Reposted from Dr. Roy Spencer’s Blog
February 5th, 2020 by Roy W. Spencer, Ph. D.
Note: What I present below is scarcely believable to me. I have looked for an error in my analysis, but cannot find one. Nevertheless, extraordinary claims require extraordinary evidence, so let the following be an introduction to a potential issue with current carbon cycle models that might well be easily resolved by others with more experience and insight than I possess.
Summary
Sixty years of Mauna Loa CO2 data compared to yearly estimates of anthropogenic CO2 emissions shows that Mother Nature has been removing 2.3%/year of the “anthropogenic excess” of atmospheric CO2 above a baseline of 295 ppm. When similar calculations are done for the RCP (Representative Concentration Pathway) projections of anthropogenic emissons and CO2 concentrations it is found that the carbon cycle models those projections are based upon remove excess CO2 at only 1/4th the observed rate. If these results are anywhere near accurate, the future RCP projections of CO2, as well as the resulting climate model projection of resulting warming, are probably biased high.
Introduction
My previous post from a few days ago showed the performance of a simple CO2 budget model that, when forced with estimates of yearly anthropogenic emissions, very closely matches the yearly average Mauna Loa CO2 observations during 1959-2019. I assume that a comparable level of agreement is a necessary condition of any model that is relied upon to predict future levels of atmospheric CO2 if it is have any hope of making useful predictions of climate change.
In that post I forced the model with EIA projections of future emissions (0.6%/yr growth until 2050) and compared it to the RCP (Representative Concentration Pathway) scenarios used for forcing the IPCC climate models. I concluded that we might never reach a doubling of atmospheric CO2 (2XCO2).
But what I did not address was the relative influence on those results of (1) assumed future anthropogenic CO2 emissions versus (2) how fast nature removes excess CO2 from the atmosphere. Most critiques of the RCP scenarios address the former, but not the latter. Both are needed to produce an RCP scenario.
I implied that the RCP scenarios from models did not remove CO2 fast enough, but I did not actually demonstrate it. That is the subject of this short article.
What Should the Atmospheric CO2 Removal Rate be Compared To?
The Earth’s surface naturally absorbs from, and emits into, the huge atmospheric reservoir of CO2 through a variety of biological and geochemical processes.
We can make the simple analogy to a giant vat of water (the atmospheric reservoir of CO2), with a faucet pouring water into the vat and a drain letting water out of the vat. Let’s assume those rates of water gain and loss are nearly equal, in which case the level of water in the vat (the CO2 content of the atmosphere) never changes very much. This was supposedly the natural state of CO2 flows in and out of the atmosphere before the Industrial Revolution, and is an assumption I will make for the purposes of this analysis.
Now let’s add another faucet that drips water into the vat very slowly, over many years, analogous to human emissions of CO2. I think you can see that there must be some change in the removal rate from the drain to offset the extra gain of water, otherwise the water level will rise at the same rate that the additional water is dripping into the vat. It is well known that atmospheric CO2 is rising at only about 50% the rate at which we produce CO2, indicating the “drain” is indeed flowing more strongly.
Note that I don’t really care if 5% or 50% of the water in the vat is exchanged every year through the actions of the main faucet and the drain; I want to know how much faster the drain will accomodate the extra water being put into the tank, limiting the rise of water in the vat. This is also why any arguments [and models] based upon atomic bomb C-14 removal rates are, in my opinion, not very relevant. Those are useful for determining the average rate at which carbon cycles through the atmospheric reservoir, but not for determining how fast the extra ‘overburden’ of CO2 will be removed. For that, we need to know how the biological and geochemical processes change in response to more atmospheric CO2 than they have been used to in centuries past.
The CO2 Removal Fraction vs. Emissions Is Not a Useful Metric
For many years I have seen reference to the average equivalent fraction of excess CO2 that is removed by nature, and I have often (incorrectly) said something similar to this: “about 50% of yearly anthropogenic CO2 emissions do not show up in the atmosphere, because they are absorbed.” I believe this was discussed in the very first IPCC report, FAR. I’ve used that 50% removal fraction myself, many times, to describe how nature removes excess CO2 from the atmosphere.
