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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Dave Springer says:
June 9, 2010 at 4:48 pm
“And your hypothesis is dependent on no mixing of surface water with deep water. As I pointed out in other threads the vast majority of the ocean lies below the thermocline at a temperature of about 4 degrees C and thousands of atmospheres pressure. ”
“The deep ocean temp below the thermocline represents the average global temperature over timeframes long enough to ecompass a full glacial/interglacial cycle. There’s nothing else that can explain why the deep ocean is so cold.”
Dave, Thanks for posting the above information, I found it very interesting and thought provoking. It makes me wonder if and how the implications of this vast amount of cold water in the deep oceans has been taken into account in the various computer models and AGW claims. Obviously the system is much more complex than many would have us believe, especially considering your explanation of how the water got so cold.
[D. Cohen says:
June 9, 2010 at 1:53 pm
Your article makes a very good point, but in retrospect the same argument can be made based on the annual variation of the CO2 data. No one (that I know of) argues that the annual CO2 variation is due to anything but the annual temperature cycle, therefore we already know that — for the annual CO2 cycle — changes in temperature cause changes in CO2 concentration. From that data alone we should expect multiyear temperature changes (like El Nino events) also to cause changes in the CO2 concentration.]
The variation in co2 annualy is from the respiration of the plants on earth. During winter the plants do dormant and our co2 increases much faster. During summer plants are absorbing co2 bringing down the concentration temporarily.
Lon Hocker,
I enjoyed your post very much.
The causality you infer, that SST temp changes drive the rate of change of CO2 concentrations, appears to me to be reasonable. What an elegantly simple agrument.
Perhaps some of the econometricians reading this post can help you with putting the equations in proper formal statistical format. [VS – where are you?]
Anthony – you are wonderful in posting this stuff!!
John
I would think Lon would know that the 6 month variation is due to plant respiration and not temperature variation. The whole thing easily falls on its face. The temperatire lags co2 increases. We are a half a degree behind the co2 increase now.
http://www.realclimate.org/index.php/archives/2007/08/the-co2-problem-in_6_easy_steps/
Jimbo says:
June 9, 2010 at 8:54 pm
“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. “
Dictionary.com: ex·trap·o·late (ĭk-strāp’ə-lāt’) v. tr. 1. To infer or estimate by extending or projecting known information. 2. Mathematics: To estimate (a value of a variable outside a known range) from values within a known range by assuming that the estimated value follows logically from the known values.
Ice cores are evaluated by doing #1 based on models for diffusion rates and other reactions. You do #2 by assuming that the bandwidth of stored information is greater than it is, so that you can see fine details like peaks and canyons which, realistically, you cannot.
“Do you know of anyone indicating that CO2 levels were near current levels during the MWP?”
Sure, if that is what floats your boat. If you have issues with it, don’t nag me. I don’t believe any of this crap can be reliably estimated after centuries have passed in the first place.
“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.”
Major non sequitur. Absence of evidence is not evidence of absence. You have to have good evidence that CO2 levels during the MWP were NOT comparable to today, to make such an either/or proposition. And, you have to make sure whatever you define as “comparable” is an appropriate measure based on the dynamics involved.
Jeff Green says:
June 9, 2010 at 9:30 pm
“I would think Lon would know that the 6 month variation is due to plant respiration and not temperature variation.”
What does that have to do with anything? His differences are over 12 months.
Jeff Green says:
“The temperatire (sic) lags co2 increases.”
No, it doesn’t. You have it exactly backwards. On every time scale, CO2 rises follow temperature rises, and CO2 declines follow temperature declines. On every time scale, from months to millennia. CO2 is a function of temperature changes, not vice-versa.
Also, please do not link to realclimate; they are no more credible than Michael Mann. Thanx.
Phil. says:
June 9, 2010 at 8:28 pm
“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!”
Complete garbage. Anthropogenic input is currently running at about 4% of natural input. The IPCC says so. Argue your “point”, whatever it is, with them.
