One of the central tenets of climate science is that the well-documented and quite significant rise in atmospheric CO2 concentration over the past century (and especially over the past 50 years) is primarily the result of combustion of fossil fuel.
This tenet is based largely on the results of carbon isotope analysis, which tracks the rise in atmospheric concentration of different “isotopes” of carbon (carbon 13 and carbon 12).
Scientists have found that the ratio of the concentration of atmospheric CO2 containing carbon 13 to that containing carbon 12 ( 13CO2/12CO2 ) has been decreasing over the past century (See U of Washington lecture notes here)
The graph below shows how this ratio has decreased at Mauna Loa (Hawaii) over the period between 1990 and 2005.
Note: The Mauna Loa (total) CO2 data starts much earlier, but the Mauna Loa 13CO2 data starts in 1990 (and 1990-2005 is the period referred to in the previous post).
(Right Click and "View Image" for full image)
Scientists specify how much a particular CO2 sample is “depleted” in the carbon 13 isotope relative to a standard with “d 13C The more negative d13C is, the more depleted the sample is in 13CO2 relative to the standard.
In a previous post, Horatio estimated the “d13C” for the carbon dioxide that accumulated in the atmosphere from 1990-2005. Using a couple different methods (see “End Notes”), Horatio obtained a value of d13C for the accumulated CO2 of about -13.6 ‰.
As expected, this indicates that the CO2 that accumulated within the atmosphere was “depleted in 13CO2”, but not quite as much as one might expect based solely on the assumption of a fossil fuel source for the CO2. In fact, d13C of the accumulated CO2 over that period (-13.6 ‰) differs significantly from the “use-weighted” mean d13C for CO2 produced by fossil fuel combustion of -28 ‰. The latter fact is an issue that certainly merits an “explanation”.
As Horatio noted in a previous post, the C13/C12 ratio of the CO2 that accumulated within the atmosphere over the period 1990-2005 is estimated to be 0.011084 +- 0.000022 (mean +- 1 std dev) . For +- 2 standard deviations about the mean (0.011084 +- 0.000044), the corresponding value for d13C is -13.6 +- 3.9 ‰. So the 2 sigma range for d13C for accumulated CO2 extends from -9.7 ‰ to - 17.5 ‰, which does not encompass -28 ‰, the use weighted mean d13C for fossil fuel combusted CO2.
The difference between d13C for "accumulated CO2" and the use weighted mean d13C for CO2 from fossil fuel combustion is also noted by scientists at U o f Washington in their lecture notes here (albeit for a different time period than 1990-2005)
On its face, the above finding (d13C of accumulated CO2 different from that of CO2 produced by fossil fuel combustion) would seem to contradict the central claim by climate scientists that “fossil fuel combustion has been primarily responsible for the increase in atmospheric CO2 concentration.” It would appear, at least, that the CO2 added to the atmosphere over that period was more enriched in (had a higher percentage of) 13CO2 than would have been the case for CO2 from fossil fuel combustion.
But appearances can be deceiving. There is more here than meets the eye. The “interchange” of CO2 between the atmosphere and other parts of the climate system (e.g., with ocean surface waters and with green plants) has not been considered.
After being added to the atmosphere, the CO2 molecules do not just “sit around” (so to speak) and the C13/C12 ratio of “CO2 reservoirs” (e.g., surface ocean waters) with which atmospheric CO2 molecules can (and do) “interchange” is significantly different from the C13/C12 ratio for CO2 produced by combustion of fossil fuel. This means that interchange affects the calculated C13/C12 ratio (and hence “d13C) of accumulated CO2.Can an exclusive fossil fuel source for CO2 combined with the interchange assumption really account for the observed change in atmospheric 13CO2 at Mauna Loa over the period 1990-2005?
Note: It is enough to find the change in 13CO2, since the change in 12CO2 is simply the difference between change in (total) CO2 and change in 13CO2.Horatio makes no claims that his (admittedly simple) approach to answering the above question is definitive, but it would nonetheless seem to indicate that the question can be answered in the affirmative – i.e., the assumption that fossil fuel burning was responsible for the rise in the concentration of atmospheric CO2 over that period is indeed valid.
The calculated interchange brings the "observed" 13CO2 change into agreement with the "expected" 13CO2 change for a fossil fuel CO2 source (within the associated 1 sigma uncertainty in the 13CO2 change).
Change in atmospheric CO2 concentration (1990-2005)
From the Mauna Loa CO2 data, one can estimate how much the (total) CO2 concentration of the atmosphere changed from 1990-2005. Together with the Mauna Loa 13CO2 data, one can then estimate the change in atmospheric 13CO2 concentration over that period, using the following relationship
“C13” represents the concentration of CO2 containing the isotope “carbon 13”, “C12” represents the concentration of CO2 containing the isotope “carbon 12”, S = 0.0112372 (the “C13/ C12” ratio for the “PDB standard”) and “d13C” is in “permil” ( ‰ or parts per thousand).
Note: what has been called "d13C" above is given simply as "13CO2" for the data found here (World Data Center for Greenhouse Gases) under "13CO2(flask)".
