Clyde Spencer
2021
Introduction
The concept of accuracy and precision is important to the analysis of the Carbon Cycle. To address the background issue of precision and significant figures, let me provide an example.
Let’s assume that one wants to assess the value of their total assets. OK, that seems straightforward enough. For most middle-class people, their biggest asset is the home that they ‘own.’ However, what is the home worth? How much money could you obtain for it in case you need to raise ransom money for your trusty pet chipmunk, Alvin? Well, that depends on how anxious you are to sell, what the current lending rates are, and the time of the year, among other things. Homes usually sell quicker in the Summer. Therefore, it turns out that there isn’t just one number that represents the value of your home. One can assign a range of values that represent a worst-case scenario at one extreme, to the intervention of an angel that wants to buy your home at any reasonable price for some emotional reason. One can hope for the best, but probably the selling price will be somewhere near the middle of the range, which might be a large range. If similar homes in your area have been selling for about $300,000 under similar market conditions, then it might be reasonable to assign a value of $300,000 ±$30,000, which amounts to a range of about ±10%. That is, one can’t say precisely what the home is worth.
We could go through a similar exercise with your other assets, such as car(s), ski boat, coin collection, etc. However, the situation is the same, with, at best, you only being able to estimate a range of values that you could receive for your possessions.
You pull out your monthly bank statement and, as you had anticipated, the bank tells you exactly how much money you have (or had!) in your checking and savings as of the end of the last month. Considering that you may not be getting any interest on your checking balance, and you should know the amount you have written checks for, you do actually know with, high certainty, precisely how much money you have in your checking account! Let’s say it is $5,000.01; you actually got a little interest last month!
The situation is similar with your savings. Monthly changes are miniscule with current interest rates, so you can estimate, probably to the nearest penny, how much money is in your savings. Let’s say it is $500.49; Therefore, your liquid assets are $5,500.50.
However, the only thing of value that you know with any precision is what is in your bank account! And, it is a small fraction of your total assets, and much less than the range in value of your tangible possessions. This is important in considering how well we understand the Carbon Cycle because what is in your bank account is analogous to the anthropogenic CO2 emissions. Let me illustrate with a little more specificity.
You might want to read some things I have previously written on the topics of accuracy and precision.
Carbon Cycle
Fig. 1. Global Carbon Cycle
The above graphic (Fig. 1) was created to illustrate and quantify what is called the Carbon Cycle. It is the relationship between sources and sinks of carbon, principally carbon dioxide. It illustrates the pools, or fixed reservoirs of carbon, and the annual rate of exchange between sources and sinks, called fluxes.
This frequently displayed graphic of the Carbon Cycle leaves out many anthropogenic carbon sources, as I have detailed here. It appears to address fossil fuel sources only. Therefore, the anthropogenic contribution may be larger. However, I’m going to work with this illustration to make a point.
Now, let’s take a detailed look at the numbers in the graphic. The annual flux of carbon into the atmosphere is the sum of the following:
Burning Fossil Fuels 7.7 ±0.05 pg 7.7 ±0.05 pg
Soil Respiration 58. ±0.5 “
Plant Respiration 59. ±0.5 “
Volcanoes 0.1 ±0.05 “
Deforestation 1.1 ±0.05 “ <1.1 ±0.05 “
Ocean Loss 90. ±0.5 “
Total 216. ±2 pg Anthropogenic Total <8.8 ±0.1 pg
The basic unit is petagrams (pg) of carbon, or 1015 grams of carbon.
(Note that “Ocean Loss” isn’t shown explicitly as having 2 significant figures, but because the “Ocean Uptake” is, I will give them the benefit of the doubt and assume that they were just careless. The uncertainty estimates are implied by the significant figures displayed.)
What percentage of the annual contribution of carbon to the atmosphere is anthropogenic? It is, <8.8 (±0.1) / 216 (±2), or <4.1%. A commonly claimed value is about 3%. Therefore, this appears to be in the ballpark, with the greatest uncertainty being how much of the “Deforestation” category is actually anthropogenic. The point is that we know the total with at least an order of magnitude less precision than the anthropogenic component.
