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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Joel Shore says:
June 10, 2010 at 8:48 am
tallbloke says:
I read this morning that human co2 emissions fell last year by 1.1%
Since you believe the increase in airbourne co2 is due to human emissions, you have a similar question to answer.
Why is the CO2 continuing to rise, if the human emissions are falling?
Because the increase in CO2 above the pre-industrial levels is due to the CUMULATIVE emissions. If human CO2 emissions fall by 1.1%, then that would mean that, all else being equal, the RATE OF INCREASE of CO2 would drop by 1.1%, not the atmospheric level itself. As this thread has rediscovered, the interannual variability in the rate of increase of CO2 is much greater than 1.1%, so it would be hopeless to be able to detect such a small change.
Just in case Joel’s reasoning is not clear: What we are looking at is the effect of a 1% drop in CO2 emissions by humans. Let’s assume that I am adding $100,000 to your bank account each year and you are spending 50K each year. Money is accumulating in your account. Now if deposits are reduced by 1% to $99,000 year wouldn’t we still expect the bank account to increase? In this example the CO2 content of the atmosphre is the bank account total. It will take much more that a 1% drop in deposits to make the account balance go down.
Nasif Nahle says:
June 10, 2010 at 4:12 pm
Please, read my post at
is nonsense. You exhale about 0.04 gram, not 88 gram. When in a hole, stop digging.
I won’t repeat my posts of 5:26pm and 8:03pm, but they explain this result by putting the CO2 derivative on the left of the equals and the ocean T anomaly on the right (as the cause). It is a simple idea that fits. That ocean T modulates the CO2 derivative is not surprising, and fits what we know about the dependence of net CO2 flux into the ocean on its temperature. Here is an equation
dCO2/dt = A – B(T)
A is the source (mostly fossil fuel burning), B is the sink, which is a function of T. Let’s say it is a linear function of T: B(T)=b1 – b2*T’ where b1 and b2 are positive constants. The sign for b2 represents that the sink is less effective for warmer temperatures, and T’ is temperature with another constant removed.
So we have
dCO2/dt = A – b1 +b2*T’
This is essentially the same formula as in the posting, just rearranged, and it is what you get when the CO2 sink is temperature-dependent, and there is a constant source. For the actual atmosphere B is about half of A, and the b2 term is much smaller than b1, so B weakly depends on T.
The response to my 9:48pm posting about runaway greenhouse yesterday seemed to suggest (a) they thought I advocated a runaway greenhouse, (b) they dispute more CO2 leads to warmer atmosphere. (a) No, this was the logical conclusion if indeed the ocean produces CO2 in response to warming, which it doesn’t since it is a sink. You can get a runaway greenhouse if your feedback loop forces CO2 to increase, but the real CO2 increase is not part of the loop, being determined by independent sources. (b) CO2 increases have a radiative effect leading to a warmer atmosphere, even if only a little as advocated by Lindzen and Spencer, or more as advocated by IPCC, they all agree there is some.
RE: tallbloke: (June 10, 2010 at 2:08 pm) “So far as i know, the tropical thermocline where a mot of the solar absorption takes place is fairly consistent at around 30-35 metres. Of more interest is the higher latitude areas where it varies a lot, both in location and time. In the winter off Newfoundland, it can be as deep as 1200m.”
I was using the term ‘thermocline’ for the upper surface of the deep cold-water zone or the hypolimnion. I would expect to see a delayed increase of the depth of this CO2-rich region as the oceans warms. We really need to show just how much CO2 that the observed 1.2 deg F warming can actually force out of the ocean.
Lon,
After raining on your parade earlier, it occurred to me that you could weaken your hypothesis a bit in order to bypass the Henry’s-Law pitfall that Andrew W mentioned. You could simply say that higher SSTs decrease the RATE at which elevated tropospheric CO2 passes in seawater. That would make sense on a qualitative level.
On a quantitative level, there’s an obvious experiment that’s begging to be performed. Is anyone game for getting their hands dirty?
