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.
Discover more from Watts Up With That?
Subscribe to get the latest posts sent to your email.
Interesting. Need to check the results of other observatories (the time is shorter), to see weather the deviations are global or local.
The late 1980s show a large departure. It would be interesting to plot these residules against the rates of increase/decrease in global temperature.
The fluctuations appear to fit global temperature fluctuations. This intuitively would make sense because warming sea surface temperatures would cause release of CO2 to the atmosphere, and conversely, as sea surface cools, would increase CO2 absorption into the oceans from the atmosphere.
Because I’m an alround bad guy, I’ll suggest that you could also have fit the data with a scaling distribution, you know, and asymmetrical one with a long tail.
Interesting that it appears the ramp starts kind of when the LIA started petering out. But that couldn’t have anything to do with it…
Shouldn’t we be looking at this sort of data on a logarithmic rather than arithmetic Y-scale?
Hmmm. It cant follow the same formula forever, of course. If it did,it appears we’ll one million parts per million by the year 2540.
I’d suggest fitting a sine curve to it, too.
And another thing which might be interesting to look at is annual cycle. That would require unadjusted data, though. Does annual cycle follow the concentration curve (i.e. does its amplitude grow with concentration) or does it stay constant?
Mauna Loa had better stop spewing out that CO2 crap other wise it will be slapped with a carbon tax, Australia PM gillard will find a way
All this means that CO2-doubling will be completed by 2050 along with
the climate forcing of 3.7 W/m2…… thus earlier than 2100 as given by
AGW…
Which GMT would result in 2050?
The last volcanic eruption of Mauna Loa was in 1984. Prior to that it had erupted quite regularly with 39 eruptions since 1832. Would this be a factor?
Doesn’t the constant emission of volcanic gases from the national park mean that perhaps this was not the best choice of monitoring sites for a gas that is known to be emitted from volcanoes ?
I’m sure they adjust the data to compensate.
If this trend continues……
who would have thought that man’s measly 5%
Joachim Seifert says:
June 2, 2012 at 3:58 pm
Which GMT would result in 2050?
Your guess is as good as anyone’s …
My shot at explaining the residuals is that the dips reflect recessions in the West — the 70s and early 90s. So why isn’t there a dip for 2008+? Ans: China never had a recession.
i would say the response to human emissions would be linear due to the time frame being considered mainly being from an upward slope of temperature rise.
if the natural component due to increasing ocean heat content is considered, then the ‘man made’ portion will be a fraction of the increase. to just draw a line through a complex system smacks of climate science at work.
what happens when the temps fall is the question, not what curve it fits.
Thanks Lance. Keep exploring.
For some detailed CO2 data and analysis with latitude and time see:
Fred H. Haynie, Future of Global Climate Change http://www.kidswincom.net/climate.pdf
And CO2 & OLR
David Stockwell in his Solar Accumulation theory predicts a Pi/2 (90 degree) phase lag for ocean temperature vs solar forcing for the Schwab solar cycle. e.g. 2.75 years for the 11 years solar cycle forcing. See Key evidence for the accumulative model of high solar inuence on global temperature
From that I predicted a similar 3 month (12/4) lag between annual solar forcing and ocean temperature, and thus the CO2 signal. similarly, the Arctic lag should be 6 months displaced from the Antarctic lag in the annual cycle. This appears to be supported by Haynie’s slides 16, 10, 11 and 18/59:
(Note the Antarctic lag is reduced from the solar forcing because of less polar latitude). See also CO2 & Temperature discussion under <a href=http://judithcurry.com/2011/09/15/on-torturing-data/On Torturing the Data
The CO2 lags corresponding with the ocean temperature lags which are predicted from the annual solar forcing and with the Arctic ~6 months different from the Antarctic lag provides strong evidence for solar driven temperature with annual CO2 variations responding to the temperature.
For economic activity vs CO2 see:
Detection of Global Economic Fluctuations in the Atmospheric CO2 Record
Just some guy says:
June 2, 2012 at 3:43 pm
Hmmm. It cant follow the same formula forever, of course. If it did,it appears we’ll one million parts per million by the year 2540.
As well, the oxygen would get too low for life to exist. See
http://www.disclose.tv/forum/atmospheric-oxygen-levels-fall-as-carbon-dioxide-rises-t29534.html
“…we are losing nearly three O2 molecules for each CO2 molecule that accumulates in the air.
