A Hiding to Nothing

Guest essay by Clive Best


The currently held belief that we must  decarbonise the world’s economy in order to to stop climate change is a dangerous illusion. It is a ‘hiding to nothing’. I have come to the conclusion that if emissions were held constant for 30 years then the airborne fraction of CO2 emissions would reduce to zero. In other words if the world can hold emissions constant at say 30GT CO2/y then sinks will increase to balance all annual emissions. Thereafter CO2 levels would remain at below 440ppm indefinitely, so long as emissions remain constant.


I will argue below that in order to stop global warming all we really have to do is simply stabilise CO2 emissions, not reduce them to zero!  This alone will stabilise CO2 levels within less than 30 years.  The origin of the ‘myth’ as promoted by nearly all 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 fallacy and I will try to explain why in this post.

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 again.


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 ever safely burn, and that we have already burned half of it.  Therefore unless all major industrialised countries stop burning fossil fuels altogether by 2050, the world will warm far above 2C (the red curve) causing a global disaster. This message worked, but I find that there is so much wrong with the hidden assumptions and even subterfuge used to produce Figure 10 that I wrote a post about it at the time.

The principal hidden assumptions, as I see it, in Fig 10. are as follows:

1. Carbon sinks are saturating (they are not)

2. ECS (Equilibrium Climate Sensitivity)  is 3.5C (Very uncertain – and could even be as low as 1.5C)

3. The subtle replacement of logarithmic forcing of CO2  with a linear forcing.

4. The assumption that past emissions stay in the atmosphere essentially forever.

As a direct consequence of IPCC successful lobbying based essentially 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 of global CO2 emissions. The minimum condition needed is that annual growth in emissions needs to be brought to zero.

Carbon Cycle

To understand the carbon cycle means understanding the difference between CO2 decay time and CO2 residence time. The decay time for an individual CO2 molecule emitted by man is only about 5-10 years (based on C14 measurements in both bomb tests and those produced by cosmic rays). Every CO2 molecule in the atmosphere is rather quickly absorbed either by photosynthesis or by the ocean. However on average most of them are simply replaced by another CO2 molecule entering the atmosphere through evaporation from the ocean surface or by biological respiration. The residence time however, is the e-folding time needed for a sudden net increase in CO2 to decay back to normal as the carbon cycle reacts. At equilibrium the total CO2 content of the atmosphere remains constant over centennial time scales. Currently though, as a result of our emissions, slightly more net CO2 molecules are being absorbed than are being returned to the atmosphere each year. As a consequence the atmosphere is not quite in equilibrium with the rest of ‘natural’ life and the oceans. We have given the carbon cycle a kick, and as a result it is reacting to return back into balance. The problem is that we have continued to kick a little harder each year so that balance is never reached.

If you sum up all the sources and sinks since 1960 then you find a remarkable fact, which was unexpected by climate scientists. About half of man-made emissions are being absorbed each year. This means that just one half of the net CO2 emitted by humans remains in the atmosphere each year. This is called the airborne fraction. The strange thing is that this airborne fraction hasn’t changed at all in 60 years, despite exponentially increasing human emissions.


AR4 plot: The fraction of Anthropogenic CO2 retained in the atmosphere (b) is unchanged in  50 years, despite increasing emissions (a). Note how the annual change stalled after the 70s oil crisis


Plot of Carbon content of air versus Cumulative Carbon emissions produced by Nick Stokes.

This means that today we are emitting about twice as much carbon dioxide as we did 30 years ago, yet still only half of it survives a full year. Or putting that another way, the equivalent of 100% of 1990 emissions are now absorbed each year. This ratio of 50% airborne fraction has been true for over 100 years while emissions have been forever increasing.


Comparison of Carbon emissions and that retained in the atmosphere. Increases in Emissions consistently remain about twice the levels of increases in CO2. Flat periods occur when growth stalls.

Natural carbon sinks are increasing dynamically to offset our emissions. The problem is that they don’t have enough time to catch up with the ever increasing rate of emission. The best they can do in a single year is offset half of them. Why is that the case and what does it really mean?

There is a ‘concentration effect’ acting on ocean sinks due to the increasing partial pressure of CO2 in the atmosphere.  Similarly land biota (plants and soil)  react to increased partial pressure by absorbing more CO2. While we are still increasing emissions then CO2 levels in the atmosphere will always continue to rise. If instead we can stabilise emissions at some fixed number of Gtons/year then CO2 levels would also stabilise, albeit at a slightly higher level than now and in the future. This is because the sinks will finally be able to catch up to balance our CO2 source.  The atmospheric faction will decay to zero.

Dissolution/Absorption of CO2 at  Ocean surfaces.

In stability there is a balance of CO2 Partial Pressures between the surface of the ocean and the atmosphere. At any given temperature the exchange of carbon dioxide molecules between the atmosphere and the ocean surface always reaches an equilibrium. This equilibrium is controlled by the partial pressure of CO2 in the atmosphere equalising to the partial pressure of CO2 in the surface of the ocean. Then the number of carbon dioxide molecules that escape from the sea surface is  balanced by the number that enter the sea from the atmosphere.

If the temperature of the ocean rises then the kinetic energy of the carbon dioxide molecules in the seawater increases and more carbon dioxide molecules will leave the ocean than would enter the ocean. This continues until the partial pressure of carbon dioxide in the atmosphere increases to balance the new pressure at the sea surface.

If instead the ocean were to cool then the reverse of the above would happen, and CO2 levels would fall. Consequently carbon dioxide is more soluble in cold water than in warm water. This is Henry’s law. One consequence of this effect is that the oceans “inhale” carbon dioxide from the atmosphere into cold sea surfaces at high latitudes and “exhale” it from warm sea surfaces at low latitudes.

Increasing the carbon dioxide concentration of the atmosphere therefore causes the oceans to take up (inhale) more carbon dioxide. Because the oceans surface layer mixes slowly with the deep ocean (hundreds of years) the increased carbon dioxide content of the surface ocean will be mixed very slowly into much larger carbon reservoir of the deep ocean. The rate of our adding carbon dioxide to the atmosphere has been too fast for the deep ocean yet to be a significant reservoir. So as the carbon dioxide content of the atmosphere rises, so too does the concentration in the ocean surface, causing short term acidification of surface waters. If  atmospheric carbon dioxide remains constant then a ph balance throughout the ocean volume can be reached.

I argue that by simply stabilising emissions, we can halt global warming because CO2 levels will stabilise as the sinks will then be able reach equilibrium with emissions. Clearly the lower total ‘stable’ emissions become then the cooler the planet will be, but even if we only managed to stabilise emissions at current values, then the net warming will still be <2C and CO2 levels will soon stop rising and stabilise at <440 ppm.

Atmospheric CO2 levels must always reach an equilibrium as the natural carbon sinks 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 increasingemissions each year, so the sinks never get a chance to catch up. Sinks will rather 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 before 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 in this context are an insignificant fraction when compared to  the buried carbon contained in sedimentary rocks.

Simple Model

CO2 levels rise when the rate of change of the sources – S exceeds the rate of change of sinks – K. Without human emissions  then S = K, averaged over one year. However with ever increasing human emissions the situation becomes dynamic

If C is the yearly value of CO2,  S  the net sources of CO2 and K the net sinks, then at time t.


However it has been measured for at least the last 60 years that

If   clip_image012   then   clip_image014

Now let’s assume that the world manages to stabilise annual emissions at current rates of 34 Gtons CO2/year  indefinitely.  CO2 sinks currently absorb roughly half of that figure – 17 Gtons and have been increasing proportional to the increase in partial pressure of CO2 in the atmosphere – currently that of 400ppm. Stabilising emissions now results in a decreasing fractional uptake by carbon sinks as the partial pressure imbalance between the surface and atmosphere begins to fall. The simplest assumption is that the sink increase depends only on the partial pressure difference for a given year. Therefore  if this pressure difference is reduced by half in one year then the next year it will be reduced by one quarter, then one eighth  and so on. The same argument applies for the case that it takes longer to reduce pressure difference by a half.

Year 1: 50%  Year 2: 25% Year 3: 12.5% Year 4: 6.25% etc. which is simply equal to the infinite sum


So in this simplest of models, CO2 levels in the atmosphere will  taper off after just ~10 years to reach a new long term value equivalent to adding an additional one year of emissions 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 in this simple model be just   1%. Therefore for the years following 2016 the resultant CO2 curve would look like the red curve below. If instead it takes say 4 years for the sinks to increase  by clip_image018 then we get the blue curve. In this case it would take 30 years for CO2 levels to to stabilise and the increase would be 5 times larger.


CO2 stabilisation curves for different time constants. The red curve assumes sinks match half the imbalance in 1 year while the blue matches it in 4 years.

Currently there is also a  good chance that the world will achieve a fixed level of annual emissions, but there is no chance that it will meet an impossible target of zero emissions this century. This  does mean that CO2 levels will remain at  ~410 ppm indefinitely, which is far higher than a planet without human beings, but it buys us time to replace fossil fuels with say new nuclear energy. If I am right then CO2 levels will begin to level off within the next 10-20  years. This would also save trillions of dollars by trying too soon now to replace all fossil fuels, and then probably failing.

Reducing emissions in the future will slowly cause such ‘stable’ CO2 levels to fall. In the long term we will have to develop non-carbon energy sources anyway, most likely nuclear, since fossil fuels must run short. However using remaining fossil fuels to control  CO2 levels may one day have another advantage. It could mean that we can eventually use ‘enhanced global warming’ as a thermostat, thereby avoiding another devastating ice age otherwise due to begin within the next 5000 years.

240 thoughts on “A Hiding to Nothing

  1. Clive..it’s late here…I want to read this again with coffee 🙂
    ..thank you!
    I have always wondered about this…when did the sinks stop working?

  2. Leaving aside the error of fact (“Reducing emissions in the future will slowly cause” — no causation has ever been proven), that is, there is no evidence proving that any meaningful effect on climate of human CO2 emissions is not completely superceded by/overwhelmed by natural CO2 emissions…..
    For all those who (like I) did not know what the British phrase “a hiding to nothing” meant:
    To be faced with a situation which is pointless, as a successful outcome is impossible. … One scenario would be that of a team which is expected to win easily but has the betting odds so strongly in its favour that no kudos or reward, that is, ‘nothing’ , would be gained from victory. The other is that of a weak contestant who is expected to be beaten, that is, get ‘a hiding’.
    The phrase is known from the early 20th century and originated as horse racing parlance. …

    (Source: http://www.phrases.org.uk/meanings/on-a-hiding-to-nothing.html )

    • Edit: “no evidence proving … OR that human CO2 emissions are any significant % of the current level of CO2 in the atmosphere — that is only a guess, an assumption, for natural sinks, two orders of magnitude greater than human CO2, could be absorbing ALL of the human CO2, making the net CO2 level all natural.

      • So far, I have seen no credible evidence that anthropegenic Carbon, in any chemical form, has any detectable effect on climate change – either warming or cooling. Lots of theories, lots of ‘models’ and ‘studies’ but no evidence of any causal relationship. Why there is any effort study the AMOUNT required to influence a change is certainly premature at best.

      • Janice – I hasd a fairly comprehensiveanswer but the dog ate the first partb of vmy answer. What remained was this:
        “The worst predictions are for the twenty-first century. What they have done is to aim the predicted temperatures (which they derive by averaging individual predictions by the hundreds) along the same trajectory that warming took place before 1980. Of course they did not know that nature would fool them and cause a slowdown of warming in the twenty-first century. They just produced a linear extension of trends before 1980 and ended up with a complete separation of model predictions and reality. Looking at a display of CMIPS-5 model predictions released this year it is obvious to even to a child that the predicted curve is way off reality, just floats up there. These data have even been shown at congressional hearings but I do not hear anyone stating publicly that climate modeling enterprise has completely failed in trying to forecast future warming and must be shut down.”
        iI will have to follow up with an article. Arno

      • Janice,
        As usual: you forget that human emissions are one-way additional and the natural emissions are only half of the natural cycle, the other half are natural sinks. With extra CO2 from humans, the natural sources, mainly from the oceans, are reduced and the natural sinks, both oceans and vegetation, expand. Without human emissions, there wouldn’t be an increase in the atmosphere, besides a small one due to temperature (~16 ppmv/K).
        90% of the current increase over pre-industrial is from human emissions, 10% from the temperature increase since the LIA. As there are huge exchanges with other reservoirs, not all human emissions (as original molecules) remain in the atmosphere but are distributed over all reservoirs. Currently about 9% of the atmosphere still are from human emissions, as can be deduced from the 13C/12C ratio.
        More detailed information:

      • Without human emissions, there wouldn’t be an increase in the atmosphere
        nonsense. temperatures have been increasing since the bottom of the LIA 250 years ago. It is well established from the ice cores that temperatures rise, CO2 increases.
        As to the magnitude of change, there is no historical proxy with the resolution of current measurements, so there is no way to gauge if current levels are exceptional. There is conjecture, to be sure, but humans have an infinite ability to rationalize anything, so good science requires conjecture be treated with a large dose of salt.

      • ferdberple,
        I have mentioned the effect of temperature on CO2 levels: 16 ppmv/K that is all. If we may assume that the MWP was at least as warm as today, the levels were 285 ppmv, 400 ppmv today.
        If you agree that ice core CO2 levels (directly measured) follow temperature levels (proxy), then the recent ice core CO2 levels (1850-1980) by far lead temperature changes:
        Different ice cores have different resolution, but over the past 1,000 years the resolution of the Law Dome DSS core is better than 20 years, with a repeatability of the samples at the same depth of better than 1.2 ppmv. Good enough to detect any one-year 40 ppmv spike or a sustained 2 ppmv increase over a period of 20 years.
        Even the worst resolution ice cores (Vostok, Dome C) would detect the current 110 ppmv increase over 160 years, over the full period of 800,000 years, be it with a lower amplitude…

      • Ferdinand Engelbeen @ December 16, 2016 at 1:12 am
        “…you forget that human emissions are one-way additional…”
        No. They are not. They induce sink activity. That induced sink activity is anthropogenic sink activity. It is two-way.

