Stabilising Climate

In order to stop global warming all we really have to do is to stabilise CO2 emissions, not reduce them to zero!  One of the ‘myths’ promoted by IPCC climate scientists is that we have to stop burning all fossil fuels i.e. we must ‘keep it in the ground’. This is a total fallacy as I will try to explain in this post.

Carbon dioxide sources and sinks must balance once stability is reached

The origin of this belief that we must stop burning any fossil fuels by ~2050 can be traced back to Figure 10 which appeared in the AR5 ‘Summary for Policy Makers’. Here it is.

Figure 10 from SPM AR5

Figure 10 was intended to send a simple message to the world’s political leaders. Namely that there is a finite total amount of fossil fuel that mankind can safely burn, and that we have already burned half of it.  Therefore unless the major industrialised countries stop burning fossil fuels altogether by 2050, the world will warm far above 2C (red curve) causing a global disaster. This message worked, but there is so much wrong about the hidden assumptions and even subterfuge used to produce Figure 10 that I wrote a post about it at the time.

The principal assumptions hidden from view under Fig 10. are:

1. Carbon sinks are saturating (they are not)
2. ECS (Equilibrium Climate Sensitivity)  is 3.5C (Uncertain – and could be as low as 1.5C)
3. Replacement of logarithmic forcing of CO2  with a linear forcing.

As a direct consequence of IPCC successful lobbying based around Figure 10, the Paris treaty now proudly “sets the world on an irreversible trajectory on which all investment, all regulation and all industrial strategy must start to align with a zero carbon global economy“. Does anyone really believe that this is even feasible, let alone realistic? It simply is not going to happen because well before then their citizens will revolt and kick them out. The best we can hope for in the short term is a stabilisation in annual global CO2 emissions.

I argue that by simply stabilising emissions, we can halt global warming. Clearly the lower total ‘stable’ emissions are then the cooler the planet will be, but even if we only managed to stabilise emissions at current values the net warming will still be <2C and CO2 levels will stop rising and stabilise at <410 ppm.

Atmospheric CO2 levels must always reach an equilibrium as the natural carbon sinks will catch up to balance emissions. For the last 40 years about half of man-made emissions have been absorbed mainly into the oceans, but also into soils and biota. The reason why CO2 levels have been continuously increasing since 1970 is that  we have been increasing emissions each year, so the sinks have never been able to catch up. Sinks will quickly balance emissions and CO2 levels will stop rising once emissions stop increasing. This fact is obvious because run-away CO2 levels have never happened in the earth’s long history. Such a balancing mechanism has always stabilised atmospheric CO2 over billions of years during intense periods of extreme volcanic activity, ocean spreading and periodic tectonic mountain building. Fossil fuels are an insignificant fraction when compared to  the buried carbon contained in sedimentary rocks.

To see how this works let’s assume that the world can stabilise annual emissions at current rates of 34 Gtons CO2/year  indefinitely. We know that CO2 sinks currently absorb half of that figure – 17 Gtons and have been increasing proportional to the increase in partial pressure of CO2 in the atmosphere – currently 400ppm. Stabilising emissions would result in the increasing fractional uptake by carbon sinks of the now fixed emissions. The remaining fraction of annual emissions that would remain in the atmosphere is therefore as follows.

Year 1: 50%  Year 2: 25% Year 3: 12.5% etc. This is simply equal to the infinite sum

$\sum_{n=1}^{\infty} 2^{-n} = 1$

So CO2 levels in the atmosphere will  taper off after just ~10 years to reach a new long term value equivalent to adding an additional 34 Gtons of CO2 to the atmosphere. The atmosphere currently contains 3.13 x 10^12 tons of CO2 so the net increase at equilibrium would be only an extra  1%. Therefore for the years following 2016 the resultant CO2 curve looks like this.

There is also a very good chance that we can achieve such a fixed limit, rather than pretend to meet an impossible target of zero emissions. However this  does mean that CO2 levels will remain at 404 ppm indefinitely, which is far higher than a planet without human beings, but that still leaves us plenty of time to replace fossil fuels with new nuclear energy. Furthermore such a strategy would save trillions of dollars from being wasted on the pipe dream of renewable energy.

Controlling CO2 levels by stabilising emissions also has one other advantage. It means that we will eventually be able to control the level of ‘enhanced global warming’, thereby avoiding another devastating ice age which otherwise is due to begin within the next 5000 years.

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49 Responses to Stabilising Climate

1. j martin says:

An immensely sensible approach.

I have two issues with the post. Firstly, co2 will likely stabilise at a higher figure given that Asia is set to increase the number of coal-fired power stations by 1000 or more. Secondly, the idea that any amount of co2 will prevent a glaciation. We know that a glaciation took place in the past with initially 7000 ppm and throughout the entire glaciation co2 did not drop below 4000 ppm.

I don’t doubt mankind will fight any impending glaciation, but co2 on its own will not suffice.

• Clive Best says:

My basic argument is that current climate policy is simply wrong. CO2 may well stabilise at a higher level if India and Indonesia continues to build more coal power stations. However the basic argument is the same.

Glaciations are ’caused’ by Milankovitch cycles and CO2 plays a minor support role. However naturally CO2 falls with onset of a glaciation as the oceans absorb more CO2 and photosynthesises reduces under arid conditions and expanding ice. By keeping CO2 levels higher we can at least benefit from enhanced greenhouse warming. At least until fossil fuels run out.

