Rather than bloviate over the implications of a unit root (integrative behavior) in the global temperature series, a more productive approach is to formulate an hypothesis, and test it.

A deterministic model of global temperature (y) and anthropogenic forcing (g) with random errors e is:

y_t=a+b.g_t+ε

An autoregressive model of changes in temperature Δy_t uses a difference equation with a deterministic trend b.g_t-1 and the previous value of y or y_t-1:

Δy_t =b.g_t-1+c.y_t-1+ε

Written this way, the presence of the unit root in an AR1 series y is equivalent to the coefficient c equaling zero (see http://en.wikipedia.org/wiki/Dickey%E2%80%93Fuller_test).

I suspect the controversy can be reduced to two simple hypotheses:

H0: The size of the coefficient b is not significantly different from zero.
Ha: The size of the coefficient b is significantly different from zero.

The size of the coefficient should be indicative of the contribution of the deterministic trend (in this case anthropogenic warming) to the global temperature.

We transform the global temperature by differencing (an autoregressive or AR coordinate system), and then fit a model just as we would with any model.

In the deterministic coordinate system, b is highly significant with a strong contribution from AGW. For the AGW forcing I use the sum of the anthropogenic forcings in the RadF.txt file W-M_GHGs, O3, StratH2O, LandUse, and AIE.

Call: lm(formula = y ~ g)
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.34054 0.01521 -22.39 <2e-16 ***
g 0.31573 0.01802 17.52 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.1251 on 121 degrees of freedom
Multiple R-squared: 0.7172, Adjusted R-squared: 0.7149
F-statistic: 306.9 on 1 and 121 DF, p-value: < 2.2e-16

The result is very different in the AR coordinate system. The coefficient of y is not significantly greater than zero (at 95%) and neither is b.

Call: lm(formula = d ~ y + g + 0)
Coefficients:
Estimate Std. Error t value Pr(>|t|)
y -0.06261 0.03234 -1.936 0.0552 .
g 0.01439 0.01088 1.322 0.1887
—
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.101 on 121 degrees of freedom
Multiple R-squared: 0.0389, Adjusted R-squared: 0.02302
F-statistic: 2.449 on 2 and 121 DF, p-value: 0.09066

Perhaps the main contribution of AGW is since 1960, so we restrict the data to this period and examine the effect. The deterministic trend in AGW is greater, but still not significant.

Prob1(window(CRU,start=1960),GHG)
Call: lm(formula = d ~ y + g + 0)
Coefficients:
Estimate Std. Error t value Pr(>|t|)
y -0.24378 0.10652 -2.289 0.0273 *
g 0.03050 0.01512 2.017 0.0503 .
—
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.1149 on 41 degrees of freedom
Multiple R-squared: 0.1284, Adjusted R-squared: 0.08591
F-statistic: 3.021 on 2 and 41 DF, p-value: 0.05974

But what happens when we use another data set. Below is the result using GISS. The coefficients are significant but the effect is still small.

> Prob1(GISS,GHG)
Call: lm(formula = d ~ y + g + 0)
Coefficients:
Estimate Std. Error t value Pr(>|t|)
y -0.27142 0.06334 -4.285 3.69e-05 ***
g 0.06403 0.01895 3.379 0.00098 ***
—
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.1405 on 121 degrees of freedom
Multiple R-squared: 0.1375, Adjusted R-squared: 0.1232
F-statistic: 9.645 on 2 and 121 DF, p-value: 0.0001298

So why be concerned with the presence of a unit root? It has been argued that while the presence of a unit indicates that using OLS regression is wrong, this does not contradict AGW because the effect of greenhouse gas forcings can still be incorporated as deterministic trends.

I am not 100% sure of this, as the differencing removes most of the deterministic trend that could be potentially explained by g.

If the above is true, there is a problem. When the analysis respects the unit root on real data, the deterministic trend due to increasing GHGs is so small that the null hypothesis is not rejected, i.e. the large contribution of anthropogenic global warming suggested by a simple OLS regression model is a spurious result.

Here is my code. Orient is a functions that matches two time series to the same start and end date.

Prob1<-function(y,g) {
v<-orient(list(y,g))
d<-diff(v[,1]);y<-v[1:(dim(v)[1]-1),1];
g<-v[1:(dim(v)[1]-1),2]
l<-lm(d~y+g+0)
print(summary(l))
plot(y,type="l")
lines((g*l$coef[2]+y[1]),col="blue")
}

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.

