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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BobN says “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.”
Steady on!
Even if it is wrong, how can it affect “your credibility” (meaning AW)?
If it is “clearly wrong” then by all means take it apart! But please….. no screening! That’s just censoring by another name and I find that approach quite tiresome. It is typical of certain other sites which shall remain nameless.
I found the propositions put by the author to be interesting. I do not necessarily require that they be correct. If the moderator were to ‘screen’ such an article, I would be deprived of something to think about.
Well, as others have pointed out – where are the emissions going if not the ocean? Deserts? Biomass?
Also, how does this reconcile with isotopic evidence? Perhaps deep ocean CO2 has a similar signature to fossil fuels due to age (I don’t know).
I’m not entirely convinced that most of the CO2 increases we’ve seen are due to fossil fuel emissions, but your theory is not persuading me at this point.
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…What you’ve shown is that the fluctuations around the rate of linear increase of CO2 correlate with the fluctuations in the temperature anomaly.
I agree. Very interesting though.
It is true that warming temperatures increases CO2 emissions from the ocean. It is also true that burning fossil fuels increases temperature.
A little bit of both going on.
Reconciliation with Ernst-Georg Beck (http://climaterealists.com/index.php?id=4302) would have us negate the LIA…
The next thing to consider is that the half life of a carbon dioxide molecule in the atmosphere is five years. Effectively carbon dioxide is in equilibrium with the oceans, or the top layer of the oceans, with a lag of only a few years. My calculations say that the top layer that the atmosphere is in equilibrium with is 100 metres thick on average. The bulk of the 100 ppm increase over the last 100 years is the anthropogenic contribution. That top layer should not be considered to be a sink. It is furiously degassing and absorbing CO2. Longer term, the deep ocean sink will have an effect. There is fifty times as much CO2 in the oceans as the atmosphere, so if we double the atmospheric concentration, in the long term it will increase the oceanic concentration by 4%. That in turn means that atmospheric concentration will be 4% above the pre-industrial level. Some future generations will watch the atmospheric CO2 concentration fall year by year and weep for the declining agricultural productivity.
John Finn says:
June 9, 2010 at 3:21 pm
You’re right – and no starting CO2 was given. But I tried reproducing Fig 5. With smoothing you might get a correlation like that shown from 1980 on, but it breaks down completely before 1980 (where the graph starts).
A problem with reproducing was that there doesn’t seem to be any indication of what “Ocean Temperature Anomaly” was used. I presume he meant SST, and I used HADSST2.
>> Greg says:
>>June 9, 2010 at 12:57 pm
>>For this to be true, the proxy CO2 records that show it almost perfectly flat for the >>last 1000 years have to be wrong.
Yes, they are wrong. You are probably referring only to ice core records. Read the comments here on the ridiculous assumption that air bubbles in ice cores are a closed system.
http://wattsupwiththat.com/2010/06/07/some-people-claim-that-theres-a-human-to-blame/#more-20260
My thanks for you all for the lively discussion. The data is available at the references I cited, and the equations I use are shown, so all are invited, and indeed urged, to redo the calculations.
I won’t attempt to teach anyone algebra. There is no background slope to the CO2 record or temperature record that I have subtracted out.
I am not wed to the theory I present, but will strongly defend figure 2. You can see this same correlation using the smoothed (annual variation removed) data, also available from NOAA. I used the raw data, and the +6, -6 months to eliminate the annual variation so nobody would think I had messed with the raw data.
I do not claim that the curve fit determines causation. The correlation, however, is so strong, it’s hard to understand how they cannot be directly related. Also, it’s hard for me to imagine a mechanism where the CO2 rise could cause the El Nino events. This leaves temperature causing the rise in CO2. Other explanations would be welcome as long as they fit the data.
I agree that it is strange that we see the CO2 concentrations so flat in the ice records, when we know there have been relatively large temperature changes. This begs the question of how reliable we feel these ice records are. If my model is correct, the medieval warm period would have had much larger CO2 concentrations than are observed in the ice record.
