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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Correction. http://www.retiredresearcher.wordpress.com
Allan MacRae says:
June 4, 2012 at 4:05 am
First, you totally miss the point of the urban CO2 readings – it’s about Ferdinand’s mass balance argument, which fails not only on a seasonal basis but even on a daily basis, imo.
The mass balance must be always obeyed, no matter what happens where. But that is only calculatable on a yearly basis, as we only have yearly inventories of the emissions. Urban readings anyway are irrelevant for the mass balance, as are all readings in the lowest few hundred meters above land. That represents only 5% of the air mass where the CO2 is not well mixed due to a lot of local sources and sinks. In the rest of the global air mass, the yearly averaged measurements are all within 2 ppmv for the same hemisphere and 5 ppmv between the hemispheres, where the SH lags the NH but the trends are exactly the same:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/co2_trends_1995_2004.jpg
Allan MacRae says:
June 4, 2012 at 5:08 am
Carrick – Here are just a few C13/C12 articles I found in 2 minutes of searching – there are many more.
Allan, I am afraid that Dr. Spencer was quite wrong with his article and I have commented there extensively and on his blog, by mail, which he published. It is clearly not his field. The main problem for the origin of the d13C decline could be the release by biomass degradation, but the oxygen balance shows that total biomass is growing…
Other main sources of low 13C are either too small (or also mainly of human origin like CH4), or unknown, but there is no reason to assume that these started to emit increasingly together with the human emissions. For underwater volcanoes: that CO2 is captured by the deep oceans in the deep oceans, which are near zero per mil d13C.
Jeeeuz! Does anyone have any idea what is going on with these friggin pastebin services today. ?
Are they rigged to ban their use from WUWT or what ?!
The last link I posted just returns an empty page , not even your basic empty html tags, Just sweet F.A.
The same link works fine locally and if I open the link in a new tab (still blank at first) then I do refresh , finally I get to see my image.
Now that looks to me like they must be checking HTTP_REFERRER and if it is this site they refuse to serve the image.
Someone care to check that?
http://imagebin.org/index.php?mode=image&id=215058
http://imagebin.org/index.php?mode=image&id=215060
If I’m going quietly mad it would be handy to have so confirmation too, then I can go and seek treatment 😉
FerdiEgb says:
June 4, 2012 at 1:06 am
“…the temperature was below your baseline for the full period 1900-1935, average -0.2°C.”
The impetus to CO2 is approximately proportional to dT + 0.5, where dT is the temperature anomaly relative to whatever the baseline is in the data. At no time in the modern era or even a little before would that quantity have been negative or zero. In fact, it suggests that CO2 will keep rising for some time to come, until long term limiting factors kick in.
The rest of your post is an appeal to magick.
P. Solar says:
June 4, 2012 at 8:49 am
You’re not mad. The images are not coming through.
Lance Wallace says:
June 4, 2012 at 2:38 am
“…but didn’t see what values you obtain for tau2 or the other parameters and wondered whether you cared to present the values here and perhaps comment on their interpretation.”
tau2 is only required to be large relative to the record length, so that the “equilibrium” level of CO2 (the level to which the current temperature is driving it) will be approximately the integral of the temperature anomaly over the relevant time interval. I need not have put in a term involving it at all to match the data, but there must be some ultimate limit to the equilibrium value, and a time constant is one way of enforcing one. For this exercise, I simply set the feedback gain to zero (tau2 = infinity).
The value of k2 is 0.2 and the value of To is 0.5. These were chosen to be consistent with the data.
The value of k1 was chosen to be 0.5. This is consistent with the IPCC insistence that roughly half of the emitted CO2 is almost immediately dissolved in the oceans. As you can see, I tried a variety of values for tau1, with the most realistic ones being on the order of 3 years or less to be consistent with the data. With such values of tau1, the contribution from H becomes negligible, so the value of k1, which must be less than or equal to one in any case, is fairly moot.
In the last figure you can see the decline of industrial production after 1990 in the former East Block.
Ferdinand, thanks for taking the time to respond to Allan’s comments. That was helpful for me at least. (I don’t claim to be an expert, nor do I choose to argue as if I were, on this topic.)
Allan, I suspect you know full well my comments weren’t intended in a condescending manner (though your original one and your responses clearly were), I suggest that you read here. I’d suggest there’s quite a bit left for you to learn before you can argue as an expert on the matter of atmospheric measurements in general, and CO2 isotopic measurements in particular.