And not one single word of your long comment thereafter evidenced any error in what I said.
Nigel Calder disagrees with this article. See
http://calderup.wordpress.com/2010/06/10/co2-thermometer/
“The Carbon Dioxide Thermometer”
And while you are at his blog, be sure to read this article
http://calderup.wordpress.com/2010/06/07/tradecraft-of-propaganda/#more-1059
“The tradecraft of propaganda” which gives the text of a very powerful speech he gave
“Global warming is just propaganda”
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.
Obviously possible, but without addressing it, you have a pretty weak presentation.
______________________________________________________________
Try reading this PDF: http://www.co2web.info/ESEF3VO2.pdf
It seems the CO2 data had the same type of “manipulation” as the temperature data.
#
#
PJB says:
June 9, 2010 at 1:15 pm
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?
______________________________________________________________________
There is a lot of dissolved Ca in the ocean that reacts with the CO2 and takes it out of solution.
“Thus, while seawater alkalinity is directly controlled by the formation of calcium carbonate as its major sedimentary sink, it is also controlled indirectly by carbonate metamorphism which buffers the CO2 content of the atmosphere” (McDuff & Morel, 1980). http://www.co2web.info/ESEF3VO2.pdf
Trying to create doubts and uncertainty about the mere distribution of information is a classic tactic of propaganda mongers, and drawing conclusions about the credibility of a whole site on the basis of one article is just the sort of tactic for doing this that I’ve watched astroturfers get up to for years. Add to that, when you then rudely tell the author, “I think this analysis is bunk”, then I don’t see any real need to be tactful in expressing my suspicions.
Next, there isn’t a single solitary word in the original post talking about the MWP. OK, you want to raise the question of the MWP. As it happens, I have shown how it could well be that this post’s ideas can coexist with a MWP with a different base concentration of CO2. But even had you been correct, then making your point was all that was needed. Drawing in issues of credibility and being rude to the author who was kind enough to share his ideas with us, there was no call for that. You turned up the thermostat on the stove, so don’t complain about the heat in the kitchen.
In my view, most climatologists (both for and against the AGW hypothesis) claim too much on the basis of inappropriate use of statistics, something that Wegman argued several years ago. Modelers cannot just ignore the peculiar properties of the data. In particular, almost all climate data is time series data.
The analysis of this data can be done appropriately in either the time domain or the frequency domain or in both domains, but eyeballing two lines drawn on graph paper will just not do. Calculating correlation and regression coefficients on raw data won’t do either because we know from experience that two random walks often show high correlation.
How well does the model fit? How are the errors distributed? Whatever physical explanation you use to build the model and whatever mathematical form the model takes, when you analyse time-series data you have to consider autocorrelation. And you have to be very careful what kind of filter you use, because filters can introduce autocorrelation not in the original data. (Moving averages can cause problems.)
You have to have some method of calculating confidence intervals. Otherwise, there is no way you can be sure that your results arise by chance and thus are no better than the spurious results obtained by some opposing model.
These aspects of modeling are not trivial. Models may incorporate both mathematics and physics, but evaluation methods should rely upon appropriate statistical techniques. This does seem to indicate that the availability of appropriate techniques should be considered when structuring the model.
Leif Svalgaard says:
June 10, 2010 at 8:53 pm
Nasif Nahle says:
June 10, 2010 at 4:12 pm
Please, read my post at
is nonsense. You exhale about 0.04 gram, not 88 gram. When in a hole, stop digging.
You’ve not read it.
John Finn says:
June 10, 2010 at 3:45 pm
tallbloke says:
June 10, 2010 at 2:35 pm
This plot shows the lag of co2 behind temperature on the short timescale
http://www.woodfortrees.org/plot/wti/from:1997/mean:12/plot/esrl-co2/from:1997/offset:-362.3/detrend:26/scale:0.3/mean:12
And we know co2 lags 800 years behind temperature on the long timescale.
So what makes the warmists think co2 leads temperature on any time scale in between?
