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Table of contents for Rahmstorf
- Recent Climate Observations Compared to Predictions by Rahmstorf et.al. - a review
- Rahmstorf et al. 2007 IPCC Error?
- Confidence Limits of Minimum Roughness Criterion
- Rahmstorf et al. 2007 Update
- Examples of simple smoothers
- Rahmstorf 7 Finale
- Rahmstorf Revisited
Rahmstorf et.al. claims that previous projections of the IPCC have underestimated climate change, particularly temperatures and sea level rise. The conclusion of the brief paper has been used to justify more vigorous action on global warming by the Garnaut review, on the grounds that global warming is ‘worst that we previously thought’. But does Rahmstorf et.al. hold water?
The method used is non-linear fitting of a trend to temperatures. The conclusion is from a marked increase in the trend in recent years beyond IPCC decadal projections. However, there appear to be many statistical black holes.
Lucia has been trying to verify the provenance of the IPCC projections as they are not described explicitly in paper, with no success.
The method is described only as
a nonlinear trend line computed with an embedding period of 11 years and a minimum roughness condition at the end
with a reference to Moore et.al. “New Tools for Analyzing Time Series Relationships and Trends“. The non-linear method appears to be singular spectrum analysis (SSA). This method decomposes a time series into orthogonal components, such a a periodic, linear trend and random noise parts. Rahmstorf et.al. also mentions a non-SSA ‘minimum roughness condition applied at the end’ without further elaboration. Any ad-hoc techniques appled to the end of the series should raise a red flag, as the part of the series of interest is the recent temperatures at the end.
Digging into Moore et.al. we find the ‘minimum roughness condition’ consists of ‘padding the series so the local trend is preserved’. The reference to the padding the data is none other than Mann 2004, “On smoothing potentially non-stationary climate time series“!. Figures. Mann has been outed for various dubious extrapolation activities at ClimateAudit here).
Second, the unique adjustment was not disclosed in the MBH98 footnotes. Worse, the start date of this series was actually misrepresented in the original supplementary information, which listed the series as starting at the “adjusted” start date rather than the true start date. We only noticed the extrapolation when we compared the Mann version to original data. We noted this in MM 2003, but were not then fully aware of the impact.
Amazing what you find with a bit of digging. It seems like the ‘minimum roughness condition’ is simply a fancy name for the extrapolation of the trend of the last few data points in the series. In that case, the conclusions of the paper — that observed trends surpass the IPCC projections — are based on only a few end points, raising the specter of ‘cherry-picking’.
Another opportunity for cherry picking is in the selection of the 11 year embedding interval in the SSA. No justification is provided in Rahmstorf for the choice. Although Moore et.al. does provide the helpful suggestion:
A wise choice of embedding dimension can be made with a priori insight or perhaps more commonly found by simply playing with the data.
Wise choice or parameter tuning?
Not having assess to SSA, as I can’t find it among the R packages at CRAN, I examined the degree that conclusions of Rahmsdorf et.al. might be cherry-picked by looking at how trends vary with length of series. Below is the plot the HadCRU temperature trend for increasing intervals starting from the present, starting with three years (2004, 2005, 2006), then four years (2003, 2004, 2005, 2006) and so on. Below is the code (which I am not proud of but shows you can program R in proceedural style when you want to).
Figure: Above is the plot the HadCRU temperature trend for increasing intervals starting from the present, starting with three years (2004, 2005, 2006), then four years (2003, 2004, 2005, 2006) and so on.
The plot shows clear peaks with a trend of +0.37C per decade at 16 years trend length (1990-2006) and declines to the long term trend of around +0.1C for longer intervals. The elevated trends reported in the paper and shown on the figure are clearly a reflection of local trends in this period. However, there are no significance tests quoted for the trend!.
Unlike other examinations of IPCC projections here and here, no attempt has been made to determine if the trends are due to climate variability. As reported, trends are declining, as expected if the increase was simply a random fluctuation.
There are multiple potential problems with Rahmsdorf et.al.:
- Uncertain data provenance
- Series padding
- Parameter tuning
- Lack of significance
These are additional reasons why Garnaut’s Climate Review Interim Report is not convincing. The urgency of the message in the review appears to be influenced by Rahmsdorf’s speculative work, but admits:
The Review team’s report says that they have neither the skills nor resources to re-visit the climate science.
Even a quick review of Rahmsdorf et.al. shows statistical deficiencies and speculation that would probably have blocked publication if it didn’t prop up the IPCC and claims of global warming catastrophe. Does Garnaut mean there are no qualified statisticians willing to work in Canberra?
