Beenstock’s radical theory needs to be tested. As discussed here, he proposed that it is the change in greenhouse gases (dGHGs) not absolute values, that produce global warming. A simple test is to develop linear regression models predicting temperature, with and without GHG and dGHG. If Greenstock’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.

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It’s incredible that a global warming theory could agree with both the IPCC (discernable anthropogenic influence) and the sceptics (low long term risk from emissions) but there you are. The analysis of Greenstock suggests it is not the amount of greenhouse gasses, particularly CO2, in the atmosphere that contributes to global warming, but the change in the amount. That is, when the rate of CO2 produced is increasing — as it was last century — this increases the global temperature. Conversely, if the rate of increase is constant so is temperature.

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Sea level data from Church appear be integrated as I(1).

d Root ADF Padf
[1,] 0 0.9713052 -0.8354583 0.9561317
[2,] 1 -0.2771277 -5.8808801 0.0100000
[3,] 2 -1.1410606 -8.1287823 0.0100000

As does Jevrejeva’s data set from 1700.

d Root ADF Padf
[1,] 0 0.7552908 -2.106932 0.5312376
[2,] 1 -0.4415736 -9.329505 0.0100000
[3,] 2 -1.3634252 -12.083777 0.0100000

And while the correlation is high when sea level is added into the linear model, the sea level almost blocks out all the other variables:

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So now the fun starts. We have established the integration order of the variables in the RadF file, we impose the rule that only variables of the same order can be combined, and in particular that they cannot be cointegrated with temperature which is I(1). In this case all the anthropogenic variables in RadF are I(2) — W-M_GHGs, O3, StratH2O, LandUse, SnowAlb, BC, ReflAer, AIE — while Solar and StratAer are I(1) or I(0).

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The test of integration order from the previous post is applied to the major atmospheric forcings used in the GISS global climate models in recent years. These are available for 1880 to 2003 in a file called RadF.txt The codes for the forcings are self explanatory: W-M_GHGs, O3, StratH2O, Solar, LandUse, SnowAlb, StratAer, BC, ReflAer, AIE.

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Here we generate and test a number of series with different integration order I(n) and polynomial order O(n). The test is the Augmented Dickey Fuller test, one of the most well known of the unit root tests. Beenstock used three tests, because the tests for unit roots are known to have low power.

The six series shown above are as follows (black, red, green):

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A draft of a paper by Beenstock and Reingewertz has surfaced in the blogosphere, but there seems to be confusion about what unit roots and cointegration are, and I can’t find anywhere on the web that explains them simply for the average Joe. Given one can’t understand the paper without a good grasp of these concepts; I am going to do a few posts in an attempt to make their argument clearer.

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A rash of stunning turnarounds have vindicated years of effort by climate sceptics. The day after ClimateGate broke I made three predictions:

. Disband the entire Federal Department of Climate Change along with all the individual State Departments of Climate Change.

. Vote down the Emissions Trading Scheme Legislation.

. Cancel Copenhagen.

Australia’s Department of Climate Change has been ‘watered down’ to become the Department of Climate Change, Energy Efficiency and Water. The ETS was voted down, and Copenhagen was such a net negative they are probably sorry they didn’t cancel it.

In another successful prediction, the end of drought in Australia came from a massive upswing in rainfall in 2010. This was done using the EMD algorithm and the assumption of stationarity of rainfall: i.e. long-term oscillations with zero trend, in contrast to a non-stationary drying trend as assumed by CSIRO climate models.

In another stunning vindication of Steve McIntyre, the Met Dept are proposing to take over global temperature data from the CRU. Steve has of course been railing for years about the sloppy, good old boys science in Jones’ department, and clearly the professionals agree with his assessment. Gladly the proposal includes a transparent verification process.

In efforts that are long overdue, Lucia reports that various people are attempting to verify the absence of bias in the CRU surface dataset in various ways. Whatever the result, this can only be a good thing, and I hope it becomes a habit.

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From Nature (see http://www.nature.com/ngeo/journal/vaop/ncurrent/full/ngeo761.html):

“The precipitation anomaly of the past few decades in Law Dome is the largest in 750 years, and lies outside the range of variability for the record as a whole, suggesting that the drought in Western Australia may be similarly unusual.”

