Beenstock’s radical theory needs to be tested. As discussed here, he proposed that CHANGE in greenhouse gases (delta GHGs or dGHGs) not absolute values produces global warming. A simple test is to develop linear regression models predicting temperature, with and without GHG and dGHG. If Beenstock’s theory is correct, then models containing dGHG should be more accurate.

The protocol was to develop and test linear regression models on all the temperature data from 1900 to 2004 (internal test), and two external tests on held back data. That is, the data is divided in half, the model is developed in one half and tested on the other. This gives two external tests.

The index of fit is the Nash-Sutcliffe coefficient of model power. The NSE compares the skill of a prediction to a mean value. The NSE is positive if the prediction has more skill, zero if skill is the same as the mean, and negative if less than the mean.

I chose the following variables based on previous models. I decided to include an ocean oscillation term as I have seen a 60 year cycle in the residuals (eg here), indicating the presence of an unexplained periodic. Here are the variables:

TEMP — temperature

OO — The sum of a standardized AMO an PDO indices

GHG — The sum of all anthropogenic columns in RadF.txt, mostly the radiant effect of CO2.

dGHG — The first difference of the above

V — Stratospheric aerosols (a proxy for volcanic eruptions)

SS — Sun spot count, a proxy for solar isolation

1) Incredibly, on the first test on all the variables, GHG is not even significant, being entirely screened by dGHG.

TEMP ~ -0.49(***)+0.06*OO(***) + 0.72*GHG() -11.1*dGHG(***) + 4.0*V() -0.09*SS() R-squared: 0.8709

The NSE coefficients that follow are: model on 1900-1950 and testing on 1950-2000, model on 1950-2000 and testing on 1900-1950, and finally model development and testing on 1900-2000.

[1] -4.83 0.625 0.871

The NSE indicates the model has some difficulty predicting temperature post 1950 from a model developed on data prior to 1950.

I then ran the model again with only GHG and not dGHG. The predictions are shown on the graph, where blue is prediction from a model developed on pre 1950 data, green the prediction from a model developed on post 1950 data, and observed global temperature is black.

You can see the difficulty in predicting post 1950 temperatures, reflected in the NSE values as well:

[1] -14.809 0.639 0.820

Finally, I ran it again with dGHG not GHG. The result when using dGHG was improved over GHG, also reflected in the NSE values. The prediction of post 1950 temperatures was still slightly worse than a mean value.

[1] -1.046 0.709 0.878

This test shows two sets of evidence in support of Beenstock’s theory:

1. dGHG is highly significant and GHG is not significant when regressed together.

2. dGHG is a more powerful predictor of global temperature than the absolute GHG in independent tests.

In other words, the empirical evidence from 1900 supports Beenstock’s theory (developed in a cointegration analysis) of a transitory global warming effect from increases in greenhouse gasses, but no long-term harmful effect on global temperature.

Call: lm(formula = TEMP ~ OO + dGHG + V + SS)

Coefficients: Estimate Std. Error t value Pr(>|t|)

(Intercept) -0.679982 0.084692 -8.029 2.31e-10 ***

s$OO 0.068453 0.008863 7.723 6.61e-10 ***

s$dGHG -11.548800 2.599261 -4.443 5.37e-05 ***

s$V 12.015335 2.380680 5.047 7.17e-06 ***

s$SS 0.135458 0.243381 0.557 0.58

—

Signif. codes: 0 â€˜***â€™ 0.001 â€˜**â€™ 0.01 â€˜*â€™ 0.05 â€˜.â€™ 0.1 â€˜ â€™ 1Multiple R-squared: 0.8652

What instead of the Keeling CO2 curve you used the true CO2 data proposed by Massen and Beck http://www.biomind.de/realCO2/papers.htm ? I think you will find that including CO2 in any model will give a poor result. The Keeling curve for CO2 is just another hockey stick example of deliberate manipulation of data. In addition there is the longer term icecore data which shows CO2 lagging temperature. Finally, heat transfer calculations (something all the pseudo-climate scientists clearly do not understand) show CO2 has no or insignificant effect on atmospheric temperature.

What instead of the Keeling CO2 curve you used the true CO2 data proposed by Massen and Beck http://www.biomind.de/realCO2/papers.htm ? I think you will find that including CO2 in any model will give a poor result. The Keeling curve for CO2 is just another hockey stick example of deliberate manipulation of data. In addition there is the longer term icecore data which shows CO2 lagging temperature. Finally, heat transfer calculations (something all the pseudo-climate scientists clearly do not understand) show CO2 has no or insignificant effect on atmospheric temperature.

