To: Simon Tett <email@example.com>,Keith Briffa <firstname.lastname@example.org>, Philip Brohan <email@example.com>
Subject: Re: Uncertainty in model-paleo uncertainty
Date: Mon, 04 Aug 2003 14:30:35 +0100
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
>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.
Dr Timothy J Osborn
Climatic Research Unit
School of Environmental Sciences, University of East Anglia
Norwich NR4 7TJ, UK