      • Bart,
        The sink activity is in ratio to the total pressure of CO2 in the atmosphere above steady state, not from human emissions of one year. If humans had emitted 4.5 ppmv/year CO2 in 1850, almost all of that would have remained in the atmosphere, as the CO2 pressure in the atmosphere increased from ~280 ppmv to 284.5 ppmv, 4.5 ppmv above equilibrium. That gives a linear net sink rate of ~0.09 ppmv, about 4.4 ppmv of human emissions remaining in the atmosphere…
        In the current circumstances only half the human emissions as mass (not the original molecules) are removed and half the mass remains in the atmosphere. That is the case for at least the past 57 years. Thus all increase (except a small part by temperature) is from human emissions and indeed most of the unbalance between source and sink rate is caused by the accumulation of the difference between human emissions and increasing sink rate…
        Compared to the (mainly temperature induced) natural fluxes still small: some 3% extra sink rate after 165 years for currently 6% of the influx… Still most of the incease is from human emissions…

      • Clive Best:
        I have followed your blog on the atmospheric carbon balance. Her is what I know, and if I can e-mail you, I can go into more detail?
        1. The capacity of the ocean to hold CO2 in a physical-chemical-inorganic form is vast. The ocean holds 50 times as much CO2 this way as the atmosphere. To the extent that the atmosphere and ocean are presumed to have at least started the 20th century in near equilibrium, the amount of CO2 in a reservoir is in proportion to the size of that reservoir.
        2. The bulk of the CO2 “dissolved” in ocean water is not in the aqueous fraction subject to Henry’s law. The aqueous fraction is in a Henry’s law relationship with CO2 in the air, but the aqueous fraction is also in chemical equilibrium with the “soluble carbonates” through a chain of fast-acting chemical reactions. This is on account of ocean water not being pure water but rather a “chemical soup.”
        3. The equilibrium of concentrations of a chemical, CO2 in this case, between different chemical species in the carbonate reaction does not follow a linear Henry’s law relation. Instead, it follows a power law relation owing to the number of molecules of different types that have to come in contact to make the reaction happen. Owing to the complicated chain of chemical reactions in the carbonate system, this follows a 10th power relationship, where this exponent of 10 is the value of the “Revelle factor”, named after ocean scientist Roger Revelle. The way the chemicals in ocean water interact in reactions to give this factor is the “Revelle buffer.”
        4. The consequence of the Revelle buffer and the Revelle factor exponent is that a 1 percent increase in the atmospheric CO2 concentration, same as partial pressure that drives the exchange, results in only about a 1/10 or .1 percent increase in concentration in ocean water. But the ocean reservoir is 50 times the size of the atmospheric one. Taking the Revelle factor of 10 into account, adding 6 measures of CO2 to the atmosphere will result in only 1 measure retained in the atmosphere and 50/10 = 5 measures of CO2 ending up in the ocean. This was the conclusion of Revelle and Suess (1957) Tellus IX Vol 1 pp 18-27.
        5. Since that paper, it is regarded that the ocean is not well-mixed but rather divided into a surface layer that exchanges CO2 rapidly with the atmosphere and of similar CO2 capacity as the atmosphere, and a deep ocean layer with an “exchange time” of 500 to 1000 years. Assuming that the anthropogenic part is the sole perturbation of the carbon cycle out of equilibrium, as you say, half the emitted CO2 stays in the atmosphere and half is absorbed by “sinks.” Recent, accurate measures of the atmospheric oxygen content indicate that of the net flow into sinks (does not account for large back-and-forth exchanges), half of the sink is in an inorganic form, such as the ocean soluble carbonates, and the other half is in organic form, such as land plants.
        6. My own modeling suggests that in a quasi-static model (no natural disturbances from equilibrium), the rate coefficient for CO2 between the atmosphere and the surface ocean is about the same for exchange between the surface and deep ocean. The “500 to 1000 year deep ocean turnover” comes from the deep ocean being so vast that it would take 500 to 1000 years to fill it up to the level by which the atmospheric CO2 has increased, not that the deep ocean acts on a time scale too long to sequester CO2 from the atmosphere during a human lifetime.
        7. Taking into account the Revelle buffer mechanism that prevents increased CO2 in the air from being swallowed up in the ocean, setting the rate coefficient for exchange between surface and deep ocean to a value that matches the ocean/land sink split from the oxygen concentration data, setting the absorption of CO2 by land plants proportional to CO2 concentration, and setting a constant release of CO2 from decaying vegetation, my model can match the 20th century rise in atmospheric CO2 from 290 PPM to short of 400 PPM, but it also matches the measured curves for C13 concentration over time, C14 radiocarbon ages for surface and deep ocean, and the “bomb test” extinction curves for C14 in the atmosphere. I also come up with an “e-folding time” for extinction of bulk CO2 added to the atmosphere somewhere in the 40-50 year range, considerably less than the IPCC Bern Model based on curve fitting, and close to what our esteemed friend Ferdinand Englebeen in claiming?
        8. There is strong evidence that the apart from the human CO2 contribution, the carbon cycle is not quasi-static. The “net emission of CO2 into the atmosphere”, by mass conservation, is simply proportional to the slope of the Keeling curve of atmospheric CO2. Not only does net emission have a strong seasonal variation, it has a year-by-year variation that is of comparable in magnitude to the anthropogenic contribution. This variable portion of net emission is highly correlated with global temperature — the Wood for Trees web site allows displaying the time series showing this.
        9. Changing my model to make the emission of CO2 from dead plants sensitive enough to temperature to match the variation in net emission, and increasing the sensitivity of plant uptake of CO2 to CO2 concentration to match the long-term Keeling curve trend from 290 to about 400 PPM, I find that only half of the increase in atmospheric CO2 is from human activity with the other half being from this temperature-stimulated emission from this natural source, which has emitted more CO2 as global temperature has increased in the 20th century. This change also reduces the e-folding extinction time for anthropogenic CO2 to about 20 years.
        10. The temperature sensitivity for natural CO2 emission required to match the model to known data is comparable to the temperature-driven emission from soils recently claimed by Bond-Lamberty and Thomson, Nature, 2010.
        11. The modified model to account for temperature-stimulated CO2 emissions from soils gives a somewhat better fit to the C13 curves, but I am still working on plausible turnover times and reservoir capacity of soil carbon to properly treat its carbon isotope fractionation and hence modification of the atmospheric values.
        12. Fellow commenter “Bartemis” has critiqued this effort for not taking into account ocean-current driven turnover of deep ocean waters along with current-induced temperature changes affecting CO2 absorption or emission.
        In challenging the consensus view of the carbon cycle, we need to take the known ocean chemistry into account, and we need to not only explain the change in atmospheric CO2 on the different time scales, we need to predict the isotope ratios too. I believe I am making progress in that direction, and I am interested in sharing more of what I have found out with interested parties.

      • Paul –
        You say: “This variable portion of net emission is highly correlated with global temperature…”
        But, it isn’t just the variability of the rate of net emission that matches temperature. The long term trend matches as well, when the data are scaled such that the variability matches:
        This is too much of a coincidence to be mere happenstance. It shows beyond any reasonable doubt that temperature anomaly is the overwhelming driver of the rate of change of atmospheric CO2, and hence the overall change in concentration. The match with the more accurate (but shorter term) satellite data is nothing short of spectacular:
        There is a lot of excellent information in what you write. But, in the end, the theory must follow the data.
        It seems, especially to people living in big cities, that we just must be having an impact on CO2 levels. But, the sum total proportion of urban area on the globe’s land mass is at most a mere 2.7%. We’re just not as big a deal to the globe as we imagine we are.

      • Paul Milenkovic,
        We largely agree with what you wrote, with a few exceptions:
        4. The Revelle factor is only important for the mixed layer, it hardly plays a role in the deep ocean mix. What goes down with the THC is far from saturated and once in the deep, it doesn’t matter how much it gets C enriched by the drop out of organics and inorganics from dead plankton (coccoliths) and other debris from the surface layer. The pCO2 difference at the main sink place (N.E. Atlantic) is ~150 μatm, where the ~250 μatm of the ocean surface remains about the same over time, as that is only temperature (and biolife) dependent and is continuously refreshed with new incoming waters from the upwelling near the equator.
        That makes that the exchange with the deep oceans gets a mass distribution of 1:50 at equilibrium, largely independent of the Revelle factor. After a few centuries all the CO2 released by humans would be distributed over (deep) oceans and atmosphere and the 400 GtC extra gives about 1% increase in C content of both atmosphere and deep oceans.
        9. The problem with the CO2 releases from the soils is that it has a huge initial response to an increase in temperature, but a limited capacity over time: maintaining the same temperature gives a rapid decline in extra release, due to a lack of “fuel” from fallen leaves and debris. That is mainly in the tropical forests. See Pieter Tans from slide 11 on:
        Once the temperature drops, photosynthesis takes over and during a La Niña (and Pinatubo) we see minimum increase rates of CO2. The net result is that the fast variations zero out after 1-3 years and that over longer time spans the biopshere is a net sink, thus not the cause of the CO2 increase. That biolife is dominant can be seen in the opposite CO2 and δ13C changes.
        The main cause of the δ13C drop is human emissions at average -24 per mil. As vegetation is a small net sink (thus including soil releases!) for CO2 and preferentially 12CO2, that increases the per mil of the atmosphere. The same for the ocean continuous CO2 flux between upwelling and THC sink.
        The upwelling waters show a shift of about -10 per mil in δ13C at the water-air border, while the sinks give a shift of +2 per mil, average -8 per mil over ocean δ13C. While most is from deep ocean upwelling at 0 to +1 per mil, biolife gives 1-5 per mil in the surface waters.
        The long term equilibrium over the whole Holocene was -6.4 +/- 0.2 per mil, probably largely caused by the ocean exchanges…
        Based both on the 14C bomb spike decay and the “dilution” of the human δ13C “fingerprint”, the continuous CO2 flux from the equator to the poles is estimated around 40 GtC/year…

      • Bart,
        As said before, near all variability in CO2 rate of change is mainly the effect of temperature on tropical vegetation. That effect levels of to below zero after 1-3 years: all biolife together is a small, but increasing sink for CO2. Thus the variability has a negative effect on the slope and is certainly not the cause of the increase of CO2 in the atmosphere.
        Then we have two possibilities left: human emissions which have double the slope of the measured increase rate slope or the temperature effect on the oceans surface (including upwelling and downwelling). which also has a limited effect. The latter not more than 16 ppmv/K for a constant upwelling. The former more than enough to explain the full increase for every year in the past 57 years and over the full period since 1850.
        There is zero evidence that temperature is the cause of the slope in the CO2 rate of change, all observations point to human emissions…

    • “A hiding to nothing”
      A ‘hiding” means “a beating”. (Students need a good “hiding” now and then to sustain their character.) In horse racing it meant whipping your horse to make him run faster. (Which came first, beating the horse or beating the student, I don’t know.) Carpets, once a year, were hung on a line and given a good hiding to knock the dust out.
      (For comparison the term “boxing his ears” [giving someone a good “boxing”] is another old time term.)
      In the past “a hiding to nothing” basically meant “frantic actions having no effect on outcome”. An example would be a last place horse being beaten by its rider.
      In our more modern times, In the few times I have seen it used, it has been used “post facto”. For instance in its generalized usage the Clinton campaign spending well over 600 million dollars could be called “a hiding to nothing” — though during the campaign it was thought that level of spending would guarantee a Clinton win. (The same certainly could be said for Jeb Bush’s spending well over 100 million dollars to win just four electors during the nomination process. The Clinton campaign saw Jeb’s absolute failure and they DIDN’T GET THE MESSAGE!! Trump did.).
      A “hiding” once had common usage but the meaning of the word has faded from our minds.
      That the English now use the phrase to mean “a frantic effort put forth when no gain can be expected” must have come about from their experiences with the fanaticism of Socialists. In that sense such fanaticism is certainly “a hiding to nothing”.
      Eugene WR Gallun

    • In South Africa ‘a hiding’ is a beating. To get or be on a ‘hiding for nothing’ (similar words) means to take or get punishment for no gain or effect, i.e. pointless pain.

      • I always felt it meant get a beating or a whipping – and still end up nowhere like a bad horse in a race.
        I.e the worst of all possible worlds. All pain and no gain.

      • Because the oceans surface layer mixes slowly with the deep ocean (hundreds of years) the increased carbon dioxide content of the surface ocean will be mixed very slowly into much larger carbon reservoir of the deep ocean.

        Oh, I thought it was Mickey Mann’s latest excuse for truncating Briffa’s tree-ring proxy: you’re on a hiding to nothing because there’s nothing to hide.
        Nice word play.

      • “Because the oceans surface layer mixes slowly with the deep ocean (hundreds of years) the increased carbon dioxide content of the surface ocean will be mixed very slowly into much larger carbon reservoir of the deep ocean.”

        You have to remember that Trenberth et. clique. allows heat to be suddenly mixed into the deep ocean much faster than the models previously allowed for, but that carbon dioxide, for some strange reason, apparently doesn’t have to follow the same laws of mass action.
        They are all at sea.

    • Bart:
      I am not saying I’m right and you are wrong. I am advancing my “temperature-stimulated natural CO2 emission on land, only” model as an alternative scenario to the “CO2 consensus” where there is no natural source and the large fluctuations in net emission are unexplained.
      In analogy to being a “luke Warmer”, my “luke CO2 increase” model has the effect that the correlation between global temperature change and net CO2 emission is a physical effect at short times, and yes, it would be a remarkable coincidence at longer times, based on the 20th century ramp-up in industrial activity just happening to be coinciding in a time when it was naturally getting warmer.
      Yes, I need to learn more about the thermohaline ocean circulation and ocean temperature effects on CO2 emission, but I haven’t gotten that far. Think of my model, “let’s not invoke ocean effects because of uncertainty in modeling them, as of right now, let’s see how far we get with a land source for the temperature-correlated emission.”
      4. There are two effects — one is a rate coefficient for CO2 exchange in response to concentration difference between reservoirs, the other is the non-linear Revelle buffer effect giving a non-linear rate coefficient. I have rate coefficients both at the air-surface ocean and surface-ocean deep ocean interfaces, but I only have the non-linear Revelle buffer effect between air and surface ocean.
      Yes, I have rate coefficient segregating surface from deep ocean (this has nothing to do with the fall of organic detritus from surface ocean through deep ocean to the bottom — this detritus in organic matter, and if it doesn’t rot in the cold, deep ocean water, it is an additional source of CO2 sequestration that I can add to my model, but it isn’t the carbonate system that I treating differently from organic uptake, whether on land or sea). This rate coefficient is a “knob” to get the known partition between CO2 uptake from inorganic (ocean carbonates) and organic(plant life, wherever it happens). This partition is known from the recent chemical analytical techniques to get a “Keeling curve” for atmospheric oxygen.
      9. A reservoir and a rate coefficient — an electric capacitor fed by a resistor — and result in a broadening of an effect (increased CO2 emission from decay) from a cause (increased temperature). The smaller the reservoir (you are claiming a small reservoir), the less broadening. But I don’t see a way to switch the resistor and the capacitor to get a sharpening of the response — this would require stimulation of CO2 emission by the rate of temperature change, and there is no plausible physical mechanisms for it in this system.

  3. Something of a “lukewarmer” article, as the author buys into many warmist assumptions. It does probably describe the real-world worst defensible case for CO2 and climate, as many of his premises, like the sensitivity number for CO2 doubling, are probably too high.

    • Agreed. I think with proper water based negative feedback, the climate sensitivity is probably under 0.5C.
      Which makes CO2 levels of only academic interest, temperature wise.
      The effects on plant growth especially in marginal rainfall regions is far more interesting, and that my in the end suck out CO2 anyway.

  4. “this does mean that CO2 levels will remain at ~410 ppm indefinitely, which is far higher than a planet without human beings” excuse me ? we have had CO2 levels well above 410 ppm when human beings didn’t exist on THIS planet … very odd claim …

    • It means that he thinks the climate during last couple of hundred years is the normal climate of the Earth. I.e. he has no knowledge of Earth history. Many people have similar difficulty visualizing time scales longer than a few human generations. Climate scientists all have this failing (and if they did, e.g. Mike Mann, get an education in geology, they have deliberately set out to forget it). How many people you know understand that we are in (an interglacial period within) an ice age? Most of them probably think that there was an ice age in the distant past and that it’s over and done with.

      • And Naomi Oreskes too. She actually did some decent research on the Olympic Dam iron-copper-gold-uranium-lanthanum mine in South Australia before getting the alarmist virus.

  5. Yup. And if sensitivity is around 1.5 we’ve got even longer to not worry. Perhaps a little time to enjoy the minimal warming and miraculous fertilizing we’re doing.

  6. Why 440ppm why not 800 ppm. Plants would love it. If, sometime in the future,, we go into another ice age or cold period more types of plant may survive longer.

    • Greenhouses that use propane to heat, can by a kit to capture fuel emissions to raise the CO2 rate to 1000ppm within the greenhouse. The plants love it and grow faster. Only people who never have farmed want to de-carbonize the world.

  7. “The strange thing is that this airborne fraction hasn’t changed at all in 60 years, despite exponentially increasing human emissions.”
    I don’t think it’s strange. Here I show why I think it is a mathematical consequence of exponential growth. And would diminish with slower growth, but not, I think, to zero.

    • The planet is greening.

      Every year, about half of the 10 billion tons of carbon emitted into the atmosphere from human activities remains temporarily stored, in about equal parts, in the oceans and plants. “While our study did not address the connection between greening and carbon storage in plants, other studies have reported an increasing carbon sink on land since the 1980s, which is entirely consistent with the idea of a greening Earth,” said co-author Shilong Piao of the College of Urban and Environmental Sciences at Peking University. link

      Do you think the extra sink due to greening would be enough to get to zero?

      • Bob,
        “Do you think the extra sink due to greening would be enough to get to zero?”
        Nt enough capacity. Above ground biomass is about 500 Gtons C. We have dug up and burnt about 400 Gtons C already. Biomass (mainly trees) is limited by availability of water and sunlight, usually not CO2. So it is a limited sink.

