My interest is in the public policy impact. I see figure 3 in the Copenhagen synthesis report as kind of like a mini-version the hockey stick, whose pubic policy impact far exceeded its scientific value.

The reason I prefer to examine trends is that the choice of baseline matters less.

What would the figure at the top of this post look like with a more widely accepted centering, such as 1961-1990 reference period?

Or asked a slightly different way, what would Figure 3 of the Copenhagen report look like if done using more generally accepted methods of centering and filtering?

Sure. But we have data back to 1900 and even earlier. So, that doesn’t end up being important in the climate-blog-war debate.

Well, it kind of does, because Rahmstorf includes the end-points in their figure.

If they go from N=11 to N=15 in going from their 2005 figure to their 2007 figure, and they had dropped the last N/2 points, wouldn’t they have stopped at the year 2000 in both cases?

Also the prior to 1900 isn’t even an issue here, because nobody is debating the Earth is warming. The only question in hand is how much of it is from anthropogenic activity.

If you look at the combined effects of CO2 (warms) and sulfates (cools) from anthropogenic activity, most models don’t show much net impact from human impact till circa 1980. (I use the criteria a net 0.1C increase for the “much” qualifier.)

See, e.g., this figure.

(See the wikipedia figure and caption for more details.)

Wouldn’t you agree that this is an argument for dropping N/2 from the front and end of the detrended series?

Sure. But we have data back to 1900 and even earlier. So, that doesn’t end up being important in the climate-blog-war debate.

Diagnosing anything withing N/2 of the endpoints using the method he selected is still bad because the uncertainty in endpoints is always enormous.

Wouldn’t you agree that this is an argument for dropping N/2 from the front and end of the detrended series?

This is what I do except in cases where (for purely mathematical reasons), I need the final series to be of the same length as the original.

Wow!
So… in fact with ‘11-year’ smoothing, when Rahmstorf’s compare between ’smoothed observations’ and projections every single one of his “smoothed” data points involve both guessed data and data known before the report was published (i.e. 2001). Plus, smoothed data from 1990-2000, was computed using data known even before the claimed “freeze” date for the projections (i.e. 1990)! Fifteen years is even worse.

One more thing to clarify. I may have been part of making this confusion (sorry for that), but M parameter is the padding period and the actual filter length is 2M-1. So when Rahmstorf et al are speaking about “11-year smoothing” it is actually “21-year smoothing”. If someone wants to give a try, here are the actual (symmetric) filter coefficients for M=11 (HadCRUT3, –>2006; others almost the same): 0.0073 0.0152 0.0235 0.0321 0.0410 0.0499 0.0587 0.0674 0.0758 0.0837 0.0910 0.0837 0.0758 0.0674 0.0587 0.0499 0.0410 0.0321 0.0235 0.0152 0.0073
and for M=15: 0.0037 0.0077 0.0119 0.0164 0.0211 0.0259 0.0308 0.0357 0.0406 0.0455 0.0502 0.0548 0.0591 0.0631 0.0668 0.0631 0.0591 0.0548 0.0502 0.0455 0.0406 0.0357 0.0308 0.0259 0.0211 0.0164 0.0119 0.0077 0.0037

Professor Phil Jones, Director of the CRU and IPCC Coordinating Lead Author, also appears to have given support to five-year smoothing. He told BBC News Online’s environmental correspondent in 2003 that:

“Globally, I expect the five years from 2006 to 2010 will be about a tenth of a degree warmer than 2001 to 2005″(‘Heat high for 2003 but no record’, published at http://news.bbc.co.uk/2/hi/sci.....325033.stm ).

With the CRU anomalies up to May 2009 now published (41 of the 60 months of the 2006 to 2010 period), the average monthly anomaly from January 2006 to May 2009 has been .07 C BELOW the average for the years 2001 to 2005.

In order to reach the same average for 2006-10 as for 2001-05, the average anomaly during the 19 months between June 2009 and December 2010 would need to rise by .23 C.

For the 2006 to 2010 average to exceed that for 2001 to 2005 by one tenth of a degree, as Professor Jones expected, the average for June 2009 to December 2010 would need to exceed the average from January 2006 to May 2009 by .76 C.

Jonathan–You are right; Nick is wrong

Yes. I was following David Stockwell’s implementation (see Fig).

But one can get too caught up in how these formulae are derived – extrapolations etc. They all in the end give smoothed values as a weighted sum of neighboring values. Internally, the weights are usually the same as you move along, but near the ends they have to change to accommodate the limits on the data.

The weights have to be such that a constant function smoothes to the same constant, which means they must sum to 1. You would also expect that a linear function should be unchanged by smoothing. Symmetric weights will ensure this on the interior. One way to ensure that this remains true near the ends is to construct the weights as the interior weights applied to some linear extrapolation, since a linear function will extrapolate as itself. Both MRC and the Grinsted method do this.

There’s not much more you could ask from a smoothing function of this general form. The remaining criticism of MRC is that it heavily weights the last term. This makes the result very sensitive to current information, which may be seen as a virtue, although it is less stable.