Will Humanity Ever Reach 2XCO2? Possibly Not

Reposted from Dr. Roy Spencer’s Blog

February 1st, 2020 by Roy W. Spencer, Ph. D.

Summary

The Energy Information Agency (EIA) projects a growth in energy-based CO2 emissions of +0.6%/yr through 2050. But translating future emissions into atmospheric CO2 concentration requires a global carbon budget model, and we frequently accept the United Nations reliance on such models to tell us how much CO2 will be in the atmosphere for any given CO2 emissions scenario. Using a simple time-dependent CO2 budget model forced with yearly estimates of anthropogenic CO2 emissions and optimized to match Mauna Loa observations, I show that the EIA emissions projections translate into surprisingly low CO2 concentrations by 2050. In fact, assuming constant CO2 emissions after 2050, the atmospheric CO2 content eventually stabilizes at just under 2XCO2.

Introduction

I have always assumed that we are on track for a doubling of atmospheric CO2 (“2XCO2”), if not 3XCO2 or 4XCO2. After all, humanity’s CO2 emissions continue to increase, and even if they stop increasing, won’t atmospheric CO2 continue to rise?

It turns out, the answer is probably “no”.

The rate at which nature removes CO2 from the atmosphere, and what controls that rate, makes all the difference.

Even if we knew exactly what humanity’s future CO2 emissions were going to be, how much Mother Nature takes out of the atmosphere is seldom discussed or questioned. This is the domain of global carbon cycle models which we seldom hear about. We hear about the improbability of the RCP8.5 concentration scenario (which has gone from “business-as-usual”, to “worst case”, to “impossible”), but not much about how those CO2 concentrations were arrived at from CO2 emissions data.

So, I wanted to address the question, What is the best estimate of atmospheric CO2 concentrations through the end of this century, based upon the latest estimates of future CO2 emissions, and taking into account how much nature has been removing from the atmosphere?

As we produce more and more CO2, the amount of CO2 removed by various biological and geophysical processes also goes up. The history of best estimates of yearly anthropogenic CO2 emissions, combined with the observed rise of atmospheric CO2 at Mauna Loa, Hawaii, tells us a lot about how fast nature adjusts to more CO2.

As we shall see, it is entirely possible that even if we continued producing large quantities of CO2, it is possible for CO2 levels in the atmosphere to eventually stabilize.

In their most recent 2019 report, the U.S. Energy Information Agency (EIA) projects that energy-based emissions of CO2 will grow at 0.6% per year until 2050, which is what I will use to project future atmospheric CO2 concentrations. I will show what this emissions scenario translates into using a simple atmospheric CO2 budget model that has been calibrated with the Mauna Loa data. And we will see that the resulting remaining amount of CO2 in the atmosphere is surprisingly low.

A Review of the CO2 Budget Model

I previously presented a simple time-dependent CO2 budget model of global atmospheric CO2 concentration that uses (1) yearly anthropogenic CO2 emissions, along with (2) the central assumption (supported by the Mauna Loa CO2 data) that nature removes CO2 from the atmosphere at a rate in direct proportion to how high atmospheric CO2 is above some natural level the system is trying to ‘relax’ to.

As described in my previous blog post, I also included an empirical El Nino/La Nina term since El Nino is associated with higher CO2 in the atmosphere, and La Nina produces lower concentrations. This captures the small year-to-year fluctuations in CO2 from ENSO activity, but has no impact on the long-term behavior of the model.

The model is initialized in 1750 with the Boden et al. (2017) estimates of year anthropogenic emissions, and produces an excellent fit to the Mauna Loa CO2 observations using the assumption of a baseline (background) CO2 level of 295 ppm and a natural removal rate of 2.33% per year of the atmospheric excess above that baseline.

Here is the resulting fit of the model to Mauna Loa data, with generally excellent results. (The post-Pinatubo reduction in atmospheric CO2 is believed to be due to increased photosynthesis due to an increase in diffuse sunlight penetration into forest canopies caused by the volcanic aerosols):

Fig. 1. Calibrated CO2 budget model compared to the Mauna Loa, Hawaii CO2 observations. The model is forced with the Boden et al. (2017) estimates of yearly anthropogenic CO2 emissions, and removes CO2 in proportion to the excess of atmospheric CO2 above a baseline value.

