Guest post by Lon Hocker
Abstract
Differentiating the CO2 measurements over the last thirty years produces a pattern that matches the temperature anomaly measured by satellites in extreme detail. That this correlation includes El Niño years, and shows that the temperature rise is causing the rise in CO2, rather than the other way around. The simple equation that connects the satellite and Mauna Loa data is shown to have a straight forward physical explanation.
Introduction
The last few decades has shown a heated debate on the topic of whether the increase of CO2 in the atmosphere is causing rising temperatures. Many complex models have been made that seem to confirm the idea that anthropological CO2 is responsible for the temperature increase that has been observed. The debate has long since jumped the boundary between science and politics and has produced a large amount of questionable research.
“Consensus View”
Many people claim that anthropological CO2 is the cause of global warming. Satellite temperature data, http://vortex.nsstc.uah.edu/data/msu/t2lt/uahncdc.lt, and Mauna Loa CO2 measurements, ftp://ftp.cmdl.noaa.gov/ccg/co2/trends/co2_mm_mlo.txt, are well accepted and freely available to all researchers. Figure 1 shows a plot of the Ocean Temperature Anomaly from the satellite data shows a general rising trend. Shown along with the temperature data is a simple linear model showing the temperature rise as a linear function of CO2 concentration. This shown linear model is:
Temperature Anomaly = (CO2 -350)/180
No attempt has been made to optimize this model. Although it follows the general trend of the temperature data, it follows none of the details of the temperature anomaly curve. No amount of averaging or modification of the coefficients of the model would help it follow the details of the temperature anomaly.
Figure 1: Ocean Temperature Anomaly and linear CO2 model
Derivative approach
An alternate approach that does show these details is that the temperature anomaly is correlated with the rate of increase of CO2. I discovered this independently and roughly simultaneously with Michael Beenstock and Yaniv Reingewertz http://economics.huji.ac.il/facultye/beenstock/Nature_Paper091209.pdf.
Applying this model to the Mauna Loa data not only shows the overall trend, but also matches the many El Niño events that have occurred while satellite data has been available. The Figure 2, shows the derivative model along with the observed Ocean Temperature Anomaly. The model is simply
Temperature Anomaly = (CO2(n+6) – CO2(n-6))/(12*0.22) – 0.58
where ‘n’ is the month. Using the n+6 and n=6 values (CO2 levels six months before and six months after) cancels out the annual variations of CO2 levels that is seen in the Mauna Loa data, and provides some limited averaging of the data.
The two coefficients, (0.22 and 0.58) were chosen to optimize the fit. However, the constant 0.58 (degrees Celsius) corresponds to the offset needed to bring the temperature anomaly to the value generally accepted to be the temperature in the mid 1800’s when the temperature was considered to be relatively constant. The second coefficient also has a physical basis, and will be discussed later.
Figure 2: Ocean Temperature Anomaly and derivative CO2 model
There is a strong correlation between the measured anomaly and the Derivative model. It shows the strong El Niño of 1997-1998 very clearly, and also shows the other El Niño events during the plotted time period about as well as the satellite data does.
Discussion
El Niño events have been recognized from at least 1902, so it would seem inappropriate to claim that they are caused by the increase of CO2. Given the very strong correlation between the temperature anomaly and the rate of increase of CO2, and the inability to justify an increase of CO2 causing El Niño, it seems unavoidable that the causality is opposite from that which has been offered by the IPCC. The temperature increase is causing the change in the increase of CO2.
It is important to emphasize that this simple model only uses the raw Mauna Loa CO2 data for its input. The output of this model compares directly with the satellite data. Both of these data sets are readily available on the internet, and the calculations are trivially done on a spreadsheet.
Considering this reversed causality, it is appropriate to use the derivative model to predict the CO2 level given the temperature anomaly. The plot below shows the CO2 level calculated by using the same model. The CO2 level by summing the monthly CO2 level changes caused by the temperature anomaly.
Month(n) CO2 = Month(n-1) CO2 + 0.22*(Month(n) Anomaly + 0.58)
Figure 3: Modeled CO2 vs Observed CO2 over Time
Not surprisingly the model tracks the CO2 level well, though it does not show the annual variation. That it does not track the annual variations isn’t particularly surprising, since the ocean temperature anomaly is averaged over all the oceans, and the Mauna Loa observations are made at a single location. Careful inspection of the plot shows that it tracks the small inflections of the CO2 measurements.
