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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edim says:
June 3, 2012 at 11:38 am
“Eli, nothing is differentiated out.”
He has a semi-valid point, one which Richard C. and Robert B. beat me over the head with on another thread. There is still an arbitrary constant which could be added and in which there is room for a (significantly reduced) anthropogenic effect.
However, the argument fails because getting a significant anthropogenic effect still demands a low bandwidth, but the data before us says the bandwidth must be high, or we will not get the excellent tracking between CO2 derivative and temperature anomaly. I illustrated this in the simulations proffered earlier (hit Next to peruse the plots up to viewing 6 of 29).
Bert:
What I am offering is a line of converging evidence–data not speculation. The only suggestion I had was why the data behave in a certain manner. But the data is the evidence I would refer to, not my speculative ideas for why it behaves that way. Any theory has to explain all of the data, not just your pet data.
Your single line of evidence showing a correlation between temperature and CO2. That suggests a cause and effect relationship? If you look at the long-term correlations, do you want to predict which sign you’ll find for the correlation, and which hypothesis that supports?
Bart, I can’t see the arbitrary constant, if you could elaborate (some tried at Climate etc). I still may be wrong, but it’s not only variation around some average growth that correlates with the temperatures. The whole of the annual growth does and at some other temperatures the average growth would be different as well, and therefore the long term accumulation. The correlation holds at other partial growths too. The conclusion is that the average growth over some period (annual, biannual, half-decadal, decadal) is determined by the average temperature during the period.
deltaCO2 = c*Tav, Tav is average anomaly
Personally I find the histrorical results from Mauna Loa a bit too exquisite, definite, and singular to be entirely believable, and I guess many of your readers feel the same.
So, I propose that it be worth a blog from someone about the results from other CO2 measuring stations/devices around the world, that are independent of the Scripps-based methods & locations such Mauna Loa.
Also, a blog on a really close look at the Mauna measuring instrument itself, especially around the Analog-Digital conversion arrangements, to identify the inherent non-linearities and assymetries. Even quite small values would be a possible source of upward bias (or drift) in the totalisation, if there is differentiation and subsequent integration in the data processing.
Bart says:
June 3, 2012 at 9:32 am
It’s all right here. The CO2 level is effectively the integral of temperature anomaly with respect to the proper baseline. These plots were made using GISS LOTI, before Werner Brozek and others pointed out that there is a better match, which is theoretically reasonable, to SST.
In essence, there is the same problem as what Edim figured out here before: at a constant temperature above a baseline, the formula applied gives a constant rate of CO2 increase. Thus with average ~0.3°C increase in temperature, one can have 70 ppmv increase over a period of 50 years.
The first problem is that both the oceans and the biosphere are proven sinks for CO2, thus can’t have delivered that amount of CO2.
The second problem is that there is no physical mechanism which can do that. The oceans give at maximum 16 ppmv/°C (dynamic equilibrium between ocean surface and atmosphere, according to Henry’s Law). The biosphere only sinks more CO2 by growing harder individually and in increasing total area, and the rest of the earth is too slow in reaction.
Then think about the glacial/interglacial events: the increase in temperature from the depth of a glacial to the height of an interglacial is ~10°C, it takes about 5,000 years and CO2 increases ~80 ppmv over that traject. With a temperature (anomaly) dependent rate for CO2, however small, that simply is impossible.
The rate of change of CO2 is influenced by the change in temperature, not the absolute temperature (or anomaly), only the equilibrium CO2 levels are absolute temperature dependent.
Bart, I also think one needs to at least look at the correlation you pointed out in the context of a simple 0-d radiative model (e.g., Lucia’s 2-box model). And then look at it in terms of a stoichiometric model of ocean/atmosphere and ask yourself what are the time constants associated with CO2 release from the ocean in response to heating.
I think Josh/Eli’s observation deserves a bit more than a rhetorical wave-off, something you are quite prone to doing, as I’ve observed in previous interactions with you. Also, if you can’t keep this at an adult level you can have the floor.