One can’t help but imagine that indeed the CO2 concentration might have been larger, and that meant that crops would have benefited from both higher temperatures and more CO2. During that period the world population supposedly doubled, and after the warm period it actually dropped, perhaps dropping CO2 concentrations as well as lower temperatures lead to dramatically less successful crops.
In summary, I invite all to redo the calculations and come up with explanations for the unexpected results I found.
Thanks again for your responses.
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.
For instance, the mid-ocean ridge system is the largest volcanic feature on the earth encircling it like the seams on a baseball. As most of us know volcanoes release a lot of CO2. At the pressure depth of the ridge the water can hold far more dissolved CO2 than surface waters. There you get plumes of CO2-rich water that generally stays below the thermocline until something like the oceanic conveyor belt brings it to the surface where it is far from equilibrium with the CO2 partial pressure of the atmosphere. There it outgasses. The warmer the surface water the more it outgasses before equilibrium is reached. So there you a have a lovely mechanism for rising CO2 due to warming of ocean surface layer.
As I said in another thread the biosphere is like a thin warm layer of scum floating on the top of a bucket of icewater. We’re at the mercy of the rate of mixing between the warm surface layer (including the atmosphere) and the deep ocean. A little less mixing and we get warmer. A little more mixing and we get colder. Too much mixing and (I suspect) we exit our ~20,000 year interglacial period and the average atmospheric temperature becomes that of the deep ocean for the next 100,000 years or so. 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.
Bart June 9, 2010 at 2:36 pm
No, my question stands. The “reasons” given there are
1. There’s a strong correlation (but that says nothing about causality), and
2. “the inability to justify…” which is just arm-waving (“I just can’t believe it could be CO2”).
As Zeke and others have pointed out, the real flaw is that this all relates to fluctuations only, not the main trend. I don’t necessarily dispute that CO2 fluctuations could be caused by ocean temp variations. I’d just like to see a proper argument.
Enneagram says:
Almost right…except that what matters is the ***partial*** pressure of the CO2 in the atmosphere…which has increased by close to 40% from the pre-industrial levels, which is why the net flow of CO2 has been from the atmosphere into the mixed layer of the ocean, despite the increase in temperature.
Sorry, I didn’t do a good job of addressing Peter Hodges and other’s concerns that I seem to be subtracting a linear component. Please look at figure 3, and the equation directly above it. It models the CO2 concentration versus time by using the temperature anomaly (plus the offset to bring it back to about 1850 when temperatures appeared to be relatively constant. This equation is exactly the same one used for Figure 2, only inverted.
Thanks for looking at this carefully. Remember, the whole analysis is based on two very well accepted data sets.
Fantasic analysis!
It would be interesting to apply the same approach to other gases, some of natural, manmade and both origins (DMS, Freons, perfluorocarbons, SO2, CH4, N2O, etc.). The chemistry and concentration of CO2 is unique, but there certainly would be additional insight to be gained.
I would have to agree with the sentiments of several others expressed here. I’m a luke warmer, but this analysis seems pretty poor, and probably acts to lower the credibility of the good stuff that is more often posted here.
Leaving the harder mathematical stuff for others more competant than myself to dissect, I’d like to revisit a point others have already made, that hasn’t been convincingly countered i.e.
If this analysis is correct, then there was almost certainly no MWP, and current warming is unprecedented.
The assertions that the ice cores are only averages at resolutions of several hundred years only applied well back in the record. The MWP is only a thousand years ago, so decadal resolution should be possible. Similarly, another answer is that you can see a faint sign of higher CO2 in the Vostok core. Why should it be faint? If the MWP was equal to or warmer than now, why would it not show similar levels of CO2 to now?
I think that the case for a MWP of similar or greater warmth to the present has been well made, and that the Hockey Stick is broken. Consequently, I think this analysis is bunk.