Fig. 2. Alternative Carbon Cycle flux estimates.
https://projects.noc.ac.uk/greenhouse_gas_science/
There is an old saw about how if a man only owns one watch, he always knows what time it is. However, if a man owns two watches, he is never sure of the time. That applies here as I show another example.
This graphic, (Fig. 2), is even more problematic. It shows, at the top, an annual increase of 240 ±10 pg. Another way of stating this is 240 pg ±4%. However, I can only account for 207 ±2 pg when I place the displayed values in a table! We are now confronted with an issue of accuracy (agreement between estimates) as well as precision (the number of significant figures).
Now, as I did for Fig. 1 above, the following is a table presenting the estimates from Fig. 2:
Fossil fuels and cement production 7.8 ±0.6 pg 7.8 ±0.6 pg
Soil and Plant respiration 118.7 ±0.05 “
Volcanoes 0.1 ±0.05 “
Land use change 1.1 ±0.8 “ 1.1 ±0.8 “
Water outgassing 79.4 ±0.05 “
Total 207. ±2 pg Anthropogenic Total 9. ±1 pg
Be-that-as-it-may, in this case, the anthropogenic fraction is, 9 (±1) / 207 (±2), or ≈4.%. Let’s assume that the stated flux of carbon (240 pg) and its associated uncertainty (±10 pg) are correct, and either I missed something, or the artist who prepared the illustration left something off the illustration. The uncertainty (±10) is equal to or larger than the estimated total anthropogenic contribution, 9 ±1 pg.
Now, an interesting thing is that the average anthropogenic flux is 9 ±1 pg/yr, while the estimate for the increase of carbon in the atmosphere is about 4 pg/y (No uncertainty provided, ±0.5 implied.). In other words, the increase of CO2 in the atmosphere is the equivalent of about 50% of the annual anthropogenic emissions. Are we sure that we understand the sinks and sources well enough to be certain that the atmospheric increases are one-half anthropogenic? How do the sinks tell anthropogenic carbon from other sources?
It appears then that an amount about half of the anthropogenic flux ends up in the ocean. Actually, some CO2 is used to create new wood and some supports phytoplankton growth and ends up being sequestered in the deep oceans.
If, as I have suggested, the correlation between anthropogenic CO2 and the rising concentration in the air is not proof of the origin, then some other indicator has to be sought. This is commonly the change in the ratio of 13C and 12C isotopes. This is because plants tend to use the lighter, more abundant, 12C isotope. Therefore, a relative increase in 12C is attributed commonly to its release from fossil fuels. There is nothing wrong with this on the face of it. However, other things can influence the ratio – notably, temperature-driven outgassing from water will favor the lighter 12C isotope because it takes less energy to release the lighter isotope. Also, bacteria decomposing leaf litter and other plant detritus will be working with 12C-rich material. Lastly, the upwelling of deep-ocean waters will bring 12C-rich water to the surface, where it will outgas.
I have previously demonstrated that the above accountings for anthropogenic CO2 emissions is probably an undercount. For the purposes of that discussion, I wrote, “I will define ‘anthropogenic’ as any production that is influenced by or created directly by humans from carbon sources that have been sequestered for short or long periods of time.”
The issue of carbon “recycling” is a matter of time scale. Ultimately, everything is recycled on Earth. Even coal beds will be exposed by erosion eventually and either burn or oxidize slowly, releasing carbon dioxide. In the absence of humans, all oxidation processes would continue, but at a slower rate than what humans cause. It is a matter of agency! My original definition included the caveat, “To the extent that biomass is burned to supply heating and cooking, at a rate greater than it is replenished, there is a net contribution of CO2 to the atmosphere that is tied to population. If deforestation of old trees is accomplished by burning to make way for expanding agriculture, then there is a net contribution of CO2 again tied to the expanding population.” The important point that distinguishes anthropogenic from ‘natural,’ is the changing flux created by human activity, probably best measured on an annual scale.
Summary
The statistical correlation between two monotonically increasing properties will be positive, even if they are unrelated. Therefore, the correlation may be spurious. The estimates for anthropogenic carbon emissions is less than the uncertainty in the total carbon flux into the atmosphere in one example, and the annual atmospheric increase is only about half the estimates. Assuming that the anthropogenic carbon dioxide flux estimates are actually valid, it still provides only about 4% of the total flux available for increasing the atmospheric pool, and can’t account therefore for 96% of the increase.
