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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I agree with Tim Ball here, that Jaworowski is crucial, and has been brutally trashed by CAGW rednecks for his temerity in challenging the corruption of the science. I personally tend to leave Beck aside as though I regard his evidence as very important, it involves too many distracting issues. I did a whole page on the CO2 issue way back in 2009 and it is still relevant as ever.
People simply forget Henry’s Law, the titanic outgassing ability of the oceans in the tropics, and the ability of plants to suck in any spare CO2 – as the recent greening of the Sahel shows. These factors are what I believe the good Ferdinand Engelbeen fails to appreciate. And many others. The above “fit” is indeed seductive. But push the boundaries and the fit breaks down.
Now think. CO2 lags temperature by 800 years, according to Caillon et al. What happened 800 years ago?? Anyone?? And what cycle takes 800 years to happen?? Anyone??
Again the same discussions com up every few months…
To begin with: The Mauno Loa and other stations CO2 data are as solid as one can have on this earth. Indeed some of the raw data are discarded (still available, but not used for daily to yearly aveages), because they are influenced by downwind conditions from the nearby volvanic vents or by afternoon upwind conditions, which brings up slightly depleted by vegetation CO2 levels from the valey. Both give raw values which are +/- 4 ppmv around the “background” seasonally variable levels. Including or excluding these outliers for averaging doesn’t influence the yearly average or trends for more than 0.1 ppmv. The Mauna Loa “extremes” don’t exist at the South Pole, where the first continuous measurements ever were made, but they have more mechanical problems in the harsh conditions there. For an impression of the raw data vs. the “cleaned” averages at Mauna Loa and the South Pole see:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/co2_mlo_spo_raw_select_2008.jpg
take into consideration the blown up scale of CO2!
The raw data of 4 stations can be found at:
ftp://ftp.cmdl.noaa.gov/ccg/co2/in-situ/
The rules for exclusion of data and the calibration procedure at Mauna Loa can be found at:
http://www.esrl.noaa.gov/gmd/ccgg/about/co2_measurements.html
Pieter Tans of NOAA has been very cooperative in the past and sent a few days of raw instrument voltage data on simple request, so I could check the calculation procedure which is used to get the raw CO2 data. No problems found.
So far so good for that part.
Then the cause of the increase.
– The oceans are not the cause:
Pure on solubility parameters, an increase of 1°C causes an increase of 16 microatm of CO2 in the oceans surface waters, thus back into dynamic equilibrium causes an increase of about 16 ppmv in the atmosphere. It doesn’t matter how much CO2 is in the oceans, only the extra pressure matters. Take a 0.5 or 1 or 1.5 liter bottle of coke and shake that, the pressure in the above space will get the same. Regardless of the triple amount in the larger bottle, if for the amount that is lost from the liquid into the atmosphere. Amounts are hardly important, the pressure (difference) is.
But an increase in temperature also increases the uptake by vegetation. The net result over very long periods is that an increase of 1°C in ocean temperature gives some 8 ppmv increase in CO2. Thus the ~1°C warming since the LIA gives at maximum 8 ppmv increase of CO2. But we see an increase of over 100 ppmv since the start of the industrial revolution…
Moreover, an extra amount of CO2 from the oceans would increase the 13C/12C ratio of CO2 in the atmosphere, but we see a continuous decrease.
– vegetation is not the cause:
In principle, if there was more vegetation decay than growth, that would increase the total amount of CO2 and give the same 13C/12C decline as observed. But one can deduce the biological balance from the oxygen balance: some less oxygen is used as calculated from fossil fuel use. Thus vegetation is a net oxygen producer, dus a net CO2 absorber.
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
all in ppmv
That explains the trend and the temperature dependent variability…
The human body consists of 70% O2.
0.7* 7,000,000,000 * 170lb = 833,000,000,000,000lb of O2 bound up in the human population of the planet. As the population grows we use up more of the O2 in the atmosphere.
170lb is just my guess for the average weight of us humans.
That’s just humans. All biomass contains O2.
Unfortunately as a number of commentators have pointed out, the predictive part of the curve assumes unlimited and increasing change.
