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.
edim says:
June 3, 2012 at 1:51 am
“…a sufficiently high constant temperature will cause rising CO2…”
I think it is likely that what we are seeing is that the end of the LIA forced a new equilibirum level for temperature which has not yet settled out, and for which humankind bears no responsibility. When it settles, or reverses, we will see CO2 levels level follow. Judging by the numbers, I expect that will be a long time yet.
FerdiEgb says:
June 3, 2012 at 3:49 am
“But as is proven in the mass balance…”
My system analogy above produces the same mass balance. I have explained to you many times why your mass balance argument is faulty.
Laws of Nature says:
June 3, 2012 at 4:58 am
“It would be interesting if you could change the constants to either support Essenhigh’s or Cawley’s conclussions”
The important one which cannot be changed is tau1. That sets the bandwidth of the system. A wide bandwidth system maintains its equilibrium point tightly, with low sensitivity to disturbances. That is what we see in the data – the (quasi-)equilibrium point, which is proportional to the integral of temperature anomaly, is tightly tracked. That demands a wide bandwidth system, which in turn demands low sensitivity to human inputs. Whatever the actual form of the system, however it may deviate from my simple analogy, the dynamics must add up to the same thing: the equlibirum dynamics are very low bandwidth, so that the CO2 level is effectively the integral of temperature anomaly in the “near” term (relative to tau2) when there has been a change of state, and the regulator dynamics are very high bandwidth, so that the CO2 tightly tracks that integral, and human inputs are quickly sequestered and have little effect on the overall level.
FerdiEgb says:
June 3, 2012 at 5:43 am
It’s all right here. The CO2 level is effectively the double 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.
FerdiEgb says:
June 3, 2012 at 5:54 am
“Except that any relationship in the derivatives has zero predictive power for any releationship in the original variables…”
We do not need to “predict” it since it is in the past, and can be inferred. I’ve had intense arguments with others who insist this is a weak point in my argument, but there really isn’t any alternative when the bandwidth of the system is observably so wide. It is the excellent tracking of the temperature anomaly in the CO2 derivative which demands that the bandwidth must be wide (short sequestration time). And, wide bandwidth constrains the effect of human emissions to be small.
Allan MacRae says:
June 3, 2012 at 8:19 am
Sorry, Allan, I should be giving you credit. I only do this as a hobby, and I forget the names of the people I have interacted with more than a few weeks ago.
From above: “The CO2 level is effectively the double integral of temperature anomaly with respect to the proper baseline.” My brain skipped a grove, it’s just the single integral.
The exponential model presented here has no coefficient that multiplies the exponential, and therefore, implies that this coefficient is 1.0ppm, and is a constant in the model–not determined by data at all. This seems extremely unlikely. Is this a typo?
The observed data are all contained within one e-folding time far along in the time series, So the coefficients are correlated to one another and not well determined.
BIll Illis:
Yep part of the state of the art in Keeling’s measurement was in picking sites where the diurnal variation in CO2 was minimized. If anybody is really interested, they should go back to the decade or so of measurements that Keeling took before he established the Mauna Loa observatory.
On another note, one should look at the ratio of C14 to C12 in the CO2 in the atmosphere. If it’s coming from fossil fuel burning, the ratio should increase. If it’s inorganic CO2, it should stay constant. EM Smith noted that the increase in CO2 corresponded to the end of the LIA. Well, since CO2 is thought to act as a GHG, does that suggest an idea for how they might be linked?
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.
If this is all faked, they thought of everything. Maybe people need to consider their sources a bit more carefully, and if somebody consistently is making outlandish claims, consider writing them off as a nut.
Just saying.
Steve Keohane says:
June 2, 2012 at 10:20 pm
I created the graph. It is in the “Water Vapour Feedback” section of my “Climate Change Science essay at
http://www.friendsofscience.org/assets/documents/FOS%20Essay/Climate_Change_Science.html#Water_vapour
A link to the NOAA data source is given just above the graph. To recreate the graph use Variable “Relative Humidity”, select “Seasonal average”, First month of season “Jan”, second month “Dec”. Select “Area weight grids”. You can select “analysis level” from 1000 mb to 300 mb.