The increase in 12C in the atmosphere is, in my opinion, weak evidence that the annual increases are driven only by fossil fuel sources. The atmosphere can’t tell ‘anthropogenic’ carbon dioxide from natural carbon dioxide. It seems unlikely that a source that represents only about 4% of the total flux is going to drive the system. The oceans sequester the vast majority of the carbon. One would expect that warming oceans (from whatever forcing) would increase the rate of out-gassing in mid-latitudes, and decrease the rate of extraction at high-latitudes. It seems more reasonable to me that, in a world with warming oceans, there would be a shift in the relative amounts of carbon in the oceans and the atmosphere. That would be the case even in the absence of any anthropogenic carbon.
The science is definitely not settled!
I haven’t provided a rigorous analysis of uncertainty because, as is so often the case, actual uncertainties aren’t provided for all the components of the Carbon Cycle.
In a follow-up article, I’ll provide a detailed examination of the atmospheric concentration of CO2 over the last 30 years, and look for the impact of the COVID-19 pandemic on the growth. This should make it more evident why the uncertainties in the input carbon fluxes, and the relatively small size of the human contribution, is important to challenge the claim that fossil fuels are responsible for the growth in the CO2 concentrations. This is important because the common assumption is that cutting back on anthropogenic CO2 emissions will stop global warming. That probably is not true!
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Clyde,
Your statement “This graphic, (Fig. 2), is even more problematic. It shows, at the top, an annual increase of 240 ±10 pg.” appears to be completely wrong since you are confusing
fluxes with stocks. The second line on the top of figure 2 says quite clearly “average atmospheric increase 4 Pg C/yr”. What the first line says is that the total amount of carbon in the atmosphere is (589+240) Pg. It is also not clear why you would worry about an unsourced diagram of a popular science website when there are plenty of detailed discussions of the carbon cycle in the scientific literature. See for example
https://bg.copernicus.org/articles/16/831/2019/
Walton,
The “240” value is the annual flux of sources, of which only 2Pg is retained. So, you are correct that the increase is small. However, that doesn’t change my claim that of the estimated 240 Pg annual flux, the anthropogenic fraction is smaller than the uncertainty. Nor does it contradict my statement that there is disagreement between the two illustrations.
The diagrams are not unsourced. They were some of the more detailed graphics I found when doing an online search, such as might be done by a layman, or a teacher looking for material to pass on to their students. It also speaks to the fact that those who consider themselves sufficiently expert to create such visual aids, aren’t in agreement on the numbers.
Thank you for the link. It is a more detailed source. However, the authors admit that it isn’t complete. The unanswered question is whether it is more trustworthy than other similar estimates. I’m reminded of the old saw about “If you have many standards, you don’t really have a standard.”
My closing remark was “The science is definitely not settled.” I’ll stand by that.
P.S.
Walton
The link you provided concludes with:
That might serve as a good summary of my article!
Clyde,
The “240” value is not the annual flux. The best evidence of that is to look at the caption on the webpage you reference. It states quite clearly “natural (black) anthropogenic (red)”. Now the top line states “atmosphere 589 (in black) +240 (in red)”. Therefore the correct way to read that is that there is 829 Pg of carbon in the atmosphere of which 240 Pg is caused by humans. And that 829 Pg agrees well with atmospheric CO2 content of about 400 ppm. There is no way that the 240 number in red can be a flux since that mean that humans were emitting 240 Pg of carbon every year as opposed to the numbers in the diagram of about 10 Pg.
Izaak is obviously right. The total in the atmosphere is partitioned into 589 Pg (black) and 240 Pg (red). 240 is not a rate.
Here is the original, with caption
Dikran and the rest of you selflessly and heroically manning the antiaircraft batteries:
Thank you for supplying the complete original caption. It clearly states,
Do bother reading the things you post?
How about some serious flak, instead of puffballs that are blown away easily?
Does the 240 figure have an arrow next to it? No.
It also says “Red numbers in the reservoirs denote cumulative changes of anthropogenic carbon over the industrial period”
You made an error, but can’t admit to it.