The C13/C12 ratio and “d13C” are used interchangeably to gage the proportion of carbon 13 to carbon 12 in a particular CO2 sample. For most CO2 samples (e.g., obtained from: fossil fuel burning, atmosphere, oceans, volcanoes), the C13/C12 ratio is less than that of the standard, so d13C is actually negative. As the ratio of C13/C12 for the atmosphere decreases, “d13C” becomes even more negative.
If we let R = C13/C12, then R / (1+R) is the fraction of the total number of carbon dioxide molecules for a particular sample (e.g., atmospheric) that contain Carbon 13. Multiplying the (total) CO2 concentration (or change thereof) by R / (1+R) yields the 13CO2 concentration (or change thereof).
For what follows, we will assume that all the increase in CO2 over the period 1990-2005 resulted from fossil fuel combustion. For CO2 produced from such combustion, the “use weighted” mean C13/C12 ratio is about 0.010922558 (corresponding to a “d13C” of -28 ‰ and a “C13/C_total” ratio of 0.010804545)
Making this assumption, we can then calculate how much the 13CO2 concentration of the atmosphere should have increased for the given addition of (total) CO2 over the 1990-2005 period, where (total) CO2 = 12CO2 + 13CO2.
The important question is the following: Is the "expected" 13CO2 (concentration) change equal to the "observed" 13CO2 change?
We find that without further assumptions, the "expected" change is not equal to the "observed" change. There appears to be a significant discrepancy.
Does that mean that we should reject the hypothesis that “fossil fuel burning was responsible for the increase in atmospheric CO2 concentration from 1990-2005”?
The answer is "no."
We have left out a critical piece of the puzzle: the "interchange" (removal and exchange) of atmospheric carbon dioxide with the oceans and with photosynthesizing plants.
If one accounts for that interchange, one discovers that the observed 13CO2 increase over the period 1990-2005 is about what one would expect under the assumption that fossil fuel burning was behind the CO2 increase. "Expected 13CO2 increase" comes out within the associated (1 sigma) uncertainty of the "observed 13CO2 increase".
Horatio will illustrate this below with some calculations, but first, it is important to understand why the CO2 “interchange” is important.
CO2 Interchange: Removal and Exchange
There are actually two aspects to the “interchange”. The first is the fact that part of the CO2 added to the atmosphere each year (from fossil fuel combustion) is removed by green plants (during photosynthesis) and by the oceans. The CO2 uptake by plants has the net effect of “concentrating” 13CO2 in the atmosphere. In other words, it increases the C13/C12 ratio over what it would be if all the added CO2 remained in the atmosphere.
The second aspect of the interchange is “exchange” of atmospheric CO2 molecules with oceanic CO2 molecules and CO2 molecules originating from land plants. Because of this CO2 exchange, there is an average time that a CO2 molecule spends in the atmosphere. This CO2 molecule “lifetime" is actually quite short: only about 5 years. The net effect of the latter process is that CO2 molecules in the atmosphere get replaced over time by CO2 molecules from the oceans and respiration of green (land) plant matter.
It is important to emphasize that the second process referred to here (the exchange of CO2 molecules) does not cause the total atmospheric CO2 concentration to decline. As the authors of “Carbon is forever” (“Nature Reports Climate Change” Published online: 20 November 2008 | doi:10.1038/climate.2008.122) put it
"Because the oceans suck up huge amounts of the gas each year, the average CO2 molecule does spend about 5 years in the atmosphere. But the oceans also release much of that CO2 back to the air, such that man-made emissions keep the atmosphere's CO2 levels elevated for millennia. Even as CO2 levels drop, temperatures take longer to fall, according to recent studies."
The average net yearly uptake of CO2 (i.e., removal from atmosphere) by green land plants (photosynthesis minus respiration) has been estimated at 1.0 +- 0.6 GtC (carbon equivalent) and the net CO2 uptake (removal) by the oceans at 2.2 +- 0.4 GtC (See IPCC AR4 Table 7.1 reproduced below).
Note: From 2000-2005, the value for uptake by plants is slightly less (0.9 GtC), but for the analysis below, we will asume 1.0 GtC for the full period 1990-2005. This has only a minor effect on the result.
Click for enlarged image of Table 7.1
IPCC AR4 Table 7.1
The yearly atmospheric CO2 exchange with green (photosynthetic) land plants is about 60 GtC, while the exchange with the oceans is about 90 GtC (see U of Washington Lecture notes here). The total CO2 content of the atmosphere is about 750 GtC, so the yearly turnover (exchange) of atmospheric CO2 as a fraction of the total is about (90 + 60) / 750 = 1 /5, which translates to a mean lifetime for CO2 molecules in the atmosphere of about 5 years. This “lifetime” has the net effect of boosting the “C13/C12” ratio of CO2 that has accumulated within the atmosphere over a given period (over that of fossil fuel combusted CO2).
Effect of “CO2 Removal” and “Atmospheric CO2 Lifetime” on C13/C12 ratio
The “use-weighted” mean “d13C” for CO2 produced by fossil fuel combustion (~= -28 ‰) and the corresponding C13/C12 ratio (0.010922558) differ from the corresponding values for atmospheric CO2 (d13C ~= -8 ‰ and C13/C12 ~= 0.0111473 ). In addition, d13C for CO2 dissolved in water at the surface of the ocean is very close to that of the atmosphere (d13C ~= -8 ‰) and, therefore very different from that for CO2 from fossil fuel combustion.