2. Andrew Carey says:

The logic is right – that stabilising emissions will ultimately lead to stable concentrations of CO2, assuming no runaway effects which is an assumption I’m happy with.
However, the arithmetic feels wrong – that the CO2 sink can increase capacity within 4 years so it is dumping 33 of the 34 Gt human output of C02 back into rocks, life-forms and other doesn’t feel right

3. Clive Best says:

It is mainly dumping CO2 into the ocean because dissolution and solution depend only on the imbalance of partial pressure. Once ocean surface partial pressure equals atmospheric partial pressure levels equalise. Yes this will cause in the short term acidification in the mixed layer, but this will disperse over 50-100 years into the deep ocean.

• Andrew Carey says:

“We know that CO2 sinks currently absorb half of that figure – 17 Gtons and have been increasing proportional to the increase in partial pressure of CO2 in the atmosphere – currently 400ppm”
Do you have estimates for the equivalent figures for the above in say 2006 and 1996? I am confident that you’ve made a major error in your model that stability could be achieved in the next 10 years if emissions are stabilised today.
Just in year+1 that sink would have to absorb 25.5Gtons of CO2 for your model to work, a stunning increase in 1 year which is totally out of proportion to the much smaller annual increases in partial pressure.

• Clive Best says:

Here is a graph of emissions versus CO2 levels. In general for every Gton added to the atmosphere by man half of it has always been absorbed by sinks. Simply put that means DC = 0.5* DE However there clearly is a time constant since otherwise the result would be DC = DE. This means that there is a half life needed to equalise sources and sinks.

No – in the first year the sinks absorb half the excess – 17.5 GT. In the second year they absorb 8.75 and so on.

4. YOU SHOULD BRUSH UP ON WHAT CLIMATE IS: -”there is no such a thing as ‘’earth’s global climate’’ – there are many INDEPENDENT different MICRO CLIMATES 1] Alpine climate 2] Mediterranean climate, 3] sea- level climate 4] high altitude climate 5] temperate climates 6] subtropical climate, 7] tropical climate 8] desert climate 9] rainforest climates 10] wet climate 11] dry climate, as in desert AND THEY KEEP CHANGING; wet climate gets dry occasionally b] even rains in the desert sometimes and improves. In the tropics is wet and dry -/- in subtropics and temperate climates changes four time a year, WITH EVERY season= migratory birds can tell you that; because they know much more about climate than all the Warmist foot-solders and all climate skeptics combined – on the polar caps climates change twice a year. Leading Warmist know that is no ”global warming” so they encompassed ”climatic changes” to confuse and con the ignorant – so that when is some extreme weather for few days on some corner of the planet, to use it as proof of their phony global warming and ignore that the weather is good simultaneously on the other 97% of the planet, even though is same amount of co2. In other words, they used the trick as: -”if you want to sell that the sun is orbiting around the earth -> you encompass the moon – present proofs that the moon is orbiting around the earth and occasionally insert that: the sun and moon rise from same place and set to the west, proof that the ”sun is orbiting around the earth” AND the trick works, because the Flat-Earthers called ”climate skeptics” are fanatically supporting 90% of the Warmist lies. Bottom line: if somebody doesn’t believe that on the earth climate exist and constantly changes, but is no global warming -> ”climate skeptic” shouldn’t be allowed on the street, unless accompanied by an adult. b] many micro-climates and they keep changing, but no such a thing as ”global climate”

5. A C Osborn says:

Stabilising CO2 output by Man will not Stabilise anything other than the CO2 output by Man.
The Earth’s CO2 output/input will do precisely what it has always done.
But anything that man can put in to the Atmosphere is GOOD for the rest of the Earth.
Greening is benificial to everything else, including Man.
Why would you waste any time, effort or money doing damage to the Earth?

• Clive Best says:

However you look at it the CO2 content of the atmosphere is increasing each year by roughly half of the net human emissions for that year. This is not the individual molecules but the balance of all the sources and all the sinks. Only one of the smallest sources (us) is increasing each year. That causes the imbalance. If it stops increasing then the sinks increase enough to balance.

Now whether or not you think that more CO2 is better for us and the planet, politicians have been convinced that it is bad. So instead of them embarking on an impossible path to ‘de-carbonise’ the economy, they simply need to keep emissions constant. Then we can all go home and relax, whether or not there was a real threat or not.

6. R Graf says:

“Controlling CO2 levels by stabilizing emissions also has one huge advantage. It means that we can eventually control the level of ‘enhanced global warming’ so avoiding another devastating ice age, otherwise due to begin within 5000 years time.”

If we have discovered we have the ability to affect climate I would think the sensible thing to do would be to explore other avenues as modulating climate, not try to remove CO2 which has fertilization benefits. Geoengineering a control knob by reflecting sunlight would provide a reversible mitigation to both natural and human caused warming or cooling events. The later is of great importance since all agree a re-continuation of the glacial cycle (new ice age) is not good.

Proposal:
If we dusted the top of the mesosphere 90km up with a nano-particle colloid we could give Earth and artificial glowing ring, shading the equator. If we had an unforeseen cooling event we could dust the ring with an oppositely charged nano-particle causing the ring to precipitate and clear out. But as a dead-man’s switch we place the ring low enough that gravity and friction degrade it over a decade with no intervention.

• Clive Best says:

No we don’t need to reduce CO2 levels at all. We just need to stop them rising. Maybe 400ppm is a perfect level for the long term and nature will thrive and adapt, maybe not.

What it does give us is a long time to decide if we should do anything or not. I don’t really like any geo-engineering proposals because no-one knows what the pay back would be. Whenever we interfere in nature there are always unforeseen knock-on effects. It’s like introducing rabbits to Australia.