A proper regression model provides residual plots that have a random pattern with mean zero. Due to the obvious pattern here, this residual plot indicates some key variable(s) is omitted or the modeling challenges of a nonlinear fit were not overcome. Seems like some basic transformations and an attempt to use a linear model is in order.
Sorry this is a misstatement on my part:
The ratio should decrease because fossil fuels have very low ratios of C14 to C12. If the CO2 is coming from the ocean the ratio of C14/C12 should stay approximately constant.
Here’s a more complete explanation lifted from another source:
I think it’s also important to emphasize that on decadal-scales there is substantial variation in the variation of ocean temperatures, and certainly you can expect CO2 to come in and out of dissolution as natural fluctuations in ocean temperatures result in CO2 releases into and absorption from the atmosphere. Thus one can get changes of C13/C12 that don’t follow the basic long-term patterns expected, because other physical processes play a more dominant role on those time scales.
No worries Bart,
I am a hobbyist as well, and NOT “trying to get on full time” in the climate science business – it is a fascinating subject, but the quality of debate is too often degraded.
The problem with too many of the climate “full-timers” is that they are drinking each-others’ bath water, and the result is the current lamentable state of climate science and its dogmatic and repressive intellectual environment.
The irony is that BOTH sides of the rancorous “mainstream climate debate” , which is basically an argument about H20 feedbacks and ‘sensitivity” to CO2, probably have “the cart before the horse” – in fact, the primary cause is increasing temperature over past centuries, and increasing atmospheric CO2 is the result.
This would all be quite funny, except that a trillion dollars has been squandered on CAGW nonsense.
Intelligent use of these scarce global resources would have easily saved as many people as died in Hitler’s WW2, or Stalin’s purges, or Mao’ s Great Leap Backward.
On my bleaker days, I must conclude that we are governed by scoundrels and imbeciles.
“The increase in (ocean) temperature since the LIA is at maximum 1°C, good for maximum 8 ppmv extra over that full period, that’s all.”
Maybe so for a static unit of water.
But how about constant upwelling of fresh water from depth being exposed to solar shortwave which has increased beyond the increase in raw TSI at top of atmosphere as a result of decreasing global cloudiness during the warming spell ?
Just as observed during the late 20th century.
And then suppose, too, that the upwelling water is not as cold as it was due to warmth injected into the depths during the MWP and only now returning to the surface.
Both those factors would reduce ocean surface absorption of atmospheric CO2 allowing it to build up in the air.
The observed large proportionate change in CO2 ppm is not reflected well in ice cores but then we don’t really know whether the ice core record is sensitive enough to record multicentennial variations in atmospheric CO2 in full detail..
Plant stomata are more sensitive and do indeed record greater variability in CO2 than ice cores but even they may be too coarse for a full representaion of actual multicentennial CO2 variability.
The isotope argument used to be invoked to justify ignoring such matters but new data is weakening that and I don’t hear it much these days. There are plenty of natural sources of CO2 showing the same isotope ratios as human emissions.
“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.”
More likely that would be caused by greater seasonal sea surface temperature changes in the northern hemisphere due to the larger landmasses obstruction energy diffusion around the globe.
The unobstructed circumpolar current would minimise variations in the most southern oceans.
Carrick says:
June 3, 2012 at 10:03 am
“There has been a decline in the 14C/12C ratio in CO2 that parallels the increase in CO2.”
14C cannot be used for anything with confidence since the birth of the Atomic Era.
“If the increased CO2 was due to warming of the oceans, there should not be a reduction in the ratios of C-13 and C-14 to C-12.”
The quirks of diffusion process do not justify such linear logic.
Thus one can get changes of C13/C12 that don’t follow the basic long-term patterns expected, because other physical processes play a more dominant role on those time scales.
Airy assertion, with no proof. Every physical process tends to become more significant over longer time scales, as a result of the inherent low pass characteristic of stable systems.