Note: ”Oceanic carbon has a trifle more 13C than atmospheric carbon, but 13CO2 is heavier and less volatile than 12CO2, thus CO2 degassed from the ocean has a 13C fraction close to that of atmospheric CO2 [Butcher,p 86] [Heimann].” From Jan Schloerer, Why does atmospheric CO2 rise? (Version 3.1, October 1996) http://www.radix.net/~bobg/faqs/scq.CO2rise.html
CO2 from fossil fuel combustion tends to decrease the C13/C12 ratio of atmospheric CO2. But net removal of atmospheric CO2 by green plants also impacts this atmospheric C13/C12 ratio. The result of such removal is a smaller measured decrease in the C13/C12 ratio of atmospheric CO2 than would have been observed in the absence of this removal.
At any given time, both “removal” and “exchange” of atmospheric CO2 molecules are occurring, so in order to estimate how the addition of fossil fuel-combusted CO2 will affect the C13/C12 ratio of the atmosphere, one must take both processes into account.
Illustration: Comparing “Observed” 13CO2 increase to Expected 13CO2 increase
Horatio will illustrate with some calculations based on CO2 and 13CO2 concentrations obtained from linear trends of the annual means of monthly Mauna Loa CO2 and d13C data (found here (under "13CO2(flask)" and "CO2(flask)") for the period 1990-2005. In all cases below, it will be assumed that fossil fuel combustion (use weighted mean d13C ~= -28 ‰) was the source of the atmospheric CO2 increase.
Below, the “observed” (i.e., calculated from measurements) increase in 13CO2 over the period in question is found and compared to the “expected” increase in 13CO2 under each of 3 different sets of assumptions.
Observed 13CO2 change with “Pure” Fossil fuel CO2 source and
- Assumption1: Zero interchange: no CO2 removal by plants and ocean and no replacement of atmospheric CO2 molecules with CO2 molecules from respiration or oceans
- Assumption 2: CO2 removal by plants and ocean, but with ZERO replacement
- Assumption 3: CO2 removal by plants and ocean combined with replacement (assuming 5-year CO2 molecule lifetime)
Note: keeping track of “13CO2” (atmospheric CO2 containing the carbon 13 isotope) will suffice for the purpose here, since knowing the change in (total) atmospheric CO2 and the change in 13CO2 allows one to find the change in 12CO2 as well, since 12CO2change = (total) CO2change minus 13CO2change.
The graphs below show (total) CO2 and d13C at Mauna Loa (along with the linear trend) over the period 1990-2005
Trend of annual means of monthly Mauna Loa (total)CO2 data (1990-2005)
(total)CO2 concentration (ppm) = 1.7373x - 3104.6 (where x is the year)
Trend of annual means of monthly Mauna Loa 13CO2 data (1990-2005)
d13C = -0.0249x + 41.737 (where x is the year)
Observed 13CO2 change (based on linear trends, 1990-2005)
From the trend line for d13C (1990-2005):
d13C (1990) = – 7.8140 ‰ (13CO2/CO2_total = 0.0110265)
d13C (2005) = – 8.1875 ‰ (13CO2/CO2_total = 0.0110223)
From the trend line for (total)CO2 (1990-2005):
(total) CO2concentration(1990) = 352.63ppm
(total) CO2concentration(2005) = 378.69ppm.
From the above, we can determine
13CO2concentration(1990) = ( 0.0110265)(352.63ppm) = 3.8883ppm
13CO2concentration(2005) = (0.0110223)( 378.69ppm) = 4.1740ppm
OBSERVED_totalCO2change (1990-2005) = 378.69ppm - 352.63ppm= 26.06ppm (slope of trend line multiplied by 15 years).
OBSERVED_13CO2change(1990-2005) = 4.1740ppm - 3.8883ppm = 0.2857ppm
Assumption 1: Expected 13CO2 Change with
- “Pure” Fossil fuel CO2 source
- ZERO interchange (No CO2 removal by plants or ocean and no CO2 exchange [“infinite” atmospheric CO2 lifetime])
Assuming that all the increase in CO2 over the period 1990-2005 (26.06ppm) was due solely to fossil fuel combustion (use-weighted mean d13C ~= -28 ‰, for which 13CO2/CO2_total ~= 0.010804545), and making no additional assumption (no removal by or exchange with plants and ocean surface waters), the expected increase in atmospheric 13CO2 concentration is found to be
EXPECTED _13CO2change = (0.010804545) (26.06ppm) = 0.2816ppm
Difference = OBSERVED_13CO2change – EXPECTED_13CO2change
= 0.2857ppm - 0.2816ppm = 0.0041ppm
There appears to be a significant difference of 0.0041ppm between “observed change in 13CO2” and “expected change in 13CO2”, which lies outside the associated (2 sigma) uncertainty for this case.
