To: Simon Tett <simon.tett@metoffice.com>,Keith Briffa <k.briffa@uea.ac.uk>, Philip Brohan <philip.brohan@metoffice.com>

Subject: Re: Uncertainty in model-paleo uncertainty

Date: Mon, 04 Aug 2003 14:30:35 +0100

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Simon & Philip,

here's some thoughts on uncertainty...

At 10:42 04/08/2003, Simon Tett wrote:

>1) Calibration uncertainty -- there is some uncertainty in the

>relationship between proxy and temperature.

>2) Residual noise -- the proxyies do not capture large-scale temperature

>variability perfectly.

>3) Internal-climate variability in "real" life -- there is some chaotic

>variability in the real climate system

>4) Internal-climate variability in the model -- ditto!

>

>3) & 4) I suggest we estimate from HadCM3 -- model var agrees well with

>paleo var so can't be too far wrong!

Yes, I'm happy that we use (3) and (4) from the model. If you use a short

baseline to take the anomalies from, then the internal variability comes in

twice in each case, both in comparing the baseline mean and the

anomaly. We can minimise this by using a long baseline.

>1) & 2) are, to some extent related, as calibration is estimate by

>regression -- thus minimising residual var (2). Nicest thing to do would

>be to estimate residual from indep. data but I don't think there is enough.....

The uncertainties that we've published with our regional and

quasi-hemispheric reconstructions attempt to take both (1) and (2) in

account already. Thus I use the standard errors on the two regression

coefficients (for the linear regression of the sub-continental regions) and

the standard errors on all multiple regression coefficients (for the

quasi-Northern Hemisphere series). And then I incorporate the variance of

the calibration residuals too (i.e., item (2)), modelled as first-order

autoregressive terms. The appendix of the Briffa part 1 paper (page

755-757 is the appendix) in the Holocene special issue paper gives an

explanation of this. Others quite often ignore (1) and just use the

residuals to quantify reconstruction error, but (1) can be important

especially for big anomalies (because the regression slope error is

multiplied by the predicted anomaly). (1) can be difficult to quantify, of

course, using some multi-variate techniques like Mann and Luterbacher use.

The regression standard errors (1) are of course computed from the

calibration period. Our published errors also use the residual variance

(2) computed from this calibration period. It is possible to compute (2)

from independent data, but as you say we are limited by data. AND I think

that the residual variance from independent data would also incorporate

some or all of error (1) (because that would contribute to differences

between reconstruction and observation). I think it is better to keep the

two terms separate and explicitly compute both, especially as their

relative magnitudes can depend upon time scale (i.e., time averaging the data).

Am I right in thinking that the error in the *observed* record would, if

taken into account, result in *reduced* reconstruction errors, because the

residual variance (2) would not all be assumed to be reconstruction error -

some would be observation error? But I suppose that the regression

coefficient errors (1) would get larger to compensate? Anyway, we don't

currently consider observed errors.

Cheers

Tim

Dr Timothy J Osborn

Climatic Research Unit

School of Environmental Sciences, University of East Anglia

Norwich NR4 7TJ, UK

e-mail: t.osborn@uea.ac.uk

phone: +44 1603 592089

fax: +44 1603 507784

web: http://www.cru.uea.ac.uk/~timo/

sunclock: http://www.cru.uea.ac.uk/~timo/sunclock.htm

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