date: Fri Jun 1 16:14:57 2007

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

subject: Fwd: Re: Philosophical Transactions

to: t.m.melvinatXYZxyz.ac.uk

Tom - see below

we could do various filters to see which matches the Vlad SSA series for each chron

Kith

Cc: Edward Cook <drdendroatXYZxyzo.columbia.edu>,

Tom Melvin <t.m.melvinatXYZxyz.ac.uk>

From: Edward Cook <drdendroatXYZxyzo.columbia.edu>

Subject: Re: Philosophical Transactions

Date: Fri, 1 Jun 2007 09:14:26 -0400

To: Keith Briffa <K.BriffaatXYZxyz.ac.uk>

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Hi Keith,

I understand exactly what Vlad is doing and why now, which makes me wonder even more now

why a simple low-pass filter that recovered e.g. 52% of the total variance wasn't used.

The results must be effectively the same and the confusing use of SSA here would be

mute. That is my take anyway, one that Vlad would probably disagree with.

Cheers,

Ed

==================================

Dr. Edward R. Cook

Doherty Senior Scholar and

Director, Tree-Ring Laboratory

Lamont-Doherty Earth Observatory

Palisades, New York 10964 USA

Email: [1]drdendro@ldeo.columbia.edu

Phone: 845-365-8618

Fax: 845-365-8152

==================================

On Jun 1, 2007, at 8:46 AM, Tom Melvin wrote:

Ed,

Vlad's explanation of embedding.

Tom

Date: Fri, 1 Jun 2007 17:43:10 +0800 (KRAST)

Subject: Re: Fwd: Re: Philosophical Transactions

From: [2]shishov@forest.akadem.ru

To: "Tom Melvin" <[3]t.m.melvin@uea.ac.uk>

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Tom,

In the paper I used embedding dimension equal to 40 years. Totally, 3

first SSA component are explained 52% of initial variance (1 SSA component

is explained 35%, 2 SSA - 17%, 3 SSA - 13%. If you see, sum of expl.

variances for these components is more than 52%. Reason is: SSA components

are not independent). If we increase embedding dimension then we will

obtain more accurate estimation for trend and oscillational components.

But in this case we should use more SSA components to explain same portion

of initial time series variation. For example, if embedding dimension is

equal to 60 years then we need to use 5 SSA components which totally

explained 52%.

So:

Embedding dimension Number of SSA comp Expl. variance

100 8 52

120 10 52

300 25 52

900 55 52

etc.

But filtering result (ammount of SSA components) are absolutely the

same!!! (I mean if you see bold curve (SSA-filtering curve) on fig.5a then

I could obtain the same curve by any bigger dimension with bigger number

of SSA components).

Of course, if we investigate a spectrum of time series we should use much

bigger embedding dimension (closely to 1/2 length of time series. In

previous message, I was wrong with 2/3). But in this case we will obtain

other problem: a grouping of closest SSA components. Probably, this

problem is most difficult in SSA analysis.

Our paper doesn't relate to any cycles in tree-ring chronologies or

spectrum analysis. From this point of view we could use such embedding

dimension (I mean 40 years). In our next paper about spectrum

characteristics (:-)), we will use bigger dimension.

Tom, do you know about Irkutsk dendroclimatic conference which will be

carried out in nice place on Baikal lake (September, 10-14, 2007)?

Vlad

> Vlad,

>

> May be worth adding a comment to Phil Trans as suggested by Ed.

> I will talk to Keith.

>

> Tom

>

> PS. June's outgoing EMail not working so reply to probably Nata

> failed to arrive.

>

>

>

> At 09:38 31/05/2007, you wrote:

>>Tom,

>>

>>I need to check it (embedding dimension) (I try to use different

>> embedding

>>dimensions and will compare results).

>>If we will use pretty big exercise or lenght of caterpillar

>>(for example, 2/3 of time series lenght as recommended in some papers )

>>then we obtain just nonlinear trend in first component. If we use shorter

>>embedding dimension then 1-st component will contain some long-term

>>oscillational (non-harmonic) components as well. So, which oscillations

>>could we consider as long-term variations for our 2000-yrs chronologies?

>> I

>>think 100-200 yrs variations are long-term. From this point of view, we

>>could use shorter embedding dimension (than 2/3 of TS length).

