From the Carbon Dioxide Information and Analysys Center (http://cdiac.ornl.gov/ftp/ndp030/global.1751_2010.ems), total anthropogenic fossil carbon emissions from 1750-2010 were 364,725 MtC (derived from industrial records, not in dispute); if you burn 364,725 MtC you get 1.336e15 kg of CO2 (basic chem). The mass of the atmosphere is 5.1480e18 kg [Trenberth, K. E., & Smith, L. (2005) Journal of Climate, 18(6), 864-875.] Divide our known contribution by the total mass of the atmosphere, and we know that we have added 1.336e15 / 5.1480e18 = 260 parts per million by mass, which for CO2 is 171 parts per million by volume. That's what we know we've added to the air, from industrial records.
But when we look at CO2 data, both historical (ftp://aftp.cmdl.noaa.gov/products/trends/co2/co2_annmean_mlo.txt) and from ice cores (ftp://ftp.ncdc.noaa.gov/pub/data/paleo/icecore/antarctica/law/law2006.txt) we don't see a rise of 171 ppmv during the period 1750-2010. We only see a rise of 113 ppmv in the atmosphere.
So what happened to the remaining 58 ppmv? Four hundred and fifty billion tonnes of CO2 cannot just vanish. It must exist somewhere. And the answer, of course, is that the natural world, the oceans and soils (plus a tiny bit for the lithosphere) has absorbed some of the CO2 that we have emitted into the air — which is why it's not in the air any more. And that means that the natural world, taken as a whole, must be acting as a net sink for CO2, which means that the natural world cannot also be acting as a net source for CO2.
Therefore, humans are responsible for 100% of the atmospheric increase in CO2. Arguments to the contrary — particularly Salby's — fail to conserve mass.
Knowing that, it's easy to see Salby's mistake. During El Niño years, when the Pacific warms, atmospheric CO2 rises, but not because the oceans are emitting more CO2 (because they're not emitting CO2 in the first place). No, atmospheric CO2 rises then because when the Pacific warms, it absorbs less of the CO2 that we emit, leaving more of what we emit in the air. And during La Niña, when the Pacific cools, it absorbs more of what we emit, leaving less of what we emit in the air.
Thank you for adding your comment regarding Murry Salby’s talk. Let’s call the calculation you describe, “Method A,” because I don’t want to make our discussion personal.
Method A uses proper values and does proper arithmetic. However, Method A does not properly set up the physical equations and, therefore, does not conserve carbon mass.
Below I will describe “Method B.” Salby uses Method B both in his presentations and in his book, “Physics of the Atmosphere and Climate.”
To simplify carbon and CO2 data, we convert all GtC values to equivalent ppmv values, using the conversion factor:
1 ppm by volume of atmosphere CO2 = 2.13 Gt C
This gives the same result as Method A’s conversion of 364.725 GtC to 171 ppmv.
We define the following terms (see References for data sources):
D = d/dt = the change of a quantity with time
CA = carbon (in the form of CO2) in atmosphere = 400 ppmv.
DCA = rate of carbon increase in atmosphere = 2.1 ppmv/year
DCS = rate of ocean carbon to atmosphere = 42 ppmv/year
DCG = rate of land carbon to atmosphere = 56 ppmv/year
DCH = rate of human carbon to atmosphere = 4.7 ppmv/year
We write the carbon conservation equation as follows:
DCA = DCS + DCG + DCH
If we insert the above numbers, this equation looks like this:
2.1 = (100 – 100 + Error + Delta) + 4.7
The errors in DCS and DCG are almost 10 percent. The flows go in both directions. That is, nature adds (DCS + DCG) about 100 ppmv to the atmosphere each year and subtracts about 100 ppmv from the atmosphere each year. The net change in DCA is the small difference between two very large numbers.
The 10 percent Error in the inflow and outflow of DCS and DCG is greater than DCA and DCH.
Nature’s exchange of 100 ppmv in and out of the atmosphere each year is 25 percent of the 400 ppmv carbon in the atmosphere.
Consider an analogy where a tub represents carbon in our atmosphere. The water flow out of the faucet represents carbon flow into our atmosphere. The water flow out of the drain represents carbon flow out of our atmosphere. The flow rate out of the drain is proportional to the height of the water above the drain.
The tub contains 400 gallons of water to represent the atmosphere’s 400 ppmv. The inflow is 100 gallons per unit time and the outflow is 100 gallons per unit time.