• who is ”WE” Ron – is there any other person naive enough, to believe that can fertilize 90km altitude..? Ron, ice ages and phony global warmings are between your ears, not in nature; don’t listen to the swindlers =/= earthworms are much bigger EXPERTS about ”the real climate” than all the swindlers combined. Garden worms refuse to live in desert climate, because they know WHY IS BAD CLIMATE IN DESERTS and definitely is not because is too much CO2, because the earthworms are smart and clever, cannot be said about the Warmist foot-solders, OR about the PHONY CLIMATOLOGIST.

• R Graf says:

Clive, Stefan, I am well aware of unintended consequences but I don’t see that as a reason to stop investigating solutions. The reason I like the 90km idea is that it is far from the biosphere and with a very small mass a nano-particles one can have a very significant optical impact. It’s a concept that can easily be scaled and experimented with and analyzed. As for who gets to decide what temperature the Earth need to be, the obvious framework is already in place with the UN. I am not against all world cooperation just when it threatens to confiscate freedoms or property rights. I’m sure there would be political battles for setting global mean temp but that would be much preferable to other kinds of battles, the ones that wars can be fought over. I think everyone want to keep the poles ice covered that the SLR to less than a foot per century.

• you are talking as if man can use the button on the Fujitsu air-conditioner to regulate the temp for he WHOLE planet… Disney job, not for politicians. b] the earth self regulate herself b] CO2 has nothing to do with earth’s temperature c] global warming is not happening; imaginary global warming never hearts anybody

7. Jefe says:

Did u factor in feedbacks?

• Clive Best says:

Feedbacks don’t matter for this argument. We are only considering the balance of CO2 in the atmosphere with carbon sinks. If we aim just to halt warming then we only need to halt increases in CO2 concentration in the atmosphere. That is easy – just keep emissions constant and the sinks will balance the sources.

• R Graf says:

Clive, If Jefe is referring to soil degassing and ocean methane release through thawing clathrates then he does have an argument there is an unknown possible natural increase in GHG through feedback. A paper came out this month where about 50 co-authors signed on to this assertion. But that could be like the scientists on the steps outside the annual AGU meeting today protesting with signs against the anti-science public.

• Clive Best says:

That’s true. There is a carbon cycle feedback caused by warming. So if global sea surface temperature rises then CO2 dissolution from the surface increases (Henri’s law) but only so far as there is also a pressure difference. Yes it’s complicated but the overall picture of a rebalancing of sinks to exactly match fixed sources must be correct. If nothing changes equilibrium must be reached.

8. It appears that you’re assuming that the Revelle factor is 0. That would seem to be inconsistent with basic ocean carbonate chemistry.

• Clive Best says:

No I don’t. The Revelle factor probably explains why sinks only absorb half of the increases of emissions in 1 year. The stabilisation of sinks with fixed emissions may have a longer half life relaxation time than one year. Even if it is 5 years atmospheric CO2 levels will stabilise within 30 years.

• The Revelle factor is

$\dfrac{\Delta pCO_2/pCO_2}{\Delta DIC/DIC}.$

You’re assuming that we can continue to emit CO2 into the atmosphere, but that pCO2 can remain constant (i.e., $\Delta pCO_2 = 0$) despite the sinks continuing to take up CO2 (i.e., $\Delta DIC \neq 0.$). Therefore you are effectively assuming that the Revelle factor is 0. This is, as far as I’m aware, inconsistent with ocean carbonate chemistry.

• cut the crap phony physicist. The more CO2 in the air-> the more is washed by the rain, to fertilize the soil. Your problem is not co2, you have much bigger problem…

9. kap55 says:

Totally, incredibly, massively wrong.

Total emissions in 2015 were 33508 MTCO2. Natural sinks absorbed about half of that, and left half in the air.
So if we emit 33508 MTCO2 this year, natural sinks will absorb about half of *that* too. And leave half in the air.
And if we emit 33508 MTCO2 next year, natural sinks will absorb about half of *that*, and leave half in the air.

Which means CO2 in the air keeps going up, as long as we keep emitting. Even if emissions stabilize.

Further, as the oceans heat, they become less and less efficient absorbers of CO2; and as the world warms, larger and larger fractions of the planet will reach temperatures at which photosynthesis stops, putting a brake on land absorption. Thus the increased heat from even constant emissions will *decrease* the rate of natural absorption, not increase it.

The only end to this process comes when it gets so massively hot on the surface that lithospheric sinks become significant at much, much higher rates than they are today. And that’s a planet which is not livable.

10. kap55 says:

Or, let me put it in a very simple way:

We’ve got a tank with some water in it. There’s a drain at the bottom which is letting water out at 1 gallon per minute. But we’re putting water in at the top, at a CONSTANT RATE of 2 gallons per minute.

How long does it take before the water level in the tank stops going up?

11. Ed Davies says:

Here’s a simple example which would appear to follow your explanation but obviously doesn’t.

Suppose all emissions where in the northern hemisphere and that all the CO? stayed in the atmosphere (none went into the oceans or soil or anywhere else). Parochially we might conclude that only half our emissions are staying in our hemisphere’s atmosphere and that therefore the “sink” which is the southern hemisphere atmosphere is absorbing the other half. If we stabilized our emissions your assumption is that the southern hemisphere would continue to absorb the extra at much the same rate it is doing now.

That obviously doesn’t make sense for a normal mixed-gas atmosphere like the southern hemisphere. The point of the IPCC presentation is that it doesn’t make sense for the oceans, either. They store CO? in the same way (in proportion to the partial pressure, though through a more complicated chain of chemical reactions) and the amount which actually sinks (to the ocean floor) is relatively small. This was the key 1950’s discovery by Roger Revelle and co which set off modern worries about AGW.

If you know why that’s wrong I’d suggest a publication in the peer-reviewed literature might be in order.

