From: Tim Osborn <t.osborn@uea.ac.uk>
To: haozx@igsnrr.ac.cn
Subject: Re: =?gb2312?B?Rnc6IFRpbXMgQW5zd2Vy?=
Date: Wed Jul  1 16:17:28 2009
Cc: Luterbacher Jürg <juerg.luterbacher@giub.unibe.ch>

   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
     authors)?

   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,
     Zhixin
     ----- Original Message -----
     From: "Juerg Luterbacher"
     To:
     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
     cheers
     Juerg
     It is a little hard to follow (some symbols got replaced by squares -- perhaps a PDF
     file
     would work better than a Word Doc?) but I think that the method looks approximately
     right
     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
     may
     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
     as
     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
     too
     narrow, especially when you add on the reconstruction SE (and +- 1.6448 SE or +- 2 SE).
     Hope this helps,
     Tim