Bart:
From your experience, I assume you are referring to the thread on McIntyre’s blog as that and Nick’s blog where you repeated the same errors are our only real brush.
I’ll let others judge who came out on top on that discussion. 😉 You are the one who claimed you can’t have negative delays in an impulse response function and confused physical causality with signal causality, not me.
Since your experience of me making “elementary errors” is so great, I’m sure you can point to one or two of them from those threads (and maybe including your admission after approximately 50 ad hominems from you, I didn’t count them, but I should have, that you were wrong).
if you take the derivative of a function, say I(tau), if I(tau) = 0 for tau < 0, then I'(tau) = 0 for tau < 0. Taking derivatives in general does not induce a group delay, phase shifts are different than temporal shifts.
This is a bit of a red herring. You were plotting derivative of CO2 against temperature, I showed that there was a delay both computationally and confirmed it with a visual plot.
But in any case, centered average can splatter some high frequency noise into negative time bins, but it doesn’t shift the low-frequency components, and you can still deduce the delay using that. (Or directly numerical as I also did.) The fact the two agree shows your argument doesn’t matter.
If you want to make an argument using an other quantity such as S_CO2, you should make it based on that quantity, not using a quantity that doesn’t show what you claim to be arguing.
P. Solar:
It’s the fact that CO2 changes that causes the forcing. I wouldn’t have plotted it the way Bart did, but that’s how he did it, and that’s why I addressed the delay the way I did.
I expected the delay for the “fast” response to be about two months, because I had previously computed it for S_CO2 versus global mean temperature. I realized from that analysis that you needed better resolution than one month to pull out the actual delay (because it’s between one and two months).
There is a real physical effect as you correctly pointed out relating to response of the oceans to atmospheric temperature in which as the temperature rises, CO2 comes out of solution in the ocean. However, there is a rather large delay associated with that, and it’s not impulsive, because there is a latency that depends on depth in the response of mean ocean temperature to forcings from atmospheric temperature. It’s on the order of years.
I knew from previous discussions that any effect where you see near simultaneous response of atmospheric temperature and atmospheric concentration of CO2 can’t be explained by CO2 dissolution from the ocean. So what Bart was showing wasn’t based on a physical understanding of the processes and his conclusions were unphysical.
(He’s not really big on admitting mistakes so don’t expect a “recall” of this theory of his anytime soon, in fact, even when he makes a mistake, it sounds like “We were both right…” even when he was completely wrong.)
You may have heard of 350.org.
Well here I am with 500.org.
Anything to try and soften the inevitable coming macro decline. But even 500 will be a mere band aid against massive forces.
Carrick says:
June 4, 2012 at 10:42 am
“but it doesn’t shift the low-frequency components”
Switch to a twelve month average, and see how your argument holds up.
“You are the one who claimed you can’t have negative delays in an impulse response function and confused physical causality with signal causality, not me.”
Obviously, you cannot have real negative delays, just apparent ones indicated by the particular analysis tool. And, I showed your argument was inapplicable to the case at hand. As was Nick’s criticism. I was right about the transfer function, and remain so to this day.
Yes, I jumped to a conclusion about a negligible matter (because you were being such a —-) but quickly came clean about it and put it aside. You should take a lesson from that experience – it does you no good to argue an untenable position into the ground. The best thing to do is come clean about it and move on to more substantive issues. There is a quote attributed to the great British economist Sir Maynard Keynes, who was known to change his positions, sometimes in mid-argument. When challenged on this by a critic, he fixed him with an unwavering stare and replied: “When I find that I am wrong, I change my mind. What do you do?”
Here is some advice: when you find yourself holding the absurd position that temperature responds to the rate of change of CO2… stop digging. Your arm-waving here merits no further response.
Carrick says:
June 4, 2012 at 10:59 am
“I knew from previous discussions that any effect where you see near simultaneous response of atmospheric temperature and atmospheric concentration of CO2 can’t be explained by CO2 dissolution from the ocean.”
You aren’t looking at “atmospheric concentration of CO2”. You are looking at its derivative. Do you know the differential (pun intended)?
You are wrong. Ridiculously, uproariously, hilariously so. Admit it, and move on, and people will think better of you.
Bart says:
June 4, 2012 at 9:25 am
FerdiEgb says:
June 4, 2012 at 1:06 am
“…the temperature was below your baseline for the full period 1900-1935, average -0.2°C.”