The red line is the annual temperatures from 1910 to 2008 based on a simple average of the data in each year. The temperature is strongly increasing, and there seems to be some sort of glitch around 1940 where temperatures increase suddenly.

The problem with averaging all these stations is that the any tendency in stations to change with latitude introduces bias. That is, if stations are introduced in warmer climates late in the century, the average will be biased to warmer temperatures.

To get around this problem, I have simply normalized each of the station records (i.e. subtracted a station’s mean value) before averaging each year. This puts all of the stations on a even playing field, so to speak, no-matter whether it is normally warm or cold.

The blue line shows the normalized result. The temperatures are only slightly increasing.

Whats more, current day temperature has yet to exceed the peak temperature achieved in 1914 (blue dotted line and marked with blue crosses).

While averages of the raw Australian data appear to be increasing strongly, a simple normalization procedure to remove the bias introduced by station changes virtually eliminates all trace of temperature increases.

One would expect a similar situation in Australia to the Nordic stations, with a lack of individual stations with strongly increasing temperatures.

For interest, here is the figure supporting the temperature curves in IPCC and also published in e.g. Forster, P. et al. 2007: Assessing uncertainty in climate simulation. Nature 4: 63-64.

Here is the data object Aus.tab, and here is the script.R. Save the data object to a directory and then run the R script in that directory.

I have a similar view to Willis Eschenbach on this issue, and don’t claim that the BoM is actually altering the global temperature figures. However, issues in New Zealand and the Fennoscandian region are also found in Australia, proving the point that the compiled data cannot be taken at face value, and the adjustments to get them into the form we usually see need to be comprehensively audited.

1. Annual OHC data from NODC.

2. Fit a regression model (M1) incorporating linear and periodic terms of period 60 years (to account for Pacific Decadal Oscillation):

x=time(OHC);
f=x*pi*2/60;
M1 = lm(OHC~x+sin(f)+cos(f))

3. Fit another regression model with the addition of a quadratic term,

M2 = lm(OHC~x+sin(f)+cos(f)+I(x^2))

4. Compare the reduction in the regression sum of squares due to the incorporation of the quadratic term, taking into account the loss of degrees of freedom due to autocorrelation (see http://en.wikipedia.org/wiki/F-test for tests of nested models)

The result below shows M1 as a solid line and M2 as a dashed line. The p value for the F test is a marginally significant 0.052 (not significant at the 95% CL) for an improvement in the model due to addition of a quadratic term.

For interest, I appended a value of 5 onto the end of the series, to anticipate the case of a precipitous fall in OHC this year. The result is below, with a non-significant p value of 0.467 for an improvement in the model due to addition of a quadratic term.

So based on these tests, taking into account the oscillation of the PDO and the autocorrelation, the empirical evidence does not strongly support an ‘acceleration’ in OHC and if it continues to decline as it appears to be doing, what support there is will vanish.

The turnkey R script and data as a zip file is here.

Update: Now available from arXiv

Comment on “Influence of the Southern Oscillation on tropospheric temperature” by J. D. McLean, C. R. de Freitas, and R. M. Carter

David R.B. Stockwell and Anthony Cox

Abstract

We demonstrate an alternative correlation between the El Nino Southern Oscillation (ENSO) and global temperature variation to that shown by McLean et al. [2009]. We show 52% of the variation in RATPAC-A tropospheric temperature (and 59% of HadCRUT3) is explained by a novel cumulative Southern Oscillation Index (cSOI) term in a simple linear regression model and 65% of RATPAC-A variation (67% of HadCRUT3) when volcanic and solar effect terms are included. We review evidence from physical and statistical research in support of the hypothesis that accumulation of the effects of ENSO can produce natural multi-decadal warming trends. Although it is not possible to reliably determine the relative contribution of anthropogenic forcing and SOI accumulation from multiple regression models due to collinearity, these results suggest a residual accumulation of around 5 ± 1% and up to 9 ± 2% of ENSO-events has contributed to the global temperature trend.

The sorry-state of Dr. Hathaway’s prediction record is in the news.

For example, in 2006, Dr. Hathaway looked at disturbances in the Earth’s magnetic field that are caused by the Sun, and they were strong. During past cycles, strong disturbances at minimum indicated strong fields all over the Sun at maximum and a bounty of sunspots. Because the previous cycles had been shorter than average, Dr. Hathaway thought the next one would be shorter and thus solar minimum was imminent. He predicted the new solar cycle would be a ferocious one, consistent with a short cycle.