The uncertainty for the OBSERVED change in 13CO2 between two years (i.e., difference between concentration for two years) is estimated to be 0.0019ppm (see “End Note” on Uncertainty) , which would mean that the difference (0.0041ppm) between “OBSERVED 13CO2 change” (0.2857ppm) and “EXPECTED 13CO2 change” (0.2816ppm) exceeds 2 sigma (0.0038ppm) for this case:
(Observed - Expected)/(sigma) = 0.0041ppm/0.0019ppm ~= 2.2
The observed increase appears to be significantly greater than what is “expected’ under the above assumption. It does not appear that a fossil fuel combustion source acting alone would have added enough 13CO2 to the atmosphere to account for the observed change in atmospheric 13CO2 concentration over the period in question.
Resolution of the apparent difference
The above difference is only apparent. Most of the above difference disappears with the proper consideration of two additional issues: “CO2 removal from the atmosphere by photosynthetic land plants and ocean surface” and “atmospheric CO2 molecule lifetime".
Several processes affect the 13CO2 increase over an extended period. Each year, CO2 molecules are added to the atmosphere (e.g., through fossil fuel emissions). But, each year, some of these "original” added CO2 molecules are “lost” from the atmosphere via
- Removal by green (photosynthetic) land plants and ocean surface water
- Exchange (replacement) with CO2 molecules from ocean surface and plants
While the increase in (total) CO2 concentration of the atmosphere over time is the sum of all the yearly “growth increments" (referred to as "annual mean growth rate" here), the increase in atmospheric 13CO2 concentration observed over an extended period is not simply the product of the total CO2 change and the “C13/C_total” ratio for the source of the added CO2. The actual increase in the 13CO2 concentration over a particular period is dependent on the details of the above “interchange” processes.
Below, we will consider the impact of each of the above interchange processes on the “Expected atmospheric 13CO2 Change” over the period 1990-2005.
Assumption 2: Expected 13CO2 Change with
- “Pure” Fossil fuel CO2 source
- CO2 removal by plants and ocean and
- ZERO replacement
The CO2 interchange that takes place between green plants and the atmosphere has an effect on the C13/C12 ratio of atmospheric CO2 because “d13C” of the CO2 taken out of the air by plants (by photosynthesis) is not the same as “d13C” of the CO2 put back into the atmosphere through respiration (including “decay” of plant matter).
Each year, there is a removal of CO2 by green (photosynthetic) land plants. The total amount of CO2 removed by such plants through photosynthesis each year is about 61.6 GtC (Carbon equivalent) while the total amount of CO2 originating from plant material that is returned to the atmosphere each year through respiration is about 60.6 GtC. About 1.0 GtC more CO2 is removed each year by photosynthesizing plants than is returned through respiration (See IPCC Table 7.1 above. Negative “fluxes” indicate net removal from the atmosphere).
In addition, the 13CO2 fraction (d13C) of the CO2 returned to the atmosphere through “respiration” (which includes decomposition) is not equal to the 13CO2 fraction (d13C) of the CO2 removed from the atmosphere (“fixed”) by plants during photosynthesis. d13C of the CO2 returned to the atmosphere through respiration (-26.2 ‰) is slightly (0.8 ‰) less negative than d13C of the organic matter presently being produced by photosynthesis (-27.0 ‰). This is a direct result of the fact that d13C of atmospheric CO2 (taken up by green plants) has been decreasing (becoming more negative) over time (for details, see “U of Washington Lecture Notes” here).
In addition to the removal of atmospheric CO2 by plants, there is also a removal of CO2 by ocean surface waters. Each year, an estimated 92.2GtC are removed by ocean surface waters but only 90.0 GtC returned by ocean surface waters to the atmosphere. About 2.2 GtC more CO2 is removed by surface ocean waters than is returned to the atmosphere each year by surface ocean waters (although the d13C of ocean surface waters and of the atmosphere are nearly equal ~= -8 ‰).
Key Point: Green land plants and ocean surface waters act as “sinks” that together suck up about 3.2GtC of the yearly total 6.4GtC emitted to the atmosphere primarily by fossil fuel combustion (and, secondarily by cement production. See IPCC table 7.1 reproduced above). This is the source of the statement that “each year about half of all fossil fuel CO2 emissions are taken up by natural sinks.”
That green plants and oceans actually act as sinks rather than as sources of CO2 each year is important because it means that “respiration” and “ocean outgassing” could not have been responsible for the observed increase in atmospheric CO2 over an extended period, as some have claimed.
Added May 13:
The claim that "ocean out-gassing of CO2 (eg, due to increased ocean surface temperature) might have been responsible for a significant part of the observed increase in atmospheric CO2 concentration" is more than a little illogical because the C13/C12 ratio of the CO2 in surface ocean water is very close to (in fact, just slightly higher than) that of the atmosphere. So, out-gassing of CO2 from ocean surface water into the atmosphere would not cause the C13/C12 ratio of atmospheric CO2 to decrease as it has (to say nothing of cause the C13/C12 ratio of surface ocean water CO2 to simultaneously decrease) See Jan Schloerer Why does atmospheric CO2 rise? (Version 3.1, October 1996) http://www.radix.net/~bobg/faqs/scq.CO2rise.html
Such out-gassing could therefore not account for the observed drop in the C13/C12 ratio of atmospheric CO2 that has accompanied the rise in atmospheric CO2 concentration.//end of May 13 addition
If we take into account the impact of all these effects -- net CO2 removal by land plants (and different 13CO2 fraction) and net removal by ocean surface waters -- on the expected 13CO2 change over the period (end) 1990-2005, we find that the “expected” increase in atmospheric 13CO2 comes out to be 0.2819ppm (see “End Notes” for details), still insufficient to account for the observed change in 13CO2 over the period.