“Do bother reading the things you post?”
Lol, clearly you don’t!
“Red arrows, AND numbers …”
The uncontested fluxes outside the atmosphere reservoir box sum to the same order of magnitude as the “240” in the box.
I double checked, that is not what the caption says, you have inserted a comma between “arrows” and “and” that is not there in the caption. What it actually says (cut and pasted from the report) is:
“Red arrows and numbers indicate annual ‘anthropogenic’ fluxes averaged over the 2000–2009 time period.”
So it evidently means the conjunction of a red number and an arrow.
As it also says “red numbers in reservoirs…” in the caption and this is a red number in a reservoir, that is obviously the correct description.
The problem with hubis and snark is that you then can’t back down when shown to be wrong without looking an utter fool for the hubris and snark, so people double down repeatedly instead. Sadly that isn’t any better to an objective observer.
OK, I acknowledge that I inadvertently inserted a comma between “arrows” and “and.” However, I don’t agree that it clearly makes the distinction that the red numbers only refer to fluxes if there is an arrow present. If you look, you will see that there are red numbers in the sub-surface reservoirs without any associated red arrows. Whereas, the atmosphere has red arrows associated with differentiated fluxes that approach in sum the red numbers in the atmosphere box.
I’d say that the meaning in ambiguous. If two reasonably intelligent people can’t agree on the meaning, then I’d say that reinforces my claim that there are issues of accuracy and precision in the Carbon Cycle.
“if you look, you will see that there are red numbers in the sub-surface reservoirs without any associated red arrows”
Yes, they are “The red numbers in reservoirs [that] denote cumulative changes in anthropogenic carbon over the industrial period”. How many times does that need to be pointed out to you?
“Whereas, the atmosphere has red arrows associated with differentiated fluxes”
Yes, arrows indicate fluxes, numbers in reservoirs represent cumulative changes in the reservoir” It’s hardly rocket science and clearly explained in the caption.
“that approach in sum the red numbers in the atmosphere box.”
Yes, *approach*, but not equal to. Common sense suggests that the IPCC report isn’t going to have a numeric error in a key diagram, so perhaps that isn’t what it means. You could look in the caption to see if there is anything that explains what the red numbers in reservoirs mean.
“I’d say that the meaning in ambiguous. If two reasonably intelligent people can’t agree on the meaning, then I’d say that reinforces my claim that there are issues of accuracy and precision in the Carbon Cycle.”
No, the meaning is disambiguated by the existence of a sentence in the caption that says “The red numbers in reservoirs denote cumulative changes in anthropogenic carbon over the industrial period” which says *exactly* what the red numbers in the reservoirs mean. But you don’t seem to want to acknowledge the existence of that sentence. It is there though, if you look.
“The uncontested fluxes outside the atmosphere reservoir box sum to the same order of magnitude as the “240” in the box.”
so you noticed that the numbers don’t actually add up, and conclude that it is more likely that the IPCC authors can’t add up (despite countless hours writing and checking the document through multiple formal stages, including input from externals) than that you misread/misunderstood the caption, on the grounds that they are of the same order of magnitude.
Monumental hubris. Skepticism ought to start with self-skepticism.
There is an old saying that when you point a finger at someone, there are three fingers pointing back at yourself. You might want to take your own advice to heart.
“There is an old saying that when you point a finger at someone, there are three fingers pointing back at yourself. You might want to take your own advice to heart.”
It was you that started the pointing when you wrote:
“Thank you for supplying the complete original caption. It clearly states,
Do bother reading the things you post?”
and then ironically (i) added a comma that wasn’t there (changing the meaning of the sentence in doing so) and (ii) failed to notice that there was another sentence in the caption that explains *exactly* what the red numbers in the boxes mean.
The hubris is all yours.
BTW you *STILL* haven’t identified a specific flaw in the mass balance analysis I provided that shows that this article is incorrect.
“instead of puffballs that are blown away easily?”
I should remind you that you still haven’t identified a specific flaw in the mass balance analysis that demonstrates this article is incorrect.
LOL, -1 for identifying the origin of a diagram – hilarious!
Got an explanation for the negative votes yet?
