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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BillD says:
June 10, 2010 at 3:51 am
“If we don’t understand that the basic monotonous upward trend in atmospheric CO2 is due to fossil fuel consumption, it’s difficult to have a discussion about newer and more controversial topics related to climate.”
This is a fundamental problem with people’s thinking. They do not understand that the existence of an equilibrium in the first place implies feedback, and feedback nullifies any projections of this sort.
Think of this situation – and I use it only because it is the most familiar feedback loop in most people’s lives which can be easily understood. The fact that it has to do with temperature is only incidental.
You are in your house with the air conditioning on and set to 65 degF. You start to feel cold, so you bring out a space heater, but no matter how high you set the heater, the temperature only rises to maybe 66 degF. Yet, you do some calculations, and find you have put in enough heat to warm the house by 10 degF. How can this be?
Then, you remember you set the thermostat for the air conditioning to 65 degF. So, you dial it to 70 degF and, mirabile dictu, it gets warmer.
Now, try to keep up with the analogy. Our anthropogenic emissions are like the space heater. No matter how much we crank up the volume, we will never get the ambient concentration up to the level we would get with a straight accumulation. But, global temperatures are like the thermostat in the house, they change the set level of the feedback loop. So, temperatures very strongly and directly modulate CO2 concentration.
Well I downloaded that data in the end.
Define:
Co2(n) = Co2 at month n
T(n) = Temperature anomaly at month n
x = Co2(n) – Co2(n-12) / Co2(n-12) = % annual change in Co2
y = T(n+1) = next month’s temperature anomaly
x is alway positive and lies between 0.1% to 1.1%. x generally increases as the years roll by, i.e. the distribution of x shifts with time. y increases as the years roll by too. Both variables are not stationary, their probability density shits gradually with time.
A simple x-y plot shows that the next month’s temperature anomaly was predictable (to some extent) by knowing the history of Co2. In general, when there was a large increase in Co2, the temperature anomaly in the next month would be higher. When the Co2 increase was smaller (closer to 0.1%), the temperature anomaly for the next month was generally smaller or negative.
If the data is split into two periods the results are qualitiatively similar apart from shifts along both axes because both variables have generally higher values in the later period. Additionally, the later period has a higher response.
Conclusion: If this month’s co2 is high relative to 12 months ago (i.e. closer to 1.1% than to 0.1%), then this is an indication that the temperature anomaly next month is more likely be higher than usual compared to lower than usual, and vice versa.
That does not mean that Co2 causes temperature changes though. It just means that co2 is an indicator which can indicate what next months temperature might be. For, coincident with when there was a large increase in co2, during the period n-12 to n, the mean temperature anomaly happened (in general) to be higher. And when there was a smaller increase in Co2, there had also been a lower temperature anomaly over that previous 12 months.
It so happens too that the planet is a heat capacitor, so when there has been a period of warmth for 12 months we can expect the next month to be warmer than usual. I.e. there is a high autocorrelation in the temperature.
I.e. an even better predictor of the temperature anomaly next month, is the temperature over the previous 12 months.
Causation is more difficult than correlation.
The thing is though, when we look at “temperature anomalies” and “temperature changes”, the numbers we are examaning are absolutely tiny. I mean, 1 degree here or there. Are you kidding me? I am supposed to worry about 1 degree celcius here or there? Compared to natural changes that we know occurred, the numbers are tiny. Compared to the diurnal changes, the numbers are tiny. Compared to the seasonal changes the numbers are tiny. Compared to the glacial cycles, the numbers are tiny. It is a red herring really, to worry about it.
Additionally, high Co2 is good for life on the planet. We need more Co2 to support our increasing population’s food needs. Milder winters would also be helpful here. So again, I don’t know why there would be any fuss about either a Co2 increase or a temperature increase. They are both positive things. Which is just as well since all of the whiners and whingers keep saying that both of them seem to be going up a bit! Good. I hope they both do. It is good for humanity. It is good for life.