“Beenstock’s radical theory needs to be tested.”

“If Greenstock’s theory is correct…”

“This test shows two sets of evidence in support of Greenstock’s theory…”

Two names. Pick one. 🙂

Oops. Thanks

“Beenstockâ€™s radical theory needs to be tested.””If Greenstockâ€™s theory is correct…””This test shows two sets of evidence in support of Greenstockâ€™s theory…”Two names. Pick one. 🙂

Opps. Thanks

On the significance of dGHG, if CO2 is dominated by ocean temperature T via Clausius-Clapeyron, then wouldn’t dCO2/dt vary with dT/dt, which in turn would vary with heat/cooling rate, ie solar driver such as discussed by Scafetta, including TSI, cosmic ray/cloud albedo, orbital changes etc. See:

Nicola Scafetta’s on evidence for solar & orbital drivers.

Note Scafetta provides further evidence of the 60 year cycle.

Interesting thought on the physical basis for I(2).

David S.

Suggest exploring the humidity temperature variations shown by O’Gorman & Muller:

How closely do changes in surface and column water vapor follow Clausius-Clapeyron scaling in climate-change simulations?

P A O’Gorman, C J Muller, Submitted to: Environ. Res. Lett.

Note:

It will be interesting to see if any of those relationships show a better statistical correlation using your methods above.

On the significance of dGHG, if CO2 is dominated by ocean temperature T via Clausius-Clapeyron, then wouldn't dCO2/dt vary with dT/dt, which in turn would vary with heat/cooling rate, ie solar driver such as discussed by Scafetta, including TSI, cosmic ray/cloud albedo, orbital changes etc. See:Nicola Scafetta's on evidence for solar & orbital drivers.Note Scafetta provides further evidence of the 60 year cycle.

Interesting thought on the physical basis for I(2).

David S.Suggest exploring the humidity temperature variations shown by O'Gorman & Muller:How closely do changes in surface and column water vapor follow Clausius-Clapeyron scaling in climate-change simulations?P A Oâ€™Gorman, C J Muller, Submitted to: Environ. Res. Lett.Note:

It will be interesting to see if any of those relationships show a better statistical correlation using your methods above.

I wrote this comment on WattsUpWithThat about Greenstock’s paper

—————

“As an amateur I do not understand this paper. Nor do I understand Miscolczi’s paper on a constant optical optical density for the atmosphere. However, I believe I got the gist of both of these papers and I believe they reinforce each other.

Miskolczi claims that the semitransparent nature of the atmosphere in contact with an essentially infinite source of greenhouse gas in the form of water vapor from the oceans is in a state of dynamic equilibrium. As CO2 increases, a little water vapor rains out to keep the net optical density of the atmosphere constant. Remarkably, radiosonde data shows that the humidity above 300 mb has decreased over the last 50 years as CO2 has gone up. This fact rejects all of the GCMs that assume constant relative humidity (which is, or was, all of them).

This new paper by Michael Beenstock and Yaniv Reingewertz looks at the statistics of the changes in temperature, solar radiance, and CO2 and finds that the first and second derivatives do not match in a series of sophisticated tests that I do not understand. Taking it on faith, that they do know their statistics, I find it remarkable that they find that changes in the rate of CO2 emissions cause a short term rise in the temperatures for only a few years. This is consistent with Miskolczi who would certainly allow a short term change before equilibrium is re-established.

Here is my model of how it could work. CO2 absorbs IR from the ground. Due to the long decay time it collides with other molecules before it re-emits the IR. Each level of the atmosphere is heated by the extra absorption and CO2 only emits IR in agreement with the local temperature. Adding heat to the lower atmosphere will drive more convection and the lapse rate will continue to a slightly higher altitude. The tropopause becomes higher and colder. The stratosphere becomes dryer as the dew point at the tropopause becomes lower. Net effect: Constant optical density per Miskolczi and the statistics of temperature rise do not follow GHG per this paper.” ———————-

I have been looking for some way to test this idea. One thought is find an estimate for the mixing time for the stratosphere to reach equilibrium to see if it compares to this new paper. Would the time for volcanic sulfates to wash out of the atmosphere be a good estimate?

Gary, comparing the decay time to other findings would seem to be of

value – Shaviv, volcanics and others have such estimates.

