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Thursday, November 7, 2013

Carbon Isotopes in the Atmosphere -- Part II

Finding Niño -- Correlating CO2 Carbon Isotopes in the Atmosphere with the El Niño Cycle

Abstract:
Carbon dioxide released by fossil fuels has a lighter isotopic composition than CO2 in the atmosphere.   The distinctive signature of light carbon released from fossil fuels provides a tool for tracking the movement of carbon through the atmosphere.  That same distinctive signature can also be used to measure the exchange of carbon between the atmosphere and carbon reservoirs on the earth’s surface.

Carbon istotope ratios in the air have been measured at monitoring stations around the globe since 1977.  Despite superficial similarity to the bulk CO2 record, isotope records tells a different story, and give deeper insight into the workings of the earth’s carbon systems. 

Part I of this post discussed how we can measure the size of carbon reservoirs exchanging carbon with the atmosphere.  We defined the term "Carbonsphere" representing the sum of all reservoirs freely exchanging carbon with the atmosphere.   We estimated the size of the carbonsphere as 5200 gigatonnes, about seven times the carbon volume of the atmosphere, based on the dilution of light isotopes from fossil fuel emissions.   

In this post, we will examine fluctuations in atmospheric carbon isotopes, and show how these can be correlated to the El Niño/La Niña climate cycle.  A number of mathematical operations on the base carbon isotope data reveal a clear correlation to the El Niño cycle.
 d C13/C12 CO2 isotope fluctuations correlate with the El Niño/La Niña climate cycle.

The El Niño/La Niña cycle controls how the Pacific Ocean exchanges carbon with the atmosphere.  The mechanism is not clear.   Two hypotheses are considered.  First, ocean currents may move carbon from shallow water into the deep ocean during La Niña events.  Or second, ocean temperatures may cause selective absorption and release of carbon isotopes, favoring absorption of light isotopes in cool water, and heavy isotopes in warm water.  The isotope cycles represent the ocean "breathing" -- taking in light isotopes during the cool phase, and exhaling during the warm phase.  Isotope data from dissolved carbon dioxide in the Pacific Ocean would answer the question.

 Carbon isotope data should be monitored throughout the earth’s carbon reservoirs to recognize and quantify the movement of carbon, and to understand the destiny of carbon emitted by burning fossil fuels.
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Carbon Isotopes in the Atmosphere
As described in previous posts, the isotope ratio d C13/C12 is the standard expression of stable carbon isotopes.   The d C13/C12 formula allows recognition of small but meaningful changes in the ratios of carbon isotopes.    In this post, d C13/C12 will be referred to by the expression “del 13”.
Let’s begin by comparing the bulk CO2 record (the “Keeling Curve”) to the del 13 record. 
Figure 1 shows atmospheric CO2, as measured at monitoring stations located from the Arctic Ocean to the South Poel.   The chart shows increasing CO2 concentration in the atmosphere due to fossil fuel emissions.  The record shows a strong seasonal cyclicity resulting from plant growth in the northern hemisphere, as discussed in previous posts.  The chart is color-coded according to the latitude of the monitoring stations.  


Figure 2, location of CO2 and Carbon Isotope Monitoring Stations.

Figure 3 shows the isotopic ratio d C13/C12, otherwise known as “del 13”, in atmospheric CO2.
The del 13 record resembles the Keeling Curve.  There is a strong cyclity in the isotope record resulting from seasonal plant growth and decay in the Northern Hemisphere, as discussed in a previous post. 
In general , the isotope record is a mirror image of the bulk CO2 record.   The long-term bulk CO2 is increasing due to fossil fuel emissions, and the del 13 record is decreasing, reflecting the light isotopic composition of fossil fuels.  The del 13 ratio of fossil fuel emissions is about – 26, compared to the del 13 ratio of the atmosphere, at about – 7.5.   The seasonal cyclicity is likewise a mirror image.  As plants take up carbon in the summer, the concentration of atmospheric CO2 decreases, while the del 13 ratio increases, because the plants preferentially remove light isotopes from the atmosphere. 

