date: Sat, 15 Dec 2007 12:21:48 -0500

from: "Thomas.R.Karl" <Thomas.R.KarlatXYZxyza.gov>

subject: Re: [Fwd: sorry to take your time up, but really do need a scrub

to: santer1atXYZxyzl.gov

Thanks Ben,

You have the makings of a nice article.

I note that we would expect to 10 cases that are significantly different by chance (based

on the 196 tests at the .05 sig level). You found 3. With appropriately corrected Leopold

I suspect you will find there is indeed stat sig. similar trends incl. amplification.

Setting up the statistical testing should be interesting with this many combinations.

Regards, Tom

Ben Santer said the following on 12/14/2007 5:31 PM:

Dear Tom,

As promised, I've now repeated all of the significance testing involving

model-versus-observed trend differences, but this time using spatially-averaged T2 and

T2LT changes that are not "masked out" over tropical land areas. As I mentioned this

morning, the use of non-masked data facilitates a direct comparison with Douglass et al.

The results for combined changes over tropical land and ocean are very similar to those

I sent out yesterday, which were for T2 and T2LT changes over tropical oceans only:

COMBINED LAND/OCEAN RESULTS (WITH STANDARD ERRORS ADJUSTED FOR TEMPORAL AUTOCORRELATION

EFFECTS; SPATIAL AVERAGES OVER 20N-20S; ANALYSIS PERIOD 1979 TO 1999)

T2LT tests, RSS observational data: 0 out of 49 model-versus-observed trend differences

are significant at the 5% level.

T2LT tests, UAH observational data: 1 out of 49 model-versus-observed trend differences

are significant at the 5% level.

T2 tests, RSS observational data: 1 out of 49 model-versus-observed trend differences

are significant at the 5% level.

T2 tests, UAH observational data: 1 out of 49 model-versus-observed trend differences

are significant at the 5% level.

So our conclusion - that model tropical T2 and T2LT trends are, in virtually all

realizations and models, not significantly different from either RSS or UAH trends - is

not sensitive to whether we do the significance testing with "ocean only" or combined

"land+ocean" temperature changes.

With best regards, and happy holidays to all!

Ben

Thomas.R.Karl wrote:

Ben,

This is very informative. One question I raise is whether the results would have been

at all different if you had not masked the land. I doubt it, but it would be nice to

know.

Tom

Ben Santer said the following on 12/13/2007 9:58 PM:

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

[1]mearsatXYZxyzss.com

707-545-2904 x21

707-545-2906 (fax))

--

*Dr. Thomas R. Karl, L.H.D.*

*/Director/*//

NOAA's National Climatic Data Center

Veach-Baley Federal Building

151 Patton Avenue

Asheville, NC 28801-5001

Tel: (828) 271-4476

Fax: (828) 271-4246

[2]Thomas.R.KarlatXYZxyza.gov [3]<mailto:Thomas.R.KarlatXYZxyza.gov>

--

Dr. Thomas R. Karl, L.H.D.

Director

NOAA's National Climatic Data Center

Veach-Baley Federal Building

151 Patton Avenue

Asheville, NC 28801-5001

Tel: (828) 271-4476

Fax: (828) 271-4246

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