From Climate Etc.
by Joachim Dengler and John Reid
A new way of looking at the the atmospheric carbon budget.
Climate science is usually concerned about the question “How much CO2 remains in the atmosphere?”, given the anthropogenic emissions and the limited capability of oceans and biosphere to absorb the surplus CO2 concentration. This has led to conclusions of the kind that a certain increasing part of anthropogenic emissions will remain in the atmosphere forever. The frequently used notion of “airborne fraction”, which is the part of anthropogenic emissions remaining in the atmosphere, seems to suggest this.
We change the focus of attention by posing the logically equivalent question “How much CO2 does not remain in the atmosphere?”. Why is this so different? The amount of CO2 that does not remain in the atmosphere can be calculated from direct measurements. We do not have to discuss each absorption mechanism from the atmosphere into oceans or plants. From the known global concentration changes and the known global emissions, we have a good estimate of the sum of actual yearly absorptions. These are related to the CO2 concentration, motivating the guiding hypothesis for a linear model of absorption. It turns out that we do not need to know the actual coefficients of the individual absorption mechanisms—it is sufficient to assume their linear dependence on the current CO2 concentration.
This is a short summary of a recently published paper, where all statements expressed here are derived in detail and backed up with references and a mathematical model.
Mass Conservation of CO2
As in a bank account, the atmospheric CO2 balance results from total emissions reduced by total absorptions:
Concentration growth = Emissions – Absorptions
The total emissions (blue) come to exceed the yearly CO2 concentration growth (green), implying the growing effective absorption (red) with growing CO2 concentration:
The assumption of approximate linearity of the relevant absorption processess is visualized with a scatter plot, relating the effective CO2 absorption to the CO2 concentration.
We see a long term linear dependence of the effective absorption on the atmospheric CO2 concentration with significant short term deviations, where the effective zero-absorption line is crossed at appr. 280 ppm. This is considered to be the pre-industrial equilibrium CO2 concentration where natural yearly emissions are balanced by the yearly absorptions. The average yearly absorption is appr. 2% of the CO2 concentration exceeding 280 ppm. As the data before 1950 are subject to large uncertainty, the following calculations were done based on data after 1950, resulting in a slightly smaller absorption percentage of 1.6%.
CO2 concentration as a temperature proxy
When we make predictions with hypothetical future CO2 emissions, we do not know the future temperatures. Without diving into the problematic discussion about the degree, how strong the influence of CO2 concentration is on temperature , we assume the “worst case” of full predictability of temperature effects by CO2 concentration.
Without making any assumptions about C->T causality, the estimated functional dependence of the temperature proxy from the regression on CO2 concentration C was found to be:
Tproxy = -16.0 + 2.77*log(C) = 2.77* log(C/(235ppm))
This corresponds to a sensitivity of 1.92° C.
The model with the assumption of constant absorption parameter and constant natural emissions is validated with a prediction of the CO2 concentration 2000-2020 based on emission data 1950-2020 and Concentration data 1950-2000.
This is an excellent prediction of concentrations on the basis of emissions and the above model assumptions. There are only small apparently variations between the predictions and the actual data. Although the model allows for varying absorptions over time, the data of the last 70 years, which is the period of the bulk anthropogenic CO2 emissions, leads to the conclusion that the CO2 absorption parameter has no significant temperature or other time-dependent component, and a current CO2 emission pulse is absorbed with a 42 year half-life time.
Future Emission Scenario
The most likely future emission scenario is the IEA stated policies emission scenario of approximately constant, slightly decreasing global emissions. The actually used data set for a realistic future projection is created by trend extrapolating the stated policies beyond 2050 and assuming that the land use change
data will follow the current trend and decrease to 0 by the year 2100 . Emissions will not be reduced to zero in the year 2100, but will remain close to the 2005 level.
Prediction of Future CO2 Concentration
From this realistic emission scenario the future CO2 concentration is recursively predicted with our model.
With the IEA stated policies scenario, i.e., no special CO2 reduction policies, a CO2 concentration equilibrium of approx. 475 ppm will be reached during the second half of this century. Based on the empirical CO2 temperature proxy equation above, this increase of CO2 concentration from 410 ppm (in 2020) to 475 ppm corresponds to a temperature increase of 0.4 _C from 2020, or 1.4°C from 1850.
Concluding, we can expect a maximum CO2 concentration level of approximately 475 ppm in the second half of this century. At this point, the emissions will be fully balanced by the absorptions, which is by definition the “net zero” situation.
Assuming the unlikely worst case that CO2 concentration is fully responsible for all global temperature changes, the maximum expected rise of global temperature caused by the expected CO2 concentration rise is 0.4 _C from now or 1.4°C from the beginning of industrialisation.
Therefore, if we keep living our lives with the current CO2 emissions – and a 3%/decade efficiency improvement, then the Paris climate goals are fulfilled.
The minor little problem is that most temperature data bases are inflated, or otherwise “adjusted”, making the apparent relationship between CO2 levels and temperature considerably more robust.
In fact, the adjustment factors are what’s being modelled. Too funny.
For Australia we sceptics can see 0.5 to 0.7 deg C warming from 1910 to now, not the official BOM figure of 1.44 deg C.
Your point is made if other large-area countries have similar differences.
Most of the records outside the US, the UK, or Australia before 1950 are mostly absent. Some from Europe, but most of the rest of the world is absent.
The 1930’s were the warmest period in the US record (unadjusted), and I understand roughly 1910 or so was the warmest in Australia (unadjusted). So claims that there has been consistent warming worldwide are rather risible.
The real questions to be answered are “Is the amount of C02 in the atmosphere important with respect to the temperature of the Earth, and if not why are we worrying about it?”
Shedloads of money are made by what one day will be known as the ‘CO2 catastrophy’ fabricatios.
If we reduce CO2 emissions too much, we will lose the benefits of greening the earth, and growing abundant crops to feed 10 billion people.
The present level of CO2 emissions is fine.
It will increase temps a little, if they are held constant
We have enough fossil fuels to last at least 150 years, at present level of use and CO2 emissions
Ok so what is it that is absorbing the added CO2 ? or is the report just simply saying the increase temperature is not a problem( which is my personal position)
John, the increased absorption might be related to the NASA reported 10% greening of the earth. Myself, I prefer around 1,000 ppm CO2 before the next glacial cycle of the Ice Age we live in starts. Wait for it.
And that does sound fine to me
I’m not addressing causation here.
