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.

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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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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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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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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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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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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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Deserving of wider attention: Ten Commandments of Statistics

THOU SHALT…

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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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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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Have you noticed a distinct change in the rhetoric around global warming? Seems like revisionism going on in the mainstream media in the form of shift in focus to the most likely values, or expectations of global warming, rather than emphasizing the low probability, worse possible scenario.

For example, this one on sea level from nature.com.

Sea level rise – not so fast.

In the latest salvo of the scientific debate over future sea level rise, a new report counters claims that rapidly swelling seas will soak estimates published by the UN climate planel in 2007.

A major “it’s worse than we thought” story out of March’s Copenhagen Climate Congress, for example, was that sea level could climb more than a metre by 2100 – seemingly far worse than the rise of up to 59 centimetres indicated in the 2007 report from the Intergivernmental Panel on Climate Change (IPCC). This was in fact something of a straw-man comparison, since the IPCC total explicitly excluded the impacts of accelerated glacier melt, and the new studies were attempting to add these impacts in.

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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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Here, out-of-sample tests are used to test the robustness of the linear regression models of natural variation in global temperature. Previous models were developed on the whole data set. Here we develop them on partial data sets and examine how well they predict temperatures on the other part. These are also called independent tests.

The models that do well on the unseen data are in some sense more robust, reliable, and it gives you a feel for the constraints the data are placing on the models. You can see what conditions are needed to give certain results.

The results are placed in the animated gif above, where the blue temperatures are the out-of-sample values.

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Zhen-Shan and Xian (2007) (PDF) was mentioned earlier, but here is the abstract in full, because their findings in China apply equally to global temperatures. Read the rest of this entry…

To continue our excursion into natural variation models of global temperature: What do they predict?

Here are a couple of different models fit with data up to the year 1990. This was in order to compare their projections with out-of-sample reality after 1990. The year 1990 is also the start of the major IPCC projections from the TAR WG1 available here.

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Below is quick review of some of the evidence and consequences of a 60 year climate cycle. According to Roy Spencer, the argument that increasing carbon dioxide concentrations alone are sufficient to explain global warming is reasoning in a circle. By ignoring natural variability, they end up claiming that natural variability is insufficient.

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