I wrote this comment on WattsUpWithThat about Greenstock's paper—————“As an amateur I do not understand this paper. Nor do I understand Miscolcziâ€™s paper on a constant optical optical density for the atmosphere. However, I believe I got the gist of both of these papers and I believe they reinforce each other.Miskolczi claims that the semitransparent nature of the atmosphere in contact with an essentially infinite source of greenhouse gas in the form of water vapor from the oceans is in a state of dynamic equilibrium. As CO2 increases, a little water vapor rains out to keep the net optical density of the atmosphere constant. Remarkably, radiosonde data shows that the humidity above 300 mb has decreased over the last 50 years as CO2 has gone up. This fact rejects all of the GCMs that assume constant relative humidity (which is, or was, all of them).This new paper by Michael Beenstock and Yaniv Reingewertz looks at the statistics of the changes in temperature, solar radiance, and CO2 and finds that the first and second derivatives do not match in a series of sophisticated tests that I do not understand. Taking it on faith, that they do know their statistics, I find it remarkable that they find that changes in the rate of CO2 emissions cause a short term rise in the temperatures for only a few years. This is consistent with Miskolczi who would certainly allow a short term change before equilibrium is re-established.Here is my model of how it could work. CO2 absorbs IR from the ground. Due to the long decay time it collides with other molecules before it re-emits the IR. Each level of the atmosphere is heated by the extra absorption and CO2 only emits IR in agreement with the local temperature. Adding heat to the lower atmosphere will drive more convection and the lapse rate will continue to a slightly higher altitude. The tropopause becomes higher and colder. The stratosphere becomes dryer as the dew point at the tropopause becomes lower. Net effect: Constant optical density per Miskolczi and the statistics of temperature rise do not follow GHG per this paper.” ———————-I have been looking for some way to test this idea. One thought is find an estimate for the mixing time for the stratosphere to reach equilibrium to see if it compares to this new paper. Would the time for volcanic sulfates to wash out of the atmosphere be a good estimate?

Gary, comparing the decay time to other findings would seem to be ofvalue – Shaviv, volcanics and others have such estimates.

Another explanation: CO2 is heat exhausted(?).

“Yes Lotharsson, no doubt I am confused. Cointegration is a statistical test for measuring the correlation between variables. The Beenstock paper compares CO2, solar and temperature; usual regression looks at the rates of change of climate data and how well the sample items of each data set correlate in respect of the sample means; cointegration conversely looks at the residuals which are individual deviations of each data sample item from the sample means. If the residuals are stationary then the bulk totals of the variables are non-correlatory. This is the case with CO2 and temperature but is not the case with solar residuals which indicate that bulk solar continues to heat. How could it be otherwise? Is this not basic physics? CO2 bulk totals, the residuals, are heat exhausted; this is verified by the log decline in the increase in CO2 from which we can conclude that the atmosphere is saturated for CO2; it has no further heating potential unless in some way the bulk aspect of CO2 concentration can increase atmospheric pressure and therefore heating. This is unlikely for 2 reasons.

The first is that if it were going to happen it would already have happened with historical levels of CO2 which were much greater than today.

Secondly, increases in CO2 seem to be matched with declines in other atmospheric content, currently water, as the Soloman paper and ESRL data shows and historically as O2 levels showed.

Cointegration does not replace the physics, it is entirely consistent with them.”

Which Solomon paper & ESRL data? Any citations/links?

Another explanation: CO2 is heat exhausted(?). “Yes Lotharsson, no doubt I am confused. Cointegration is a statistical test for measuring the correlation between variables. The Beenstock paper compares CO2, solar and temperature; usual regression looks at the rates of change of climate data and how well the sample items of each data set correlate in respect of the sample means; cointegration conversely looks at the residuals which are individual deviations of each data sample item from the sample means. If the residuals are stationary then the bulk totals of the variables are non-correlatory. This is the case with CO2 and temperature but is not the case with solar residuals which indicate that bulk solar continues to heat. How could it be otherwise? Is this not basic physics? CO2 bulk totals, the residuals, are heat exhausted; this is verified by the log decline in the increase in CO2 from which we can conclude that the atmosphere is saturated for CO2; it has no further heating potential unless in some way the bulk aspect of CO2 concentration can increase atmospheric pressure and therefore heating. This is unlikely for 2 reasons.The first is that if it were going to happen it would already have happened with historical levels of CO2 which were much greater than today.Secondly, increases in CO2 seem to be matched with declines in other atmospheric content, currently water, as the Soloman paper and ESRL data shows and historically as O2 levels showed.Cointegration does not replace the physics, it is entirely consistent with them.”