The only thing that’s differentiated out is the start condition (atmospheric CO2 at t0), but it’s a known value.
edim says:
June 3, 2012 at 11:32 am
You say that constant temperatures causing the rise cannot be true, well you don’t know that. It could very well be that cycles in SST, even without any long term trend, are driving the rise. Degassing CO2 from the oceans is faster (when warming in the cycle, due to volumetric source) than the uptake by oceans (when cooling, due to surface sink), so after every cycle CO2 ends up somewhat higher, depending on temperatures. A reciprocating-type CO2 pump, sort of.
Sorry, but degassing/uptake by the oceans surface is already fast; a new CO2/temperature equilibrium is reached in 1-2 years. Deep oceans exchange is a different matter, but that doesn’t go faster by higher temperatures (seems more the contrary). It is the absolute temperature of the oceans surface which governs how much CO2 is absorbed or released (Henry’s Law), not influenced by any cycle. The latter can influence the speed at which that happens, but that is not the problem here. And at what CO2 increase rate you think a glacial-interglacial transition would be?
But let’s go the other way out:
If you agree that in the past (and today) the CO2 levels are temperature dependent, shouldn’t be the dCO2 rates dT dependent?
Carrrick says: June 3, 2012 at 9:47 am
“This is one of my favorite graphics. It shows that the Northern hemisphere (where most of the trees are) shows the largest annual variation in CO2, and the south pole (where there are very few trees ;-)), shows almost no variation.”
http://scrippsco2.ucsd.edu/images/graphics_gallery/original/co2_sta_records.pdf
A beautiful graphic, thank you Carrick – I plotted it from raw data years ago. It clearly shows the huge magnitude of seasonal (natural) atmospheric CO2 flux compared with humanmade
CO2 emissions.
The seasonal CO2 “sawtooth” varies almost 20ppm at Barrow Alaska, and about 2ppm at the South Pole. I think this primarily reflects the larger land mass in the Northern Hemisphere. In comparison, global atmospheric CO2 concentration is increasing at a rate of about 2ppm/year.
Further, the daily flux in CO2 is also huge.
Here is recently observed Rose Park data at Salt Lake City:
http://co2.utah.edu/index.php?site=2&id=0&img=30
Please examine the Daily CO2 and Weekly CO2 tabs for all measurement stations.
.
Peak CO2 readings (typically ~500ppm) occur during the night, from midnight to ~8am, and drop to ~400 ppm during the day.
1. In contrast, human energy consumption (and manmade CO2 emissions) occur mainly during the day, and peak around breakfast and supper times.
2. I suggest that the above atmospheric CO2 readings, taken in semi-arid Salt Lake City with a regional population of about 1 million, are predominantly natural in origin.
IF points 1 and 2 are true, then urban CO2 generation by humankind is insignificant compared to natural daily CO2 flux, in the same way that (I previously stated) annual humanmade CO2 emissions are insignificant compared to seasonal CO2 flux.
IF these results are typical of most urban environments (many of which have much larger populations, but also have much greater area, precipitation and plant growth), then the hypothesis that human combustion of fossil fuels is the primary driver of increased atmospheric CO2 seems untenable.
Here is one of my favorite graphics. I can see no impact of man in this impressive display of nature’s power.
http://svs.gsfc.nasa.gov/vis/a000000/a003500/a003562/carbonDioxideSequence2002_2008_at15fps.mp4
Humanmade CO2 emissions are lost in the noise of the much larger natural system, and most humanmade CO2 emissions are probably locally sequestered.
Finally, I have no confidence in the C14/13/12 ratio argument. I think others have demolished it and I need not do so again.
“Sorry, but degassing/uptake by the oceans surface is already fast; a new CO2/temperature equilibrium is reached in 1-2 years. Deep oceans exchange is a different matter, but that doesn’t go faster by higher temperatures (seems more the contrary). It is the absolute temperature of the oceans surface which governs how much CO2 is absorbed or released (Henry’s Law), not influenced by any cycle. The latter can influence the speed at which that happens, but that is not the problem here. And at what CO2 increase rate you think a glacial-interglacial transition would be?”
