date: Sat, 23 Mar 2002 09:40:14 -0500 from: Eric Swanson subject: Re: SCIENCE - Blowing Hot and Cold to: Keith Briffa Keith R. Briffa Hi, Thanks for the great reply. I am somewhat familiar with "digital filters", such as the Gaussian filter. I have used both a "Welch" and a "Hamming" filter on some data I worked with. All three are better than a simple moving average (ie, equal weights), since they induce less aliasing in the resulting filtered time series. These filters have a lower "frequency" cutoff than just the number of years of data used in the filtering algorithm. As a guess, I would think a 50 year Gaussian filter would have a cutoff around 30 years. You might try your filter on a set of random numbers and do a power spectrial analysis of the result, if you haven't already done so. I was concerned about the ends of the time series. Padding the data to extend the filtered curves an extra 25 years may be OK for series with slowly varying characteristics. I wonder whether this gives the wrong impression for a data set which has a relatively strong trend at the end of the set. I think it might be better to persent the curves without the 25 years of data attached at each end. Best Regards, Eric Swanson -------------------------------------------- At 02:55 PM 03/22/2002 +0000, you wrote: > >This is a simple smoothing function , comprising a set of symetric weights >(with a bell , actually Gaussian distribution, shape) that are applied , >like a moving window, to the original series to provide a curve showing the >underlying trend . The actual response of the filter is determined by the >magnitude of the weights and in this case acts to reduce the amplitude of a >50 year cycle by 50 percent (and reduces the variance associated >with 50-year cycle by 25 per cent), Longer timescale variance is pretty >much unaltered and higher frequency (shorter timescale changes) are removed . >In this application we pad (extend) the original series at each end by >sufficient yearly values (here the mean of the adjacent real values) to >allow the filter to run up to the end of the series - hence the smoothed >line is the same length as the original series ( it would other wise be >shorter at each end by the number of weights in the filter each side of the >central weight). >For more information on Guassian filters see >Mitchell,V.L. et al. Climate Change . World Meteorological Office Technical >Note 79, Geneva (1966) . Appendix. > >At 09:18 AM 3/22/02 -0500, you wrote: >>Keith R. Briffa (and Timothy J. Osborn) >>Climatic Research Unit >>University of East Anglia >>Norwich NR4 7TJ >>United Kingdom >> >>Sir: >> >>I saw your commentary in today's SCIENCE magazine and have a question. >> >>Your graph, Figure 1, presents several time series of reconstructed >>temperature data for the Northern Hemisphere. You mention that the >>curves are filtered with a 50 year filter. >> >>I wondered what type of filter was used to smooth the data? >> >>Thanks, >> >>R. Eric Swanson > >-- >Professor Keith Briffa, >Climatic Research Unit >University of East Anglia >Norwich, NR4 7TJ, U.K. > >Phone: +44-1603-593909 >Fax: +44-1603-507784 > >http://www.cru.uea.ac.uk/cru/people/briffa/ > >