Instead, the new cycle did not arrive as quickly as Dr. Hathaway anticipated, and the disturbances weakened. His revised prediction is for a smaller-than-average maximum. “There was a long lull of several months of virtually no activity, which had me worried,” Dr. Hathaway said.

Predicting trends will continue, like the stock market always going up, or the housing market never dropping more than 20%, is a fool’s bet.

Fresh Bilge is a little kinder:

I have watched Hathaway’s NASA press releases for a couple of years, with the increasingly comical upcurves of an active solar cycle projected from the solar minimum that just kept going and going. It was clear that someone was resisting reality. I always surmised that Hathaway was a global warming ideologue who did not want the AGW paradigm disturbed by news of a quiet sun. But the man finally proved himself a scientist rather than an ideologue and went with the evidence. Good for him.

If the AGW ideologue is finally becoming a scientist, what was he before?

This week I am going to work on getting the disproof of sea-level acceleration paper done. Basically, the so-called acceleration of sea level is not significant on a century scale, so there is no basis for belief in anything other than a linear model of sea level rise, and correspondingly small rises in the centimeters (not meters) by 2100.

Apologies for not having an RSS prediction question up, but the providers have blocked my ssh access for some reason, and I have to get that reinstated.

Fifteen of ‘Australia’s top climate scientists’ published their creed.

Around the world, thousands of scientists have devoted their professional lives to studying the climate. Not centrally organised, they sometimes build temporary affiliations but they remain scientists throughout – that is, they are independent, constantly challenge each other and are committed to searching for truth through objective, independently verifiable evidence.

As we used to say in grad school, they are “pulling back the foreskin of science”. You would think by now enough instances of collusion, bias, sloppiness, lack of critical evaluation of the AGW hypothesis, and basic mistakes have been documented that there is little cause for such pretentiousness.

Like the Copenhagen conference report Figure 5, based on the now-discredited Rahmstorf et al 2007 paper, altered by Stefan Rahmstorf to enhance the impression of warming, and then misreported in the figure caption. I wonder if its been fixed yet? Or the growing list of discredited AGW papers, as well as

Harries who claimed to detect the greenhouse effect from CO2 spectral brightening but whose later (unreported) publications were much more equivocal;

Soden, who claims to have detected increase in specific water vapor from spectral brightening using false assumptions.

History shows the proclamations by ‘top’ scientists such as Harries, Santer, and Sodon, that proof of AGW had been found, only fade away later. What the article fails to mention is that the case of AGW remains circumstantial, as it always has been. CO2 is blamed for temperature increases since 1960 because ‘we can’t find any other explanation’. However, the literature is replete with other possible explanations — UHI, solar, CRF, and SOI — sources of ongoing controversy totally ignored in their article.

I believe there are a number of responses being written.

That mean global tropospheric temperature has for the last 50 years fallen and risen in close accord with the SOI of 5–7 months earlier shows the potential of natural forcing mechanisms to account for most of the temperature variation.

While the bottom line of this paper is that the change in SOI accounts for 72% of the variance in global temperature for the 29-year-long MSU record and 68% of the variance in global temperature for the longer 50-year RATPAC record, I think the claim of a longer term temperature effect could have been better supported. They stated:

Lean and Rind [2008] stated that anthropogenic warming is more pronounced between 45°S and 50°N and that no natural process can account for the overall warming trend in global surface temperature. We have shown here that ENSO and the 1976 Great Pacific Climate Shift can account for a large part of the overall warming and the temperature variation in tropical regions.

However, the assertion comes down to Figure 4 where they identify that the mean of the SOI (and temperature) seems to change at 1976. This model is not identified rigorously with any analysis, but is stated as an observation in the text.

For the 30 years prior to the 1976 shift (i.e., 1946 – 1975) the SOI averaged +1.93 but in the 30 years after 1976 (i.e., 1977 – 2006) the average was -3.06, which represents a shift from a La Nina inclination to an El Nino inclination. The standard deviations for the two periods were 9.48 and 10.40 on monthly SOI averages, and 6.56 and 6.35 on calendar year averages, which indicates consistent variation about a new average value. … From 1959 to 1975 the RATPAC LTT averaged -0.191°C and from 1977 to 1993 it averaged +0.122°C. The standard deviations on the seasonal data were 0.193° and 0.163 C°, and on monthly data 0.162°C and 0.146°C. We have already illustrated the close relationship between SOI and GTTA, but this descrip- tion of the respective changes before and after the Great Pacific Climate Shift indicates a stepwise shift in the base values of each factor but otherwise relatively consistent ranges of variation.