• Ed Davies says:

PS, CO? is supposed to be CO2, of course, but there seems to be some sort of objection to the Unicode subscript 2 (U+2082) I typed. Mishandling basic Unicode like that is getting pretty rare these days. Pretty sure it works on other WordPress blogs.

12. Frank says:

Clive: Man is currently emitting enough CO2 to increase atmospheric CO2 by 4 ppm/yr, but we only observe an increase in atmospheric CO2 of 2 ppm/yr. Presumably that means that 400 ppm of CO2 is enough to drive 2 ppm/yr from the atmosphere. My intuition says that if we cut emissions in half, sinks would continue to take up 2 ppm/yr (until sinks begin to “saturate”) and atmospheric CO2 would stabilize at the current level. On the other hand, you say that a 1% increase in CO2 to 404 ppm is enough to double the rate at which CO2 disappears into sinks from 2 to 4 ppm/yr.

(I never been comfortable switching between CO2 in Gtons_CO2/year, Gtons_C/yr, or other mass/yr units. What we care about is how much emission changes atmospheric CO2 in units of ppm. You tell me that current global emission is 34 Gtons_CO2/yr and I’ll say that is the equivalent of 4 ppm/yr. (If I were a thorough scientist, I’d look up the mass of the atmosphere, find out if ppm are by weight or by molecules, and prove that 1 ppm/yr is 8.5 Gtons_CO2/yr. Since this is a blog, I simply talk about emissions and uptake in units of ppm/yr – it is much more intuitive and the math is far simpler).

I think this is the correct mathematical formulation* may be:

d[CO2_atm]dt = -k_u_n*[CO2_atm] + k_e_n1*[CO2_sink_1] + k_e_n2*[CO2_sink_2] + k_e_a

d[CO2_atm]dt = rate of change in [CO2_atm]
k_u_n = rate constant for Uptake of CO2 by all Natural sinks.
k_e_n1 = rate constant for Emission of CO2 by Sink #1 by Natural processes.
[CO2_sink_1] = concentration of CO2 in Sink #1. Could be DIC in ocean.
k_e_n2 = rate constant for Emission of CO2 by Sink #2 by Natural processes.
[CO2_sink_2] = conc. of CO2 in Sink #2. Could be organic material in soil in CO2 equiv. Or plant matter growing above ground. Some of this is emitted as CH4 and then oxidized,
… Other sinks and rate constants.
k_e_a = rate of Emission of CO2 by Anthropogenic mechanisms.

During the 10 millennia before the Industrial Revolution, d[CO2_atm]dt and k_e_a were both near zero and a steady state relationship existed.

k_u_n*[CO2_atm = 280 ppm] = k_e_n1*[CO2_sink_1] + k_e_n2*[CO2_sink_2]

If we assume that the size of the sinks is much larger than the amount of CO2 they have taken up so far, then the second and third terms on the right hand side and if we assume that their rate constants are independent of global warming, these terms haven’t changed. For the sink that is the deep ocean, we know that the MOC takes about a millennia to overturn the ocean. So the deep ocean sink isn’t going to saturate in the near future. The mixed layer of the ocean is rapidly mixed by wind, so the CO2 content of the mixed layer is always in equilibrium with the atmosphere and that equilibrium is only slightly temperature sensitive. It doesn’t saturate. The land sinks are a little trickier, but let’s make the assumption their rate constants and capacity haven’t yet changed appreciably. So we can substitute:

d[CO2_atm]dt = -k_u_n*[CO2_atm] + k_u_n*[CO2_atm = 280 ppm] + k_e_a

Today:
d[CO2_atm]dt = 2 ppm/yr
[CO2_atm] = 400 ppm
k_e_a = 4 ppm/yr

Substituting:

2 ppm/yr = -k_u_n*[120 ppm] + 4 ppm/yr
k_u_n = 1/60 yr-1

To double-check for consistency, go back to 1960 when (IIRC)
d[CO2_atm]dt = 1 ppm/yr
[CO2_atm] = 330 ppm
k_e_a = 2 ppm/yr

1 ppm/yr = -k_u_n*[50 ppm] + 2 ppm/yr
k_u_n = 1/50 yr-1

I really should look up the 1960 values and not trust my memory. No sign of saturation here.

So what happens if we continue to emit a constant (not growing) 4 ppm/yr, [CO2_atm]=404 ppm and nothing else changes:

d[CO2_atm]dt = -(1/60)*[124 ppm] + 4 ppm = +1.93 ppm/yr

[CO2_atm] needs to rise to 520 ppm (280+240) for d[CO2_atm]dt to be zero and atmospheric CO2 to stabilize when we are emitting the equivalent of 4 ppm/yr.

And my intuitive answer that we need to cut back to 2 ppm/yr to stabilize near 400 ppm (for as long as the sinks don’t saturate) agrees with this mathematics.

Are sinks saturating?

Reservoirs of carbon (in GtC) in the ocean (blue labels), in biomass in the sea and on land (tan and green labels), in the atmosphere (light blue label) and in anthropogenic emissions. Fluxes of Carbon between reservoirs are depicted by the arrows, the numbers represent GtC. (From: IPCC)

We’ve emitted 240 ppm of CO2, 120 ppm is in the atmosphere, 60 ppm-equivalents is in the ocean, and 60 ppm-equivalents. This Figure is using units of GtC and 400 ppm = 750 GtC. The land biomass reservoir is about 2000 ppm-eq and the deep ocean reservoir is about 20,000 ppm-eq. The increased CO2 stored in these reservoirs since 1750 is trivial compared with their size, so there isn’t an obvious reason why emission from the reservoirs should have increased already or increase in the future.