The Mauna Loa data actually goes back to 1958, so one can use the model to calculate the temperature anomaly back before satellite data was available. The plot below shows the calculated temperature anomaly back to 1960, and may represent the most accurate available temperature measurement data set in the period between 1960 and 1978.
Figure 4: Calculated Temperature Anomaly from MLO CO2 data
Precise temperature measurements are not available in the time period before Satellite data. However, El Niño data is available at http://www.cpc.noaa.gov/products/analysis_monitoring/ensostuff/ensoyears.shtml making it possible to show the correlation between the calculated temperatures and the and El Niño strength. Note that the correlation between temperature anomaly and El Niño strength is strong throughout the time span covered.
Figure 5: Calculated Temp CO2 from CO2 and ENSO data
An Explanation for this Model
The second free parameter used to match the CO2 concentration and temperature anomaly, 0.22 ppm per month per degree C of temperature anomaly, has a clear physical basis. A warmer ocean can hold less CO2, so increasing temperatures will release CO2 from the ocean to the atmosphere.
The Atmosphere contains 720 billion tons of CO2 (http://eesc.columbia.edu/courses/ees/slides/climate/carbon_res_flux.gif), the ocean 36,000 billion tons of CO2. Raising the temperature of the ocean one degree reduces the solubility of CO2 in the ocean by about 4% (http://www.engineeringtoolbox.com/gases-solubility-water-d_1148.html)
Figure 6: Solubility of CO2 in water (While CO2 solubility in seawater is slightly different than in pure H2O shown above in Figure 6, it gives us a reasonably close fit.)
This releases about 1440 billion tons of CO2 to the atmosphere. This release would roughly triple the CO2 concentration in the atmosphere.
We have seen what appears to be about a 0.8 degree temperature rise of the atmosphere in the last century and a half, but nowhere near the factor of three temperature rise. There is a delay due to the rate of heat transfer to the ocean and the mixing of the ocean. This has been studied in detail by NOAA, http://www.oco.noaa.gov/index.jsp?show_page=page_roc.jsp&nav=universal, and they estimate that it would take 230 years for an atmospheric temperature change to cause a 63% temperature change if the ocean were rapidly mixed.
Using this we can make a back of the envelope calculation of the second parameter in the equation. This value will be approximately the amount of CO2 released per unit temperature rise (760 ppm/C)) divided by the mixing time (230 years). Using these values gives a value of 0.275 ppm /C/month instead of the observed 0.22 ppm/C/month, but not out of line considering that we are modeling a very complex transfer with a single time constant, and ignoring the mixing time of the ocean.
Conclusion
Using two well accepted data sets, a simple model can be used to show that the rise in CO2 is a result of the temperature anomaly, not the other way around. This is the exact opposite of the IPCC model that claims that rising CO2 causes the temperature anomaly.
We offer no explanation for why global temperatures are changing now or have changed in the past, but it seems abundantly clear that the recent temperature rise is not caused by the rise in CO2 levels.
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Lon Hocker describes himself as: “Undergrad physics at Princeton. Graduate School MIT. PhD under Ali Javan the inventor of the gas laser. Retired president of Onset Computer Corp., which I started over 30 years ago. Live in Hawaii and am in a band that includes two of the folks who work at MLO (Mauna Loa Observatory)!”
Data and calcs available on request
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kim says:
June 9, 2010 at 1:27 pm
Do you mean ‘nowhere near the factor of three rise of CO2 concentration’ in the second to last paragraph before the Conclusion?
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You are exactly right. Thanks for catching that! Sorry for being so late responding.
kramer says:
I agree with your basic points here but just have one small correction: the swings of ~12 C in temperature seen in the ice core records reflect the larger variations that occur in the polar regions and are understood to correspond to global temperature swings of only about half that amount (i.e., around 6 C).
John Finn says:
June 9, 2010 at 3:59 pm
“The only reason the ‘model’ appears to work is due to the fact that both CO2 and temperatures have been rising in the last few decades. If temperatures started to fall the model would break down.”
That could definitely be said of some reconstructions which share no fine details except for a superficial trend, e.g., comparisons of absolute CO2 with temperature anomaly. However, the level of fine correlation here is compelling.
Almost all of the objections I have read here rely on the ice core reconstructions for refutation. This is putting an awful lot of faith in an artifact which, by its very nature, cannot be validated against actual measurements in the distant past. I saw one citation of the isotopic ratio – but this, again, is based on a hypothesis which cannot be directly verified.