Absolute temperatures of the ocean surface oscillate in annual cycles. Land surface temperatures too. Different latitudes in different phases and different amplitudes. In oceans we have currents, upwelling, downwelling etc, which must influence CO2 fluxes at ocean/atmosphere interface.
“But let’s go the other way out:
If you agree that in the past (and today) the CO2 levels are temperature dependent, shouldn’t be the dCO2 rates dT dependent?”
I can’t say what they should or not. The observed behaviour is that dCO2 is T dependent. Like I said, I cannot accept ice core records, different methods splicing etc. There’s no need.
Edim and Bart,
Have a look at what Pieter Tans of NOAA says about CO2 growth rate and temperature anomaly + precipitation:
from page 14 on:
http://esrl.noaa.gov/gmd/co2conference/pdfs/tans.pdf
He shows everything with the trends removed and the resp. response functions of CO2 vs. temperature and precipitation.
Regarding measurements in close proximity of volcanoes:
The amount of carbon dioxide (and other volcanic gases) is an indicator when an outbreak is about to occur. The amount increases exponentially before …
You are pointing at something important …
The “green stuff” takes care of that (as you know) … Not to forget, because there are a number of different oxidation processes in nature, including those in our bodies, we need an abundance of carbon dioxide, so that the “green stuff” can produce the oxygen we need … (More carbon dioxide contributes to more “green stuff” contributes to more oxygen …)
Yes, even a “dead” volcano emit gases, including carbon dioxide.
Friends:
The important point is that the dynamics of the seasonal variation in atmospheric CO2 concentration indicate that the natural sequestration processes can easily sequester ALL the CO2 emission (n.b. both natural and anthropogenic), but they don’t: about 3% of the emissions are not sequestered. Nobody knows why not all the emissions are sequestered. And at the existing state of knowledge of the carbon cycle, nobody can know why all the emissions are not sequestered. But that is the issue which needs to be resolved.
Importantly, it is certain that accumulation of the anthropogenic emission is NOT the cause of the rise in CO2 indicated by the Mauna Loa data.
The curve fitting exercise of the above article is pointless. If a curve is fitted then the equation of the curve provides a description of the shape of the curve but no information is gained by such an exercise. And it cannot assist in explaining why all the emissions are not sequestered.
In the above discussion, Bart claims his model of the carbon cycle is ‘right’ so all other models should be ignored. However, there are several models of the carbon cycle which each assumes a different mechanism dominates the carbon cycle and they each fit the Mauna Loa data. We published 6 such models with 3 of them assuming an anthropogenic cause and the other 3 assuming a natural cause of the rise in CO2 indicated by the Mauna Loa data: they all fit the Mauna Loa data.
These issues were ‘done to death’ in the thread at
http://wattsupwiththat.com/2012/05/24/bob-carters-essay-in-fp-policymakers-have-quietly-given-up-trying-to-cut-%C2%ADcarbon-dioxide-emissions/
The discussion in that thread is worth a read by those interested in the ‘carbon cycle debate’.
Richard
edim says:
June 3, 2012 at 1:13 pm
I can’t say what they should or not. The observed behaviour is that dCO2 is T dependent. Like I said, I cannot accept ice core records, different methods splicing etc. There’s no need.
Regardless of what you think about ice cores, there are plenty of other proxies which show a lot ot temperature change over glacials and interglacials.
E.g. the previous Interglacial was 2°C warmer than today (up to 10°C in Alaska, Siberia,…) during about 3,000 years, followed by a period of 7,000 years with 1°C warmer than today. With a constant CO2 rate over these periods, where should the CO2 levels be at the end?
The opposite is one of the main problems with that theory: glacials were 100,000 years long and far below the current temperatures, thus certainly with a huge negative CO2 rate according to your assumptions. Thus ending at zero CO2 already after a few hundred years…
edim says:
June 3, 2012 at 12:16 pm
The point those other guys made is that anthropogenic inputs are effectively linear in rate over the time span. With medium level bandwidth, that becomes a linear output in CO2. It still says the output would be drastically reduced from a straight accumulation, though.