The model even captures the slowly increasing trend in the apparent yearly fractional removal of CO2 emissions.

Fig. 2. Yearly apparent fraction of anthropogenic emissions removed by nature, in the Mauna Loa observations (red) versus the model (blue).

Model Projections of Atmospheric CO2

I forced the CO2 model with the following two future scenario assumptions:

1) EIA assumption of 0.6% per year growth in emissions through 2050
2) Constant emissions from 2050 onward

The resulting CO2 concentration is shown in Fig. 3, along with the CO2 concentration scenarios, RCP2.6, RCP4.5, RCP6.0, and RCP8.5, used in the CMIP5 climate model projections.

CO2-model-for-blog-post-fig03-550x453Fig. 3. CO2 model projection of atmospheric CO2 assuming EIA estimates of CO2 emissions growth through 2050, followed by constant CO2 emissions afterward.

Interestingly, with these rather reasonable assumptions regarding CO2 emissions, the model does not even reach a doubling of atmospheric CO2, and reaches an equilibrium CO2 concentration of 541 ppm in 2240.

Discussion

In my experience, the main complaint about the current model will be that it is “too simple” and therefore probably incorrect. But I would ask the reader to examine how well the simple model assumptions explain 60 years of CO2 observations (Figs. 1 & 2).

Also, I would recall the faulty predictions many years ago by the global carbon cycle modelers that the Earth system could not handle so much atmospheric CO2, and that the fraction which is removed over time would start to decrease. As Fig. 2 (above) shows, that has not happened. Maybe when it comes to photosynthesis, more life begets still more life, leading to a slowly increasing ability of the biosphere to remove excess CO2 from the atmosphere.

Given the large uncertainties in how the global carbon cycle responds to more CO2 in the atmosphere, it is entirely reasonable to hypothesize that the rate at which the ocean and land removes CO2 from the atmosphere is simply proportional to how high the atmospheric concentration gets above some baseline value. This simple hypothesis does not necessarily imply that the processes controlling CO2 sources and sinks are also simple; only that the net global rate of removal of atmospheric CO2 can be parameterized in a very simple form.

The Mauna Loa CO2 data clearly supports that hypothesis (Fig. 1 and Fig. 2). And the result is that, given the latest projections of CO2 emissions, future CO2 concentrations will not only be well below the RCP8.5 scenario, but might not even be as high as RCP4.5, with atmospheric CO2 concentrations possibly not even reach a doubling (560 ppm) of estimated pre-Industrial levels (280 ppm) before leveling off. This result is even without future reductions in CO2 emissions, which is a possibility as new energy technologies become available.

I think this is at least as important an issue to discuss as the implausibility (impossibility?) of the RCP8.5 scenario. And it raises the question of just how good the carbon cycle models are that the UN IPCC depends upon to translate anthropogenic emissions to atmospheric CO2 observations.

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February 2, 2020 12:26 pm

Dr Spencer wrote: “And it raises the question of just how good the carbon cycle models are that the UN IPCC depends upon to translate anthropogenic emissions to atmospheric CO2 observations.”

Clearly they are not good at all. I have frequently pointed over the past year here at WUWT the OCO-2 results that came out in 2017, and then the OCO-2 team has gone quiet for 3+ years now despite their continuing to acquire post the OCO-2 CO2 Level-2 data to the NASA data portal.
Those OCO-2 results destroyed the predictions made by the Bern Model used by the IPCC.

“The Bern Simple Climate Model (BernSCM) v1.0: an extensible and fully documented open-source re-implementation of the Bern reduced-form model for global carbon cycle–climate simulations”
https://www.geosci-model-dev.net/11/1887/2018/

Why does the Bern Model fail?
Well just one of several ways is the lack of biological uptake modeling.
From their own paper:

“BernSCM (Fig. 1) is designed to compute decadal- to millennial-scale perturbations in atmospheric CO2, in climate and in fluxes of carbon and heat relative to a reference state, typically preindustrial conditions. The uptake of excess, anthropogenic carbon from the atmosphere is described as a purely physicochemical process (Prentice et al., 2001). As in pioneering modeling approaches with box-type (Oeschger et al., 1975; Revelle and Suess, 1957) and general ocean circulation models (Maier-Reimer and Hasselmann, 1987; Sarmiento et al., 1992), modification of the natural carbon cycle through potential changes in circulation and the marine biological cycle (Heinze et al., 2015) are not explicitly considered.

