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Friday, March 16, 2012

The Keeling Curve and Seasonal Carbon Dioxide Cycles

Take a deep breath.   If you are about as old as I am, every breath you  take now contains about 23% more CO2 than your first breath at birth, and about 40% more CO2 than when George Washington took his first breath. The Keeling Curve is a remarkable series of CO2 measurements taken at Mauna Loa, Hawaii, since 1957, showing a steadily rising CO2 trend, with an annual cycle of fluctuation.  This article is an update to an earlier post regarding the Keeling Curve, found here:

I began this exercise with a simple thought.

Ice cores from Antarctica provide a record of atmospheric composition and temperature (inferred from oxygen isotopes).  There is a strong correlation between the concentration of Carbon Dioxide and temperature:  high temperature corresponds to high CO2.  The details of the correlation are interesting enough for another post, but for now, the correlation demands the simple question: Does CO2 cause global temperature to rise, or does high temperature cause high CO2?
Overlay of CO2 content  and inferred Temperature from the Vostok ice core.  
Horizontal scale is thousand years before present.

Modeling and physics suggests that CO2 drives temperature; and that CO2 accumulating from carbon emissions is causing global warming.   On the other hand, the past thirty cycles of glaciation, occurring at intervals of about 100,000 years, are generally accepted to be caused by Milankovitch orbital cycles, which change the amount of solar radiation received by Northern Hemisphere land masses.  

 This suggests that orbital cycles drive temperature change; therefore temperature drives CO2 variation.

It occurred to me that the world conducts an annual experiment for us.  The seasons change, for reasons that are well understood, and there is an annual change in CO2 concentrations.  CO2 concentrations have been recorded since 1957 and documented by Charles Keeling, of the Scripps Institution of Oceanography.  The usual presentation of the Keeling Curve shows only data recorded at Mauna Loa, in Hawaii.
The Scripps Institute sites are mostly located in the Pacific Basin, and range in latitude from 82.5 North to the South Pole.  Additional data is available from Italy and the Indian Ocean.  The following map shows the observation locations.  Charts will generally be color-coded as shown below, with warm colors indicating stations in the Southern Hemisphere, and cool colors in the Northern Hemisphere.

There's a seasonal cyclicity to the data.  In summer months, CO2 concentration falls in the Northern Hemisphere, suggesting rising temperature actually reduces CO2 concentration (at least on an annual time scale).  We might expect to see the opposite polarity in the Southern Hemisphere, to confirm the hypothesis.   But when I looked at the data, things became more complicated.   The simple experiment failed.  Let's look at the data.
This chart shows CO2 concentrations from fourteen stations, ranging in latitude from the South Pole to the Arctic Ocean.  There is a remarkable consistency to the rising trend and cyclicity.  An exponential curve can be fitted to the data.  This black curve is an exponential function with a starting value of 281 ppm CO2 in the year 1800, which is close to the pre-industrial values for CO2 found in ice-cores in Antarctica and Greenland.
As an aside, the exponential function would forecast reaching a global CO2 concentration of 450 ppm by 2031.  This level has been suggested as an irreversible tipping point by climate scientists.

We see some interesting features when we look at the data closely.  Northern Hemisphere cycles are high amplitude, while the Southern Hemisphere is very low amplitude.  The expected polarity reversal only occurs in high Southern latitudes (near the pole).  Readings from latitudes less than 30 degrees south (near the equator; Kermadec Islands and American Samoa) share the polarity of the Northern Hemisphere.
We can the long-term trends to study the cyclicity more closely.   I first subtracted the exponential function, and I then removed residual fluctuation (reflecting temporary events, such as the volcanic eruption of Mt. Pinatubo) by subtracting a 12-month moving average from the monthly data.
The resulting cycles are asymmetric. Negative excursions are roughly double the magnitude of positive excursions.  Area under the curve has been normalized to zero, so this means that negative deflections are brief, compared to positive deflections.  It is also easy to note that the cycle from the South Pole has an opposite polarity to the most of the other cycles.
This chart presents the normalized cycles by latitude.  The horizontal scale is time; CO2 seasonal cycles are displayed at the appropriate latitude of the monitoring station which recorded the data.   
A clear distinction can be seen.  Cycles in the Northern Hemisphere are high amplitude, while those in the Southern Hemisphere are low amplitude.

Here is a closer look at cycles by latitude.   The following chart expands the horizontal scale, showing only seven years of data.
As noted previously, polarity of the southernmost cycles (south of - 30 latitude) is reversed with respect to the Northern Hemisphere, but with much lower amplitude. 
If we take readings in the southern hemisphere as the global baseline, it is clear that there are both positive and negative factors influencing the seasonal fluctuation in CO2 in the northern hemisphere.
Close examination shows that cycles in the low southern latitudes (markers) share the polarity of the Northern Hemisphere.  Also, the peak and trough of Northern Hemisphere cycles shifts slightly according to latitude, and the onset of seasons.  In the fall, it seems clear that the early onset of winter causes an earlier trough at higher latitudes.  But in the spring, it is not clear why high latitudes have an earlier peak than low latitudes.  Both features may relate to the timing of atmospheric mixing between the hemispheres.
The seasonality and asymmetry of the cycles is quite apparent.  In the Northern Hemisphere, CO2 falls 
sharply in the three months of summer, followed by an increase during the fall, winter and spring.  The increase is initially sharp, then more gradual.
Northern Hemisphere cycles by season.
Southern Hemisphere cycles by season.  The low amplitude is striking, relative to the Northern Hemisphere.  The polarity reversal at low latitudes is also apparent.
 The following chart is a plot of trough-to-peak amplitude by latitude. 
Carbon dioxide concentration reflects many factors: fossil fuel usage, the natural carbon cycle of the biosphere, the influence of agriculture and livestock, the dissolution of limestones on land, and precipitation of limestone in the ocean.   In this plot, the observed amplitude of CO2 fluctuation is shown by latitude.
The Northern Hemisphere contains about two-thirds of the world's land mass, and 90% of the world's populations, and a similar proportion of the world's agriculture.  The prominent seasonal cyclic source for CO2 would be fossil fuel use, and the prominent seasonal sinks would be land plant growth, particularly agriculture.  I hope to do the math or find the data, and compare the sources and sinks for CO2, and present the results in a new post. (By the way, the respiration of 7 billion human beings contributes about 950 million kg of excess CO2 to the atmosphere on a non-seasonal basis.  We can also conclude that this volume (plus agricultural wastage) is a summer seasonal CO2 sink, due to agriculture.  But there's probably a better way to get the number).   For the moment, let's compare the amplitude of CO2 cycles to the distribution of population.
The bulk of the world's population lives in the Northern Hemisphere. Here's the chart of population, superimposed on the chart of the amplitude of CO2 cycles.
As we have seen, seasonal factors are concentrated in the highest latitudes, whereas the bulk of the population lives in middle latitudes.  However, I suspect (as a director of an Alaskan electrical company) that seasonal fossil fuel usage is higher per capita in higher latitudes.  Also, the curvature of the earth results in a smaller volume of atmosphere for dispersion.  However, I do not have a chart for population density, or fuel usage by latitude.