There remains a difference of 0.0038ppm between the observed 13CO2 change (0.2857ppm) and expected 13CO2 change (0.2819ppm) although the expected change now lies (just barely) within the expected (2 sigma) uncertainty for this case (0.0038ppm/0.0019ppm = 2.0 ).
But much of the difference is a still only apparent. The “atmospheric CO2 lifetime” issue has yet to be accounted for and this has a significant effect on the atmospheric 13CO2/12CO2 ratio and brings the “expected 13CO2 change” more into line with the “observed 13CO2 change” (within the associated 1 sigma uncertainty).
Assumption 3: Expected 13CO2 Change with
- “Pure” Fossil fuel CO2 source
- CO2 removal by plants and ocean and
- CO2 replacement (with 5-year CO2 molecule lifetime)
In addition to the removal referred to above, there is an “exchange” (replacement) of CO2 going on which does not lead to a net removal of (total) CO2, but does affect the C13/C12 ratio of the atmospheric CO2.
We will assume here that the exchange process follows a simple exponential decay. Because of the 5-year CO2 molecule lifetime, only about 4/5 of the "original" CO2 molecules that cause a particular year's CO2 "growth increment" (i.e., of the accumulated CO2) remain in the atmosphere 1 year later.
We first weight each of the annual CO2 "growth increments" over the period 1990-2005 by an exponential factor “e-t/5 ” whose "decay" depends on the number of years “t” before (end) 2005 that the increment got added to the atmosphere. Summing these weighted increments over the given period, we discover that only about 35% of the "original" CO2 molecules that contributed to these annual growth increments over the period remained in the atmosphere at the end of 2005.
In other words, only about 35% of the original fossil fuel-generated CO2 molecules that caused the 26.06ppm increase in atmospheric concentration over the period 1990-2005 remained in the atmosphere by the end of 2005.
By the end of 2005, the remainder (about 65%) of the individual CO2 molecules that had contributed to the annual atmospheric CO2 "growth increments" (i.e., to the 26.06ppm increase) between 1990 and 2005 had been replaced by CO2 molecules from the surface of the ocean and by CO2 molecules from the respiration of terrestrial plant material.
***The 35%/65% split refers only to those molecules that contributed to "yearly growth increments" in atmospheric concentration (ie, “accumulated” CO2). It does not include all the CO2 removed by sinks soon (within months) after emission to the atmosphere. Roughly half of the human CO2 emissions are sucked up almost immediately, so these emissions do not show up in the yearly “growth increment" and hence do not accumulate within the atmosphere.
The different “reservoirs" of CO2 molecules -- original (added fossil fuel CO2) and replacement (surface ocean and respired organic matter) -- have different C13/C12 ratios. Since the “surface ocean CO2 reservoir" has a greater C13/C12 ratio than the “fossil fuel CO2 reservoir", the net effect over time of the replacement is to boost the C13/C12 ratio of the accumulated CO2, over the C13/C12 ratio for CO2 produced by fossil fuel combustion.
Imagine three “buckets” (“reservoirs”) of balls, with each bucket (reservoir) containing white and black balls (representing 13CO2 and 12CO2 molecules) in different proportions. Random exchange of the balls between the “added fossil fuel CO2” bucket and the other two changes the relative proportion of black and white in the “added fossil fuel CO2” bucket.
We can treat the 26.06ppm of fossil fuel-generated CO2 that was added to (and accumulated) in the atmosphere over the period 1990-2005 as a single “Added fossil fuel CO2” bucket (d13C ~= -28 ‰). Even though this added CO2 has mixed fairly uniformly with the rest of the CO2 in the atmosphere (which has overall d13C ~= -8 ‰), we can nonetheless treat it as if it were a separate bucket, since the CO2 lifetime applies equally to all CO2 molecules in the atmosphere (and the above percentages therefore apply equally to all atmospheric CO2 samples.)
A random exchange (replacement) of balls in the “added fossil fuel CO2” bucket (d13C ~= -28 ‰) with balls in the “surface ocean CO2” bucket (d13C ~= -8 ‰) changes the proportion of white to black balls in the “added fossil fuel CO2” bucket. In other words, the replacement causes the d13C (13CO2/12CO2 ratio) of the “added fossil fuel CO2” reservoir to change, which also changes the d13C (13CO2/12CO2 ratio) of atmospheric CO2 taken as a whole.
Similarly, a random exchange (replacement) of balls in the “added fossil fuel CO2” bucket (d13C ~= -28 ‰) with balls in the “respired organic matter CO2 ” bucket (d13C close to -27 ‰) changes the proportion of white to black balls in the “added fossil fuel CO2” bucket. Again, the replacement causes the d13C (13CO2/12CO2 ratio) of the “added fossil fuel CO2” reservoir to change, which also changes the d13C (13CO2/12CO2 ratio) of atmospheric CO2 taken as a whole.
