a log scale plot of the decline of 14C levels in the atmosphere, following the 14C “bomb spike.”

When atmospheric tests of A-bombs and H-bombs suddenly ceased (following the atmospheric test ban treaty), the 14C concentration dropped on a near-perfect exponential decay curve, with a half-life of 11.5 years, implying a residence time of 16.6 years.

(Note: 14CO2 is 4.5% heavier than normal 12CO2, which affects biological uptake and diffusion rates slightly. But not much.)

However, some of the processes which remove 14CO2 from the atmosphere do so by exchanging it for 12CO2. Those processes cause the fraction of 14C in the atmosphere to decline without actually reducing the amount of CO2 in the atmosphere. That means the 11.5 year half-life and 16.6 year residence time are necessarily less than the effective lifetime of CO2 emissions.

The effective lifetime of anthropogenic additions to CO2 in the atmosphere, variously defined as the time it would take for 2/3 or 63% (1-(1/e)) is roughly fifty years, making the half-life about 35 years.

That’s the result that Prof. Richard Lindzen reported during the Q&A (3rd video) of this (excellent!!!) lecture:
● Part 1:
● Part 2:
● The Q&A which followed: (including his discussion of CO2 atmospheric lifetime)

That’s also the approximate result that Dr. Roy Spencer found:

That’s also the approximate result that I got, first with a little program to simulate declining CO2 levels, based on the historical CO2 removal rate as a function of CO2 level, and then with a modified version of the program based on Dr. Spencer’s model; source code here:

Ferdinand Engelbeen reported roughly the same result, here:

That last one is a link to Ferdinand’s comment on a blog article by Ed Berry, in which Ed claims that the residence time of anthropogenic CO2 is very short, mankind’s CO2 emissions have little effect on the CO2 level, and the rise in atmospheric CO2 level is due to a warming climate. (Ferdinand is right, and Ed is wrong.)

What this means is that if anthropogenic CO2 emissions suddenly ceased, it would take about 30-40 years before half of the cumulative anthropogenic CO2 increase was gone from the atmosphere.

The essential insight to perform these calculations is that the rate at which various chemical and biological processes remove CO2 from the atmosphere is, very closely, a function of the atmospheric CO2 level. The question is, what is that function?

We needn’t wonder, because:

We know, very precisely, what the annually averaged atmospheric CO2 level has been for the last sixty years, and how it has changed from year to year.

We also know, with pretty good precision, from economic data for the production and use of coal, oil, natural gas, and cement, how much CO2 mankind releases each year. (There are other factors, like land use changes, which are less precisely known, but they’re small relative to fossil fuel emissions, so they can’t affect the calculation very much.)

The difference between the amount of anthropogenic CO2 emitted, and the amount by which CO2 level increases year-to-year, is the “removal rate.” That’s the rate at which negative feedback mechanisms, like terrestrial “greening” and dissolution into the oceans, remove CO2 from the atmosphere.

Another figure sometimes mentioned is the “airborne fraction.” It is just the amount by which CO2 level increases year-to-year divided by the anthropogenic emission rate. It doesn’t represent anything meaningful. (It is sometimes inaccurately described as the portion of CO2 emissions which go into the atmosphere; that’s wrong, because ALL the CO2 emissions go into the atmosphere, and hardly any of the CO2 that is removed actually comes from that year’s emissions.)

The key point is that we have excellent records from which we can calculate, quite precisely, what the CO2 removal rate has been every year, and we can tabulate that as a function of the same years’ annual average CO2 levels, from 315 ppmv (in 1958) to 410 ppmv (now). Then, since we know removal rate as a function of atmospheric CO2 level, we can easily calculate the residence time.

Caldeira would doubtless object that the CO2 removed from the atmosphere has not been returned to coal beds. Rather, it’s moved from the atmospheric carbon reservoir to the ocean’s carbon reservoir and the biosphere / soil reservoir, and it won’t stay there forever.

That’s true, but irrelevant, for practical purposes.

In the case of the oceans, it’s a distinction without a practical difference, because the oceans’ carbon storage is so vast, compared to the atmosphere, and calcifying coccolithophores transport carbonates from surface water, where the CO2 dissolves, to the ocean depths.

In the case of the biosphere / soil, the objection is less obviously unreasonable. But there’s no good reason to expect the carbon sequestered by “greening” (enlarging the biosphere) to return to the atmosphere, until CO2 levels are someday again very low.

The hypothetical “long tail,” which so drastically exaggerates Caldeira’s “residence time” figure is not based on measurements. It represents modeled predictions of carbon theoretically released into the atmosphere from oceans and biosphere / soil in the distant future, when atmospheric CO2 levels are very low (well below 350 ppmv).

But when CO2 levels are very low, the climate threat will be cooling rather than warming, and browning from CO2 starvation rather than greening from CO2 fertilization. So, even if you accept the IPCC’s foolish claim that the next 0.5° or 1.0° of warming will be bad, there’s no denying the proven fact that the last 1°C of warming, and the ≈20% agricultural production boost from higher CO2 levels, were good. So when CO2 levels are very low, the release of CO2 from the biosphere / soils and oceans into the atmosphere will indisputably be a very good thing.

Yet Caldeira wants you to think it’s a bad thing. That’s just crazy talk.

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