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

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The UAH Index is approaching new highs, but there is overhead resistance immediately ahead, and primary medium-term indicators are becoming modestly overheated.

Does this spell trouble ahead for the AGW bulls? Eventually. Overheated conditions generally indicate an imminent drop, usually between -0.6-0.8 degrees C.

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The Australian reports a major new controversy after Britain’s Met Office denounced research from Stefan Rahmstorf suggesting that sea levels may increase by more than 1.8m by 2100.

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Environment minister Peter Garratt claimed recent figures on Australian temperature prove Opposition leader Tony Abbott was wrong to claim that the world had stopped warming.

Substitute Australia for the World, and the last 100 years for 10 years, and you might get close to the actual claim, similar to that made by respected climate physicist Roy Spencer that “there has been no net warming in the last 11 years or so”.

It’s easy — but confused — to find a limited region with a different climate, over a different time period, then use it for rebuttal.

David Jones of the BoM claims, referring to their Annual Report that the upward trend of temperature since 1920(?) should silence the critics once and for all.

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Digging deeper into the Australian Temperature Adjustments, below are data from 224 stations in the Torok and Nicholls network. It looks like most of the increase in Australian temperature in the last 150 years is due to a step-like increase in the mean annual minimum temperature since 1975!

CA examined the sometimes considerable adjustments of individual stations here and here. Steve also plotted up the raw station data. I don’t know how he did the plots for ‘before adjustment’ as all the data seems to be ‘post adjustment’ by Torok.

Here I use a differenced normalization method described previously to account for the differences in mean temperature at each station, without averaging over areas. Its not exactly the same, but it produces a similar trend result, as shown in the last figure below.

The Torok network contains the mean annual maximum and minimum temperatures of 224 stations, and these are plotted below with the ‘official’ BoM mean temperature (blue) of high quality network of 103 stations. While the minimum and mean temperatures are clearly increasing, the maximum temperature has not increased at all.

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If you have seen the articles on the NZ temperature adjustments and Nordic temperature adjustments you might be interested in the Australian data.

The issue with NZ and Nordic data that the raw temperature data for weather stations do not show the temperature increases indicated by the IPCC, raising the question of how the data have been adjusted.

As Prof. Karlen states in the ClimateGate email #1221683947, temperature at many stations has not exceeded early 20th century temperatures:

.. data sets show an increase after the 1970s to the same level as in the late 1930s or lower. None demonstrates the distinct increase IPCC indicates.

Here is the plot of means of Australian raw data for 103 temperature stations, based on the file Aus.tab downloaded from the Australian BoM web site and collated by Steve McIntyre.

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Steve’s new site is here. Search the emails from CRU here. Browse the leaked FOIA files here.

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Below are the results of applying the EMD algorithm (Empirical Mode Decomposition) to Australian Rainfall, and predicting the future rainfall with a VAR model (Vector Autoregression).

First, EMD splits the rainfall into IMF’s (Intrinsic Mode Functions) that are cyclical but variable in amplitude and frequency.

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How to predict with EMD? Because the EMD algorithm decomposes time series into a number of periodics of different frequency (IMFs), and a residue trend, prediction in EMD is by extrapolating each of the IMFs separately (a VAR model is recommended) and fitting a cubic polynomial to the residue (example code at end of here). The predictions are then added together.

Below are a couple of examples of EMD predictions on familiar data sets, the HadCRU global surface temperature, and the TLT series from the satellite MSU RSS data. In both I have also applied the recommended prediction techniques to extend the result into the future.

The first is the satellite TLT, and I have used up to IMF 5 so that variation up to annual quasi-periodicity is represented. The residue in this case, the red arch, has peaked and is projected to decline, along with the overall temperature, in the next few years. The amplitude of variability is also declining.

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Our approach so far has been to model natural climate variation of global temperature with sinusoidal curves, and potential AGW as increasing trends. A new algorithm called EMD (Empirical Mode Decomposition) promises to more robustly identify cyclical natural variation (NV), showing the contribution of NV and AGW to global temperature, and testing the IPCC claim that most of the recent warming is due to AGW.

Underestimation of natural variation (NV) is a crucial flaw in the IPCC’s logic, according to Dr Roy Spencer:

They ignore the effect of natural cloud variations when trying to diagnose feedback, which then leads to overestimates of climate sensitivity. … By ignoring natural variability, they can end up claiming that natural variability does not exist. Admittedly, their position is internally consistent. But then, so is all circular reasoning.

The relative contribution of AGW to temperature increase in the late 20th century underpins the IPCC global warming claims, according to the Wiki page on Scientific Opinion on Climate Change:

National and international science academies and scientific societies have assessed the current scientific opinion, in particular on recent global warming. These assessments have largely followed or endorsed the Intergovernmental Panel on Climate Change (IPCC) position of January 2001 that states:

An increasing body of observations gives a collective picture of a warming world and other changes in the climate system… There is new and stronger evidence that most of the warming observed over the last 50 years is attributable to human activities.[1]

Since 2007, no scientific body of national or international standing has maintained a dissenting opinion.

So estimating the relative proportion of natural variation vs. trend is very important. While widely used in other fields, EMD is relatively little used in climate science.

As an example, Lin and Wang (2004) used EMD for analysis of solar insolation. They claim that the solar eccentricity signal is much larger than previously estimated, more than 1% of solar irradiance, and adequate for controlling the formation and maintenance of quaternary ice sheets. This is a potential resolution of the 100,000 year problem, that has also been used to justify the necessity of CO2 feedback in producing ice ages.

Conventional spectral methods are strictly periodic — the period is constant in both frequency and amplitude. EMD relaxes these assumptions, allowing quasi-periodicity, which might explain why more variation is potentially explained. The EMD algorithm proceeds by first extracting out the highest frequency, called an intrinsic mode function (IMF) and leaving a residual. It does this to the next highest frequency, and so on, until only a trend is left.

While it is possible the residual is also part of a cycle — it is always possible to model a trend with a sinusoidal of long enough period — we treat this as AGW trend in order to estimate the maximum possible contribution of AGW to global warming.

Here are the results of applying EMD to the CRU global temperature series. Figure 1 below shows each of the 5 IMF’s and the residual, the remainder after subtracting out the periodics.

Each of the IMF’s is shown, with mean periods of 4.0, 6.6, 11.9, 23.4, and 55.1 years respectively. Most readers would be well aware of the similarity of these periods to major solar and oceanic cycles.

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