The impetus to CO2 is approximately proportional to dT + 0.5, where dT is the temperature anomaly relative to whatever the baseline is in the data. At no time in the modern era or even a little before would that quantity have been negative or zero. In fact, it suggests that CO2 will keep rising for some time to come, until long term limiting factors kick in.
OK, that is the “fudge factor” to match the increase rate and its variability. No problem with that. But still so, if the period 1900-1960 still was positive, I am quite interested how much CO2 that injected in the atmosphere (or how little there was at the beginning of the 20th century). And further back to the LIA which was, depending of the reconstruction, 0.3-1.0°C cooler than today. Still no problem for CO2 levels? Even further back: near 100,000 years of glacials…
The rest of your post is an appeal to magick.
I am sure that you are a very good theoretician, but sometimes one need to bring that kind of people back to the ground on their two feet. What you have worked out is theoritically magnificent, but there are some practical problems:
There is no natural process that I know of or ever heard of or ever read of that can deliver 70 ppmv (and according to your formula far beyond that in the future) in only 50 years, only based on a sustained increase of a few tenths of a °C.
If you think that is possible, please give an indication what process that might be with references.
FerdiEgb says:
June 4, 2012 at 6:15 am
Myrrh says:
June 3, 2012 at 5:13 pm
Despite the low data density, the CO2 contour in troposphere and stratosphere confirms the direct measurements near the ground that suggest a CO2 maximum between 1930 and 1940.
Myrrh, I have had a lot of discussions with the late Ernst Beck about the validity of his data. The tropospheric data don’t confirm the direct measurements on the ground, simply because these were sometimes hundreds of ppmv higher than near ground. Shows that the data are completely useless. Unfortunately so. That is also the case for most data which show the 1942 “peak”, mostly taken at places with a huge diurnal variation and extreme variation. That alone already shows that the data are highly contaminated by local sources.
Ferdinand we’ve been through this argument before – your premise begins with belief in “well-mixed global” so everything you see as out of the ordinary is “local contamination” – but, again, until you can show how Keeling arrived at his “well-mixed” claim then all that exists in reality is local.
AIRS data found that; the pictures they showed downplayed what they actually said in their conclusion – that to their astonishment carbon dioxide was not at all well mixed, but lumpy, and so couldn’t be playing any major role in ‘global warming’, and, that they needed to go and understand wind systems to get a grasp of what was going on.
There is no, none, zilch, nada, eff all, way that Keeling could establish such a thing as “well-mixed” background level from where he was measuring. It is simply not physically possible to tell apart even if such a creature existed as “well-mixed global”. He was measuring local and they are still measuring local, arbitrarily deciding what local they will include and what not to present this mythical “well-mixed global”.
I have shown you the man had an agenda, his only interest was to show a rise in man-made CO2 levels – so his curve. You may well be shocked by the enormity of what it takes to link all those stations into his and Callendar’s avowed agenda, but as we’ve had reams and reams of proof, this is done regularly and with coordinated exactness in manipulating world temperature records.
I’m sorry Ferdinand, you may well trust this, but nothing I’ve learned about it shows Keeling and Callendar as anything but cherry pickers who came up with the unproven idea that there is such a thing as “well-mixed background”. AIRS did not find it. AIRS will not release top of troposphere or bottom of troposphere, why not?
Because they can fudge the mid troposphere regardless they came out with the HONEST conclusion that “it was not at all well-mixed, but lumpy” and was “insignificant in global warming”.
It’s lumpy, because, it’s all local.
All you’re doing is what Callendar did, taking out everything that doesn’t fit your unproven premise.
And you believe it because they kept repeating that it exists. What that means to all the hard and dedicated work you’ve built on it, I can only imagine, but first prove “well-mixed background” exists, because Callendar showed not such thing in his cherry picking:
“Considering Figure 8 we can see that Callendar selected only the lowest sample values and omitted several data sets.”
The data at Mauna Loa are sometimes contaminated by local sources too, but not more than +/- 4 ppmv, compared to e.g. Giessen where the longest 1939-1941 series was taken with a variability of 68 ppmv (1 sigma!). How can one deduce a “global” signal from such a series?
As above, their adjustments are arbitrary, there is no physics that can separate a supposed ‘global’ signal from local production. There is no global signal, it’s all local. Global is lumpy.
