date: Sat, 23 Mar 2002 09:40:14 -0500

from: Eric Swanson <e_swansonatXYZxyzbest.com>

subject: Re: SCIENCE - Blowing Hot and Cold

to: Keith Briffa <k.briffaatXYZxyz.ac.uk>

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/

>

>

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