Climate science has a colorful history of hyperbole: hurricanes, droughts, floods, fires, famines. Old habits die hard and so do true believers. I want to turn attention to the highlighted phrase and what it really means.

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A recent Nature paper we have been reviewing, claims recent snowfall at Law Dome, Antarctica and the drought in Western Australia “lies outside the range of variability for the record as a whole”. Being about precipitation (often more important to us than temperature), and claims of evidence of AGW causing drought, its interesting.

I finally succeeded in replicating the results but only after resorting to viewing the code, due to omissions in the description of methods. Below I argue (at the end) that the precipitation in LD (and therefore in Western Australia) is not unusual, finding a better than 5% chance of an anomaly that size occurring in a record of that length.

To his credit, Tas van Ommen has been incredibly helpful, open with his code and data, and patient with my WTF moments.

The core presentation of the ice core anomalies is in Fig 3 from the paper, from which the method is described, shown below:

The focus of attention is on the size of the last anomaly that starts in 1970 (red far right), relative to the others. The supplementary information states:

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I try not to pen editorials. OK here goes. I respect the attention given to this blog, as there are plenty of other great blogs on climate change, politics, finance, etc to read. I try to stay an ‘on message’ advocate for numeracy. Everyone has something to offer from their experiences though. Right at this moment, there is something to say that is important about numeracy, but takes a bit to explain.

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While the US has had record snowfalls, Australia has had its own excesses of precipitation. Below is a 30 day loop of precipitation. The sequence starts with cyclone Olga crossing the coast in the far north east, moving into the Gulf, and tracking south with widespread rain down through the central east and south east.

The rain quickly moves to the east, with heavy rain and storms on the east coast, especially Sydney, but then appears to ‘bounce west’ and collide with a very large trough to bring more widespread rain to inland areas and sweeping to the east again.

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Just posted on arXiv: The virial theorem and planetary atmospheres by Viktor T. Toth.

Abstract
We derive a version of the virial theorem that is applicable to diatomic planetary atmospheres that are in approximate thermal equilibrium at moderate temperatures and pressures and are sufficiently thin such that the gravitational acceleration can be considered constant. We contrast a pedagogically inclined theoretical presentation with the actual measured properties of air.
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Please discuss the new paper by Michael Beenstock and Yaniv Reingewertz here.

Way back in early 2006 I posted on an exchange with R. Kaufmann, whose cointegration modelling is referenced in the paper, entitled Peer censorship and fraud. He was complaining at RealClimate about the supression of these lines of inquiry by the general circulation modellers. The post gives a number of examples that were topical at the time. ClimateGate bears it out.

Steve McIntyre wrote a long post on the affair here.

[R]ealclimate’s commitment to their stated policy that “serious rebuttals and discussions are welcomed” in the context that they devoted a post to criticize Ross and me and then refused to post serious responses. In this case, they couldn’t get away with censoring Kaufmann, but it’s pretty clear that they didn’t want to have a “serious” discussion online.

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The claim that “the precipitation anomaly of the past few decades in Law Dome is the largest in 750 years, and lies outside the range of variability for the record as a whole”, is a ‘Hockeystick-like’ claim. Such claims have a considerable literature, and the analysis I have been doing is reminiscent of Rybski et.al. on the temperature record.

Koutsoyiannis has a career of work grappling with non-normal statistics in hydrological data, using models with long-term-persistence, and the difficulty of prediction. These more advanced analysis attempt to account for the fact that precipitation has a long-term correlation structure, extreme events happen more frequently than expected, etc, and are well worth the study. That is, there is no need to reinvent the wheel here.

Below is the Law Dome snowfall data illustrating aggregation at the scales of 10, 20, 30 and 40 years where previous posts suggested the divergence of recent snowfall is significant.

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Here is the distribution of annual snowfall in Law Dome Antarctica over the last 750 years (blue), compared to a normal (dashed red) and a lognormal (solid red) distribution.

Remember that in the finest Popperian tradition we are trying to disprove that the snowfall in the last few decades at Law Dome has been unusual. To do this, I have used a robust approach of aggregation (splitting the series into equal sized section), estimating the parameters of the lognormal distribution, then plotting the actual mean snowfall in the final aggregate against the calculated confidence limits.