Now if humans are the cause then there will ultimately be a point when the rate of increase in fuel consumption slows. Personally I doubt this because the curve is far too even to be of anthropogenic origin. Consider this for example, when this curve started most of europe used open fire coal heating, through a series of clean air legislation this changed until ultimately most people were using gas. Equally 1958 was the year that the Ford Edsel came out. Since then cars world- wide have become increasingly more fuel efficient. I would think that these changes would have some impact if humanity was the cause, but no apparently not.
If the cause is a natural cycle then it will end, when it ends.
Laws of Nature says:
June 3, 2012 at 12:21 am
Just yesterday I was looking if there would be any news on the discussion of the Essenhigh paper
I found this:
http://www.skepticalscience.com/news.php?n=1259
The Essenhigh paper was fully responded to in another article in Energy & Fuels by Dr. Gavin Cawley:
“On the Atmospheric Residence Time of Anthropogenically Sourced Carbon Dioxide”
See: http://pubs.acs.org/doi/abs/10.1021/ef200914u
The essence of the error by Essenhigh (and many others) is that he uses the residence time of human CO2 in the atmosphere, which is short, but that doesn’t tell us anything about how long it takes for an injection of an extra amount of CO2 (whatever its source) to bring the whole cycle back into dynamic equilibrium (the “adjustment” time)… It is the same as the throughput of goods and thus capital in a factory (which can be huge) and the financial gain of the same factory, which can be positive, zero or negative, whatever the throughput is.
For some reason, it seems to be very difficult to see the difference between the residence time and the adjustment time, even by very knowledged people…
I don’t see how you can get an exponential growth from a cyclic process using a limited product.
Harold Pierce Jr says:
June 2, 2012 at 5:21 pm
What you write is true, but completely unimportant for the distribution of CO2 and other gases. The only reason that the air is made bone dry for CO2 analyses is that water vapour interferes with the CO2 measurements. As water vapour is extremely variable in any direction, counting CO2 as in dry air makes a comparison of CO2 levels in different altitudes and latitudes far more easy.
The only place where the difference between dry and wet air is important is for the CO2 exchange between oceans (and plant alveoles) and atmosphere. In that case, the pCO2 in the atmosphere is used, thus taking into account the water vapour. The difference between ppmv and pCO2 assumes full water vapour saturation, but even then is quite small.
Bart really has this thing figured out.
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.
Neither. In fact, the regularity indicates that no natural process is responsible for the increase. The regularity is caused by the regularity of the human emissions:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/temp_emiss_increase.jpg
Even in times of economical crisis, the emissions hardly change and in general show a steady increase over time, which results in a near constant increasing increase of what resides in the atmosphere. The year by year variability in atmospheric increase rate is caused by temperature swings, but that largely cancels out over time.
Keith Battye says:
June 3, 2012 at 3:16 am
Bart really has this thing figured out.
Bart is a very good theoretician, but he makes an essential error: he only looks at the inputs. That makes that the human input is only a fraction of the total input and simply disappears in the cycle. And error many here seems to make. But as is proven in the mass balance: the natural sinks are larger than the natural sources, at least over the past 50+ years. Thus it doesn’t make any difference what the height of the natural input is, or what its trend or variancy is, as the only point that counts is the difference between natural inputs and outputs, which is negative all over the years and the human input is the only source of the increase in the atmosphere. That doesn’t need a fast response from the natural sinks. The observed sink rate is about 40 years half life time…
Ferdinand,
I would greatly appreciate it, if you would do a peer review of http://www.retiredresearcher.wordpress.com and let me know where I may have made errors in my analysis. I agree with you that the CO2 data is our best source for following climate change. However, it is a lagging indicator. The effects of anthropogenic emissions on background levels as reported as monthly averages shows up about 10 years after they have been originally put into the air. These effects are added to always changing natural cycles that are indicated by the ice core and other proxie data. You can comment here or on my blog as you wish. Also, you can click on my name and then click on the URL there. I welcome others to do the same.
edim says:
June 3, 2012 at 1:51 am
Interestingly, according to the dCO2 vs T correlation, it doesn’t take warming to rise the atmospheric CO2 – a sufficiently high constant temperature will cause rising CO2 (dCO2 = const).