      • Commiebob,
        The main long-term sinks are the deep oceans, but these have a limited exchange with the atmosphere (~40 GtC/year) and a limited unbalance due to the increased CO2 pressure in the atmosphere (~3 GtC/year more sink than source). Over long time spans deep oceans and atmosphere would get in equilibrium (half life time ~35 years). If we stop all emissions today, that would mean that the 400 GtC emitted up to now, would be redistributed into the ~36,000 GtC in the deep oceans, leaving just over 1% or ~3 ppmv extra in the atmosphere.
        With constant emissions, there still would be an increase until sinks and emissions are in equilibrium, while the acceptance of extra CO2 in the deep oceans still is near unlimited and only increases with a few % over centuries…
        The uptake by vegetation is huge, but mainly bidirectional (leaves, small stens). The more permanent uptake in peat, (brown)coal,… is near unlimited, but much slower over longer periods compared to the deep oceans.

      • The rate of greening can actually increase. Higher CO2 concentration means plants do not need to keep stomata open for as long to get the CO2 they need to grow. Therefore plants can respire less, so lose less water to the atmosphere. So plants in arid areas can grow using less water. Making plant growth in arid regions better than a linear projection.

      • Ocean phytoplankton are already responding to increased pCO2. The limiting factor for their growth is mostly iron and phosphate. They sequester CO2 into their carbonate skeletons that sink to the ocean floor.

      • Ferdinand,
        You said, “Over long time spans deep oceans and atmosphere would get in equilibrium (half life time ~35 years).” I think that you are overlooking the role of biology in adding to the CO2 of the deep oceans. Also, the warmer, low-pressure surface waters would potentially saturate with CO2 long before they reached the concentration of CO2 in the deep, cold waters.

      • Nick Stokes (at 10:51pm),
        “Biomass (mainly trees) is limited by availability of water and sunlight, usually not CO2. So it is a limited sink.”
        This is an incorrect statement. At a given CO2 level biomass production may be limited by water and sunlight, but the biomass production at a given water and sunlight level increases with increase of CO2. In addition an increase in CO2 reduces the water requirement while at the same time increases biomass production.

      • Nick says, “Biomass (mainly trees) is limited by availability of water and sunlight, usually not CO2.”
        I don’t think that this is true. The main limit on plant growth is availability of CO2. Until the industrial revolution released large amounts of CO2 that had been, until then, captured in coal deposits, the plants were starving for lack of CO2.

      • “The main limit on plant growth is availability of CO2.”
        You can see that can’t be true if you just look at an area like Congo. Some of it gets plentiful water, and has dense forest. All on 400 ppm CO2, but was still true with 280 ppm. Then as you go north, the rainfall diminishes, and so does the forest. Same CO2. Water is the limit. Then Sahel, then desert.
        Plants with adequate water have as much CO2 as they want, by opening stomata. Under water stress, they have to part close them to conserve water, which then limits CO2. Higher ppm can help there, but it is a restricted regime. With further stress, the stomata close completely, and the plant struggles, with or without CO2.
        And CO2 does nothing to help with lack of sunlight.

      • Above ground biomass is about 500 Gtons C. We have dug up and burnt about 400 Gtons C already. Biomass (mainly trees) is limited by availability of water and sunlight, usually not CO2. So it is a limited sink.

        Not usually, but there are vast stretches of area that might benefit.
        And yet, you’ve been told that one of the effect of CO2 is warming, which will ultimately put more water vapor in the air. More water vapor = more opportunity for water for plants. Example: greening of the deserts.
        More plants = more CO2 sinks, which could very well be a natural break on the run-away warming scenario that the models show, as they assume the sinks are static.

    • Nick,
      You explain why the exponential growth of annual emission has forced the airborne fraction to be stable, but you don’t explain why it is 0.5. This is one of two mysteries which no-one as far as I am aware has ever explained. The other one is
      Why is the natural CO2 atmospheric concentration 280ppm (why not 600ppm or 200ppm) ?
      (I have a theory as to why it is exactly 280ppm)

      • No theory is needed. Start with the ‘observation’ of ~ constant 280ppm preindustrial. Now that must be a rough equilibrium value. There are two sinks and one source. The first sink is biological (some biomass, but long term mostly marine calcification (limestone is a massive carbon sink). That has some sink ‘productivity’ in equilibrium with 280ppm. (For example we know that calcifying coccolithphores have increased 10 fold in the North Atlanric over the past 30 years as CO2 ppm has increased.) The second sink is the physical chemistry of Henry’s Law acting on the oceans via the mixed layer. Thatnis proven bynthe ~800 year lag of CO2 behind temp seen in the ice cores, the lag nicely matching one overturning of the thermohaline circulation. Neither the area of the mixed layer nor its global temperature has changed very much in the Holocene, ego ocean dissolved CO2 equilibrium at 280ppm. The primary souce of CO2 is subduction zone decomposition of carbonates with associated volcanic venting of regenerated CO2. Plate techtonics changes very slowly, and we know volcanism is roughly constant (about 60 eruptions per year, and over the past hundred years a roughly constant distribution of VEI). So 280ppm is simply the number at which the marine calcification ‘permanent’ sink happens to equal the volcanism ‘permanent’ source during a blink of geological time like the Holocene.
        Of course, none of this holds on geological time scales.

    • Nick : “I don’t think it’s strange. Here I show why ”
      Very nice derivation of the constancy of AF under a constant exp growth. Simple and elegant.
      Panel b) in the second IPCC graph does seem to back up this relationship in that AF is less during the temporary reductions in emissiosn, although the rather clunky 5y averages makes it a little less easy to see.

  8. Sorry, Clive. Your math is likely wrong. I might get up the energy to prove mathematicaly why tomorrow. You can figure it out from your comment simple model.

    • Clive and Ristvan,
      Too long ago for me to make the right calculation…
      My rough estimate is that with the current emissions twice the current sink rate at ~110 ppmv above steady state, one need ~220 ppmv above steady state to get rid of the full ~4.3 ppmv/year human emissions. That is a level of 510 ppmv, far above the 440 ppmv of Clive…
      The observed e-fold decay rate of the extra CO2 in the atmosphere is around 51 years, surprisingly linear over the past 57 years. No reduction in sink rate to see…

      • Thanks Ferdinand,

        My rough estimate is that with the current emissions twice the current sink rate at ~110 ppmv above steady state, one need ~220 ppmv above steady state to get rid of the full ~4.3 ppmv/year human emissions. That is a level of 510 ppmv, far above the 440 ppmv of Clive…

        I am sure my model is far too simplistic, but what is more important is that you also agree that CO2 levels will stabilise once emissions are held constant. This is the key message that needs to be got out there !

      • The natural absorption rate has been 1.8% of the “excess” CO2 in the atmosphere since about 1950.
        If CO2 levels keep rising, the natural absorption rate will continue increasing at 1.8% of the excess above 280 ppm.
        If we can limit our emission, eventually the natural absorption rate will catch up.
        But when you run the numbers, this won’t happen for many decades out.
        The point is you need to model the natural absorption rate and how that varies with the levels of CO2 in the atmosphere.
        Some have asked when the natural absorbers of oceans, vegetation and soils will run out of capacity? In the history of Earth, the natural absorbers have shown unlimited ability to bury Carbon. During the Carboniferous, vegetation buried 10,000 billion tons of Carbon over 60 million years. At.24 million years ago, the newly evolved C4 grasses dropped the equilibrium CO2 level from 1,200 ppm to 280 ppm. That is a lot of capacity and will dwarf any number we can add.
        The only real limit is now 280 ppm in an interglacial and 185 ppm in a deep ice age. Oceans and plants will go on being a net absorber until CO2 gets down to these levels. This appears to be net natural equilibrium level in today’s vegetation biome and ocean arrangement.

    • Clive, I was wrong. My more complex model roughly reduced to yours when I worked it over today. The more complex model was created to check Salby, who is way off base in several ways. Your 0.5 is a good enough approximation; last night I suspected it wasn’t over sufficiently large delta PPM. My intuition last night was just off. And, as you point out, constant emissions must eventully equilibrate S to K so long as K doesn’t saturate. All the available evidence says it doesn’t, rather ocean calcification just increases. Theoretically this eventually could become micronutrient limited (iron) as in ‘barren oceans’. But that appears experimentally overcome by species substitution.

  9. I think this is a good study to understand the carbon sinks and how to obtain an equilibrium. This is good knowledge to have to add to the understanding of how our world works.

  10. Is it even possible to get to a 700-800 ppm doubling given that the cost of recoverable carbon will eventually rise and we might even come to our senses and discover thorium reactors.

    • David T
      No, it is impossible with the known reserves and the time it would take to extract and burn them, plus 100% more. 800 ppm is not achievable by 2200.

  11. I will argue below that in order to stop global warming …
    Perhaps you should include a nod to CO₂ in this.
    Insofar as Earth appears to be capable of warming or cooling without help from humans it is astonishing to think of stopping either. Whatever warming human-added CO₂ is causing may be slowed or stopped. I think that is what you intended to mean.

  12. If we only knew the optimal CO2 atm concentration, we would have a target to maintain. I have never heard scientific evidence as to the ideal ppm level. Without a target, there cannot be a plan. I can only suggest 600 – 800 ppm will be closer to optimum then the near starvation current levels, but that has yet to be studied. I really don’t understand the conversation until we know. GK

  13. This sounds like the radical idea that the federal budget could be balanced by increasing natural growth in the economy if the federal spending were simply held constant.

  14. First I’d like to see proof that CO2 from burning fossil fuels is actually causing global temperature to rise before doing anything to mitigate it. If we can prove CO2 causes temperature to increase then we’d know by how much and whether or not stopping it is worthwhile. Forget the defense of AGW. Concentrate on the proof. If any.

  15. The problem is even less than he says. As the IR from CO2 sent downward is from -17 deg C air and the land surface is 15 deg C, there is no way that the former can warm the latter. Simple thermodynamics indicates that a cold tropical upper troposphere cannot warm the Earth’s surface. They also ignore that most of this region’s downwelling IR would be into the oceans and have little effect.
    The bottom line is that a trace gas of any kind cannot drive Earth’s climate. Water vapor vastly overwhelms CO2 and CO2 is not a slave master of water vapor. To think that a trace gas drives the water vapor levels is sheer stupidity. Water vapor rules and humans are not altering water vapor. CO2 is a minuscule actor at most and undetectable in effect. Methane and Nix are much too short-lived like CO2 to have any lasting effect.
    The author started out dissing the idea of decarbonizing and then said we should stabilize our carbonizing. Darn, he missed the target. We should completely ignore our carbon usage as all it does if green the planet and increase the food supply. It is true that the globalists do not want a burgeoning food supply as their goals include a 95% decrease in the human population. That’s another reason that they push the decarbonizing meme.

    • The surface will be warmer facing a -17 C layer of greenhouse gases than if it faces -270 K deep space. Thermodynamics only says that net flow of thermal radiation be from warmer to colder.

      • yes. we don’t radiate as MUCH towards cold clouds as sub zero space.
        Desert nights are chillier than tropical nights…

      • Donald L. Klipstein December 15, 2016 at 8:29 pm
        You wrote:
        “The surface will be warmer facing a -17 C layer of greenhouse gases than if it faces -270 K deep space. Thermodynamics only says that net flow of thermal radiation be from warmer to colder.”
        Thank you for this concise and exact statement for refuting the assumption that downweliig radiation from GHGs have no effect on earths temperature.
        GHGs actually are slowing down the cooling, that’s all.

      • Herbst,
        You said, “GHGs actually are slowing down the cooling, that’s all.”
        I don’t think that anyone other than a few extremists have claimed otherwise.

      • Desert nights are chillier than tropical nights…Bingo we have a winner. Likewise Desert have a higher daytime temp than “tropical” type areas along the same longitude. REF: Tucson, Arizona compared to Shreveport, Louisiana

    • Higley7,
      If the globalists want to decrease population, why are they bringing people that breed like flies into the rich economies, where they can breed even faster and in more places?

    • “Water vapor rules and humans are not altering water vapor.”
      With increasing urban lawn watering and rural agricultural irrigation, humans certainly are not decreasing water vapor in the atmosphere.

      • NOAA,
        You left out golf courses, especially in Phoenix and Las Vegas. But numerous reservoirs also provide for more evaporation than what would take place without the rivers being dammed. Also, one of the byproducts of combustion is water, even pure hydrogen.

  16. “I argue that by simply stabilising emissions, we can halt global warming because CO2 levels will stabilise as the sinks will then be able reach equilibrium with emissions”
    As a matter of maths, this just isn’t true. Suppose the sea was infinitely deep, and CO2 diffuses in subject to the ordinary diffusion equation. Initial concentration uniform, and constant influx of CO2 commence at time zero. Boundary (sea surface) pCO2 rises as sqrt(t). (For proof see case 2(d) here and set z=0). It never reaches a stable level. Yet the sea is an infinite sink.
    That is s simplification, of course, but there is no reason to suppose the real situation is more favorable. If CO2 in air is to be stable, with constant emissions, the flux will have to match the emissions.

    • Don’t see relevance there, your reference would be true if the ocean were the only sink and unbuffered. The article deals with the observation that half the extra CO2 is taken up in the first year and proposes that this is adaptation of carbon sinks to the CO2 partial pressure that the CO2 is fixed into carbohydrates or calcium carbonate. In the second year Half the remaining half is taken up, so the Biosphere would grow to be capable of consuming 3/4 of the human emission each year, then 87.5 in the 3rd year. By Year 5 if emissions were held stable the Biosphere would adapt to take up over 95% of emissions. I contend however that in this process, the biosphere will overshoot the equilibrium level and would in fact draw down sufficient CO2 to reduce the CO2 partial pressure if emissions were held constant.

      • “if the ocean were the only sink and unbuffered”
        The ocean is the only plausible near-infinite sink. The amount of carbon we have already burnt is comparable to biomass; that can’t keep doubling.
        Buffering only acts to change the diffusivity, but not the euation.
        There is ageneral principle that as sinks fill up, the next lot are less accessible. That is what is really behind the sqrt(t) dependence.

      • Nick, the ocean is governed by Henry’s law while the biological processes are not. Biological processes drew down CO2 from very high levels to fractional percentages over the history of the earth.
        The amount of carbon we have already burnt is comparable to biomass;
        It doesn’t work like that because you have ignored TIME, how does emission compare with all growth produced over the time we have emitted CO2? Most of that biomass cycles carbon in it’s growth processes. Particularly remembering the bulk of the weight 32/44 ths of the related CO2 is released as Oxygen back into the atmosphere. The Carbon component of consumption is well less than total biomass.

      • Nick, is eddy diffusion a sufficient model?
        CO2 is absorbed by warmer water cooling. This means we need to be looking at the thermo-haline circulation and the absorbed CO2 being taken down to depths in the Arctic Ocean by ocean currents , not diffusive processes.
        Once in the abyssal depths some of it will form calthrates and not resurface.

    • That’s correct Nick. One of the problems with the language here is that we are dealing with differentials. When we talk about emissions we are really mean emissions/year or DE/DT. When we refer to sinks here we mean the net flow rate out of the atmosphere per year DS/DT
      If DS/DT = DE/DT then annual CO2 levels in the atmosphere would be constant. However mankind has been constantly accelerating emissions. During this entire period of exponentially increasing emissions i.e DE^2/DT^2 > 0 the airborne fraction has been ~0.5 so DS/DT = 0.5 DE/DT. If we now continue indefinitely with DE^2/DT^2 = 0 then will slowly increase i.e DS/DT = 0.7 DE/DT…..DS/DT = 0.8 DE/DT and reach unity.

      • “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.

      • 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.

    • 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 μatm, hardly influenced by temperature or saturation over time…

      • Ferdinand,
        Yes, assuming uniform diffusivity is obviously wrong. But the problem is, the deviation goes the wrong way. Diffusivity decreases with depth. So new CO2 entering the sea not only has less concentration gradient to help it along, but resistance to flow gets worse.

      • Ferdinand,
        I didn’t really engage with the advective aspect of these currents. It depends on their capacity. But I don’t think they fit with the simple half-life model any better than with diffusion.

      • Nick,
        Indeed it is difficult to know how well mixed the deep oceans are over time, but looking at the distribution of oxygen, which is only coming from mixing with the surface and looking at the disribution of traces of recently introduced chemicals (14C, CFC’s,…) there is more mixing than was expected.
        Until now it is not possible to make a differentiation between the linear model and the IPCC’s Bern model (which expects saturation of the deep oceans and vegetation), because there still is little difference between the two results. Time will tell us…

  17. I have been arguing this for a while, and also that the fact that only half the CO2 rise survives a year, trivially means the half-life is 1 year!
    I think you are wrong though, when you have a perturbation in a system the rate rises in the system dependent on the difference between the driving force and the no-growth equilibrium level. As CO2 partial pressure grows the biosphere grows to meet it but the acceleration in the rate of emission means that the CO2 level must BE ABOVE the equilibrium. If we were to immediately stop increasing CO2, the CO2 Level WOULD FALL to the equilibrium level as the biosphere adapts, and takes up the difference between current CO2 and the equilibrium.
    You only need to know that the biosphere is EXPANDING to know that CO2 is above equilibrium level.

