date: Tue May 5 12:10:16 2009 from: Phil Jones subject: Re: Fw: RE: Re: Urbanisation to: Dear Qingxiang, Away all last week and Monday was a national holiday. The formula David has sent by the email has the SE formula. The bottom line has (n-2) in it. This n should be reduced to allow for autocorrelation, so calculate the lag-1 autocorrelation and then calculate n'. The difficult point is to add in the effect of the bias adjustments. There is more in Brohan, P., Kennedy, J., Harris, I., Tett, S.F.B. and Jones, P.D., 2006: Uncertainty estimates in regional and global observed temperature changes: a new dataset from 1850. J. Geophys. Res. 111, D12106, doi:10.1029/2005JD006548. but this is about errors on individual estimates, nt on how this affects standard errors on trends. I think as your bias adjustments have little effect overall on the overall 'China average' then you can ignore this - and just use the formula and the adjustment of n. Cheers Phil At 09:03 04/05/2009, you wrote: Dear Phil, I looked around, and find little help about how to calculate the 95% uncertainty range of trend of the climate series. Dave's suggestion is asking for your help. Would you give some instructions? Best Qingxiang ------------------ liqx 2009-05-04 ------------------------------------------------------------- 发件人：Parker, David 发送日期：2009-03-25 23:11:26 收件人：liqx@cma.gov.cn 乘停簆.jones@uea.ac.uk 主题：RE: Re: Urbanisation Dear Qingxiang See [1]http://www.okstate.edu/ag/agedcm4h/academic/aged5980a/5980/newpage24.htm for a formula for the standard error of a least-squares trend. But if the residuals are autocorrelated you will need to decrease n to n' using the formula n' = n(1-r)/(1+r) where r is the lag-1 autocorrelation of the residuals from the regression line (Trenberth, 1984, reference cited below). In addition you should really take account of the uncertainties in your bias-adjustments, but I don't know how to do this other than by Monte-Carlo experiments, creating lots of time series with each bias adjustment varied by a random proportion of its own standard error. Maybe consult Phil Jones too. Regards David CITATION Trenberth K. E. 1984. Some effects of finite sample size and persistence on meteorological statistics. Part II: Potential predictability. Monthly Weather Review, 112, 2369-2379. David Parker, Climate Research scientist Met Office Hadley Centre FitzRoy Road Exeter Devon EX1 3PB United Kingdom Tel: +44 (0)1392 886649 Fax: +44 (0)1392 885681 Email: david.parker@metoffice.gov.uk Website: [2]www.metoffice.gov.uk See our guide to climate change at [3]http://www.metoffice.gov.uk/climatechange/guide/ -----Original Message----- From: liqx@cma.gov.cn [[4]mailto:liqx@cma.gov.cn] Sent: Wednesday, March 25, 2009 2:36 PM To: Parker, David Subject: RE: Re: Urbanisation Dear david, I cannot find any arithmetics here to calculate the 95% uncertainty range of trend, can you give me some help? Best Qingxiang Prof. Phil Jones Climatic Research Unit Telephone +44 (0) 1603 592090 School of Environmental Sciences Fax +44 (0) 1603 507784 University of East Anglia Norwich Email p.jones@uea.ac.uk NR4 7TJ UK ----------------------------------------------------------------------------