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Wednesday, April 18, 2012

Modeling Global CO2 Cycles

This article is the fifth post in a series about Global CO2 trends and seasonal cycles.

1)  The Keeling Curve
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

In this post, I generate a model for the global CO2 record from 1971 - 2009.  Inputs to the model include agricultural biomass, fossil fuel emissions, absorption of excess CO2 by carbon sinks, and atmospheric mixing between the Northern and Southern Hemispheres.
The final model begins in the year 1971, and yields a set of CO2 curves, by latitude, that closely matches the actual record.

The important thing is that this model is made entirely by data resulting from human influences.   Natural factors also exist and clearly influence global CO2.  But the quantitative influence of agriculture and fossil fuel use is more than enough to model the annual cycles and long-term rise of CO2 in the atmosphere.

The ease with which the model was created, and the lack of any reasonable, quantifiable alternatives, indicate that changes in atmospheric CO2 are primarily the result of human activity.

Modeling performs an important function in science.   After gathering data and making observations about pertinent parameters of a problem, it is necessary to put the pieces together in a quantitative model, to see if the parameters are acting as we expect.

The model “talks back” to us, in a way.   The model will show a fit to real-world data when our assumptions are reasonable, and a mis-fit to the data when the model is built on incorrect assumptions.   In this case, the model shows that the seasonal cyclicity of the Keeling curve is not the result of seasonal fossil fuel use, but instead is the result of seasonal photosynthesis and oxidation.  There is a good quantitative and geographic fit between the observed carbon cycles and the volume of carbon in agricultural biomass.   The increase of amplitude in CO2 cycles in proportion to population growth also supports the idea that the observed annual cycles are largely the result of agriculture.

This model considers separately the CO2 flux in the Northern Hemisphere and the Southern Hemisphere, and matches observations for the rate of mixing between the hemispheres.  A more complex model could be built, perhaps at increments of 5 or 10 degrees of latitude, and more closely identify the location of agriculture and fossil-fuel emissions, and that might be useful to addressing deeper questions.  But I believe a model should be simple in essence; sufficiently complex to answer the question at hand, and not any more complex.  This model is intended to answer the question of human influences on global CO2, and the division of the globe into two hemispheres is sufficient to answer that question.

Fossil Fuel Use and Annual Cycles
Fossil-fuel use has a cyclicity with the appropriate seasonal peaks for the Northern Hemisphere.  I spent quite a bit of time finding data on global fossil-fuel usage, assuming that it was a major factor in the Keeling curve annual cycles.  I extrapolated the seasonal patterns of use for coal, natural gas, and oil in the United States to global figures from the International Energy Agency (IEA) for the three commodities.  (I made an adjustment for the summer "air-conditioning"  bump in coal and natural gas, when extrapolating to the entire world.)
I converted the volumes (in gigatonnes) of CO2 emitted from fossil fuels to atmospheric CO2 concentrations in parts per million for the northern hemisphere and southern hemisphere.

In my last post,, we saw that fossil fuel emissions are responsible for the long-term increase of atmospheric CO2.  But the peak of fossil fuel usage is in the months of December and January, but the steepest gains of CO2 occur in September through November.   In the fall months in high northern latitudes, CO2 concentrations rise by about 15 ppm.  The sum of fossil fuel emissions in those months total only about 1.5 ppm, an order of magnitude lower than the rise seen in the seasonal data.  Factors other than fossil fuels are causing most of the seasonal fluctuation of atmospheric CO2.

The Model

We can build a simple model to help identify the significant parameters driving global CO2 cycles, and quantify parameters wherever possible.   From our earlier observations, we can construct the model using the following parameters:
  • CO2 taken up by Plants during the growing season
  • Oxidation  of carbon in plants following the growing season
  • CO2 emissions from Fossil Fuels
  • Absorption of CO2 by carbon sinks (e.g. oceans)
  • Exchange of CO2 between Northern and Southern Hemispheres.
 We already observed that the behavior of CO2 cycles differs greatly by latitude.  The Northern Hemisphere, with 68% of the world’s landmass, 88% of the world’s population, and 83% of the worlds GDP, has a cycle showing very large seasonal fluctuations in CO2.  The Southern Hemisphere shows much less annual CO2 fluctuation.  The sharpest and largest fluctuations in CO2 occur in the summer and fall months of the Northern Hemisphere.  In the summer, plants are taking up carbon through photosynthesis, and atmospheric CO2 declines.  Immediately following the growing season, CO2 concentration rebounds sharply, as plants give CO2 back to the atmosphere through oxidation.