Break tests on both SOI and global temperature indicating the date 1976, and finding of a 7 month lead in the position of the break for SOI over global temperature would have lent more support to this (crucial) claim. As it is, the finding of high frequency correlation between SOI and GT is not as important to the AGW debate, as is the finding of a low frequency (ie. step change) in SOI leading (and hence causing) the change in temperatures.

It can also be seen in Figure 4 that the slope of temperature is upward while the SOI is constant (but higher) after 1976. This would tend to support Bob Tisdale’s hypothesis that recent warming since 1976 can be attributed to a gradual accumulation of heat, due to higher frequency of El Nino events. He has dug up a long-recognized, but little studied mechanism of re-emergence to explain it.

The paper was followed by two critical comments, both bashing the statistics, and these are attached to the link above. Rahmstorf replied to those comments. The issues raised are familiar to readers of this, CA, Lucia, and other statistical blogs: significance, autocorrelation, etc. and worth a read.

Worthwhile as the comments are, they do not look into the problem of the end-treatment used by Rahmstorf, and I look at that here.

All of the papers projecting these high end rates, and they all depend on the assumption of recent ‘acceleration’ in sea levels. That is, seem to depend on the rate of increase getting faster and faster.

Rahmstorf 2007 paper uses the smoothing method most recently savaged at CA here, where it was shown despite all the high-falutin’ language to be equivalent to a simple triangular filter of length 2M, padded with M points of slope equal to the last M points. My main concern is that at this crucial end-section, the data has been duplicated by the padding, effectively increasing the number of data points of very high slope.

The figure below shows a replication of the Rahmstorf smoothing with and without padding (moved down for clarity) (code below). Two sea level data sets are shown, one by Church “A 20th century acceleration in global sea level rise” (used in Rahmstorf, data available from CSIRO here) another by Jevrejeva “Recent global sea level acceleration started over 200 years ago?” (data here)

It should be noted this data ends in 2001-2, a truncation bound to maximize recent temperature increases.

You can already see how much the padding adds to the impression of acceleration at the end. Also note that the simple triangular smooth is a very good replication to the Rahmstorf combobulation (lower fig 3 below).

Having modeled the sea level rise, the next step in the replication is to calculate the rate of sea level increase, from the smoothed sea-level data (upper figure 3 above). The figure below shows my replication. The black line is a close as I can get, though it seems like Rahmstorf’s rate line rises even higher at the end. The red line shows that removing the padding effectively removes part of the increasing sea-level rise at the end.

The green and blue lines illustrate an undescribed part of the method. Figure 2 in Rahmstorf 2007 says that the rate curves are “time derivative of this sea-level curve”. In fact, it takes the calculation of a moving 15 year regression line to give a smooth rate curve. The green line is a 2 year regression, the time derivative, and it is still very bumpy.

Which made me think, why not just apply a moving 30 year trend line to the raw sea level data without any other smoothing? The result is the blue line, which as you can see, is not too dissimilar in shape to the smoothed lines, although there is no uptick at the end.

He then goes on the bin the data into 5 year intervals to get the result in Fig2 – another ad-hoc smoothing technique. The Rahmstorf patented smoothing method so far has used singular spectrum analysis (SSA), convolution (filtering), and now linear regression and binning. Is there any form of smoothing this guy cannot use!

Above is my replication of Rahmstorf’s figure 2, with and without padding. The corrrelation between temperature (on the x axis) and rate of sea level rise (on the y axis) is the crux of the paper. The padded version is a fairly close replication. The unpadded version of course sees a number of points truncated at the end where the rate of sea level increase is highest.

I get a padded slope of 2.9 mm rise per degree C, and unpadded of 4.06 mm rise per degree C, both significant. Rahmstorf got 3.4 mm rise per degree C. He also claims that this figure is robust to changes in the smoothing from M=2 to M=17, and this appears to be the case from the plot below at M=2.