Re: claim of unsourced data
Globe.gov is a public resource for government data and information, and is sponsored and informed by several agencies of the U.S. government, primarily NASA, but also NOAA and NSF.
https://www.globe.gov/about
and the graphic in question comes from a recently updated Globe page, indeed a popular article, but written from NASA and NOAA perspective and data.
“They were some of the more detailed graphics I found when doing an online search, such as might be done by a layman, or a teacher looking for material to pass on to their students.”
No, a teacher would have been able to find the original source – the IPCC report. That is basic scholarship.
No, the Globe’s NASA-NOAA approved information is for teachers, scientists, citizens and anyone who has interest. Basic scholarship doesn’t require closed mindedness and obsessive repetition of baseless criticism.
It is actually figure 6.1 from the IPCC 5AR WG1 report (page 471). It is somewhat ironic that someone wants to overturn carbon cycle research but doesn’t recognize the key diagram from the relevant chapter of the IPCC report.
The caption is fairly lengthy, but the red figures refer to changes since the pre-industrial era. The arrows represent fluxes (where not indicated by the units) and the numbers not next to an arrow represent stocks. So this is basically saying that the atmopsheric mass of carbon has risen by 240 ±10 Pg since pre-industrial times. It is clearly not an annual flux.
Thank you for pointing out the importance and legitimacy of the graphic. It makes the comparisons all the more valid.
See my quote above!
Clyde,
Belaboring the point well after the referee’s review, trophies awarded (and the cheerleaders have all gone home, more’s the pity), I wonder if either of this pair(?) noticed how many NOAA and NASA scientists, current and alumni, contributed to Chapter 6 of the IPCC report in question. And since NASA is responsible for Globe.gov content and data management, I wonder if either thought to find if the IPCC report was archived by NASA, so that NASA could source it without reference in their own Globe “popular science” article.
I was long ago taught that the first principle of scholarship was literacy, and that coupled closely with an open mind. Was that the first thing that the school systems forgot?
AR5 link
FYI Chap 6 images link
Chap 6 link
Simplistic view: 1ppm out of 400ppm is small, but add 100 years of 1ppm/yr adds 100ppm on top of that 400ppm.
Likewise, the effect of this on temperatures in 1 year is small but they calculate a running sum of energy increasing over time to get wild increases.
Natural processes can amplify but more likely to work against the imbalances (negative feedback) so the models are hard to get right. It would take something like the top500 supercomputers to model the climate in realtime (24hrs to compute 1 day of climate). Current models are toys with lots of shortcuts, assumptions & limits trying to stay in the ballpark. The science of climate models is not settled & not reliable.
Isotope analysis says carbon is cycled more quickly. Carbon cycle mathematics assume only natural carbon is cycled back into nature from the atmosphere.
The isotope analysis & carbon cycle mathematics don’t agree because nature doesn’t care where the Carbon came from.
Imagine 3 buckets: atmosphere, nature, fossil. Start with 50 black balls in the fossil bucket. 200 grey balls in nature & 100 grey in the atmosphere. One person takes 5 balls from nature to place into the atmosphere per 5seconds. Another person takes 2 from fossil to place into the atmosphere per 5secs. A 3rd person takes 6 balls from the atmosphere bucket to place back into nature every 5secs, every 10 minutes adds 1 extra back into the fossil bucket.
You can bias which colour balls are moved from the atmosphere which change the colour ratios but the grey+black would be the same each time. Each person mixing the colours they move will mix the colours in the nature and the atmosphere buckets like we see in reality.
The number of balls in the atmosphere is still increasing over time.
A ball may only stay in the atmosphere a short time but it’s effect on the total number lasts longer. The effect of adding fossil carbon looks diminished when looking at the atmosphere but looking at the total system you notice a larger change. Grey & black are taken from the atmosphere but grey & black are both added back to the atmosphere.
The only difference between grey & black was the ratio of Carbon-14 to Carbon 12 & 13. You can’t tell where individual carbon atoms came from but you can measure the overall trends.
“Carbon cycle mathematics assume only natural carbon is cycled back into nature from the atmosphere.”