Some people seem to think the 0.58 degree offset is significant. But, in fact, this is merely an artifact of the baseline chosen for the temperature anomaly. All it means is that, with a proper baseline chosen, CO2 level is well represented as a scaled and low pass filtered version of temperature. The inverse of this relationship, temperature sensitivity to CO2 being represented by a high pass response, is a type of dynamic rarely observed in nature.
Good story, but as a few readers (e.g. Richard Telford @ur momisugly1:43)pointed out, the reasoning that ENSO events have been recognized since 1902 and thus are not caused by CO2 is pretty weak. Much stronger is the argument, not proposed in the article, but much more valid , that ENSO events are essentially a release of latently built up heat over many years, released intermittently with 3-5 year intervals (at least in the last 50 years). Since the tight correlation presented does not show these preceding heat build-up years, it is a fair conclusion that CO2 follows the T, which was something we already knew from other lines of evidence (Ice core data). In between all the comments more errors and mistakes have been introduced that might need some correction. (Steven Goddard @ur momisugly 12:56) Reefs are not formed in the tropics due to lower CO2 solubility. They are formed in the tropics because most reef building organisms really like that warm water. Cold water limestones are also possible and have been documented (south of Australia) but are just not as dominant and pretty as the tropical reefs and associated carbonate sands. Secondly (BobN @ur momisugly2:58) the ocean is not the only Carbon sink. Vegetation (all vegetation, including algae in the ocean) is the other big one. The discrepancy between the annual increase in CO2 and the “human output” has been a constant difficulty within the climate science. A satelite was launched recently to search for the missing CO2; the deployment failed, so we are still in the dark. With oceans being undersaturated and the Global CO2 cycle being some 40 times larger than the total human output it still is a bit of a conundrum (the annual uptake of CO2 by oceans alone is more than 10 times the annual human CO2 production) why not all CO2 is cycled through, except of course if one accepts that a warmer ocean takes up less than a colder one, or , for that matter, out-gasses at the same time. Lastly, (back to Richard), the Isotope signature has been identified dating back to late 1700 early 1800, where lower isotopes (biogenic CO2) almost immediately showed up in properly dated cored reef sections, well before any global warming has been identified; in effect , early 1800 still saw glacial expansion en very cold weather. The isotope signature reflects the onset of coal burning, and illustrates the rapid and immediate uptake of CO2 by oceans. It also is nothing more than a signature, like a drop of ink in a large aquarium, cycled through, with an annual addition for as long as we burn fossil fuels. It says nothing about increased CO2 concentrations. Just like water is cycled endlessly. If we could put a signature on water molecules, we would notice an increased signature as well, since we cycle an awful lot of water (and much more now than 150 years ago); and just like CO2 there is generally (certainly potentially) more water vapor in the air during warm times than cold times (one of the dreaded feedbackloops).
Xi Chin says:
June 9, 2010 at 3:37 pm
and
Les Johnson says:
June 9, 2010 at 6:32 pm
Thanks for your input. You are no doubt leading us in the right direction. There are a lot of folks posting here that understand parts of this vastly better than I do, and I am thrilled by the insights that have been shown. Feel free to work on this any way you like and carry concept forward! I just wanted to escape the apparently incorrect hypothesis that the temperature anomaly is linearly related to the CO2 concentration.
Bart,
“No, the reason given is that the CO2 tracks the El Nino events, and El Nino is NOT caused by CO2.”
But El Nino isn’t caused by temperature either. It still doesn’t show CO2 dependence on temperature. It could be El Nino bringing CO2-rich water to the surface.
“Applying this model to the Mauna Loa data not only shows the overall trend…”
No, it doesn’t. The trend is determined by the constants 0.58 and 0.22, which are obtained by fitting. To see this, you can go to Fig 3 and add the curve found by setting the temp anomaly to zero, just keeping the constants. You get a straight line which fits the CO2 data about as well as the red curve. With no temperature info at all.
“Using two well accepted data sets, a simple model can be used to show that the rise in CO2 is a result of the temperature anomaly, not the other way around.”
——–
Sounds like a “chickens make eggs, but eggs don’t make chickens” argument.
I think my previous post was not understood, but Phil makes the same point independently.
Conventional wisdom is that the atmospheric CO2 is rising quite steadily, especially since the start of the industrial age. However the carbon budget shows that only about half of man’s input is seen as CO2 in the atmosphere, and the rest goes into the ocean and biosphere. (I don’t know why the posting ignores these basic facts about the carbon budget which give the direction of the CO2 flow).