Believe me, you do not want this to be true. Think about it.
Warmer ocean -> more CO2 -> warmer atmosphere -> warmer ocean -> more CO2 -> runaway greenhouse effect.
noaaprogrammer says:
June 9, 2010 at 1:47 pm
I think that at the scale we are talking about (a change of ~ 100 ppmv in the last 50 years) claiming that the causation runs in the direction of “temperature causes CO2” is as nonsensical as claiming “CO2 causes temperature”.
Both of them run aground on the same reef – since 1959 the CO2 rise has been steady and monotonic, while the temperature has risen and fallen in fits and starts.
In fact that’s a bigger problem for the claimed causation in this direction (temperature causes CO2) than in the opposite direction. In the opposite direction, you can always fake it by claiming confounding factors, known or unknown, are keeping the rise in CO2 from causing a corresponding rise in temperature.
But going in the direction claimed here (temperature causes CO2), there is little wiggle room. There is no statistically significant warming since 1995 … but CO2 has continued to rise. This is bad news for the AGW crowd, they’re tap dancing as fast as they can to explain that.
But it’s much worse for this hypothesis. Why is the CO2 continuing to rise, if the temperature isn’t rising?
Me, I say neither one is true at the scale we are talking about here.
Finally, the ice-age to interglacial change shows clearly that CO2 does rise as a result of temperature, but only at a rate of about 10 ppmv for each 1°C change in temperature. So for the post-1959 temperature rise (about 0.7°C), that would only give us about a 7 ppmv change in CO2, far from the 100 ppmv change that we have observed. The numbers just don’t support his claims.
Another lovely theory mired down in inconvenient observations …
Jim D says:
June 9, 2010 at 9:48 pm
Warmer ocean -> more CO2. Period.
Willis Eschenbach says:
June 9, 2010 at 9:51 pm
“There is no statistically significant warming since 1995 … but CO2 has continued to rise. “
You are stuck in your old paradigm. In this model, the temperature anomaly is proportional to the yearly difference in CO2. So, CO2 can rise linearly without indicating a rise in temperature. To be associated with a rise in temperature, it has to rise superlinearly. See Figure 2 in the article and the equation before it. He’s already done the calculations for you.
….speaking of hockey sticks….
http://www.chicagotribune.com/
Jim D says:
June 9, 2010 at 9:48 pm
Believe me, you do not want this to be true. Think about it.
Warmer ocean -> more CO2 -> warmer atmosphere -> warmer ocean -> more CO2 -> runaway greenhouse effect.
Jim D,
1) Truth is truth. It cannot be moral, i.e. good or bad. If Lon’s post is true, it will advance knowledge . . . .
2) Please demonstrate the existence of “runaway greenhouse effect”. I think this does not exist except in minds of some people. Please show us proof of it, since you claim it exists.
John
The interaction of the ocean and its dissolved CO2 with atmospheric CO2 is mainly through the “thermohaline” circulation, where very cold water (~0C to ~4C) at high latitudes that has absorbed CO2 out of the atmosphere sinks (due to it’s high density) to the abyss. CO2 is continuously removed from the atmosphere wherever very cold water is sinking. This cold water flows in deep ocean currents until upwelling at lower latitudes, where it warms at the surface and releases CO2 to the atmosphere. The overall circulation is primarily driven by ocean currents that are powered by dominant winds (like easterly trade winds in the tropics and westerlies in the temperate regions). Ocean currents carry warmer surface water (relatively low in CO2) water northward and southward, where it cools and absorbs CO2 before sinking to the deep. Because of the enormous volume of the deep ocean (compared to the thin surface layer), water that sinks at high latitude does not typically surface via upwelling for (on average) about 1,000 years. The thermohaline circulation runs continuously, so CO2 is constantly being released from the ocean at low latitudes and absorbed at high latitudes.