I constructed a model for annual CO2 uptake through photosynthesis, beginning with the volume of biomass generated through agriculture.  Agriculture generates about 140 gigatonnes of biomass every year.
Adjustments for moisture content (50%), carbon content (45%), and conversion to CO2 (3.67x) results in about 96 gigatonnes of CO2 removed from the Northern Hemisphere atmosphere annually.   Keep in mind that this is only half of the air on the planet.  Thus, during the growing season, CO2 in the Northern Hemisphere falls sharply.

In the model, I distributed agricultural carbon and fossil fuel use according to economic output by hemisphere.  The Northern Hemisphere represents 83% of global economic output, and the Southern Hemisphere represents 17% of global economic output.

I assigned the 96 gigatonnes of agricultural CO2 intake in the summer growing months, as shown in the following graph.  For the oxidation part of the cycle, we can observe a very sharp rebound in CO2 in the data during the fall months.  It is possible that some of the rebound is from CO2 sinks, seeking equilibrium after the change during the growing season.  However, isotope data shows an equally sharp rebound. (   It appears to me that vegetation is giving back to the atmosphere the very same CO2 that was absorbed during the summer.
I adopted an oxidation/respiration model to return the CO2 to the atmosphere as a zero-sum annual exchange.  I tried an exponential decline for the oxidation part of the cycle, then tweaked it to match the annual CO2 cycles of the Northern Hemisphere high latitudes (with the long-term trend removed).

This model produced a surprisingly easy fit to the high latitude data of the Northern Hemisphere (see below).
Note that the long-term rising CO2 trend has been removed from the real world data, and there are no CO2 emissions from fossil fuels in the model at this point.

The total volume of vegetation includes both natural as well as agricultural biomass.  I found a single estimate for the net global annual uptake by plants, of about 60 gigatonne of carbon, or about 220 gigatonnes of CO2.   According to these estimates, agriculture represents 52% of the total annual carbon uptake by plants.  Of the total annual carbon cycle, some carbon is exchanged with carbon sinks (soil) and some carbon exchanged with the atmosphere.  The fit of the model to observed data shows that the NET amount of carbon taken out of the atmosphere by plants, and returned by oxidation, is very close to the volume of carbon taken up by agricultural activity.

I followed a similar procedure to model the Southern Hemisphere.  I found that 17% of global agricultural biomass produced CO2 fluctuations that were far too large to match the data in the Southern Hemisphere. I found a good match by using only 5% of global agricultural biomass.   The chart below shows the model parameters.
The following chart shows the match of the model to the data from the Southern Hemisphere.

Annual cycles from intermediate latitudes have lower amplitude than cycles from the high northern latitudes.  This was the topic of an earlier post:  The Northern Hemisphere, with its large CO2 fluctuations, dominates global CO2 cycles.  CO2 cycles from low latitudes in the Southern Hemisphere (pink) follow the seasonal pattern of the Northern Hemisphere, showing the range and influence of atmospheric mixing between Northern and Southern Hemispheres.
I tried a simple mixing model to represent the cycles observed in intermediate latitudes.   The chart below shows a 50%-50% mixture at the equator, and 70% - 30% mixtures at intermediate latitudes.   As shown in the data above, the cycles of intermediate latitude (pink line) in the Southern Hemisphere follow the seasonal pattern of the Northern Hemisphere.
A more sophisticated model could be created, using greater detail in the location of agriculture by latitude, but I think this model demonstrates that atmospheric mixing between the Northern and Southern Hemispheres can reasonably explain the range of amplitude in CO2 cycles in intermediate latitudes.

Global CO2 data show distinctive characteristics of annual cyclicity and a long-term rising trend ("the Keeling Curve").   Subtle aspects of the curve include a rising rate of increase, and an increase in the amplitude of the cycles.

