date: Tue Sep 20 16:15:00 2005
from: Tim Osborn
subject: Re: optimal fingerprinting
to: Gerard van der Schrier
At 08:17 20/09/2005, you wrote:
The correlation between 'best-guess' amplitude and 'observed' is ca. 0.7, not too bad
and obviously not produced by any rescale. Your observation that there was some
overshoot in the best-guess was very valid: the results in the little report have been
rescaled.
yes, I see now the 0.26 scaling factor listed in the conclusions.
In the optimal-fingerprinting algorithm of Allen and Tett is a scaling argument which I
don't completely understand. Also, I use a NAG-routine to compute the prinicpal
components, which applies a scaling. A quick calculation shows that if I made a mistake
here, it would produce results which may not be needing this ad-hoc rescaling.
There are a few different "conventions" regarding the scaling of EOFs/PCs. The one that I
prefer is to scaling the EOF patterns so that they are unit vectors, and applying the
opposite scaling to the PCs so that their variance is equal to the eigenvalue (I think).
But other conventions are to scale the EOFs so that their "length" is equal to
sqrt(eigenvalue) and the variance of the PC becomes equal to the eigenvalue-squared, or to
scale EOFs so that their "length" is equal to 1/sqrt(eigenvalue) and the PCs have unit
variance. I don't know which of these options the NAG-routines apply, nor which the
Allen/Tett algorithm requires. I can ask Nathan if you first check what the NAG-routines
do (if it isn't documented, then just calculate the "length" of each EOF vector and see if
it is 1, sqrt(e), 1/sqrt(e) or something else!).
I'm now a little more excited about this fingerprinting. Do you think it would make a
nice RAPID paper if we applied the fingerprinting tehnique on actual SSH measurements?
The TOPEX/Poseidon data are available and they show a strong trend over the 90s. In the
RAPID annual meeting, we've seen 3 estimates of the decrease in THC (or MHT) strength
over this period. Ours would be a fourth complementary way, and the first time optimal
fingerprinting is applied in an oceanographic context.
I realize that this would mean a further alienation of the original idea to couple
*proxy* data to ocean circulation.
Despite this difference to the original idea, such a paper would be worthwhile. But the
biggest problem is likely to be distinguishing the MHT-trend from the GHG-warming-trend,
both of which will influence SSH. The GHG-warming signal in SSH is not well known, being
very different between models and also already incorporating a combination of GHG-warming
plus MHT-weakening in some models. Perhaps GHG-warming without any ocean circulation
response would produce a more uniform pattern of SSH increase? In which case, using the
deviations in SSH from the spatial-mean increase might help? Also, reviewers might
complain that we only used HadCM3 to estimate the SSH signal pattern - they might ask
whether other models would yield very different patterns? That might be avoided by calling
this a first attempt, allowing multi-model comparisons to be left until later work (by us
or others)?
I realize that. I've downloaded the DAI-precipitation, so a quick comparison should not
be too difficult.
Yes - a quick comparison to see if differences in precipitation data explain the
differences in recent PDSI trend should be sufficient.
I have done that already. The results are not very spectacular. I did the trick with
replacing actual temperatures for the climatological temperatures in a paper on the
ALP-IMP data. A huge impact of higher surface temperatures on the areal extent of
drought was found. For the US, no such thing happens. Phil recently send me an email,
predicting this result! He also wrote that this result would indicate that there is
nothing wrong with the CRU-temperatures. I don't quite understand this remark, so I will
have to get back on that.
I don't understand Phil's remark either. But the result itself could be mentioned in the
paper, because it is interesting to know that the temperature changes aren't causing much
trend in PDSI.
Ken Kunkel replied to my email (I'll forward it.) His datasets are available and seem to
be well-documented. Do we really want to get into the trouble of making a second scPDSI
dataset with his data? After all, we focus on (sc)PDSI, rather than precipitation. I
guess your first reaction was to avoid it, if possible.
Hmm. I still want to avoid much extra work. These are all daily data, so would need to be
made into monthly totals. Then you would need to locate which 0.5deg boxes each station
was in, take the 0.5deg monthly temperatures and the Kunkel station precipitation together
to compute PDSI and compare that with the 0.5deg box PDSI that you already computed.
Sounds like a lot of work to do for all 0.5deg boxes with Kunkel stations in them. Should
I ask Keith - he's back from his holiday tomorrow (Wednesday).
Cheers
Tim