Clyde Spencer



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.

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.


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!

via Watts Up With That?

June 7, 2021