Apparently to the authors it’s not important to specify how much the land vs. the ocean are absorbing. All they care about is the total- at least for the current discussion.
one of my favorite TV celebrities/comics is John Oliver- something about that English accent is very funny and he is very witty- he said once that he wasn’t very successful in England but he’s done great here on this side of the pond – some but not all of his dialogues are far to the left, which I don’t agree with, but I still enjoy watching him – no relationship I presume
There is a retired professor William Moomaw (Tufts) who has fantasized a new concept he calls “proforestation” whereby we lock up all the forests- or most of them- so their only value to mankind is carbon sequestration. We’ll just forget about producing wood for construction, furniture, paper products, energy, etc. He speculates that this will “help save the planet” by truly lowering “carbon pollution”. This fantasy is now a big deal with enviros/greenies as it spreads from the American northeast. Some of his missionaries are now promoting the idea in the EU, which favors woody biomass as a renewable resource. If he were right- and he isn’t right all things considered, this would increase the capability of the biosphere to absorb all that terrible, toxic CO2. 🙂
Of course he lives in a rather large wood home (over 4,000 sq. ft.) covered with heavily subsidized solar panels- so he can preach how green he is while depriving future generations of a great, low carbon footprint resource.
Obvious flaws in this analysis are the assumptions that IEA projections will occur and land use change will decline to zero net emissions. No matter what the Western world does, Asian and African emissions are most likely to continue to climb unabated and come to dominate continuously increasing world emissions. As for land use change, which has largely stabilized in the West and is becoming a net carbon sink, growing populations in Asia, Africa and South America, along with insane “green” biofuels development, net land use emissions are likely to increase.
Even so, there is still no looming catastrophe. Nothing to see here. The West, out of self-preservation from global totalitarianism, must abandon all talk of “net zero” and climate emergency, abandon the insane war on fossil fuels, halt the “everything electric” delusion, and eliminate the failed ruinables (wind and solar) from the grid.
We must repudiate the ESG movement and reclaim a proper, technically-based sense of environmental stewardship, not the UN version of so-called “sustainability” (a word I try not to use or acknowledge) or the version of “sustainability” being pushed by ignorant, cultish social justice warriors as seen in colleges, universities and governments large and small.
As you know, predictions are always difficult, in particular if they concern the future.
Tell me a better scenario, if the aim is to be able to enter a constructive dialogue with decision makers. You need to have some “official” institution, and to me the IEA “stated policies” scenario appears plausible, because it is the continuation of policies that are applied today.
The land use change seems to play a minor role, even those who publish about it, attach very high error rates to it. To be honest, the results of my computations become much better if I drop them after 1950 altogether (in the first half of the 20th century they are needed for consistency reasons).
This is an excellent approach to countering the alarmist narrative. A purely empirical approach based on historical data. The authors have not “denied” anything explicitly.
There is no controversial attempt to claim that our emissions are irrelevant to concentration, no distracting dispute about the reality of “back radiation”. Basically accepting for the sake of argument that the observed correlation between CO2 concentration and temperature will continue to hold in the next 75 years as it has in the past 75 years.
Not indulging the alarmists’ fantasies about feedbacks and tipping points that have not been observed, but just acknowledging the reality of the temperature and concentration record. Even avoiding any hint of skepticism about the quality of the temperature record. No need to point out urban heat island effects or allege that adjustments are illegitimate.
The conclusion being in effect, “assuming you’re right that our emissions explain the gradual milding of the climate, nothing alarming will result from continuing to live our lives as we have been doing.”
Yes , some times I feel like saying “ calm down children , everything is going to be just fine with the Climate, we re going to be OK.! Go back to your play! Then I realize I m speaking to adults.
Part of the message is taking a moderate approach to reducing CO2 emissions as it will much cheaper and less disruptive than the Net-Zero by 2035, 2040, 2050, etc approach. A lot of the technologies being prooted to achieve net-zero have some significant problems, e.g. battery fires and resource issues with EV’s, environmental impacts of renewable energy, the lack of reliable renewable electric generation.
Yes! A moderate response would suffice. No need to dismantle our economies.
Down below we see a myriad of examples of how this simple-to-understand message can be muddied and obscured.
I have some second thoughts on this.
The authors are saying that the sufficient response is a 0.3% annual reduction in GLOBAL CO2 emissions going forward for 77 years to the year 2100.
The alarmists are saying that we need a 100% reduction over the next 17 years. That’s 5.9% per year or nearly 20x more abrupt. But of course the alarmists are proposing that Western countries alone make those suicidal cuts while China, India, Africa, and Latin America continue to increase emissions.
in order for a 0.3% global reduction per year to be “moderate”, all nations, including China, India, et al. must reduce emissions. That is an unjust and unrealistic request of poor countries trying to lift their populations out of poverty.
If we want to achieve modest global reductions in CO2 emissions while not unjustly blocking economic development in poor countries, then we’re back to needing to unjustly dismantle Western economies. Clearly that is also unlikely to actually happen. If it did, it would in no way be “moderate” for the Western countries.
The other side of the equation is that if rich countries are bled dry, developing countries will lose their primary markets and won’t actually develop in any case.
A better use of the authors’ model would be to assume that all countries cap their per capita emissions at the current US rate while allowing unrestricted growth for any country not yet at that level, and assuming continuation of recent growth rates.
In that scenario, where does their model predict that CO2 concentration will top out and what temperature increase does that imply based on their empirically-derived ECS value of 1.9?
Limiting temperature rise to 1.5C is completely arbitrary and unnecessary. A truly moderate response would be where the wealthiest nations maintain their economic growth by improving efficiency and shifting energy sources so as to avoid increasing per capita CO2 emissions. More fracking to shift from coal to gas, much more nuclear, especially developing molten salt breeder reactors that can supply process heat rather than trying to electrify everything.
Without doing the math, I’d guess that would not entail more than an additional degree of warming above current conditions.
As a further suggestion, we could have a global treaty on climate adaptation insurance. All countries would share the actual costs of adaptation to things like rising sea level, paying in on a formula based on the country’s cumulative CO2 emissions. If we climate realists are right, and no significant impacts are on the horizon, then this won’t cost much—particularly as compared to Net Zero schemes. If we are wrong and there are significant costs to necessary adaptation, then we should be prepared to pay our just portion.
Even if adaptation costs may be substantial, as Lomborg argues, a much wealthier world will have no difficulty covering those costs.
I am glad you brought up these second thoughts, because these are the real issues worth debating about.