The latter exchange is not really random because when green plants remove atmospheric CO2, there is actually a slight “preference” for 12CO2. The CO2 removed through photosynthesis has d13C ~= -27 ‰ and the CO2 returned through respiration has d13C ~= -26.2 ‰ (see U of Washington Lecture Notes here).
However, this “removal/return” process can effectively be treated as an exchange of CO2 from the “added fossil fuel CO2” bucket (d13C ~=-28‰) with CO2 from a reservoir with d13C ~= -27.2 ‰. In both cases, the change in d13C is 0.8‰ and assuming the d13C of the removed(returned) CO2 to be -28‰(-27.2 ‰) rather than -27 ‰(-26.2 ‰) changes the “13CO2 budget” very little. For the calculation below, we will assume that the “respired organic matter” reservoir has d13C ~= -27.2 ‰.
Adjustment to “expected” 13CO2 change based on “atmospheric CO2 molecule lifetime”
To calculate the “expected” increase in atmospheric 13CO2 over the period 1990-2005, we will now make use of the above estimate that only 35% of the CO2 molecules associated with the increase in atmospheric CO2 concentration over that period came from the “fossil fuel CO2 reservoir” ( mean d13C ~= -28 and mean "13CO2/(total)CO2" ratio ~= 0.010804545 ).
We will assume that the remaining 65% came from the “ocean surface CO2 reservoir” (with a d13C ~= -8 ‰, and 13CO2/(total)CO2 ~= 0.01102441) and from the “respired plant matter reservoir” (with a d13C ~= -27.2 ‰, and 13CO2/(total)CO2 ~= 0.010813342). This 65% is apportioned between “ocean surface” and “respired plant matter” according to the approximate yearly interchange for each (90 GtC oceans and 60 GtC plants) as a fraction of the total yearly interchange (90 + 60 = 150 GtC).
(adjusted)EXPECTED _13CO2change =
(0.65)(26.06ppm) [ ( 90/150 )( 0.01102441) + ( 60/150 )(0.010813342) ] + (0.35)(26.06ppm)( 0.010804545)
OBSERVED_13CO2change – (lifetime_adjusted)EXPECTED_13CO2change
If we take both “CO2 molecule average lifetime” and “CO2 removal by land plants and surface oceans” into account, “expected” 13CO2 change comes out even closer to the “observed” 13CO2 change:
OBSERVED_13CO2change – (lifetime_&_removal_adjusted)EXPECTED_13CO2change
In the latter case, "expected” 13CO2 change lies within 0.8 sigma of the “observed” 13CO2 change over the period 1990-2005
(0.0015ppm/ 0.0019ppm ~= 0.8)
Expected 13CO2 Change under above “Assumption 3” but using different values for “Net CO2 removed by green land plants” and “Net CO2 removed by oceans”
Because of the uncertainty (+-) associated with the “fluxes” given in IPCC AR4 table 7.1 (“Net ocean-to-atmosphere flux”= -2.2 +- 0.4 GtC/yr and “Net land-to-atmosphere flux” = -1.0 +- 0.6 GtC/yr), it is possible that the difference between “EXPECTED 13CO2 Change” and “OBSERVED 13CO2 Change” is actually smaller (or larger) than the 0.0015ppm difference we found above.
If we assume different values for the net amount of CO2 removed by green plants and oceans (still within the uncertainties specified in Table 7.1) we find a difference between EXPECTED_13CO2change and OBSERVED_13CO2change that is slightly less than or greater than the value we obtained above using the “central” values from Table 7.1 (2.2 GtC atmosphere to ocean flux, 1.0 GtC atmosphere to land flux).
For example, instead of using 2.2 GtC net CO2 removed by oceans and 1.0 GtC as the net CO2 removed by plants, let us instead use values that lie 1 sigma away from the central values: (2.2 – 0.4 ) GtC = 1.8 GtC net removed by oceans) and (1.0 + 0.4 ) GtC = 1.4 GtC net removed by plants. These values are very close to the (negative of the) values given for “net ocean-to-atmosphere flux” and “net land-to-atmosphere flux” in the IPCC TAR.
For calculation purposes, we will assume 62.0 GtC for the (total) CO2 removed by plants each year, 60.6 GtC for the (total) CO2 returned to the atmosphere through respiration, and 91.8 GtC and 90.0 GtC as the estimates for (total) CO2 removed and returned (respectively) by ocean surface waters. These values are very close to those given in the U of Washington Lecture Notes here.
Under the latter set of assumptions, we find that
(lifetime_&_removal_adjusted)EXPECTED_13CO2change = 0.2848ppm
OBSERVED_13CO2change – (lifetime_&_removal_adjusted)EXPECTED_13CO2change
= 0.2857ppm - 0.2848ppm = 0.0009ppm
Under the latter set of assumptions “Expected13CO2change” is within 0.5 sigma of “Observed13CO2change” (0.0009ppm/0.0019ppm ~= 0.5).