*In my main equation I should include a term for the increase in photosynthesis (primary productivity) with rising CO2. The incorporation of CO2 into organic material is the rate limiting step, so it could have increased by a factor of 400/280 – at least in areas where water and other nutrients (N, P, K, and micronutrients) are not limiting.

• Frank says:

Clive: Sorry I went on for so long above. I’ve tried to work out this mathematics in the past, but never gotten this far before, so I kept on going.

I suspect (but don’t know) that the key difference is that others treat CO2 as a diffusion problem (zeroeth order rate equation), but I’m thinking in terms of a first-order chemical reaction.

https://en.wikipedia.org/wiki/Rate_equation

• Clive Best says:

Frank,

I have been under attack from various people for this post and the one on WUWT, because if true it would undermine the storyline that we must cut emissions to zero. What emerged from all this, is that nearly everyone agreed that freezing emissions at some level will lead to a reduction in the airborne fraction. The main argument is as to whether it will reduce to zero – stabilization, or whether it remains smaller meaning that levels will continue to rise, but only more gradually, for a few hundred years.

“My intuition says that if we cut emissions in half, sinks would continue to take up 2 ppm/yr (until sinks begin to “saturate”) and atmospheric CO2 would stabilize at the current level.”
makes a lot of sense to me. Sinks are not saturated and if emissions were cut in half and held stable then initially AF would fall to zero. Would they increase thereafter ? I doubt it.

The mixing of the mixed layer with the deep ocean is probably quicker than previously estimated anyway. so I doubt whether sinks will saturate. The Revelle factor is a bit if a red herring as it really says that there are many different chemical routes CO2 can take rather than simply dissolving as CO2..

In any case just by stabilising emissions we can buy sufficient time to find realistic alternative energy sources which basically have to be nuclear.

sorry for not answering properly earlier.

cheers

• Frank says:

Clive: I appreciate your reply (prompt or not) and the interesting things you post. There is less noise replying here compared with WUWT, so I didn’t try to follow that discussion. According to my equation, today’s emission rate (4 ppm-eq/yr) will plateau at 520 ppm, at which point its air-borne faction will have dropped zero. That assumes sinks don’t saturate.

I’m confident that bulk convection, not molecular diffusion is responsible for the transport of CO2 into the deep ocean. The mixed layer is turbulently stirred with equilibration times of a few months. I can see the ocean “exhale” 50% more CO2 (3 ppm rather than 2 ppm) during the 97/8 El Nino and then take up less (1 ppm) the following year.

I’m not sure how much transport into the deep ocean is due to “eddy diffusion” and how much is due to MOC – bulk convection along a conveyor belt like system with localized downwelling and upwelling. Large amounts of CFC11 started entering the atmosphere around 1950 and it has been used as a marker for downwelling. The temperature dependence of the solubility of CFC11makes it a non-quantitative marker, but the solubility of CO2 (and therefore its transport) is also temperature dependent. CFC11 looks like it is moving on a “conveyer belt”, not by Eddy diffusion.

I’m not sure of the mathematical implications of either mechanism. I’m a chemist, so I wrote my basic equation as if CO2 uptake by land involved a first-order reaction where the rate was proportional to [CO2], which is true for the main CO2 fixing enzyme Rubisco. I think I properly treated the a) uptake and b) emission of CO2 by the ocean as proportional to a) [CO2] today (400 ppm) and b) centuries ago when deep-water formed (280 ppm) on a conveyor. I don’t know if the math should be modified for a “diffusive” model.

What I don’t know is whether the rate of transport to land sink is limited by diffusion. I read somewhere that CO2 is depleted from between the blades of grass in a lawn on a sunny day without wind (or in a corn field).

If I remember correctly, the Bern model is purely curve fitting exercise to match observed changes in CO2 accumulation. The capacity and time course of CO2 in various compartments has nothing to do with the size of any real compartments (ocean, for example) and rate of transport between real compartments. Perhaps I have this wrong.

• Clive Best says:

Frank,
If it’s OK with you I am going to make your first comment a ‘guest’ post. I’ll improve the maths by using latex. I think the logic is very good and the equilibrium CO2 level agrees with that from one of the best carbon cycle experts: Ferdinand Engelbeen.

• Frank says:

I think others start with the Fisk law of diffusion, but I haven’t mastered applying this mathematics to CO2. I’m very confused about the use of the term diffusion, when the mechanism is convection, but “Eddy diffusion” apparently a form of convective mixing. Any references would be appreciated.

Where can I read Ferdinand Engelbeen on the carbon cycle?

• Clive Best says:

You can find some of his writing here:

http://www.ferdinand-engelbeen.be/klimaat/co2_variability.html

I agree about diffusion. Here is an extract from the discussion on WUWT,

Nick Stokes December 15, 2016 at 11:01 pm
“If DS/DT = DE/DT then annual CO2 levels in the atmosphere would be constant. “
Yes, I’m talking about flow rates. And you’re talking about DE/Dt constant. And I’m saying that the diffusion solution to that has surface pCO2 (and so air pCo2) rising with sqrt(t). No limit.

Clive Best December 16, 2016 at 1:02 am
Here is a comparison between your sqrt(t) rise and my fast equalisation out over next 300 years. Your solution is not too bad either. We could live with that perfectly well for the next 100 years !

Greg December 16, 2016 at 6:00 am
reiterating my point made above, the transport to deep ocean is not really diffusive, that is unrealistically slow when it is short-circuited by the themo-haline circulation which goes straight into the abyssal depths.