No, it doesn’t. Read my paper on the topic
https://pubs.acs.org/doi/abs/10.1021/ef200914u
publicly available pre-print here:
http://theoval.cmp.uea.ac.uk/publications/pdf/ef2011a.pdf
Particularly section on “Fraction of Carbon Dioxide of Anthropogenic Origin in the Atmosphere”, which explain why it is that even though anthropogenic emissions are causing the rise in CO2 levels, only about 3% of the CO2 in the atmopshere is directly of anthropogenic emissions. The reason is that it gets exchanged with “natural” CO2 withing only a couple of years, but this is a straight swap and does not affect atmospheric CO2 levels.
That wdirectly contradicts the assertion that “Carbon cycle mathematics assume only natural carbon is cycled back into nature from the atmosphere.”
Fossil fuels have not been active in the carbon cycle for a very long time. By combusting those fossil fuels a corresponding amount of CO₂ will add up to the present carbon cycle, primarily in the atmosphere but as time goes by as well to other sinks (land & ocean) because of the steadily increasing atmospheric CO₂ concentration.
From the atmospheric CO₂ analysis (Mauna Loa and others) and the globally reported amount of fossil fuels combusted, we calculate that there have to be a net CO₂ transfer from the atmosphere to the other sinks. Mauna Loa are at +-0.2 ppmv and the reported amount of combusted fossil fuels is also rather accurate, assume +-10 %, then the net transfer is for sure from atmos to land and ocean.
If we assume some other sources in parallel also add up CO₂ to the atmosphere, then the Mauna Loa data will show up with figures higher than the corresponding fossil fuels equivalent but Mauna Loa shows lower figures.
Even if the nature’s flow of CO₂ into the atmosphere is very big and not fully known, the nature’s flow out from the atmosphere, into the nature is bigger and accurately calculated from the atmospheric CO₂ mass balance.
Those very big natural CO₂ flows are the main reason for the fluctuating atmospheric CO₂ concentrations seen to follow very close to ocean surface temperature.
Today, as there is a higher CO₂ partial pressure in the atmosphere than prior to the industrial era, there is a lower potential for CO₂ to be released from, and a higher potential for CO₂ to be absorbed into the oceans ==> the yearly net CO₂ flow is from the atmos into the oceans as the system is heading to fullfill the Henry’s law and increased biological activity (bio pump). Also the oceans concentration of dissolved inorganic carbon is going up and pH value is going down as reported from the 1950’s and the land is greening, nice.
Kind regards
Anders Rasmusson
Sorry, my fourth chapter above should be as with the capital letters in :
“Even if the nature’s flow of CO₂ into the atmosphere is very big and not fully known, the nature’s flow out from the atmosphere, into the nature is bigger and THE NET FLOW IS accurately calculated from the atmospheric CO₂ mass balance.”
/ Anders Rasmusson
The carbon cycle graphics are fantasy estimates by confirmation biased people advocating their prejudices.
Recently, diamonds have been proven to have fossil carbon inclusions.
Which provides proof that carbonates and fossilized life have been subducted up to sixty miles deep.
Given that even the youngest diamond pipes are millions of years old. It highlights that carbon compounds are well distributed deep into our Earth.
Plant growth above ground is matched by plant growth underground. Yet those graphic carbon estimates are curiously lacking regarding underground plant growth.
Starting with the fact biased people estimate human CO₂ emissions then fill in the blanks with fantasy estimates for many CO₂ and carbon exchanges for which they have zero to minimal knowledge.
Fantasy natural carbon cycle estimates allows advocates to cause human emissions appear larger than it is.
Fantasy models, including static carbon cycles and their inaccurate results are throughout the entire alarmist enterprise.
A fact that the OCO-2 satellite kept proving as natural carbon cycles overwhelmed human.
Whiten doesn’t believe that! 🙂
The man with one watch that doesn’t run knows precisely what time it is. Each time he checks he gets exactly the same value with zero deviation. The accuracy of thet time may be in doubt. Not much different than a climate model.
Often missed is that the “plus/minus” deviation is a measurement range, a deviation in measured values and isn’t necessarily the range in which the actual value can be found.
Yes, standard deviations are commonly used for sampled data, and depending on the individual and their discipline, one or two sigma may be used. However, 2-sigma is only about 95% of the range.