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.
================================================
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
Bart and Phil: Glad there some folks here that actually can do math. Thanks to the folks at Mauna Loa and the satellite folks, we have real data to work with. Please expand this model and get rid of my simplifying assumptions.
m4cph1sto: Very interesting proposition. There is certainly plenty of good data to use. Please let us know how well your model fits the data.
To anybody still looking at this thread: The key point is CO2 levels and the temperature anomaly seem related, but not in a simple linear way. If we can carefully study data we are sure we can believe in, maybe we can actually understand what is going on.
Thanks for your participation.
Nasif: “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.”
Why do you think I’m concerned about the CO2 increase?
I am not a biologist but I doubt that you exhale 1 kg of CO2 each minute.
Nasif Nahle says:
June 10, 2010 at 9:21 am
Take this assertion from a biologist who exhales ca. 88 g of carbon dioxide 11 times each minute.
more like 0.04 gram 11 times each minute, or ~2000 times as little…
So that biologist must do a lot of heavy breathing…
Well I plan to print out a hard copy of Lon’s paper; if only to have access to the “data” he presents; but right off the bat, I have some serious problems with his exposition; and parts of his thesis.
I’m not averse to his primary claim that the Temperature change might be causing the CO2 change; I can buy that. We are just 800 years AFTER the Mediaeval Warm period; and as AlGore points out in his book; “An Inconvenient Truth.” and other data sources show; the long term ice core history tends to show that CO2 changes cause the Temperature to change 800 years before the CO2 changes that cause it. One might say that the Temperature guesses that it had better change to preact to an expected CO2 change 800 years down the road.
So the mediaeval Warm period temperature increase; could have been caused by the CO2 increases we are seeing now.
But as to Lon’s assertion that it is the rate of change of CO2 that causes the The Temperature to change 800 years earlier; will I can’t buy that.
I was never a PhD undergrad student; just took some undergrad Batchelor’s course as Mike pointed out once. But one thing I remember from my Physics/Maths Undergrad Radio-Physics course; specifically the Electronics portion; is that “DIFFERENTIATORS ARE NOISY.”
The derivative of ANY data set matching ANY mathematical function, is noiser than the raw data itself. So if the data itself doesn’t fit any well behaved function; and we are told it is a logarithmic function; not a linear one as Lon claims; then it is for sure that the derivative of that data won’t.
Then there’s that pesky propagation delay problem. How do you determine exactly what time offset to use between the Temperature data, and the CO2 data IN WHATEVER DIRECTION YOU BELIEVE IN to get it to fit.
I should point out (shouldn’t need to) that somone once “FITTED” the value of one of the fundamental constants of Physics : the fine structure constant; alpha = e^2/(2hc.epsilon nought) = 1.0973731534 E7 m^-1 +/- 1.2 E-9 to a completely fictitious mathematical “formula” with an error less than 2/3 the value of the error band of the then best known experimental value (mid 1960s). Everybody then jumped to the conclusion that the formula had to be correct; because you couldn’t get such a close match by just ******* around with numbers. The theory of that formula had absolutely no observable input from the Physical Universe; but it simply had to be correct. A computer search uncovered about ten more completely fictitious mathematical “formulae” of the same generic form; that also fell within the error band of the best experimental measured value; and one of those was more than twice as accurate, as the original one that started all the ruckus. Then an astute mathematician described a multi-dimensional lattice space; where each of the parameters in this generic formula was one of the dimensions; and the radius of this multidimensional “sphere” was the value of (1/alpha); and the complete set of lattice points that fell within a multidimensional shell with inner and outer radii of 1/alpha +/- the error band of the best experimental value; was a solution of that generic form that satisfied the criterion; and then he derived the complete set; which consisted of about 12 equally fictitious mathematical formulae; all unrelated to any physical universe.
So please don’t try to convince me that correlation even vaguely implies causation whether known or unknown.
Then there is an additional problem with this CO2 data thing. All the books and papers and protagonists, keep on insisting that CO2 is “WELL MIXED” in the atmosphere. Well one glance at the NOAA three dimensional global Pole to Pole variation in atmospheric CO2 over about a ten year period, is quite enough to convince me that there is simply no way that atmospheric CO2 can be well mixed; given that the annual cyclic CO2 variation at Mauna Loa is about 6 ppm peak to peak, with about a 5 month fall time and a seven month rise time; BUT, at the north pole this same cyclic vartiation is 18 ppm peak to peak; not 6ppm; and at the south pole it is only about 1 ppm, instead of 6 or 18 ppm; and moreover at the south pole it is reversed in phase from the north pole.