The influence of ocean surface temperature on short term variation in atmospheric CO2 is due to release or absorption of CO2 from relatively warm surface water (that is, warmer than the deep ocean). The surface layer where this short term absoptions/desorption takes place is quite thin… on the order of 100 meters deep. The underlying cold water (with much higher CO2 concentration) does not warm, nor does it communicate with the atmosphere, so it contributes nothing to the short-term temperature driven change in CO2. The short term effect of ocean surface temperature changes on atmospheric CO2 is well known, and has been estimated at somewhere between 3 and 5 PPM for a 1C change in average ocean surface temperature.
The response of atmospheric CO2 to surface temperature changes has nothing to do with temperature changes in the deep ocean. There has been virtually no change in the deep ocean temperature for as long as temperatures have been measured. Nor would we expect any change: only very cold water reaches the deep ocean via the thermohaline circulation.
It is clearly not correct that the observed increase in atmospheric CO2 has been caused by a warming ocean. The warming has been limited to a very thin surface layer, and that thin layer has warmed by < 1C; the total CO2 that could out-gas from this thin layer due to a <1C rise is far too low to increase atmospheric CO2 by more than several PPM. Rising CO2 concentration in the atmosphere causes a net absorption of CO2 by the ocean, not a net release, because at higher atmospheric CO2 level the volume of CO2 absorbed by cold water increases, while at the same time, the volume of CO2 released by upwelling water (as it warms) is reduced. The quantity of CO2 released to the air during warming of upwelling water is less because the equilibrium concentration of CO2 in the ocean surface (at any temperature) must be higher when the atmospheric concentration is higher; the warming water does release CO2, but not as much as it would have release were the concentration of CO2 in the air lower.
The net is that the thermohaline circulation "buries" much more CO2 in the deep than it releases from upwelling surface waters. When considered over multi-year periods, the ocean is currently a large net absorber of CO2, not a source of CO2, and will remain a net absorber for a very long time. Short term ocean surface temperature variations will of course continue to cause small variation in atmospheric CO2, but the long term term trend is for the ocean to remove a large volume of CO2 from the atmosphere.
All of these factors are well known and understood by oceanographers, Mr. Weinstein. Plankton blooms draw down atmospheric pCO2; this has been measured numerous times, particularly recently during open ocean iron fertilization experiments. Deep ocean processes remineralize organic carbon, such that ocean upwelling zones where the water warms at the surface (such as the world’s largest upwelling zone, the equatorial upwelling zone) are areas where CO2 is released. But more CO2 is absorbed in cold and windy oceanic regions. NOAA has done exemplary work in this area. Also note that measurable oceanic pH decrease (much of that done by NOAA) indicates net absorption of CO2 by the oceans. The oceans are not releasing CO2 due to warming. Hocker’s premise is flawed and his analysis produces erroneous conclusions (as several other commenters have already noted).
Willis Eschenbach says:
June 9, 2010 at 9:51 pm
But it’s much worse for this hypothesis. Why is the CO2 continuing to rise, if the temperature isn’t rising?
Willis,
Nice you see you here. : )
I think that the causation Lon appears to be showing is SST to the rate of change of atmospheric CO2 concentration in time. It is not with the levels of CO2 concentration.
John
Bart says:
June 9, 2010 at 9:45 pm
Phil. says:
June 9, 2010 at 8:28 pm
“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!”
Complete garbage. Anthropogenic input is currently running at about 4% of natural input. The IPCC says so. Argue your “point”, whatever it is, with them.
Actually since you’re the one posting it here I’ll argue it with you! Try doing a mass balance, the rate of increase in atmospheric [CO2] is ~half the rate of emission of CO2 from fossil fuel sources. Check out Willis’s graph if you like:
http://wattsupwiththat.files.wordpress.com/2010/06/emissions_sequestered_airborne.jpg
Thanks, Willis for the comment. Don’t forget I was writing that the temperature anomaly is related to the rate of increase of CO2. No temperature anomaly increase means that the rate of increase is constant, which it seems to be.
Dave F says:
June 9, 2010 at 9:10 pm
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?
