cc: SHERWOOD Steven , Tom Wigley , Frank Wentz , "'Philip D. Jones'" , Karl Taylor , Steve Klein , John Lanzante , "Thorne, Peter" , "'Dian J. Seidel'" , Melissa Free , Leopold Haimberger , "'Francis W. Zwiers'" , "Michael C. MacCracken" , Thomas R Karl , Tim Osborn , "David C. Bader" , 'Susan Solomon'
date: Thu, 13 Dec 2007 18:58:12 -0800
from: Ben Santer
subject: Re: [Fwd: sorry to take your time up, but really do need a scrub
to: carl mears
Dear folks,
I've been doing some calculations to address one of the statistical
issues raised by the Douglass et al. paper in the International Journal
of Climatology. Here are some of my results.
Recall that Douglass et al. calculated synthetic T2LT and T2
temperatures from the CMIP-3 archive of 20th century simulations
("20c3m" runs). They used a total of 67 20c3m realizations, performed
with 22 different models. In calculating the statistical uncertainty of
the model trends, they introduced sigma{SE}, an "estimate of the
uncertainty of the mean of the predictions of the trends". They defined
sigma{SE} as follows:
sigma{SE} = sigma / sqrt(N - 1), where
"N = 22 is the number of independent models".
As we've discussed in our previous correspondence, this definition has
serious problems (see comments from Carl and Steve below), and allows
Douglass et al. to reach the erroneous conclusion that modeled T2LT and
T2 trends are significantly different from the observed T2LT and T2
trends in both the RSS and UAH datasets. This comparison of simulated
and observed T2LT and T2 trends is given in Table III of Douglass et al.
[As an amusing aside, I note that the RSS datasets are referred to as
"RSS" in this table, while UAH results are designated as "MSU". I guess
there's only one true "MSU" dataset...]
I decided to take a quick look at the issue of the statistical
significance of differences between simulated and observed tropospheric
temperature trends. My first cut at this "quick look" involves only UAH
and RSS observational data - I have not yet done any tests with
radiosonde datas, UMD T2 data, or satellite results from Zou et al.
I operated on the same 49 realizations of the 20c3m experiment that we
used in Chapter 5 of CCSP 1.1. As in our previous work, all model
results are synthetic T2LT and T2 temperatures that I calculated using a
static weighting function approach. I have not yet implemented Carl's
more sophisticated method of estimating synthetic MSU temperatures from
model data (which accounts for effects of topography and land/ocean
differences). However, for the current application, the simple static
weighting function approach is more than adequate, since we are focusing
on T2LT and T2 changes over tropical oceans only - so topographic and
land-ocean differences are unimportant. Note that I still need to
calculate synthetic MSU temperatures from about 18-20 20c3m realizations
which were not in the CMIP-3 database at the time we were working on the
CCSP report. For the full response to Douglass et al., we should use the
same 67 20c3m realizations that they employed.
For each of the 49 realizations that I processed, I first masked out all
tropical land areas, and then calculated the spatial averages of
monthly-mean, gridded T2LT and T2 data over tropical oceans (20N-20S).
All model and observational results are for the common 252-month period
from January 1979 to December 1999 - the longest period of overlap
between the RSS and UAH MSU data and the bulk of the 20c3m runs. The
simulated trends given by Douglass et al. are calculated over the same
1979 to 1999 period; however, they use a longer period (1979 to 2004)
for calculating observational trends - so there is an inconsistency
between their model and observational analysis periods, which they do
not explain. This difference in analysis periods is a little puzzling
given that we are dealing with relatively short observational record
lengths, resulting in some sensitivity to end-point effects.
I then calculated anomalies of the spatially-averaged T2LT and T2 data
(w.r.t. climatological monthly-means over 1979-1999), and fit
least-squares linear trends to model and observational time series. The
standard errors of the trends were adjusted for temporal autocorrelation
of the regression residuals, as described in Santer et al. (2000)
["Statistical significance of trends and trend differences in
layer-average atmospheric temperature time series"; JGR 105, 7337-7356.]
Consider first panel A of the attached plot. This shows the simulated
and observed T2LT trends over 1979 to 1999 (again, over 20N-20S, oceans
only) with their adjusted 1-sigma confidence intervals). For the UAH and
RSS data, it was possible to check against the adjusted confidence
intervals independently calculated by Dian during the course of work on
the CCSP report. Our adjusted confidence intervals are in good
agreement. The grey shaded envelope in panel A denotes the 1-sigma
standard error for the RSS T2LT trend.
There are 49 pairs of UAH-minus-model trend differences and 49 pairs of
RSS-minus-model trend differences. We can therefore test - for each
model and each 20c3m realization - whether there is a statistically
significant difference between the observed and simulated trends.
Let bx and by represent any single pair of modeled and observed trends,
with adjusted standard errors s{bx} and s{by}. As in our previous work
(and as in related work by John Lanzante), we define the normalized
trend difference d as:
d = (bx - by) / sqrt[ (s{bx})**2 + (s{by})**2 ]
Under the assumption that d is normally distributed, values of d > +1.96
or < -1.96 indicate observed-minus-model trend differences that are
significant at the 5% level. We are performing a two-tailed test here,
since we have no information a priori about the "direction" of the model
trend (i.e., whether we expect the simulated trend to be significantly
larger or smaller than observed).
