There’s a paper out today (just published online) by J. C. Fyfe, N. P. Gillett, and F. W. Zwiers, called “Overestimated global warming over the past 20 years”. I’ve addressed this “pause in warming question” at this blog earlier, and the argument they make, based upon the Supplement to the article (which is not behind a payment), is predominantly statistical. The authors are well-known in IPCC circles and, statistically speaking, Zwiers is a co-author with von Storch with the good but somewhat dated book *Statistical Analysis in Climate Research* (which I own).

But, Judith Curry has commented on the article, and I’m sure it’s going to be a major feature of discussion with the latest IPCC report due out soon. (Added 16th September 2013: In case the reader is not familiar with Judith Curry, this is an example of what’s wrong with Curry’s kind of analysis.)

So, I’m buying a copy of the article, and will do an analysis, reporting here. What’s odd about the material in the Supplement, and I hope they address in the article, is the difference in methodology in apparently what Fyfe, Gillett, and Zwiers did, and what’s been done earlier, which hopefully they’ll contain in their references. I’m thinking specifically of:

- S.-K. Min, D. Simonis, A. Hense, “Probabilistic climate change predictions applying Bayesian model averaging”,
*Philosophical Transactions of the Royal Society A*, 15 August 2007,**365**. - R. L. Smith, C. Tebaldi, D. Nychka, L. O. Mearns, “Bayesian modeling of uncertainty in ensembles of climate models”,
*Journal of the American Statistical Association*, 104(485), March 2009.

I also think it odd that they claim they made no distributional assumptions in the derivation in their Supplement, which I find highly dubious. I mean, there are no *explicit* distribution assumptions made when you do linear least squares, but it’s provable that it is equivalent to a Gaussian model of errors.

~~Later.~~

*Postscript*: 30th August 2013, 12:56 EDT.

I am delving deeply into the techniques of this interesting meta-analysis, with kind help of Professor Francis Zwiers. Of course, anything I say or present here is my own technical responsibility, not his. I will probably write a white paper on this, sharing it with Professor Zwiers, and presenting highlights here.

*Postscript*: 31st August 2013, 09:52 EDT.

JokimÃ¤ki posts “Global warming … Still happening” at the *SkepticalScience* blog and indeed it is. Has to be, lest basic, 19th century-derived physics be violated, not to mention our engineering of spacecraft and semiconductors. It will be very interesting rationalizing the Rahmstorf (with Foster and Cazenave) kinds of projections he reports with this Fyfe, Gillett, and Zwiers paper. And a good chance to contribute to improving the statistical arsenal applicable to climate work. Right now I’m having a serious look at *empirical likelihood techniques*, as used in *nested sampling* and *approximate Bayesian computation*. (See, for instance, Professor Christian Robert’s talk, or Lazar, “Bayesian empirical likelihood”, *Biometrika*, 2003.)

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One observation from a climate change science neophyte: 117 draws from the model distribution seems insufficient to accurately estimate a 95% CI (or an empirical reference distribution) for hypothesis testing. Presumably the 117 comes from limitations of computational power/time, but I would imagine that an importance sampling type strategy could have been used to choose from uncertain inputs targeting the tails of the model reference distribution. As a trivial example, 117 draws from the standard normal gives an empirical 2.5% quantile with repeat simulation (from 1000 repeats) mean of -1.88 with standard deviation of 0.22. Importance sampling 117 draws from a Student’s t gives a repeat simulation mean of -1.98 with standard deviation of 0.17. The truth being -1.96, of course!

Dr Cameron, honored to have your opinion here. As an aside, I am learning and admiring the work the astro community has done with Bayesian inference, notably embracing the Nested Sampling work of Skilling and his disciplines (Feroz, Hobson, Bridges, and others), which I greatly admire.

As to Fyfe, Gillett, Zwiers, as noted, I am working a critical review where I think I know what’s going on, but am going back to original papers on HadCRUT4 and summary papers describing the 37 models from CMIP5 they used to try to understand what’s going on. That, and other commitments, have delayed the project.