“if the oxygen level in such an environment falls below 19.5% it is oxygen deficient, putting occupants of the confined space at risk of losing consciousness and death.”
EVERYBODY PAY ATTENTION!!! THE FOLLOWING IS SUPER IMPORTANT!!!
The concentration of CO2 in the atmosphere as determined at Mauna Loa is valid only for highly-purified, bone dry air which is comprised only of nitrogen, oxygen, the inert gases, and carbon dioxide and which does not occur anywhere in the atmosphere. In real air, there is always water vapor and the concentrations of the gases are lowered in portion to that volume fraction of water vapor.
The use of the concentration of CO2 based upon the data from Mauna Loa is an absolute fatal flaw for all climate model calculations. For fluid dynamic calculations, mass per unit volume should be used.
At STP (273 K and 1 atmosphere pressure), one cubic meter of dry air presently has about 390 mls (390 ppmv) or 17.4 mmoles. If this dry air is heated to ca. 333 K (60 deg C), which slightly higher than max temp every recorded in the desert in Pakistan, the concentration of CO2 is still 390 ppmv but its mass is 14.3 mmoles. If the dry air is cooled 183 K (-90 deg C, lowest temp ever recorded in Antarctica), the concentration of CO2 is still 390 ppmv but its mass is 26 mmoles.
The mass of atmospheric gases in any unit volume of the atmosphere depends upon temperature, pressure and absolute humidity. Weather maps show there is no uniform distribution of temperature, pressure and rel humidity in space and time. Thus there is no unifrom distribution of the greenhouse gases in real air.
The reason the climate scientists say the greenhouse gases are well-mixed is due to the methods of atmospheric gas analysis. In general a sample of local air is filtered to remove particles, dried to remove water, scrubbed to volitile organic compounds, oxides of sulfur and nitrogen, and CFC’s. This procedure produces the highly-purified bone dry air mentioned above.
The composition of the atmosphere of local air from remote locations is fairly uniform thu out the world except for minor variations in the concentration of CO2. However, in locals where there is lots of human activities the concentration of CO2 can vary greatly in space and time suchas during rush hour in major cities or in winter in temperate zones.
All the guys who do atmo. gas analyses know what I have stated above is the absolute truth. But they keep their mouths shut so the climate scientists can make the claim that the greenhouse gases are well-mixed and to avoid vilification. We all know what happened to Ernst Beck after he published he review of atmospheric CO2 gas analyses.
For really good data on the composition and properties of the atmosphere go to:
http://www.uigi.com/air.html
Ya know, these climate science guys really don’t know what they are doing.
I plotted Mauna Loa with tropics temps over at woodfortrees and there is no correlation.
I presume the curve matches the world population curve without much of a residual. Still, the CO2 sinks into the oceans eventually, don’t know how fast that happens.
So strange that the curve follows such a simple mathematical pattern and doesn’t seem correlated to economic activity, world oil consumption, etc. The residual doesn’t seem correlated either. See http://www.indexmundi.com/energy.aspx Oil consumption was dropping in the early 80’s and here the residual is increasing.
The fluctuations in the residual do seem to track the fluctuations in global temperatures though. Makes me wonder if outgassing from the oceans is what’s driving CO2, not fossil fuel use.
I recall reading that the guys on Mauna Loa throw out the “outliers,” when they take CO2 readings. The reasons for throwing out the high CO2 readings involved possible burps of the volcano, and mobs of exhaling tourists in belching busses. However the reasons for throwing out the low readings of CO2 always puzzled me, (and made me a little nervous, because if you throw out enough low readings you can get the reading that “fits” a preconcieved theory.)
My understanding was that the low readings were due to “upslope winds.” Can anyone explain what happens downslope that uses up the CO2? Lush foliage?
http://www.woodfortrees.org/plot/esrl-co2/isolate:60/mean:12/scale:0.2/plot/hadcrut3vgl/isolate:60/mean:12/from:1958
(from http://forum.wetteronline.de/showthread.php?p=181540 )
It looks like the temperature changes are similar to El Nino/La Nina, with CO2 lagging temperature.
From 1948, there seems to have been a steady downward trend in global atmospheric RH. Could this effect Mauna Loa CO2 measurement ?
http://members.shaw.ca/sch25/FOS/GlobalRelativeHumidity300_700mb.jpg
Harold Pierce Jr says:
…For really good data on the composition and properties of the atmosphere go to: http://www.uigi.com/air.html”
Harold, don’t take this the wrong way, but that link leads to some sort of classified ads website.