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Yes I watch “House”. I wanted to return to the issue of whether the snowfall in Antarctica is normally distributed, as it has bearing on the claim in van Ommen and Morgan from the abstract:

The precipitation anomaly of the past few decades in Law Dome is the largest in 750 years, and lies outside the range of variability for the record as a whole, suggesting that the drought in Western Australia may be similarly unusual.

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Here is the second major claim contained in van Ommen and Morgan from the abstract:

Here we report a significant inverse correlation between the records of precipitation at Law Dome, East Antarctica and southwest Western Australia over the instrumental period, including the most recent decades.

The actual figures quoted for correlation are as follows.

The results show significant negative correlation between seasonal June–August average values of the SWWA regional series and LawDome. The correlation r=−0.16 (P=0.05, effective sample size, Neff=105) increases in strength to r=−0.55 (P=0.05, N5eff=10) for 5-year smoothed data.

With the following regional pattern (of interest to Geoff).

For individual stations, a general pattern emerges with stronger correlations (reaching r=−0.69, N5eff =9, P=0.02, at Boyanup, five-year smoothed) for stations in the west and centre, diminishing to the east and far south.

I think aggregation is a much better approach than smoothing data, as smoothing adds a lot of autocorrelation that you then have to compensate for in your significant test. You can never be sure that you have compensated enough. In aggregation you slice the series into even sized pieces and take the mean. It produces fewer data points for coarser aggregations, but this is what you want to accurately reflect the actual information in the series. Smoothing is good for visualization, bad for estimating correlation.

In the figure below I show the adjusted R2 value (black) and the significance of the slope parameter (red) at a range of aggregations from one to 20.

For the raw data (aggregation=1) the R2 value is 0.016 and the correlation is non-significant at P=0.10. Taking the square root of my R2 value gives 0.1264911, which could be consistent with a Pearson coefficient R=-0.16. The P value is way off though, P is stated as a significant 0.05 while I get a non-significant P=0.10.

There are a number of significant correlations (below P=0.05) at coarser aggregations, particularly from 6 to 11 years. The 10 year aggregation has an R2=0.71 and a significant P=0.0007 corresponding to the stated values of r=−0.55 (P=0.05, N5eff=10) for 5-year smoothed data.

Notably these correlations are more pronounced at some scales, indicating important periodicity in the data that should be teased out. The strength of the correlation is subject to the specific scale the data is tested at.

In summary, there is a puzzling disagreement why I find no correlation between rainfall in SWWA and snowfall at LD on the raw data that should be reconciled.

However I agree within reason on the correlation of the aggregated (climate scale) data, and won’t pursue this avenue further.

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An issue in question here is whether the recent snowfall at Law Dome is unusually high relative to the 750 year long record (and therefore, so the argument goes, probably due to AGW).

Below is the snowfall at Law Dome from the ice core. Above is the actual snowfall, and below is the accumulation of the series minus the mean (using the R function cumsum) indicating where snowfall is above or below average.

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After yesterdays post on the gibberish proof of global warming due to increased Antarctic Circulation, Andrew drew attention to Jones, J. M. and M. Widmann, 2004, Early peak in Antarctic oscillation index claiming that the Antarctic Oscillation has changed in the last thirty to forty years, but is only where it was in the late fifties to early sixties.

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A transcript of an interview with Tas van Ommen on the link between Antarctic excess and West Australian deficits of precipitation displays questionable proof of anthropogenic global warming.

A natural circulation pattern surrounding Antarctica has three lobes because of the three continents and three ocean basins in the Southern Hemisphere. Tas claims in the past 30 to 40 years the strength of that three-lobe pattern has increased, bringing moisture and warmth into Antarctica and dry air back up to Western Australia.

He claims that a natural explanation has a 1:1000 probability.

Well, it is a real smoking gun I guess. It could be that we have just happened to find something that is really one in actual fact, thousands flukey event to get such a large snowfall. The more natural interpretation is that there is something been going on in the last 30 to 40 years and we know what that something is. It is the human impact on the atmosphere.