Recently I realized this is not a very useful metric, and as phrased above is factually incorrect and misleading. In fact, it’s not 50% of the yearly anthropogenic emissions that is absorbed; it’s an amount that is equivalent to 50% of emissions. You see, Mother Nature does not know how much CO2 humanity produces every year; all she knows is the total amount in the atmosphere, and that’s what the biosphere and various geochemical processes respond to.
It’s easy to demonstrate that the removal fraction, as is usually stated, is not very useful. Let’s say humanity cut its CO2 emissions by 50% in a single year, from 100 units to 50 units. If nature had previously been removing about 50 units per year (50 removed versus 100 produced is a 50% removal rate), it would continue to remove very close to 50 units because the atmospheric concentration hasn’t really changed in only one year. The result would be that the new removal fraction would shoot up from 50% to 100%.
Clearly, that change to a 100% removal fraction had nothing to do with an enhanced rate of removal of CO2; it’s entirely because we made the removal rate relative to the wrong variable: yearly anthropogenic emissions. It should be referenced instead to how much “extra” CO2 resides in the atmosphere.
The “Atmospheric Excess” CO2 Removal Rate
The CO2 budget model I described here and here removes atmospheric CO2 at a rate proportional to how high the CO2 concentration is above a background level nature is trying to “relax” to, a reasonable physical expectation that is supported by observational data.
Based upon my analysis of the Mauna Loa CO2 data versus the Boden et al. (2017) estimates of global CO2 emissions, that removal rate is 2.3%/yr of the atmospheric excess above 295 ppm. That simple relationship provides an exceedingly close match to the long-term changes in Mauna Loa yearly CO2 observations, 1959-2019 (I also include the average effects of El Nino and La Nina in the CO2 budget model).
So, the question arises, how does this CO2 removal rate compare to the RCP scenarios used as input to the IPCC climate models? The answer is shown in Fig. 1, where I have computed the yearly average CO2 removal rate from Mauna Loa data, and the simple CO2 budget model in the same way as I did from the RCP scenarios. Since the RCP data I obtained from the source has emissions and CO2 concentrations every 5 (or 10) years from 2000 onward, I computed the yearly average removal rates using those bounding years from both observations and from models.
Fig. 1. [fixed] Computed yearly average rate of removal of atmospheric CO2 above a baseline value of 295 ppm from historical emissions estimates compared to Mauna Loa data (red), the RCP scenarios used by the IPCC CMIP6 climate models, and in a simple time-dependent CO2 budget model forced with historical emissions before, and assumed emissions after, 2018 (blue). Note the time intervals change from 5 to 10 years in 2010.
The four RCP scenarios do indeed have an increasing rate of removal as atmospheric CO2 concentrations rise during the century, but their average rates of removal are much too low. Amazingly, there appears to be about a factor of four discrepancy between the CO2 removal rate deduced from the Mauna Loa data (combined with estimates of historical CO2 emissions) versus the removal rate in the carbon cycle models used for the RCP scenarios during their overlap period, 2000-2019.
Such a large discrepancy seems scarcely believable, but I have checked and re-checked my calculations, which are rather simple: they depend only upon the atmospheric CO2 concentrations, and yearly CO2 emissions, in two bounding years. Since I am not well read in this field, if I have overlooked some basic issue or ignored some previous work on this specific subject, I apologize.
Recomputing the RCP Scenarios with the 2.3%/yr CO2 Removal Rate
This raises the question of what the RCP scenarios of future atmospheric CO2 content would look like if their assumed emissions projections were combined with the Manua Loa-corrected excess CO2 removal rate of 2.3%/yr (above an assumed background value of 295 ppm). Those results are shown in Fig. 2.
Fig. 2. Four RCP scenarios of future atmospheric CO2 through 2100 (solid lines), and corrected for the observed rate of excess CO2 removal based upon Mauna Loa data (2.3%/yr of the CO2 excess above 295 ppm, dashed lines).