Which Solomon paper & ESRL data? Any citations/links?

No idea. The comment was in this long discussion. http://www.abc.net.au/unleashed/stories/s2842091.htm

I was just interested in the simple expression of the effect of CO2 being “maxed out” as an explanation for the relatinoship.

It’s a weird comment. The stats seems written by someone with some familiarity with the language, but is quite garbled. I think he’s referring to the well-discussed log relationship of heat flux to CO2, but that’s not maxed out – a log does not have a maximum.

Yes, anyway, did you have a comment on the test above? More garbled

than I would like unfortunately.

One obvious issue is confounding. Especially with GHG rising approx exponentially, GHG and dGHG are far from independent. So it’s a matter of numerical chance which is identified as the main factor.

And as I’ve said, there’s no way that either B or you can deduce what is “transitory” or “no longterm effect” from a century of data. You aren’t applying any underlying physical model. It’s only stochastic, and can’t be used for prediction.

OK, I can estimate the improbability of that numerical chance with an F test.

And a function and its derivative are independent.

And a function and its derivative are independent.Of course not. That’s why I referred to exponential growth – where the function and its derivative are highly correlated.

But if you want to get technical, the correlation is the sum of products of function f and derivative – which is pretty much half the difference f^2 final – initial. For an increasing function that’s positive.

No idea. The comment was in this long discussion. http://www.abc.net.au/unleashed/stories/s284209…I was just interested in the simple expression of the effect of CO2 being “maxed out” as an explanation for the relatinoship.

It's a weird comment. The stats seems written by someone with some familiarity with the language, but is quite garbled. I think he's referring to the well-discussed log relationship of heat flux to CO2, but that's not maxed out – a log does not have a maximum.

Yes, anyway, did you have a comment on the test above? More garbledthan I would like unfortunately.

One obvious issue is confounding. Especially with GHG rising approx exponentially, GHG and dGHG are far from independent. So it's a matter of numerical chance which is identified as the main factor.And as I've said, there's no way that either B or you can deduce what is “transitory” or “no longterm effect” from a century of data. You aren't applying any underlying physical model. It's only stochastic, and can't be used for prediction.

OK, I can estimate the improbability of that numerical chance with an F test. And a function and its derivative are independent.

And a function and its derivative are independent.Of course not. That's why I referred to exponential growth – where the function and its derivative are highly correlated.But if you want to get technical, the correlation is the sum of products of function f and derivative – which is pretty much half the difference f^2 final – initial. For an increasing function that's positive.Hi David,

Very nice evaluation set up. We’ll need you pretty soon over here, and you’re wholeheartedly invited (do bring your results with you 😉

http://ourchangingclimate.wordpress.com/2010/03/01/global-average-temperature-increase-giss-hadcru-and-ncdc-compared/

Bishop Hill also made a post about the thread in question, here:

http://bishophill.squarespace.com/blog/2010/3/17/statistical-death-match.html

Watch out for strawmen and trolls!

VS

That discussion is only marginally to do with B&R, who claim that delta CO2 cointegrates with temperature. This analysis agrees with B&R, without calling on unit roots. Its because of all these issues that we do analysis in completely different ways, in an attempt to falsify.

Hi David,

Note that I said ‘pretty soon’ 🙂

We’ve just spent some two weeks establishing the presence unit roots in the series (this was disputed by many ‘online experts’), implying the need to perform cointegration analysis. As soon as we get there, your input will be invaluable.

The idea is to reproduce and explain everything ‘bottom up’.

VS

If I had to guess at what these tests ‘mean’, I would guess that it shows a tendency for temperature within the range we have data for, to ‘absorb GHG shocks’ with a long memory, but not to form a long term equilibrium with GHG levels. However, this does not apply to ‘direct radiative shocks’ like volcanic aerosols or solar variations. It seems to me this would be consistent with the effects of CO2 being ‘maxed out’. But the unit root concept is very abstract, and so its realization in reality is one-to-many. As I say, this is an interesting middle ground.

Hi David,

I understand what the tests/estimations mean and imply. I also really appreciate your analysis here, and your efforts to disseminate information about cointegration analysis.

My invitation referred to a thread containing the first part of the analysis (i.e. we established unit root presence) justifying the whole cointegration approach.

We now need to move on from there and explain both cointegration and the results. I believe we can truly reach some people in that way.

Since I’m not a TSA expert (far from it, I simply had a proper formal education in it, i.e. a Dutch one ;), I’m really eager to call in experts who seem to have a good grasp of the matter at hand.