Now, what I say is that this fraction of a half is modulated by the ocean temperature being slightly less when the ocean is warmer. This means atmospheric CO2 would rise faster when the ocean is warmer and more slowly when it is cooler. This is exactly what is seen, but the mechanism is much more mundane and conventional. However, it is impressive that such a signal was seen even if their explanation is wrong.
Xi Chin says:
June 9, 2010 at 3:37 pm
“You need to use the backward differential only and make sure that you do not pollute the predictor with future information.”
He did it right to get a zero group delay, exp(j*w*T/2)-exp(-j*w*T/2) = 2*cos(w*T), i.e., the response is real. Do a backwards one, and the group delay is T/2.
BobN says:
June 9, 2010 at 2:58 pm
“Based on the amount of CO2 emitted from the burning of fossil fuels, the increase in atmospheric CO2 concentrations should actually greater than what has occurred. The oceans are absorbing CO2, not releasing it.”
What that proves is that we are dealing with a feedback system in which the sinks expand or contract with the sources after a particular lag time, regulating the overall level and decreasing the sensitivity, in the normal way feedback loops do. What changes the output level significantly in such a system is NOT increasing the input, because that is what the feedback reacts against, but changing the equilibrium position, which in this case is quite apparently directly sensitive to temperature.
“I wish you would use a little more discretion or prescreening before posting guest posts with what are clearly flawed analyses.”
Clearly, you are not familiar with feedback systems, which is about par for most AGW believers. It is so annoying when they are so smug in their ignorance.
R Shearer says:
June 9, 2010 at 6:54 pm
Prior to the 1980′s, ice core analyses (sic) routinely showed CO2 levels at 2-3 times higher than today.
A reference or link would be very interesting. Or as they say, “Sources!”.
Bart says:
June 9, 2010 at 6:50 pm
Jim D says:
June 9, 2010 at 5:26 pm
“Could this not just be explained by the fact that a warmer ocean has a reduced uptake rate of CO2?”
Since nature is always generating CO2 at 24X the rate of anthropogenic input, any reduction in uptake means an immediate increase in airborne concentration, with the extra build-up from natural far outpacing that from anthropogenic.
Total rubbish, the anthropogenic CO2 is added to the atmosphere at ~twice the rate of increase of the atmospheric CO2 so nature is a net sink of ~half the anthropogenic input!
Nick Stokes says:
June 9, 2010 at 7:54 pm
“But El Nino isn’t caused by temperature either.”
But, it causes large temperature swings, which then causes CO2 swings.
“The trend is determined by the constants 0.58 and 0.22, which are obtained by fitting.”
And, the fitting determines those constants by minimizing the error between the calculated and measured data, so they are not just random and arbitrary.
>> BobN says:
>>June 9, 2010 at 2:58 pm
>>… The oceans are absorbing CO2, not releasing it.
This is incorrect. The oceans release about 20 times as much CO2 as man. They absorb a similar amount. Different areas of the ocean are absorbing and outgassing at different times of the year.
old construction worker says: “Could anyone be this DUMB?”
June 9, 2010 at 6:38 pm
Well I once knew a man…………
http://www.snopes.com/travel/trap/congress.asp
So I don’t understand why the derived anomaly only goes back to 1980. There are measured values much further back, and Beck has a graph going quite far back. It would be nice to see the derived anomaly for this.
This is not necessary. On the time scale you model, and for the accuracy available, the “0.58” could easily be an approximation for a slowly varying function of other parameters, which only shows significant influence on a century or longer timescale. Thus the observed following of temperature by CO2 in the ice record could hold over a long timescale, whilst fluctuations around it on a timescale of a few decades could be modeled by your equation, but with a different constant term in different epochs. But the clear goodness of fit of your equation on the short term more or less demolishes the IPCC model.
While I’m fascinated with the discussion, and constantly learn more about analysing scientific reports just by watching you guys, I haven’t anywhere near the expertise to comment on the science or math.
But urban legends are a horse of a different kettle of fish. And I’m afraid Old Construction Worker has just passed along one of the classics. Snopes lists this one as going back at least to 1998 at which the foolish people were merely “a man,” “a woman,” “another man,” and so on (Trip Witless).
Snopes. It won’t help solve the debate on global warming, but it can sure help avoid spreading misinformation of other types.