So CO2 is not mixing from pole to pole, and whatever natural processes add or remove CO2 from the atmosphere, they can remove 18 ppm of CO2 from the atmosphere in as little as 5 months; and if the global excess over the stable base condition of perhaps 280 ppm is at present about 110 ppm excess, then at the north pole, that 110 excess ppm could be removed in as little as 110/18 x 5 months; which is about 2.5 years. Now that is the starting removal rate; so the 2.5 years is the time constant of that process so 99% could be removed in 5 times constants, or under 13 years 9if the process continued without interruption.
So much for a 200 year lifetime or residence time or whatever they want to call it. But even with susch rapid change possible; it still isn’t even vaguly well mixed to maintain that pole to pole asymmetry; so wherever CO2 is released locally it isn’t going to spread pole to pole in any great hurry.
Besides all of that; Mother Gaia does not do Statistical Mathematics; she uses real time data in real time; and obeys all the laws of Physics. We should do what Gaia does; not look for pseudo ancient astrological soup recipes to homogenise inadeuqately sampled data.
Well that’s my opinion any way. But I am going to make a copy of his paper.
Rereading Lon’s Bio, I see I had it a bit wrong; seems like Hawaii is a good pace to settle; might run into barefootgirl on a beach somewhere.
RE tallbloke: (June 10, 2010 at 5:46 am ) “A better answer might be that CO2 always lags behind temperature. And that sea surface temps have been high recently as energy has headed upwards from the deep during the solar minimum, so outgassing will also be a factor.”
Perhaps this lag is due to the heating or cooling of a deep CO2-rich region in the ocean where there may be a multi-decadal thermal time delay relative to the surface. If available, it might be interesting to see a graph of measured depths of the tropical ocean thermocline over the years.
George E. Smith says:
June 10, 2010 at 12:09 pm
“DIFFERENTIATORS ARE NOISY.”
Not inherently, but they amplify high frequencies (the response rises approximately proportional to frequency in the range well below the Nyquist rate), so if your input has high frequency noise in it, you will tend to amplify it. So, the first question is, how much high frequency noise is there in the signal?
In most electronics, there is almost always high frequency noise, which is why we generally low pass filter things like tachometer signals. Lon has effectively done this to some degree by taking his differential over a year’s time and dividing by 12, which produces a scaled average of the 12 monthly differentials.
Niels A Nielsen says:
June 10, 2010 at 11:46 am
Nasif: “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.”
Why do you think I’m concerned about the CO2 increase?
I am not a biologist but I doubt that you exhale 1 kg of CO2 each minute.
Sorry… It appeared that I was addressing my post to you, but not; actually, I used your post as a standing platform; I sincerely apologize.
Regarding my assertion, it’s true… I exhale ~2 moles of carbon dioxide 11 times per minute. Making the conversion, it gives ~88 g each time I exhale. In terms of percentages, I exhale a volume of air containing 5% of CO2, which means 50000 ppmV.
The trick consists in omitting the volume of mixed air that I exhale in each breathing movement and applying pure mathematics.
George E. Smith –
If you’ve not done so already I think you’ll find the Glassman paper I cited in post #2 on this thread to be profitable reading on the points you just made, as well as many others that have come up in this thread.
Bart, the same.
Apart from showing that the pattern of temperature and CO2 in the Vostok record reflects the solubility of CO2 in water according to Henry’s Law, it also extensively discusses and refutes the IPCC assertions that CO2 is well-mixed, and that oceanic uptake of CO2 is constrained and causes anthropogenic CO2 to accumulate, among other things. These are huge problems for the IPCC view, which doesn’t do Henry’s Law.
Glassman has responded to 171 comments, which further illuminate the points under discussion.
Best regards,
Can anyone comment my percieved insignificance of 1 degree celcius of warming? I just can’t see why there would be such a big hoo ha about such a small change. Am I wrong to view this as an insignificant change?
Now, I exhale approximately 0.006 m3 of mixed air during one breathing movement. This gives a real molecular mass of carbon dioxide of 0.012 moles during each exhalation. It means about 0.53 g in each exhalation, which gives ~3.1 metric tons per year. We have to put special attention to these small things when we are investigating volumes of CO2 forming part of any medium.
Following with the same example on my respiration, if I don’t take into account the volume of air in my lungs, I would conclude that the partial pressure of the carbon dioxide in my lungs would be 0.05 atm m, which is a subatmospheric pressure that makes possible the respiration. However, given the small sample of mixed air in my lungs, the real partial pressure of carbon dioxide in my lungs is 0.0003 atm m. It happens because my lungs expand when I lower my diaphragm, so the concentration of CO2 into my lungs diminishes.
Anne van der Bom
Solar radiation differences are the driver you say? Thanks for getting my point without realizing it.
