date: Tue May  5 12:10:16 2009
from: Phil Jones <p.jones@uea.ac.uk>
subject: Re: Fw: RE: Re: Urbanisation
to: <liqx@cma.gov.cn>

    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
     -------------------------------------------------------------
     ˣParker, David
     ڣ2009-03-25 23:11:26
     ռˣliqx@cma.gov.cn
     ͣp.jones@uea.ac.uk
     ⣺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
   ----------------------------------------------------------------------------