Why is it that there is a ‘push’ from certain quarters to talk about the “credibility” of the site and to try to suppress articles, if only by making Anthony self-censor?
I am calling astroturf on some of the comments on this post. I hope and believe that Anthony won’t be influenced by this strategy.
See my previous post for why this does not follow.
Bart says:
“Leaving the harder mathematical stuff for others … If this analysis is correct, then there was almost certainly no MWP, and current warming is unprecedented.”
Translation: “I really don’t understand any of it, but I have absolute faith in the ice core extrapolations.”
1) No translation was needed, and your translation was pretty dumb. I said what I mean. I have a fairly good idea of what is being claimed, but recognise that there are others here more confident on what is actually being shown e.g. Zeke. But that wasn’t the core of what I was saying in any case.
2) What exactly are the ice cores allegedly “Extrapolating?”. They cover the entire period I am talking about (MWP till present). They may well be imperfect records of CO2, but I don’t see how they extrapolate anything.
3) Ice cores aside, I’m not aware of anything like studies of stomata etc. which put CO2 content at any period in the last 2000 years up around 350 – 400ppm (correct me if I’m wrong). Do you know of anyone indicating that CO2 levels were near current levels during the MWP?
4) If there is no good evidence that CO2 levels during the MWP were comparable to now, then one of two things is true. Either the MWP did not exist, or this model is wrong.
Faith doesn’t enter into it. My money is on there being a MWP. Obviously, if there is reasonable evidence that CO2 levels were comparably high during the MWP, then it would strengthen the case for this model.
Ron House says:
June 9, 2010 at 8:39 pm
“On the time scale you model, and for the accuracy available, the “0.58″ could easily be an approximation for a slowly varying function of other parameters, which only shows significant influence on a century or longer timescale.”
Or, it could simply mean that the arbitrary baseline used for the temperature anomaly is… wait for it… arbitrary. Are you listening, Nick?
Nick Stokes says: “The sea water chemistry is very bad. There is a large volume of dissolved CO2 equivalent, mainly as bicarbonate. But only about 1% is free CO2. Just using water solubility curves and relating them to total CO2 is quite wrong.”
Heavens, we agree again, almost fully.
I’m playing around with cyclicities of noble gases, especially argon, but it is oversaturated and only helpful in some respects, like seasonal outgassing at various ocean latitudes.
BTW, there is some interesting interaction by biomass effects at http://www.seafriends.org.nz/
but the terminology is not consistent with mine and I’m having to translate it a little. It does however, do what I have been looking for for years, namely simply titration ocean water with CO2 to see how the pH changes. Some surprising results have set me thinking.
Mechanisms have to dominate over math correlations in the long run; but the math can be useful in early stages to point to where the mechanisms need attention; then they are needed for final confirmation and error/confidence analysis.
Ron House,
I think you need to re-read my post. My position is that there was a MWP, and that the current warming is not unprecedented. That is why I think this model is wrong. There are multiple lines of evidence for the MWP, not the least of which is the great pains some climate researchers took to hide it.
I am not aware of anything indicating comparably high levels of CO2 during the MWP. If there were, we can be quite confident that warmists would have jumped on it to “prove” that CO2 causes global warming. They couldn’t find such evidence, so instead they had to make the MWP disappear.
I am following the golden rule of when the observations don’t fit the model, then it is the model that needs correcting. A bit more thought before calling “Astroturf” might be in order.
old construction worker’s list of political travel bloopers is false. Some may be old stories reattributed to politicians.
Ok, so here is a thought. You would expect that the r^2 in a regression between CO2 and temp would be high either way in either argument of causality. What other evidence can be looked at in terms of causality?
If the oceans are absorbing as much CO2 as possible in these higher temperatures, which is the argument presented with the lowering of PH values, then it would mean CO2 is being stuffed into the oceans faster as the temperature rises. And so the r^2 between PH value and atmospheric CO2 will be high, while r is negative.
If temperature is releasing CO2, then CO2 would be accumulating at the surface of the ocean doing its best to pop out and release into the atmosphere. The value of r^2 is again expected to be solid, with a negative r.
But what about deep water CO2 saturation? That should go up if CO2 is causing temperature, and down if temperature releases the CO2. Right?
Great article and one that restores my faith in the scientific community. There is also the factor of hysteresis to consider as the seasons change from warm to cold and vice versa. This would stymie attempts at an exact fit of temperature trend and anomaly trend.