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.
Ferdinand, no one’s claiming that the natural environment is a net source of CO2, it’s obvious that the annual growth is smaller than the anthropogenic input, so the environment has been a net sink. The claim is that the growth in atmospheric CO2 is determined by global temperature. What do you think would have happened with CO2 if the temparatures haven’t increased since ~1960s? According to the correlation, the growth would be in average let’s say ~0.9 ppm/year instead of 1.45 ppm/year and the total accumulation until now would be ~45 ppm instead of ~80 ppm. So, we would be at ~360 ppm instead of 395 ppm.
Total accumulation is dependent on the average temperature during the period of accumulation. That’s the observed behaviour.
>>Steve Keohane says:
>>June 2, 2012 at 10:20 pm
>> … but do not know the source …
http://www.esrl.noaa.gov/psd/cgi-bin/data/timeseries/timeseries1.pl
Steve McIntyre and Roy Spencer have papers discussing the effects and how the trends differ from IPCC model assumptions.
>> Ferdinand Engelbeen says:
“Again the same discussions com up every few months…”
Well, this tends to happen if someone decides basically mid-sentence to remove himself from the discussion! The topic doesnt go away by itself
>> FerdiEgb says:
“The essence of the error by Essenhigh (and many others) is that he uses the residence time of human CO2 in the atmosphere,”
These numbers are known well enough, so Essenhigh and Barts choice are reasonable and not in “error”. What is missing from your side is any prove that they did anything wrong!
In what way does Essenhighs or Barts choices contradict not your believe, but a value measured in nature?
“Bart is a very good theoretician, but he makes an essential error: he only looks at the inputs. That makes that the human input is only a fraction of the total input and simply disappears in the cycle. And error many here seems to make. But as is proven in the mass balance: the natural sinks are larger than the natural sources, at least over the past 50+ years.”
Wow, a full circle again.. perhaps time to read again, what I wrote yesterday:
Laws of Nature says:
“Essenhigh came up with a model, which basically removes anthropogenic CO2 from the equation due to its low residence time, the published answer by Cawley uses a very similar model to “reinstate” the anthropogenic CO2, but fails to disprove Essenhighs assumptions and conclussions.”
The very reason Essenhigh published his paper was to show that there is indeed another possible solution, taking realistic parameters.
Just you saying its wrong doesnt prove it wrong, I sense a lack of arguments!
Ferdinand Engelbeen says:
“But one can deduce the biological balance from the oxygen balance:”
Here you seem to ignore soil bacteria and the whole NOx-circle.
Ferdinand Engelbeen says:
“The oceans are not the cause:
“Pure on solubility parameters, an increase of 1°C causes an increase of 16 microatm of CO2 in the oceans surface waters, thus back into dynamic equilibrium causes an increase of about 16 ppmv in the atmosphere.”
Over at http://www.seafriends.org.nz/issues/global/acid2.htm#why_problem we can read the following statement:
“The oceans contain far more CO2 than air: 38,000Gt versus 700 Gt (about 50 times). A slight warming of the ocean expels CO2 while becoming more acidic, about 1000-1500Gt per degree C (see graph in part 1 => http://www.seafriends.org.nz/issues/global/global16.gif ) .”
Would you agree to that?
Bart says:
“dC/dt = (Co – C)/tau1 + k1*H
dCo/dt = -Co/tau2 + k2*(T-To)”
It would be interesting if you could change the constants to either support Essenhigh’s or Cawley’s conclussions. And then compare them
All the best regards,
LoN
edim says:
June 3, 2012 at 4:17 am
The claim is that the growth in atmospheric CO2 is determined by global temperature. What do you think would have happened with CO2 if the temparatures haven’t increased since ~1960s? According to the correlation, the growth would be in average let’s say ~0.9 ppm/year instead of 1.45 ppm/year and the total accumulation until now would be ~45 ppm instead of ~80 ppm. So, we would be at ~360 ppm instead of 395 ppm.
You still make the assumption that the growth rate remains the same at a constant (increased or decreased) temperature.