It is true that global reductions by even a small amount will hit all countries, even those which are in urgent need of growth (Accordings to Judith Curry these poorest countries will account for less than 10% of the emissions). Interestingly the country with the highest emissions, China, had a massive bend in emission rates in 2010 and currently a close-to-0 growth. India has still some emission growth but is heavily engaged in renewables. To get a feeling what the “stated policies” scenario acutally means, you may want to have a look into its description: https://www.iea.org/reports/global-energy-and-climate-model/stated-policies-scenario-steps
I think if anybody has the overview of making such scenarios, it is the IEA.
I will ponder your suggestion and think about an online simulator, where you can enter the emission scenario of you choice. Or do you want to create that – I will certainly give you all the input/support you may need for it?
Your suggestion of a climate adaptation insurance sounds good, obviously there is a long way to go for the implementation of such a concept. Maybe the (growing number of) BRICS countries is more open to such a suggestion than the brainwashed west?
Thanks for making this point. You caught the intention of our paper and post 100%.
(it will take a bit more time to respond to your second thoughts …)
The climate in 100 years will be warmer or cooler
No one knows the future today
The effect of CO2 can be measured in a laboratory with and without water vapor.
CO2 is a weak greenhouse gas above 400ppm …
In the atmosphere, there are too mamy climate variables to know exactly what each one has done to the climate in the past 50 years.
Many people look at the change in average temperature for the past 80 years and just assume that was caused by CO2. That would be a worst case assumption, but not a realistic assumption.
No one knows the ECS (Equilibrium Climate Sensitivity) for CO2, which would include an unknown water vapor positive feedback and something that limits that positive feedback, possibly a cloud negative feedback.
And the whole process takes 200 to 400 years, according to the IPCC. Anyone who claims to know ECS is just guessing.
The fact that the past eight years had the highest eight years of manmade CO2 emissions, with no global warming, proves that CO2 is just one of many climate change variables. Not a climate controller.
The most important climate science fact is that humans have been extremely unsuccessful in predicting the future climate.
Even simple extrapolations have failed, such as assuming the past 30 to 50 years of climate change can be used to predict the next 30 to 50 years of climate change.
In the past 125 years, that simple extrapolation prediction has been much less accurate than even the climate confuser games.
The bottom line:
Climate is always changing
The changes have not been predictable
The actual changes in the past 50 years have been pleasant.
There is no reason the assume changes in the next 50 years must be bad news.
There is no need to try to change the climate because it has been improving since the cold 1690s — the coldest decade of the Maunder Minimum period — why try to stop good news?
CO2 is so important for plant life on this planet that more CO2 in the air is what plants prefer — at least double the current CO2 level.
We should be celebrating the current climate.
It is the best climate since the Holocene Climate Optimum ended 5,000 years ago.
Better, from the point of view of C3 plants (85% of 300,000 species).
If we are almost as warm today as in the last Optimum period, that’s a good thing.
They didn’t call it an Optimum because the climate was bad news.
Few if any of these points are included in the article.
Therefore, it is not a good article.
It is just another wild guess of the future climate
We already have too many climate predictions
That’s the main problem with climate science — too many wild guesses of the future climate that are consistently wrong,
‘”The climate will get warmer,
unless it gets colder”
In a previous thread “Climate Change isn’t particularly dangerous” Richard Lindzen, you said “No global warming from 2015-2023…101 months”
This is incorrect!
The temporary 2015-6 temperature spike was a man-made peak, caused by a Chinese edict to reduce industrial SO2 aerosol pollution. It was highly successful, with industrial SO2 aerosols dropping by 33 million tons, between 2014 and 2015, a massive reduction, with.temperatures peaking in 2016 to 0.93 deg. C.(Hadcrut5, land-ocean). The warming was short-lived, dropping to 0.76 deg. C.in 2018, after which temperatures have been rising (0.89, 0.92, 0.76, 0.80, thru 2022)
You CANNOT claim that there has been no warming since 2015.
The UAH global average temperature statistic shows no warming since 2015. Monckton has an article about it here.
Why can’t I tell the truth about UAH?
Are you against the truth?
SO2 emissions have been declining since 1980.
If they were an important climate change variable, the global average temperature would have been rising since 1980
In fact a warming trend began in 1975 even though SO2 emissions were still rising, which should have caused global cooling, but did not.
And SO2 emissions were falling since 2015, which should have caused global warming, but that did not happen
Conclusion: SO2 emissions are a minor climate change variable that are not a temperature “control knob”, except in your biased mind.
The 2015 / 2016 global average temperature peak was from a STRONG El Nino Pacific Ocean heat release, unrelated to SO2.
You suffer from SO2 delusions.
You said “SO2 emissions have been declining since 1980: If they were an important climate change variable, the global average temperature would have been rising since 1980”.
I agree. It was 0.196 deg. C. in 1980, and 0.81.in 2022 (Hadcrut5), and for NASA/GISS it was 0.27 in 1980, and 0.88 in 2022.
Both data sets show that temperatures HAVE been rising.
You also said that the 2015/16 peak was a strong El Nino heat release, unrelated to SO2. Can you not read? I explained that it was caused by a 33 million ton decrease in industrial SO2 aerosol emissions. Decreases in atmospheric SO2 aerosol levels ALWAYS cause temperatures to rise. And fall, if they are increased.
You are the delusional one!
You need to read this article:
Simply not true. The only way to understand the effect of CO2 at various concentrations requires including the effects of gravity, evaporation, convection, condensation, etc. You can’t do that in a lab or at any point in the atmosphere. Sorry. You also need to learn some physics.
You can look at data from multiple altitudes over time and determine if changes in CO2 have led to any changes in the average atmospheric profile. There’s a NOAA dataset (TIGR2) that contains data from 1948-2008) with exactly this information. Oh wait, that was already done in a peer reviewed paper.
“The present results show an apparent warming associated with no apparent change in the absorption properties. Change in absorption properties cannot have been the cause of the warming.”
There’s nature’s lab result. It shows the human lab results are wrong.
Miskolczi says “changes in absorption cannot have been the cause of warming”. And then his own fig 9 shows increasing temperature with increasing CO2 and his fig 10 shows increasing optical depth hand in hand with fig 9 temperature increase as well. Referring to his conclusions in a discussion with knowledgeable warmunists will result in embarrassment for you….
No one is saying that CO2 hasn’t increased or that it hasn’t warmed. The increasing optical depth change is very small.