There’s a huge amount of data of this lumpy CO2, which, is fully part of the Water Cycle, and which, is one and a half times heavier than air so will always sink displacing Air without work being done – either way, however high it gets it will come down to Earth where plants exist waiting for it…
And, because it is heavier than Air is will not readily rise into the atmosphere. It takes wind, or heat as gases expand, or as it joins with water vapour rising into the cold heights as carbonic acid where it condenses into rain releasing its heat in the cold heights, or, it can be expelled direct into the heights by volcanic force, or planes. And all that within the wind systems, which do not cross the equator but stick to their own hemispheres, winds are volumes of Air on the move because of the difference in temperature, pressure – hot air rises and cold sinks – this is convection, exactly what happens in a classroom when a bottle of scent is opened… There is no “spontaneous diffusion of molecules into empty space” – Air is not empty space. That’s why we have sound, because the molecules don’t “spontaneously diffuse as per ideal gas law” – but vibrate where they are making their neighbour volumes of gas vibrate passing on sound, and then stop vibrating.
All this to show, there is no physics which makes “well-mixed global background”. That premise has to be rejected, or empirically and by real physics proved..
Myrrh,
If you look at the at the raw event flask data, you will find many spikes in the CO2 data that are flagged and not included in monthly averages. Most of these spikes are not errors because there is usually a corresponding spike in the 13CO2 data. The recorded monthly averages represent background levels that vary with latitude but not longitude. I think that cold water in clouds is absorbing the CO2 and transporting it to the upper atmosphere and the poles.This process is moderating the measured concentration near the surface and gives the appearance of “well mixed”.
Also, it can explain the higher concentrations in the upper atmosphere in the mid latitudes. The equator is the source and the cold water near the poles are the sinks.
Looks a lot like the growth curve for human population. Try fitting one on top of the other. Good fit eh? Not surprising. We all make our little contribution.
Bart:
You’re the one who was originally looking at dS_CO2/dt versus HADSST and now I’m wrong.
LMAO. Sure.
Well, I have worked out the simplest formula of all to mimic the CO2 increase in the atmosphere. That is just a start, based on yearly averages for temperature and CO2 levels, so that may need fine tuning to monthly values and the coefficients need fine tuning too.
Here is the simple formula:
CO2(new) = CO2(old) + 0.55*emissions + 4*dT
That holds for any change in temperature, any period or any amount of emissions (the latter pure coincidence for the past 110 years…). Even ice ages and interglacials, but for longer periods the factor 4 for dT increases to a factor 8 (you know, that 800 year lag via the deep oceans…).
Here the plots:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/acc_der_temp.jpg
and
http://www.ferdinand-engelbeen.be/klimaat/klim_img/acc_temp_atm.jpg
Discussion: The first term is essentially the integral of Bart’s first formula:
dC/dt = (Co – C)/tau1 + k1*H
where k1 = 1 and H = emissions, C is the current CO2 level, Co the pre-industrial level at ~290 ppmv, the latter influenced by temperature, at a rate of about 8 ppmv/°C.
As the current difference is over 100 ppmv, a small shift in Co has little effect on Co – C and that change can be neglected for the current period. tau1 is large, so that only about halve H is removed, despite the large Co-C difference.
Co in my opinion is simply directly correlated with absolute temperature and not anomaly dependent. That is one difference with what Bart made. The other is that the except for the shift in Co, the influence of temperature on CO2 levels is constrained to temperature differences, with a finite amount and time duration. That means that for fast changes (1-3 years, ocean surface, vegetation), the influence is about 4 ppmv/°C temperature difference, while for longer time spans that increases to 8 ppmv/°C.
The essential difference with Bart’s solution is that except for the “equilibrium” setpoint, the influence of the emissions and the temperature influence on CO2 levels are completely independent of each other, where the temperature influence is mainly visible in the variability of the increase rate and around the trend, while the influence of the emissions is mainly visible in the average height of the increase rate and in the trend itself.
FerdiEgb says:
June 4, 2012 at 1:34 pm
“The essential difference with Bart’s solution is that…” Ferdinand’s solution does not match the derivative of CO2 to the temperature anomaly, as is clearly indicated by the data. Hence, Ferdinand’s model fails to reflect the real world.