======================================================
In light of the above I offer:
http://www.sciencemag.org/cgi/content/abstract/1138679v1
The isotope ratio is not evidence for CO2 driving temperature and against temperature driving CO2. The isotope ratio reflects there are is some level of emission taking place from fossil fuels–not a disputed matter. That is completely independent of what determines the atmospheric concentration.
Saturation is irrelevant in this context. Read up on Henry’s law. There is a gas:dissolved-gas equilibrium based on the partial pressure and the dissolved concentration.
Willis: Both of them run aground on the same reef – since 1959 the CO2 rise has been steady and monotonic, while the temperature has risen and fallen in fits and starts.
But if the idea presented in this article were right (personally I’m not convinced), this is not a valid argument, because, given the CO2->temperature formula presented above, CO2 will rise as long as the temperature anomaly is above -0.58. If the anomaly drops below that, the formula says that we should see CO2 levels dropping. I don’t think I want that to happen 😉
Lon Hocker says:
June 9, 2010 at 10:24 pm
Thanks, Willis for the comment. Don’t forget I was writing that the temperature anomaly is related to the rate of increase of CO2. No temperature anomaly increase means that the rate of increase is constant, which it seems to be.
Can we just look at that last statement and think about what it implies
No temperature anomaly increase means that the rate of increase is constant, which it seems to be.
Lon seems to be saying that if there was a plateau in temperatures for 5, 10, 15 years, say, we would still have a CONSTANT CO2 INCREASE each month. In fact even if we had negative anomlaies for 5,10, 15 years we would, according to the model, still have a monthly increase in CO2.
Lon
Can I ask you to use your model to calculate the CO2 level for month N where N= 240 (20 years) in the following case.
1. A Dalton-type minimum has occurred and temperatures have declined at the rate of 0.3 deg per decade (0.0025 deg per month)
2. Assume CO2 concentrations at month (N=0) are 390 ppm
3. Assume temp anomaly at Month(N=0) is +0.5 so that anomaly at Month(N=1) is 0.4975
Cheers
“There is no statistically significant warming since 1995 … but CO2 has continued to rise.”
In the current climate regime, statistical significance in the warming trend since 15 years ago is unlikely. I watch, amused, as the year cherry-picked to deny that global warming is happening shifts forward. 1998 or 2002 are more common now than 1995. In 2020, you will no doubt be saying “there is no statistically significant warming since 2005”.
“This is bad news for the AGW crowd, they’re tap dancing as fast as they can to explain that.”
Not really.
Espen says:
June 9, 2010 at 11:52 pm
Willis: Both of them run aground on the same reef – since 1959 the CO2 rise has been steady and monotonic, while the temperature has risen and fallen in fits and starts.
But if the idea presented in this article were right (personally I’m not convinced), this is not a valid argument, because, given the CO2->temperature formula presented above, CO2 will rise as long as the temperature anomaly is above -0.58. If the anomaly drops below that, the formula says that we should see CO2 levels dropping. I don’t think I want that to happen 😉
Quite. The model says that CO2 levels will continueto rise beyond their current level (390 ppm) even if tempratures drop by ~1 deg. According to the model, if temperature anomalies dropped to -0.58 for the next 20 years CO2 levels would stay at 390 ppm. It’s nonsense.
Lon’s used the difference (in CO2) as a function of the anomaly. If he’d also used the month to month anomaly difference then the model might have some merit.Unfortunately it wouldn’t have fitted the data because whe n the anomaly went down the calculated CO2 level would fall (e.g. 2007 to 2008).
This theory will be confirmed, if the CO2 growth rate goes down, even became negative with cooling oceans. Up to now, there is slight hint of this – the rate of CO2 rise has stabilized despite increased emissions, as the SST reached plateau in recent years.
http://climate4you.com/images/CO2%20MaunaLoa%20Last12months-previous12monthsGrowthRateSince1958.gif
It will also prove, that ice core CO2 data are over smoothed by diffusion and alternative stomata data are much more realistic.