Ferdinand Engelbeen December 16, 2016 at 1:58 am
Nick,

Your formula is right for the ocean surface, but fails for the deep oceans, the same problem as in the Bern model…

The main exchange between atmosphere and deep oceans is via the THC and other ocean currents. These take lots of CO2 out of the atmosphere due to colder temperatures near the poles and release lots of CO2 at the upwelling places. The net sink rate is directly proportional to the extra CO2 pressure difference between the atmosphere and the ocean surface, mainly at the sink place, which is temperature (and bio-life) dependent, hardly influenced by saturation from previous years: what is upwelling is deep ocean water, hardly influenced by humans, what is downwelling has taken all CO2 possible for the moving temperature over its trajectory on the surface.

The long term equilibrium (half life time ~35 years) between deep oceans and atmosphere for all CO2 released in the past 166 years is just over 1% of the total CO2 in atmosphere + deep oceans.

The observed pCO2 difference at the main sink place (N.E. Atlantic) is ~150 ?atm, hardly influenced by temperature or saturation over time…

• Frank says:

Clive: Please feel free to use my comment however you see fit. However, please include and endorse my self-criticism that I don’t understand the conventional approach to this problem and therefore haven’t clearly explained why I may have reached a different result from the consensus.

As a scientist, I think I should be putting my contribution in the proper context compared with what is already known. And I have seen far too many amateurs make fools of themselves at WUWT because they don’t understand where they differ from the consensus. When I figure out what they have done differently, all too often their mistake is obvious.

The best result would be for some commenter to provide the proper context, because I may never figure it out.

I looked up the real 1960’s data:

d[CO2_atm]dt should be d[CO2_atm]/dt

1/60-1/70 CO2 rose 0.87 ppm/yr 316.6 to 325.3 ppm seasonally adjusted data

1960-1970 averaged 3170 million metric tons of C emitted per year, which I believe is about 11 Gtons CO2/year = 1.3 ppm/yr

To double-check for consistency, go back to 1960-1970
d[CO2_atm]/dt = 0.87 ppm/yr
[CO2_atm] = 320 ppm
k_e_a = 1.3 ppm/yr

0.87 ppm/yr = -k_u_n*[40 ppm] + 1.3 ppm/yr
k_u_n = 0.011 yr-1

The real numbers for today are also slightly different: For 2009-2014

d[CO2_atm]/dt = 1.86 ppm/yr
[CO2_atm] = 393 ppm
k_e_a = 4 ppm/yr but I still haven’t properly converted Gtons CO2/year to ppm properly in either case.

1.86 ppm/yr = -k_u_n*[113 ppm] + 4 ppm/yr
k_u_n = 0.016 yr-1

Roughly the same as above.

Uptake has increased by about 50% since the 1960’s.

frankwhobbs
icloud.com

13. chipstero7 says:

Would just like to re-post this here, regarding the Revelle Factor, I reply to Ferdinand. (WattsUpWithThat’s apparently didn’t like my tone and have put my comment into moderation).

I disagree. I think you selectively gather evidence to support your assertion that the increase in CO2 is man-made and do you best to dismiss all evidence suggesting otherwise. There is so much confusion surrounding the Revelle Factor that I groan inwardly whenever I see it come up in public discussion. Everyone who has heard about it seems to be an authority on it yet most who profess to understand it don’t and unwittingly peddle illusions about it that just add to the general confusion. The reason why the Revelle Factor contradicts Henry’s law is explained in the article, and also by Segalstad (1998). But I shall explain it briefly here again, just so you can respond by saying “Sorry, you misunderstand”. The Revelle Factor sets a fixed equilibrium partitioning ratio for CO2 between air and water of around 1:10 respectively at the current oceanic DIC relationship, meaning the surface-ocean can only absorb around 10% of our emissions at equilibrium (according to the IPCC the ocean is currently absorbing around 30% of our emissions (2.2Gts) and this is because 1.6Gt of anthropogenic CO2 is diffused to the deep-oceans every year, which is not in immediate equilibrium with atmospheric CO2. This diffused CO2 essentially acts to free-up space in the surface-ocean. Without it, the oceans would only be absorbing 0.6Gts. The Revelle Factor applies at equilibrium and because it is chemically-generated it should apply to any water, not just the oceans). It suggests that the reason oceanic water cannot efficiently absorb anthropogenic CO2 is due to the fact that CO2(g) exists in equilibrium with CO2(aq) which only comprises a small percentage of total oceanic DIC. This means that as the partial pressure of CO2 increases, CO2(aq) will decrease (relative to CO32 and HCO3) and the oceans’ ability to absorb atmospheric CO2 will diminish (but only down to an alkalinity of about 7.5 where the relationship breaks down). But the solubility of CO2 is unaffected by changes to the relative concentrations of DIC, as the Revelle Factor implies. If this were the case then Henry’s coefficient for CO2 would change as the partial pressure of CO2 changed, and it does not. This is explained in more detail in the article. The solubility of CO2 is unaffected by changes to the relative concentrations of CO2, as can be appreciated by a Bjerrum plot, where the relative concentrations of DIC change in proportion to each other, leading to net-change in total DIC, irrespective of pH, and this is what gives the plot its characteristic mirror-image appearance. As the Handbook of Chemistry says: “Solubilities for gases which react with water, namely ozone, nitrogen, oxides, chlorine and its oxides, carbon dioxide, hydrogen sulfide, and sulfur dioxide, are recorded as bulk solubilities; i.e. all chemical species of the gas and its reaction products with water are included”. There is no such mechanism that constrains water from absorbing CO2 based on changes to the relative concentrations of DIC. It does not exist. Furthermore your pH “bubble-bomb” example (which you have regularly used as “proof” of the Revelle Factor) is not valid, as has been explained to you exhaustively by Jeff Glassman.

