From	Tim Osborn	Date	Wed Jul 1 16:17:28 2009
To	haozx@igsnrr.ac.cn
CC	Luterbacher Jürg
Subject	Re: =?gb2312?B?Rnc6IFRpbXMgQW5zd2Vy?=
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