>>

>>Concerning

>> "so there appears not to have been a very clear spectral separation and

>>also some mixing of frequencies in your components"

>> it is a normal situation for SSA decomposition (it's the algorithm

>>feature by autocorrelation structure of correlation matrix and linear

>>algebra) as we don't use any harmonical functional space for

>>decomposition (in comparison with Fourier transformation, for example).

>>It's a weakness of this method but a strength in the same time, because

>> we

>>don't need to make any assumptions concerning a nature of fluctuations in

>>time series.

>>

>>Vlad

>>

>>

>>

>>

>> > Vlad,

>> >

>> > Does Ed's comment mean anything to you - "what is embedding

>> dimension"?

>> >

>> > Have not asked Keith yet.

>> >

>> > Tom

>> >

>> >

>> >

>> >

>> >>Cc: Edward Cook <[5]drdendro@ldeo.columbia.edu>,

>> >> Keith Briffa <[6]k.briffa@uea.ac.uk>

>> >>From: Edward Cook <[7]drdendro@ldeo.columbia.edu>

>> >>Subject: Re: Abisko

>> >>Date: Wed, 30 May 2007 07:09:05 -0400

>> >>To: Tom Melvin <[8]t.m.melvin@uea.ac.uk>

>> >>X-Mailer: Apple Mail (2.752.3)

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>> >>

>> >>Hi Tom and Keith,

>> >>

>> >>Thanks for sending this stuff. I took a very quick look at the paper

>> >>you sent. Having done a fair bit of SSA work in the past, I am

>> >>curious what embedding dimension you used, something that is usually

>> >>provided in the description. It looks very short based on the very

>> >>wiggly form of the first component, so there appears not to have

>> >>been a very clear spectral separation and also some mixing of

>> >>frequencies in your components. That being the case, wouldn't a

>> >>simple low-pass filter of some pre-defined cutoff have been

>> sufficient?

>> >>

>> >>Cheers,

>> >>

>> >>Ed

>> >>==================================

>> >>Dr. Edward R. Cook

>> >>Doherty Senior Scholar and

>> >>Director, Tree-Ring Laboratory

>> >>Lamont-Doherty Earth Observatory

>> >>Palisades, New York 10964 USA

>> >>Email: <[9]mailto:drdendro@ldeo.columbia.edu>[10]drdendro@ldeo.columbia.edu

>> >>Phone: 845-365-8618

>> >>Fax: 845-365-8152

>> >>==================================

>> >>

>> >>

>> >>On May 30, 2007, at 6:50 AM, Tom Melvin wrote:

>> >>

>> >>>Ed,

>> >>>

>> >>>Attached is the Abisko temperature series (there also is a daily

>> >>>version somewhere).

>> >>>

>> >>>Keith mentioned that some of the overheads stuff is not yet

>> >>>published - so needs treating with care.

>> >>>

>> >>>Also attached is a draft paper (some minor amendments are in

>> >>>process) submitted to Philosophical Transactions.

>> >>>

>> >>>Tom

>> >>>

>> >>>Dr. Tom Melvin

>> >>>

>> >>>Climatic Research Unit

>> >>>University of East Anglia

>> >>>Norwich, NR4 7TJ, U.K.

>> >>>

>> >>>Phone: +44-1603-593161

>> >>>Fax: +44-1603-507784

>> >>><AbiskoSweden.dat>

>> >>><BriffaPhilTrans.pdf>

>> >

>> > Dr. Tom Melvin

>> >

>> > Climatic Research Unit

>> > University of East Anglia

>> > Norwich, NR4 7TJ, U.K.

>> >

>> > Phone: +44-1603-593161

>> > Fax: +44-1603-507784

>> >

>> >

>

> Dr. Tom Melvin

>

> Climatic Research Unit

> University of East Anglia

> Norwich, NR4 7TJ, U.K.

>

> Phone: +44-1603-593161

> Fax: +44-1603-507784

>

>

Dr. Tom Melvin

Climatic Research Unit

University of East Anglia

Norwich, NR4 7TJ, U.K.

Phone: +44-1603-593161

Fax: +44-1603-507784

--

Professor Keith Briffa,

Climatic Research Unit

University of East Anglia

Norwich, NR4 7TJ, U.K.

Phone: +44-1603-593909

Fax: +44-1603-507784

[11]http://www.cru.uea.ac.uk/cru/people/briffa/

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