Myrrh says:
June 4, 2012 at 12:41 pm
AIRS data found that; the pictures they showed downplayed what they actually said in their conclusion – that to their astonishment carbon dioxide was not at all well mixed, but lumpy, and so couldn’t be playing any major role in ‘global warming’
The CO2 data from AIRS looks lumpy, because their scale is only +/- 4 ppmv. If you see a variability of 2% of full scale, while about 20% of all CO2 goes in and out the atmosphere over the seasons, then I call that well-mixed. How much difference do you think that it makes for global warming (as far as there is) if you have 396 ppmv or 404 ppmv? It is the 100+ ppmv increase which may make the difference…
About Keeling: I have the highest respect for him. He was only interested in better CO2 measurements and devoted all his life on that one item, including the invention of new measurement methods of unprecedented accuracy and allowing continuous measurements. Read his autobiography for what obstructions he did overcome to continue the measurements at Mauna Loa and other stations against the administrations:
http://scrippsco2.ucsd.edu/publications/keeling_autobiography.pdf
I have not the slightest interest in complot theories that the CO2 data are manipulated in any way. I have controlled them from raw voltage data to what is openly archived. There is no manipulation. Or how can you convince hundreds of people involved from some 70 baseline stations (+400 others over land), from different countries, and different instutions to collectively and continuously lie about the data? Even the pensioners, that they still shut their mouth over such huge scientific scandal?
Please, it is not because you don’t like the data that they must be proven false at all cost, you only disprove yourself as a valid opposant on other items where the other side is not on such firm ground…
Bart says:
June 4, 2012 at 1:45 pm
Ferdinand’s solution does not match the derivative of CO2 to the temperature anomaly, as is clearly indicated by the data. Hence, Ferdinand’s model fails to reflect the real world.
Peanuts. If I should use the monthly values like you did, that would show a better match, but I can return the favor: your temperature influence doesn’t match the CO2 trend as good as the emissions:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/temp_co2_1900_2004.jpg
where a temperature change of halve the scale gives 5 ppmv change in CO2 levels, but the whole scale should give a 80 ppmv increase?
And:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/acc_co2_1900_2004.jpg
a near perfect match…
Thus we may agree that the temperature variation is a real world perfect match for the variability in increase rate, while the emissions are a real world perfect match for the trend itself. But I think that it is of more interest to know what the cause is of the trend than the cause of the variability of the increase rate…
BTW, I am still interested in your backcalculation to 1900 and over the LIA. For the latter you may use any recontruction, except Mann’s HS, for obvious reasons…
And already a process found which can deliver 70 ppmv CO2 with a a continuous elevated temperature of a few tenths of a degree C?
Bart and Ferdinand,
I submit my statistical model is a better fit than both and better satisfies mass balance. It includes both anthropogenic and natural sources. http://www.retiredresearcher.wordpress.com.
To Ferdinand Engelbeen /
Since there have been a number of recent posts/threads on CO2 and the Carbon cycle here at WUWT, I have been wondering when you might show up!
Re your comment @ur momisugly 6/3 – 2:10 a.m.: You state in part, “The net result over very long periods is that an increase of 1 deg. C in ocean temperature gives some 8 ppmv increase in CO2. Thus the ~ 1 deg. 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…” I have always been impressed by this argument (which you often make) which turns on the observed (or better, reconstructed) glacial-interglacial temperature vs. CO2 relation. But I am somewhat puzzled by the 1 deg. C = 8 ppmv CO2 premise, for in that case then either (1) the resulting shifts in temperature increase and CO2 increase are significantly smaller than those reconstructed from ice cores, or (2) granted that the glacial-interglacial temp. increases at the poles were greater than the estimated globally averaged increases [5-6 deg. C], then during the G-IG transitions, CO2 was not at all “well mixed.” There may be something packed into the “ocean temperature” qualification you make, but even at or near the poles, I doubt that ocean temperatures increased nearly as much as ice cap temperatures. They were significantly warmer at glacial maxima to begin with. So, same problem. Does my concern make any sense?
FerdiEgb says:
June 4, 2012 at 2:30 pm
“…your temperature influence doesn’t match the CO2 trend as good as the emissions:”
Sure it does. You forgot to integrate, since it is the CO2 rate of change which is proportional to temperature.
fhhaynie says:
June 4, 2012 at 2:49 pm
I will have to look it over more carefully when I have a moment to spare. However, this plot is not something I think I agree with. As I believe CO2 is essentially controlled by temperature, I do not see “controls” making much difference.
…which is proportional to temperature anomaly.