“”” Bart says:
June 10, 2010 at 12:23 pm
George E. Smith says:
June 10, 2010 at 12:09 pm
“DIFFERENTIATORS ARE NOISY.”
Not inherently, “””
Well pedantically true; since arguably a “differentiator” is a mathematical operation on a mathematical function. Practical differentiators (as in electronic) aren’t very accurate differentiators anyway.
So perhaps I should have said the the OUTPUT of differentiators; with noisy data inputs is even noisier outputs.
But then you knew that.
In any case, I can’t even imagine a data stream that is any more noisy than what purports to be the CO2 composition of the earth’s atmosphere; to the extent; that the available directly measured data is incapable of showing whether the CO2-Temperature relationship fits a straight line T=m.CO2 + c or a curve T = T0 + m.log(CO2 + c) make up your own; as Stephen Schneider did.
Peronally, I think it can be fitted to the form:- y = exp (-1/x^2) to as good a fit as to either of the above. Remember that the standard IPCC error acceptance limit seems to be +/- 50%; which gives the obligatory 3:1 ratio of predicted ; excuse me, projected future values; to IPCC concensus satisfaction. And I am sure my form can equally well be fitted to the differential of the CO2 also; with the same hogwash factor. My form can also likely be equally well fitted for any possible propagation delay; either forwards or backwards. I haven’t tried fitting the numbers in the Manhattan telephone directory to the mean global Temperature; but I’ll bet somebody can; to at least as good a fit as the global CO2.
Spector says:
June 10, 2010 at 12:12 pm
RE tallbloke: (June 10, 2010 at 5:46 am ) “A better answer might be that CO2 always lags behind temperature. And that sea surface temps have been high recently as energy has headed upwards from the deep during the solar minimum, so outgassing will also be a factor.”
Perhaps this lag is due to the heating or cooling of a deep CO2-rich region in the ocean where there may be a multi-decadal thermal time delay relative to the surface. If available, it might be interesting to see a graph of measured depths of the tropical ocean thermocline over the years.
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.
Bart says:
So, you compare yourself to Paul Dirac AND Albert Einstein in one sentence?!?! I am sure you are a smart guy, Bart, but you don’t lack humility…It continually amazes me how many people around here seem so confident that they are the next Einstein, Galileo, or whatnot, rather than just one of the thousands of people who languish in relative obscurity because their “paradigm-breaking” scientific discovery turned out to be just plain wrong.
As for mathematics, it is indeed a powerful tool but it is only a tool. You still need to put the correct physics into the mathematical equations to get a result that actually pertains to the real world. And, the physics that you are missing is the fact that the atmosphere, mixed layer of the oceans, and biosphere + soils form a subsystem that has rapid exchange of carbon between the different components but only slow exchange of carbon with the deep ocean. The slug of carbon from our fossil fuel burning introduces new carbon into this subsystem and, while any such slug quite rapidly equilibrates between the different components of the subsystem, it does not rapidly disappear from this subsystem. The temperature and other changes are capable of changing the balance of the carbon between the different components of the subsystem a little bit…and this is the aspect of interannual variability in the atmospheric CO2 increase that Lon has rediscovered here, although it has been well known for more than 30 years, as I documented in this post: http://wattsupwiththat.com/2010/06/09/a-study-the-temperature-rise-has-caused-the-co2-increase-not-the-other-way-around/#comment-406435 .
Nasif Nahle says:
June 10, 2010 at 1:07 pm
Regarding my assertion, it’s true… I exhale ~2 moles of carbon dioxide 11 times per minute. Making the conversion, it gives ~88 g each time I exhale.
No you don’t.
Try again.
Murkowski resolution fails, 47 to 53
Lisa Murkowski’s resolution blocking the EPA’s authority to regulate carbon failed in the Senate today, 47 to 53. Six Democrats crossed over: Mark Pryor, Evan Bayh, Ben Nelson, Jay Rockefeller, Blanche Lincoln and Mary Landrieu. Some people were surprised that Bayh crossed, but I’m not. He’s retiring, but his votes will reflect on Brad Ellsworth, who’s running to replace him, so he’s going to stick with the state’s most important interests. Zero Republicans voted against Murkowski.
So the good news, I guess, is that Murkowski’s resolution went down. The bad news is that in a 60-vote Senate, it’s hard to imagine a climate bill, or even a mere energy bill that does something about coal-fired plants, getting through.
http://voices.washingtonpost.com/ezra-klein/2010/06/murkowski_resolution_fails_47-.html
Nasif Nahle says:
June 10, 2010 at 1:07 pm
Niels A Nielsen says:
June 10, 2010 at 11:46 am
Nasif: “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.”
‘Why do you think I’m concerned about the CO2 increase?