As the seawater temperature changes up and down year by year, it is hard to see that the CO2 growth rate is temperature change related and not absolute temperature related, there are no multi-year periods with a near constant temperature…
If you start at constant 1 ppmv/yr at e.g. 15°C global average sea surface temperature and the next year there is a 0.1°C increase, that would give an increase in the growth rate to ~1.4 ppmv for that second year. The third year there is no further seawater temperature increase, so the CO2 increase rate falls back to ~1 ppmv/year. The influence of seawater surface temperature is short (~1.5 years) to bring the ocean surface layer and the atmosphere in equilibrium for CO2 levels.
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.
Bart says:
June 3, 2012 at 1:21 am
I know, we have been there many times… but…
When I found the glaringly evident temperature to CO2 derivative relationship, I knew I had found proof.
Except that any relationship in the derivatives has zero predictive power for any releationship in the original variables…
Dr Burns says: June 3, 2012 at 4:37 am
Thank you sir! I was taking flak from joelshore on another thread for posting that without providence. I see implications regarding enthalpy.
Just noting that the AIRS satellite has a number of videos for mid-tropospheric CO2 concentrations covering 6 or 7 years now.
Just search “Airs CO2” on Google video.
(they are mainly Youtube products so putting up a direct link would imbed the video in the thread and I don’t think that is necessary).
You will see there is considerable variability and it is entirely possible that someone might measure 500 ppm in Europe or some locality every few days. The numbers have to be averaged out over long periods and there will always be outliers. The Arctic has a strong outburst in the winter months as one of the videos is a polar view.
Also search for “Airs Methane”. With all the Arctic methane bubbles stories going around, it is helpful to see that the actual global data shows Methane comes from everywhere and cycles around the planet extremely fast with the prevailing winds.
How does the CO2 data fit a bell curve with the current rise the left side of the bell? Once oil production goes into terminal decline, CO2 increases should slow, then level off, then drop.
Wow, it seems that I have missed the Salby discussions of April 19 on -again- the same topic… Had a nice trip in Western Australia in the past 5 weeks (Perth to Darwin), should have contacted Dr. Salby, but I suppose he was somewhere at the other side of that (large, did drive over 7000 km…) continent.
Continued (near) exponential growth is a physical impossibility, since fossil fuel resources are finite. The rate of growth in use will fall as price drives conservation and substitution. If one believes the “peak petroleum” predictions, liquid fuels growth will turn negative within a decade or so. Coal and natural gas are more complicated, but these too must eventually stop increasing. From a practical standpoint (say 25 – 30 years horizon), it makes little difference what the historical record says; atmospheric CO2 will continue to increase between about 2.5 and 3 PPM per year.
jrwakefield says:
June 3, 2012 at 6:38 am
Nah, I think all that is just religious crap. Mankind is to blame, repent, and all that.
Have a look at what Prof. Salsby has to say about it;
Bart says: June 3, 2012 at 1:21 am
This question has been solved. The derivative of CO2 tracks the variation in sea surface temperature remarkably well. Temperature drives CO2. Human inputs are rapidly sequestered and have no significant observable impact.
________
Probably true.
I discovered this dCO2/dt relationship with temperature in late Dec2007 and published in Jan2008. And the CO2 signal lags temperature by ~9 months. See
http://icecap.us/index.php/go/joes-blog/carbon_dioxide_in_not_the_primary_cause_of_global_warming_the_future_can_no/
Murry Salby came to the same conclusion in his 2011 video at
The warmists arm-waive that this relationship and resulting lag is a “feedback effect”.
But there is also a CO2-after-temperature lag of ~800 years in the ice core record on a longer time cycle, probably related to deep ocean phenomena.
And there are probably other intermediate cycles as well.
And of course there is the seasonal CO2 “sawtooth”, apparently dominated by the larger Northern Hemisphere land mass.
My hypothesis is that these natural cycles all contribute to the resulting CO2 curve, which is more likely to be a ~sine curve than the subject ~exponential curve.
Natural CO2 flux is much greater than the humanmade component. Furthermore, I have sought and found no human component in the CO2 signal. The increase in atmospheric CO2 appears to be entirely, or almost entirely natural.