A linear output is also the result of integrating the anomaly offset in the temperature. Ergo, they claimed, I could trade off the one for the other.
But, I cannot, because it would lessen the tracking efficiency to the point where the CO2 derivative would not keep pace with the temperature variation.
I assert that these are the facts, folks:
1) CO2 is very nearly proportional to the integral of temperature anomaly from a particular baseline since 1958, when good measurements became available.
2) Because of this proportionality, the CO2 level necessarily lags the temperature input, therefore in dominant terms, the latter is an input driving the former.
3) The temperature relationship accounts for all the fine detail in the CO2 record, and it accounts for the curvature in the measured level.
4) This leaves only the possibility of a linear contribution from anthropogenic inputs into the overall level, which can be traded with the only tunable parameter, the selected anomaly offset.
5) Anthropogenic inputs are linear in rate. Therefore, to get a linear result in overall level from them, there has to be rapid sequestration. (Else, you would be doing a straight integration, and the curvature, which is already accounted for by the temperature relationship, would be too much.)
6) With rapid sequestration, anthropogenic inputs cannot contribute a significant amount to the overall level.
Now, you may quibble about this or that, and assert some other relationship holds here or there, but your theories must conform with the reality expressed by these six points, because this is data, and data trumps theory.
mondo says:
June 2, 2012 at 3:42 pm
Shouldn’t we be looking at this sort of data on a logarithmic rather than arithmetic Y-scale?
Indeed if we subtract the constant term of 260 ppm, we get a straight line on semilog paper:
ln (CO2) = 0.0169 (t-1958) + 3.979 with an R^2 of 99.86%
richardscourtney says:
June 3, 2012 at 2:31 pm
“We published 6 such models with 3 of them assuming an anthropogenic cause and the other 3 assuming a natural cause of the rise in CO2 indicated by the Mauna Loa data: they all fit the Mauna Loa data.”
I’m sure neither of us wants to revisit the rancor of our earlier exchange, but I must insist that the phrase “they all fit” be qualified. I think I am being fair in characterizing your definition of “fit” as “within the instantaneous uncertainty level of the MLO data.” I have insisted, reliably I might add, that it is quite possible to dig below that level for long term underlying processes by filtering, and that is where you will find whether they agree or not with the fine detail mandated by the temperature relationship. For the life of me, I do not know why you refuse to do that particular analysis.
Unfortunately, as you have informed us, your paper is not generally available to the general public, being behind a paywall, and we cannot check your assertion for ourselves. Nor do I have access to the precise data you used to verify your models. So, until presented with evidence otherwise, I am not going to believe that all of the “fits” are equally good. In fact, I very much expect that the fits which use less anthro and more natural will be better.
jorgekafkazar says:
June 2, 2012 at 7:16 pm
Thanks, Lance, this was fun. But there’s not a whole lot of science, here. Using a curve fit for a 56 year period, then extrapolating backwards and forwards is very shaky. There’s no reason to assume that the multiple mechanisms resulting in atmospheric CO2 concentrations are identical at the start and end of the period; thus the exponential, though convenient, is not necessarily valid as a predictor or analytical tool of any sort.
If you have the time, though, you might want to push this a stage further. At a minimum, I’d like to see error bars fore and aft, as well as a correlation coefficient adjusted for autocorrelation. I think you’ll find your 1723 date should be ±200 years. Worse, trying to tie the date of the knuckle of the exponential to any invention is completely unjustified. Natural CO2 variation may likely overwhelm any man made emissions, distorting the actual curve beyond recognition.
Thanks Jorge, indeed I did it just for fun and make no scientific claims. The fit was so good I assumed the error would be small, but since you ask I redid the nonlinear fit in Statistica (I had used Excel before). There were some small differences in the point estimates: Background CO2 was 257 ppm (SE 1.05 ppm) compared to 260; the start year was 1711 instead of 1723 (darn! missed Newcomen’s invention by a year!) (SE 3.94 years, well short of your suggestion of about 100); and tau was 61.3 (SE 0.7) years, compared to 59. So indeed the errors are amazingly small, especially considering the last 20 years of intense focus on CO2 with apparently little effect.