This was reported as ‘proof of climate change‘. But he admits it is an assumption.

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The latest submission to arXiv:physics.ao-ph is entitled Interglacials, Milankovitch Cycles, and Carbon Dioxide by Gerald E. Marsh. Here is a review of the evidence regarding the timing of Termination II, the penultimate interglacial transition 140k years ago, and factors that may have caused it: CO2, Milankovitch induced insolation changes, or changes in solar magnetic flux, altering the Earth’s albedo through cosmic ray flux.

To appreciate the importance of this period, and a clear logical analysis of it, consider the recent lecture tour of Australia by Lord Monckton and Prof. Plimer. Lord Monckton argues strongly that climate sensitivity to CO2 is very low, too low to be of concern, and an increasing number of peer-reviewed papers using independent observational methods — Douglass, Lindzen, Spencer, Schwartz, Pinker, Shaviv — back him up. Prof. Plimer argues that the history of climate has been enormously variable, and not related to CO2 levels in the atmosphere.

This contrast of low sensitivity but high natural variation has prompted criticism on the irony of a tour by sceptics with contradictory viewpoints. As I understand their view, they maintain “the sensitivity of the climate to CO2 cannot be as low as suggested by these results because low sensitivity cannot explain the large glacial-interglacial transitions”. A solar cause for the penultimate transition has been scoffed at because the timing is wrong. It must have been a volcano or something that kicked off the chain of CO2 feedback that resulted in the warm interglacial.

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Until recently, even hardened climate skeptics when asked about the science would say: “Well we think it is warming, but how much is caused by humans is uncertain”. Now a rash of revelations are coming out to challenge even this bedrock claim, e.g.

It seems that when we leave out the great number of weather stations that were introduced in the last 50 years or so, that the tendency is absolutely not a rise in temperature, see Global Warming Vs Clojure!.

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A few impressions from Monckton’s talk at the Brisbane Irish Club, providing some novel points not seen elsewhere. Some interesting impressions did come out of it.

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Monckton’s main argument seems to be represented by the statement that climate sensitivity to CO2 has been overestimated by the IPCC by around 6-7 times, giving exaggerated projections of warming for a business as usual scenario of CO2 emissions. The IPCC range is around 2-6C degrees warming by 2100, and Monckton’s is 0.5C. While he provides some calculations, this view is also supported by a measure of respectable scientific literature.

The view that CO2 sensitivity is being grossly exaggerated is the one that is shared by myself and the likes of Spencer, Shaviv, Lindzen, Douglass and others. The most concise illustration of this is the one produced by Spencer, showing where the various authors lie, relative to the IPCC model projections.

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WUWT reports in The IPCC: More Sins of Omission – Telling the Truth but Not the Whole Truth the greatest failing of the IPCC, if not environmental sciences. The article describes how the effects of climate change on climate, hunger and water storage are misrepresented to exaggerate negative effects. Here I show that the same deception is in play with the statements on species extinctions in AR4.

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The Brisbane Institute luncheon Panel Debate (Monckton, Plimer, Readfearn, Brook) in the Grand Ballroom, from 12:00 – 2.00pm is sold out. Seats are still available at the Irish Club, across the street from 3pm to 5pm.

Historic. Not to be missed. I will be at the Brisbane events. Come and say hi.

SYDNEY
Wednesday 27 January,
12:15, Luncheon, The Union Club, SOLD OUT
17:30 Public lecture, Sheraton on the Park download PDF
contact: John Smeed, phone or SMS 0417 269 216 johnsmeedATadna.com.au

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An opinion on the The Social Cost of Transparency — a defense of secrecy — was given by an Australian economist on Mish’s blog.

Steve Keen says:

One quick perusal of that article and I could consign it to neoclassical gibberish. The key giveaway is in the first sentence of the abstract:

“I study a class of models commonly used to motivate monetary exchange, extended to include a physical asset whose expected short-run return is subject to exogenous news events, but whose expected long-run return is independent of this information”

The part of bold is the give: this is a model where the future is subject to randomness, but not change: whatever happens in the short term has no impact on the future.

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JoNova noticed a Canberra Times article that the Tasmanian drought may not be due to global warming after all.

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