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
----------------------------------------------------------------------------