Thursday, November 30, 2017

Implicit priors and the energy balance of the earth system

So, this old chestnut seems to keep on coming back....

Back in 2002, Gregory et al proposed that we could generate “An observationally based estimate of the climate sensitivity” via the energy balance equation S = F2x dT/Q where S is the equilibrium sensitivity to 2xCO2, F2x = 3.7 is the (known constant) forcing of 2xCO2, dT is the observed surface air temperature change and Q is the net radiative imbalance at the surface which takes account of both radiative forcing and the deep ocean heat uptake. (Their notation is marginally different, I'm simplifying a bit.)

Observational values for both dT and Q can be calculated/observed, albeit with uncertainties (reasonably taken to be Gaussian). Repeatedly sampling from these observationally-derived distributions and taking the ratio generates an ensemble of values for S which can be used as a probability distribution. Or can it? Is there a valid Bayesian interpretation of this, and if so, what was the prior for S? Because we know that it is not possible to generate a Bayesian posterior pdf from observations alone. And yet, it seems that one was generated.

This method may date back to before Gregory et al, and is still used quite regularly. For example, Thorsten Mauritsen (who we were visiting in Hamburg recently) and Robert Pincus did it in their recent “Committed warming” paper. Using historical observations, they generated a rather tight estimate for S as 1.1-4.4C, though this wasn't really the main focus of their paper. It seems a bit optimistic compared to much of the literature (which indicates the 20th century to provide a rather weaker constraint than that) so what's the explanation for this?

The key is in the use of the observationally-derived distributions for the quantities dT and Q. It seems quite common among scientists to interpret a measurement xo of an unknown x, with some known (or perhaps assumed) uncertainty σ, as implying the probability distribution N(xo,σ) for x. However, this is not justifiable in general. In Bayesian terms, it may be considered equivalent to starting with a uniform prior for x and updating with the likelihood arising from the observation. In many cases, this may be a reasonable enough thing to do, but it's not automatically correct. For instance, if x is known to be positive definite, then the posterior distribution must be truncated at 0, making it no longer Gaussian (even if only to a negligible degree). (Note however that it is perfectly permissible to do things like use (x- 2σ, x+ 2σ) as a 95% frequentist confidence interval for x, even when it is not a reasonable 95% Bayesian credible interval. Most scientists don't really understand the distinction between confidence intervals and credible intervals, which may help to explain why the error is so prevalent.)

So by using the observational estimates for dT and Q in this way, the researcher is implicitly making the assumption of independent uniform priors for these quantities. This implies, via the energy balance equation, that their prior on S is the quotient of two uniform priors. Which has a funny shape in general, with a flat region near 0 and then a quadratically-decaying tail. Moreover, this prior on S is not independent of the prior for either dT or Q. Although it looks like there are three unknown quantities, the energy balance equation tying them together means there are only two degrees of freedom here.

At the time of the IPCC AR4, this rather unconventional implicit prior for S was noticed by Nic Lewis who engaged in some correspondence with IPCC authors about the description and presentation of the Gregory et al results in that IPCC report. His interpretation and analysis is very sightly different to mine, in that he took the uncertainty in dT to be so (relatively) small that one could ignore it and consider the uniform prior on Q alone, which implies an inverse quadratic prior on S. However the principle of his analysis is similar enough.

In my opinion, a much more straightforward and natural way to approach the problem is instead to define the priors over Q and S directly. These can be whatever we want and are prepared to defend publicly. I've previously advocated a Cauchy prior for S which avoids the unreasonableness and arbitrariness of a uniform prior for this constant. In contrast, a uniform prior over Q (independent of S) is probably fairly harmless in this instance, and this does allow for directly using the observational estimate of Q as a pdf. Sampling from these priors to generate an ensemble of (S,Q) pairs allows us to calculate the resulting dT and weight the ensemble members according to how well the simulated values match the observed temperature rise. This is standard Monte Carlo integration using Bayes Theorem to update a prior with a likelihood. Applying this approach to Thorsten's data set (and using my preferred Cauchy prior), we obtain a slightly higher range for S of 1.2 - 4.8C. Here's a picture of the results (oops, ECS = S there, an inconsistent labelling that I can't be bothered fixing).

The median and 5-95% ranges for prior and posterior are also given. As you can see, the Cauchy prior doesn't really cut off the high tail that aggressively. In fact it's a lot higher than a U[0,10] or even U[0,20] prior would imply.  

Wednesday, November 15, 2017

Watt's up with Pat Frank?