I am drilling down into what “exchangeability” means precisely in this context, trying to connect it to de Finetti’s Theorem. But, I think, more importantly, even if the HadCRUT4 observations represent ensembles, they capture essentially one run of Earth for the period in question. So, thinking Rubin and Aitkin Bayesian bootstrap, I wonder if there aren’t other ensembles which were very possible and so should be represented in some kind of prior, but aren’t manifest. I see the primary sin of the frequentist bootstrap limiting values to only those observed, where there are actually those values and whole neighborhoods of them which are admissible.

I also worry about interdependency …. Climate models have ancestries and common components. Fyfe, Gillett, and Zwiers chose to use them as if they were black boxes but I bet that if denotes the HadCRUT4 ensemble data and the -th model, is dependent upon one or more and to pretend otherwise makes things seem more inconsistent than they are.

Finally, there are a slew of small things, such as how trends are ascertained and what precisely is meant by “internal variability”. They say (in their supplement) “ and are perturbations to and respectively due to internal variability. These are different for each model run, but are essentially identical for each resample of the observations.” That last bit seems quite incomplete. I don’t know how they would fix it, but, then, maybe the idea of comparing this set of observations and the model runs is just a broken one.

All these somewhat deep issues and trying to describe them in understandable and compelling language.

This is exactly why I enjoy your blog: to discover these statistically interesting climate change papers and to get some insight into why they do things they way they do them! The common ancestries of climate change models must indeed introduce some difficulties into the interpretation of their ensemble predictions via frequentist style tests. This Eint_ij, Mij notation and explanations from the supplementary data look quite like the structural equation modelling used in some survey-based meta analyses. But one very basic question which I couldn’t glean from the paper itself is: are these “predictions” the output of models run with only data available up to the starting year, or do they update their models from partial data throughout the duration of the simulation?

Re: nested sampling. There is indeed a lot of good work on this from the astronomical (& physics) community; particularly with the production of publically-available codes for running quick NS analyses. NS hasn’t been widely embraced by the general statistics community though: one reason might be that it only works efficiently (via ellipse-based sampling) on R^n space problems with separable priors, and another reason might be that it’s not amenable to Gibbs sampling techniques.

My understanding of Fyfe, Gillett, and Zwiers 2013 (“FGZ” hereafter) is that on one side there’s HadCRUT4 and its ensembles, and on the other side there are the models from CMIP5, run against presumably representative forcings from measurements of the years in question, and then results then compared against the HadCRUT4 ensembles. The basic thing is that HadCRUT4 comes in low, and the smear of the CMIP5 models comes in on median higher, even if there is overlap. They then declare that the models are exaggerating warming and use a p-value to assess how badly.

Without getting too long or technical — happy to share my write-up after I share it with Zwiers, which I promised I would do — there are three possibilities ….

(1) Maybe the HadCRUT4 realizes a particular Earth climate future which is one of a possible many. After all, we only see one path from an initialization, even if many were stochastically possible.

(2) Maybe the initial and boundary conditions of the models did not precisely capture the same conditions that HadCRUT4 implies or induces and, so, even if the models were physically correct, they were not simulating the same Earth climate.

(3) Maybe there is something fundamentally off about the assumption of exchangeability, by which I assume they mean de Finetti exchangeability, which invalidates the comparison they want to do.

I am, of course, intrigued by this last possibility, although I don’t know how I would construct an assessment of whether the exchangeability assumption was warranted or not. It’s not like we can construct the joints directly. Maybe there’s some chain of conditionals by which we can get there?

At least, my consensus is that I think the conclusion in the title is extreme considering the evidence of the paper, which is basically just a curious study, perhaps worthy of the “Comment” status the journal affords it, but people, like Dr Judith Curry, apparently declared it to be much more.

There is something profoundly unsatisfying about the Chinese menu approach to statistical analysis which von Stoch and Zwiers appear to embrace in their STATISTICAL ANALYSIS IN CLIMATE RESEARCH, as it offers a bunch of techniques with only technical authority and citation density as being their justification. I’d rather have a more uniformly calculated set of methods which could be compared with greater ease, and I feel the Bayesian mindset just gives us that.

As in medicine, a lot, but far from all, of the geophysical community is still back in Frequentist Land.

Regarding your comment on NS, to the degree the narrow algorithm has those limitations, yeah. But it seems to me its insight is that level sets of likelihoods (or sampling densities) explored by supports implied by priors is a good way to look at things, however way each of those pieces gets realized.