    • That is another possibility. The sinks could well overshoot unity for a short while before the system relaxes to a slightly lower CO2 level. It would be far higher though than zero emissions. However a stable atmosphere is the priority.

      • “A stable atmosphere is the priority”
        So your solution is to make emissions stable, because your assumptions is that optimal CO2 levels are 280 ppm. You are wrong, Clive. And you seem to be under the warmist assumption that CO2 regulates temperature.
        Aside from the brouhaha, your solutions really don’t strike me as any different from James Hansen’s.

    • Bobl,
      Your half life time is a little too short…
      The sink rate doesn’t depend of the emissions of one year, it depends of the total CO2 pressure above the long time dynamic equilibrium, which for the current (area weighted) average ocean temperature is ~290 ppmv over the past at least 800,000 years. It is the 110 ppmv (~μatm) above steady state which gives enough extra pressure to push ~2.15 ppmv CO2 of the 4.3 ppmv CO2 emissions into the (deep) oceans and vegetation.
      That gives an e-fold decay rate of 110 / 2.15 = 51.2 years, the same as it was 55 years ago. The slightly quadratic increase in human emissions over the years compensated for the increasing sink rate caused by the increasing CO2 pressure in the atmosphere above equilibrium, thereby maintaining the ~50% residual increase in the atmosphere. But that is just coincidence caused by the increase in emissions.
      Halving human emissions from the current rate would give a flat CO2 level. Maintaining the same emissions level would give a slowing increase until emissions and sink rate are equal.

      • “It is the 110 ppmv (~μatm) above steady state which gives enough extra pressure to push ~2.15 ppmv CO2 of the 4.3 ppmv CO2 emissions into the (deep) oceans and vegetation.”
        Correct. The 2016 paper on “Recent Paul in the growht ratoe of atmospheric CO2” has this equation:
        .Fsink = B(M – M0) where M is mass in atmosphere, and M0 is background mass.
        Growth(CO2) = F_anthro – B(M-M0). So B, a constant, is about 2.15 ppmv per 110 or about 2% of the delta.
        Fsink = 4.3 ppmv when (M-M0) is double of corrent levels when we get another 110 ppmv, or around 510ppm CO2.

  18. As I understand it the oceans at most locations are not at CO2 equilibrium ever.
    Remember CO2 is a well mixed gas. Per Henry’s law the cold polar waters can’t be at equilibrium at the same time the warm tropic waters are.
    When the overall ocean/atmosphere CO2 levels are stable for 10’s of thousands of years, it is because the tropics are sourcing the appropriate amount of CO2 to match the polar oceans CO2 sink.
    After absorbing CO2, the cold polar surface water in turn sink to the ocean floor to emerge centuries or millennia later in a warmer climate. When those waters surface they outgas the sequestered CO2. Over centuries/millenia those surface waters make their way to polar regions and during the trip they cool down and absorb CO2.
    I suspect you can incorporate that dynamic in your description, but for now you’re not describing earth’s oceans.

    • That is of course correct. Warm surfaces in the tropics are net emitters of CO2 and it is absorbed in high latitude oceans. I am simplifying things too much but it is really about the net annual change.

      • I am not sure if I missed it, but isn’t it the case that CO2 is stored in the ocean ground as Limestone (CaCO3 / Calcium Carbonate)? So not all of it can be emitted again.

      • and all the coal and oil was once CO2 in the atmosphere.
        until something sank it.
        what could that have been?

      • The storage of CO2 as limestone from rock weathering and ocean sedimentation has pumped out vast quantities of CO2 over billions of years. The buried organic carbon in rocks is equal to the oxygen content of the atmosphere. Eventually some of this CO2 gets recycled back to the atmosphere by plate tectonics which is a good thing too since otherwise life would run out of phosphorous.

      • Clive,
        As I said, I think the basic argument can address the dynamics of non-uniform ocean surface temps, but I didn’t even see a cursory statement that you were modelling the ocean as having a uniform global temp.
        Even more importantly, you aren’t discussing the long term sequester of CO2 caused by the ocean currents. When those cold waters sink they take CO2 with them and that CO2 doesn’t get a chance to interact with the atmosphere for centuries/millenia.
        I would think that long term sequester would bolster the argument that once CO2 emissions level off a global CO2 equilibrium will kick in.

    • gregfreemyer,
      It doesn’t make any difference for the equations: indeed there is a continuous flow of CO2 from the upwelling zones near the equator (mainly the East Pacific) and the polar sink places (mainly the N.E. Atlantic). At dynamic equilibrium (“steady state”) the upwelling amounts of CO2 equal the absorption of CO2 at the sink places. Calculated on the base of the 14C bomb spike decay and the “dilution” of the 13C/12C ratio from human emissions by the CO2 release from the deep ocean upwelling (not influenced by humans), some 40 GtC/year as CO2 is passing from warm upwelling to cold uptake. That doesn’t influence the total amount of CO2 in the atmosphere at equilibrium, which is ~290 ppmv for the current ocean surface temperature.
      If the average ocean temperature increases, that gives an increase of 16 ppmv/K to reach a new steady state, the same as for a single sample in a laboratory, per Henry’s law.
      If the CO2 pressure in the atmosphere increases, that decreases the release at the upwelling side and pushes more CO2 in the sinking waters at the other side. The difference is currently ~2.15 ppmv for 110 ppmv extra CO2 pressure above steady state in the atmosphere (inluding the uptake by the ocean surface and vegetation).

      • Thanks Ferdinand,
        My mind tells me that fact that the polar CO2 absorbed is removed (sequestered) from the equilibrium process as an impact on the dynamics of how long the equilibrium takes to reestablish itself.
        The main post argues for 30 years. I would think the long term sequester would accelerate that process and reduce the number of years required to reach equilibrium?
        But I’ve done no calculations to confirm my gut feel.

      • My issue is that the main co2 sink is not the ocean via Henry’s law. It is biological sequestration via marine calcification via calcarious phytoplankton such as coccoliths (White Cliffs of Dover).

      • gregfreemyer,
        Over the long term indeed the deep oceans will remove most of the extra CO2 in the atmosphere. The main problem is the relative small exchange between the two and the relative long decay rates that gives for the extra CO2…

      • Bart,
        Incorrect, Ferdinand. You are only looking at equlibration with the surface oceans. But, the equlibration period with the entire oceans is long.
        I am looking at both: the ocean surface has an equilibrium rate with the atmosphere of less than a year, but can’t take more than 10% of the change in the atmosphere.
        The deep oceans are near unlimited in capacity, but the exchange is much smaller, which gives a decay rate of ~51 years (including a small, but growing contribution from vegetation).
        Your graph shows mainly the variability caused by the influence of temperature on (tropical) vegetation, which zeroes out over periods longer than 1-3 years. For longer periods, vegetation is a small, but growing sink for CO2. The integral of the effect of the temperature variability on biological CO2 levels is below zero… Thus not the cause of the increase, neither are the oceans, as the effect of temperature on ocean-atmosphere equilibrium is rather small: ~16 ppmv/K…

      • ristvan,
        You need to take the time period into consideration: the white cliffs of Dover needed some 0.1 mm/year of sediments to form over tens of million years… Sedimentation may play a role, if that depends of the increase of CO2 in the atmosphere which is followed by an increase in the ocean surface.
        On the other hand, oceanic CO2 releases from upwarming upwelling waters near the equator are suppressed by higher CO2 pressure in the atmosphere and the uptake near the poles get increased. These two are linear in ratio to the pressure differences between ocean surface and atmosphere. That is what is observed over the past 57 years: a linear increase in net uptake in ratio to the pCO2 difference between ocean surface and atmosphere… I am not sure if a bio-life reaction in the ocean surface is that linear…

      • “On the other hand, oceanic CO2 releases from upwarming upwelling waters near the equator are suppressed by higher CO2 pressure in the atmosphere and the uptake near the poles get increased.”
        Not even close. Higher pressure in the atmosphere does not increase uptake near the poles, because it is merely a splitting of the flow that otherwise would be confined to the ocean currents. What gets transferred via atmospheric currents is reduced in the ocean currents. It does not suppress what is upwelling in the ocean waters because that flow is driven by centuries of inertia, and cannot be stopped over any timeline short relative to the turnover interval.

      • Bartenis:
        Not even close. Higher pressure in the atmosphere does not increase uptake near the poles, because it is merely a splitting of the flow that otherwise would be confined to the ocean currents. What gets transferred via atmospheric currents is reduced in the ocean currents. It does not suppress what is upwelling in the ocean waters because that flow is driven by centuries of inertia, and cannot be stopped over any timeline short relative to the turnover interval.
        Bart, I was talking about the release of CO2 from the upwelling waters into the atmosphere. At a constant CO2 concentration in the upwelling water and an increased CO2 pressure in the atmosphere, less CO2 is released into the atmosphere in the warm zones and more remains in the transported water. Near the poles, more CO2 is pressed into the already CO2 richer water, thus a part of the extra CO2 in the atmosphere sinks with the waters into the deep oceans.
        Currently that gives an unbalance of ~3 GtC more sink than source, no matter how much CO2 is transported by the total THC circulation.
        In all cases, an increase in CO2 pressure in the atmosphere gives an extra uptake by the deep oceans, as release and uptake are directly proportional to the pCO2 difference between ocean surface and atmosphere.

        • Ferdinand,
          It is my impression that much, if not most, of the CO2 (and derivative carbonate species) in up-welling waters is biogenic, derived from detrital material in the water column that oxidizes as it drifts downward. That is why the pH is so much lower than surface waters at any latitude. The CO2 levels are therefore, primarily related to the biological productivity of surface waters in years past. I think that your characterization is assuming the up-welling waters are saturated with CO2 and previously (years past) gave up excess CO2 as it reached lower pressures and higher temperatures. We now have a situation where the CO2 partial pressure in the atmosphere is higher, suppressing effervescence, but at the same time, the surface waters are warmed by a warmer atmosphere, increasing effervescence. How does that balance?
          After giving up the excess CO2, the water is transported laterally. It doesn’t always move poleward, at least not immediately. In California, the long-shore transport current moves water and sand southward. I’m not personally acquainted with what happens off the coast of South America. However, a quick check indicates that the Humboldt (Peru) current flows northward towards the equator. So, for true up-welling, it appears that the movement is NOT poleward (at least initially).
          In any event, for something like the Gulf Current, which does flow northward, and cools as it does so, I expect it to stay in equilibrium with the solubility of CO2 for its ambient temperature. When it does sink, it will have a CO2 content determined by temperature and CO2 partial pressure. Again, the question is, how does the interplay between temperature and partial pressure play out?
          You said, “In all cases, an increase in CO2 pressure in the atmosphere gives an extra uptake by the deep oceans, as release and uptake are directly proportional to the pCO2 difference between ocean surface and atmosphere.” This seems simplistic and dogmatic. The down-welling water will always be saturated for the given temperature and pressure. However, something to consider is the role of coccolith blooms in northern waters depleting the CO2 and having the water sink before it can re-establish equilibrium. In any event, as I stated at the beginning, the atmospheric CO2 going into solution is probably only a fraction of what comes back up in the future.
          The outgassing depicted by the OCO-2 satellite along the tropics is clearly the result of warming, and I suspect that the origin of the water is from shallower water than what rides up the continental shelves from submarine canyons. I think that there is a great deal more complexity to the situation than what you are explaining to Bartemis.

  19. If it was not that the World Temperature controls CO2 levels and not the other way around, there would be something interesting in this article.

    • Ntesdorf, what you say is true in the ice cores via Henry’s law for long time scales (millennia, ice ages) in the absence of anthropogenic CO2. It is not necessarily true on shorter time scales (centuries) for ‘extra’ anthropogenic emissions. CO2 is a GHG. We know that in the absence of feedbacks doubling increases GAST ~1.1-1.2C (Monkton’s third post in his recent ‘error’ series enables the calculation of 1.16C). What we don’t know for sure are the feedbacks. Observational evidence says they are weakly positive, resulting in observational ECS about 1.5-1,7 rather than 3-3.2. In other words, no C in CAGW.

  20. Moderator —
    Yet again my post has not appeared. Has Santa’s “Naughty or Nice List” been hacked and the information contained therein being used against me?
    Eugene WR Gallun
    [Nope . . . mod]

  21. The rate of ice formation is the highest it has been in a very long time. It comes later by a matter of hours later than typical, but it is raging steep. If global warming were a thing this would be impossible and yet it has been happening for several years. Earth is retaining its ability to refreeze the arctic despite the increase in CO2 ppm. Something we’re sure of is very wrong.

  22. The article explains the reasons why the rise in CO2 follows temperature. However there are numerous mistakes in the arguments, too many to itemize.
    The conceptual errors I see as most important are 1) the idea that CO2 is largely responsible for the whole GHG effect and 2) the implication by omission that there are no external influences altering the temperature of the atmosphere.
    Water vapour is a far greater contributor to raised temperatures and there is no need for any CO2 at all to accomplish, contrary to what Tonyb persists in trying to sell. Even snowball Earth had water vapour subliminating off the ice.
    The article previous to this one shows that CME’s can heat the upper atmosphere 750 degrees C, followed by net cooling from the NO produced. GCR seed clouds, and the oceans can themselves create large swings in the temperature of the air above them. This cannot be reduced to simplistic explanations, as evidenced by the temperature record.
    However, all things considered, the calculation is sound: the CO2 would indeed stabilise because of the presence of such a huge amount of water and the vastness of the plant population which I think hardly gets a mention.
    What is not at all clear is what would happen to the air temperature given a stable CO2 level. In the past there have been huge and rapid changes in temperature, the most recent being the late 1700’s when it rose at a rate of 4 C per century with, apparently, no change in the CO2 concentration. So obviously there is more to it.
    We can expect that the heating and cooling cycles will continue, as will ice ages and passably warm interregna. The reason for this is straightforward: CO2 only has a weak influence on global temperatures. As Anthony and Willis’ presentation shows clearly, water vapour is by far the main GHG forcing and even that is being neutered by other more powerful influences.
    So, yeah, the CO2 will stabilise and life will carry on, a bit more productively when it comes to farming.

    • The aim is to prove that rise in CO2 levels can halted by halting the increase in emissions. The activists say we must stop ALL emissions, but we know this is economic suicide. How sensitive the climate is to CO2 levels is another question. The governments of the world are being told that all emissions must stop now. This is not true.

  23. Regarding “The subtle replacement of logarithmic forcing of CO2 with a linear forcing”: IPCC is not doing that – their favored figure for direct effect of CO2 change is 3.7 W/m^2 per 2x change of CO2 – obviously indicating the effect is logarithmic. Also, the climate sensitivity figures in or near the range of 1.5-3.5 degrees C are degrees C per 2x change of CO2 – which indicates the effect being logarithmic.

    • Here is Fig 10 again with a logarithmic forcing. I asked Prof. Gregory at the Royal Society meeting on AR5 why the different emission lines were linear. He admitted that they all Earth System Models assumed that sinks slowly saturated and that other ‘feedback’ forcings like methane etc. etc. kicked in at exaclt the rate to give a linear line. That was the picture that was storyline needed.

      • This chart is as horrendously misleading as the TAR hockeystick.
        Let’s review:
        1) The land and ocean sinks are rising not falling and NOT saturating.
        2) if we stabilize emissions at any level, we will EVENTUALLY stablilize at a CO2 level.
        3) Because of #2, there is no fixed amount of carbon to be limited to, there is emissions PER YEAR limits if you want to stop CO2 rises. The “carbon budget” is a bogus and incorrect approach! There is no ‘carbon budget’ and it does matter if you emit that carbon in 2 decades (see a sharp rise in CO2) or 10 decades (and see most of it abosorbed. If we reduce emissions by merely 50%, we effectively end any significant rise or impact of CO2, as the remainder is tiny rise in CO2. Thus, the Paris efforts to reduce by 80% are an insanely counterproductive effort.