Now we can see the effect of just the differences in the carbon cycle models on the RCP scenarios: those full-blown models that try to address all of the individual components of the carbon cycle and how it changes as CO2 concentrations rise, versus my simple (but Mauna Loa data-supportive) model that only deals with the empirical observation that nature removes excess CO2 at a rate of 2.3%/yr of the atmospheric excess above 295 ppm.
This is an aspect of the RCP scenario discussion I seldom see mentioned: The realism of the RCP scenarios is not just a matter of what future CO2 emissions they assume, but also of the carbon cycle model which removes excess CO2 from the atmosphere.
Discussion
I will admit to knowing very little about the carbon cycle models used by the IPCC. I’m sure they are very complex (although I dare say not as complex as Mother Nature) and represent the state-of-the-art in trying to describe all of the various processes that control the huge natural flows of CO2 in and out of the atmosphere.
But uncertainties abound in science, especially where life (e.g. photosynthesis) is involved, and these carbon cycle models are built with the same philosophy as the climate models which use the output from the carbon cycle models: These models are built on the assumption that all of the processes (and their many approximations and parameterizations) which produce a reasonably balanced *average* carbon cycle picture (or *average* climate state) will then accurately predict what will happen when that average state changes (increasing CO2 and warming).
That is not a given.
Sometimes it is useful to step back and take a big-picture approach: What are the CO2 observations telling us about how the global average Earth system is responding to more atmospheric CO2? That is what I have done here, and it seems like a model match to such a basic metric (how fast is nature removing excess CO2 from the atmosphere, as the CO2 concentration rises) would be a basic and necessary test of those models.
According to Fig. 1, the carbon cycle models do not match what nature is telling us. And according to Fig. 2, it makes a big difference to the RCP scenarios of future CO2 concentrations in the atmosphere, which will in turn impact future projections of climate change.
So if that’s the case, a sudden stop in fossil fuel burning would leave us with 97.7% of the excess CO2 after 1 yr, then 97.7%x97.7%=95.5% after 2 yrs, and so on, right?
If 350ppm is supposed to be the “safe” level (according to Bill McKibben and 350.org), we would hit that after about 32 years. If we drive CO2 up to 560ppm before we perfect thorium reactors (or whatever), then we will take about 68 years to get back to 350ppm. But at 2.5ppm/yr increase, it would take us until 2080 to reach 560ppm. So we would have 60 years to perfect nuclear. By 2148 when we would be back at 350ppm, we’d need to start burning fossil fuels again to keep agriculture working smoothly.
If ECS is around a lukewarmist’s 1.8K and the transient response is half of that, then at 560ppm (doubling from 280) we’d be about 0.9K hotter than 1850. How can that possibly be a problem? It’s a benefit in every regard, slightly milder winters and nights, much higher crop yields, better water utilization.
On the other hand, let natural cooling set in and agricultural output plummets. That’s the real problem, folks, and there’s not much we could do about it.
In fact, it’s not 50% of the yearly anthropogenic emissions that is absorbed; it’s an amount that is equivalent to 50% of emissions.
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Agreed. I made that same point years ago when studying this question. As i recall it has a huge impact on the underlying math, because it throws cause and effect into question.
How can the absorption remain at 50% of human emissions, when nature has no way to distinguish between human and natural emissions.
Coincidence is not a good explanation.
People should note that Fig. 1 (the main plot) was incorrect, and Charles has put the correct one in there now. It is the key figure, and most people here commented before the figure was corrected.
So, more CO2 in ocean, more phyto, more pyramid…
The Oceans are not just Base, they are BUFFERED Base.
Me too, but I bet dimes for Dollars that they make some unsubstantiated assumptions about the rate of CO2 absorption at ocean surfaces and other air-water interfaces.
The rate of CO2 absorption and conversion to aqueous carbonate/bicarbonate is actually quite a slow reaction. This is why the enzyme carbonic anhydrase is truly ubiquitous in nature, typically speeding up the chemical reaction by a factor of a million or more(*). It makes for a quite interesting undergraduate teaching/demonstration experiment.
