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Sunday, November 3, 2013

Carbon Isotopes in the Atmosphere, Part I -- How Big is the Carbonsphere?

How Big is the Carbonsphere?

The term “biosphere” is commonly used to describe all of the living creatures on earth; and the term hydrosphere is used to describe all of the water at the surface of the earth.   In the same sense,  I would like to propose a new term: “carbonsphere”, to describe the sum of carbon reservoirs freely exchanging carbon with the atmosphere.   For the purpose of modeling CO2 in the atmosphere, and understanding interactions of the atmosphere, biosphere and oceans, it is important to answer the question: “How big is the carbonsphere”?

Carbon released by burning fossil fuels is isotopically lighter and distinct from atmospheric carbon.   The distinct signature of fossil fuel emissions provide a tool for tracking the movement of carbon through the atmosphere and through reservoirs exchanging carbon with the atmosphere.  We can estimate the size of the carbonsphere, given the known volumes of fossil fuel emissions and the change in isotopic composition of the atmosphere.  The calculation makes a simplifying assumption, that there is no fractionation of isotopes during the exchanges with carbon reservoirs.  These estimates may prove useful in climate change research and modeling atmospheric CO2.
Carbon isotopes provide an important tool for understanding the destiny of carbon emitted by burning fossil fuels.  The distinctly different isotope ratio shows us the movement of carbon in the atmosphere, oceans, the earth’s surface and biosphere.

Imagine a cup of strong coffee, and a large barrel of weak coffee.  We pour the cup into the barrel.  If we know the volume of the cup, the concentration of coffee in the cup, and the change in the concentration of coffee in the barrel, we can calculate the volume of the barrel.  The barrel may have hidden compartments and baffles, but the change from coffee in the cup will soon be seen throughout the barrel.  The simple dilution model allows us to calculate the size of the carbonsphere, based on the volume of fossil fuel emissions, the carbon isotope ratio of fossil fuels and carbon isotope measurements in the atmosphere.

Carbon isotopes on earth exist in a ratio of about  1% C13 and 99% C12.    A measure of the ratios was devised to easily represent small but meaningful differences in the isotopic composition of different materials.   The measure is d C13/12, usually called “del 13”.  This measure expresses the ratio of the stable isotopes carbon 13 and carbon 12, as compared to the C13/C12 ratio in a standard material. 

The calculation of del 13 and seasonal fluctuation of carbon isotopes are explained in my earlier blog post:

The atmosphere is constantly exchanging carbon with carbon reservoirs on land and in the ocean.   The most obvious carbon reservoirs are plants, which exchange carbon with the atmosphere through photosynthesis and decay in a seasonal cycle.   Other reservoirs include soils, plant detritus, dissolved CO2 in shallow ocean waters, etc.   These reservoirs are often called “carbon sinks”, but I prefer the term reservoirs, because the reservoirs do not simply receive carbon from the atmosphere, but also actively return carbon to the atmosphere. 

Fossil fuels have released a measurable amount of isotopically light carbon into the atmosphere. The light carbon is very useful as a tracer, showing how carbon disperses in the atmosphere and moves between the atmosphere and carbon reservoirs.   The isotopic composition of the atmosphere has changed as a result of fossil-fuel use, similar to what we have seen in bulk atmospheric CO2 in previous posts.   

Figure 1 shows the location of global monitoring stations.   The monitoring stations have been collecting bulk CO2 data since the 1950s, but only began recording carbon isotope data in the 1970s.   

 Figure 2, for reference, shows the bulk CO2 concentration, commonly called the "Keeling Curve".  We can compare the rising bulk CO2 curve to the falling carbon isotope curve shown below.

Figure 3 shows the carbon isotope record, color coded by monitoring station according to latitude, with cool colors representing the Northern Hemisphere, and warm colors in the Southern Hemisphere.    As with bulk CO2, the isotope data show a strong seasonal cyclicity resulting from plant growth and decomposition in the Northern Hemisphere.   The isotope data appear noisier than the bulk CO2 data.

The atmospheric carbon isotope data appears noisy in comparison to the graph of bulk atmospheric CO2 seen in previous posts.   We’ll simplify the problem by taking the annual global average del 13 in data available from CDIAC, the Carbon Dioxide Information Analysis Center (Andres, Boden, and Marland, 2009).   [In fact, much of the "noise" in the carbon isotope record is actually meaningful data.  We explore these variations in part 2 of this post, "CO2 Carbon Isotopes and the El  Nino Climate Cycle".

