Tuesday, February 21, 2012

SMOOTH OPERATORS

In the IPCC Technical Assessment Report of 2007 many of the graphs used smoothed values of data series. This is perfectly valid as it facilitates seeing trends among the year-to-year fluctuations. The methods used are described in 'Appendix 3.A: Low-Pass Filters and Linear Trends'. They use for annual data as filter which has 13 weights 1/576 [1-6-19-42-71-96-106-96-71-42-19-6-1]. An example of this is in figure 3.8. It is interesting to note that have used a algorithm which allows smoothing right to the end of the data series.


We give below the three main global temperature series using the 13 point filter. At the end of the series we used only the part of the filter which applies retrospectively. This curve appears to shows that the rate of temperature increase has fallen off in recent years.




The same annex also mentions using regression to estimate trends. For simplicity we have done this using 13-year series and the LINEST algorithm in Excel.



Using the 13-year period for trends gives the clear impression that the rate of warming has slowed dramatically. Perhaps as a result of this, it is now being suggested that we need at least 30 years to detect a trend. (Though, it should be noted that I can find no reference to the need for a 30-year trend in IPCC report.) In the following graph we have plotted the 30-year trend lines and the 30-year trend from the average of a model ensemble.



Even using the 30-year trend it is clear that rate of temperature increase has fallen back. This graph also shows that the modelled 30-year trend was close to the observed one for the period 1975 to 2005 but outside that period diverged widely.

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