Panel c shows values of the normalized trend difference for T2LT trends.
the grey shaded area spans the range +1.96 to -1.96, and identifies the
region where we fail to reject the null hypothesis (H0) of no
significant difference between observed and simulated trends.
Consider the solid symbols first, which give results for tests involving
RSS data. We would reject H0 in only one out of 49 cases (for the
CCCma-CGCM3.1(T47) model). The open symbols indicate results for tests
involving UAH data. Somewhat surprisingly, we get the same qualitative
outcome that we obtained for tests involving RSS data: only one of the
UAH-model trend pairs yields a difference that is statistically
significant at the 5% level.
Panels b and d provide results for T2 trends. Results are very similar
to those achieved with T2LT trends. Irrespective of whether RSS or UAH
T2 data are used, significant trend differences occur in only one of 49
cases.
Bottom line: Douglass et al. claim that "In all cases UAH and RSS
satellite trends are inconsistent with model trends." (page 6, lines
61-62). This claim is categorically wrong. In fact, based on our
results, one could justifiably claim that THERE IS ONLY ONE CASE in
which model T2LT and T2 trends are inconsistent with UAH and RSS
results! These guys screwed up big time.
SENSITIVITY TESTS
QUESTION 1: Some of the model-data trend comparisons made by Douglass et
al. used temperatures averaged over 30N-30S rather than 20N-20S. What
happens if we repeat our simple trend significance analysis using T2LT
and T2 data averaged over ocean areas between 30N-30S?
ANSWER 1: Very little. The results described above for oceans areas
between 20N-20S are virtually unchanged.
QUESTION 2: Even though it's clearly inappropriate to estimate the
standard errors of the linear trends WITHOUT accounting for temporal
autocorrelation effects (the 252 time sample are clearly not
independent; effective sample sizes typically range from 6 to 56),
someone is bound to ask what the outcome is when one repeats the paired
trend tests with non-adjusted standard errors. So here are the results:
T2LT tests, RSS observational data: 19 out of 49 trend differences are
significant at the 5% level.
T2LT tests, UAH observational data: 34 out of 49 trend differences are
significant at the 5% level.
T2 tests, RSS observational data: 16 out of 49 trend differences are
significant at the 5% level.
T2 tests, UAH observational data: 35 out of 49 trend differences are
significant at the 5% level.
So even under the naive (and incorrect) assumption that each model and
observational time series contains 252 independent time samples, we
STILL find no support for Douglass et al.'s assertion that: "In all
cases UAH and RSS satellite trends are inconsistent with model trends."
Q.E.D.
If Leo is agreeable, I'm hopeful that we'll be able to perform a similar
trend comparison using synthetic MSU T2LT and T2 temperatures calculated
from the RAOBCORE radiosonde data - all versions, not just v1.2!
As you can see from the email list, I've expanded our "focus group" a
little bit, since a number of you have written to me about this issue.
I am leaving for Miami on Monday, Dec. 17th. My Mom is having cataract
surgery, and I'd like to be around to provide her with moral and
practical support. I'm not exactly sure when I'll be returning to PCMDI
- although I hope I won't be gone longer than a week. As soon as I get
back, I'll try to make some more progress with this stuff. Any
suggestions or comments on what I've done so far would be greatly
appreciated. And for the time being, I think we should not alert
Douglass et al. to our results.
With best regards, and happy holidays! May all your "Singers" be carol
singers, and not of the S. Fred variety...
Ben
(P.S.: I noticed one unfortunate typo in Table II of Douglass et al. The
MIROC3.2 (medres) model is referred to as "MIROC3.2_Merdes"....)
carl mears wrote:
> Hi Steve
>
> I'd say it's the equivalent of rolling a 6-sided die a hundred times, and
> finding a mean value of ~3.5 and a standard deviation of ~1.7, and
> calculating the standard error of the mean to be ~0.17 (so far so
> good). An then rolling the die one more time, getting a 2, and
> claiming that the die is no longer 6 sided because the new measurement
> is more than 2 standard errors from the mean.
>
> In my view, this problem trumps the other problems in the paper.
> I can't believe Douglas is a fellow of the American Physical Society.
>
> -Carl
>
>
> At 02:07 AM 12/6/2007, you wrote:
>> If I understand correctly, what Douglass et al. did makes the stronger
>> assumption that unforced variability is *insignificant*. Their
>> statistical test is logically equivalent to falsifying a climate model
>> because it did not consistently predict a particular storm on a
>> particular day two years from now.
>
>
> Dr. Carl Mears
> Remote Sensing Systems
> 438 First Street, Suite 200, Santa Rosa, CA 95401
> mears@remss.com
> 707-545-2904 x21
> 707-545-2906 (fax))
--
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Benjamin D. Santer
Program for Climate Model Diagnosis and Intercomparison
Lawrence Livermore National Laboratory
P.O. Box 808, Mail Stop L-103
Livermore, CA 94550, U.S.A.
Tel: (925) 422-2486
FAX: (925) 422-7675
email: santer1@llnl.gov
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