What you cannot get around is this relationship. Temperature variation accounts for the entire shooting match. Any role of human emissions in overall atmospheric concentration is small (I estimate 4-6%). See my preceding posts for background.
Allan MacRae says:
June 3, 2012 at 10:05 am
Those are my good days!
Stephen Wilde:
That’s another possibility. Do you have a reference? I haven’t looked at the latitudinal variation in ocean temperatures, so that’s something that would be a test of your hypothesis.
but the variation increases with latitude.
Either mechanism would predict a peak in atmospheric CO2 in summer months, so you can’t use that to eliminate either hypothesis. I’ll have a look at HADSST3 when I get a chance and see if I can produce a plot.
One thing that works against your hypothesis is the ocean surface is only accounts for 20% of the surface the Earth at high Northern latitudes and nearly 100% at high southern latitudes see this—this would suggest you’d need a huge variation in temperature south-to-north to account for what amounts to a factor of 8 difference in annual variation.
Bart, I’m not certain it’s considered scientifically rigorous to hand-wave away ever piece of evidence that doesn’t fit your theory. 😉
Carrick says:
June 3, 2012 at 10:34 am
You offer speculation and call it “evidence”. I’m giving you hard data with a direct bearing on the problem. Physician, heal thyself.
“you’d need a huge variation in temperature south-to-north to account for what amounts to a factor of 8 difference in annual variation”.
Would I ?
We are considering a tiny proportionate annual variability in CO2 release / absorption rates not absolute quantities.
The SH could produce a vast amount with virtually no seasonal variation whilst the NH could produce a much smaller amount with a significant seasonal variation.
Anyway, the essence of my point is that you can’t just pin it on trees which is what you tried to do.
.
Forgive an innocent little bunny for asking, but how does the derivative of the smoothed CO2 concentration with time explain the roughly 90 ppm increase in CO2 concentrations over the last century? You differentiated that out.
Now the derivative may have some relationship to the variation in global temperature through NPP or outgassing of the oceans but that is a different matter.
It is much the same as the fit to a quadratic or an exponential. That has no explicative power. If, on the other hand, you fit it to emissions you might have something interesting. Of course to know what will happen in the future, you would have to know what future emissions will be.
REPLY: you aren’t a bunny, and you aren’t innocent. When are you going to give up this bizzare persona/charade? -A
How does any quadratic or exponential curve fit with historical A-CO2 generation?
Does the putative cumulative A-CO2 generation show a similar quad/expon relationship?
Would this not mean that the presence of CO2 is facilitator of more CO2? Would this not mean the residence time of CO2 was >1000 years?
Regression is the most erroneously applied statistical tool. It doesn’t take much knowledge and skill to use (leads to poor application) and there are too many who need specific results, thus biased (leads to “cooked” results). Without knowing the process by which the model was built and the accompanying diagnostics (various stats and residual plots), any regression model should be treated with skepticism. Academia has been corrupted by performance demands that are impossible. Research supported by proper statistics take much longer and desired results much harder to achieve. Due to poor training and apathy, it is quite likely most of today’s PhD’s would not meet the statistic bar of a generation ago. If the results are welcome, how the statistics were achieved are likely to be given only a glance. If the results were distasteful, the post hoc cycle then begins. But that is off the main topic.
And then there is the data factor. Data are everything. Anyone who does not provide full access to their data is hiding something. It is juvenile to think any work can be taken seriously if the history of its input cannot be independently verified so the results can be duplicated. To minimize proper review, academia hides behind processes that would inspire Rube Goldberg. Those pushing the CO2 game take the cake. In the climate game, they claim global catastrophe if their advice is not adhered to. Yet they were unable to or refuse to do what is necessary to validate their work. Original data lost? Researchers protect their data better than their children. If they can’t maintain a data base, how can their analyses be trusted. They don’t know what the input is.
The real point here is due to the cost of doing nothing and the cost of the “fix” that the climate “scientists” claim and demand, absolutely in no uncertain terms, an environment of total transparency is required. To do otherwise is too self-serving. Are they willing to let the world cook while some arcane academic principle is maintained? I think not. It must be because their work is garbage.