We add a second faucet set to input 4.7 gallons per unit time to the tub, to represent human emissions of 4.7 ppmv per year. The total inflow is now 4.7 percent greater than before. The height of the water will increase 4.7 percent to cause an equal outflow. Now, the tub will contain 418.8 gallons in this new equilibrium.
Similarly, human CO2 emissions will increase the natural CA by 4.7 percent using 2015 data. Nature has caused natural CA to be 381.2 ppmv, and human emissions have added 18.8 ppmv to make today’s 400 ppmv.
In 2015, nature caused 95.3 percent of the CO2 increase and human emissions caused 4.7 percent of the increase. The amount of human-caused increase was much less when human emissions were less.
Method A does not use the carbon conservation equation and it does not conserve carbon mass. Method B uses the carbon conservation equation and it conserves carbon mass.
Method A attempts to follow carbon transfer by looking only at DCA and DCH, and excludes DCS and DCG. Method A finds 58 ppmv missing in 260 years because it does not include all natural flows of carbon into and out of our atmosphere. Method B shows the 58 ppmv error over 260 years is in the noise level of DCS and DCG natural flows.
Method A constrains nature to either a net inflow or a net outflow. Method B includes both inflow and outflow simultaneously, and it allows oceans to add to atmospheric carbon while land subtracts from atmospheric carbon.
Professor Salby goes further and shows that temperature (meaning ocean temperature) drives the increase in atmospheric carbon. Specifically, using mathematics, the data show that CA follows the integral of temperature, which means DCA follows temperature.
Nature causes 20 times more increase in atmospheric CO2 than do human emissions. Human emissions are insignificant to climate change.
The numerical data for DCA, DCS, DCG, and DCH come from:
The average increase in CA from 2005 to 2010 was 2.1 ppmv per year. ftp://ftp.cmdl.noaa.gov/ccg/co2/trends/co2_annmean_mlo.txt
IPCC “Report 3. The Carbon Cycle and Atmospheric Carbon Dioxide”
Fossil fuel burning and cement production in 2015 was about 10 GtC or 4.7 ppmv per year. http://www.globalcarbonproject.org/carbonbudget/1…
You provide a non sequiter when you assert;
"So what happened to the remaining 58 ppmv? Four hundred and fifty billion tonnes of CO2 cannot just vanish. It must exist somewhere. And the answer, of course, is that the natural world, the oceans and soils (plus a tiny bit for the lithosphere) has absorbed some of the CO2 that we have emitted into the air — which is why it’s not in the air any more. And that means that the natural world, taken as a whole, must be acting as a net sink for CO2, which means that the natural world cannot also be acting as a net source for CO2.
Therefore, humans are responsible for 100% of the atmospheric increase in CO2. Arguments to the contrary — particularly Salby’s — fail to conserve mass."
The fact that the natural system is observed to be a net sink only proves that the carbon cycle system is not in equilibrium. It does NOT prove nature is not providing the observed rise in atmospheric CO2 concentration.
The natural system has many sources and sinks for CO2 which operate simultaneously and many vary (e.g. ocean that is a sink in summer is a source in winter).
I refer you to one of our 2005 papers
(ref. Rorsch A, Courtney RS & Thoenes D, ‘The Interaction of Climate Change and the Carbon Dioxide Cycle’ E&E v16no2 (2005) )
It provides six models of the carbon cycle system. There are three basic models and they each assume a single mechanism dominates the carbon cycle system. In each basic model it is assumed that
1. the rise is purely natural
2. there is a significant anthropogenic contribution to the rise in atmospheric CO2 concentration.
Thus we provided six models.
Each of the models in that paper matches the available empirical data without use of any ‘fiddle-factor’ such as the ‘5-year smoothing’ the UN Intergovernmental Panel on Climate Change (IPCC) uses to get its model (i.e. the Bern Model) to agree with the empirical data.
The superior performance of each of our models over the IPCC’s Bern Model results from our modelling assumption. The Bern Model uses the assumption of anthropogenic CO2 emissions being in excess of what nature can sequester (which is now refuted by the OCO-2 data). Our models assume something has altered the equilibrium state of the carbon cycle system.
Some processes of the carbon cycle system are very slow with rate constants of years and decades. Hence, the system takes decades to fully adjust to a new equilibrium. The observed rise in atmospheric CO2 is easily modeled as being continuing slow adjustment towards an altered equilibrium.
This raises the question as to what may have altered the equilibrium of the carbon cycle.
One possibility is the anthropogenic CO2 emission. In our models the short term sequestration processes can easily adapt to sequester the anthropogenic emission in a year (which now seems to be confirmed by the OCO-2 data). But, according to our models, the total emission of that year affects the equilibrium state of the entire system with resulting rise in atmospheric CO2 concentration as is observed. This possibility is real but unlikely.