Figure 4 shows the global average isotope record, by year (R.J.Andres, T.A.Boden and G.Marland, 2009).  Andres, Boden and Marland (2012) also calculated the volume of global emissions by year and the average del 13 values of those emissions.   These data allow calculation of the expected change in atmospheric del 13, given the known annual volumes and isotope ratios of fossil-fuel emissions.  
Atmospheric del 13 declined from a value of – 7.6 in 1978 to – 8.2  in 2008, reflecting the influx of light CO2 from fossil fuels.  But the decline in del 13 is much less than would be expected if all of the fossil-fuel emissions stayed in the atmosphere.   The difference shows that light isotopes from fossil fuels are being diluted into a much larger volume of carbon.

We can use a dilution model to solve for how much carbon from fossil fuels remains in the atmosphere.   Using the known volume of fossil fuel emissions, and average del 13 ratio of those emissions, we can calculate, for each year, how much the del 13 ratio of the atmosphere should have changed.   A weighted average equation is used for the dilution model.

((Ve/Ve+Va)* d13e) +((Va/Ve+Va)* d13a )  = Vna* d13n

Ve = Volume of Emissions
Va = Volume of Atmosphere
Vna = New Volume of Atmosphere
d13e = d C13/C12 of Emissions
d13a = d C13/C12 of Atmosphere
d13na = New d C13/C12 of Atmosphere

If all of the carbon from fossil fuel emissions remained in the atmosphere, the del 13 ratio of the atmosphere would have declined to  – 12 by 2008.  If about 60% of fossil-fuel emissions remained in the atmosphere, the del 13 ratio would be about – 10.  But the dilution model shows a fit to the observed average atmospheric del 13 trend when only about 14% of fossil fuel emissions remain in the atmosphere, yielding a del 13 value of – 8.2 in 2008.  This value is in marked contrast to the data for bulk CO2 composition, which indicates that 60% of fossil-fuel emissions remain in the atmosphere over the time range of our observations.  

Carbon isotope data show that the picture is complicated.  Isotopes ratios show that the greater part of fossil-fuel emissions are exchanged with other earth systems, while bulk CO2 levels seem to show a much larger retention of fossil fuel emissions in the atmosphere.   The process involves exchange and displacement.  As fossil fuel emissions are absorbed by carbon reservoirs,  other carbon is displaced, and enters the atmosphere to maintain equilibrium.   The specific molecules released by fossil fuels exchange places with carbon in carbon reservoirs, and atmospheric CO2 continues to rise.
Let’s look at some of the isotope data, and then consider the size of the carbonsphere.

The volume of fossil fuel emssions is known, and about 60% of fossil fuel emissions appears to accumulate in the atmosphere.   [The percentage would be somewhat lower, if carbon from burning forests is included in the calculation.]  We can calculate the expected change in del 13 based on the volume of fossil fuel CO2 emissions, and compare this figure to the observed isotopic change in the global average del 13.  

Between 1979 and 2008, 194 Gigatonnes of carbon (=710 Gt CO2) was released to the atmosphere by burning fossil fuels and manufacturing cement.   The weighted average del 13 ratio of these emissions was -28.4, reflecting the very light isotopic composition of most fossil fuels.  The atmosphere in 1979 contained about 3 1/2 times that volume of carbon, 718 Gt (=2634 Gt CO2), with an average del 13 of -7.6.  

If we assume that 60% of the fossil fuel emissions remain in the atmosphere, and run a simple mixing calculation, we conclude that the del 13 ratio of the atmosphere should have declined to about -12, a change in del 13 of -4.4.   Instead, we see a decline of only -0.7, from the initial value of -7.6 in 1979 to a value of -8.3 in 2008.   Looking at the thirty-year history of carbon isotope observations, we can calculate that only about 14% of the carbon released by fossil-fuel emissions remains in the atmosphere, by matching the results of a mixing model to the observed decline in global del 13.   The rest of the fossil-fuel carbon is diluted into a much larger reservoir of carbon than the atmosphere. 

Figure 5 shows the expected change in del 13, based on varying models of fossil fuel emissions remaining in the atmosphere.   The isotope ratio shows that only 14% of fossil fuel emissions remain in the atmosphere.
I’m going to coin a term, and call the sum of all carbon reservoirs freely exchanging carbon with the atmosphere, within an annual time-frame, the Carbonsphere.  The Carbonsphere includes the atmosphere, all plants and animals on earth (including you), dissolved carbon in the shallow ocean, weathering surfaces on limestones, coral reefs, seashells and limestone precipitating directly in the ocean.   The Carbonsphere does not include limestone below the weathering surface or carbon in the deep oceans.  These do not participate in the annual exchange of carbon with the atmophere.

With the same data used above, we can solve the inverse problem: what is the volume of reservoirs exchanging carbon with the atmosphere?  It is a dilution problem, described by the coffee analogy in the introduction.  We know the volume of fossil fuel emissions, the isotopic composition of those emissions, and the isotopic change in the atmosphere.  We can find the volume of the carbonsphere by the dilution of fossil fuel emissions.  (Note, this calculation assumes negligible fractionation of carbon isotopes during exchange with carbon reservoirs.)