Code
readCRU< -function(source="http://hadobs.metoffice.com/hadcrut3/diagnostics/global/nh+sh/monthly",temps=2:13,plot=T) {
f<-read.table(source,fill=TRUE)
d<-as.vector(t(as.matrix(f[seq(1,length(f[,1]),by=2),temps])))
#d<-c(d,-0,-0)
ts(d,frequency=length(temps),start=1850)
}
rahmstorf<-function() {
t<-readCRU(temps=14)
trendCy<-rep(NA,100)
for(i in 4:100) {
x<-1:i
y<-t[(length(t)-i+1):length(t)]
l<-lm(y~x)
trendCy[i]<-l$coefficients[2]
}
plot(trendCy,type="l",lab=c(10,5,7))
trendCy
}
14 responses so far ↓
David– Thanks for looking at this. I am very puzzled by that Rahmstrof paper on so many levels. I’ve been trying to do some rather simple minded things– but using the figure that I actually find in the TAR “Scientific Basis” (the document they cite as providing the IPCC predictions!
If you can make heads of tails of Rahmstorf, more power to you!
Lucia, I am looking forward to the outcome of your search, although I think this is not a paper that should occupy attention for very long.
“Does Garnaut mean there are no qualified statisticians willing to work in Canberra?”
One hopes not. There are many statisticians of the highest calibre in Canberra, including at the Australian National University (Ross Garnaut’s own institution). In 1995 an eminent Committee of Review found that the ANU School of Mathematical Sciences ‘is active in research at the highest international level in statistics, nonlinear analysis and partial differential equation, and statistical physics.’ Canberra is also the headquarters of the Australian Bureau of Statistics, which is one of the world’s most highly regarded national statistical offices.
Ian, yes. I majored in maths at ANU. My point is that the following statement by Garnaut, that he has no resources to evaluate controversies, is not convincing.
It is my opinion he should use statisticians to perform due diligence on such studies as Rahmstorf et al 2007 where they have obviously been pertinent, and not take them at face value, e.g.
And in fact he has a duty to perform diligence, as science and the IPCC process is not set up to provide unbiased views. Else why are so many climate scientists only expressing their reservations after they retire?
David–
Out of curiosity, can you get an uncertainty estimate for the “true mean” near 1990?
The reason I ask is the procedure in Rahmstorf is to rebaseline (that is shift) all the temperatures to the “mean” temperature at 1990. (The TAR just sets the baseline at 1990 to zero, and includes no data. So, you see, it’s set to the entirely unknown and unknowable “true mean temperature” for 1990.)
To do the eyeball method of data analysis, Rahmstorf finds one specific temperature, then shift the whole shebang up. No uncertainty is attributed to the shift. However, if I were to say the 95% uncertainty in the mean was 0.1C or so, (as consistent with estimating based on a 11 year centered mean) and shift up or down a different amount, we get different results using the “calibrated eyeball test” used in Rahmstorf.
Lucia, I would have to look up the SD, which would be a SD of a temperature ‘estimate’ at a given year. As the SD at the start point SD_1 and the slope SD_2 are then independent, the variances should add to SD_o. So the overall error should then be SD_o = sqr(SD_1^2+SD_2^2).
David,
Like you (and Ian Castles) I am really puzzled that Ross Garnaut, whom I have known for 30 years as a professional analyst, would hang his case so heavily on a brief piece of advocacy (Rhamstorf et al).
Thank you for your insights into the ‘padding’ of the Rhamstorf series. I had not bothered to read the Moore paper.
Best wishes
Peter
When the Garnaut review claims not to have the time or resources ‘to adjudicate on the relative merits of various expert scientific opinions’, I don’t think that it occurs to them that the study by Rahmstorf et al of ‘Recent Climate Observations Compared to Projections’ is anything other than a routine reporting of results using standard and well-accepted statistical methods.
If the late (and sadly missed) Chris Heyde was still with us, I would certainly be seeking his views on the statistical methods underpinning the Rahmstorf study. Surely there are other statisticians with the time and interest to set Garnaut straight on this matter?
David, you can locate the SSA “toolkit” here: http://www.atmos.ucla.edu/tcd/ssa/ The toolkit is described:
All that appears to be involved is a SVD/principal components analysis of the autocovariance matrix. The MTM part appears to be a SVD/principal components analysis of the spectrum - and this was Mann’s specialty prior to MBH.
Hi Steve, Yes I have used it now. Its a neat technique particularly with mixed trends and periodic signals. However, total overkill to use it to trend the last 20 years of temperatures ala Rahmsdorf etal, where a linear trend or cubic spline is more than adequate.
The 11 members of the SSA-MTM Group, as listed in Steve McIntyre’s post above, are also the 11 co-authors of Ghil et al (2002), ‘Advanced spectral methods for climatic time series’, Reviews of Geophysics, 40, DOI 10.1029/2001RG000092. Thus, Rahmstorf et al (2007) cited Moore et al (2005), which in turn cited Ghil et al (2002) - and, for the ‘minimum roughness criterion’, Mann (2004).
