Figure 3 of the Synthesis Report of the Copenhagen Congress presents the long-term trend of increasing temperature and the range of IPCC projections.

The sharp-eyed JeanS over at Lucia’s smelt a fish, noticed the trend appeared to be too high, and did a number of replications indicating the window used was 14 years, and not 11 years as claimed in the caption, and also in the list of Figures.

Figure 3: Changes in global average surface air temperature (smoothed over 11 years) relative to 1990. The blue line represents data from Hadley Center (UK Meteorological Office); the red line is GISS (NASA Goddard Institute for Space Studies, USA) data. The broken lines are projections from the IPCC Third Assessment
Report, with the shading indicating the uncertainties around the projections3 (data from 2007 and 2008 added by Rahmstorf, S.).

Figure 3: Changes in global average surface air temperature (smoothed over 11 years) relative to 1990, p. 9

Below is my replication of the figure (using an SSA package in R) with 11 and 14 year periods and the ‘minimum roughness criterion’. The trend lines are displaced by the software, but it makes it easier to see.


Black are the CRU temperatures, and the linear extensions are the data points appended to the end of the series for the ‘minimum roughness criterion’, which adds a line with the same slope as the slope of last window size (11 or 14) points. You can see that the slope of the added points increases a lot from 11 to 14 point, which explains why an increase in the window size would change the ssa curve.

Blue lines are the ssa, first EOF for the 11 (dashed) and 14 (solid) embedding periods. The removal of the downturning in the 11-window by the 14-window as shown above is clearly shown.

The red lines are the actual ssa forst EOF trends, without the ‘minimum roughness condition’. The MRC is not necessary. This is an arbitrary end condition selected by the authors in Rahmstorf 2007.

So its pretty clear that expanding the window would be necessary to maintain an alarming uptrend in the ssa curve.

JeanS put the question directly to RC.

254. Jean S Says:
Your comment is awaiting moderation.
25 June 2009 at 7:46 AM

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

Interesting the no-one at RC has responed to JeanS’s straightforward question yet.

Does the report err in stating in the caption of Fig 3 that the smoothing length is 11?

Did Rahmstorf change the smoothing length in order to maintain the alarming appearance?

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