The final model runs from the year 1971 to 2009.  As a starting point, the model used values for the average CO2 concentration of the Northern and Southern Hemispheres in 1971, of 327 and 325 parts per million CO2, respectively.

The photosynthetic model, which was developed for the year 2009, was adjusted for earlier years as a function of global population. This resulted in cycles with increasing amplitude through the range of the model.
Agricultural production was assumed to vary directly as a function of population, but incremental agriculture was assumed to displace natural vegetation.  Growth of CO2 intake through photosynthesis was increased at a rate of 50% of incremental agricultural output (back-calculated from the 2009 model).

Carbon dioxide from fossil fuel emissions was added, according to estimates from IEA and the BP statistical review of world energy.  Annual figures given in these reports were scheduled on a monthly basis, by analogy to US monthly consumption of coal, natural gas, and oil, as described above.  As noted in a previous post, about 40% of fossil fuel CO2 emissions are absorbed by carbon sinks, including the ocean.  This fraction of new carbon emissions was removed from the model on a monthly basis.

The Northern Hemisphere receives the bulk of fossil fuel CO2 emissions, and modeled CO2 rises rapidly in Northern Hemisphere, unless a transfer to the Southern Hemisphere is allowed.  In an earlier post, we saw that rising CO2 in the Southern Hemisphere lags CO2 in the Northern Hemisphere, by a period of about 22 months.  In the model, I transfered half of the excess CO2 of the Northern Hemisphere to the Southern Hemisphere, using a lag of 22 months to represent the necessary mixing time.
Despite the general simplicity of the model, the resulting CO2 curve shows a reasonable correlation to actual data recorded across the global range of latitudes, and after 38 years of CO2 addition and subtraction, the model concludes at the appropriate concentrations of CO2 across the globe.

1)  A model can be generated which provides a very good match to the long-term global CO2 record.  The model includes estimated fossil fuel use, absorption of CO2 by carbon sinks, carbon accumulation in agricultural biomass, and oxidation of agricultural biomass.  The volume of agricultural biomass was varied in the model according to world population growth.
2)  Surprisingly, fossil fuel use does not have a significant effect on seasonal CO2 cycles.   Known volumes and timing of fossil-fuel emissions do not match the cyclicity in CO2 observations.
3)  Photosynthesis in the Northern Hemisphere, dominates the seasonal cycles.  The volume of CO2 absorbed through agriculture closely matches the net volume of CO2 taken up by both natural and agricultural photosynthesis.
 4)  Oxidation of vegetation occurs quickly.  Three quarters of the net plant biomass is oxidized in the first three months following the growing season.  It seems likely to me that burning of agricultural waste accounts for some of the rapid oxidation following the growing season.
5)  The Northern Hemisphere dominates both seasonal and long-term trends in atmospheric CO2.
6)  Mixing between the hemispheres accounts very well for the gradation of cyclicity observed at intermediate latitudes.

The model shows that the long-term trend of rising CO2 is attributable to fossil-fuel emissions.  Fossil fuel emissions account quantitatively for the rise in CO2 over the last 38 years, and fit the data with regard to differences in concentration in the Northern and Southern Hemispheres.
The model also shows that the annual cyclicity of the biologic cycle is strongly influenced by agriculture.  Agricultural biomass alone can be used to model  and match observed data for seasonal CO2 cyclicity.

And finally, the uptake of CO2 through agriculture clearly outpaces emissions of CO2 from fossil fuels, at least on a seasonal basis.  As a tool for the management of CO2 concentrations, policy-makers should consider banning the burning of agricultural waste, and consider options for disposal of agricultural waste as a means of sequestering significant volumes of carbon.
Global CO2 concentration data in this report is credited to C. Keeling and others at the Scripps Institute of Oceanography, also Gaudry et al, Ciattaglia et al, Columbo and Santaguida, and Manning et al.  The data can be found on the Carbon Dioxide Information Analysis Center.
Data for CO2 released by fossil fuels is available from EIA CO2 Emissions from Fuel Consumption,
And the BP Statistical Review of World Energy:

Monthly data for US fossil fuel consumption were taken from the EIA website:

Global population figures from 1970 - 2010 were taken from Wikipedia.
The estimate for annual global biomass, circa 2009 was taken from a UN report: