Guest post by Lance Wallace
The carbon dioxide data from Mauna Loa is widely recognized to be extremely regular and possibly exponential in nature. If it is exponential, we can learn about when it may have started “taking off” from a constant pre-Industrial Revolution background, and can also predict its future behavior. There may also be information in the residuals—are there any cyclic or other variations that can be related to known climatic oscillations like El Niños?
I am sure others have fitted a model to it, but I thought I would do my own fit. Using the latest NOAA monthly seasonally adjusted CO2 dataset running from March 1958 to May 2012 (646 months) I tried fitting a quadratic and an exponential to the data. The quadratic fit gave a slightly better average error (0.46 ppm compared to 0.57 ppm). On the other hand, the exponential fit gave parameters that have more understandable interpretations. Figures 1 and 2 show the quadratic and exponential fits.
Figure 1. Quadratic fit to Mauna Loa monthly observations.
Figure 2. Exponential fit
From the exponential fit, we see that the “start year” for the exponential was 1958-235 = 1723, and that in and before that year the predicted CO2 level was 260 ppm. These values are not far off the estimated level of 280 ppm up until the Industrial Revolution. It might be noted that Newcomen invented his steam engine in 1712, although the start of the Industrial Revolution is generally considered to be later in the century. The e-folding time (for the incremental CO2 levels > 260 ppm) is 59 years, or a half-life of 59 ln 2 = 41 years.
The model predicts CO2 levels in future years as in Figure 3. The doubling from 260 to 520 ppm occurs in the year 2050.
Figure 3. Model predictions from 1722 to 2050.
The departures from the model are interesting in themselves. The residuals from both the quadratic and exponential fits are shown in Figure 4.
Figure 4. Residuals from the quadratic and exponential fits.
Both fits show similar cyclic behavior, with the CO2 levels higher than predicted from about 1958-62 and also 1978-92. More rapid oscillations with smaller amplitudes occur after 2002. There are sharp peaks in 1973 and 1998 (the latter coinciding with the super El Niño.) Whether the oil crisis of 1973 has anything to do with this I can’t say. For persons who know more than I about decadal oscillations these results may be of interest.
The data were taken from the NOAA site at ftp://ftp.cmdl.noaa.gov/ccg/co2/trends/co2_mm_mlo.txt
The nonlinear fits were done using Excel Solver and placing no restrictions on the 3 parameters in each model.
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Gail Combs says:
June 11, 2012 at 6:13 am
There is absolutely no reason to believe that CO2 mixing in the atmosphere is any better than that of the mixing of water vapor. You can see the east west bands in both gases.
Gail, never heard of the maximum humidity of air with temperature? There is reason to assume that water vapour is NOT well mixed, because there is a maximum limit and it drops or freezes out of the air. But there is no reason at all that CO2 drops out or freezes out at any rate and any mixture (except at -80°C and 1 bar, thus for 100% CO2).
BTW, the CO2 in water is true, but irrelevant, as the amounts are low and what is absorbed at the condensation places is released at the evaporation places, hardly influencing the overall CO2 levels.
Hi Gail, my post to you hasn’t appeared yet.
Gail – I’d posted it here, http://wattsupwiththat.com/test-2/#comment-1007003 just before posting in this discussion. Scuse typos and such and a few missing edits, but you’ll get the picture.
[SNIP: Eli, you are waving a red flag at a bull. This will only divert the discussion away from the topic at hand. Please don’t do that. -REP]
fhhaynie says: June 11, 2012 at 5:49 am
Allan,
Google “Metabolic Fractionation of C13 & C12 in Plants” and http://www.ncbi.nlm.nih.gov/pmc/articles/PMC406107/ tops the list.\\
Thank you Mr. Haynie,
SUMMARY
C13/C12 ratio analyses of chemical fractions from several plant phyla show that in all cases the lipid fraction is enriched in C12 compared to the whole plant. The C13/C12 ratio of the plant lipids corresponds roughly to the Cl 13/C12 ratio of petroleums. The C12 enrichment in petroleums as compared to present day plants can be explained if selective preservation of plant lipids occurred during the sedimentation process. The degree of C12 enrichment in the plant lipid fraction is inversely related to the amount of lipid in the plant. The C12 enrichment which occurs in plant lipids may be balanced by the 03 enrichment which occurs in respired C02• Isotope selection at the level of acetate or pyruvate is a possible mechanism for explaining our results.
I note that Figure 1 shows the C13/C12 ratios for petroleum, coal and land plants are all about the same.
So please help me out again: where is the human signature in the oxidation in these three materials when they all have similar C13/C12 ratios?
Allan MacRae says:
June 13, 2012 at 3:16 am
So please help me out again: where is the human signature in the oxidation in these three materials when they all have similar C13/C12 ratios?
There is no direct way to make a differentiation between CO2 released from burning fossil fuels or burning organics (either by humans or bacteria or forest fires), based on the 13C/12C isotope ratios. But there are two independent indirect ways:
– fossil fuels contain no 14C, but all recent organics do. That showed up in the pre-bomb tests atmosphere as soon as ~1870 and needed a correction of the carbon dating.
– the oxygen use. Fossil fuel burning needs oxygen. The amounts of oxygen used can be calculated from type of fuel and burning efficiencies. The measurements were very difficult to give the necessary accuracy (lass than a ppmv on 20,000 ppmv oxygen…), but since about 1990, that is obtained. That shows that the oxygen use has a small deficit compared to what was calculated. That means that the biosphere as a whole (plants + animals + bacteria) is a net producer of oxygen, thus a net user of CO2 and thus preferential 12CO2, leaving more 13CO2 in the atmosphere.
Thus vegetation is a net sink for CO2 and not the cause of the declining levels of 13CO2.
See:
http://www.bowdoin.edu/~mbattle/papers_posters_and_talks/BenderGBC2005.pdf
For the period 1900-2000 in graph form:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/bolingraph.gif
Corrections:
Thus vegetation is a net sink for CO2 and not the cause of the declining levels of the 13C/12C ratio in the atmosphere.
And of course, Bolin’s graph is for the 1990-2000 period, but one can calculate it further back in time, based on ice core CO2 and d13C measurements, be it that O2/N2 measurements in the ice cores are not reliable enough..
correction 2: there is over 20% oxygen in the atmosphere, thus over 200,000 ppmv… To see a change of a few ppmv, the accuracy of the method must be better than 1:200,000. Not a simple task…