Stated simply, they ignore the biological consequences of increasing fertilization and uptake of CO2. And universally, all the models get the sign of CO2 sensitivity wrong.

From their earlier work:

“All models simulated a negative sensitivity for both the land and the ocean carbon cycle to future climate. ”
Climate–Carbon Cycle Feedback Analysis: Results from the C4MIP Model Intercomparison
https://journals.ametsoc.org/doi/10.1175/JCLI3800.1

Yet we can predict certainty that IPCC AR6 WG1 authors won’t (aren’t allowed to?) admit that past CO2 modelling efforts are utter failures to refelct the reality seen in the OCO-2 data. And Judith Curry has pointed put they are devising an even worse case scenario for AR6 than the bogus, impossible RCP8.5 from AR5. There is far too much money and power at stake in the climate scam for them (the scientists who might find a conscience) to be allowed to ruin the march to global socialism under the auspices of the UN.

Reply to  Joel O'Bryan
February 3, 2020 8:25 am

The Bern model, or a minor correction of it, has not yet failed. Non-exponential decay of an atmospheric CO2 bump-up by a pulse or injection of CO2 into the atmosphere cannot be disproven by atmospheric CO2 data until anthropogenic CO2 emissions deviate greatly enough from exponential growth long enough to cause atmospheric CO2 level to deviate greatly from exponential growth of its excess over some “pre-industrial” baseline. Until that happens, atmospheric CO2 level will be consistent with both exponential and non-exponential decay (towards some “pre-industrial” baseline) of the atmospheric CO2 gain from each year’s anthropogenic CO2 emissions.

Patrick
February 2, 2020 12:34 pm

If we magically burned every gram of proven reserves of coal, oil, and natural gas, and none of it dissolved in the oceans, or was taken up in the biosphere, we would reach 735 ppm – max.

That amounts to 1.39 x climate sensitivity = warming °C. That’s it, and no more. The only way to get more CO2 into the air is to burn biotic carbon, or dissolve *lots* of limestone. That’s not even close to enough to stave off the next glaciation. So much for gloom and doom.

Reply to  Patrick
February 3, 2020 9:08 am

I figure below 868 not 735 ppm from burning the proven reserves according to BP, which is 1.63 log scale doublings from 280 ppm. Then there’s the matter that the world has a lot more coal, oil and natural gas than proven reserves.

As of the end of 2017, the world’s proven reserves of oil was 1696.6 billion barrels according to https://www.bp.com/content/dam/bp/business-sites/en/global/corporate/pdfs/energy-economics/statistical-review/bp-stats-review-2018-full-report.pdf That is 231.45 billion tonnes, of which about 198 billion tonnes is carbon.

That source says the world’s proven reserves of natural gas at the end of 2017 was 193.5 trillion cubic meters, and I figure the mass of that being 127.13 billion tonnes, of which 95 billion tonnes is carbon.

That source says the world’s proven reserves of coal at that time were 1035 billion tonnes. I figure that has 650 billion tonnes of carbon.

All three of these total 943 billion tonnes of carbon at the end of 2017. I’m pretty sure proven reserves are growing and are no less than 943 billion tonnes now. 943 billion tons of carbon would get oxidized to 3,457 billion tonnes of CO2. The earth’s atmosphere has a mass of 5,000,000 billion tonnes, and 3,457 is 691.4 parts per million of that by mass. Dividing 691.4 by 29.1/44 (molar masses of air and CO2 respectively) means 455.7 parts per million by volume, which is the unit normally used for atmospheric CO2. We’re currently at about 413 PPMV, and adding 455 to that means 868 PPMV.

February 2, 2020 12:48 pm

Roy, in a number of my comments over half a dozen years on the “Great Greening” that alarmists are loathe to discuss and at great pains to find something alarming about, I thought it self evident that natural sequestration by ‘fattening’ existing trees and shrubs and new growth fringing concentrically into arid barren lands would be exponential and would therefore flatten the rising CO2 curve to some equilibrium plateau.