Because this time the CO2 rise is not due to natural factors. The ice core data shows that this recent rise is unprecedented over the past several thousand years.
This is a complete non-sequiteur. Do you think the radiation interacting with the co2 molecules gives a crap whether they were emitted by the ocean or my motorcycle?
And It doesn’t matter that I’ve detrended the data, the important issue is cause and effect, which is determined by the timing, not the amplitude. Changes in co2 happen after changes in temperature, in the short term, in the long term. If a small drop in temperature causes a drop in the rate of co2 increase as large as a small increase in temp causes a rise in the rate of co2 increase, it’ s a fair indicator that the co2 rise isn’t driving temperature.
This is my opinion on this issue:
Perhaps we must to investigate the oceans and land total biomass regarding to photosynthetic organisms living during the MWP and comparing it with the total biomass at present. We must consider the kind of materials constituting the shells of mollusks, protists, e.g. the proportion of organisms with shells built of calcite or aragonite. There are many “sinks” of CO2 which we have not considered until now for describing the relatively low concentration of CO2 in the atmosphere during the MWP.
One thing is certain, discussing on issues without certainty is a hopeless task.
June 10, 2010 at 5:02 pm
Joel Shore says:
June 10, 2010 at 8:48 am
tallbloke says:
I read this morning that human co2 emissions fell last year by 1.1%
Since you believe the increase in airbourne co2 is due to human emissions, you have a similar question to answer.
Why is the CO2 continuing to rise, if the human emissions are falling?
Because the increase in CO2 above the pre-industrial levels is due to the CUMULATIVE emissions. If human CO2 emissions fall by 1.1%, then that would mean that, all else being equal, the RATE OF INCREASE of CO2 would drop by 1.1%, not the atmospheric level itself. As this thread has rediscovered, the interannual variability in the rate of increase of CO2 is much greater than 1.1%, so it would be hopeless to be able to detect such a small change.
Just in case Joel’s reasoning is not clear: What we are looking at is the effect of a 1% drop in CO2 emissions by humans. Let’s assume that I am adding $100,000 to your bank account each year and you are spending 50K each year. Money is accumulating in your account. Now if deposits are reduced by 1% to $99,000 year wouldn’t we still expect the bank account to increase? In this example the CO2 content of the atmosphre is the bank account total. It will take much more that a 1% drop in deposits to make the account balance go down.
Tallbloke’s misunderstanding is right at the heart of this post. He reads a reduced ‘rate of increase’ as falling. This entire post has generated the same misunderstandings. In fact the whole post is based on the same misunderstandings To add to the bank account analogy think of driving a car. If I’m driving a 50 mph I’ll cover a certain distance in a given amount of time (t). If I reduce my speed to 30 mph, due to local traffic conditions, say, I won’t cover the same distance in time (t). But I will still be moving forward.
It’s the same with the CO2 temperature model. Fossil fuel burning can be considered as the car engine which drives CO2 levels upwards. Temperature can be related to the local traffic conditions which determine how fast the level moves upwards.
To put the effect of a 1.1% decrease in CO2 emissions into perspective, we can just look at the basic numbers. Each year ~8GtC is released into the atmosphere. This equates to a rise in atmospheric CO2 levels of ~4 ppm. However an increased rate of sequestration means that an amount equivalent to about half of this (~2 ppm) remains in the atmosphere. A reduction of 1% is ~0.02% so the effect of a 1% reduction would be to reduce the rise to 1.98 ppm. As we know temeprature anomalies have a far bigger influence on the rise (typically between +/-0.5 ppm).
Ron House says:
June 10, 2010 at 10:50 pm
“…..Trying to create doubts and uncertainty about the mere distribution of information is a classic tactic of propaganda mongers, and drawing conclusions about the credibility of a whole site on the basis of one article is just the sort of tactic for doing this that I’ve watched astroturfers get up to for years. ”
Maybe, but another classic tactic of people wanting to discredit a forum is putting up weak theories, which are simple and credible enough (at least in overview) to get the enthusiastic support of the less thoughtful members of the local cheer squad, only to be thoroughly discredited later on. (for the record, I do not think that is the case here. I think this theory has been posted in good faith).