    • Clive,
      Very interesting finding!
      That means that the difference between the linear model (no saturation: sinks remain in ratio with the extra pressure) and the Bern model (saturation of the different sinks) would be obvious between now and 2020…

  24. Regarding “The decay time for an individual CO2 molecule emitted by man is only about 5-10 years (based on C14 measurements in both bomb tests and those produced by cosmic rays). Every CO2 molecule in the atmosphere is rather quickly absorbed either by photosynthesis or by the ocean. However on average most of them are simply replaced by another CO2 molecule entering the atmosphere through evaporation from the ocean surface or by biological respiration. The residence time however, is the e-folding time needed for a sudden net increase in CO2 to decay back to normal as the carbon cycle reacts.”:
    Not quite stated here is that the e-folding time for decay of a “sudden net increase” (AKA a pulse of CO2 injected into the atmosphere) is longer than the atmospheric residence time of individual CO2 molecules. Willis Eschenbach explained this well in https://wattsupwiththat.com/2015/04/19/the-secret-life-of-half-life/
    There, he said that for individual CO2 molecules, the e-fold time (time constant referred as tau) is 10 years and the half life of that is 6.9 years. And for e-fold time (time constant mentioned as tau) of a pulse of CO2 – Willis E. comes up with 59 years, which means half-life of 41 years. Have a look at Figure 3 and its caption in the above-mentioned https://wattsupwiththat.com/2015/04/19/the-secret-life-of-half-life/

    • A correlary here, in consideration of Figure 3 and its caption in https://wattsupwiththat.com/2015/04/19/the-secret-life-of-half-life/: The rate at which nature does net removal of CO2 from the atmosphere year-by-year is proportional to how much atmospheric CO2 exceeds 283 PPMV. If during any short period of time (per month year-round average, a year, or 4 years) nature removes an amount equal to half of what mankind adds, then if CO2 emissions stabilize and get sustained at current levels – atmospheric concentration of CO2 will stabilize at a level twice as much above 283 PPMV as it is now. Using 405 PPMV for current, I figure that is 527 PPMV. The half-life of the difference between 527 and 405 PPMV would be 41 years.
      This 527 PPMV figure would increase by 10 PPMV per degree C of warming of the ocean surface (less because ocean surface warming reducing ocean absorption of CO2 caused the half-life to be 41 years instead of mid-upper 30s that would be the case if the oceans weren’t warming). Also, as the deeper oceans gain CO2, the long term equilibrium figure for atmospheric CO2 increases a little for a given global ocean surface temperature. Overall, I think this means atmospheric CO2 stabilizing around 550-580 PPMV if we maintain CO2 emissions at the current rate (2014-2016 average) for a few centuries – if our fossil fuels last that long.

  25. A very interesting article, clearly and well written, Mr. Best. The implication of the constancy of the airborne absorbed fraction of CO2 had never struck me before in this light. The argument seems quite convincing at a first read; however, Nick Stoke’s point that the uptake by biological sources will reach saturation at some point needs further attention, and the relative importance of ocean and biota in the CO2 uptake. I need to look at Nick’s other points and look at the maths some more, but at first glance there’s some original ideas here. I rate as a lukewarmist and wonder – has Dr Roy Spencer seen this?

  26. ” The simplest assumption is that the sink increase depends only on the partial pressure difference for a given year. “
    That’s where I think it goes wrong. In terms of diffusion, that is characteristic of a layer of finite thickness with an infinite zero-impedance sink behind. Then you get exponential behaviour. Flux proportional to partial pressure difference.
    But when diffusing into an infinite but resistive sink, you get behaviour associated with gaussians, error functions etc. And that is where the rising with sqrt(t) comes from.
    Imagine a very well insulated house that is cooling. Heat escapes through the walls in that exponential way, with half-life etc. Because the windy environment is an infinite low impedance sink. Heat can also flow into the ground, also infinite. But the ground warms up, and takes more heat with increasing reluctance. For a maintained temperature, the flux drops as 1/sqrt(t).
    The problem with CO2 is that we don’t have a wind to take it away where it won’t bother us. We only have small biomass sinks, and the diffusive sea.

    • That’s where I think it goes wrong
      Well it is not really very wrong though is it? You are just saying that there is impedance damping to delay or offset rebalancing. Well maybe you’re right and maybe not.

      • “Well it is not really very wrong though is it?”
        Yes, it is. You are basically assuming that each new bit of CO2 released can get to a sink in the same way as its predecessors, independently. That’s where the half-life stuff etc comes from.
        But it isn’t like that. New CO2 has to make its way (in the sea) through previous CO2. That is the big diffrence between maintaining a constant flux indefinitely with no partial pressure rise, and an inevitable and continuing rise (sqrt(t) behaviour). The sea doesn’t saturate. But resistance to flux increases.

      • Nick,
        As said before, and affirmed by Greg, the THC (and other ocean currents) are simply renewed at high rate, where the upwelling is not affected by humans (it will over ~1000 years) and thus will absorb the same amount of CO2 when sinking near the poles (assuming the same low temperature there)…
        Btw, wind speed is another big factor that influences the speed of exchange. For the whole mixed layer that makes that the equilibrium with the atmosphere has an e-fold exchange rate of less than a year, but the problem there is that the ocean buffer gets saturated at about 10% of the change in the atmosphere (the “Revelle factor”). That doesn’t play a role for the deep oceans…

  27. Or we could maybe repair the 42% destruction of our life support system and never have to worry about CO2 in the atmosphere again?

  28. “so long as emissions remain constant.”
    NO. CO2 emissions will continue to climb and climb for MANY years.
    And once this ant-science, socialist scam, anti-CO2 agenda is consigned to the SCRAP HEAP where it belongs, the world will rejoice at the massive increase in food and prosperity that fossil fuels have given.

  29. Burning gas is decarbonisation since energy is also the product of burning hydrogen.
    we know from the experience of the US with shale, that the switch from coal powered generation to gas powered significantly reduces CO2 emissions.
    By contrast Germany that has gone down the renewable route, has seen no reduction in CO2 emissions these past 15 years.
    Gas works, renewables do not.

    • This was exactly my thought also. But it could be even better.
      a lignite power plant has about 30% efficiency and produces 1200 gr CO2/per kwh
      A standard gas turbine has an efficiency of about 40-45% and emits about 600 gr CO2/kwh
      A state-of-the-art Combined Cycle Gas power plant has an efficiency of more than 60% and emits only 330 gr/kwh
      and if you use the remaining heat for communal heating, the efficiency is over 90% and the emission only 220 gr/kwh.
      And its not only about CO2. It’s also to save energy and production sources for further generation and better environmental protection (e.g. less mining or land use of wind turbines) and lower energy costs.

    • There are three factors. 1. Per dry kg, natural gas (methane) has about twice the energy content of steam coal (I used Powder River coal for the comparison). 2. Stoichiometrically, methane produces half the CO2 per unit of combustion ( 2C+4O=2CO2, 1CH4+4O= 1CO2+ 2H2O). 3. CCGT is 61% thermally efficient while new USC coal is 41-45% depending on details. Run the numbers and CCGT produces about 36% the CO2 per MWh of electricity. Roughly a third.

  30. A first thought here is that this would be fantastically important if true. If the work could be done to get this verified and if so accepted by the mainstream, the ability of environmental groups to leverage CAGW into forcing the world to change its lifestyle would disappear.
    A second thought is that it seems to imply a relationship between the growth rate of emissions and the airborne fraction. The stability if the airborne fraction rather argues against that. However, the case of the first oil crisis is very intriguing. In the mid-70s, the increase of CO2 in the atmosphere touched zero, around about the time that global emission GROWTH ground to a halt. That sounds very like what is being postulated here. Just an anecdote though.
    Lastly, we know that only a couple of percent of global CO2 is in the atmosphere. Doubling atmospheric CO2 from fossil sources just increases the size if the total reservoir by say 2%. In the long run one would expect the amount in all sinks – air, biosphere, ocean – to rise by the same percentage. In other words, for atmospheric CO2 to fall back to within a few ppm of pre-industrial – eventually. I guess the IPCC time constant of a few hundred years would say that would take a few thousand years.

    • Yes the 1973 Opec oil embargo is the right analogy. CO2 levels did begin to stall but emissions were not held down long enough to measure the full effect. I think the stability of the airborne fraction is as Nick says related to the continuous exponential growth in emission flux. This will reduce gradually to zero if growth is also zero indefinitely.
      How else did the atmosphere survive millions of years of super volcanoes without forever rising CO2 levels?

  31. Here is another analogy of what I think happens, with the proviso that all analogies are not fully true.
    I have a very large bath of water with the plug out and the tap on. For thousands of years the depth of water has remained 28 inches because the water pressure induced flow out of the plug exactly balance the flow in from the tap. A little boy turns up and starts peeing in the bath and the level rises ever so slightly, but then he gets a hose pipe and keeps increasing the flow into the bath and the water level keeps rising. Next he gets a firehose and increases that to full throttle then he gets another, then three firehoses forever increasing the flow rate. Finally he gives up the game and goes away leaving all the hoses still running. By that time the level has risen to 40 inches and is still rising. The water pressure finally equalises the drain rate in-flow rate and the level stops rising.
    The giant’s house doesn’t get flooded!

    • But does this analogy only work when the drain capacity (the sink) has they same flow rate as the water in (the source)?
      Are you correct when you state:

      By that time the level has risen to 40 inches and is still rising. The water pressure finally equalises the drain rate in-flow rate and the level stops rising.

      In your analogy, we know the drain capacity (the sink). It is the same as the flow rate when the tap was on and water depth remained constant at 28 inches. If the drain capacity had been greater than that, the level would not have remained constant at 28 inches and the level would gradually have reduced below 28 inches. Had it been less than the flow rate when the tap was on, the level would have increased,
      The reason why the level has increased to 40 inches when additional water from the fire hose(s) is added is because the drain capacity can only handle the flow rate of the tap on scenario and cannot cope with the tap on plus fire hose(s) scenario.
      The issue here is whether the capacity of the sink can increase over time and if so, whether it can retain its increased capacity for long enough.
      We know that in absolute terms carbon sinks are increasing in capacity over time. But if we were to stop increasing the amount of CO2, it does not necessarily follow that the carbon sinks will retain their present high capacity, and it may be that they would fall back more in line with the sink capacity as it was when CO2 was say 300ppm. If that was to happen, ie., the absolute capacity of the sinks was to fall back, then this undermines your premise.

      • The assumption is that the flow rate out of the fixed diameter drain depends just on pressure – so the depth. I didn’t work out the numbers and didn’t specify the area of the bath. Luckily I also didn’t specify the gravity so we might need to move the bath close to a neutron star!

  32. Menicholas needs to revise his estimation of people breeding like flies when they move to richer countries, the exact opposite happens when people leave a state of abject poverty. Birth rates fall dramatically when people anywhere in the world are lifted out of poverty – it is poverty that creates large families because infant mortality is high and parents are frightened about being looked after in old age. High birth rates are a defence against a poor old age.
    An excellent example I heard quoted recently is Bangladesh, which many people think of as a country “where people breed like flies” (a pretty disgusting way of describing poor people actually).
    Well, it seems a comprehensive health programme and a gradual improvement in the lives of many people in Bangladesh has seen the birth rate in Bangladesh fall below replacement rate. A remarkable achievement but consistent with what happens everywhere.
    The most objectionable part of the green movement’s lies and intentions is to keep poor people in a poverty stricken “sustainable lifestyle” and that they view human beings as a “problem”. So did Hitler and the comparison is apt. Human beings are the answer to all the questions we face, but environmentalists think they are chosen and have the right to meddle in things they clearly don’t understand or intend to choose for themselves as a lifestyle.
    The world is not overpopulated anywhere, nor heading for a population meltdown.
    Blue planet in green chains (new book) is where we are.

    • That’s exactly what we’ve seen here with turkish immigrants of the second and further generation. The birth rate is the same than of average Germany. Which also means an adaption to the western culture.
      But if you keep immigrants in quarters resembling their old culture, the birth rate will be much higher.
      (Me, being an original German, it seems that I have not so well adopted to the prevailing culture. I have five children… 😉 … )

    • Moderately Cross,
      You said, “The world is not overpopulated anywhere, nor heading for a population meltdown.”
      To take such a claim seriously, you need to define “overpopulated,” and get agreement. Also, not everyone is going to see it the same. Someone who grew up in rural Wyoming would probably consider Manhattan to be overpopulated. A Manhattanite might well consider an Asian city with higher population density to be overpopulated. From my point of view, I have lost a lot of freedoms to travel where I want and do what I want because of the population in the US doubling in my lifetime. If one puts no value on freedoms, then we can easily accommodate a lot more people.

      • “From my point of view, I have lost a lot of freedoms to travel where I want and do what I want because of the population in the US doubling in my lifetime” How so?

      • markl,
        I could easily write an essay of the things I could do as a child and a young man that I cannot do now. When I was a boy, my dog and I had free run of woods about 1/2 mile in radius; it is now built up with homes. when I lived in Vermont in the late-’60s, it was rare to see a “No Trespassing” sign. One could hunt or fish virtually anywhere. I went back there a couple of years ago and most of my favorite haunts were now posted. The government has bulldozed the roads into former mining areas and defined them as being de facto Wilderness Areas. California and Vermont have prohibited using suction dredges for gold mining in streams and rivers. An area in California near Hollister, called Clear Creek, was off limits for years as the BLM tried to decide what to do. Now you can enter the area only with a permit, and the time allowed is limited. I could easily go on!

        • Clyde Spencer–have you considered that much of the restrictive access is due to liability lawyers on private land and the greens on public land? I have seen press reports of landowners with former swimming holes being told by their insurance companies to not allow swimming due to the risk of lawsuits, and one can only guess how much the greens want to keep the peons off what they regard as their land. It might not be population as such.

        • I see, the march of civilization bothers you. There’s more than enough room to get away from it and then some. I’m still amazed of the view from airplanes of all the natural space left in the world. One can only get the perspective from the air when you leave the cities. But yes, you can’t go home again.

          • mark1,
            Who said anything about civilization? I appreciate technology and art. One can have civilization without large population densities. Most dynamic systems have an optimum design or parameters that characterize the system. There is a good reason that steam engines have speed governors on them. Any system without feedback loops to restrain runaway behavior is at risk of destroying itself. Yes, when in an airplane at 30,000 feet you can’t see individual people and even cars are hard to make out. But the impact of Man can be seen even in those apparently empty spaces, even from the air. One of the things that is not commonly appreciated is that (at least in the US) there is a positive correlation between urban population density and crime rates. Renowned landscape architect Ian McHarg claimed that 4/5 of all Manhattan residents had serious neuroses, and 3/5 had serious psychoses. Perhaps that explains why there are so many liberals to be found on the East Coast.

          • Tom Halla,
            Obviously, it isn’t that population itself is directly responsible for the changes I decry. But, lawyers have an easier time earning a living when there are more people. And, increases in population create increased liability because there are more people who are inclined to damage private property or become injured on someone else’s property. It is a complex intertwining of bureaucracy and people thinking that they need to pass laws to protect people from themselves. One sees it here on this blog, where those who believe in AGW act as though they have a divine authority to tell everyone else how to live. If one studies cultures such as Japan, where a common saying is, “The nail that stands up gets hammered down.”, it should be evident that large population densities are only workable when people give up some freedoms. I understand that the Frontier is closed, but I’m not ready to live in a Brave New World.

  33. I’ve modelled this before.
    Basically, the natural absorption rate used to be up and down, let’s say trying to keep the CO2 level at 280 ppm, although it was always +/- 10 ppm from this level. This natural up and down use to completely dwarf our emissions until about 1950. Even in WWII when we were pumping CO2 out like crazy in weapons manufacturing, CO2 levels actually fell because the natural net absorption was greater than our emissions. By 1945, CO2 was only 310 ppm, barely above the 280 ppm equilibrium level.
    By 1950, however, we started to exceed the natural absorption rate and CO2 started rising faster. At this point, the natural sink rate (trying to get back down to 280 ppm again) began absorbing 1.8% of the “excess above 280 ppm” each year. It is just a fluke that it turns out to be close to 50% of our emissions. What matters more is how much “extra there is in total” in the atmosphere, not how much we “add” each year.
    1.8% of the “excess”.
    Although it might be rising slightly, going from 1.6% to 1.7% to 1.8% is really not that much of a change.
    If we started to slow down our emissions and then started to very slowly reduce them, the 1.8% of the “excess” per year absorption rate does not catch up to our emission rate until 2180.
    Stabilize at 530 ppm. Or just 1.1C or so higher given global warming is exaggerated. We are already half way there so the amount of extra temperature lift is small and we will be “fine”.