12 Niche Modeling » Rahmstorf et al. 2007 IPCC Error? // Apr 9, 2008 at 8:55 pm
[...] As previously reported here, the conclusions of Rahmstorf’s 7 (Rahmstorf, Cazenave, Church, Hansen, Keeling, Parker, and Somerville) rely on a trend line lying above the IPCC projections on their Figure 1, shown enlarged below. No statistical tests are performed, the basis for their claim is purely based on the visual aid. Their Figure 1 is below, with the key part of the image containing the IPCC projection enlarged. Figures 1 and 2: Rahmstorf et al. (2007) Figure 1. Whole and enlarged. Rahmstorf’s 7 state in the figure caption that “All trends are nonlinear trend lines and are computed with an embedding period of 11 years and a minimum roughness criterion at the end (Moore et.al. 2006 [2])”. On reading Moore’s paper, it would appear the nonlinear methodology used was Singular Spectrum Analysis (SSA). The Moore paper suggests the minimum roughness criterion (MRC) would follow the Mann 2004 [3] recipe of padding the end of the series with data reflected about the final value. Figure 3 and 4: GISS temperature with SSA trend, unpadded and padded. The peculiar property of MRC of “pinning” the trend line to the final end point of the series has been noted in a post “Mannomatic Smoothing and Pinned End-points” at ClimateAudit. The comparison of MRC and non-MRC padded series is shown in figures captured from CaterpillarSSA. The first figure “unpadded.png” shows a SSA trend line that approximates the Rahmstorf figure result. The second figure “padded.png” shows the SSA trend line with an MRC padded GISS series, passing directly through the 2006 value. This is as it should be, as the MRC effectively ‘pins’ the trend line to the final value due to the symmetry about the final value. Was a direct application of the SSA trend line used and not an MRC padded series as described? If an MRC padded series had been used in the figure, it would have been end-pinned to the 2006 value, at the center of the IPCC projections. The figure would then not have conveyed the impression that temperatures are in the upper range of the IPCC projections, as claimed. As it was in 2006, it appears that SSA without MRC padding produces a higher trend line than with MRC padding, necessary for supporting their claim. An additional puzzling factor is the reference to MRC padding at all. Padding the end of the series is not actually necessary to ensure a SSA trend line is drawn to the end of the series values. Padding is only necessary in acausal filters such as moving averages that stop a window length short of the end of the series. To date, attempts to contact Prof. Rahmstorf and clarify the actual methodology used have been unsuccessful. [...]
13 Niche Modeling » Free CO2 for all // Apr 25, 2008 at 10:22 pm
[...] Unlike the models currently used to simulate global warming, the semi-infinite theory suggests very little warming from increases in greenhouse gases, around 0.24C for CO2 doubling. This is because the earth’s atmosphere adjusts for the CO2 by changing the water vapor levels, in order to maintain a constant level of greenhouse effect. If correct, there would be no concerns for ‘runaway warming’ if the theory is correct. More importantly, the nations could continue their economic development with fossil fuels, producing as much CO2 as they like, and increasing the levels in the atmosphere without any fears of climate catastrophe. Previously, in a post with my initial impressions, that the approach Ferenc was taking was sound. The next question I had was how a theory with constant greenhouse might produce changes in surface temperatures. The result of my ruminations on that will be published in Australian Institute of Geologists (AIG) shortly. Briefly, even though the temperature of the troposphere stays relatively constant, the temperature of the stratosphere could influence the surface temperature. Other ways of influencing surface temperature are changes in emmissivity and albedo. [...]
14 Blog-Reviews « Climate Review // May 6, 2008 at 8:48 pm
[...] Alle drei vorgestellten Rezensionen bezogen sich auf Paper mit Inhalten, die “Skeptikern” zu Gute kamen. Gegenteiliges - also Skeptiker, die alarmistische Studien auf inhaltlicher Ebene und anhand konkreter Eigenarbeit in Frage stellen - ist sehr selten zu finden. Kürzlich (bei den Recherchen zum Miskolczi-Paper) entdeckte ich allerdings die Seite “Niche Modeling” auf welcher sich der Statistiker Stockwell kritisch mit der Studie “Recent climate observations compared to projections” von Rahmstorf et al. auseinandersetzte. Die Arbeit von Rahmstorf et al. sagte aus, dass fast alle beobachteten Klima-Indikatoren (Meeresspiegel- und Temperaturerhöhung sowie die CO2-Zunahme) am oberen Ende der vom IPCC prognostizierten Werte liegen. In gleich vier Beiträgen (jedes Wort ein Link, Beiträge chronologisch geordnet, beginnend mit dem “ältesten” Artikel) äusserte Dr. Stockwell Kritik zu den von Rahmstorf et al. verwendeten statistischen Verfahren. Erfreulich zu sehen, dass wissenschaftliche Kritik auf Blogs auch von der “anderen” Seite stammen kann. [...]
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