‘In Rahmstorf et al (2007) it is stated that ‘The global mean surface temperature increase (land and ocean combined) in both the NASA GISS data set and the Hadley Centre/Climatic Research Unit dataset is 0.33 C for the sixteen years since 1990 …’

‘In the light of (a) the above analysis, (b) previous related posts on this blog, (c) David Stockwell’s posts at Niche Modeling and (d) comments by others at both blogs, including Stefan Rahmstorf’s replies to David, does any reader care to defend this unqualified statement by Rahmstorf and his co-authors?’

For information.

Scare quote intentional because, even if we all agree such a thing exists, then “real” temperature is not the actual GMST from 1990, but something obtained by averaging. It must be estimated based on other data.

Using any statistical method, there is always an uncertainty in the determination of the “real” 1990 value.

David’s various tests using different analytical techniques show what has always been obvious: The uncertainty in the determination of the the temperature for the “real” 1990 would result in different positioning of the IPCC projection on that graph. The conclusions could range from all temperatures fall below to all fall above the centerline of the projections.

Since we use an 11-year embedding period, the uncertainty in the trend determination and the boundary condition only affect the last 5 years, agreed?

To test this I have shown three different methods with variation here. http://landshape.org/enm/examples-of-simple-smoothers/
The results are as follows:

1. Singular spectrum analysis (SSA used in your paper Rahmstorf7), 11 year embedding period, comparing ‘minimum roughness criterion’ end padding with no padding. The trend lines flex about the 8th point, deviating every other point in the trend line, particularly the last 7.

2. Smooth spline, 11df, end-padding from top and bottom of trend channel (95%CL of a single value). The trend lines flex about the 11th point.

3. Moving average with final point varied to top and bottom of trend channel (95%CL of a single value). The last point in the trend changes, but the it stops 5 points short of the end of course.

In general, the causal filters do not localize variations, while the acausal moving average does. Perhaps you were thinking of a moving average when you said it only affects the last five points?

Now I don’t know what happens in the Matlab implementation you used. Unfortunately, estimates of uncertainty are not included in Rahmstorf et al. 7, which is most of my concern.

So you have to choose a strange boundary condition to come up with a trend line that is not in the upper half here.

The green line in first SSA figure in the post is the simple linear regression of the 34 years data. This trend line is virtually the same as middle of the IPCC trends, is not in the upper half, and is not ’strange’.

I maintain that in our paper, the choice of boundary condition does not affect any of the conclusions.

The simple regression line is almost the same as the SSA with the MRC, and an example where choice boundary conditions affects the conclusions of your paper. As a point of interest, what was the result of the other choice of boundary condition in matlab that you mention? Did it shift the end of the trend line above or below the one you used?

the temperature values of 2002-2006 are all without exception in the upper half of the IPCC range, no matter whether you use the Hadley or the NASA data.

You suggest that 5 points above is significant. However, you do not know unless you test it, and in series with high serial correlation, such runs are probably not unusual. That’s a kind of non-parametric runs test and I forget what it is called.

Stepping back from this analysis, the whole point of statistical testing is to ensure your conclusions are not overturned by subsequent data. The final figure in the post above shows a smooth spline of monthly temperatures from Hadley and GISS. The more recent data suggests that if an orthodox statistical test had been performed in 2006 in Rahmstorf et al. 2007 it would have given a different conclusion, borne out by the subsequent data — these are random fluctuation about a long term trend.

Note: Simultaneously posed to RealClimate.org. Yet to appear.