    • You are basically agreeing that we can halt warming by not exceeding current emission rates.Even if that yellow line were flat in your scheme equilibrium would be reached at ~550 ppm.

      • Flat emission rate starting in 2030 results in CO2 stabilizing at 548 ppm around 2250.
        Flat emissions starting in 2017 results in CO2 stabilizing at 536 ppm around the same time 2250.
        If we never cut emissions growth, let’s say it always grows at 0.5% or 0.05% per year, the natural absorption rate will never catch up and CO2 will just keep rising. We get something close to stability with a 0.01% growth per year but this isn’t until 2300.
        So, I guess some day we have to commit to a peak emission rate. It doesn’t make lots of difference to get there slowly, even by 2050, since the peak CO2 levels don’t change by that much, it just takes longer to get there.

  34. Your basic assumption is off base: there is nothing worth the costs of the ‘solution”you offer. There is no great problem of “global warming” except the problem of the nonsense policies and vast sums of money the nonsense is costing. And holding CO2 emissions at 0 change is going to enslave billions of people. You don’t seem to support slavery, or am I wrong?

  35. Clive, not correct. The math is wrong. If you put a certain amount of CO2 into the atmosphere each year, x, and take out x/2 at atmospheric concentration y, then if the amount you take out every year is proportional to y, the concentration y has to go to 2y to balance the amount taken up with the amount emitted.
    Thus, if we are at 400 ppm, we would have to get to 800 ppm in order for uptake to equal emissions, and the process would take centuries..

    • No because the fraction x/2 changes with the rate of change of emissions. If the rate of change falls to zero then x/2 slowly changes becoming first 5x/8 then 2x/3, 3x/4 etc. so the process to reach equilibrium is faster.

    • You can increase energy production and even lower CO2 and costs. It’s all bout efficiency of production and use.
      People im developing countries need no gas guzzler with 20-30 liters per 100 km. In India they sell small non-smelling motorbikes using 1 liter per 100 km.
      The same is with a small gasoline generator compared to a block-type thermal power station.
      Or building houses which need no or minimal A/C or heating because of their special construction.

      • As it so happens, India still needs air conditioning. I’m guessing you don’t know what the summers are like there. Unless you consider ‘special construction’ of poor villages.

  36. As a direct consequence of IPCC successful lobbying based essentially 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“.

    Love the “irreversible”. Typical propagandists’ trick. Assert that something as an inalienable certainty in the hope that it will make it so, and crossing you fingers.”
    They know that it is NEITHER irreversible NOR “set” but think ( hope ) that no one will spot that obvious fallacy and will thus stop resisting.

  37. In addition to the OPEC embargo, another event worth examining would be the fall of the Soviet Union, when plummeting Soviet and East European emissions dropped 36%, stalling worldwide CO2 growth. To global warmists, why isn’t Ronald Reagan their hero?
    Beginning in that same 1980s-90s timeframe, global warmists must blame themselves for the continuing rise in U.S. emissions to the present. Before green, anti-nuclear activism, U.S. nuclear power was on a trajectory that would today easily have the U.S. at 1972 emissions levels. If nukes grew enough to charge an electric vehicle fleet, the U.S. could already be at 1955 emissions levels.
    If global warming were really a problem, which it isn’t, enviros have only themselves to blame.

    • Actually there is indeed evidence of a stall in CO2 increases during 1980s. I hadn’t made the connection but yes the collapse of the Soviet Union could well be responsible.

  38. It is quite true that global warmists have tunnel vision. They only think of reduction of CO2 , not optimization of CO2 levels. If all sources of man-made CO2 were eliminated, which is exactly what Warmists are attempting to do, the results likely would be catstrophic even if the reduction only
    stopped at the pre industrial levels existing before our illegal, unconstitutional Civil War,. Like most govt programs that are the result of pressures from an ignorant public, the likelihood of deadly side effects is pretty high, to judge from experience. And, of course, the govt never guarantees anything it does – approve drugs that kill, cars that kill, information about their own IRS laws. etc

  39. Okay so how dynamic is the plant response and the microbial response and the plankton response? These are not small matters.

  40. Clive,

    The strange thing is that this airborne fraction hasn’t changed at all in 60 years, despite exponentially increasing human emissions.

    This article claims that there are changes in the airborne fraction, and that since 2002 there has been a pause in the rate of growth of atmospheric CO2. This pause obviously (temporarily?) ended with the 2015-16 El Niño.
    Keenan, Trevor F., et al. “Recent pause in the growth rate of atmospheric CO2 due to enhanced terrestrial carbon uptake.” Nature Communications 7 (2016).
    The researchers track this increased carbon sink to the decrease in the rate of change of plant respiration due to the temperatures pause. You talk about the oceans, but it is the plants that are doing the heavy sink work.
    If this research is correct, then the stabilization of atmospheric CO2 levels can be achieved without actually having to achieve zero-growth in emissions. We could still increase our emissions by some amount, and plant growth would take care of that.

    • CO2 growth rate in 2015 was the highest on record at about 2.95 ppm and, in 2016, it is looking even higher at maybe 3.4 ppm. So, the study is already out-of-date once the newer numbers are plugged in.
      Of course, in El Nino and warmer years, CO2 increases a little faster than La Nina and cooler years but then the study should have taken all that into account.

      • the study is already out-of-date once the newer numbers are plugged in.

        The question is that while the pause in temperatures was in place it appears there was also a pause in atmospheric CO2 rate of change. There are two important considerations:
        – Atmospheric CO2 rate of change appears to follow not only emissions but also temperatures. Possibly by affecting the balance between photosynthesis and respiration.
        – Strong ENSO distorts measurements while taking place, and data correction to ENSO effects is questionable. We don’t know what the situation is and won’t know it until a few years have passed. There is a distinct possibility that global warming remains subdued.
        Both have huge repercussions for policy decision making, unless it is agenda driven and immune to evidence. If both considerations are true, then we are not facing any crisis, but a possible long term problem.

      • Javier,
        The CO2 rate of change indeed follows all temperature variations very closely, but that levels off to near zero after 1-3 years. The main effect of a Pinatubo or El Niño is on tropical vegetation: changed rain patterns, drying out for some parts of the Amazon give extra CO2 release, together with warming oceans. That reverses when the temperature drops again. The long term (>3 years) is that vegetation is a small, but growing sink for CO2, thus while it reacts fast on temperature changes, it is not the cause of the long term increase in CO2 neither – I suppose – of a drop large enough to overwhelm human emissions if these keep increasing…

      • Ferdinand,
        Read the article as it is open. They are not talking about the seasonal variation in CO2 that is known to follow temperatures since the late 70’s. They are talking about the long term trend between 2002 and 2014.

      • Javier,
        Indeed interesting article. Remains to be seen in how much temperature influences the sink rate on long term. Here the calculated sink rate based on the extra pressure of CO2 in the atmosphere above the (temperature controlled) steady state:
        Which is nicely within the huge natural variability. The largest deviation is after the Pinatubo eruption: measurements did show that despite less incoming sunlight, the scattering enhanced photosynthesis, probably from leaves which were normally part of the day in the shadow of other leaves, but then received more light…

    • Is this the same NYT that said Trump was shady because he didn’t release his tax returns? Funny how no one cared about Venezuela until it became convenient.

  41. Just a bit of looking around, it appears the IPCC and NOAA believe natural sources put about 200 gigatons of CO2 out each year and man contributes about 6 gigatons per year. Does anyone have any idea how accurate any of this data is? What are the error margins on this data? Do we have any data about how that may vary over time or change with say, a natural 1 degree rise in global temperatures.
    Yes, once again I’m harping on data accuracy. It offends my science training when people try to make anything of data that has error margins so large it permits any interpretation desired.

    • Patrick B,
      The 200 GtC (carbon as CO2) is based on the CO2, O2 and δ13C changes over the seasons. O2 and δ13C changes over the seasons are mainly from vegetation. The margins of error are huge, may be 10% or so, but not that important, as all what goes into the atmosphere is removed in the same year, plus some extra.
      Global CO2 levels in the atmosphere are known to within +/- 0.2 ppmv, that is 0.05% of atmospheric content. No problem there.
      Human emissions are calculated from national sales inventories (taxes!) and burning efficiencies, less accurate and its error margin is estimated around 0.5 ppmv, total amounts probably more underestimated than overestimated, due to human nature to avoid paying taxes…
      The net sink rate, the difference between what humans emit and what remains in the atmosphere (the “airbrone fraction”) thus has a maximum margin error of +/- 0.7 ppmv, around the 2+ ppmv/year increase rate. Any error will be forwarded to the next year and that will level off over several years for the direct measurements, not so for the fuel use inventories.
      Whatever the error margin in total and individual natural CO2 fluxes, that doesn’t influence the error margin of the global CO2 balance, which was more sink than source over the past 57 years…
      Of course research is going on to make more detailed inventories of individual CO2 fluxes, both natural (over the tropical rain forests, the oceans,…) and human (tall towers measuring CO2 fluxes over large areas), but that doesn’t influence the overall balance…

      • One key point is the land sink isn’t even calculated. It the leftover term from taking emissions estimates, subtracting out ocean sink, looking at measured co2 increases, and if co2 increase is lower than that number, putting the difference to close the gap into land sink number. Co2 is rising less than expected.

      • So our margins of error on the nature side far exceed what we estimate humans contribute.
        Further, what humans contribute has a large margin of error (if we are basing these calculations on sales inventories – how accurately is that reported from country to country and what about all other human activities – agricultural burning etc.?)
        Sorry, I just don’t buy it with what info you provide – there’s so much slop in those numbers that I don’t believe you can tell (1) how much carbon is being cycled in nature each year or (2) what amount man is contributing, so as to make a reasonable analysis. I think the only solid number in the whole analysis is what is the CO2 in the atmosphere.

      • patmcguinness,
        It is the reverse: the net uptake by plants is reasonably well known, based on the oxygen balance and the uptake by the ocean surface is well known by DIC (dissolved inorganic carbon) measurements, the uptake by the deep oceans is used as remainder to close the balance… Even if there are rough estimates of the uptake by following several tracers (14C from the atomic bomn spikes, CFC’s, changes in 13C/12C ratio,…).

      • Patrick B,
        It is of zero interest for the balance how much CO2 is cycling within natural releases and uptake. All what counts is the difference between human emissions and increase in the atmosphere at the end of a full year seasonal cycle. That is currently ~4.5 GtC/year more sink than source.
        If nature releases 100 GtC/year, it sinks 104.5 GtC/year.
        With 500 GtC/year, it sinks 504.5 GtC/year.
        With 1000 GtC/year, it sinks 1004.5 GtC/year,…
        What do you thionk that most individuals and countries will do: give their sales as correct as possible, or maybe underestimate them by under-the-counter sales? That only makes that human emissions are larger than calculated and thus nature is a larger sink than calculated…
        I didn’t include releases from slash and burn human emissions, as these are much too uncertain, but these too add to human emissions, making the natural sinks even larger… Moreover, we know that balance too from the oxygen measurements…

    • Patrick B,
      I suspect that the 200 gigatons of CO2 is more like a lower bound on natural sources. There is approximately 44,000 miles of continuous spreading centers encircling the Earth. The volcanic activity is very poorly known. About 20 years ago, trees starting dying in a USFS campground on the margins of the Long Valley Caldera on the east side of the Sierra Nevada (CA). It was discovered that CO2 was killing the trees. Therefore, the USFS closed the campground out of an abundance of caution lest some campers not wake up in the morning. I can’t believe that that particular location is the only one that is giving off lots of colorless, odorless, invisible gas. If other volcanoes are emitting CO2 above the timberline, there would be little to give it away. There are known to be soda springs throughout the world, and there are known to be massive CO2 seeps in the southern ocean.

  42. Based on a quick review, and I could have missed it, but missing from this is a consideration of the effects of biology on the oceans. Not only is water buffered chemically, but it is buffered all over the surface of the oceans by photosynthetic organisms, prospering on the conversion of CO2 to O2. That amount of life in the Oceans would increase in response to increasing CO2.

    • Yes and that is where Ferdinand comes unstuck.
      Ever seen a 100m limestone cliff that stretches over a 1000km ? And thats just one of them. What was that ? Just a cyclical predictable “sink” event.
      You could do a back of the envelope volumetric calculation on known Miocene Limestones to reduce these sink rate calculations to irrelevance.

      • Taking into account the time span, the cliffs needed millions of years to build up: about 0.1 mm/year in average, Current sink rate of all organics + skeletons is ~6 GtC/year, largely compensated by upwelling waters which move CO2 enriched waters back to the surface…

        • Current sink rate of all organics + skeletons is ~6 GtC/year, largely compensated by upwelling waters which move CO2 enriched waters back to the surface…”
          Largely, but not totally, because that CO2 was/is at 290ppm equivalent, so we gradually are putting more CO2 into the deep oceans, at the 2.5GtC/year rate, increasing as the gap between Co2 in atmosphere and Co2 in deep oceans, gets better (apparently linear rate).

  43. Clive,
    Your CO2 emissions versus CO2 Levels graph shows CO2 levels via direct measurement as going up and down (some years lower than previous years) through the recent decades. Is that a really a rate the graph is showing (as in a delta CO2/yr)?
    Because as I’m sure you know, by the MLO record no year’s average measured CO2 has been lower than a previous year’s average.

  44. It seems to me that we should want to reach atmospheric optimum CO2 levels, apparently 600-800ppm. This would help the impoverished throughout the planet, and likely not be a less stable level. Those who oppose any CO2 increase appear to be more interested in their own income than helping impoverished.

  45. Excellent article. The key observation here is that ocean and the biosphere are carbon sinks and are at different levels of equilibrium. In particular the oceans have 37000 Gt of co2 and except for surface are at 290ppm equilibrium, and so there is capacity to soak up a lot of carbon front the atmosphere, turning co2 into carbonates and getting eaten by plankton then sent to the deep ocean. The key is the rate, and the rate seems to have increased linearly relative to difference of co2 above 290ppm preindustrial baseline. I calculated that the ocean sink could run at current rates for over 200 years at the current 2.5 Gt C per year level before saturation.
    The dK calculated estimate value should be determined by this co2-atm and co2-ocean difference, as le chetaliers principle is the driving factor. So I agree with the main thrust but question some of the calculation. You need to base equation on le chetaliers the factor in rate limits on absorption and for ocean apply revellers factor. My own calculation is that steady state man made emissions at current levels would take us to 460 to 480ppm and then level to steady state. To summarize ocean sink per year=k*(co2-atm – co2-ocean), where co2-ocean is around 290ppm. The higher co2 goes the bigger sinks get, they are a big negative feedback and date shows they remain so for now.

    • Revelle factor is correct term, regarding how much co2 gets taken up by ocean and becomes carbonates. Danged autocorrect made it Revellers. Well Merry Christmas wuwt Revellers!

    • Thanks,
      We have good agreement. Yes we can argue about the details and yes I have grossly over-simplified things, but the overall picture is clear. We have to counter the propaganda that emissions have to fall to zero by 2050. They don’t because first all we need to do is stabilise emissions which gives us plenty of time to plan an effective energy policy. This message can stop the profligate wasting of economic resources today for no net public benefit. Hence the title ‘ A Hiding to Nothing’. The bookies will take all the money and the dissapear.