I also noted that photosynthesis is endothermic and would therefore have a significant cooling effect given the magnitude of the Greening. The recent study from Boston College discussed the other day here, attributed cooling to release of water vapor. This would actually be in addition to the endothermic reaction I was positing. The amount of endothermic cooling should be equal to the enthalpy of oxidation of the carbon sequestered as a bare minimum (imagine burning this amount of anthracite coal). Ocean life is likely also expanding (phytoplankton, etc). The reduced growth of CO2 in the atmosphere plus the cooling effect further attenuates any reason to be alarmed about fossil fuel use.

holly elizabeth Birtwistle
February 2, 2020 12:51 pm

I certainly hope we more than double the ppm CO2 in the atmosphere. That would be a benefit to plants and agriculture, and IF CO2 slightly warms the atmosphere, and Dr. Spencer is assuming it does without knowing how the planet warmed occasionally over the last few thousand years, then it would be a benefit to the Northern Hemisphere as well. I really don’t like the assumption that human beings MUST be changing the climate, when we can only estimate how much CO2 going into the atmosphere from natural sources, 97%? and how much is from burning fossil fuels 3%? +/- 3% or more? So why all the jumping to conclusions? It could easily be 99.999% from the oceans that cover 70% of our planet, along with land-based sources, and 0.001% human activity. We have no way of measuring accurately. And CO2 may not increase the temperature of the atmosphere, at all anyway. We don’t know yet. According to ice core studies, rise in CO2 follows rise in global temperature. There are so many other variables to be studied: Heat from the Earth’s mantle seeping into the oceans, slightly warming oceans= more CO2 into the atmosphere maybe? How much? The Sun’s cycles, gravitational pulls from other planets, Earth’s elliptical orbit, cosmic radiation, Earth’s spin, and who knows how many other variables we haven’t considered yet.

AGW is Not Science
Reply to  holly elizabeth Birtwistle
February 3, 2020 7:38 am

“There are so many other variables to be studied: Heat from the Earth’s mantle seeping into the oceans, slightly warming oceans= more CO2 into the atmosphere maybe? How much? The Sun’s cycles, gravitational pulls from other planets, Earth’s elliptical orbit, cosmic radiation, Earth’s spin, and who knows how many other variables we haven’t considered yet.”

Yup that in a nutshell is the problem. Even some skeptical of the junk climate science are guilty of it. They all want to look at ONE “factor” which is the climate “driver,” when the reality is that there are MANY “factors,” and we don’t even know what they all are, much less have any data regarding any of them.

Of course, the Climate Fascists are just working backwards from the preconceived conclusions and looking to justify them, so you can’t expect them to change their stripes, ever. No way they’re going to “kill the golden goose.”

Reply to  holly elizabeth Birtwistle
February 4, 2020 9:35 am

holly says:
I certainly hope we more than double the ppm CO2 in the atmosphere.

That would be a benefit for the planet. But on the planet’s timescale, fossil fuels will quickly become scarce and a CO2 doubling would go back to a standard level (getting dangerously close to CO2 starvation levels) in the blink of a geologic-eye — unless we purposely “burn” abundant limestone to keep the levels up.

Antero Ollila
February 2, 2020 1:19 pm

Maybe the best example of the grossness of the IPCC and the climate establishment is in the acceptance of the Joos et al. and Bern2.5CC model. They state it clearly that the whole increase of the atmospheric CO2, which was about 270 GtC in 2017, is totally anthropogenic. The direct permille observations show that it is impossible: model-calculated value would be -13‰, and the observed value is -8.5‰. Nobody has commented on this issue.

An explanation might be this. People do not know what is the permille, and therefore they do not know if I have calculated this value correctly or not. Because people do not know about these observations, the IPCC and the climate establishment can be silent about this conflict between the models of Joos et al. and Bern2.5CC and the reality.

The permille values of the present atmosphere can be calculated by a simple equation:
Permille = ((100- CO2ant) * (-6,35) / 100 + (CO2ant) * (-28)) / 100 (2)

CO2ant is the percentage portion of anthropogenic CO2 in the atmosphere and in 2017 it was according to the IPCC = 100*270/866 = 31.2. The permille value of the natural CO2 before 1750 was -6.35‰, and the permille value of fossil fuels is -28 (the same as with plants). By applying these figures, the permille value should have been -13‰ according to the IPCC. The Mauna Loa value in 2017 is -8.6‰ and the error is really massive.

