From: Ben Santer <santer1@llnl.gov>
To: carl mears <mears@remss.com>
Subject: Re: [Fwd: sorry to take your time up, but really do need a   scrub of this singer/christy/etc effort]
Date: Thu, 13 Dec 2007 18:58:12 -0800
Reply-to:  santer1@llnl.gov
Cc: SHERWOOD Steven <steven.sherwood@yale.edu>,  Tom Wigley <wigley@cgd.ucar.edu>, Frank Wentz <frank.wentz@remss.com>,  "'Philip D. Jones'" <p.jones@uea.ac.uk>, Karl Taylor <taylor13@llnl.gov>, Steve Klein <klein21@mail.llnl.gov>,  John Lanzante <John.Lanzante@noaa.gov>, "Thorne, Peter" <peter.thorne@metoffice.gov.uk>,  "'Dian J. Seidel'" <dian.seidel@noaa.gov>, Melissa Free <Melissa.Free@noaa.gov>,  Leopold Haimberger <leopold.haimberger@univie.ac.at>, "'Francis W. Zwiers'" <francis.zwiers@ec.gc.ca>,  "Michael C. MacCracken" <mmaccrac@comcast.net>, Thomas R Karl <Thomas.R.Karl@noaa.gov>, Tim Osborn <t.osborn@uea.ac.uk>,  "David C. Bader" <bader2@llnl.gov>, 'Susan Solomon' <ssolomon@al.noaa.gov>

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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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