1) It is possible that el nino events influence vegetation, including plankton, and thus the CO2 levels of the atmosphere, and not a temperature of water effect. This is the same reason the even larger annual fluctuations at mona loa are visible. One might be able to tell this effect by examining C isotopes since plants have a distinct signature of uptake.
2) Why don’t ice cores show CO2 fluctuations? Because it takes hundreds of years for the snow to become ice dense enough to permanently trap gases (if ever) so gas is diffusing up and down, homogenizing the concentration. An alternate method based on stomatal density on leaves clearly shows historical fluctuations in CO2, not perfectly flat.
Re: Basil
The lack of understanding of “interannual” in this thread is so far beyond a pure disgrace that I didn’t even bother commenting.
We agree on both counts. Indeed, my choice of the words “disaster” & “absolutely hilarious” stemmed from the abysmal “interannual” naivety.
IF regulars like you, I, & a few others did not speak up here and call a spade a spade, WUWT would suffer in reputation simply for running this hopeless article.
“Why should the current warm period have caused CO2 concentrations to rise to >385ppm, when previous warm periods in the last several hundred thousand years only ever saw them reach 300ppm?”
The CO2 concentrations in ice cores are implicitly averaged over 1000 years or more because of the low temporal resolution. Studies of peat bogs have shown centennial and decadal averages much higher than the millennial averages. We would expect that decadal averages of CO2 could be much higher. This means that previous warm periods may have reached much higher that 300 ppm over short periods like 100 years or 50 years and the uncertainties in the ice-core record may be as large as 25%.
We may not be are comparing the same things when we compare the Mauna Loa data to the ice core data. This seems similar to splicing the instrumental temperature record onto the temperature estimates from the proxy record.
OK, it’s an interesting academic exercise, but the result may not be something you would want to use to decide on global policy for fossil fuel use, especially when the bill might be in the order of trillions of dollars.
BQuartero
One of the reasons why reefs building organisms thrive in the tropics is because the chemistry of the tropics is suitable for building reefs – due to the lower CO2 solubility at higher temperatures. People are hysterical over the idea that pH might drop 0.01, when in fact temperature has a much stronger effect on solubility.
tallbloke says:
June 10, 2010 at 5:46 am
>>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?
That’s simple: Because human emissions cause airborne CO2 to rise.
Dave Springer says:
June 9, 2010 at 4:48 pm
“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.”
Agreed! This will also cause a big change to CO2 levels as the colder surface water has the capacity to absorb more CO2. It would be useful to understand more about what climatic conditions effect the ongoing mixing rate, or if change could be triggered by a black swan event, such as a deep ocean super-volcano erupting.
Implied causality and multiple exogenous variables. We are beating a mosquito to death with a sledge hammer here. Reminds me of the AGW crowd.
Re: Basil
and further to this
Also: CO2′ has been more tightly coupled with NAM (AO & NAO) since the big El Nino. (This dovetails with some of Bob Tisdale’s observations.)
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.
Paul Vaughan says:
June 10, 2010 at 8:42 am
‘Also: CO2′ has been more tightly coupled with NAM (AO & NAO) since the big El Nino. (This dovetails with some of Bob Tisdale’s observations.)’
You guys are wearing blinders. What happens in the small also happens in the large. One of the most egregious errors introduced by the AGW crowd is when they arbitrarily decouple dynamic systems, creating discontinuous models of systems which must be continuously variable to have an internally consistent physical basis.
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.”
This is exactly what statisticians do when testing for autocorrelation and stationarity. Otherwise, they can end up making clever statements based on spurious correlations. (Granger and Engle got a Nobel prize for work in this field. See: Granger and Newbold, Spurious regressions in econometrics, Journal of Econometrics 2, 111—120, 1974.)
Random walks can look like trends with noise. To test, “differencing” is followed by tests of autocorrelation of Y with itself lagged. (Not “differentiation”.) If the coefficient of “differenced-Y-lagged” is equal to unity, there is a “unit root”, which incidates that the apparent trend may be a random walk with drift.
