I only have time to post a quick note on this interesting aspect of Rahmstorf’s diagram – how the centering of Rahmstorf et al 2007 interacts with Rahm-smoothing (now conceded by everyone except Rahmstorf to be a simple triangular filter of 2M-1 years) to enhance “successful” prediction.
I noticed this effect when I did a plot using a standard reference period of 1961-1990 (as opposed to Rahmstorf’s unusual selection of 1990. Rahsmtorf had centered on 1990 (using Rahm-smoothed values). Centering on a single year is a procedure that was severely criticized in the blogosphere a couple of years ago and it was odd to see Rahmstorf also center on a single year, even if it was a smoothed version. But it made me think about the impact of centering on Rahm-smoothed 1990 and the results were interesting.
I had collated A1B model information from KNMI (a large 57-run subset of the 81 PCMDI runs) and presumably representative. I converted all models to 1961-1990 anomalies to match HadCRU and did an unsmoothed comparison of model ensemble average and observations showing 1-sigma limits as in the original. Unlike the original diagram, observations are not in the “upper part” of the models. Indeed, they weren’t even in the upper part” when Rahmstorf et al 2007 was written.
An important difference was that 1990 model values were noticeably above observed 1990 values using a standard 1961-1990 reference period, whereas Rahmstorf centered both the model ensemble and observations on the Rahmstorf-smoothed value in 1990. Think about it – now that we’ve confirmed that Rahm-smoothing is a triangular filter with 2M-1 years.
Rahmstorf’s triangular filter has a lot of weight on the edges relative to a more common gaussian filter. For M=15, in the calculation of the 1990 value, a 2M-1 triangular (Rahmstorf) filter will place as much weight on values from 2000-2005 as 1990 values! Let’s stipulate for a moment that the models were designed with an eye on history to the early 1990s (and the model response to Pinatubo is overwhelming evidence that they did) – nothing wrong with that. Actually, AR4 models probably had their eye on history even later than that.
But let’s take a best case: suppose that peeking was cut off after Pinatubo and everything after that was untuned modeling. Let’s further suppose for the simplicity of illustration that models tracked observations exactly up to Pinatubo and then models ran x% hotter than observations and consider the implications under Rahm-smoothing and Rahm-centering.
In the calculation of the Rahm-smoothed 1990 values, Rahmstorf looks forward. Under the above assumptions (i.e. models running hotter than observations), the Rahm-smoothed 1990 model value will be raised relative to the Rahm-smoothed observations. The use of the triangular filter will cause a noticeable larger effect than a gaussian filter.
Rahmstorf now centers both models and observations using these values. The centering step lowers the models relative to observations, in effect, offsetting part of the divergence. The effect is large enough to make a difference on the rhetorical effect of the Rahmstorf diagram.
To be clear, I am not claiming that Rahmstorf et al did this intentionally. Indeed, there is considerable evidence that they had negligible understanding of the properties of their smooth and perhaps even misunderstood what it was doing. However, scientists and reviewers need to be wary of confirmation bias and, once again, this seems to have interfered with the identification of the problem.
UPDATE: This is what the Rahm graphic would look like using IPCC smoothing.