  46. What you’ve got here, Clive, is a simple relaxation model. Basically, what you are saying is that CO2 concentration is achieved by a balance between the inflow and an outflow that is proportional to the current level.
    dC/dt = -C/tau + u
    where u is the input rate, and tau is a time constant. At equibrium, with u constant, C = u*tau.
    We can disaggregate u into natural and anthropogenic terms, u = a + n. Since the equation is linear, we can then disaggregate C into terms Ca and Cn such that C = Ca + Cn, and
    dCn/dt = -Cn/tau + n
    dCa/dt = -Ca/tau + a
    But, this means that
    d/dt(Ca/Cn) = (n/Cn)*(a/n – Ca/Cn)
    If a is less than from fractional value of n, say f*n, then
    d/dt(Ca/Cn) (is less than) (n/Cn)*(f – Ca/Cn)
    That means that, if Ca/Cn starts out less than f, it can never grow greater than f, as the rate of change at that point is bounded above by zero.
    Common estimates of f are about 3%, or 0.03. That would mean that, if Cn = 280 ppm, Ca can never be greater than 0.03*280 = 8.4 ppm. The claim that Ca = 400-280 = 120 ppm then falls flat on its face. That is 120/8.4 = 14.3X greater than it could possibly be using this model.
    The conclusion that ineluctably follows is that the great majority of the observed rise is due to natural phenomena.

    • I am not sure I fully follow your logic. However, I don’t think tau is a constant. It depends on CO2 partial pressure. Unfortunately we are responsible for the rise in CO levels but these are also being offset by natural responses. We just need to stabilise emissions to a fixed level that best meets our short term needs while we develop new (most likely nuclear) energy supplies.

      • Clive,
        Tau is constant over the past 57 years, about 51 years e-fold decay rate for any excess CO2 above steady state or about 35 years half life time. The response of the (oceanic) sources/sinks disequilibrium is surprisingly linear over the full period of accurate measurements.
        The error in Bart’s reasoning is that he mixes two largely independent processes as being similar. That is not the case: the largest natural fluxes are largely temperature dependent: mostly (NH extratropical forests) seasonal, partly differential (equatorial release vs. polar uptake), while the removal of any extra CO2 injection, whatever the source, is largely pressure dependent…
        There is hardly any influence of pressure on the seasonal CO2 fluxes and hardly any influence of temperature on the sink rate of any extra CO2 in the atmosphere above steady state…

      • It does not matter if tau is constant or not. The equation
        d/dt(Ca/Cn) = (n/Cn)*(a/n – Ca/Cn)
        is independent of tau, and the bound holds regardless.

      • Bart,
        Two (in fact several) near independent processes at work with different tau:
        dCn+a/dt = -ΔT/tau1
        dCn+a/dt = -ΔP/tau2
        tau1 is for temperature dependent processes and is a matter of months (except for the deep oceans). That gives the bulk of the fluxes over the seasons and smaller fluxes for year by year variability.
        tau2 is for pressure dependent processes and is a matter of decennia, no matter what caused the increase above the (temperature dependent) steady state.
        The variabilty over the seasons and 1-3 years is practically independent of the total amount (pressure) of CO2 in the atmosphere.
        The average net sink rate is largely independent of temperature over periods longer than a few years.

      • To make it more complete (not exhaustive):
        dCn+a/dt = – ΔT/tauT1 – ΔT/tauT2 – ΔT/tauT3 – … – ΔP/tauP1 – ΔP/tauP2 – ….. + a + n1
        Where n1 = the small, not temperature related CO2 releases by nature above equilibrium (like volcanic vents), not the total natural emissions, as these are caused by -ΔT/tauTn…
        Natural processes can be both pressure and temperature dependent (oceans, CO2 uptake by plants), or only temperature dependent (CO2 release from organic decay by bacteria and fungi), each process with its own decay rate for pressure and/or temperature…

      • This is mathematical gibberish, Ferdinand. But, whatever idea it is you are trying to express, it would not matter anyway, because the same equations affect Ca in equal measure.

      • Bart,
        It may be mathematically wrong, but the basic point is that the natural releases and sinks are mainly temperature dependent and that human emissions don’t influence these processes in the same way: they increase the CO2 pressure in the atmosphere and therefore increase the sink rate in all pressure sensitive processes.
        Natural releases don’t influence the sink rate because they are caused by temperature. For the ocean surface in the same direction, for plants even reverse with temperature: higher temperatures in spring and summer give more uptake by plants and lower CO2 levels in the atmosphere over the warm seasons. Plants are dominant over the seasons. Thus there is zero extra pressure from natural sources in the atmosphere to store more CO2 in plants or oceans as plants already use too much CO2…
        Thus your formula that natural and human releases are threated equally is only right for the natural emissions above the steady state at any moment of time, not for the changes in equilibrium level itself, which are driven by temperature changes.

  47. 440ppm is too low. Something around 1,500ppm (0.15%) would normal for the late Phanerozoic. But when the interglacial ends, it’ll drop by half. I’d say 2,000ppm (0.2%) should be the target..

  48. Thanks, Clive Best, for this post. I suspected a limit on atmospheric CO2 with a constant energy output, but had’t read anything on the subject.
    My suspicions arouse from high school chemistry, and personal observation. After my 20s, when I was lifting weights and jogging regularly, I cut the strenuous exercise in my 30s, while eating as much or more than I had before. Needless to say, my weight did not increase indefinitely, but stabilized at a somewhat higher weight.

  49. Once again I don’t do math all that well so let me get this straight. The atmosphere has 400ppm of CO2.
    There is 200GT of the stuff added annually which goes away because the earth eats it one way or another.
    Of the 200GT of CO2 put in every year maybe 5 to 10 of it is from human activity. Therefore of the 400ppm
    lets call it 5 to10 ppm is from us and of that 5ppm(simplifying) only 2ppm (lots of uncertainty) remains annually to increase the total. After all the mathematical minutia.I think Alfred E. Newman has it right – what, me worry. AGW is total BS, enough said.

  50. Why would you abet the know-nothings [to] create a true ecological catastrophe as the Plants eat out all atmospheric CO2 and then die from lack of CO2 and CO2 starvation?
    Besides America produces less than ZERO net atmospheric CO2, as our useful bio- remediation provided by our farmers, already sequestrates more than North America produces. It already sequestrates a goodly amount that China and Japan create?
    Under the IPCC toothless “treaties” China and India meets their obligation which is do NOTHING until 2035, and then think about maybe [consider] restricting its CO2 emissions! Lets promise to do the same !!!!
    It is past time to Declare Victory in our 43 year war on Pollution and turn to a pure maintenance Policy of keeping our now clean Air and Water, clean.

  51. 1. Carbon sinks are saturating (they are not)

    All sinks saturates eventually. After all, the Earth is only finite, right? Finite sinks have to saturate sooner or later.
    All sinks have to be smaller than the Earth and therefore have to be finite as well.
    The question is not whether the sink saturate or not, they do. The question is whether the time to saturate is so long that the saturation may be irrelevant or not.
    To the problem at hand; we know that the oceans and the biosphere are the main sinks. The oceans holds fifty times carbon than the atmosphere and will therefore not be saturated for some time, but the amount of carbon in the biosphere is comparable to the amount in the atmosphere. This means that the biosphere will saturate quite quickly.

    • The concept of saturation is easily misconstrued. A growing organic biosphere will always be able to absorb more CO2 in the same way that an adult can eat more food than a baby. Thus it is better to consider rates of uptake, rather than imagined ultimate limits.
      Now one could argue that an adult will “saturate” with food because they will reach a limit at which the adult cannot grow any more. This postulate is debatable in humans, but defensible as a way of illustrating a point. However, there is no evidence that the biosphere is currently behaving anything like this with regard to carbon dioxide, nor good reason to argue that it will at any clearly defined point in time. The rate of uptake of CO2 from the atmosphere is still rising commensurately with the rise in atmospheric CO2. Thus there is no evidence of sinks “saturating”, quickly or slowly, whatever you may suggest.

      • Now one could argue that an adult will “saturate” with food because they will reach a limit at which the adult cannot grow any more.

        Thank Michael, I think this is a good parable to the carbon uptake in the biosphere. A human body will grow in weight as long as the uptake of carbon is larger than the rate of loss though respiration. The body can become huge, but not infinite.
        Similar with the biosphere; the living biosphere will grow as long as the carbon uptake is larger than the loss though the rate of respiration in all living organisms. Exactly how big it can become is hard to say, but obviously there is a space limit for living organisms on the surface of the Earth.
        This also holds for the carbon in dead plants and animals. We see no unlimited deposits of dead organic material around. The carbon is returned to the atmosphere when the organisms decay, and almost all is retuned within a few years.

      • In the Carboniferous, CO2 levels fell from 4,131 ppm to 359 ppm over 60 million years due to the vigorous vegetation of the time. That is a sink of 8,034 billion tons Carbon over that time.
        Between 32 to 24 million years ago, CO2 fell from 1,200 ppm to 280 ppm, most likely to the evolution of C4 grasses which now allowed plants to grow in all the dry and forest floor places where no plants could grow before. This increased the annual flows in the Carbon cycle and CO2 fell to 280 ppm for perhaps the very first time in Earth history. This is a sink of 2,000 tons Carbon over 8 million years.
        Right now, the Oceans, plants and soils (don’t forget that one) are sinking about 4 billion tons Carbon per year and this continues to increase as the level of CO2 increases.
        We are producing 9.5 billion tons Carbon per year today and the atmosphere has only increased by 265 billion tons Carbon since 1750.
        The sinks have huge capacity over the long-run compared to our puny emissions but the annual sink rate is probably going to be smaller than our emissions for a long time out.

  52. Clive,
    I have issues with some of the statements you make in your article.
    1) “If atmospheric carbon dioxide remains constant then a ph [sic] balance throughout the ocean volume can be reached.”
    I doubt that this statement is true. There is a constant rain of organic debris through the water column that oxidizes as it falls, producing CO2; this increases the pH such that up-welling water has a low pH compared to surface water. The deep water can probably take in considerably more CO2, but I doubt that an equilibrium will be reached unless there is a substantial increase in surface pH. That is true partly because CO2 is more soluble in cold water under high pressure. Therefore, the surface conditions are not as conducive to high pH as are deep water conditions.
    2) “This fact is obvious because run-away CO2 levels have never happened before in the earth’s long history.”
    Paleoclimatologists claim that there have been spikes in CO2 an order of magnitude greater than what is predicted for the worst-case scenario of anthropogenic CO2 emissions.
    3) You claim that the rate of change of sequestration is approximately 1/2 the rate of change of emissions. What evidence do you have that the constant of proportionality (0.46) is actually constant? Might it actually change with the rate of change of emissions or the partial pressure? I would expect that as surface water approaches saturation with CO2 that the constant of proportionality would decline, perhaps even to zero.
    4) “This does mean that CO2 levels will remain at ~410 ppm indefinitely, which is far higher than a planet without human beings,…”
    As I commented in 2) above, paleoclimatologists dispute this claim. Indeed, high CO2 levels have persisted for geologically long periods of time, calling into question your prediction of rapid stabilization.

    • Clyde,
      1) You’re right. The statement is incorrect. What I should have said is that ever accelerating rate of CO2 emissions is causing a change in ph in surface layers. This will stabilise once emissions are held constant and CO2 levels stabilise.
      2) Yes there have been varying levels of CO2 in the atmosphere through different epochs. What has never happened though is a run away greenhouse effect caused by ever increasing CO2 levels. The only spike in the data is the PETM event which released more CO2 than that contained in all known reserves of fossil fuels. This spike decayed back to normal within ~ 100,000 years.
      3) Nick Stokes has a proof that the exponential growth in emissions since 1930 has forced the airborne fraction to be a constant value. However this will change gradually to 100% once emissions stabilise. I have been scratching my head as to why the current value is ~0.5 I have no asnwer as yet.
      4) By that statement I really meant that 410ppm is larger than 280ppm which presumably would be the current value if we were still in the stone age. Of course over geological time scales CO2 will always vary. For example it will fall as low as 190ppm during the next ice age.

      • Clive,
        With respect to items 2) and 4), if you go to the illustration in the comment by Bartemis December 16, 2016 at 10:14 am, or the following one by LarryD, it is hard to even find the PETM ‘spike.’ Yes, the fact that Earth didn’t acquire a climate like that of Venus argues against the possibility of any kind of irreversible “Tipping Point.” The phrase is yet another scare tactic to try to get political action on what isn’t settled science. It isn’t even clear why there was a CO2 increase during the PETM. The Oligocene, which followed the Eocene, had unusually high volcanism, releasing CO2, yet the climate cooled.

  53. I would dispute that in the next few decades that global emissions can be stabilized at 30 GtCO2e. Currently they are about 55 GtCO2e and rising by 1-2% a year. The reason that they cannot be stabilized is that developing countries as the 1992 Rio Declaration recognized

    “The extent to which developing country Parties will effectively implement their commitments under the Convention … will take fully into account that economic and social development and poverty eradication are the first and overriding priorities of the developing country Parties.”

    This is fair enough to any reasonable person. However, in the period 1990-2012 global GHG emissions increased by just over 40%. Developing countries collectively accounted for all of this growth and by 2012 these developing countries accounted for nearly two-thirds of global emissions at 34.5 GtCO2e. This is slightly more than the level of global CO2 emissions Clive Best believes GHG levels will be stabilized.
    There is a distinction to be made here. Following Robin Guenier’s notes of a year ago I looked at total GHG emissions, whilst Clive Best concentrates on CO2 emissions – two-thirds of the total. The near-saturation of Methane (CH4) means that stablization is achievable in the medium term if the developed countries make massive and fast emissions reductions. Using the policy proposals put forward for COP21 Paris 12 months ago this seems unlikely. But in the longer term the non-policy developing countries with >80% of the global population will, by their economic development, cause global CO2 emissions to rise well beyond 30 GtCO2e even if we assume that from 01/01/2017 emissions from developed countries are zero. This can be conclusion can easily be derived the historical trends in my recent post.

  54. According to the palio record 150 million years ago the CO2 content of the atmosphere was 2,500ppm.
    The planet was lush (very green) and the critters were “yuge”. What’s not to like?

  55. Best concludes: “there is also a good chance that the world will achieve a fixed level of annual emissions, ….If I am right then CO2 levels will begin to level off within the next 10-20 years.”
    I may misunderstand Best’s argument, BUT it seems to ignore simple chemical-physical equilibrium.
    IF an additional 2 ppm of CO2 is added to the atmosphere each year, and IF half of that is removed yearly into the oceans, plants, etc., then 1 ppm is added each year to the atmosphere. This is the constant increase rate Best favors. That will continue to increase atmospheric CO2, and warming will increase in proportion to whatever the CO2 climate sensitivity happens to be. Warming will not stop simple because the atmospheric addition rate is constant. Considerations of equilibrium CO2 climate sensitivity versus equilibrium CO2 sensitivity does not change this.

    • No the argument is that by holding emissions constant the sinks will begin to increase the fraction of emissions they remove until eventually they remove all of it. How long this takes will depends on the ‘half life’ of the sinks as they act to equalise CO2 partial pressure in Ocean, Soils and Biosphere with the atmosphere. A half life of just 1 year would achieve this in 10 years, whereas a half life of 4 years would achieve this in 30 years.
      Thereafter CO2 levels stabilise at say 440ppm and reduce slowly as and when we cut back on emissions.

      • Chipstero7,
        Where you write in your blog:
        Probably the most incredible thing about the Revelle Factor is that it implies that the world’s oceans are absorbing naturogenic CO2 molecules at a vastly greater rate than anthropogenic ones preferentially.
        I have the feeling that you don’t have understood what the Revelle factor implies: It implies that for natural and human releases alike, any increase in the atmosphere is met with a an increase in the ocean surface of about 10% of the atmospheric change. That still is 10 times the amount that gets absorbed by fresh water at the same temperature for the same change in the atmosphere.
        The Revelle factor and Henry’s law work perfectly together: All what Henry’s law says is that for a 100% change in the atmosphere, there is a 100% change in what gets absorbed by the oceams. But that only counts for CO2 as gas in solution, not for C in the form of bicarbonates and carbonates, as these give zero CO2 pressure in the surface waters.
        A 100% change in CO2 pressure in the atmosphere will give a 100% change in free CO2 in solution for fresh and seawater alike, but as in fresh water 99% of all C is free CO2, there it stops. In seawater, free CO2 is only 1% of all inorganic carbon species and as that doubles to 2%, the reaction chain increases also bicarbonates and carbonates, leading to a much larger uptake by seawater than by fresh water for the same change in the atmosphere. That is the Revelle factor…
        Further, you are still using the arguments of the late Dr. Jaworowski: completely wrong on several points and ciompletely outdated for other points. See:

    • No Ferdinand, it is you who does not understand and have not taken the time to seriously consider my comment. I think that is because your mind has rejected it before you have had a chance to assimilate it and accommodate it in your thinking. In other words, you have put up a mental block to it – a wall of denial that prevents it from reaching your intelligence and being processed by it. The presence of the block in your mind is clear to me because you have made it explicit in saying: “The Revelle factor and Henry’s law work perfectly together” and that “It implies that for natural and human releases alike any increase in the atmosphere is met with an increase in the ocean surface of about 10% of the atmospheric change”. When you have embraced the scientific method (and basic logic) then we will be able to discuss the science. But until you have done that I have no interest in going round in circles with you ad nauseam, as Bart does.