Two series that appear to be random walks may nevertheless be co-integrated. Imagine a man and his dog both drunk staggering home from a pub, the dog on an very elastic leash. The distance between the two will vary, but their paths will be correlated so they both end up at home. Depending on the lag-lead relationship, we can infer that one of the drunks leads the other one home, probably the dog leads the man. This would show “Granger causality”. There is extensive literature on this subject.
Global temperates may or may not be a random walk. The coefficient has been estimated as nearly unity and the error bars might well include unity. This arguable, but is not the critical issue. The critical issue is whether or not global temperature is cointegrated with GHG, mainly CO2 and if so, can we infer Granger causality.
There may or may not be flaws in the argument in the paper presented here, but we should expect that statisical techniques that have been around for 20 years or so would have been applied.
That’s what Beenstock and Reingewertz were attempting. (See the comment near the top of this page with the URL.) By the way the word “Nature” appears in connection with the Beenstock and Reingewertz paper, but I could not find the paper using Google Scholar. Has it been published?
Niels A Nielsen says:
June 10, 2010 at 8:20 am
tallbloke says:
June 10, 2010 at 5:46 am
>>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?
That’s simple: Because human emissions cause airborne CO2 to rise.
I cannot understand… Why the concern on increases of CO2? It’s good for life. Take this assertion from a biologist who exhales ca. 88 g of carbon dioxide 11 times each minute.
Very interesting article. A lot of comments along the lines of linear AGW component to the CO2 increases, which one could conclude would mean CO2 couldn’t go negative.
I had a closer look at the Mauna Loa data: April 1970 328.14 – April 1971 327.78…the only month in the history of the record where there was an annual decrease in CO2 (hey it is possible).
…but look at this, wouldn’t be possible now would it, 40 years no couldn’t be…but hang on 2008 was cold was it not? and behold:
April 2007 386.26 – April 2008 386.71
It was damn nearly negative. Of course it was one month, but the temperature plunge was also short lived, so kind of , matches. Just imagine if the temps had stayed down for the whole year, now that would be interesting!!
If the sea temperatures do plunge next year, we might be in for some interesting CO2 readings.
Frank White says:
June 10, 2010 at 9:06 am
Quite good, yes. However, random walk is an idealized construct. Systems which have a correlation time must longer than the data record, and are driven by processes with wider bandwidth than the Nyquist rate, are indistinguishable from random walk.
All: I am not saying this model is “truth”. It is, however, clear that it is an approximation of truth. A more complete model for CO2, which is mathematically rigorous and consistent based on very few assumptions, is
Cdot = (Co – C)/tau + adot + F[T]
where “C” is the atmospheric concentration, Cdot is its time rate of change, Co is a local equilibrium level, tau is a time constant, adot is the rate at which we are adding CO2 to the atmosphere (about 4% of Co/tau), and F[T] is a linear operator acting on temperature T. What the analysis in the above article shows is that F[T] is effectively a very low bandwidth, low pass filter of T. We can rewrite this equation as
Cdot = (Co+tau*F[t] – C)/tau + adot
which can be subsumed into a new operator C1[T] such that
Cdot = (C1[T] – C)/tau + adot
Which says that C will track a temperature dependent equilibrium value C1[T] with a small offset due to adot.
This is how it is. I know I will be attacked, and stupid people, who don’t know sensitivity from complementary sensitivity or a pole from a zero, who have never designed a feedback loop and seen it incorporated into and perform flawlessly in real products in the real world, and wouldn’t know a differential equation from a quadratic equation, will make stupid comments to the effect that I am stupid. Fine. Have at it. But, ultimately, you will learn that I am right.
Bart says:
June 10, 2010 at 9:42 am
Cdot = (C1[T] – C)/tau + adot
Which says that C will track a temperature dependent equilibrium value C1[T] with a small offset due to adot.