February 2, 2020 1:31 pm

Will Humanity Ever Reach 2XCO2 (800 ppm)? Sadly no. Humanity will be powerless to bring about this highly desirable goal. As for the Plants’ desire to return to 1,200 ppm, they are likely to be disappointed in our puny efforts.
At least, however, if we can keep the Geo-Engineering Nuts in check, we will not further damage the previously precariously low levels of CO2 for our plant partners.

February 2, 2020 3:11 pm

Simple calculations using data from Hitran show increased water vapor has been about 10 times more effective than increased CO2 at ground level warming. https://watervaporandwarming.blogspot.com

AGW is Not Science
Reply to  Dan Pangburn
February 3, 2020 7:44 am

Which is only a “surprise” to deluded pseudo-scientists that think CO2 is a “climate driver,” when there is no empirical evidence of that.

michael hart
February 2, 2020 3:40 pm

In my experience, the main complaint about the current model will be that it is “too simple” and therefore probably incorrect.

Bingo.
And is the “diffuse sunlight under the canopy” theory the correct explanation? Or maybe thermal effects over the Pacific? Or deposited nutrients from ash dispersal increasing Pacific photosynthesis? Or plenty of other things I could suggest?

Or are they just making it up as they go along? I know which one I believe.

Stevek
February 2, 2020 5:09 pm

Co2 is a nutrient. Add more of a nutrient to a plant system and expect the system to change.

Antero Ollila
February 2, 2020 8:27 pm

There are two permanent isotopes of carbon molecules. The most common is 12C having 6 positrons and 6 neutrons but 13C has one extra neutron. Isotope 13C is the most common being 98.9 % of all carbon and the rest is 13C. There is also a very small concentration of unstable isotope 14C, which is radioactive. Cosmic radiation produces 14C all the time by splitting nitrogen molecules in the atmosphere. Its half time is 5730 years and it is used in the radiocarbon timing method.

The measurement unit of 13C proportion (also marked as δ13C) and it is a fraction of carbon isotope 13 expressed as ‰ (written also in forms per mil, per mill, permil, permill or permille). This unit is linearly dependent on the relationship 13C/12C per eq. (1)

Permille = ((13C/12C) / (13C/12C)standard -1 ))*1000 (1)

This measurement unit is odd because all the values for CO2 mixtures are negative. The reason is in the standard value of 13C/12C. It can be found in a sea fossil by name Pee Dee Belemnite (PDB) and its value is very high 0.0118. Observations show that the permille value of plants and fossil fuels is -28‰ (13/12C = 0.010922). The permille value of natural CO2 in the year 1750 was -6.35‰. This value is from the research studies, which assume that in 1750 the mixing layer of the ocean and the atmosphere were in balance having the same relationship of 13C/12C. Because of anthropogenic emissions, the permille value of the atmosphere has increased continuously being -7.0‰ in 1960 and now it is about -8.6‰.

Here is the link to the observations and trends (rather difficult to find, why??):
https://scrippsco2.ucsd.edu/graphics_gallery/other_stations/global_stations_co2_concentration_trends.html

Bert Robe
Reply to  Antero Ollila
February 3, 2020 3:53 am

@Antero
This publication has very similar results than you have got:

http://www.esjournal.org/article/161/10.11648.j.earth.20190803.13

Clyde Spencer
Reply to  Antero Ollila
February 3, 2020 10:26 am

Antero
Proton, not “positron.”

Your second sentence should say, “Isotope 12C is the most common …”

Antero Ollila
February 2, 2020 8:58 pm

One more example about the cheating by the climate establishment. There is a nice animation about the carbon cycle in Youtube made by Robert Rohde who works at Berkley Earth organization. I sent an email asking this question:
– On which research papers the numbers and the model is based on?
– What is the nature of the atmospheric carbon dioxide increase being about 276 GtC in 2018? Is it totally anthropogenic (permille value about -28) as reported by the IPCC, Joos et al. (2011) and Le Quere et al. (2018)? “

Rohde replied very promptly that the animation is based on AR5 of the IPCC and Global Carbon Project 2018 report. The animation assumes that the entire perturbation is anthropogenic, through a combination of fossil fuel production and land-use changes.

As you can see, Rohde did not answer univocally to my question about the nature of atmospheric CO2. We can understand the reply in the way that all the values – including the total increase of atmospheric CO2 – is anthropogenic by nature.

Because this was a typical answer of a politician who never replies directly to an inconvenient question but talks about something else, I sent another email asking again about the nature of the atmospheric CO2. I have not received any answer so far. I think that Rohde noticed or found out, that I am aware of this cheating.

crosspatch
February 2, 2020 9:03 pm

People need to realize that the Mauna Loa data aren’t data in the usual sense. They are a model. Mauna Loa is a volcano and emits CO2. Yes, that’s right, our primary CO2 monitoring station sits right on top of a volcano emitting CO2. So the CO2 measurements can vary all over the place depending on variability in CO2 emissions and wind direction. What they do is model how much they think CO2 should increase and measurements that fit the model are included and ones outside the expected values are discarded.

Antero Ollila
Reply to  crosspatch
February 2, 2020 9:57 pm

In both the CO2 concentration data and permille data you can see the measurement values in different places of the Earth. There are small differences in the levels and fluctuations but the overall trends are the same in all locations.

CO2 concentration and permille measurements are not man-made scams. They are real. .

Clyde Spencer
Reply to  Antero Ollila
February 3, 2020 10:43 am

Antero
You are assuming that the other locations don’t have similar problems to Mauna Loa. In the case of Pt. Barrow, the village is a little hot spot of CO2 generation. If the wind is blowing towards the recording station, it will generate outliers that need to be discarded. There is some subjectivity in deciding what wind conditions or anomalous readings warrant eliminating data. It is less than an ideal situation for recording CO2! I wouldn’t be surprised to find other stations around the world have had their scientific integrity compromised for the sake of convenience in reading or maintenance.

Robert of Texas
February 2, 2020 10:00 pm

The concentration of CO2 in the atmosphere more closely resembles a balance being achieved with a warming ocean than it does a gross concentration of CO2 being established in the atmosphere that is slowly absorbed by the ocean. It just looks like they have cause and effect completely backwards, and more ancient climate data backs this up (CO2 follow temperature).

Another problem I see is that scientists seem to think that removal of CO2 by a warming ocean is not affected. The ocean not only has a huge potential to absorb CO2, but to chemically bind it into an inert form – carbonate rocks. If this chemical process increases with either CO2 concentration or warmth (or both) then vast quantities of additional CO2 are being deposited on the ocean floor over and above what was occurring 50 years ago.

So I agree, the higher end of CO2 concentration in the atmosphere is nothing but a huge guess, and likely wildly over estimated. Even it CO2 were to triple, I still fail to see a giant threat. I do not care if sea ice melts. The oceans are already rising and we will already have to adapt to it. More rain in places like Egypt and the Southwestern U.S. are not frightening to me. Canadians baking in 60F degree heat is not too concerning – they have plenty of cold beer up there. Faster growing more abundant food crops is hard to be frightened of. I could care less if polar bears end up eating berries along shores instead of eating baby seals on ice packs.

Now rafts of angered baby penguins…that kind of frightens me. I have seen video’s of them slapping each other.

Loydo
Reply to  Robert of Texas
February 3, 2020 1:13 am

“I do not care if sea ice melts.”

You will. You just don’t enough about the consequences.

AGW is Not Science
Reply to  Loydo
February 3, 2020 7:56 am

Since “we” (humans) are not in control of the CAUSES of any “sea ice melt” anyway, what’s your point? And since sea ice is stubbornly “average,” there’s no “consequences” to BE concerned about.

Clyde Spencer
Reply to  Loydo
February 3, 2020 10:48 am

Loydo
It looks like you left a word out of your last sentence, making the meaning ambiguous. However, if the intended word was “know,” then I think the sentence would apply to you. Melting sea ice will not affect the level of the oceans.

Reply to  Robert of Texas
February 3, 2020 9:20 am

The oceans did not warm enough to bump up CO2 from 280 PPMV (or whatever pre-industrial value) to the current 413 PPMV.