Natural factors are more likely to have caused alteration to the equilibrium of the carbon cycle system. Of these, the most likely cause is the centuries-long rise in global temperature which is recovery from the Little Ice Age.
As mentioned above, each of the models in our paper matches the available empirical data without use of any ‘fiddle-factor’. But if one of the six models of our paper is adopted then there is a 5:1 probability that the choice is wrong. And other models are probably also possible. Also our six models each give a different indication of future atmospheric CO2 concentration for the same future anthropogenic emission of carbon dioxide.
Data that fits all the possible causes is not evidence for the true cause. Data that only fits the true cause would be evidence of the true cause. But the above findings demonstrate that there is no data that only fits either an anthropogenic or a natural cause of the recent rise in atmospheric CO2 concentration. Hence, the only factual statements that can be made on the true cause of the recent rise in atmospheric CO2 concentration are
(a) the recent rise in atmospheric CO2 concentration may have an anthropogenic cause, or a natural cause, or some combination of anthropogenic and natural causes,
(b) there is no evidence that the recent rise in atmospheric CO2 concentration has a mostly anthropogenic cause or a mostly natural cause.
Hence, using the available data it cannot be known what if any effect altering the anthropogenic emission of CO2 will have on the future atmospheric CO2 concentration. This finding agrees with the statement in Chapter 2 from Working Group 3 in the IPCC’s Third Assessment Report (2001) which the IPCC has not reversed and says; “no systematic analysis has published on the relationship between mitigation and baseline scenarios”.
You state: "The fact that the natural system is observed to be a net sink only proves that the carbon cycle system is not in equilibrium. It does NOT prove nature is not providing the observed rise in atmospheric CO2 concentration."
The fact that the natural system is observed to be a net sink proves both. Since you admit that the natural world is a net sink, then the only possible net source is anthropogenic.
You state: "Natural factors are more likely to have caused alteration to the equilibrium of the carbon cycle system. Of these, the most likely cause is the centuries-long rise in global temperature which is recovery from the Little Ice Age."
Still begging the question: where did the CO2 come from? And still violating conservation of mass by doing so. It's also rather disappointing that someone who considers himself a carbon-cycle expert is apparently unaware that oceanic CO2 concentration is rising just like it is in the air, and at the same rate — just as we would expect from Henry's Law (a critical but completely ignored factor in your 2005 paper, which contains far too many errors to refute here.)
And not once, in any of those models, do we find a single case where Fout < Fo. In other words, EVERY SINGLE TIME you model, you show the natural world absorbing more CO2 than the natural world emits. It's simply dumbfounding that you fail to recognize what that means.
At issue is whether the rise in atmospheric CO2 concentration would differ if the small anthropogenic emission were not present. If you were to read the explanation I took the trouble to write for you then you will understand why available data does NOT enable this question to be resolved.
I explained why and how you are wrong when you assert,
“Since you admit that the natural world is a net sink, then the only possible net source is anthropogenic.”
but you have ignored my explanation and have parroted your error!
Please try to understand that your assertion would only be right if each of the sources and sinks operated at constant rate and – as I explained – THE SOURCES AND SINKS VARY. I add the following in hope of assisting your comprehension.
We know the natural sources and/or sinks have been varying over time because the accumulation rate of CO2 in the atmosphere (~1..5 ppmv/year which corresponds to ~3 GtC/year) is equal to almost half the human emission (~6.5 GtC/year).
THE ACCUMULATION RATE WOULD NEED TO EQUAL THE ANTHROPOGENIC EMISSION FOR YOUR ASSERTION TO BE CORRECT.
Importantly, the observed accumulation does NOT mean that half the human emission accumulates in the atmosphere, as is often stated. There are several other and much larger CO2 flows in and out of the atmosphere. The annual fluctuation of CO2 in the atmosphere (see http://www.esrl.noaa.gov/gmd/ccgg/trends/ ) shows the total CO2 flow into the atmosphere is at least 156.5 GtC/yea. About 150 GtC/year of this is from natural origin and ~6.5 GtC/year from human origin. So, on the average, ~3/156.5 = ~2% of all emissions accumulate.
Frankly I'm rather dumbfounded that you believe that the source of increased atmospheric CO2 is observational error. I can assure you that not only is that untrue, it's unphysical. Observational errors don't create molecules, and they don't move them around.