I am not a biologist but I doubt that you exhale 1 kg of CO2 each minute.
“Regarding my assertion, it’s true… I exhale ~2 moles of carbon dioxide 11 times per minute. Making the conversion, it gives ~88 g each time I exhale. In terms of percentages, I exhale a volume of air containing 5% of CO2, which means 50000 ppmV.”
So 1 mole occupies 22.4 l which gives about 50l CO2/breath if that’s 5% I make it 5,000l/breath. Apparently we’re conversing with a whale, how do you manage the keyboard?
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?
Lon, a thought about the difference operator you use on the CO2: By subtracting 2 values at a distance of 12 months, you get a kind of comb filter when you analyse the spectral response. It would be interesting to run the CO2 time series through a better high pass filter – a phase-neutral one with a clearly defined steepness, for instance. I have no idea where this could lead and i haven’t bothered to read the papers cited by the people who think your post is irrelevant (was that polite? hope so. I wanted to avoid a word ending with -ists or starting with astro-) but usually climatological papers are weak on the spectral considerations so it might be uncovered ground.
Fitting curves to time series data or using multivariate analysis to fit cuves to dependent and independent variables does not prove cause and effect. The most ellegant equations, be they linear, curve fitting, first differential or second differential still do not prove cause and effect. The premise that warming temperatures may be causing more CO2 is at least as valid as the premise that CO2 is causing temperature change. Neither is provable. Knowing how to use statistical methods is not the same as knowing PROPER use of those methods and interpreting the meaning of the results. My guess is that any comprehensive attempt at a multivariate regression analysis of all of the potential independent variables that could potentially be causal to temperature change would show high multicolinearity and at the same time those independent varialbles would not, of course, be predictable into the future at any rate. Predicting, or even explaining, climate change is, at least at this time, a fools errand. You only need to look at the non-science that has been used by the proponents of AGW to see this. But I have enjoyed reading about this issue and watching the sledgehammer swing at the mosquito.
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
Why have you detrended the CO2 data? All this does is show that the short term fluctuations are driven by temperature. But we know this. There have been several posts on this. CO2 rises. How much it rises depends on ocean conditions (mainly). But it still rises because we are burning fossil fuels. The underlying trend which you’ve removed shows this.
And we know co2 lags 800 years behind temperature on the long timescale.
We know that this was true following the ice ages. But the warming periods after ice ages lasted for thpousands of years, It was a long drawn out process. The CO2 peak occurred ~800 years after the temperature peak.
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.
On the general point of this post. The model that has been developed is flawed. Consider, for example, hat happens if you have a monthly temperature anomaly of -0.5 deg for the next 100 years… or 1000 years. If Lon Hocker wants to develop a model that predicts CO2 change he needs to include a term for the anthropogenic CO2 contribution and another one for the decay. A simple model equation might take the following form
delta_CO2 = alpha*anthro_CO2 + beta*deltaT + gamma*total_CO2
where alpha =~0.5 (i.e. the proportion of human emitted CO2 which is retained in the atmpshere)
and gamma < 0
I'm sure someone can do much better than this and there may be other variables that need to be considered but at least it seems to make sense.
“So what makes the warmists think co2 leads temperature on any time scale in between?”
Because co2 is a greenhouse gas. It causes warming.
Please, read my post at
Nasif Nahle says:
June 10, 2010 at 1:41 pm
DirkH says:
June 10, 2010 at 2:57 pm
“Lon, a thought about the difference operator you use on the CO2: By subtracting 2 values at a distance of 12 months, you get a kind of comb filter when you analyse the spectral response. It would be interesting to run the CO2 time series through a better high pass filter – a phase-neutral one with a clearly defined steepness, for instance. I have no idea where this could lead and i haven’t bothered to read the papers cited by the people who think your post is irrelevant (was that polite? hope so. I wanted to avoid a word ending with -ists or starting with astro-) but usually climatological papers are weak on the spectral considerations so it might be uncovered ground.”
Dirk, I tried several filters on the smoothed Mauna Loa data, and they all acted pretty much the same. I chose this one for the paper so I could use the unsmoothed data, and keep the filter as simple as possible. The data is easy to get. Pop it into a spreadsheet and see what happens when you use different filtering.
The goal here was to move folks beyond the mindless: CO2 is trending up, and temperature seems to be doing it too, so clearly we are seeing the greenhouse effect. We have real data, and can do a lot better than the IPCC if we keep an open mind.
Onion says:
June 10, 2010 at 3:54 pm
“So what makes the warmists think co2 leads temperature on any time scale in between?”
Because co2 is a greenhouse gas. It causes warming.
But… How much? Almost zero warming:
I = ECO2 (σ) (T)4 / π (Leckner, B. 1971, Pages 37-44)