“This is one third of the no-feedback change of = 0.0246 for CO2 doubling. In other word, GCMs or other climate models, using a no-feedback optical thickness change for their initial CO2 sensitivity estimates, they already start with a minimum of 200 % error ”
Why would you be embarrassed when the claimed warming is not even close? I realize that nothing is exact when dealing with measurements that are also affected by normal weather variations. But this is so significant that it calls into question all the science involved. Figure 11 puts it all into perspective.
“The fact that the virtual change is about four times the actual change is strong empirical evidence that there is a very strong dynamic compensation that stabilizes the atmospheric energy transport process against a potential perturbation by CO2 change.”
The only reasonable “compensation” comes from water vapor. This means the entire positive water vapor argument is DOA. Most skeptics consider a zero water vapor feedback to mean CO2 increases are not a problem. With this level of negative feedback there’s not even the hint of a problem.
The study here says CO2 pulses have a half life of 42 years. Below is a paper that says the rpulse and residence time is about 5 years. It also says that this means the majority (77%) of CO2 in the atmosphere right now is NOT anthropologic but “natural”.
While both posit a stable higher rate, the referenced paper says looking to anthropological sources of CO2 as the majority soyrce causes the error of callculating multidecadal residence time, as noted here with a half-life of 42 years.
This is a revolutionary paper. It undermines almost all of the IPCC assumptions on atmospheric CO2 history, stability and time parameters of residence. It supports anomalous and contradictory CO2 data that has been discarded as erroneous.
It seems straightforward. I’d love to see it being challenged.
It’s a claptrap “study”
Manmade CO2 is the cause of the 50% increase of CO2 estimated since 1850
Nature has been a CO2 absorber in that period.
5 years is claptrap
Multiply by 10 to get a good guess.
A Dave Burton responded to the 5 years claim at No Tricks Zone. He wrote a good article disguised as a comment.
HE ALSO MADE THE NEXT COMMENT HERE.
This is a cut and paste version of his excellent comment from No Tricks Zone. I tried to fix the formatting the best I could:
“The (five year) article is wrong, for multiple reasons.
1. The MINOR reason it is wrong is that residence time is precisely determined from the decay rate of the 14C “bomb spike” after the atmospheric test ban treaty. This is a log scale plot of the decline of 14C levels in the atmosphere:
When atmospheric tests of A-bombs and H-bombs suddenly ceased (because of the atmospheric test ban treaty), the 14C concentration dropped on a near-perfect exponential decay curve, with a half-life of 11.5 years, implying a residence time of 16.6 years. (Note: ¹⁴CO2 is 4.5% heavier than normal ¹²CO2, which affects biological uptake and diffusion rates slightly. But not much.)
2. The MAJOR reason it is wrong is because it confuses “residence time” with “adjustment time” (a/k/a “effective residence time”).
The “residence time” is implied by the percentage of isotopically identifiable carbon remaining in the atmosphere, some period after a perturbation of its level. But it is much shorter than the “effective residence time” or “adjustment time,” for a change in the total amount of carbon in the atmosphere.
The reason is that some of the processes which remove ¹⁴CO2 from the atmosphere do so by exchanging it, one-for-one, for ¹²CO2. Those processes cause the fraction of “fossil carbon” in the atmosphere to decline without actually reducing the amount of CO2 in the atmosphere. That means the 11.5 year half-life and 16.6 year residence time are necessarily less than the effective lifetime of CO2 emissions.
The effective lifetime of anthropogenic additions to CO2 in the atmosphere, defined as the time it would take for (1-(1/e)) = 63% (sometimes rounded to 2/3) is roughly fifty years, making the half-life about 35 years.
That’s the result that Prof. Richard Lindzen reported during the Q&A (3rd video) of this (excellent!!!) lecture:
● Part 1:
● Part 2:
● The Q&A which followed:
https://www.youtube.com/watch?v=69kmPGDh1Gs (including his discussion of CO2 atmospheric lifetime)
That’s also the approximate result that Dr. Roy Spencer found:
That’s also the approximate result which I got, first with a little program to simulate declining CO2 levels, based on the historical CO2 removal rate as a function of CO2 level, and then with a modified version of the program based on Dr. Spencer’s model. The source code is here:
Ferdinand Englebeen reported roughly the same result, here:
3. We have solid data which proves beyond legitimate dispute that mankind can claim credit for all of the 105 ppmv increase in atmospheric CO2 concentration since precise atmospheric CO2 concentration measurements began in 1958:
The mistake which the climate alarmists make is in their claim that the increase in atmospheric CO2 is harmful, or even a “crisis” or “emergency.” Actually, the scientific evidence is compelling that man-made climate change is modest and benign, and CO2 emissions are beneficial, rather than harmful.
Scientists call the periods of warmest climate “climate optimums,” including periods like the Eemian climate optimum, which is believed to have been several degrees warmer than now.
The supposed major harms are all merely hypothetical (& mostly implausible). None of them are actually happening:
* Sea-level rise has not significantly accelerated.
* Storms have not worsened.
* Droughts have not worsened, and drought impacts have been significantly mitigated by higher CO2 levels.
* Floods have not detectably worsened.
* Fires have not worsened.
* Corals and polar bears are doing fine.
The benefits of rising CO2 levels are real, measured & very large: improving crop yields, and a greening planet.
The benefits of CO2 for agriculture have been settled science for over a century. Note the date on this article!
Gradenwitz A. Carbonic Acid Gas to Fertilize the Air. Scientific American, November 27, 1920.
This NASA video is about how CO2 is greening the Earth:
You can learn more, and find documentation for the facts I’ve mentioned, here:
Thank you, Richard, and thank you for trying to reason with K______ over at No Tricks Zone.
BTW, I tried to post a comment on your blog, but when I clicked on “Publish” it reported:
Comments on this blog are restricted to team members
I wish your site had told me that before I typed the comment (and I wish there was a way to contact you, other than replying to one of your comment on another blog).
The problem is that it confused dwell with residency.
The ‘residency time’ is that of an individual CO2 molecule in the atmosphere. We know from the C14 ‘Abomb spikes’ that it is about 5-7 years. A number of papers on it readily available. Photosynthesis related.
Dwell time is the ‘half life’ of the bulk of all CO2 put into the atmosphere in a year from fossil fuel combustion, encompassing all eventual sequestration and desequestration processes (mostly via forests and ocean organism calcification). Also approximated by the similar 2/3 gone Efold time. Been discussed by Willis E here previously years ago, because Murray Salby had the same definitional confusion in his now discredited three papers. Dwell/Efold is on the order of 42-50 years or so, and can be guestimated from changing 12C/13C ratios as fissil fuels preferentially sequester lighter 12C. So at the beginning of the industrial era, 13C was at a max proportion.