      • chipstero7,
        My background is chemistry and later process automation but I am interested in all kinds of science. I do look at facts and simply accept them as base of any science, until proven wrong.
        Henry’s law is for the ratio between CO2 as gas in the atmosphere and CO2 as gas in solution. A 100% change of CO2 in the atmosphere gives a 100% change of free CO2 in water. No matter if that is fresh water or seawater. Nothing to do with the Revelle factor and completely independent of that factor.
        In fresh water almost all inorganic carbon present is free CO2, thus there the solubility stops.
        In seawater free CO2 is only 1% of all inorganic carbon present,the rest are bicarbonates and carbonates. These three species can be transferred into each other in either direction: if the CO2 pressure in the atmosphere changes (thus free CO2 in the ocean surface changes) or if the pH of the water changes.
        With a 100% increase in the atmosphere, the amount of free CO2 in the ocean surface doubles, but the other species (bicarbonates and carbonates) don’t double, as the chain reaction with more free CO2 gives also more H+, thus the pH lowers, and that pushes the reaction chain back towards free CO2.
        At the new equilibrium, there still is 100% more free CO2, but the ultimate increase in all C species together is ~10% of the change in the atmosphere. That is what the Revelle factor says.
        If you have a different explanation of what the Revelle factor means, please show me the chemistry…
        That is not only theory. It is actually measured in several places over time, here for Bermuda which has the longest series. See Fig. 5:
        CO2 in the atmosphere increased with ~15% in the period 1984-2012.
        DIC (total dissolved inorganic carbon) increased with ~1.7% in the same period…
        When you have embraced the scientific method (and basic logic) then we will be able to discuss the science.
        Wow, what do you know about ocean chemistry?

      • “No it doesn’t, it applies only to the surfac”I do look at facts and simply accept them as base of any science, until proven wrong”.
        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. I find it hard to believe that you have a background in chemistry and I am even more amazed that people here still regard you as a top-expert on this issue. It baffles my mind. Truly, it does. 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 (albeit only down to an alkalinity of about 7.5). However 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”. Hence 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. But of course, you ignored it, and just pretended that he was the one who was misunderstanding everything.

  56. The first thing that struck me about the math is this article was the assumed instantaneous response of the removal of CO2 to the increase in CO2. While this may be a good approximation for ocean systems, my understanding of the more permanent removal of CO2 is mostly through chemical reaction with erosion products (>2/3) and bio-remains (<1/3) such as ocean floor deposits. More likely there is a time delay factor to the rate response, which I think has been hinted at in the comments but not explicitly. There are probably several of these factors but they could be possibly approximated by a single term in the form of a function of the CO2 level at t – C where C is the effective time response. If this is found then the response to making the CO2 levels entering the atmosphere a constant could be any of three responses: 1) an exponential drop in the levels, 2) a decaying oscillation like a ringing bell, leveling out such as in the results above, or 3) a varying but ongoing oscillation such as observed in rabbit/coyote populations. The later could be around a constant, a decreasing or increasing average value. The exponential decrease is the one to be avoided as we don't want to over do it.

  57. My thinking has been along this line for some time. Why was the CO2 level so low in the atmosphere in the recent past? Because the biosphere (and limestone production) scavenged it out of the system until it hit starvation levels. No matter what rate CO2 is added, as soon as that rate becomes constant, the biosphere will increase until CO2 is reduced back to starvation levels.

  58. YOU WROTE:
    “I will argue below that in order to stop global warming all we really have to do is simply stabilise CO2 emissions, not reduce them to zero!”
    Why would anyone in their right mind want to stop global warming?
    After 150 years of warming, the climate in 2016 is wonderful !
    Plants are growing faster, and the Earth is greening.
    The warming measured in the weather satellite age (the only measurements accurate enough to discuss) is mainly at night in the northern half of the Northern Hemisphere — I can’t imagine the few people living in those cold climates are unhappy about slightly less cold nights !
    In addition, there is no scientific proof that CO2 is more than a minor factor in determining the average temperature.
    In the past 75 years alone, we have had three different relationships of CO2 and average temperature:
    1940 to 1975:
    CO2 up / Temp. down
    1975 to early 2000s:
    CO2 up / Temp up.
    Early 2000s to 2015:
    CO2 up / Temp. flat trend
    Other evidence that CO2 is not very important:
    — No warming of Antarctica in satellite age — which means the warming is not really global
    — No tropical troposphere hot spot ever found
    In summary, Mr. Best:
    (1) By starting with, and apparently believing, the assumption that CO2 is causing all the warming, you demonstrate that you are not very bright on the subject of climate science, and should not be listened to.
    (2) Even if it was true that CO2 since 1975 has controlled the average temperature (which it has never done in the past 4.5 billion years), you would have us believe that you are smarter than all the scientists supporting the IPCC, and have a much ‘easier’ way to stop global warming.
    By implying that you know more than the IPCC, which is very unlikely, you again demonstrate you are not very bright on the subject of climate change, and should not be listened to.
    This article is a complete waste of bandwidth.
    PS: I am in a good mood today, in case you thought otherwise

    • I forgot to mention almost no one will know what “a hiding to nothing” means, so it should not be used as a title of an article, or anywhere else, if lear communication is your goal.
      The writing style is also tedious and hard to follow.
      It should go without saying that I favor more CO2 in the air to further green the Earth.
      If that additional CO2 caused warming too, that would be even better news !
      I have observed the climate history in the past 150 years, and even if I assume ALL the warming was caused by man made CO2 (a more radical position than the IPCC), then I would still say: GIVE US MORE OF THAT !
      I wasn’t going to comment on your closing remarks, but I changed my mind:
      YOU WROTE:
      “Using remaining fossil fuels to control CO2 levels may one day have another advantage. It could mean that we can eventually use ‘enhanced global warming’ as a thermostat, thereby avoiding another devastating ice age otherwise due to begin within the next 5000 years.”
      That is a fantasyland statement no more useful than the fantasyland claim that manmade CO2 will cause runaway warming.
      You must have an advanced degree in something because you learned some math and science — and both have replaced common sense.
      No one knows when the next peak glaciation will happen.
      And no one knows when the 1950 modern warming will end and a cooling trend will begin.
      A multi-hundred year global cooling trend could have already started – no one knows yet.
      The flat average temperature trend between the 1998 El Nino and 2015/ 2016 El Nino temperature peaks is very suspicious, given how much CO2 was added to the atmosphere between those natural climate events.

      • IMO, based upon prior warm periods during the Holocene, it’s too soon for the Modern WP to end. But who knows?
        On average, it’s close to a millennium between temperature peaks and troughs, or about 500 years between a peak and a trough. For example, peak heat of the Medieval WP occurred around AD 1200 and the low of the LIA cold period shortly before 1700. The trough of the Dark Ages CP was circa 700. So, a rough estimate of the Modern WP peak would be near 2200.
        How many centennial-scale cold periods remain before descent into the next glacial interval is anybody’s guess. Based upon its orbital mechanics, the Holocene could be a super interglacial, lasting longer than 20,000 years.

  59. The airborne fraction is a merely an assumption based on a misuse of the mass-conservation law and it disregards Henry’s law. Until Clive (and the people making these sort of posts) decide to wake up one day and ever take into account Henry’s law (as it properly should be taken into account) and the fast equilibrium for CO2 (as evidenced by the bomb spike data) then their equations are utterly meaningless and have no relationship to reality. Read Segalstad 1998 (which is the only decent paper on this subject, together with Salby and Humlum), comprehend the evidence and arguments into your understanding, and then come back with something better.

    • chipstero7,
      Sorry, I did and all three persons you name were wrong – be it for different reasons:
      – Segalstad because he uses the residence time which is of zero interest to know what the decay rate is for an extra shot CO2 into the atmosphere. The residence tim for any CO2 molecule, whatever its origin, is about 5 years. The e-fold decay rate of an extra shot CO2, whatever its origin, above equilibrium is ~51 years. a factor 10.
      – Humlum used the 14C decay rate, but didn’t take into account that besides (more or less) the same mass ratio 14C/12C does sink in the deep oceans, a much smaller mass ratio is upwelling from the deep: what sinks is the isotopic composition of today, what is upwelling is the composition of ~1000 years ago.
      That makes that the decay rate of the 14C bomb spike is at least 3 times faster than for a 12CO2 spike…
      – I don’t remember if Salby was wrong on the residence time – e-fold decay rate, but he was certainly wrong on several other points…

  60. Leaving the science of CO2 sinks aside …. in order to keep atmospheric CO2 from human sources constant that means no economic growth in either the wealthy first world nations or the poor third world nations. In addition population growth is going to make that more difficult to accomplish. I suppose greater efficiencies in use of fossil fuels might help, but can the rate of increase in efficiencies keep up with the rate of population growth? In addition, “alternate sources of energy” have not been shown to be a viable alternative. So basically the argument is either 1) rich nations stay rich and poor nations stay poor or 2) rich nations become less rich so that their fuels can then be used by the poorer nations, and since poor nations are, by definition, poor, the wealthy nations will have to make gifts of their energy to the poor nations. Does anyone see option 2) happening? Is option 1) going to be a popular choice?

  61. Clive Best writes “I accept that the simplistic ‘half life’ reduction model is incorrect, but I kind of knew that anyway. ”
    Clive Best writes “I didn’t claim it was correct. I just said it was the simplest model you could take”
    Drawing conclusions based on a model you know to be incorrect? Good to see skepticism at work ;o)
    “The strange thing is that this airborne fraction hasn’t changed at all in 60 years, despite exponentially increasing human emissions.”
    Ironically, the reason that the airborne fraction hasn’t changed much in 60 years is because of exponentially increasing human emissions. Drive a first order linear dynamical system with an exponential signal and the response will be exponential signal with the same time constant, so if you take the ratio of the two you get a constant. This is not exactly rocket science. Of course the carbon cycle (on short timescales) is only approximately described by a first order linear DE, and anthropogenic emissions are only rising approximately exponentially, but then again the airborne fraction is only approximately constant.

    • I quote:

      The simplest assumption is that the sink increase depends only on the partial pressure difference for a given year.

      I agree this is very likely “wrong”. Ocean chemistry and dynamics are indeed complex, so please read the responses above before dismissing the basic argument that fixed sources and sinks must stabilise.
      You are also relying on an elegant mathematical result of Nick Stokes when you state.

      Drive a first order linear dynamical system with an exponential signal and the response will be exponential signal with the same time constant, so if you take the ratio of the two you get a constant. This is not exactly rocket science.

      However what you write makes no sense. Neither nature itself or the Berne model could be considered a ” first order linear dynamical system”.
      If AF decreases as emissions stabilise the Fig 10 above will be proved wrong.

      • Clive Best wrote “I agree this is very likely “wrong”.”
        There is no reason for the quotes around wrong, it is just wrong. Apparently you “kind of knew that anyway.” but carried on promulgating the idea anyway. Not very “skeptical”.
        Clive Best wrote “Ocean chemistry and dynamics are indeed complex, so please read the responses above before dismissing the basic argument that fixed sources and sinks must stabilise.”
        Of course atmospheric CO2 will stabilise, just not on the sort of timescale you are suggesting and at a much higher level. Please read the responses on your own blog and at ATTPs that explain why.
        Clive Best wrote “You are also relying on an elegant mathematical result of Nick Stokes when you state.”
        No, you will find the same result obtained in a different way in my journal paper (note date):
        Gavin C. Cawley, On the atmospheric residence time of anthropogenically sourced carbon dioxide, Energy & Fuels, volume 25, number 11, pages 5503–5513, September 2011. (preprint).
        You will find it in the section “Modelling the Ariborne Fraction” (page 22, and the result is mentioned in the abstract). Now I pointed this paper out to you here on your own blog, but your comment above suggests you didn’t actually bother to read it (despite requesting me to read the “responses above”, again not very “skeptical”). I rather doubt I am the first person to derive this result, as I said, it is hardly rocket science.
        The simple model in my paper would suggest that stabilisation would happen on the timescale of 70 years or so, but the paper also has a section on the limitations of this sort of simplistic model (which is still more realistic than yours), which means that is not actually the case and in reality it will take much longer if emissions were stabilised.
        Clive Best wrote “However what you write makes no sense. Neither nature itself or the Berne model could be considered a ” first order linear dynamical system””
        LOL, I can see you didn’t bother reading the whole paragraph, which ended:
        “Of course the carbon cycle (on short timescales) is only approximately described by a first order linear DE, and anthropogenic emissions are only rising approximately exponentially, but then again the airborne fraction is only approximately constant.” [emphasis mine].
        Again pretty ironic given that you requested me to read the “responses above” when you clearly didn’t bother (or did and chose to ignore the parts that didn’t suit you, which is arguably worse).

    • “The Revelle factor is about 10, which means that the fractional change in atmospheric CO2 will be about 10 times bigger than the fractional change in DIC. What this tells you straight away is that you can’t change the amount of CO2 in the oceans without also change the amount in the atmosphere; stabilising emissions will not stabilise concentrations.”
      This is where ATTP is full of thermally enhanced gas (aka hot air)… Yes, he gave the Revelle factor as 10 – good. He mentions DIC, and that the fractional change in DIC will be lower than the fractional change in CO2. BUT HE FAILS TO MENTIONS THE AMOUNT OF DIC. You see, DIC is about 37,000 Gt C, almost 60 times the amount of CO2 in the atmosphere. So the fractional change would not be 25% but closer to 80-85%.
      But there is a reason it is only 25% and not 80% absorbed and that is that the whole ocean, including the deep ocean, is not in direct contact with the atmosphere; the process of moving CO2 to the deep ocean is a slow one. Only the ocean surface and surface waters absorb CO2, which then has both chemical (carbonates) and biological processes that absorb the CO2, convert it into other DIC forms, and then send it to the deep ocean. slowly. Or at least at a slower rate than we are adding CO2 today.
      Which further means that even though we changed atmospheric CO2 from 300ppm to 400ppm, the process of adjusting the deep ocean is catching up. So ATTP fails to mention is that DIC IN THE DEEP OCEAN IS STILL CLOSE TO THE 290 PPM EQUIVALENT IN THE ATMOSPHERE. In other words, DIC is both huge AND far from the equilibrium it would be at were the
      That’s why ATTP’s rejoinder is wrong. He sets 20% as the “lower limit”, but that is a lower limit ONLY AFTER REACHING EQUILIBRIUM. Before then, the oceans capacity to absorb is based on the CO2 disequilibrium and the limits of ocean-surface-air interface.
      One merely has to ask: “How much CO2 has to go into the oceans to get to equilibrium?” And it is about 6 times the CO2 we’ve emitted thus far. In other words, we could continue to emit at current levels of CO2 into the air for about 200 years before hitting ‘equilibrium’ in the oceans; we would hit CO2 equilibrium well before then, in fact, in about the next 30-40 years. In the intervening 200 years, we would be at stabilized CO2 levels, more or less.

  62. Don’t believe in
    “Reducing emissions in the future will slowly cause such ‘stable’ CO2 levels to fall.”
    – Do want heated highways, no snow no ice.
    – What’s wrong with.

  63. But isn’t there a limit to the effect that carbon dioxide can have on average climate temperature, most of which has already been realized?
    Reason is basic physics of absorption and emission of energy from “greenhouse gas” molecules and the overlap of spectra of carbon dioxide and the vapour of dihydrogen monoxide (the most plentiful greenhouse gas).
    Then note that runaway warming did not occur during the Medieval Warm Period when Vikings farmed southwest Greenland – i.e. climate was stable at temperatures warmer than today.
    So why do you want to bother even limiting CO2 emissions by humans?
    As for an individual’s weight plateauing at a higher level, some obese individuals have gotten to 600 pounds or beyond. Bad analogy.

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