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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Response of a warmist worm to this paper: http://images.clipartof.com/thumbnails/35089.jpg
Along similar lines is The Acquittal of CO2, by Jeffrey A. Glassman, http://www.rocketscientistsjournal.com/2006/10/co2_acquittal.html.
The Abstract:
Looking at the graph – Modeled CO2 vs. Time – comparing measured CO2 to Model predictions – any reasonable, scientificly trained person would have to believe that CO2 controls the temperature of the seasons to believe CO2 controls global temperature rises.
Use some common sense Warmers.
The first rule of regression analysis, or any other correlation method, is to beware of implied cause and effect. Many dependent variables can be correlated to many independent variables but cause and effect should not be implied. The stock market’s swings with the length of women’s skirts was a classic used many years ago. Another rule is to beware of exogenous variables. The hypothesis that increase in co2 is caused by temperature increase is just as viable as the AGW hypothesis but also just as subject to potential effects of other variables. I love this site for its lack of “lemming instinct” and challenge of the conventional wisdoms of the day. However, I think we many times are picking at flycrap in trying to disprove what has never been scientifically proven in the first place.
Good grief, Lon! I hope you are’nt dependent on AGW grants.
You would be out of a job before you know it!
Very elegant to think of the derivate, I must say. Well done!
This is one of the first things an undergraduate geology student learns (a warmer ocean has lower CO2 solubility.) That is why limestone reefs form in the tropics.
Some climate “scientists” could avoid embarrassing themselves by learning some basic science – before getting their PhD
http://en.wikipedia.org/wiki/Limestone
I made quickly a similar calculation with woodfortree.org
http://www.woodfortrees.org/plot/esrl-co2/mean:12/derivative/from:1979/normalise/plot/uah/from:1960/normalise
the result is astonishing
For this to be true, the proxy CO2 records that show it almost perfectly flat for the last 1000 years have to be wrong.
Obviously possible, but without addressing it, you have a pretty weak presentation.
Make data and calculations available online please! Let’s follow the practices we want from others.
Wow. Someone tell Willis.
Lon, this is very well done. However, I am simply stunned that this has never been done before. There have been numerous posts here and debates on RealClimate about the fact that CO2 rise/fall lags temperature rise/fall. You’d think that explaining the CO2 variation would be one of the key products of MLO. So what do they say?
Regarding ocean acidification, if the rising temperature is providing less CO2 for the same “amount” of ocean water, should the ocean pH not be rising?
Just as we suspected all along, but what will it take to convince those who wear the blinkers? Especially as for a variety of reasons it doesn’t suit them to know…
What one can invent with a simple spreadsheet and two Mauna Loa friends!
Looks like good science to me… and makes good sense too!!!
Thank you!
Dear Lon Hocker,
A confirmation of your argument in this article is evidenced by the paleobiological register. In this graph I eliminated the temperature line for the correlation between the mass fraction of carbon dioxide in the atmosphere and the area of continents flooded is seen clearer. You can see the expansion of the oceans happens many years before any increase of the mass fraction of the carbon dioxide in the atmosphere:
http://www.biocab.org/SL_and_CO2.jpg
I seem to recall that on a geologic timescale CO2 lags temperature by about 600-800 years. How can this be reconciled with the about 6 months lag found in this study?
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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An inconvenient paper. Congratulations!
If this was true how do we explain that the CO2 levels in ice core data are almost totally flat before 1850. (you’d think same process would have applier during e.g. MWP)
1) global temperature variation has been very small (and current warmins IS unprecedented) – not likely
2) ice core CO2 data can not be trusted – not likely
3) this mode breaks down prior to 1850
Anthony
This is one of the few times I disagree with you.
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.
REPLY: You might look at who wrote it before disagreeing with me. – Anthony
At first glance this would appear to be a brilliant discussion. I can’t get over Figure 2. And he plays in a band. Nice work.
Well this post get one thing right, almost. There is a relationship between atmospheric CO2 concentrations and El Niño. Congratulations for finding this relationship over 30 years after it was first described by Bacastow in Nature. If your research had extended to reading this paper, you would have learnt that the main driver is not the ocean, but vegetation dynamics.
Your model captures the short term variability, but cannot explain the trend (because your analysis removed the trend!). The short term variability is interesting, but it is the trend is of most concern.
And how does your model account for the changing carbon isotopic ratio (the Seuss effect); the decline atmospheric in O2 concentrations; that the ocean is undersaturated in CO2, so is absorbing not emitting CO2. Simple – it cannot.
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.
This is a strawman. Nobody is claiming that El Nino is caused by the increase in CO2, indeed, there is evidence for El Niño throughout the Holocene (Rodbell et al. 1999 – Science)
So…what does Willis Eschenbach think of this?
From Wiki: “Henry’s law is used to quantify the solubility of gases in solvents. The solubility of a gas in a solvent is directly proportional to the partial pressure of that gas above the solvent. ”
Over the last 150 years the partial pressure of CO2 has risen by about 35%, so CO2 is moving into the oceans, not out of them.