cc: "Tim Osborn" <t.osbornatXYZxyz.ac.uk>, <K.briffaatXYZxyz.ac.uk>, "Brohan, Philip" <philip.brohanatXYZxyzoffice.gov.uk>
date: Tue, 22 Aug 2006 13:05:36 +0100
from: "Rob Wilson" <rob.wilsonatXYZxyzac.uk>
subject: Re: Coral reconstruction - a more complicated approach but no
to: "Tett, Simon" <simon.tettatXYZxyzoffice.gov.uk>, "Sandy Tudhope" <sandy.tudhopeatXYZxyzac.uk>
yes, certainly calibrating against a more spatially restricted (Indian/Pacific) mean SST
series could improve the results.
This was really just an academic exercise to answer a query of Sandy's and see if R2 could
be inflated significantly beyond what we already have. As a method it may not be too
realistic anyway as no such data massaging is done to the SST grids when they are averaged
to derive the large scale mean.
I suppose the optimal approach would be a spatial field reconstruction, but then we are
dogged with the problem of using relatively short coral records and relying on
teleconnected relationships between the longer coral series. I am not keen on this as I do
not feel we can assumed that teleconnected relationships are time stable
I am happy with what we have done especially as it was derived using a relatively simple
I am sure in the future someone will developed a better series as more coral series are
made available. But that is for the future.
----- Original Message -----
From: Tett, Simon
To: Rob Wilson ; Sandy Tudhope
Cc: Tim Osborn ; K.email@example.com ; Brohan, Philip
Sent: Tuesday, August 22, 2006 12:05 PM
Subject: RE: Coral reconstruction - a more complicated approach but no significant gain
My feeling is that the additional data improves things a bit but not a lot! You could try
and calibrate against Indo-Pacific SST rather than tropical SST.
Dr Simon Tett Managing Scientist, Data development and applications.
Met Office Hadley Centre (Reading Unit)
Meteorology Building, University of Reading, Reading RG6 6BB
Tel: +44 (0)118 378 5614 Fax +44 (0)118 378 5615
Mobex: +44-(0)1392 886886
E-mail: firstname.lastname@example.org http://www.metoffice.gov.uk
Global climate data sets are available from http://www.hadobs.org
From: Rob Wilson [mailto:email@example.com]
Sent: Monday, August 21, 2006 5:14 PM
To: Sandy Tudhope
Cc: Tim Osborn; Tett, Simon; K.firstname.lastname@example.org; Brohan, Philip
Subject: Coral reconstruction - a more complicated approach but no significant gain
I could not resist looking into your question below.
One of the main weaknesses in the coral reconstruction is perhaps the autocorrelation in
the model residuals as measured by the Durbin-Watson statistic. It is possible that this
weakness comes from not including those corals located from the Warm Pool region down to
the southern tropical Pacific (where SSTs are inversely correlate with large scale tropical
SSTs - i.e. Raratonga, Laing etc).
So to address your query, I added to the JGR data-set the coral records from the Warm Pool
paper (Bunaken, Lombok and Laing), plus the DO18 series from Raratonga and Fiji (I do not
think the Sr/Ca records would make much difference). I also included the New Caledonian
(AML) record of Crowley although it does not pass screening against local SSTs.
This results in an expanded data-base of 19 series (MAI and TAR combined).
I then band pass filtered the series (and the TROP HADISST series) to high (< 10 year), mid
(10-30 year) and low (> 30 year) frequency fractions.
Table 1 in the attached PDF shows the correlations (1897-1981 common period) between each
coral record and HADISST tropical temperatures using the unfiltered series and their
The expected opposite sign of the correlations, at high frequencies, of the RAR, FIJ, AML,
BUN, LNG and LOM series is clear.
I then chose arbitrary correlations levels for acceptance for inclusion in the final
High - > 0.20 (equates roughly to the 95% C.L.)
Mid - > 0.40
Low - > 0.50
Higher acceptance values for the mid and low frequencies could have been used, but I wanted
to use as many of the coral records as possible.
Table 1 also highlights (grey shading) those coral records in each frequency band that were
used for the final mean function:
High - 15
Mid - 9
Low - 15
At each frequency band, the accepted series were normalised and the sign changed to be
consistent with each other.
I then made a frequency band mean by averaging the accepted series.
The correlations between the coral mean and HADISST temperature data at each frequency band
High - 0.76
Mid - 0.75
Low - 0.86
To ensure consistent variance in the final time-series, the variance of the frequency band
mean series were re-scaled to the grand mean of the standard deviations of the original
band-pass series within each band-width. The re-scaled high, mid and low time-series were
then summed and a final tropical mean function developed.
This final series was then calibrated (regressed not scaled) to the unfiltered HADISST data
over the 1897-1981 period. This equates to the most replicated nest in the JGR paper.
The attached PDF file compares the JGR reconstruction with the new band-pass derived
reconstruction along with some calibration results.
The JGR reconstruction explains 57% of the variance, while the new one explains 60%.
The DW in the original was 0.95, while the new one is worse at 0.90.
The two reconstructions correlate with each other at 0.94.
So - in this version, Raratonga (the high frequency fraction of it at least) has been
included (plus other new series of course).
However, there has really been no significant gain using this approach.
In fact, the DW value is still poor which frustrates me. This may mean that some sort of AR
modelling may be required to improve the reconstruction in this regards in the future.
Something I keep meaning to play with.
Of course, it could be argued that the individual coral series should be screened at each
frequency band with local SSTs. However, overall, I do not think it will make a huge
difference no matter what games we play. My gut feeling is that one big problem is the lack
of data from the Atlantic. From SST data that Philip sent me, greatest warming occurs in
Atlantic SSTs. As the coral data-set is biased to the Pacific where warming is least
(Indian Ocean in-between), then the autocorrelation may simply reflect this spatial bias in
anyway, I hope this answers your query. I am happy I finally did this as it has been
bugging me for a while and the method needed to be explored. This band pass approach is
more time consuming, but holds promise. However, at least for the most replicated period it
makes little difference to the results. However, in the earlier less replicated periods, a
few more additional coral series could make a huge difference (e.g. the Lombok series). I
think this is probably the sort of approach that may need to be considered in the future.
----- Original Message -----
From: Sandy Tudhope
To: Rob Wilson
Sent: Wednesday, August 16, 2006 4:52 PM
Subject: Re: SAGES lectureship
b) CORAL RECONSTRUCTION:
- There was quite a bit of discussion about whether we should have kept
in the Rarotonga and other coral sites that show the inverse
relationship with Tropical SST. I suppose an important question is: does
it make any difference to the overall reconstruction? I said I didn't
think it did, but that I couldn't be certain if you'd tried the exercise
including them. Did you?