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
Its interesting that the residual flux in CO2 is so closely related to temperatures, but not that unexpected.
However, this analysis explicitly detrends a smoothed CO2 curve, and in doing so obscures the fact that the resulting year-to-year variation is orders of magnitude smaller than the rise in overall CO2 concentrations for the period in question.
Specifically, the temperature-induced variability of CO2 concentrations is about 0.5 ppm. The change in CO2 concentrations from 1960-present is about 70 ppm.
There’s a basic flaw in this argument. Taking the differential and then subtracting out the constant term basically leaves you with fluctuations around a linear trend. The trend itself has been removed, and it’s far larger than the fluctuations. What you’ve shown is that the fluctuations around the rate of linear increase of CO2 correlate with the fluctuations in the temperature anomaly. That is interesting, but it doesn’t justify your conclusion.
D. Cohen says: June 9, 2010 at 1:53 pm “No one (that I know of) argues that the annual CO2 variation is due to anything but the annual temperature cycle”
Philip Foster beat me to it. The Co2 variation has everything to do with botanical seasonality. As the plants with the strongest CO2 uptake (grasses) and others are covered in snow or are otherwise outside the growing season, CO2 levels rise. As spring kicks into gear, the botanical growth takes the CO2 in.
I suppose one could say that the botanical seasonality is driven by temperatures, but is not a good connection to say temperature causes changes in CO2 concentration. (If it did, higher temps would cause lower CO2 concentrations.
To supplement my prior comment, interested observers can see the actual data here:
http://www.woodfortrees.org/data/esrl-co2/mean:12/from:1979/normalise/plot/esrl-co2/from:1960/mean:12
beatk says:
June 9, 2010 at 1:26 pm
You are talking very large CO2 differences during geological time, differences measured in thousands of ppm. Today, the differences are only a few tens of a ppm. The 600-800 years lag in the past represents the peak after thousands of years gradual increases.
Bart, the increased capacity of the oceans to dissolve CO2 as a result of the increased atmospheric CO2 partial pressure overwhelms the 4% (using Lon Hocker’s figure) reduction in solubility from the temperature rise.
Peter Miller says (June 9, 2010 at 1:30 pm): “Your hypothesis is dependent on the oceans being saturated with carbon dioxide – the current level is circa 90ppm, a very long way from saturation level at current global temperatures.”
That was the first thing I thought of. Then I wondered if just the near-surface layer of the ocean (mixing more-or-less rapidly with the atmosphere) could be CO2-saturated,
only mixing with deeper layers on longer time scales.
I have no idea if this is even reasonable–just speculating.
Richard Telford points out several awkward problems with this idea. Here’s another: we can calculate how much CO2 human industry emits, and it’s rather more than is being accumulated in the atmosphere. There’s only one place the excess can be going, and that’s into the oceans.
Consider a model that says the CO2 level is the sum of anthropogenic emissions, following some relatively smooth monotically increasing curve, plus a variable delta driven by temperature. The second may be smaller in absolute value but exhibit significant year on year fluctuations. If you take the derivative you will see, wow, a really close fit to the year by year temperature changes.
Try a model that encompasses both directions of causality and then tune the parameters for best fit.
Sorry, that should have been 0.1 ppm vs. 70 ppm. Had a normalize still stuck in there :-p
The actual data (in ppms for both measures) is here: http://www.woodfortrees.org/data/esrl-co2/mean:12/derivative/from:1979/plot/uah/from:1960/normalise
Has anyone actually checked these equations out. The whole thing looks like total drivel to me – but perhaps I’m not readin it right. Take this, for example:
Month(n) CO2 = Month(n-1) CO2 + 0.22*(Month(n) Anomaly + 0.58)
It seems to me that, providing the anomaly for month(n) is greater than -0.58, then the CO2 concentration will always be greater than in the previous month. Similarly if it’s below -0.58 the latest CO2 concentration will always nbe less than the previous month. You can see that if we re-arrange the equation, i.e.
Month(n) CO2 – Month(n-1) CO2 = 0.22*(Month(n) Anomaly + 0.58)
Take a hypothetical situation, i.e. Jan anomaly =+0.5; Feb anomaly= -0.5
After Jan CO2 goes up by 0.24 ppm (it doesn’t seem to matter what the Dec anomaly is)
After Feb CO2 goes up by 0.02 ppm (but temps have dropped by one degree)
I’ve just had my 3rd brandy so I’ll need to look at this again, but there appears to be a problem using differencing as a function of the anomaly. Basically a given anomaly will give the same CO2 rise regardless of the background CO2 levels.
No one can prove this theory any more than the warmistas can prove theirs. Implied cause and effect is implicit in both cases and too many other variables are in play in both. Picking at fly crap, as I said above. Where are the knowledgable statisticians? Actually the real value of this analysis may be that it shows exactly why the Global Warmers are also without a proven theory.
Nice job of curve-fitting for the intermediate term, Lon. It beats the hell out of the IPCC models. But to rephrase an old saying: Curve-fitting does not establish causation. (Hat-tip to Jim G.) Moreover there’s room for improvement in the proposed mechanism, as pointed out by Andrew W.
BobN,
I am also a mild “lukewarmer” (very mild), but I disagree in principal with your basic point on the oceans. The problem with your comment on the oceans absorbing CO2 is that you completely leave out biology. The oceans almost surely do absorb CO2 when cooled and emit when warmed, but then plankton growth in the oceans, and land based growth also take in more or less CO2 depending on temperature, rain, and mineral movement (upwelling currents and river drainage). Changes in ocean currents may also be major causes of absorption or emission. We do not presently know enough to make positive statements on the net result. Even the quoted pH changes are probably misleading for these reasons. I agree the points of this paper are not without question, but I look at all views with an open mind until I have more data to come down on a specific position.