It doesn’t take an expert to know whether a speaker, presenting himself as an expert in the same area, is a fraud or not. A well-educated man can see through whatever flimsy is present. Not being able to produce data is a bad joke anyone with a modicum of sense can get.
Eli Rabett says:
June 3, 2012 at 11:05 am
“You differentiated that out.”
As I explained, the excellent tracking between the temperature and the CO2 derivative demands a high bandwidth system. And, that high bandwidth necessarily means human inputs are attenuated to a level of insignificance.
This is a sophisticated argument which requires an advanced level of understanding of how feedback systems work.
Doug Proctor says:
June 3, 2012 at 11:17 am
“Would this not mean the residence time of CO2 was >1000 years?”
Would this not mean that CO2 regulation in the planet’s atmosphere would be extremely weak, and there is no way to maintain any kind of narrow equilibrium under those conditions given random contributions to the CO2 level?
Why yes, yes it would.
Doug Proctor says:
June 3, 2012 at 11:17 am
And, please note, scale and bias similarity between emissions and CO2 measurements means very little. It is necessary, but not sufficient for the one to be driving the other. A similar quadratic/exponential curve emerges when integrating the temperature anomaly.
Ferdinand wrote:
“There is a fundamental problem here: your formula assumes that the CO2 level continuous to rise with a constant elevated temperature, but that can’t be true. The main source in the past were the oceans. These emit CO2 with rising temperatures until a new equilibrium is reached, that is when the pCO2 of the ocean surface and the pCO2 in the atmosphere are in average equal (thus as much CO2 is absorbed as is released).
So there is an increase if the temperature increases, but limited to at maximum the new equilibrium. which in the past was about 8 ppmv/°C (MWP-LIA, glacials-interglacials), on short term that gives about 4 ppmv/°C of variability around the trend.”
I think we have to forget about the past for a moment – no splicing and different methods please. No need, we have more than 50 years of continuous measurements at ML and other sites as well. Annual growths and therefore the long term accumulation (sum of the annual growths) seem to be dependent on global temperature indices. The conclusion is that the average temperature during the period of accumulation drives the total accumulation. It did since 1959. This still doesn’t mean that the warmth is the sole cause – it could be only because of the human input that the climate system is doing something in response to the human emissions.
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.
Eli, nothing is differentiated out. Any accumulation (smallest being the annual one) is dependent on the average temperature during the period of accumulation. That’s the correlation. The annual growths only increased because temperature increased since 1959. At the 60s level the annual growth was ~0.9 ppm. If temperatures declined in 70s/80s/90s, the annual growth would have been lower and maybe even negative, at sufficiently low temperatures.
As Just some guy says: June 2, 2012 at 3:43 pm
However, it is useful to compare this CO2 concentration extrapolation to the IPCC CO2 concentration projections.
The IPCC uses a large number of emission scenarios, and calculates a forecast of CO2 concentrations using the Burn carbon-cycle model. The data is here:
http://www.ipcc.ch/ipccreports/tar/wg1/531.htm
There are six main story-lines: A1B, A1T, A1FI, A2, B1 and B2.
The Burn CC model gives a “reference”, a “low” and “high” case for each of the six scenarios, so 18 cases in all.
The “low” case assumes a “fast ocean” (ocean uptake of 2.54 PgC/yr for the 1980s) and no increase of animal respiration. A “high”case assumes a “slow ocean” (ocean uptake of 1.46 PgC/yr for the 1980s) and capping CO2 fertilisation.
Here is a graph of the CO2 extrapolation using the parameters given in the lead post, with some selected IPCC scenarios. Note the huge range of CO2 projections to the year 2100; 1248 ppm in the A1F1 high case, 486 ppm in the B1 low case.
http://www.friendsofscience.org/assets/documents/CO2_IPCC_ScenVsActual.jpg
The A2 Reference case is very close to the CO2 model extrapolation.