And now for your scheduled return to the climate blogosphere wars. I haven't missed it at all. Pat Frank has posted a rather tedious pile of blether on WTFUWT which mentions me, albeit tangentially. Well, maybe a bit more than tangentially. The story, such as it is, is that he submitted a paper (which apparently has been rejected 6 times already by different journals) to GMD where I'm an editor. I took on responsibility for dealing with it, which was a fairly simple task as the glaring error in the manuscript is not really that well hidden. A bit of googling confirmed that several others had already seen this and dealt with it appropriately, so rather than waste the time, effort and good-will of hard-pressed reviewers I summarily rejected it. There followed the inevitable appeal which was sent to Jules (dealing with appeals happens to be one of her specific roles as an Exec Ed) who passed it on to fellow Exec Ed Didier Roche due to the obvious conflict of interest. He has upheld the appeal but not before several more rambling screeds appeared, and the blog post, and several hundred comments.

I'd suggest the comment thread for general entertainment purposes, but I defy anyone to wade though it all (never was it more true that comment threads on blogs are a write-only medium). A couple of sane voices did their best to uphold my honour but the vast majority is just boring vacuous idiocy. Sigh. Are there not any interesting sceptics around these days?

Tuesday, October 10, 2017

We have corporate sponsorship

I've been waiting a long time to use this clip!

Finally signed our first contract for some work which is due to start shortly. It's not a huge project but should be interesting and generate some worthwhile results. We didn't really have to punch ourselves in the face or threaten to reveal the dirty secrets of climate modelling (jules already has a journal dedicated to that cause).

If anyone else wants to jump on the bandwagon and pay jules or me to do something interesting, leave a comment :-)

Sunday, October 01, 2017

Stockholm art

Stockholm has a modern art museum and we all know how important it is to open one's mind to surrealist thoughts before a science conference...

We've never had a cargo disaster like this bicycle case, despite shipping 3 tandems across the oceans to Japan and back!

I soon discovered one of the escaped bicycle wheels spinning in a corner:

Wonder what beautiful piccies will be added to these frames, presently labelled "Plingeling" and "Pling":

Perhaps I should have looked behind this sheet to see the exhibit behind, but I was too shy:

But there was also some good stuff:

Can't beat Klein bloooooo! The handy information board informed me that he spent time in Japan learning Zen. That must partly explain why it is just so good. Ahhhh...

And then there was the extensive MODEL GRID SECTION of which this is a small part!!!!! 
Woo Hooo! 
If GMD had any money it could sponsor this!

[jules' pics] Stockholm

#PMIP2017 was held in Stockholm. Maybe it was the unusual warmth and sunshine, but Stockholm seemed like a very happy kind of place.


Nowhere else have I seen children swinging joyfully from the street signs.

Construction is always good sign of prosperity...?

Then there is the river

Private yachts.

Public life saving.

Posted By Blogger to jules' pics at 10/01/2017 02:17:00 PM

Sunday, September 24, 2017

Running hot...or not?

The question has been asked (repeatedly): are the CMIP models “running hot”? By which it is not meant, are the models too warm - they have a wide range of temperature biases which are normally subtracted off by the use of anomalies (which is a separate debate) - but whether they are warming up too much relative to observations.

But I don't care about that, because I've been running too! It's been a bit warm in Hamburg and humid too, so I was a bit apprehensive about this morning's half marathon up and down a bit of river bank at the north edge of the city. 

However I didn't need to worry about that, it was grey and chilly this morning. What I should have been more concerned about is the lack of recent training and surfeit of pastries (not to mention currywurst).

It's a funny affair with another identical half marathon going off 20 mins ahead of us, that being the “Cup” event (part of a series of three races). (Fortunately I didn't find that web page until just now or I might have had to enter all of them.) But the cup runners are not all that quick, so I spent most of the race overtaking them. This wasn't really a problem as the small field of 500 runners was fairly well strung out by the time I caught them. The course was a riverside path, just hard-trodden earth which was mostly dry but a little slippery in parts.

It wasn't all as flat and smooth as this!

Plenty of sharp turns and short rises too. Despite being about 500m too short, it was still a personal worst, slower even than my very first half marathon when I'd never run that far before! 9th finisher in my race in 1:29:14, 2nd MV45 and also well beaten by one woman who was 2nd overall.

Saturday, September 23, 2017


I had curry for lunch on Thursday.

It was the wurst!

(Actually it was rather good, however we forgot to take a pic so you'll have to make do with this less appealing version from wikipedia.)

By massive coincidence I saw this tweet from Gavin on the same day:

which quotes from this NY Times article.

Google tells me Curry's been all over this "fundamentally dumb" idea like a rash. It must have seemed like a good wheeze to earmark some funding and publicity for those who can't raise it on the merits of their research. But now she's obvioulsy been tapped up for membership of the “team”, it's finally dawned on her that she'd have to work with a bunch of crazies and losers who have no idea what the hell they are talking about.

