Thursday, December 29, 2011


From: Tim Osborn <>
Subject: Re: =?gb2312?B?Rnc6IFRpbXMgQW5zd2Vy?=
Date: Wed Jul 1 16:17:28 2009
Cc: Luterbacher J�rg <>

Dear Zhixin,
At 15:14 01/07/2009, you wrote:

Do you mean Se should be the standard error from the invidual reconstruction series

yes, that's what I mean.

(before I got your answer, I calculated the standard error for the 5 reconstruction
data at one time point, e.g. 1470s, it is not from the original papers given by the

Ah. I understand what you've done now.

But my question is if the author did not publish the uncertainty, how can I deal with
the value of Se?

Well, the original purpose of constructing IPCC Fig. 6.10c was to display the published
uncertainty estimates of each study. If no uncertainties had been estimated by the
original authors then we wouldn't have produced the figure in the first place!
So, do you really want to produce such a figure to show the uncertainty ranges when the
uncertainty ranges haven't been calculated before?
If you do, then you'd need to somehow estimate the uncertainty. You could do this
yourself, perhaps, e.g. from the differences between each reconstruction and the
instrumental temperatures during some overlap (calibration, or independent verification)
period? But this wouldn't measure any increase in uncertainty during periods when each
reconstruction is perhaps based on less input proxy data.
Estimating the uncertainty from the spread of individual reconstruction values in a
particular year, like you've done, is open to criticism. Do you really think that in a
particular year when the three recons have very similar values that the uncertainty is much
less than other nearby years? If you had a high number of

And now I understood the meaning of 5%-95% range, I will follow this, and replot my
figures with +-1.645SE for the half scores.
Thank you very much again, hopefully I can give the uncertainty of reconstruction
results over China region soon. After finished, may I send the manuscript to you and
give us comments and suggestions?
Best wishes,
----- Original Message -----
From: "Juerg Luterbacher"
Subject: Tims Answer
Sent: Wed, 1 Jul 2009 12:27:44 +0200

here is the answer of Tim.
cheers maybe you can now email him directly to make things clear
It is a little hard to follow (some symbols got replaced by squares -- perhaps a PDF
would work better than a Word Doc?) but I think that the method looks approximately
but not quite right. Some things that look a bit different:
Se: it appears that the same value is used for all 4 reconstructions (in the example,
Se=1.3165 is used). Why would the uncertainty on one reconstruction be the same as the
uncertainty on all the others? Perhaps she has used the standard deviation of the
instrumental temperature rather than the standard error of each reconstruction? Did the
authors actually publish estimated uncertainties along with their best-estimate
reconstruction series? You should also note that reconstruction errors/uncertainties
depend on time scale -- the IPCC fig 6.10 showed variations on timescales of 30-yrs and
longer, so I attempted to use uncertainties estimated for that timescale (or a similar
multi-decadal timescale).
IPCC wanted to mostly standardise on the 90% range (5%-95%), so for my scoring I awarded
100%/N to any temperature that falls within the +- 1 SE reconstruction range (the same
noted in her document) but awarded 0.5*100%/N to any temperature that falls within +-
1.6448 SE reconstruction range (this differs from the +-2 SE in her document). I
originally used +- 2 SE, but (under assumption of normality), +- 1.6448 SE should
encompass 5%-95% range, while +- 2 SE is of course approx 2.5%-97.5%. Either is of
course equally defendable, but if you want to reproduce IPCC, then its +- 1.6448 SE for
the half score (0.5*100%/N).
This is of course repeated for all N reconstructions.
I was a little unsure about the actual plot produced too. When the Xu2003 curve is very
low or very high, the brown shading extends in both directions (to very low *and* very
high values at once). e.g. AD 650 (but there are others too). Also the range is very
narrow at about AD 1050; although the 3 recons are quite similar here, it still looks
narrow, especially when you add on the reconstruction SE (and +- 1.6448 SE or +- 2 SE).
Hope this helps,

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