The annual value for Cdot is ≅adot/2
so adot/2 = (C1[T] – C)/tau + adot
-adot/2 = (C1[T] – C)/tau
C=C1[T]+tau⋅adot/2
Why do you assume that tau⋅adot/2 is small relative to C1[T]?
June 10, 2010 at 9:42 am
In the above, I should have used T-To, where “To” is the equilibrium temperature at which Co is the equilibrium CO2, in all places. I had thought just to subsume the effect into the constant Co but, since I made the explicit claim that adot is currently about 4% of Co/tau, I have to decouple Co from it. So, we should have
Cdot = (Co – C)/tau + adot + F[T-To]
and the last equation should read
Cdot = (C1[T-T0] – C)/tau + adot
where C1[T-To] is the output of an affine operator on T-To.
Phil. says:
June 10, 2010 at 10:15 am
“Why do you assume that tau⋅adot/2 is small relative to C1[T]?”
It’s not an assumption, it’s based on IPCC data. Not including the temperature dependent term, the difeq is
Cdot = (Co – C)/tau + adot
adot is currently about 4% of Co/tau, but has been smaller in general over the last century. We can bound it’s effect up to the present time by the difeq
Bdot = (1.04*Co-B)/tau
and up to the present time, C .lt. B .lte. 1.04*Co.
Note to all: I am not a climate scientist. The arguments against this from climate scientists tend to be on their turf, and add up to arguments from ignorance, i.e., if I cannot cite a source and a sink specifically, then I must be wrong.
But, the mathematics tell me I am right, in the same way that Paul Dirac knew antimatter existed before it was ever observed, or the way Einstein knew General Relativity was correct before the bending of starlight was ever observed. Mathematics is a very powerful tool, which allows us to see truth beyond our fallible and limited human intuition.
If you do not know how the requirements of my equation can be satisfied, you need to keep looking until you find out, because I am supremely confident it describes truth. I would suggest many of you need to quit treating some of the data which has been collected, e.g. from ice cores, as unassailable, and estimated quantities with error bars as large as the values themselves as certain.
In my previous post, I of course meant to say “their probability density shifts”, but unfortunately did not hit the f key…
It’s well-known that temperature changes cause CO2 changes. This is undisputed except by the most uninformed AGW fanatics (and Al Gore). This paper is using the derivative (rate of change) of CO2, but the simple model’s results are actually from the change in the rate of change, not the rate of change itself. In reality what we have is a “baseline” increase in CO2 from human emissions that is essentially linear, and on top of that another, smaller signal that is the result of the changing solubility of CO2 in the oceans as temperatures change. Unless I’m mistaken (which is possible), this paper verifies a well-known phenomenon that, to my knowledge, has not previously been verified on a global scale. However, the results do not show that the large roughly-linear increase in CO2 in recent years is caused by changing temperatures. Rather, it shows that the small fluctuations in that linear trend are caused by changing temperatures.
okki says:
June 9, 2010 at 1:57 pm
What I like about this site is that papers are presented, and are subjected to criticism.
We get a hypothesis and then that hypothesis is subjected to analysis by the group mind from various perspectives.
If only we had a word to describe this kind of analytical approach to trying to discern the truth.
I thought that we had – the scientific method!
Re: Bart
You’ll have to clarify (unless you really have been sucked in by this article).
m4cph1sto says:
June 10, 2010 at 10:49 am
“This paper is using the derivative (rate of change) of CO2, but the simple model’s results are actually from the change in the rate of change, not the rate of change itself.”
No, the initial equation relates temperature anomaly, which is effectively a low bandwidth differential, to the differential of CO2. The result is that CO2 is effectively represented by a very low bandwidth filtered and scaled version of the temperature relative to a particular baseline.
“Rather, it shows that the small fluctuations in that linear trend are caused by changing temperatures.”
And, the way in which it causes those small fluctuations must smoothly transition into the way it causes large fluctuations. You cannot just arbitrarily draw a line between the small and the large domains with satisfying smooth continuity conditions.
You cannot just arbitrarily draw a line between the small and the large domains without satisfying smooth continuity conditions.