Next, we should quantify the relationship between atmospheric carbon cycles, and annual cycles of emissions from fossil fuels.  However, to my surprise, there is no source with monthly data for global fossil fuel emissions.  Andres and others have published an study with hard data for 21 countries with the highest CO2 emissions, and extrapolated to the other countries with a Monte Carlo model.  Here is the result of their study on CO2 emissions.
The annual cycle of emissions matches the annual cycles of CO2 observed the northern hemisphere.   
Here is a similar chart for CO2 emissions from various sources in the United States.
We should ask whether the magnitude of CO2 emissions matches the magnitude of CO2 annual fluctuation.
It is a matter of simple math.   There are 3160 gigatonnes of CO2 in the atmosphere.  Estimates of annual CO2 emissions from fossil fuels range from 27 gigatonnes to 35 gigatonnes; about 1% of the total, if dispersed through the entire atmosphere, or currently about 3.8 ppm, out of 390 ppm.   This is less than the observed cycles.  However, at least 90% of emissions are delivered in the northern hemisphere, which would create an annual signal of 7.6 ppm.  And finally, fossil fuels are consumed with a peak in winter.  If we assume that 65% of annual emissions occur during 6 winter months of the year, the amplitude of cycles due to fossil fuel consumption would be about 10 ppm, approaching the amplitude of cycles seen in the middle latitudes of the Northern Hemisphere, including the United States.  Of course, fossil-fuel CO2 emissions are not the entire story.  The natural respiration of the biosphere must be added to the signal from fossil fuels.  But the cyclicity of fossil fuel emissions appears to be of the right magnitude and timing to account for much of the positive CO2 fluctuation during winter months.
This chart shows the cyclicity of European gas consumption.  

The last factor to consider as an influence on seasonal CO2 cycles is agriculture.  Like landmass and population, agriculture is concentrated in the northern hemisphere.  
Globally, 140 billion metric tonnes of biomass is generated from agriculture each year.   Assuming 50% moisture content, and 45% carbon content of dry biomass, and converting from weight of carbon to carbon dioxide, we can calculate that 115 gigatons of CO2 is removed from the atmosphere during every growing season. This is roughly 4 times the volume of CO2 generated annually from fossil fuels. This is equivalent to a northern hemisphere, seasonal fluctuation of 37 ppm, about 3 times the amplitude of the largest observed cycles.  If the given estimates are correct, agriculture is the dominant driver of CO2 cycles.  The only surprise is that the cycles are not larger.
This article is the second post in a series about Global CO2 trends and seasonal cycles.  The final article consolidates and summarizes results of the previous posts.

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

6)   The Keeling Curve Summary: Seasonal CO2 Cycles, and Global CO2 Distribution


All CO2 data in this article is credited to C. Keeling and other 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;
World Background Map for charts courtesy ESRI.
The Milankovitch chart can be found on ClimateDataInfo:
Vostok Ice Core charts can be found at a variety of sites.  I created an overlay from the chart posted here:
The population chart was prepared by "Radical Cartographer" Bill Rankin.
I used the version of the map posted here:
Andres, R.J. et al, 2011, Monthly, global emissions of carbon dioxide from fossil fuel consumption, Tellus B, 63B, 309-327.
Monthly CO2 emissions USA, from CDIAC.
Quarterly report on European Gas markets, EU commission, Market Observatory for Energy


  1. Impressive analysis! Thank you for sharing the graphs as they can prove the rising carbon dioxide in the atmosphere. Great post.

  2. Doug--extremely comprehensive analysis. How reliable are CO2 data before 1900 or so-- the ice cores? Are there any sources going back over 500 years or a millennia available? Why is CO2 a stronger green house gas than H2O? The correlation with El Nino is fascinating, and global distribution patterns. I have read of direct CO2 capture technology--does it have enough scale to make a difference? Wow!

    1. Hi Greg,
      The CO2 data before 1900 are primarily drawn from ice cores, supplemented by a few early atmospheric measurements of questionable accuracy. There are some critics who quibble with the ice-core data, because of the question of how much ice overburden is necessary to seal the bubbles. But for me, the ice-core data is validated by back-calculating CO2 concentrations based on estimates of how much fossil fuel we've burned since 1800. If we use the same ratio of fossil fuel CO2 retained in the atmosphere (44%) to atmospheric CO2, we land right on the pre-industrial CO2 concentration from the ice cores.
      Free-air carbon capture technology is a big question, and would be a big project! I wonder if there would be an alternative bio-engineering solution -- building reefs, or algal blooms in anoxic basins.