Are you saying the C14 graph in Dave Burton’s comment is incorrect?
No.I was going from memory based on core top datings and an old critique of Salby.
I did a similar analysis and got only slightly different numbers. I concluded that if we continue emissions at the current rate indefinitely, then the CO2 concentration will plateau around 515 ppmv. That is only 30% of a “doubling” of CO2 (from the current 420 ppmv).
We’ve already had 58% of a doubling, and we’ve gotten at most perhaps 2/3 of 1.1°C from that CO2 level increase. At that rate, another 30% of a doubling = about 0.5°C. (And that’s assuming that none of the 1.1°C of warming was natural, which I doubt.)
Add to that about 0.1°C of warming “in the pipe” from the current radiative imbalance (which is no more than about 0.3 W/m²), and we get at most 0.6°C of total additional warming.
The 1.1°C of warming that it’s estimated we’ve already since the late LIA had has been entirely benign. So is it plausible that another 0.6°C could be significantly harmful?
The question answers itself: obviously not. It’s literally not even noticeable:
0.6°C is less than half the “hysteresis” (a/k/a “dead band” or “dead zone”) in most home thermostats. (That’s the amount by which “constant” indoor temperatures continually fluctuate, probably without you even noticing.)
0.6°C is about the climate change you get from an elevation change of 300 feet (calculated from a lapse rate of 6.5°C/km).
In the United States, 0.6°C is about the climate change you get from a latitude change of 30-40 miles.
Midwestern farmers could fully compensate for 0.6°C of warming by planting about 3-4 days earlier in the springtime.
Do any of those things sound like a catastrophe, to you?
Well, I’ve never been a farmer, but planting 3-4 days earlier for what reason? The growing season won’t shift in time, it will extend earlier AND later. There would still be a long enough growing season to plant later than before, allowing all risk of a k!lling frost to pass before planting, but still having enough time for the crop to mature.
I would think that the other logical adaptation would be to plant varieties that yield more but require longer to mature. Then it would make sense to also plant earlier. Of course there are other considerations such as the relative cost of seed, optimum amounts of fertilizer and pesticides potentially shifting the costs, etc.
I disregard that 2-3 day thing,to remind you of the extra growing area available because 0.6degrees might make frost, a spirit-killer for small farmers, less common over entire landscapes. Now that can extend your growing season by weeks, months even, allowing multiple crops and multiple harvests.
0.6°C of warming would lengthen Midwestern growing seasons by about one week: about 3-4 days at each end. That is, the average last frost date each winter would come 3-4 days earlier, and the average first frost date each autumn would come 3-4 days later.
Longer growing seasons are generally a good thing. They can reduce risk of frost damage, or they can enable the use of slower-maturing, higher yield cultivars.
This is in fact a wild claim: “We do not have to discuss each absorption mechanism from the atmosphere into oceans or plants. From the known global concentration changes and the known global emissions, we have a good estimate of the sum of actual yearly absorptions.”
Known global emissions? How much did the boreal forest of Canada emit last year? How about the Gulf of Mexico? The Amazon? Kansas?
Nothing is measured so we have no idea. It is all fantasy. Unfounded guesses claiming to be science.
Most of the emissions probably never make it out of the biospheres (terrestrial and oceanic) before they are absorbed nearby. We have no idea what the global emissions are nor how they change over time.
The claim is not “wild,” it is correct.
By the sum of actual yearly absorptions they mean the net sum of “natural emissions and removals of CO2” into and from the atmosphere.
We know that net sum because it is the difference between anthropogenic emissions (which we know quite closely) and the actual change in atmospheric CO2 content (which we know even more closely, since March 1958).
True in part. The uncertainties around total CO2 balance are huge.
But the climate thing is about anthropogenic emissions from burning fossil fuels. This we have a much better handle on because:
The argument (point 2) that the decreasing 13C/12C ratio is sufficient on its own to prove anything meaningful is woefully incorrect. The ratio, as used in the literature as δ13C, proves that the incremental atmospheric CO2 reflects an average increment of CO2 that has a δ13C ratio of -13 per mil. This is clearly demonstrated by both the mass balance equations and the relevant Keeling plots (I am happy to show these). It is this specific value that needs to be discussed. Further, this ratio increases (less negative) during La Niña events (and Pinatubo) and decreases during El Niño events. Any proposed explanation must address these observations from the actual data.
“Biggest sinks are the oceans (phytoplankton calcareous exoskeleton formation) with essentially no change”
The oceans have substantially more calcium and magnesium ions than phytoplankton. When a CO2 molecule is exposed to these ions calcite and magnesite are produced and precipitate to the ocean floor. Which means that most of the Anthropogenic CO2 is accumulating in deep ocean sediments as a mineral. The distribution of these chemical buffering IONS within the oceans are directly related to how much CO2 the oceans can hold, which is subsequently directly related to how much CO2 the oceans will allow the atmosphere to hold. Atmospheric CO2 levels are merely a proxy for average oceanic global temperature.
Annual growth (MLO) was low in 2022 (1.79 ppm) and it’s to be expected to keep following the temperature. If the temperature keeps decreasing in following decades…
edim, the influence of temperature on CO2 levels is very modest: about 4%/K, starting at 295 ppmv in dynamic equilibrium with the current average ocean temperature.
Or 16 ppmv/K over the past 800,000 years as measured in ice cores or less than 5 ppmv increase over the past 70 years… The measured increase is 90 ppmv over the past 70 years while humans emitted near 200 ppmv in the same period…
See the formula of Takahashi to calculate the pCO2 increase of seawater here:
I beg to differ. The authors start with this assumption, “the effective zero-absorption line is crossed at appr. 280 ppm. This is considered to be the pre-industrial equilibrium CO2 concentration where natural yearly emissions are balanced by the yearly absorptions.” As anyone with the most basic understanding of history is well aware, the period before the industrial revolution was a bleak and dismal era. Frozen rivers, crop failures, massive deforestation and general human misery. Instead we should look to the optimum periods, Minoan, Roman or Medieval and make the logical assumption that the CO2 concentration would be closer to the ideal and strive to achieve that by increasing CO2 atmospheric levels by all possible means. Or as the wise climate scholar Bugs Bunny would say….. https://pbs.twimg.com/media/DwFWXAmVYAMU2qH?format=jpg&name=small
A different perspective. The past historical climate ‘optima’ and ‘minima’ you cite had nothing to do with fossil fuel consumption and CO2. That began only about 1810-1820 with coal in the UK with Watts first steam engine. Earlier, it was all natural variation. Probably mostly still is now.
While I agree, an increase in CO2 has long been attributed to the use of coal during the industrial revolution, my point was that using 280 ppm as a benchmark is analogous to using the industrial production during the depths of the 1930s depression as the apogee of all industrial development. And arguing that this level (280 ppm) is even relevant and must be the basis of mitigated is just another contrivance of the green blob. Considering 1000 ppm was the norm during the rise of primates, we have a lot of ground to make up.
You’re misinterpreting the meaning of the 280ppm baseline.
The significance of the 280ppm number is that 280ppm is the observed value in the absence of significant forcing from fossil fuel emissions. It is needed to estimate how much of current CO2 concentration is due to anthropogenic forcing.
It is NOT put forward by the authors as an ideal target value. Indeed you are correct that pre-industrial conditions were dismal from a human flourishing point of view. Your argument that life is better off with more CO2 is absolutely correct, but not a conflict with what the authors are saying.
We could quibble about whether steady state had been reached in 1850, but a stable CO2 concentration in the absence of significant fossil fuel emissions makes it a reasonable estimate.
The zero absorption line under current sea surface temperature conditions would be a little higher. As Ferdinand Engelbeen noted, there should be a modest adjustment of 3% higher partial pressure of CO2 per Kelvin of temperature rise in the sea surface temperature. So maybe 290ppm-ish. The rest of the 420-290=130ppm is the anthropogenic forcing.
Sources and sinks are dynamic. If the “driving force” is higher, the emissions or absorptions will vary proportionately. The greater the excess CO2 in the atmosphere, the more various natural sinks will absorb. Something analogous to the force on a spring determining its elongation.
Natural sinks respond to the current ambient concentration, not to human emission rates. If the zombie apocalypse arrives tomorrow, and all fossil fuel emissions suddenly cease, CO2 concentration would probably only decrease slightly each year. Natural sinks would not change very much, only slowly diminishing as CO2 concentration decreases asymptotically toward that equilibrium point.
The authors’ model predicts how the dynamic natural sinks will respond to a scenario of very modest emission reductions (attributed to efficiency improvements by the authors). The 280ppm baseline is a necessary initial condition for the calculations, nothing more.
Look around, and you will see the enormous benefit of the human forcing.
The world gross product increased at least 100 times, population 8 times,
We have vastly more biomass and huge crops to feed all these people.
All that and more for a measly 1.2C increase in temperature
What in hell is everyone complaining about?
I agree with you. Certainly another degree to 2.4C rise would still be net beneficial, perhaps overwhelmingly beneficial with no discernible downsides. Probably even 4 degrees would be net beneficial. As long as we don’t run out of economically extractible fossil fuels.
At some point, a failure to transition away from increasingly scarce fossil fuels would be a humanitarian catastrophe. Not due to warming or sea level rise, but due to starvation and food riots.
World population is expected to top out around 11 billion. If it becomes too expensive to make fertilizer and run mechanized agricultural equipment, how many will starve when the whole world has to follow Sri Lanka’s practices—not by policy fiat but by economic necessity?
Developing molten salt breeder reactors is a no-regrets policy. Used for both electricity generation and process heat, the complete replacement of fossil fuels is possible when in the far-distant future that becomes necessary. After fossil fuels are depleted, there will still be thousands of years supply of thorium.
There’s no immediate urgency obviously, given likely centuries of remaining fossil fuel supplies. The only urgency is as an economically viable approach to capping CO2 concentration while retaining our wealthy technological society.
If we could be confident that we could simply defeat the climate doomsayers, obviously the best choice would be to keep using fossil fuels as our primary source of energy and leave the problem of fossil fuel depletion to generations closer to that prospect. Since most of the world is in thrall to the delusion that CO2 is dangerous, it’s a reasonable strategy to work toward thorium MSRs.
MSRs might end up being more cost-effective and less impactful on nature even than continuing to use fossil fuels. As the saying goes, the stone age didn’t end because we ran out of stones.
“That began only about 1810-1820 with coal in the UK with Watts first steam engine.”
Rud; Let me correct that for you
‘ That began in 1712 with coal in the UK with Newcomen’s first steam engine.’
Erected at Coneygree Coal Works near Dudley Castle in Staffordshire. It worked at 12 strokes per minute and had 5.5 horse-power, raising 10 gallons of water from a depth of 150 feet at each stroke
Thomas Newcomen (1664-1729) designed and installed the first practical and successful steam engine, used initially for pumping water out of coal mines.
Over 2000 Newcomen engines were installed world-wide during the 18th and 19th centuries, over 600 of them before 1775 when James Watt was able to improve their efficiency.
( James Watt invented the steam condenser NOT the steam engine )
Is it reasonable or not to consider this scenario?
CO2 from a strong point source like a coal power station travels only a short distance like under 1,000 km, before it is mostly taken up in growing vegetation or water. The remainder gets mixed into air that eventually reaches Mauna Loa.
Therefore the Mauna Loa levels (or Cape Grim or Barrow or South Pole) are not a proper measure of total emissions.
There is little, if any, doubt that SOME CO2 is taken up in transit. The ML ups and down each year are commonly related to vegetation growth. The question is about how much gets to the vegetation before it gets to ML.
Help needed. I recall a study at the big base metal smelter at Mt Isa, Queensland with sensors placed at intervals up to a few hundred Km downwind to measure SO2 dispersion. Possibly in the 1975-85 era. Maybe they measured greening also. Any links from readers here?
A tree in spring only can absorb the amount of CO2 that its photosynthesis allows. If it captures a fossil fuel CO2 molecule, a natural CO2 molecule will reside longer in the atmosphere. Thus what reaches Mauna Loa anyway is higher in mass than without human emissions.
Mauna Loa doesn’t measure the emissions, only the growth in CO2 each year. Figures for the emissions are obtained from fossil fuel sales (taxes!) and burning efficiency of the different fuels.
Of course, if you increase total CO2, both oceans and vegetation will absorb more CO2 due to the increased CO2 pressure (pCO2) in the atmosphere, but that doesn’t catch up with the emissions, that is the point the authors are making…
But is there an argument that not all emissions get into the well-mixed air that is measured at ML? Could thyat be an explanation for the missing 50% or so of CO2 between calculated and emitted flux?
BTW, each time I read of a location or a mechanism being a source or a sink for CO2, I wonder how this is determined. If you simply measure CO2 in the air above a place, you cannot know if the CO2 is going into the air or out of the air (unless it is patently visible, like a smokestack in action). Is there a way to look at the OCO satellite data, to point to a map and say “This is a source” and “This is a sink”?
Most human emissions are going straight into the atmosphere, but then part already may be absorbed into the next available trees or after a year into the deep oceans via the THC sink place in the N.E. Atlantic…
I have the impression that the OCO satellites don’t perform as good as expected: theoretically, they can focus on a certain spot for a limited time (industrial area, towns) and attribute local elevated CO2 levels to that spot, but in reality the measurements are too jumpy, compared to local measurements.
The overall data are easier to obtain: temperature changes in SST do change CO2 and O2 in/out the sea surface somewhat, but uptake/release by vegetation shows a stoichiometric relationship between O2 and CO2. By measuring the residual O2 decline after counting for the O2 use from fossil fuel burning, one can calculate the amount of O2 that was used or released from CO2 release/uptake by vegetation:
https://tildesites.bowdoin.edu/~mbattle/papers_posters_and_talks/BenderGBC2005.pdf see the last page Figure 7.
Even in the ocean surface the increase is measured:
https://tos.org/oceanography/assets/docs/27-1_bates.pdf see Figure 3 and Table 2.
The rest is going into the deep oceans where measurements are very difficult, but tracers are used (14C, CFCs, noble gases,…)
That results in following estimates in graph form for the period 1990-2000. I have seen a more recent one, up to 2010, but didn’t find it back:
Geoff, there are several tall towers in use that measure CO2 fluxes at different heights, so that one can know if CO2 is coming out or getting into the land plants below. Here an example from The Netherlands (Cabauw tower 200 meter high).
While part of human emissions may reach Mauna Loa, other parts are rather fast absorbed by vegetation and cold parts of the oceans and also “diluted” by the about 40 PgC “old” CO2 out of upwelling from the deep oceans near the equator.
The problem with all of these general rules brought up is that they do not account for all the variables. The oceans chemically mineralize most of the CO2 that is absorbed via calcium, magnesium, etc.. ions and a host of other chemical processes as well as biological processes, and consequently precipitate to the ocean floor. The distribution of these CO2 binding agents within the oceans and the oceans temperature determines the amount of dissolved CO2 within the oceans. The chemical components within the oceans that bond with CO2 are continually being replenished by deep ocean vents (black smokers) and consequently best estimates indicate that these ocean vents could account for as much as 10% of the heat flux leaving the planet.
As rain falls through the air if it is below 28 degrees C. absorbs CO2. If those rain raindrops stay below 28 degrees and hits the surface which is below 28 degrees, then the CO2 will bond with a variety of molecules within the near surface soil. If the ground is warmer, the CO2 will be released and likely be used by biological processes. That is why rain is better than well water for irrigation because it is ladened with Nitrogen and CO2.
Best estimates indicate that 100 Gigatons of natural CO2 are cycled through the biosphere each year and if there were no human CO2 emissions, it is highly likely that atmospheric CO2 levels would be no different, as atmospheric CO2 levels are determined by ocean temperature and have nothing to do with emissions.
The missing CO2 is being mineralized by saltwater bodies and are accumulating in the ocean surface sediments.
Atmospheric CO2 levels are an effect not a cause.
My impression is that you overestimate the influence of all what you describe:
As far as I know, reminealisation of CO2 is a relative slow process and more or less in equilibrium with the CO2 emissions of subduction and subareal volcanoes.
Rain drops are already saturated at the cold temperatures where rain is formed, which is not even measurable in the CO2 level of the atmosphere at that atmospheric height. The amount that fresh water can absorb at 0.0004 bar CO2 pressure is a few mg/liter and when it drops on the ground gives less than 1 ppmv increase in the adjacent 1 m3 of air for 1 mm/m2 rain when fully evaporated. The addition to the soils doesn’t look very huge to me, compared to all the decaying organics in the soil itself…
See the engineering toolbox at:
The measured increase of CO2 in vegetation is about 1/4 of the emissions over time and 1/10 in the ocean surface: the latter still dissolved as CO2 (1%), bicarbonates (90%) and carbonates (9%) together called DIC (dissolved inorganic carbon). The rest of about halve human emissions sinks into the deep oceans and 1/2 remains (temporarily) in the atmosphere.
I am constantly being told that I must do everything possible to save the World from a Catastrophe so, therefore, I and my family must reduce our personal emissions of CO2 by, for instance, giving up my beloved Landrover and tearing out my very efficient oil boiler. If I was to consider doing this could I see how this will affect the overall battle for our very survival on, say a Keeling Curve?
So, the question for me is, if I were to consider making my life so much, much worse, is it possible for some Scientist who is demanding we all do everything to reduce our emissions, to produce a Keeling Curve separating Natural CO2 and just depict Anthropogenic CO2 so I can show my family how successful our major sacrifices would help in reducing emissions to save the Planet? If not, how can I possibly prove to my family, by taking our lives back to the 1950s, we are ‘saving the Planet’?
What you are forgetting is that CO2 produced by nature is good and in equilibrium.
CO2 produced by man is rejected by nature and therefore ends up in the atmosphere only to poison us. Nature knows the difference.
I guess you got the negative tick because you forgot the “sarc” ending.
If this is a serious remark, you may read the original paper, where natural and human emissions are treated exactly the same way. There is nothing mysterious about it.
The first graph which shows emissions as atmospheric PPM equivalent, does not make sense. I thought that 1 ppm of atmospheric CO2 is equal to a mass of 2.12 gigatons. So, if just the annual human emissions are 40 gigatons that would be an atmospheric equivalent of 18.86 ppm.
You need be be very careful with these numbers and their units. 1ppm = 2.124 GtC, and 1 GtC = 3.664 Gt CO2 => 1 ppm = 7.78 Gt CO2 => 5 ppm = 38.9 Gt CO2. voila!
ppmv is as CO2
gigatons is a GtC (carbon)
a difference in molecular weight of 44 to 12
Human emissions are above 9 GtC/year (or mostly written nowadays as 9 PgC/year) which is equivalent to around 4.5 ppmv/year…
It would be interesting to see a sensitivity analysis of the size of CO2 emissions over the rest of the century against the final CO2 level in the atmosphere. This report gives one data point, I think that Dave Burton provides another. I remember Willis E doing some work on this, some years ago. Perhaps an update, Willis?
CO2 in the atmosphere:
Which of these statements is flawed?