Figure 6 shows a set of models, assuming a range of sizes for the carbonsphere.    The best match shows a carbonsphere of about 5200 gigatonnes in 1977.  There is fluctuation in the isotopic composition of the atmosphere which does not match the model, which we will explore in the next blog post.   The initial model of 1500 Gt is about twice the carbon volume of the atmosphere.  Over time, for the past 40 years, a carbonsphere of about 5200 gigatonnes is required to quantitatively match the dilution of the global average isotopic composition of the atmosphere.  
Estimates for the size of carbon reservoirs are available from a variety of sources.   Estimates are generated by estimating the carbon inventory for the atmosphere, land vegetation, soil, plant detritus, ocean biomass, and carbon dissolved in surface waters of the ocean.  There is a considerable range in the estimates for individual reservoirs, but general agreement about the total.  
Here is a sampling of estimates, randomly selected from the Internet: 
Traeger, C., 2009                                             3555 Gt  
Falkowski, 2000                                               3390 Gt
World Ocean Review, 2013                              3797 Gt
Corrosion Doctors                                            3000 Gt
Wheeling Jesuit University                                  3675 Gt
US Climate Change Program                             4918 Gt
CDIAC (2012)                                                 3948 Gt                                                                
All of these estimates are less than the result (5200 Gt) produced by calculating dilution of del 13 from fossil fuel emissions. 

We can speculate about the discrepancy between the results of the dilution calculation, and those obtained by making a carbon inventory.   One possibility is that the atmosphere is not in equilibrium with the carbonsphere, i.e., that isotopically light carbon from fossil fuel emissions is tied up in reservoirs near the point of emission.  Thus, there is a transient effect, a lag before the equilibration of the emissions and the atmosphere.   We will see some evidence of this in the second part of this article.   Secondly, it may be that there is a greater dispersion of carbon in the ocean than estimated in the carbon inventory.  We will see some evidence of that, also, in the second part of this article.   But for the moment, the conclusion of this work is that the carbonsphere – the sum of all carbon reservoirs freely exchanging carbon with the atmosphere – is larger than previous estimates.

I should note that these data and calculations include only fossil-fuel emissions and making cement.   The emissions volumes and del 13 averages do not include carbon released through changes in land use, principally clearing forests for agriculture by burning.  Addition carbon from burning forests is also isotopically light.  If carbon from changes in land use is included in the calculations, we would see that an even smaller percentage of carbon emissions remain in the atmosphere, and the calculated size of the carbonsphere would be even larger.

1)  Isotopically light CO2 released by burning fossil fuels provides a tool for tracking movements of carbon through the earth’s systems, and for calculating the size of carbon reservoirs exchanging carbon with the atmosphere.

2)  Carbon isotope ratios show that the percentage of carbon remaining in the atmosphere from fossil fuel emissions is about 14% of those emissions.  This is in marked contrast with estimates based on bulk atmospheric CO2, which indicate that 60% of fossil fuel emissions remain in the atmosphere.   The difference is due to the exchange of carbon between the atmosphere and carbon reservoirs on the earth’s surface.

3)  The Carbonsphere can be defined as the sum of all reservoirs freely exchanging carbon with the atmosphere.   The size of the Carbonsphere can be calculated, based on the observed dilution of the del 13 carbon ratio.   The calculated size of the carbonsphere is about 5200 gigatonnes.  This estimate is substantially larger than published estimates of the size of carbon reservoirs interacting with the atmosphere.   Sources of error might include disequilibrium of the atmosphere with carbon reservoirs near the source of fossil fuel emissions, resulting in an overestimate of the size of the reservoirs diluting the fossil fuel emissions.

This study could be improved by incorporating data for emissions relating to land use.    
Annual  Isotope Global Average:
Andres, R.J. T.A. Boden, and G. Marland. 2009.  Monthly
Fossil-Fuel CO2 Emissions: Mass of Emissions Gridded by One Degree
Latitude by One Degree Longitude.  Carbon Dioxide Information Analysis
Center, Oak Ridge National Laboratory, U.S. Department of Energy, Oak
Ridge, Tenn., U.S.A.  doi: 10.3334/CDIAC/ffe.MonthlyIsomass.2009

Global Emissions average isotope data:
Andres, R.J., Boden, T.A, and Marland, G., 2012

Previous posts om this site regarding atmospheric CO2:
2)  The Keeling Curve and Seasonal Carbon Cycles
3)   Seasonal Carbon Isotope Cycles
4)   Long-Term Trends in Atmospheric CO2
5)   Modeling Global CO2 Cycles
6)   The Keeling Curve Summary:  Seasonal CO2 cycles and Global CO2 Distribution
8)   Carbon Isotopes in the Atmosphere, Part II
       Finding Niño -- Correlation CO2 Carbon Isotopes in the Atmosphere with the El Niño Cycle   


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