Looking at this data, when you take out the extension due to the padding, I see a cluster of points at about a rate of 2.0 mm of sea level rise, with a smaller cluster at a lower rate. The conclusion that the rate of sea level rise will increase as temperature increases (aka acceleration) depends very much on the position of the LOWER cluster. Relying on the middle cluster alone, there would be no correlation between rate of increase and temperature.

Based on these results, I would say that the padding is not contributing much of an artifact to the results. Need to look elsewhere for problems, and I have a few ideas.

Look here for non-turnkey code (but not hard to work out).

Anthony asked if it would be difficult to statistically justify the breaks in temperature between 1976 and 1979 proposed by Quirk (2009) for Australian temperature. He has an interest in oceanographic regime-shifts and climate change. Sure, I said, a simple Chow test.

We ended up rebutting the Easterling & Wehner (2009) claim that describing temperatures since 1998 as declining is ‘cherry picking’, finding a major regime shift occurred in 1997, statistically justifying the use of 1997 as a starting point for temperature trends.

A regime-shift based temperature forecast follows logically from identification of significant breaks. Our paper, “Structural break models of climatic regime-shifts: claims and forecasts“, has been submitted to the International Journal of Forecasting, and is downloadable from arXiv.

The figure above shows the positions of statistically significant breaks (blue) in 1978 and 1997. Based on the dates of regime-shifts (established with statistical significance and corroborating oceanographic evidence), a presumed underlying warming of 0.5C per century (green line), and no other major changes, the current stable temperature regime will continue until around 2050 until it hits the underlying uptrend, finishing about 0.2C above present temperatures at the end of the century.

This model suggests we are in a period similar to the 50 year period from the 1930′s through to the late 1970′s of very variable, but overall flat temperature trend.
Here is the abstract.

A Chow test for structural breaks in the surface temperature series is used to investigate two common claims about global warming. Quirk (2009) proposed that the increase in Australian temperature from 1910 to the present was largely confined to a regime-shift in the Pacific Decadal Oscillation (PDO) between 1976 and 1979. The test finds a step change in both Australian and global temperature trends in 1978 (HadCRU3GL), and in Australian rainfall in 1982 with flat temperatures before and after. Easterling & Wehner (2009) claimed that singling out the apparent flatness in global temperature since 1997 is ‘cherry picking’ to reinforce an arbitrary point of view. On the contrary, we find evidence for a significant change in the temperature series around 1997, corroborated with evidence of a coincident oceanographic regime-shift. We use the trends between these significant change points to generate a forecast of future global temperature under specific assumptions.

As shown by 102 citations in Google Scholar already, Rahmstorf et al 2007 has been one of the main references for alarmist calls to action because the “climate system is responding more quickly than the climate models indicate”. Taking the first one off Google:

The strong trends in climate change already evident, the likelihood of further changes occurring, and the increasing scale of potential climate impacts give urgency to addressing agricultural adaptation more coherently. There are …

Adapting agriculture to climate change – pnas.org, SM Howden, JF Soussana, FN Tubiello, N Chhetri, M … Proceedings of the National Academy of Sciences, 2007 – National Acad Sciences.

Respected on-line authors like Peter Gallagher, Mark Lawson and Lucia were concerned with the paper. Lucia attacked the ‘slide and eyeball’ approach. I engaged with Rahmstorf at RealClimate and wrote a number of articles on the uncertainty, until he told me in effect to ‘sod off and publish’. But rather than try to diagnose a sloppy methodology and be ignored, time and evidence has done the job instead. Here is my abstract.

Abstract: The non-linear trend in Rahmstorf et al. [2007] is updated with recent global temperature data. The evidence does not support the basis for their claim that the sensitivity of the climate system has been underestimated.

Its gratifying to read that the authors of the Copenhagen Synthesis Report do not seem to agree with Rahmstorf et al 2007 either, in reference to analysis in a figure that ostensibly used the same method as Rahmstorf et al 2007.

Figure 3 … shows the long-term trend of increasing temperature is clear and the trajectory of atmospheric temperature at the Earth’s surface is proceeding within the range of IPCC projections.

However, five days ago JeanS, a talented data analyst, pointed out an inconsistency in Figure 3 of the synthesis report at Lucia’s in a post, Fishy odors surrounding Figure 3 from “The (Copenhagen) Synthesis Report”, which he illustrated with replications of Figure 3 with different variations on a smoothing parameter. I did some replicating too. It turns out that the global temperature trend had a higher slope than it should have had if it was produced with an 11 year embedding period, as was reported in the caption.