Do this often enough (intentional or not) and the well is poisoned for anyone who wants to refer to other, good material which has been aired on that site. If this theory is as weak as many posters here have indicated ( I presume Willis, Zeke tc. aren’t all secret bolshie agents), don’t you think that might make people a bit hesitant to using other things, like the material coming out of the temperature stations project, with authority in arguing against CAGW?
I’m not arguing for censorship, but I think it is important for people who believe that something is not up to scratch for a forum site to say so clearly. This is especially so when the proposition starts gathering poorly thought out praise, and so the apparent endorsement of the denizens of said forum. Well, I don’t contribute often here, but I consider myself a denizen and I want it known that it sure hasn’t convinced me.
A lot of people have already explained what the problem with your analysis is, but let me rephrase their point.
The most general model for the increase of the concentration of CO2 is
\dot c = f(c,T) + a
where a is the rate of emission caused by humans, and f(c,T) describes the net contribution of absorption and emission due to physical effects. Now I guess what you want to do is to show that in our current situation a is negligible compared to f(c,T), right? You assume f(c,T) to be linear in T (and independent of c), so that we can make the most general ansatz
f(c,T) = b*(T-T_0)
I think you implicitly take T to be the temperature anomaly, which is certainly ok, since it simply shifts T_0. In total we thus get
\cdot c = b*T + (a-b*T_0)
You then proceed to fit this to your data and obtain about 0.13/month for (a-b*T_0). The problem is however that we don’t actually care about (a-b*T_0), but only about a. If T_0 is big enough, then a can be as big as we like. To actually argue that a is small and negligible compared to f(c,T), you need to know T_0. (You mention at some point that you used data from the 1850’s check its plausibility— could you be more specific?)
To sum it up, it doesn’t matter how strong the correlation is. What matters is how big T_0 is, i.e. how far from (natural) equilibrium we are according to your model.
Nasif Nahle says:
June 11, 2010 at 12:06 am
You’ve not read it.
apart from being wrong by a factor of 10 [you exhale 0.0006 m3, not 0.006], you seem to agree with me that you exhale 0.053 gram, not 88 gram.
The signal you detect in the CO2 concentration tells us NOTHING about the source.
Rather, it tells us how efficient is the SINK.
The source is anthropogenic.
The sink are the oceans. The higher the surface temperature, the worse the sink efficiency. That is why you see the Al Nino signal.
Further, it is impossible to increase the ocean water temperature through all the depths. The temperature must follow the thermocline. Only the top layers of the ocean (about 400 m) can change the temperature.
Jim D –
Why was there no runaway warming in the Vostok record?
Ron House says:
Other than noting that the interannual variations observed and their causes are well-understood by the IPCC and that the IPCC report in fact gives one a lead into the scientific literature on the subject. What is observed here empirically is in fact not at all in contradiction with what the IPCC says. (The extrapolation of this to a claim that the general rise in CO2 since the beginning of the industrial revolution can be attributed to temperature change is, of course, in contradiction with the IPCC and also with a wealth of data and understanding on the issue.)
Six liters of air in my lungs are 0.006 cubic meters, not 0.0006 cubic meters:
http://www.metric-conversions.org/volume/liters-to-cubic-meters.htm
Joel and John,
Yes, I made a mistake with my question to Willis. Too early in the morning. :o/
My points about lag stand however.
ck says:
June 11, 2010 at 3:19 am
\cdot c = b*T + (a-b*T_0)
Your analysis exposes my point, that indeed there seems to be no evidence for the time varying a in the data! Check http://www.eia.doe.gov/oiaf/1605/ggccebro/chapter1.html to see how huge the variation of a has been.
The A_0 plausibility comes from the top figure, or http://www.newscientist.com/data/images/ns/cms/dn11639/dn11639-2_808.jpg
Thanks for your input.