What hasn't dawned on her yet, is that that's where she belongs.

Seriously, who is she trying to kid? This is the very same Judith Curry who infamously puffed some brain-meltingly abysmal drivel by Murray Salby, doesn't know what the word “most” means, and wrapped herself in flags of convenience but couldn't explain what they meant. To name just three episodes early in her blogging career before I gave up even bothering to check what she was saying.

Apropos of not very much, she sent me her CV a couple of days ago.

Wonder why she thought I might be interested in it?

This “red team” stuff is hardly new. Who can forget the “Not the IPCC” report that never saw the light of day? Or the various attempts to set up sceptical journals or scientific societies that are invariably still-born (or more often, never-born). You think they'd work it out eventually. Same shit, different day, as they say in Georgia.

Thursday, September 21, 2017

Beyond equilibrium climate sensitivity

New(ish, but I'm just getting round to writing about it) review article by Knutti et al on climate sensitivity. The detailed review of published estimates is impressive, a lot of work must have gone into that. It has been spotted that the Callendar estimate is wrong: the value in the paper is about 1.8C for a doubling of CO2, which is rather lower than the value plotted in the figure. (This calculation ignores changes in clouds, so it's impressively close to what we would estimate today for the same processes).

Probably the most important aspect of the update, however, is summarised in the figure of how radiative imbalance changes with temperature as a model warms up (after an abrupt quadrupling of CO2). Simple linear first-order modelling of the energy balance would suggest that the points should lie on a straight line, with the intercepts on the y and x axes being the initial forcing  and the equilibrium temperature change respectively (and these values can be halved to get those pertaining to a doubling of CO2). A handy consequence of this is that the equilibrium response could be estimated in a climate model, without the need to run the model to equilibrium. Based on this idea (often referred to as the “Gregory method ”), the equilibrium sensitivities of the CMIP models are typically estimated on the basis of a 150 year simulation following a quadrupling of CO2.

However models - and quite probably, the real world - doesn't behave like that. Instead, the points appear to cluster around a curve which implies the true equilibrium change is greater than that which would be estimated from analysis of an initial segment of the run.

I can't help wonder how rapidly and widely this method would have been accepted if it had been proposed by someone less eminent. I suspect there would be more of a “nice idea, but it doesn't really work that well”. Incidentally, the behaviour is nothing to do with quadrupling per se, you get similar results for greater and lesser forcing changes. I believe quadrupling was just chosen (rather than the more conventional doubling) to get a greater signal/noise ratio in the changes.

Tuesday, September 19, 2017

Make our Planet Great Again

Our kind host has pointed us towards the German call for applications for 4-year fellowships under the joint France-Germany “Make our Planet Great Again” program. This was originally Macron's brainchild, which attracted a certain amount of media attention possibly disproportionate to its scientific importance. Now the Germans have jumped on board with an essentially parallel (albeit smaller) scheme which offers awards of up to €1.5m over 4 years to attract overseas scientists to set up groups in Germany, again focussing on climate and sustainable energy sciences. It may not be a huge initiative but it will surely be very attractive to a lot of people, including perhaps those in the UK who are uncertain what Brexit will bring. If we were remotely interested in going abroad and setting up a new research group we'd probably be applying. But we aren't.

Monday, September 18, 2017

More D&A and FvB.

By chance I happened to notice another paper with an interesting title appearing in Climatic Change on the very same day as the recent Mann et al paper: Is the choice of statistical paradigm critical in extreme event attribution studies? While my noticing it was fortuitous, the publication date was no coincidence, as it was clearly intended as a "comment on" in all but name. I am not particularly impressed by such shenanigans. I know that Nature often publishes a simultaneous commentary along with the article itself, but these are generally along the lines of a sycophantic laudation extolling the virtues of the new work. The climatic change version seems to be designed to invite a critical comment which does not provide the authors under attack any right to reply. Jules and I were previously supposed to be a victim of this behaviour when we published this paper. However the commentary never got written, so in the end we suffered nothing more than a lengthy delay to final publication.

Anyway, back to the commentary. Is the choice of statistical paradigm critical? I can't really be bothered discussing it in any detail. The arguments have been hashed out before (including on this blog, e.g. here). The authors provide a rather waffly defence of frequentist approaches without really providing any credible support IMO, based on little more than some rather silly straw men. Of course a badly-chosen prior can give poor results, but so can an error in your computer program or a typo in your manuscript, and no-one argues that it's better to just take a guess instead of doing a calculation and writing down the answer. Well, almost no-one.