Regardless of the science, it will be interesting to see what alternate explanations are given for such an incredible correlation between temperature and CO2 (Figure 2). This is not arm waving. Then to match El Nino (temperature only) events prior to the 1950s that confirm the high correlation (temperature and CO2) is brilliant. So if temperature is not driving CO2 out of the oceans, then why is the correlation between temperature and CO2 change so strong? Great post Lon Hocker!
Liquid CO2 droplets emitted by arc volcano at 1600 meters deep.
NOAA Research 2007 Outstanding Scientific Paper Awards
“Submarine venting of liquid carbon dioxide on a Mariana Arc volcano”
It’s worse than I thought. I never would have imagined that underwaters volcanoes could emit so much CO2 that it forms at the triple point. I guess you really do learn something new every day! Unless of course you’re a CAGW apologist and then you don’t learn a damn thing after your graduate school indoctrination into the dogmatics of the loony left is completed.
I just think it’s appropriate that the founder of a company that produces weather stations ( http://www.onsetcomp.com/products/weather_stations ) should present his new theory on WUWT.
My interpretation. CO2 is pumped by man into the atmosphere at a fairly constant rate (constant compared to ocean temperature anomalies at least). As shown, in warm-ocean years, CO2 in the atmosphere increases more quickly than in cold-ocean years. Could this not just be explained by the fact that a warmer ocean has a reduced uptake rate of CO2?
Joel Shore says @5:01 pm [ … ]
Joel, the central fact is that rises in CO2 follow rises in temperature — at all time scales.
I have some charts. Would you like to see them?☺
peterhodges says:
June 9, 2010 at 4:20 pm
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…What you’ve shown is that the fluctuations around the rate of linear increase of CO2 correlate with the fluctuations in the temperature anomaly.”
I agree. Very interesting though.
Quite, the OP has the process backwards too.
An excess of CO2 is released into the atmosphere as a result of fossil fuel combustion, this excess is partially absorbed into the biosphere and oceans. The concentration of CO2 in the ocean depends on the partial pressure of CO2 in the atmosphere so by increasing pCO2 you would expect a compensating absorption by the ocean. This process is temperature dependent however so if the temperature of the ocean is raised then less is absorbed and so more remains in the atmosphere. This relationship holds no matter how the temperature is raised and so finding it says nothing about whether there is GHG forcing. Under present conditions the direction of flow is CO2 into the ocean, with an approximately constant fraction of annual anthropogenic production being removed each year.
Jimbo, this isn’t complicated math. Give it a try. Excel isn’t all that hard to use, though I admit I had a bunch of learning to go though to write this. Remember I’m just using well accepted data, and high school math. Contrary to some assertions, I don’t believe I am leaving out any linear terms.
Thanks for looking at it, and hope you can keep an open mind once you have duplicated the results.
If we assume the ocean is the primary source of the temperature induced CO2 variation, then, I believe, we need estimates global sea volume temperature anomalies over time in order to calculate the actual amount of CO2 that might be released as a result of a general temperature increase at the surface. Lacking this data, all we may have is a correlation open to several interpretations. I do not expect it to be easy to obtain this data unless such estimates are already being made as a matter of routine.
Nice analysis… I did a similar one and got (not surprisingly) a very similar chart. There is virtually no lag in the reaction of dCO2 to atmospheric temps.
http://home.comcast.net/~naturalclimate/CO2_growth_vs_Temp.pdf
While the above does use moving averages, they are centered on the month in which they occur.
No correlation there, huh…!
It’s interesting to me that CO2 is so smart, that when it does change (caused by who knows what), it INSTANTLY changes the global temperature! Who’d a thunk it. It would make an interesting theory for someone to work on though. But someone has probably already thought of that. Yep.
This has the same problem CO2 causing -> temp, has …. carbon build-up PER YEAR quintupled from the 1950s to 1988 — then in 1988, suddenly leveled out at around 2 ppm/ year:
http://en.wikipedia.org/wiki/File:CO2_increase_rate.png
At first Glance you may think this seems to keep increasing, BUT:
1. Your eyes are drawn to the 1998 peak — after 1988 the DISPERSION is much greater — up: yes, but DOWN, also.
2. The last couple years are missing: both are well below 2ppm/year
— just cover the right half of the graph with your hand, and then the Left:
— left is a consistant increase,
— Right is Grossly dispersed — like a Rorschach test.