I wasn’t actually too serious about the Newcomen invention, just trying to track the beginning of the curve to the beginning of the Industrial Revolution since that is so often fingered as the culprit. Note that the curve takes 40 years(!) to increase from 261.4 ppm to 262.4 ppm.
Pamela Gray says:
June 2, 2012 at 6:08 pm
Anything as regular as this data says one of two things.
1. Manmade CO2 pump sitting next to the sensor and never shuts off and is exquisitely tuned to a rythmic increasing beat.
2. Artifact of the “fudge” factor part of the CO2 calculation.
I too am gobsmacked by the regularity of the curve. If it is mostly due to increasing anthropogenic emissions, one would think as others have pointed out that there would be more serious impacts of economic lulls and booms. If mostly natural on the other hand, why the constant acceleration rather than a linear or possibly deceleration following the LIA? But it is rather fun to see the complete lack of any visible effect of all the Kyotos, Balis, Copenhagens,and Rios.
George E. Smith; says:
June 2, 2012 at 8:40 pm
1) So I didn’t see any conclusion as to whether the Mauna Loa CO2 data best fits an exponential curve or whether a power series curve is a better fit for the 1722 to 2050 data.
2) Why did you choose to start your extrapolated prediction; excuse me, that’s projection, from the year 1722. Aren’t you concerned about being accusede of cherry picking, by selecting that year; rather than say 1769; the year that Captain Cook, (re)discovered New Zealand ?
Well, as to 1) above, I did mention that the quadratic gave a better fit over the 50-odd years than the exponential. But the exponential fit has much more attractive interpretations of the three parameters. For example, I did not “choose to start” at 1722–that was a free-floating parameter that was “chosen” by the Excel nonlinear fitting function. The other parameters (background of 260 ppm, doubling period of 41 years for the incremental CO2 above background) were also completely a function of the fit. The background value, for example,is fairly close to the 280 ppm that is presently regarded (I presume due to multiple lines of observational evidence–at least I hope so) as the level before the Industrial Revolution. These parameters did not have to come out so nicely, and in that case there would be no particular reason to look further at the exponential fit.
MikeG says:
June 3, 2012 at 12:48 am
Sorry, your curve fitting is quite meaningless and has no predictive properties whatever. The data would make an equally convincing fit to a sine curve, and many other functions.
Well, the exponential fit did have some nice properties, like predicting a background level and an initial starting point both of which have observations in fairly close agreement. Also, based on the 50-year period with residuals seldom exceeding 1 ppm, I would be willing to bet that the curve will be no more than 1 ppm in error 5 years from now.
Bart says:
June 3, 2012 at 1:21 am
A simple analogous (not precise in every detail, but able to provide guidance as to physically possible and plausible behavior) system model is as follows:
dC/dt = (Co – C)/tau1 + k1*H
dCo/dt = -Co/tau2 + k2*(T-To)
Well,you have 5 adjustable parameters here and you know what von Neumann said about that.
Freddy Hutter, TrendLines Research says:
June 2, 2012 at 11:29 pm
The projected co2 chart is scary only ‘cuz it assumes unlimited supply of fossil fuels (as in IPCC scenarios). It is rather more reasonable (423-ppm 2029) when adjusted to reflect peak oil, peak gas & peak coal
I actually assumed nothing, just let the observations do what they would. The idea that peak fossil fuels drive the curve is certainly possible, but is also an assumption.
Ferdinand Engelbeen says:
June 3, 2012 at 2:10 am
Oh by the way, a simple formula to calculate the CO2 levels at any moment in the future (or past);
CO2(new) = CO2(old) + 0.55xCO2(emiss) + 4xdT
Thank you Dr. Engelbeen for the useful references. Your proposed formula seems to suggest that at times of decreasing or plateauing temperatures, the CO2 emissions would need to increase at just the right speed to offset the reduced effect of temperature and maintain the eponential increase.