You are such an individual.

Let’s do this.

Kind regards, VS

VS – I am always willing to help promote numeracy though like you I am really not an expert in it. Be warned, my philosophy of science is that the best explanation is that somebody screwed up, including me 😉

CLT suggests that two would be better at it than one.. 😉

2 would be better at screwing up than 1??

;>)

Ended up over at OurChangingClimate and appreciate your efforts.

As here, if I keep reading I might actually learn something!!

True. You know a thread is near the end when they start talking about

philosophy of science.

Hi David,Very nice evaluation set up. We'll need you pretty soon over here, and you're wholeheartedly invited (do bring your results with you 😉http://ourchangingclimate.wordpress.com/2010/03…Bishop Hill also made a post about the thread in question, here:http://bishophill.squarespace.com/blog/2010/3/1…Watch out for strawmen and trolls!VS

That discussion is only marginally to do with B&R, who claim that delta CO2 cointegrates with temperature. This analysis agrees with B&R, without calling on unit roots. Its because of all these issues that we do analysis in completely different ways, in an attempt to falsify.

Hi David,Note that I said 'pretty soon' :)We've just spent some two weeks establishing the presence unit roots in the series (this was disputed by many 'online experts'), implying the need to perform cointegration analysis. As soon as we get there, your input will be invaluable. The idea is to reproduce and explain everything 'bottom up'.VS

If I had to guess at what these tests 'mean', I would guess that it shows a tendency for temperature within the range we have data for, to 'absorb GHG shocks' with a long memory, but not to form a long term equilibrium with GHG levels. However, this does not apply to 'direct radiative shocks' like volcanic aerosols or solar variations. It seems to me this would be consistent with the effects of CO2 being 'maxed out'. But the unit root concept is very abstract, and so its realization in reality is one-to-many. As I say, this is an interesting middle ground.

Hi David,I understand what the tests/estimations mean and imply. I also really appreciate your analysis here, and your efforts to disseminate information about cointegration analysis.My invitation referred to a thread containing the first part of the analysis (i.e. we established unit root presence) justifying the whole cointegration approach.We now need to move on from there and explain both cointegration and the results. I believe we can truly reach some people in that way.Since I'm not a TSA expert (far from it, I simply had a proper formal education in it, i.e. a Dutch one ;), I'm really eager to call in experts who seem to have a good grasp of the matter at hand.You are such an individual. Let's do this.Kind regards, VS

VS – I am always willing to help promote numeracy though like you I am really not an expert in it. Be warned, my philosophy of science is that the best explanation is that somebody screwed up, including me 😉

CLT suggests that two would be better at it than one.. 😉

2 would be better at screwing up than 1??;>)Ended up over at OurChangingClimate and appreciate your efforts.As here, if I keep reading I might actually learn something!!

True. You know a thread is near the end when they start talking aboutphilosophy of science.

On the scale of a century, forcings and temperature are not linearly related. There are time constants involved. For a two box model, the time constants are on the order of 1 and 19 years. Also, a linear combination of the forcings with independent coefficients not equal to 1 is unphysical and the results are meaningless.

On the scale of a century, forcings and temperature are not linearly related. There are time constants involved. For a two box model, the time constants are on the order of 1 and 19 years. Also, a linear combination of the forcings with independent coefficients not equal to 1 is unphysical and the results are meaningless.

Oceanic Specific Humidity +6 monthsSST +6 monthsOceanic Wind -2 monthshttp://www.remss.com/papers/wentz_science_2007.pdfCO2 -10 – -15 yearshttp://ocean.mit.edu/~mick/Papers/ItoFollows-pr…

Oceanic Specific Humidity +6 months

SST +6 months

Oceanic Wind -2 months

http://www.remss.com/papers/wentz_science_2007.pdf

CO2 -10 – -15 years

http://ocean.mit.edu/~mick/Papers/ItoFollows-pr…

On the scale of a century, forcings and temperature are not linearly related. There are time constants involved. For a two box model, the time constants are on the order of 1 and 19 years. Also, a linear combination of the forcings with independent coefficients not equal to 1 is unphysical and the results are meaningless.

Oceanic Specific Humidity +6 monthsSST +6 monthsOceanic Wind -2 monthshttp://www.remss.com/papers/wentz_science_2007.pdfCO2 -10 – -15 yearshttp://ocean.mit.edu/~mick/Papers/ItoFollows-pr…

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