Let’s begin the investigation of atmospheric carbon isotopes by removing the seasonal cycle.   For reference, we will first look at the bulk CO2 data, after filtering the seasonal cycles with a one-year rolling average, seen in Figure 4 below.


 Let’s compare the del 13 carbon isotope data, after removing the seasonal cycle with the same technique, shown in Figure 5.

 This is an amazing chart!    There are two surprises immediately apparent in the del 13 chart, in comparison to the bulk CO2 chart.   First, there is a wide separation between the curves on the del 13 chart, whereas the bulk CO2 curves are in a narrow band.   Second, the del 13 chart shows large waves moving through the data, whereas the bulk CO2 curves are smooth and nearly linear.   Let’s explore these two differences.
The del 13 chart shows a wide separation of curves by latitude.  The time required for equilibration between northern and southern hemisphere is much longer in the isotope data than in the bulk CO2 data.   The falling del 13 ratio at the South Pole lags the readings in Alaska by about eight years, while the rising bulk CO2 concentration at the South Pole lags the northernmost readings by only about two years.
Figure 6 shows the 2- year time lag required for the concentration of CO2 at the South Pole to equilibrate with the far northern hemisphere.  
Figure 7 shows the 8-year time lag required for the CO2 del 13 ratio at the South Pole to equilibrate with the far northern hemisphere.

What can account for the difference in the time required for equilibration between bulk carbon and carbon isotopes?   I suggest that light isotopes released in the northern hemisphere by fossil fuels have a long residency time in carbon reservoirs.    The difference in equilibration times shows exchange of carbon between the atmosphere and carbon reservoirs.  These reservoirs are not simply carbon sinks, but are actively exchanging carbon with the atmosphere.   Light carbon from fossil fuels is absorbed by carbon reservoirs near the point of emission; the bulk CO2 concentration of the atmosphere is maintained by the release of heavier carbon from the reservoir back to the atmosphere.

There is a second surprise in the del 13 chart, compared to what we see in the bulk CO2 data.  When we remove the seasonal cycle from the bulk CO2 data, the curves are very smooth, almost linear.   However, when we remove the seasonal cycle from the del 13 data, we see a series of large waves, observed at every monitoring station across the globe.  These are events which were not removed by the seasonal filter.  There are a few events which occurred only in the northern hemisphere, and a few which occurred only in the southern hemisphere. 

There is a remarkable paradox in the del 13 chart.   The paradox lies in the different responses of the atmosphere to perturbations of the carbon isotope ratio.   Following a perturbation in del 13 as a result of fossil fuel emissions in the northern hemisphere, nearly a decade is required for the air at the South Pole to reach to the same level of isotopic composition.   But the waves moving through the del 13 chart occur nearly simultaneously at every monitoring station on earth!   Although the del 13 values do not equilibrate to the same value, this signal is felt around the world with a lag of less than six months.   I would speculate that this indicates two carbon reservoirs; one on land, and the other in the ocean.   The land system locks up carbon in forests and soils, accounting for the long residency time, while the ocean system more readily propagates changes around the globe. 

On that hunch, I plotted measurements of the El Niño – La Niña cycle on the del 13 plot.   Figure 8 shows an apparent correlation of strong El Nino events to periods of rapidly falling del 13. 
Figure 8.  Atmospheric carbon isotopes and El Niño events.

To clarify the wave-like signal in the data, I took the average of all curves, and a linear regression through the average curve.  
Figure 9.   Atmospheric CO2 del 13 ratios, with average curve and linear regression.

I then subtracted the linear fit from the data, to produce a chart of the residual values after removing the linear trend.
Figure 10.  Chart of Residual del 13, after subtraction of linear trend.
We can compare the residual chart with the El Nino events.  El Nino events tend to correspond to negative slopes on the residual chart. 
Figure 11.  Chart of Residual del 13, with El Niño events.