• The Revelle Factor sets a fixed equilibrium partitioning ratio for CO2 between air and water of around 1:10 respectively at the current oceanic DIC relationship, meaning the surface-ocean can only absorb around 10% of our emissions at equilibrium

No, this isn’t what the Revelle factor means. It means that the fractional change in atmospheric CO2 will be 10 times greater than the fractional change in DIC. This is not the same as the ocean only absorbing 10% of our emissions at equilibrium.

• Richard says:

No, I explained it correctly. I did not say that the oceans as a whole would be absorbing 10% of our emissions at equilibrium. I said the surface-ocean would absorb 10% of our emissions, i.e. 10% of an increase in atmospheric CO2 from our emissions. So, say we increased atmospheric CO2 by 10ppmv, the surface-ocean would absorb about 1ppmv upon equilibrium. The reason the surface-ocean is absorbing more than 10% of anthropogenic CO2 is because of the diffusion of CO2 from the surface-ocean to the deep-ocean. Admittedly the explanation above was rather rushed. Here is a better one:

Quote:

“Once again, the Revelle Factor arises due to the way dissolved inorganic carbon (DIC) is partitioned in the oceans (although of course this should apply to any water with the same partitioning of DIC). Atmospheric CO2 exists in near-equilibrium with dissolved CO2 in the oceans. However most of the dissolved CO2 exists in the form of ?CO32 and HCO3. Dissolved CO2 comprises about 1% of total DIC in the surface-ocean, CO32 comprises about 10%, and HCO3 makes up about 89%. The Revelle Factor implies that because dissolved CO2 in the ocean only makes up a small proportion of total DIC and because it exists in equilibrium with atmospheric CO2, then a change in atmospheric CO2 should produce a correspondingly small change in dissolved CO2. It implies that the relative concentrations of DIC and the availability of CO2 relative to CO32 and HCO3 changes the solubility of CO2. The Revelle Factor implies that the surface-ocean can only absorb about 10% of an increase in atmospheric CO2 upon equilibrium. However the oceans are absorbing more than 10% of our emissions because of the transport of CO2 to the deep-oceans. The IPCC assume that the oceans are absorbing 8Gts of anthropogenic CO2 every year and the amount of anthropogenic CO2 being transported to the deep-oceans they say is about 5.8Gts. Meanwhile our emissions (in AR4) amounted to 23Gts. The oceans are absorbing more than 10% of our CO2 (10% would be 2.3Gts per year) because 5.8Gts is being transported to the deep-oceans, which are not in immediate equilibrium with atmospheric CO2. This diffusion essentially frees-up space in the surface-ocean, allowing the surface-ocean to absorb CO2 at a faster rate. Now, anyone who takes the time to look at Henry’s law will notice that Henry’s constant (which determines the solubility of gases) is unchanged by changes to CO2 concentration. It is fixed at a given temperature and is not dependent on the availability of CO2 relative to CO32 and HCO3. The Handbook of Chemistry makes this clear when saying: “Solubilities for gases which react with water, namely… CO2… are recorded as bulk solubilities; i.e. all chemical species of the gas and its reaction products with water are included”.

• Do you agree that the Revelle factor is, by definition, the ratio of the fractional change in atmospheric CO2 to the fractional change in DIC.

• Richard says:

Your definition is incomplete. That should read “The Revelle factor is, by definition, the ratio of the fractional change in atmospheric CO2 to the fractional change in DIC in the surface-ocean”. It applies only to the surface-ocean. Simply put, a 10% increase in atmospheric CO2 will lead to a 1% increase in dissolved CO2 (as DIC) in the surface-ocean/mixed-layer (upon equilibrium).

• No, it’s not just the surface ocean. It’s a direct consequence of ocean carbonate chemistry.

• Richard says:

I agree it is a direct consequence of carbonate chemistry and therefore should apply to some degree to the whole oceans. But from reading the literature on the subject it appears to only apply to the surface-ocean. See ‘Sabine 2004: The Oceanic Sink For Anthropogenic CO2’. You might want to ask for an explanation from Ferdinand Engelbeen as to why it applies only to the surface-ocean, as I have asked before. Good luck with that. Quote from the Sabine paper: “The efficiency with which the ocean can absorb CO2 at the surface is related to how much CO2 can be converted to DIC. The measure of this is called the Revelle Factor”. My understanding as to why it only applies to the surface is that the deep-oceans are not in direct equilibrium with the atmosphere and also because the DIC ratio is different in the deep-oceans, thereby perhaps giving a considerably lower Revelle Factor. The different removal times for atmospheric CO2 are apparently due to different sequestration processes, such as absorption by vegetation and soil, ocean invasion, silicate weathering and CaCO3 sedimentation. The ocean invasion (governed by the Revelle Factor) is essentially complete before 1000 years (see the IPCC’s AR5 graph for CO2 lifetime), and this is apparently due to the deep-ocean turnover time; it is then the CaCO3 sedimentation process that removes the excess 20% of atmospheric CO2 on thousand-year time-scales. The Solomon quote I gave you months ago I think was a mistake by Solomon. It is the CaCO3 process that is happening alongside and mostly independently of the Revelle Factor that removes the excess 20% of atmospheric CO2 on thousand-year time-scales. If the Revelle Factor applied to the whole oceans, as you claim, and not to the surface, then Henry’s law would most definitely be violated, because it applies that the oceans, as a whole, should absorb 98% of an increase in atmospheric CO2 upon equilibrium, and the Revelle Factor (which also applies at equilibrium) would only allow the oceans to absorb 10%, if it applied to the whole oceans, as you say.

• Richard,
I’ve been reading this David Archer which (on page 4) seems to consider the whole ocean when determing the buffer capacity. It also runs a set of calculations, some of which exclude CaCO3 and silicate weathering and which then result in remaining atmospheric fractions that seem consistent with considering the whole ocean, rather than simply the surface (i.e., if it were only the surface the remaining fraction should be much greater).