And you're making exactly the same error that Salby does (plus adding a few more). First, Method A and Method B are exactly the same method. It is incorrect to say "Method A does not use the carbon equation" (it does, but I omitted the math to make the argument easier to follow.) It is incorrect to say Method A "excludes DCS and DCG". (When I write about "the natural world, the oceans and soils," that's exactly the same thing as your DCS and DCG.)
The error you make is assuming that since observational errors in individual components are rather large (and they are), you are therefore absolved from the responsibility of actually balancing the equation! (you're not!) And by failing to balance the equation, you're assuming that it's perfectly all right for observational error to violate Conservation of Mass. And that's simply not true.
So here's my challenge to you: find *any pair of numbers* for DCS and DCG within observational error, that balances the equation, and for which the sum of DCS + DCG is positive. If you can't do that, humans are responsible for 100% of the atmospheric increase.
Because you say so, I will allow that Method A uses the carbon conversation equation even though Method A does not show it explicitly. We must allow Salby the same privilege because he uses the conservation equation explicitly in several parts of his lecture and emphasized its importance. Therefore, both Method A and Method B use the conservation equation, and we must look at other parts of the arguments to evaluate each method.
Let me address your challenge using 2015 data. Clearly, if we can resolve how carbon transfers in 2015, we can apply the same logic to all previous years and to the total of all years.
The carbon conservation equation (as defined in this post) is:
In this equation, DCS and DCG are the net differences of very large carbon flows in each direction.
If the human emissions DCH were zero, we could have, for example:
2.1 = 4.3 – 2.2
With DCH = 4.7 ppmv, we can have, for example:
2.1 = 3.0 – 5.6 + 4.7
2.1 = 2.1 – 4.7 + 4.7
In all three examples, the carbon increase in the atmosphere DCA is 2.1. In the last two examples, the net DCS and DCG are within their measurement errors.
These examples assume higher CO2 concentration in the atmosphere results in higher carbon output to land DCG. There are data that suggest the Earth has “greened” since the rise in atmospheric CO2.
In your challenge, you added a second condition that the sum of DCS + DCG be positive. That is not a valid condition. We can’t measure it and can't prove it is valid. The only additional valid condition is that DCA be positive, and that it be 2.1 ppmv for 2015. Therefore, I have successfully responded to your challenge. Carbon is conserved in the above examples and the values fit measured data.
Therefore, Method A does not prove that human emissions DCH are the primary cause of the observed increase in DCA.
Now let’s look at possible physical errors in Method A. Method A would like to see the carbon conservation equation for 2015 look like this:
2.1 => 4.3 – 2.2 + 4.7 = 6.8 ppmv
Method A assumes nature’s carbon conservation will not adjust to changes in inputs, and assumes nature’s carbon conservation represents a simple system. These are unwarranted and invalid assumptions.
Nature’s carbon conservation is a complex system, not a simple system. This complex system responds and adjusts to changes in inputs. This system will always balance carbon. Method A’s “missing 58 ppmv” is an error in calculating carbon transfer, nothing else. This error arises because Method A assumes incorrectly that nature’s carbon conservation does not adjust to changing inputs.
Salby shows the carbon change in the atmosphere DCA follows the integral of temperature. Salby shows this relationship in more detail in his previous lecture.
If Salby is not correct then changes in DCH will change DCA. If Salby is correct then changes in DCH will not change DCA.
Salby shows at the beginning of his lecture how DCH increased by about three times after the year 2000. Here is one report on this increase in CO2 emissions:
However, as Salby shows, DCA remained the same for the next 15 years.
In conclusion, Method A makes invalid assumptions to support its case. It assumes the atmosphere is a simple system that will not adjust to changing inputs. Method A predicts that DCA would have increased by 3 times when DCH increased by 3 times after the year 2000. The data show DCH increased by 3 times but DCA remained constant. Method A makes a wrong prediction. Therefore, Method A is wrong.
Thank you again for your participation in this discussion.
I guess, I have a question that nobody seems to be willing to address. If nature is a net sink for CO2, why have ice core information determined that CO2 has been much higher in the distant past than it is today? Was there no situation that may have caused CO2 increases in a natural manner? If not, what was causing the increase during those periods?
Dear Charles, In the distant past, more than 600 million years ago, the Earth's atmosphere contained more carbon dioxide than oxygen. As plants formed and grew, they converted carbon dioxide into oxygen. Only then could animals evolve.
Without animals or some other process to convert oxygen into carbon dioxide, the plants would had almost depleted carbon dioxide. Plants that evolved millions of years ago grow much faster and use less water when carbon dioxide concentration is higher than today.
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