If we recall Part I of this post on carbon isotopes, a relative increase in del 13 corresponds to a larger carbonsphere; relative decreases in del 13 correspond to a smaller carbonsphere.   It is the slope of the residual function that is significant, rather than the peaks and valleys.   Changes in slope indicate a change in conditions.  A positive slope indicates an expanding carbonsphere – fossil fuel emissions are being diluted into a larger volume of carbon reservoirs.  A negative slope indicates a shrinking carbonsphere – fossil fuel emissions are being diluted into a smaller volume of carbon reservoirs. 
So, to complete the transformation of the del 13 data, we now take the derivative, or instantaneous slope of the residual curve.   On this chart, positive values will indicate an expanding carbonsphere, and negative values will indicate a shrinking carbonsphere. 
Figure 12.   Derivative of Residual del 13 data; all curves.

The initial chart is rather noisy.   A better signal to noise ratio can be obtained by taking the average of all curves, to produce the following curve.  Positive values indicate an expanding carbonsphere (the light isotope is being diluted into a larger volume), and negative values indicate a shrinking carbonsphere (the light isotope is being diluted into a smaller volume). 
Figure 13.  Derivative of residual del 13 data, from average of all curves.

La Nina/El Nino
El Niño is an oceanic phenomenon, involving anomalously warm surface waters in the Pacific Ocean.  The warm waters develop off the western coast of South America, and extend westward across the equatorial Pacific Ocean.  El Niño events have profound meteorological impact, and influence weather around the globe.   The opposite of the El Niño event is termed La Niña, and involves anomalously cool Pacific waters.
Figure 14.  Pacific Ocean Temperature Anomalies, showing El Niño and La Niña events;(from  NASA).
                  http://www.elnino.noaa.gov/lanina.html

The National Oceanographic and Atmospheric Administration keeps a record of the strength of the El Nino – La Nina cycle, and expresses that record as the Oceanic Nino Index (ONI).    The data are a time series of three-month average sea surface temperature anomalies.    For the purposes of this blog post, I have reversed the sign of the ONI values, making La Nina events positive, and El Nino events negative.
Figure 15.  Here is the chart of the Oceanic Nino Index (polarity reversed).  

We can superimpose the chart of the Oceanic Niño Index, and the slope of the residual del 13 measurements.   Despite some noise, there is a clear and perceptible correlation between the curves.  

Figure 16.   Averaged derivative of residual del 13 data, and Oceanic Niño Index (from NOAA).
The ONI curve does not match the isotope data, in terms of the timing of events.  There is a brief lag between the ONI curve (representing surface temperature anomalies, and the del 13 data indicating isotopic changes in the atmosphere.  I added a six month lag to the ONI curve, in order to make a better match to the observed isotope data. 
Figure 17.  Average derivative of the residual del 13 data, and ONI curve with a 6 month lag.
We’ve performed a number of transformations of the atmospheric CO2 carbon isotope data, in order to reach the curve that corresponds to the Oceanic Niño Index. 
Figure 18.   Here is a summary slide indicating the transformations. 

The meaning of the correlation is not clear at this time, but it is clearly a significant phenomenon for global climate study.  I can advance two hypotheses. 

Deep Current Hypothesis
My first thought was that La Niña conditions indicated currents which displaced waters of the shallow Pacific Ocean into deeper water.  When La Niña conditions prevail, carbon which is enriched in light isotopes due to fossil fuels is transported and sequestered in the deep ocean.  The shallow water would be replaced by deeper waters, which still carry pre-industrial del 13 ratios (of about -6.5, based on ice core data).   Such a current would expand the Carbonsphere (as discussed in the previous post) and dilute light isotopes from fossil fuels into a larger volume of carbon reservoirs.   El Niño conditions would be stagnant, allowing heat to build up in shallow waters, and light isotopes from fossil fuels to accumulate.  El Niño would shrink the Carbonsphere, relative to La Niña.