But of course, we could also have gone in the opposite direction (assuming (2.2 + 0.4 ) GtC = 2.6 GtC net removed by oceans) and (1.0 - 0.4 ) GtC = 0.6 GtC net removed by plants., in which case the difference between Expected13CO2change and Observed13CO2change comes out greater than the 0.0015ppm given above (but still within the uncertainty)
The key point here is that the difference between Expected13CO2change and Observed13CO2change is within the associated uncertainty.
From the above analysis, Horatio concludes that the assumption (based on CO2 isotope analysis) that “combustion of fossil fuels was primarily responsible for the observed increase in the atmospheric CO2 concentration over the period 1990-2005” is most probably a valid one.
“Surprise! Surprise! Surprise!” (as Gomer Pyle would say)
-- by Horatio Algeranon
The upward climb
Has now been studied
Through and through.
The climate scientists
Are no dopes.
They track the rise
Of carbon atoms
C13 and C12
And C14 too!
The "isotope ratio"
Is the key.
Its change over time
Is plain to see
That burning fossil fuel
Has caused the climb
As a general rule.
Notes on Uncertainty
The uncertainty associated with the measured annual mean (total) CO2 concentration is 0.12ppm (as specified by NOAA here under "Mauna Loa CO2 annual mean data"). So, the uncertainty associated with the difference between two annual mean CO2 values (i.e., for the difference in (total) CO2 between two years) should be approximately SquareRoot[ (0.12)^2 + (0.12)^2 ) ] ~= 0.17 ppm . Since the change in 13CO2 is approximately 0.011 times the change in (total) CO2, the uncertainty associated with the difference in 13CO2 between any two years should be approximately (0.011)(0.17ppm) ~= 0.0019 ppm.
Notes on Calculation of Expected 13CO2 Change assuming
- “Pure” Fossil fuel CO2 source
- CO2 removal by plants and ocean and
- ZERO replacement
To estimate the effect of “CO2 removal” on the expected 13CO2 Change over the period (end) 1990-2005 , we assume the net CO2 removed by plants each year to be that given in AR4 Table 7.1 shown above (1.0 GtC ), combined with the estimate of 60.6 GtC for the CO2 returned to the atmosphere each year through respiration of plant material (see U of Washington Lecture notes here).
The amount of (total) CO2 removed by plants each year is therefore assumed to be 61.6 GtC.*** We will also assume 92.2 GtC and 90.0 GtC for the (total) CO2 removed and returned (respectively) by ocean surface waters.
Since the yearly flux estimates (GtC) given in Table 7.1 are average values for a specified period, we will multiply these by the average (Mauna Loa) atmospheric CO2 concentration for the period 1990-2005 (366.5 ppm) and divide by 750GtC (total CO2 content of the atmosphere in carbon equivalents) to convert GtC to the equivalent in ppm.
Note that 366.5 ppm/750GtC ~= 0.49ppm/GtC is close to the value obtained from the conversion given in “Note b” below IPCC Table 7.1: “2.12 GtC/yr = 1ppm” which equates to 0.47ppm/GtC.
***The 61.6 GtC differs from the value given in the U. of Washington Lecture Notes and on the carbon cycle graphic above (from IPCC TAR), since the value of “net land-to-atmosphere flux” given in the IPCC TAR is 1.4 GtC, yielding a removal by plants of 60.6 + 1.4 = 62 GtC.
(total)CO2 removed from (returned to) atmosphere due to photosynthesis (respiration) over 15 years
Removed by photosynthesis:
[(61.6 GtC/yr)/ 750 GtC] (366.5 ppm) (15yrs) = 451.528ppm
Returned by respiration:
[(60.6 GtC/yr)/ 750 GtC] (366.5 ppm)(15yrs) = 444.20ppm
Net (total) CO2 removed by plants over 15 years = 7.33ppm
(total) CO2 removed (returned) by ocean surface waters over 15 years
[(92.2GtC/yr)/ 750 GtC] (366.5 ppm)(15yrs) = 675.826ppm
[(90 GtC/yr)/ 750 GtC](366.5 ppm)(15yrs) = 659.70ppm
Net (total) CO2 removed by ocean surface waters over 15 years = 16.126ppm
Net 13CO2 removed by plants over 15 years
To estimate this, we use the “13CO2/(total)CO2” fraction corresponding to d13C of CO2 returned to the atmosphere through respiration (-26.2 ‰) and d13C of the organic matter currently produced by photosynthesis (-27.0 ‰).
For CO2 removed, 13CO2/(total)CO2 = 0.010815541
For CO2 returned, 13CO2/(total)CO2 = 0.010824337
So, Net 13CO2 removed by plants over 15 years = (451.528ppm)( 0.010815541) – (444.20ppm) (0.010824337) = 0.07535ppm
Net 13CO2 removed by ocean surface waters over 15 years
To estimate this, we use the 13CO2/(total)CO2 fractions corresponding to the d13C of CO2 returned to the atmosphere from oceans (-8 ‰) and d13C of CO2 removed from the atmosphere (-8 ‰, the mean d13C of the atmosphere over the period 1990–2005 ).