Now I was reading an Alaskan News sheet talking of Squid increasing their Range from Mexico to Southern Alaskan fisheries when I realized: THIS COULD BE IT !
Squid have no bones.
Bony fish sequester Carbon (bones are Calcium CARBONATE) for 250 million years on average (the IPCC tells its researchers to ignore bones: the carbon in bones returns to the Air Very fast because fish bones dissolve in Water ! — sure: ask any Geologist: fish bones dissolve: in RAIN – – AFTER they accumulate into rock, and the Sea Bottom rises up into a Mountain Range, and then: erosion wears it down. In 250 million years. ).
More Squid, Jellyfish, etc. mean CO2 RETURNS TO THE AIR, rather than being BURIED. The BALANCE is distorted.
Further, the “top” of any food chain gets hit hard by LEAD. Most “Squishy Fishies” are smaller & more Tropical. The CO2 ACCELLERATION agrees with the high-lead period in Greenland Ice.
Plus, at the end of the Last Ice Age, more Trees grew, so CO2 went into the Trees & should have DROPPED, thus, something MORE IMPORTANT outeweighed THAT — I figure: the Sea got more BONELESS fish = MORE CO2 — which makes sense as the increased temperature EXPANDED the Tropics. But that is a dozen Degrees (F) in the Northern Hemisphere — not just TENTHS of a degree. Today’s CO2 rise is mainly Over-fishing and/or LEAD opening a “niche” & the Squishy Fishies filling it … e.g. ever hear of the recent Tropical Jellyfish “Plague” ? —
The Jellyfish trend was reversed in New Zealand by establishing No-fishing zones so young bony fish can grow up — I think we can REVERSE CO2 growth & ALSO restore lost fisheries with the Same method applied Globally. What ? – – you don’t think a Green Plan should HELP an Industry ?
>> “Bones” also explains the 100-year & 5.4 year “residence time” for CO2 — they are both MEASURED, how can Either be wrong ? — but IF fish patterns account for 94.6% of the CO2 rise, we can reconcile both Measures (ie, CO2 acts Like it had a 100-year residence, but the decline in added Radioactives in the Test ban era — a 19% decline per year = 5.4 years, has been Re-done in Recent times, leading to the same 5.4: So: … the Seas’ absorbtion of CO2 has not changed at all, despite the amount of CO2 in the atmosphere increasing much. If CO2’s rise was 100% from Industry the CO2 Emissions increase of 50% since the mid 1980s, means it should exceed 3 ppm/year by now — but it never has even REACHED 3. The 5.4 rate is thus input, the 100 is input minus output. An increase in Industrial CO2 of 50% still increases CO2 — but just that part, ie.e a 2.5% increase in the CO2 increase rate — too small to notice.
Note “Bones” also explains the post-1500 DROP in CO2
— as caused by the 1500 A.D. Stewart Island Meteor’s tidal wave that reached 2200 feet at New Zealand & 850 at Australia = Kill the Fishermen, & Bony Fish recover, thus CO2 drops (the AGW idea that Columbus killed all the Indians is from a Legit Study: Dobyns’ idea that 95% of Indians perished in plagues over 285 years was not relevant : Primitive Agriculture limits population so, as Parish records proved in Peru, — plagues DID kill many people, many times, but no LOSS was permanent — population always recovered – – until people began starving again: population varying roughly a factor of 2, locally).
Here is a source for Particle accumulation rates in the Greenland Ice: http://www.pnas.org/content/105/34/12140.figures-only
Note the PARTICULATES peak pre-1920 from home-heat with Coal: this explains the 1922 Low Sea Ice (when the 60-year cycle would have PEAKed the ice around 1920) see VERY near the END of the fascinating Skeptical compilation of charts: http://www.appinsys.com/GlobalWarming/RS_Arctic.htm