CO2 Solubility and Isotope Differentiation Hypothesis
My daughter suggested a different hypothesis to me; one that is more probably correct.  She suggested that temperature changes in the shallow ocean should change the solubility of CO2, and the rate of exchange with the atmosphere.  An extension of that thought is that changes in the temperature of the water may differentiate the carbon isotopes being exchanged with the atmosphere.   Thus, during La Niña events, with cold Pacific water, light isotopes may be better absorbed by the water, raising the del 13 of the atmosphere.   During La Niño events with warm Pacific water, heavy isotopes may be better absorbed by the water, lowering the del 13 of the atmosphere.

NOAA is now conducting research and modeling on sea-air carbon exchange, with a focus on the Pacific Ocean, and the El Nino-La Nina cycle.  However, I have not seen data regarding isotope differentiation through that process.  Figure 19 shows one map from that study.
Figure 19.  Carbon Flux map from NOAA study.  The upper map shows carbon flux in absolute terms; the lower map shows relative variability from the normal pattern.  Positive values (reds) indicate less uptake of CO2 by the ocean from the atmosphere.  The year chosen is a strong La Nina year.  However, the published maps do not address the behavior of carbon isotopes as a function of temperature.  

Carbon isotope data in the waters of the tropical Pacific is needed to resolve the question.  If the current hypothesis is correct, the cool waters of La Niña would be have high, pre-industrial del 13 values of about -6.5 (from ice-core data).   If the isotope differentiation model is correct, La Niña waters would be enriched in light isotopes relative to the atmosphere, lower than -8.2.   This question of interpretation would seem to be easily resolved by additional data.   Physical solubility data and modeling would be helpful, but direct measurements of carbon isotopes in water would be definitive.   The isotope data must target chemical species related to aqueous carbon dioxide – carbonate, bicarbonate, and carbonic acid. 

Further, if the current hypothesis is correct, La Niña is transporting a measurable quantity of atmospheric carbon into the deep ocean.   From that information, the volume of water and quantity of heat carried by the current could also be calculated, providing key data in understanding the pace of global warming on earth.

Isotope data through all of earth’s carbon reservoirs would be helpful in understanding the movement of carbon through those systems, and the destiny of carbon emitted by burning fossil fuels.
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References:
Atmospheric CO2 Carbon Isotope Data:
Keeling, R.F. S.C. Piper, A.F. Bollenbacher, and S.J. Walker. 2010. Monthly atmospheric 13C/12C isotopic ratios for 11 SIO stations. In Trends: A Compendium of Data on Global Change. Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, U.S. Department of Energy, Oak Ridge, Tenn., U.S.A.

Global Emissions average isotope data
Boden, T.A., G. Marland, and R.J. Andres. 2013. Global, Regional, and National Fossil-Fuel CO2 Emissions. Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, U.S. Department of Energy, Oak Ridge, Tenn., U.S.A. doi 10.3334/CDIAC/00001_V2013

El Nino/La Nina Climate Cycle
Oceanic Nino Index

Carbon Flux Models -- NOAA

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
       http://dougrobbins.blogspot.com/2013/05/the-keeling-curve-seasonal-co2-cycles.html
7)   Carbon Isotopes in the Atmosphere, Part I -- How Big is the Carbonsphere?
       http://dougrobbins.blogspot.com/2013/11/how-big-is-carbonsphere.html      

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.
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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: http://dougrobbins.blogspot.com/2012/03/seasonal-carbon-isotope-cycles.html.

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

Where:
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 of 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.

Conclusions:
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.    
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References:
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
       http://dougrobbins.blogspot.com/2013/05/the-keeling-curve-seasonal-co2-cycles.html
8)   Carbon Isotopes in the Atmosphere, Part II
       Finding Niño -- Correlation CO2 Carbon Isotopes in the Atmosphere with the El Niño Cycle
        http://dougrobbins.blogspot.com/2013/11/carbon-isotopes-in-atmosphere-part-ii.html