Eike, it seems that the rest of the reaction is lost… Here again:
3) Agreed to a certain extent: most natural in/out fluxes are temperature dependent, thus not dependent of the total amount of CO2 above equilibrium.
The only extra influx above equilibrium is from human emissions, as these are twice the observed increase in the atmosphere. Thus with constant human emissions, there would be a new equilibrium where human input = extra out0flux.
5) Disagree: the current observed amount of human CO2 in the atmosphere is already over 10%, based on the fast declining 13C/12C ratio in the atmosphere, caused by the low 13C/12C ratio in fossil fuels.
That is because the natural fluxes are mainly bi-directional and part of the human CO2 absorbed in plants en ocean surface are brought back to the atmosphere in the next season or year(s).
6) The source is known: human emissions have risen a fourfold per year from 1960 to 2020 at a total increase that is near twice the increase in the atmosphere…
One problem with the calculations used to predict global temperature peaking at 1.4 degree C above what it was in 1850 is assumption that CO2 is the only manmade greenhouse gas.
A second problem is that the calculation of only .4 degree C temperature rise after 2020 based on CO2 increasing from 410 to 475 PPM and a climate sensitivity figure that I agree with (1.92 degrees C per 2XCO2), because this does not include warming that is still in the pipeline from emissions that happened before 2020.
A third problem I see is an optimistic assumption of future emissions, namely “IEA stated policies emission scenario”, which I found as being the STEPS scenario by the International Energy Agency. They say this is a conservative (low side) projection of future CO2 emissions, and is dependent on countries adhering to a policy for pushing down their future CO2 emissions.
A fourth problem I see is assuming that in the future, nature will continue absorbing CO2 from the atmosphere at an annual rate of 1.6% of (PPM minus 280), and that a short term CO2 “pulse”/emission (such as a single year’s emissions) has exponential decay describable as having a half life such as the claimed 42 years, as opposed to a Bern model. Yes, I know there are Bern model equations that are oversimplified with too few terms and skewed by unrealistically high climate sensitivity causing unrealistically great decrease of solubility of CO2 in water from warming, causing the coefficient of the permanent term to be unrealistically high. However, Bern models are based on the ability of the ocean to absorb CO2 decreasing as CO2 concentration increases below the upper ocean.
There is the matter that since 1950, CO2 emissions and atmospheric surplus above 280 PPM have both increased nearly enough exponentially. One mathematical property of these increasing exponentially is consistency with a wide range of shapes of decay curves of a short term emission, including half-life of 42 years and some Bern model equations. Until CO2 emissions downturn from exponential growth enough to get atmospheric surplus above 280 PPM downturning substantially from exponential growth, consistency of emissions and atmospheric concentration with an exponential shape of decay curve of a short term emission does not disprove other decay curve shapes such as Bern models.
Thank you for making such nice, useful list of the potentially open issues.
P.S. (point 5): Even if one cannot decide from the measured data which model is correct, Occam’s razor would force us to use the simplest possible model with the fewest number of parameters, which happens to be ours.
Reply to Ferdinand Engelbeen, April 1, 2023, 1:11, and April 2, 12:41
1. Since only very small quantities of CO2 are generated or destroyed within the atmosphere, concentration change (the net out-flux or net in-flux) always must be the difference between total in-flux and total out-flux, whatever the natural variability.
2. Misunderstanding: I refer to total out-flux, not to net out-flux. Being mainly driven by diffusion, the total out-flux from the atmosphere principally must be proportional to the absolute concentration, and it must be independent of simultaneously occurring in-flux. Atmosphere reacts very fast to changes in the concentration and transfers CO2 to the ocean proportional to the concentration. The answer of the ocean to getting more CO2 from the atmosphere is delayed by some 1000 years. Therefore, we do not have this answer yet (but we do have the enhanced out-flux from the atmosphere!). Therefore, to achieve the high concentration, the emissions from the ocean must have risen independent of its uptake (see also No. 5).
3. My statement Nr. 3 assumes other parameters being constant. If you change other parameters, this can override almost everything. Due to physics, natural out-fluxes are principally proportional to absolute concentration, not to the concentration above any equilibrium. The atmosphere cannot remember any equilibrium, the atmosphere only knows the (absolute) concentration and reacts to it, not to the difference to any historical equilibrium. The in-flux into the atmosphere is driven by temperature, ocean currents, volcanic activity, etc. We do not know it and can only calculate it by the measured change of concentration and the assumption of out-flux being proportional to concentration. You write: “The only extra influx above equilibrium is from human emissions”. This is probably not correct, first, since ocean and biomass must emit more CO2 today than 150 years ago (elevated temperatures, grown biomass), second, because the concentration has risen much higher than the human emissions (50 % compared to %!), and third, because it has risen much faster than human emissions have risen (for example, within the last 10 years by some 2 ppm/y compared to only some 0.1 ppm/y). There are some more reasons to assume higher natural emissions, but I do not want to expand the discussion unnecessarily.
5. Sure, part of the increased natural fluxes is an answer to increased concentration in biomass and upper ocean layer due to human emissions into the atmosphere, but only part of it. I think, the whole process can be divided into two stages: First, the increased emission into the atmosphere is divided evenly between atmosphere, biomass, and upper ocean layer. Due to the large exchange fluxes between these three reservoirs, and their small inventories, equilibrium is reached within a few years, respectively a transient always proceeds close to equilibrium. Second, CO2 is transferred from the equilibrium within these three reservoirs to the deep ocean at a substantially lower pace, but still with a flux much higher than the human emissions and still with this flux being proportional to the concentration in these three reservoirs. So, replace in the above, especially in No. 2 and 3, the word “atmosphere” by the three reservoirs “atmosphere, biomass, and upper ocean layer”, and you have exactly the same situation as above, only with slightly reduced fluxes. The deep ocean still answers not yet to its increased CO2 uptake, but must emit more CO2 to achieve the high concentration in the three reservoirs (third possibilities like volcanic emissions neglected).
6. Mathematically correct, but there are infinite mathematically correct solutions: The concentration rises at the difference between total in-flux and total out-flux. We only know this difference, and we have good physical reasons to assume the out-flux to be proportional to the concentration (in the atmosphere, respectively in the three reservoirs atmosphere, biomass, and upper ocean layer). It is this physical reasoning, which selects the correct mathematical solution. And then, there must be much stronger natural emissions than human emissions, by chance simultaneously with the human emissions and by chance in that height, as to fit mathematically to the assumption of halve of the human emissions staying in the atmosphere (but if it would be any other correlation, it still would be just by chance).