P.S.
Apologies for the sentence fragments, … and starting three sentences with “and”. But there are worse sins, like squandering a trillion dollars on global warming nonsense.
I also predicted global cooling in an article written in 2002. If this cooling is severe enough to affect the grain harvest, we will look back on current days with great fondness. Hope I’m wrong, but just in case: Bundle up.
Laws of Nature says:
June 3, 2012 at 4:58 am
As I said, it seems very difficult to see the difference between the residence time of human CO2 in the atmosphere and what happens to any injection of extra CO2 into the same atmosphere…
1. The residence time;
Every year, some 20% of all CO2 in the atmosphere is exchanged with CO2 from/to other reservoirs. Thus if human input ceased, the remaining human CO2 molecules should reduce by about 20% per year (as is seen in the 14C record). That gives a residence time of slightly above 5 years. But be aware: this exchange doesn’t change the total amount of CO2 in the atmosphere. as long as there is balance between inputs and outputs.
2. The adjustment time:
If we may assume that temperature (as seen in the past) is the main driver for CO2 levels, then at a certain temperature, there is a given “normal” CO2 level. Any extra amount of CO2 (whatever its source) above that level would be removed until the equilibrium is reached again. Currently we have a level of 100 ppmv CO2 above the temperature dictated setpoint. That is the driving force which moves extra CO2 into the oceans an plants. This causes an unbalance in the natural inputs and outputs: some 4 GtC (2 ppmv) more CO2 is absorbed by nature than is released. If we should stop to emit any CO2, the 100 ppmv difference would be the same at the start, 98 ppmv next year, 96.2 ppmv, etc… until back to the temperature equilibrium. The adjustment e-fold time therefore is 210/4 or ~53 years, quite a difference with the residence time.
The problem now is that many use the residence time to show that the human contribution is negligible, but that only shows how fast the human CO2 molecules are replaced by natural molecules, but that is completely irrelevant of what happens to the total amount in the atmosphere, which still is (near) completely caused by the human addition.
To illustrate that, here a graph of what happens if humans should have added all emissions to data at once some 160 years ago:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/fract_level_pulse.jpg
All “human” CO2 is gone in about 60 years, while CO2 levels remain higher even after 160 years. The extra level above the old equilibrium still is caused by the initial human injection, even if no single human CO2 molecule is left…
Ferdinand Engelbeen says:
“But one can deduce the biological balance from the oxygen balance:”
Here you seem to ignore soil bacteria and the whole NOx-circle.
soil bacteria are included in the oxygen balance (they use O2 to produce CO2). NOx is not, but how much does that change the oxygen balance?
A slight warming of the ocean expels CO2 while becoming more acidic, about 1000-1500Gt per degree C
I fear that the NZ coalition is completely wrong here: expelling CO2 from the oceans makes the oceans more alkaline, which is not observed and the DIC (totally dissolved inorganic carbon) content of the ocean surface is increasing, thus these are absorbing more CO2… Moreover as said previously, it doesn’t make any difference how much CO2 is in the oceans, only the CO2 pressure difference between the atmosphere and the oceans matters. If the oceans heat up 1°C, that gives at maximum 16 ppmv extra in the atmosphere, no matter how much resides in the oceans.
Hi Ferdinand,
I hope you are well.
For the record, I have no problem with CO2 measurement accuracy. The CO2 measurements at Barrow, Mauna Loa, the South Pole and many other sites correlate well and make sense.
Also, we don’t need to discuss yet again your “mass balance” argument – I will leave that to you and Richard C. I agree with Richard – the system just does not work the way you say it does.
Humanmade CO2 emissions are very small compared with natural CO2 flux, which is not only huge on a seasonal basis, but also huge on a daily basis.
I would really like you to be correct, because if you were, humanity would survive better than under my most probable scenario, which is moderate or severe global cooling.
The only impact I can see of humanmade CO2 emissions is that we are making little flowers happy.
To counter the wild claims of the global warming alarmists, I leave all of you with this note from George Carlin, and wish you a very pleasant Sunday. 🙂
Regards, Allan
Warning: Language.
George Carlin – The Planet is Fine !