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/
>
>