JeanS queried Stefan about the inconsistency at RealClimate. Five days later his comment was released from moderation and Stefan admitted:

Did you change the filter length from M=11 to M=14 in the temperature graph (Figure 3)?

[Response: Almost correct: we chose M=15.

The reason he gave was essentially to address the same concerns the bloggers had raised about Rahmstorf et al. 2007 in the first place, that Stefan had refused to acknowledge, and are the subject of my paper:

In hindsight, the averaging period of 11 years that we used in the 2007 Science paper was too short to determine a robust climate trend. The 2-sigma error of an 11-year trend is about +/- 0.2 ºC, i.e. as large as the trend itself. Therefore, an 11-year trend is still strongly affected by interannual variability (i.e. weather).

Obviously, I am glad he finally appears to have agreed. But as a later poster pointed out, the misrepresentation of the embedding period in the legend raises questions about the motivation:

Stefan’s inline comment implies that he changed the smoothing method only after he realized that m=11 showed a flattening of the trendline, while m=14 did not. Changing things on the fly like this and leaving the erroneous caption just gives skeptics more ammunition.

Indeed. Of course, Stefan claims it was an innocent error in the figure caption:

[Response: I hadn’t noticed the error in the caption of our graph yet, thanks for drawing my attention to it. I have notified the editors of the report of this mistake. Not sure why a small technical error in the caption would give ammunition to anyone except conspiracy theorists:

This error was not noticed despite the warrant concerning the extensive peer review of the Synthesis Report made in the preface.

This report has been critically reviewed by representatives of the Earth System Science Partnership (ESSP), by the parallel session chairs and co-chairs, and by up to four independent researchers from each IARU university. This extensive review process has been implemented to ensure that the messages contained in the report are solidly and accurately based on the new research produced since the last IPCC Report, and that they faithfully reflect the most recent work of the international climate change research community.

On the relevance, Stefan apparently finds no problem with arbitrarily changing the parameters of the smoothing, and regards the error in the caption as not important:

None of this has anything to do with the smooth trend line or is affected by whether one happens to choose 11-year or 15-year smoothing.

Apparently it does affect the message communicated by the figure enough to want to increase the smoothing from 11 years to 15 years.

So this raises a number of issues:

1. What is to be done with the many sources that already reference Rahmstorf et al 2007, and will in the future, to justify faster actions on controlling emissions, including Australia’s Garnaut Report?

2. Why were the obvious shortcomings of the original article, by a number of lead chapter authors of the IPCC, not pointed out (and defended even) by other members of the climate science community (with a comment in Science say), and only skeptical bloggers noticed or were concerned by it?

3. As Jan Pompe remarks, if temperatures continue to stay flat, is it justified to keep increasing the smoothing period of the trend lines to ensure the appearance of an increasing trend, as Stefan appears to think?

Call me a conspiracy theorist, but when a short smoothing gave a high warming, Rahmstorf and his coauthors were quick to cry ‘the sky is falling’. But when the trend turned down due to random fluctuations, he changed the parameters to stay on message. As Marcellus said, “Something is rotten in the State of Denmark” (Hamlet).

Update: Lucia does a fine job of explaining the history and issues in Source of fishy odor confirmed:
Rahmstorf did change smoothing.

But looking into fractal data is like seeing pictures in clouds. Be suspicious of magic methods that pull explanations out of the air. Below I have plotted SSA decompositions of the the monthly global temperature anomaly from the HadCRU dataset from 1976 to the present, the period of most recent rise, and attributed largely to GHGs. Kind of zooming in.

The similarities to the previous post are there in the initial series, although the year ranges are different. The thing I noticed was the first two series, the main ones, have very noticeable downturns at the end. Clearly, neither of series 1 or 2 could represent a signal due to steadily increasing GHG’s, with a hook in the end like that. Perhaps the downturn in the last few years is significant, and the exponential seen in the previous decomposition from 1900 on is due to something else, or nothing, an endogeneous trendiness!

I think I need to lie down. I need to understand a lot more about the limitations of SSA before jumping to conclusions. Can SSA reliably recover exponential signals anyway? Here is were you need to start running SSA on simulated data.

For reference I plotted the first series (red line) in the figure above onto the actual temperature data (black line). The hook down really only starts in the last few years.