The bulk of ocean surfaces are quite probably covered by a bacterial biofilm acting as one enormous catalytic layer, maybe only ~one cell thick. Depending on the presence or absence and effectiveness of this catalytic biofilm the actual observed absorption rates may (or may not) be governed by mass transfer and not necessarily the expected rates based upon simple chemical thermodynamics. As far as I am aware carbon cycle modelers may consider direct CO2 sequestration by photosynthesis, but ignore such possible effects of biology upon “inorganic” carbon dioxide pathways.
(* One paper I read some years ago undertook a study of gene expression by E. Huxleyi under conditions of increased carbon dioxide. The biggest change they found was, unsurprisingly to me, a change in the amount of expressed genes coding for carbonic anhydrase.)
The test for Fig. 1 has “the RCP scenarios used by the IPCC CMIP6 climate models”. In the article at drroyspencer.com, it says these are the RCPs used by the CMIP5 models.
Let’s say humanity cut its CO2 emissions by 50% in a single year, from 100 units to 50 units. If nature had previously been removing about 50 units per year (50 removed versus 100 produced is a 50% removal rate), it would continue to remove very close to 50 units because the atmospheric concentration hasn’t really changed in only one year. The result would be that the new removal fraction would shoot up from 50% to 100%.
I have been saying this since years ago, although certainly not often enough. If currently only the equivalent of 45% of our emitted CO2 is being added to the atmosphere every year, then for CO2 to stop rising we do NOT need to cut our emissions 100%. Just reducing them to half the current ammount will make the CO2 levels stop rising (and plants will not be very happy about it, although they should still thank us for the increased levels compared to preindustrial).
Thanks, folks, for a very interesting discussion, conducted politely, and with some interesting new-to-me science.
Anthony, Charles and all: keep up the good work! Science does self-correct, even if frustratingly slowly. Recalling Richard Feynman: “Reality must take precedence over public relations, for Nature cannot be fooled.” Likewise, environmental politicians. I think there are signs that the worm turns. I hope so!
Regarding “Note that I don’t really care if 5% or 50% of the water in the vat is exchanged every year through the actions of the main faucet and the drain; I want to know how much faster the drain will accomodate the extra water being put into the tank, limiting the rise of water in the vat. This is also why any arguments [and models] based upon atomic bomb C-14 removal rates are, in my opinion, not very relevant. Those are useful for determining the average rate at which carbon cycles through the atmospheric reservoir, but not for determining how fast the extra ‘overburden’ of CO2 will be removed.”:
This is the difference between C14 dioxide removal rate after the end of “the bomb tests” (half life about 10 years) and either the Bern model or a competing exponential decay model, such as one with a half life of 41 years (time constant “tau” or “e-folding” time of 59 years), mentioned in https://wattsupwiththat.com/2015/04/19/the-secret-life-of-half-life/
Dr. Spencer’s model appears to me as similar to the model by Willis Eschenbach, apparently same type model (exponential decay of short term pulses / injections of CO2 into the atmosphere, constant percentage per year of “excess” over some “pre-industrial baseline” being absorbed from the atmosphere with moderate differences in numbers: Spencer’s model is annual removal by nature being 2.33% of “excess” above 295 PPM, and Eschenbach’s model was 1.695% of “excess” above 283 PPM (that I worked out from Eschenbach’s statement of time constant of 59 years). Spencer’s model has a somewhat shorter time constant of about 43 years and half life around 29.4 or 29.7 years (with discrepancy being from using time two different calculation methods, at least one of them assuming a time step of one year).
It’s not a vat or a bucket. It’s a river. Not of water, but of CO2, transported along with the waters that make up the vast flows of the THC.
CO2 levels in the atmosphere follow the levels in the upper oceans. The oceans are continually draining CO2 laden waters through downwelling at the poles, and replenishing it via upwelling at the equator. CO2 content of the surface waters can increase two ways: 1) increased upwelling content, and 2) decreased downwelling content.
The upwelling waters were set in motion perhaps 1,000 years ago, and they cannot be stopped or modulated. But, downwelling transport can be modulated by surface temperatures. This begets a temperature dependency in the rate of change of CO2 concentration. This dependency is starkly observable in the data:
http://woodfortrees.org/plot/esrl-co2/mean:12/from:1979/derivative/plot/uah6/scale:0.18/offset:0.144
The way data is being moulded by humans lead me to name the current era not the Anthropocene, but the Plasticine..