One difference between this and the Sabine paper is that the latter is considering what has actually happened to our emissions, while the Archer paper is considering more general scenarios of what would happen given different anthropogenic releases.

• Richard says:

That’s a very useful paper. I wonder why so much of the literature (including Wikipedia) defines it as applying to the surface-ocean.

• Richard,
I don’t the answer. One reason may simply be that the surface ocean is what is relevant to today (i.e., it determines how much of our emissions have been sequestered in the ocean to date) but the entire ocean becomes relevant on multi-century timescales.

14. Frank says:

I finally found a description of the Bern model that I may understand. That model says that the fate of emitted CO2 is determined in the year it is emitted. Every year’s emissions will be taken up by one sink or another with a different time constant for each sink. It’s fate is determined in the year it is emitted.

“The CO2 concentration is approximated by a sum of exponentially decaying functions, one for each fraction of the additional concentrations, which should reflect the time scales of different sinks. The coefficients are based on the pulse response of the additional concentration of CO2 taken from the Bern model (Siegenthaler and Joos, 1992)”.

http://unfccc.int/resource/brazil/carbon.html

Such a model isn’t very realistic. The fate of CO2 emitted in 1960 (when CO2 was 315 ppm) that still remains in the atmosphere today is determined by what is happening today (when CO2 is 400 ppm). There is not a one-way path from the atmosphere to a sink or reservoir; there are two-way paths between many different reservoirs (as shown in the diagram above). Furthermore, the rate of two-way transport between two different compartments (which sometimes involves a chemical reaction) is usually determined by what chemists call first-order kinetics – a rate proportion to the CURRENT amount CO2, k*[CO2], where k is a rate constant and [CO2] is the current amount of CO2 or some other species that can be converted to CO2 like [HCO3-] or “biomass” in CO2 equivalents. Chemists call the Bern pulse-response model “zeroth-order kinetics”, the fractional change is independent of CO2 concentration. Radioactive decay follows zeroth-order kinetics.

It is possible that an impulse-response model can correctly simulate the first-order transport and reactions of CO2. Given enough parameters, one can often find a reasonable fit between any model and observations. However, unless a physically reasonable model is used, good agreement with past observations is no guarantee that future projection will be valid. If the model described below disagrees with the Bern model about the future, any model that properly with a proper mechanism should be preferred.

• Clive Best says:

Frank,

I have been using this exact Bern model to calculate the CO2 response to constant emissions held at 2013 levels for the next 500 years. It is true that it doesn’t fully stabilise because the airborne fraction (AF) tends asymptotically to the a0 parameter. However the levels are not as bad as is predicted by the doom mongers. In 2620 atmospheric CO2 is about 700ppm using the AR3 parameters and about 1270ppm using the AR4 parameters. Remember that is all in 500 years time! If we can’t solve cheap limitless nuclear power by the, then we deserve to become extinct or revert to the stone age.

As you note there are arguments as to why a fixed fraction of past emissions cannot stay in the atmosphere essentially for ever. But taking the model at face value means that in 500 years time temperatures rise would be limited to ~ twice climate sensitivity. Depending on your prejudice that is a 3C rise or a 7C rise.

The Joos paper estimates errors on parameters of ~30% anyway.

• Clive,
The Bern model assumes that the residual term is independent of the total amount we emit; it is not – it increases with increasing total emissions. The Bern model also does not consider other carbon cycle feedbacks. You yourself quoted David Archer on another post, where he said:

But in the long run, it seems likely that the carbon cycle will start acting as a positive feedback, as for example melting permafrost soils allow peat deposits to decompose. The carbon cycle will have begun to release co2 rather than absorbing it. The conclusion we come to is that the natural carbon cycle is a wild card, as large an uncertainty as that of our own co2 emissions.

It’s uncertain, but it seems likely that it will – at some stage – start acting as a positive feedback; releasing CO2, rather than taking it up. So, yes, the Bern model does indeed suggest that it won’t be as bad as the “doom mongers” (given your complaints about your critics, maybe you should avoid using pejorative terms?) suggest, but that could well be because it is simply not considering factors that could led to increased atmospheric CO2 concentrations. Finding a model that suits your preconceptions is not necessarily a reason to simply accept it!

• Clive Best says:

Nor is your blind faith in catastrophic global warming simply a reason to accept the contrary, and since AF has remained ~ 0.5 for 60 years, we know that CO2 has not (yet) started acting as a feedback.

• Clive,

Nor is your blind faith in catastrophic global warming

I don’t have a blind faith in catastrophic global warming. If anything, my view is that severe global warming is entirely avoidable. I appreciate I’m probably annoying you, but does misrepresenting me really make you feel better?

a reason to accept the contrary, and since AF has remained ~ 0.5 for 60 years, we know that CO2 has not (yet) started acting as a feedback.

I didn’t say you have to accept it. I’m pointing out reasons why it may not remain around 0.5. For example, (as I think Nick Stokes pointed out to you on WUWT) the biosphere has a total carbon mass of around 1000 GtC. Your constant emissions scenario for 500 years would emit around 5000GtC. If the airborne fraction were to remain constant, that would suggest that the biosphere has continued to take up about one-quarter of our emissions. That would be around 1250 GtC, comparable to the entire mass of the biosphere. Do you really think it can double? Maybe, but seems unlikely and my understanding is that there are also nutrient limits.

This, however, isn’t an argument that you should simply accept the alternative. It’s a suggestion that you shouldn’t promote your alternative without making the assumptions and caveats clear.