For CO2 removed, 13CO2/(total)CO2 = 0.01102441
For CO2 returned, 13CO2/(total)CO2 = 0.01102441
So, Net 13CO2 removed by surface ocean waters over 15 years = (675.826ppm – 659.70ppm) (0.01102441) = 0.17778ppm
Overall Net 13CO2 removed over 15 years =
[Net 13CO2 removed by plants] + [Net 13CO2 removed by ocean surface waters] = 0.07535ppm + 0.17778ppm = 0.2531ppm
Overall Net (total) CO2 removed over 15 years=
[Net (total) CO2 removed by plants] + [Net (total) CO2 removed by ocean surface waters] = 7.33ppm + 16.126ppm = 23.456ppm
But the (total) CO2 concentration actually increased by a net 26.06ppm over that period, which implies that the gross amount of (total) CO2 added to the atmosphere over that period would have been 23.456ppm + 26.06ppm = 49.516ppm.
Assuming this all came from fossil fuel burning, this would imply a gross 13CO2 addition to the atmosphere of (49.526)(0.010804545) = 0.5350ppm.
Under the above assumptions (“Pure” Fossil fuel CO2 source, CO2 removal by plants and ocean and ZERO replacement (no consideration of the “atmospheric CO2 lifetime”),
Net increase in atmospheric 13CO2
= (13CO2 added from fossil fuel burning) – (13CO2 removed by plants and ocean)
= 0.5350ppm - 0.2531ppm = 0.2819ppm.
This brings the “expected” increase in atmospheric 13CO2 (0.2819ppm) within 0.0038ppm (within 2 sigma, where sigma = 0.0019ppm) of the “observed” increase in 13CO2 (0.2857ppm)
As noted above, if the atmospheric CO2 molecule “lifetime” is also taken into account, the “expected” 13CO2 change (0.2842ppm) comes out within 0.0015ppm ( within 0.8 sigma, where sigma = 0.0019ppm) of the “observed” 13CO2 change (0.2857ppm).
Same result obtained using values for the individual years 1990 and 2005
The above results were based on CO2 and 13CO2 concentrations obtained from linear trends of the annual means of monthly Mauna Loa CO2 and d13C data (found here (under "13CO2(flask)" and "CO2(flask)") for the period 1990-2005.
But one gets very similar results if one repeats the analysis based on "Mauna Loa CO2 annual mean data" (found here) and the annual mean of monthly d13C data (found here under "13CO2(flask)") for the specific years 1990 and 2005 and determines the change in 13CO2 concentration and change in (total)CO2 concentration between those two years.
As before, it is assumed that the change in the 13CO2 concentration of the atmosphere over the 1990-2005 period resulted purely from fossil fuel combustion. If one makes no adjustment for atmospheric “CO2 lifetime” or “CO2 removal” (by plants and ocean surface) , there remains a significant (albeit only apparent) discrepancy of 0.0041ppm between the OBSERVED and EXPECTED change in the atmospheric 13CO2 level between the years 1990 and 2005.
But, as before, if one takes into account “CO2 lifetime” and “CO2 removal” (by plants and ocean surface), one again finds that the "expected” change in 13CO2 is within the expected uncertainty of the "observed” change in 13CO2 for the period 1990-2005.
Note on calculating the C13/C12 ratio of CO2 that accumulated within the atmosphere (1990-2005)
Perhaps the most straightforward way to get the C13/ C12 ratio (or, equivalently, d13C) for the CO2 that accumulated within the atmosphere over the period 1990-2005 is to use a “mass isotope balance”:
Using the “annual mean” (mean of monthly values) of d13C and of (total) CO2 concentration for 1990 and 2005 (obtained from the Mauna Loa data found here (under "13CO2(flask)" and "CO2(flask)" and given in the "illustration" above), a "mass and isotope balance" (see "U of Washington Lecture Notes" ) yields a d13C for “accumulated” CO2 (d13Cacc) for the period 1990-2005:
(-7.82417)(354.20ppm) + (d13Cacc) (25.77ppm) = (-8.20083)(379.97ppm)
So, d13Cacc ~= -13.4 ‰ (C13/C12 ~= 0.0110866)
This is essentially the same value for d13Cacc that was obtained with the differential method (-13.6 ‰) and with the method given immediately below.
From the trends in 13CO2 and (total) CO2 over the 1990-2005 period (graphed above) we find that
OBSERVED_13CO2change / OBSERVED_12CO2change = 0.2857ppm / 25.77ppm = 0.011087
or, d13C ~= -13.6 ‰ for accumulated CO2
Again, this represents the observed C13/C12 ratio of the CO2 that accumulated in the atmosphere over the period 1990-2005.
Note that this is close to the value obtained for the ratio "dC13/dt / dC12/dt" (0.011084 +- 0.000022) with the differential method (given in the previous post).
As explained above, the C13/C12 ratio for accumulated CO2 differs significantly from the “use weighted” mean C13/C12 ratio for CO2 produced by fossil fuel combustion (0.0109226). The two values would only be close to one another under the (incorrect) assumption that there is zero removal of atmospheric CO2 by plants and that the average lifetime of a CO2 molecule in the atmosphere is very long (essentially infinite).
Since there is removal and the real CO2 molecule lifetime is relatively short (about 5 years), the C13/C12 ratio for accumulated CO2 (d13C ~= -13.6 ‰) comes out significantly different from the mean C13/C12 ratio for CO2 from fossil fuel combustion (d13C ~= -28 ‰).