It would be a simple matter to make a table with global warming factors, including the contribution from CO2, from 1979 to present, and list CO2 ppm for each year. This would give factor change and PPM change for each year. That can be compared with global temperature change.
If CO2 removal rates are 4X higher, then a new table could be constructed, with a new value for contribution from CO2. This would give a NEW factor change and the same PPM change for each year. That can be compared with the same global temperature change.
The table would show the CO2 contribution increases VERY SLOWLY with PPM, much slower than IPCC, etc., are claiming.
That should lead to much less fear-mongering regarding CO2 and banning fossil fuels.
“Nature Has Been Removing Excess CO2 4X Faster than IPCC Models”
How fast do models remove CO2?
“Let’s assume those rates of water gain and loss are nearly equal, in which case the level of water in the vat (the CO2 content of the atmosphere) never changes very much. This was supposedly the natural state of CO2 flows in and out of the atmosphere before the Industrial Revolution, and is an assumption I will make for the purposes of this analysis.”
There is the whole problem, in a nutshell. The whole notion that “we” are responsible for atmospheric CO2 changes is based on nothing more than an ASSUMPTION.
Assumptions are not facts. The simple FACT is that we don’t know what the “drivers” behind changes to the atmospheric CO2 level are, because we’re not measuring the vast majority of the “sources” and none of the “sinks.”
And there IS NO “excess” CO2; the present levels are barely sufficient, given how they are likely to plummet with the next glaciation, and given how close we are to reaching a level that is so low that it would mean the end of photosynthesis and with it, all life as we know it. More is better; let’s stop acting like the supposed “pre-industrial” level (which is likely a falsehood since it is based on poor proxies) is some kind of “ideal.”
That lowermost RCP model curve insists that the levels would try to return to the preindustrial levels from the Little Ice Age. The math might try to do so, but it seems like an unwarranted assumption for warmer periods.
One also needs to consider that when CO2 rises, conditions become more favorable for plant growth. This leads to an increase in planetary vegetation, which consumes more CO2 to sustain itself. This is the part of the equation that is not adequately addressed, and may explain the shortcomings of the climate model “predictions”.
Update: Dr. Roy Spencer found his error. Natural removal rate of CO2 from the atmosphere from 2000 to 2020 is consistent with the RCPs, not 4 times what is indicated by the RCPs. It is also consistent with both Spencer’s simple model. Spencer’s update is at
http://www.drroyspencer.com/2020/02/corrected-rcp-scenario-removal-fractions/
If Spencer’s model is correct, that the NET CO2 removal rate from the atmosphere is 2.3%/yr of the excess CO2 concentration over 295 ppm, then at 410 ppm, the removal rate should be 0.023 * (410 – 295) = 2.645 ppm/yr. A mass balance on the atmosphere shows that 1 ppm CO2 corresponds to about 8 gigatons (8 * 10^12 kg) of CO2, so that the current NET removal rate would be 2.645 * 8 = 21.2 GT/yr.
Spencer’s model assumes that the NET removal rate varies linearly with concentration, but what is the significance of the X intercept of his straight line at 295 ppm? If the processes removing CO2 from the atmosphere (such as photosynthesis) were first-order reactions, where rate is proportional to CO2 (reactant) concentration, then the total CO2 removal rate at 410 ppm should be 0.023 * 410 = 9.43 ppm/yr = 75.4 GT/yr. This would be partially counteracted by a natural CO2 emission rate of 0.023 * 295 (the X intercept of Spencer’s line) = 6.79 ppm/yr = 54.3 GT/yr (which could be due to animal respiration, volcanos, rotting vegetation and animals, and net emissions from the oceans).
Current human CO2 emissions are running about 37 GT/yr, which means that according to Spencer’s model, total CO2 input is 54.3 (natural) + 37 (human) = 91.3 GT/yr, with absorption of 75.4 GT/yr, for a net gain of 15.9 GT/yr, or about 2 ppm/yr increase in CO2 in the atmosphere.