Steve Z
February 3, 2020 2:26 pm

If we assume that all man-made CO2 remained in the atmosphere, a mass balance shows that the CO2 content of the atmosphere would increase by about 1 ppm per gigatonne (GT) CO2 emitted. Worldwide CO2 emissions for 2018 are estimated at about 36.8 GT, so that if all the CO2 remained in the atmosphere, the CO2 concentration should rise at a rate of 4.6 ppm/year. If the actual rate of increase is 2.5 ppm/yr, then CO2 is being removed at a NET rate of 2.1 ppm/yr, or about 16.8 GT/year, which represents about 46% of the human CO2 emission rate.

If it is assumed that the net removal rate is linearly proportional to the CO2 concentration in the air (first-order reaction), then the net removal rate should catch up to the emission rate when the CO2 concentration is 1/0.46 = 2.2 times the current level, which would be about 900 ppm, and the concentration would remain in equilibrium thereafter.

The net natural removal rate is actually the CO2 emission rate of all natural sources (animal respiration, emission from oceans, volcanic emissions, etc.) minus the CO2 absorption rate of all natural sinks (photosynthesis, absorption into oceans, conversion to carbonates in oceans, etc.). Accounting for the natural sources would mean that the total natural absorption rate is actually higher than the net absorption rate of 16.8 GT per year. It would be expected that the total natural absorption rate would be proportional to the CO2 concentration, but that the natural emission rate would likely remain constant. Depending on the magnitude of the natural emission rate, it would be likely that the CO2 concentration will reach equilibrium at less than 900 ppm, although the numerical value of the plateau would depend on the value of the natural emission rate.

What natural CO2 emission rate did Dr. Roy Spencer assume in his CO2 budget model?

barry
Reply to  Steve Z
February 4, 2020 11:41 pm

I don’t know why one should assume a linearly proportional rate of removal/emissions of atmospheric CO2, Steve.

But taking that model as read, observations demonstrate that despite the increased removal rate, it hasn’t caught up with the increased emissions rate. Over the long term atmos CO2 accumulation rate is accelerating.

“It would be expected that the total natural absorption rate would be proportional to the CO2 concentration, but that the natural emission rate would likely remain constant.”

There is a good basis for this – the ice core records show relatively steady concentrations for the last few thousand years, particularly compared to the last 60 (Mauna Loa) or so. However, the implicit assumption here is that there are no significant feedbacks when total concentration changes significantly.

Sinks are blind to source, whether anthropogenic or natural. Sinks respond to the sum – the total content of the atmosphere.

Chic Bowdrie
Reply to  barry
February 5, 2020 4:05 pm

Barry,

No, as shown in Fig. 2, observations demonstrate that the absorbed fraction is increasing. That means the removal rate is more than keeping up with the emissions rate.

Secondly, assuming natural emissions remain constant doesn’t mean they have. At least two sources come to mind. As world population grows, land use changes–especially soil cultivation–would provide an additional source of emissions. Warmer temperatures augment those emissions. These are in addition to the outgassing due to warmer ocean temperatures.

Greg Freemyer
February 3, 2020 8:21 pm

Don’t forget fungi. Lots of beneficial fungi like arbuscular mycorrhizal fungi in pristine grasslands and forests.

Plowing land kills most fungi as the soil is turned over.

75% of US soil is no longer plowed as farmers are trying to allow beneficial fungi to grow in their cropland soil. I have no idea how the global rate of plowed cropland is decreasing, but I’m pretty sure it is decreasing.

Arbuscular mycorrhizal fungi in particular sequester more carbon in soil than plants.

Thus, it is likely much of not all the increasing ability of earth to drawdown CO2 is actually a farmer induced behavior.

Herbert
February 4, 2020 2:52 am

In “Climate:The Counter Consensus” by the late Professor Robert M.Carter-
“The Global Carbon Dioxide budget.
The effect of human emissions on global levels of atmospheric carbon dioxide is not well understood because no one, including the IPCC can satisfactorily account for the observed levels in detail; our best estimates of carbon dioxide sources and sinks have large error bars.
….One estimate by Canadian climatologist Tim Ball is that the human production of carbon dioxide ( 7.2 GtC/year, IPCC 2007) is more than 4 times less than the combined error (32 Gt) on the estimated carbon production from all other sources.
A perspective that follows is that even were human emissions to be reduced to zero, the difference would be lost among other uncertainties in the global carbon budget.”
What are the error bars in Le Quere 2018, the World Carbon budget paper accepted as central by the IPCC.
For all sinks they appear to be quite considerable.
So, the carbon budget is not well constrained.