Bart says:
June 9, 2010 at 1:10 pm
Wow. Someone tell Willis.
3…. 2… 1…..
You cannot use the CO2 level in 6 months from now as a predictor of current temperature anomaly.
I know why you did it, you thought that it is the best way to get the rate of change of CO2. But in this case, since you are doing temporal predictions, it is incorrect to do this. You need to use the backward differential only and make sure that you do not pollute the predictor with future information.
I.e.
x = [CO2(now) – Co2(i months ago)] / i
vs
y = Temperature Anomaly Now
Forget about using a linear model too. You are looking for E(y|x) i.e. expectation of temperature anomaly conditioned on the change in CO2. you can use x-y plot and overlay a patameter free Kernel estimator on the data to show the relationship.
If you get a strong relationship, which I think you will, then you will have pretty much proven that Co2 drives temperature and not vice-verse. And that, that is a very, very interesting result. Congratulations 🙂
http://en.wikipedia.org/wiki/Kernel_density_estimation
Please redo the work using the backwards differential. Please plot E(y|x).
PS Using the n+6 Co2 data for the x value of the month n {x,y} datapoint is horrendus, because it always leaves you open to the possiblity that the response is already in the independent variable. I have looked at many, many, different types of signals similar to this one. Look, to cut a long story short, just try it and you will see what I am saying.
BobN says:
June 9, 2010 at 2:58 pm
“I wish you would use a little more discretion or prescreening before posting guest posts with what are clearly flawed analyses. It really affects your credibility on the stuff you discuss which is good.”
I disagree Bob. This site is educational. The open peer review which this article has received by the very knowledgeable commenters here allows people like me to learn more about the basics and how to spot potential errors.
Thus I learn as much or more from the comments as from the articles here.
If this article had been published in a journal your comment would be more valid. And far more obviously questionable papers than this have indeed passed supposed peer
review and been published in supposed scientific journals – which is why so many of them, not to mention the peer review process, have lost so much credibility.
So then.
1. Where did all the fossil fuel CO2 go?
2. Why has the 13C content of atmospheric CO2 been dropping since about 1750, after hundreds of thousands of years of relative stability?
3. Why should the current warm period have caused CO2 concentrations to rise to >385ppm, when previous warm periods in the last several hundred thousand years only ever saw them reach 300ppm?
I recommend that you retake your last Thermodynamics course (if any).
“Using these values gives a value of 0.275 ppm /C/month instead of the observed 0.22 ppm/C/month”
One should also note that the more CO2 one puts into the atmosphere, the greater the rate at which it is removed. Many factors would cause this but the primary ones being the increased uptake from biomass (mainly in the oceans) and subsequent sequestration from being buried by various processes (falls to the bottom of the ocean, turned to charcoal in a fire and buried, dissolves in rain then reacting with rocks creating insoluble carbonates that are washed into the ocean, deposited as minerals in caves, etc.)
The more CO2 you place into the atmosphere, the more efficiently nature removes it. So seeing that X amount of CO2 is released but finding only X-y amount in the atmosphere would be consistent with the notion that the amount removed per month increased by y.
Richard Telford:
The trend for CO2 is removed via the derivative. A trend for the temperature anomaly is *NOT* removed because Lon takes it as it is. In Figure 2, the derivative of the CO2 level (trend removed) and the anomaly (including its weak trend) look like they correlate very well.
For me, this results in the obvious conclusion that the trend in CO2 level is not having an effect on the temperature anomaly. Is there a flaw in my logic? If so, please point it out.
Gerard Harbison says:
June 9, 2010 at 3:08 pm
There’s a basic flaw in this argument. Taking the differential and then subtracting out the constant term basically leaves you with fluctuations around a linear trend. The trend itself has been removed, and it’s far larger than the fluctuations. What you’ve shown is that the fluctuations around the rate of linear increase of CO2 correlate with the fluctuations in the temperature anomaly. That is interesting, but it doesn’t justify your conclusion.
That’s it. Gerald has phrased his post better than I did earlier but it amounts to pretty much the same thing. I think Zeke (above) has also made a similar point. This ‘study’ simply shows what we already knew, i.e. CO2 levels rise a bit more in warmer years and a bit less in colder years.
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.
If I may add, no where in your observed relationship is there an anthropogenic factor. That’s two strikes on AGW.
Lon, you should label the red and blue lines in Figure 2 clearer, i suggest
Blue: Measured temperature anomaly
Red: Derivative of CO2 level
and drop the caption,
“Measured and Derived Anomalies” just confuses people, i would reserve the word “anomaly” for the measured temperature anomaly.
I think your result is highly significant, it surely has stirred up a storm of belittling comments from certain people – they fear it.
Friends:
Several of the above comments seem to suggest that the ocean surface layer must be near to saturation for the exchange rate of CO2 between air and ocean to be affected by temperature. That suggestion is a misunderstanding because it assumes the exchange rate is governed by the existence of an equilibrium state.
The rate constant for the exchange is affected by the water temperature and the atmospheric partial pressure of CO2. Seasonal variations occur to both the temperature and the partial pressure, so the oceans emit CO2 during warming months and sequester CO2 during cooling months. A change to ocean temperature (e.g. as a result of ENSO) could be expected to affect the rate constant for exchange of CO2 between air and ocean whether or not the system is near to the equilibrium state (that it never achieves).
Richard
John Finn says:
June 9, 2010 at 3:21 pm
I’ve just had my 3rd brandy
Good move. I reckon you’ll need a bit of cushioning when you realise the implications fully. Good to see you can envisage co2 levels falling though. 😉