According to this model, if human emissions remained constant at 37 GT yr, the equilibrium concentration X, at which human emissions = net removal rate, could be calculated as 37 = 0.023 * 8 * (X – 295), from which X = 295 + 37 / (0.023 * 8) = 496 ppm. If human emissions increased beyond 37 GT/yr, the equilibrium concentration would be higher, by about 5.4 ppm per additional GT/yr emitted. In order to reach an equilibrium concentration of 600 ppm, human emissions would have to rise above 56 GT/yr, or about 51% above current emission rates.
Roy,
From a chemical exchange and equilibrium viewpoint, I give some thoughts about the atmospheric (Atm) CO2 removal rate, which likely has steadily increased over time.
If Atm CO2 were suddenly increased in one step and nothing changed in the characteristics of those CO2 uptake reservoirs (e.g., oceans, plants & soil), then the two concentrations would be out of equilibrium. An increased amount of CO2 would then flow from Atm to these other reservoirs until a new equilibrium was established.
But this simple scenario does not consider either the rate (kinetics) of the CO2 exchange process nor of changes in the uptake reservoirs. Here is one example. Increasing Atm CO2 is not immediately absorbed by the oceans. Rather, as Atm CO2 gradually increases, the rate of CO2 uptake into the oceans likely falls further behind. Most CO2 uptake into oceans occurs near-surface, whereas decades to centuries are required for the surface ocean to transfer that CO2 to the deeper ocean. The potential for oceans to absorb more Atm CO2 is there, but the kinetics (rate) of the transfer process cannot accommodate the much faster rate Atm CO2 is increasing.
This implies that as Atm CO2 increases, the amount by which the CO2 concentration difference between Atm and ocean grows larger and the equilibrium condition falls further and further behind. An increasing rate of Atm CO2 would therefore bring the Atm–Ocean exchange further and further out of equilibrium and would steadily increase the rate that CO2 is removed from the Atm.
This view also has implications if CO2 addition to the Atm were to totally stop (not just slow to a zero rate increase). The exchange rate of Atm CO2 into the ocean would continu at a slowly decreasing rate for many years. Changing the rate of Atm CO2 increase (now positive) to zero (i.e. a constant, not increasing rate of CO2 addition), would require even more time to achieve a new reservoir concentration equilibrium.
One ought to see today a higher rate of Atm CO2 removal compared to decades ago, and a higher rate of Atm CO2 removal in future years compared to today.
Instead of a drain at the bottom of the vat, assume that there is a vertical slot cut in the side of the vat. Initially no water will run out until it reaches the level of the slot. And then as the water rises further, the water will run out faster and faster until it reaches equilibrium.
Now increase the rate of water flowing in. The level will rise, more will flow out of the slot until a new equilibrium is reached.
In such a case, the sink rate lags the source rate. But the sink does not stop increasing immediately after the source stops increasing. Rather the sink will continue to increase until a new equilibrium is reached.
it is found that the carbon cycle models those projections are based upon remove excess CO2 at only 1/4th the observed rate –> it is found that the carbon cycle models’ projections are based upon remove of excess CO2 at only 1/4th of the observed rate
a comparable level of agreement is a necessary condition of any model that is relied upon to predict future levels of atmospheric CO2 if it is have any hope of making useful predictions of climate change –> a comparable level of agreement is a necessary condition for any model to get relied upon predicting future levels of atmospheric CO2 having any hope of making useful predictions of climate change
/ sheer mikado
where I have computed the yearly average CO2 removal rate from Mauna Loa data, and the simple CO2 budget model in the same way as I did from the RCP scenarios –> where I have computed the yearly average CO2 removal rate from Mauna Loa data, and have computed the simple CO2 budget model in the same way as I did from the RCP scenarios
which produce a reasonably balanced *average* carbon cycle picture (or *average* climate state) will then accurately predict –> which produce a reasonably balanced *average* carbon cycle (or *average* climate state) picture will then accurately predict
Donald L. Klipstein February 7, 2020 at 8:50 am
The oceans have been a net absorber of CO2 since burning of fossil fuels became a significant source of CO2 –> The oceans have been a shock-absorber of CO2 since evah !