Monday, April 16, 2018 EGU2018 Day 5

One final push…we were back on paleoclimate again first thing, more data than models though a bit of a mix of both. Just as the session ended and I started to think about going in search of lunch, lunch arrived in the form of sandwiches for the Atmospheric Sciences Division meeting. I usually attend the Climate Division meeting so thought it might be interesting to see if AS would have a different style. It didn’t really (even the sandwich was the same), and the most interesting points of discussion were rather similar – mostly, how to cope with the meeting outgrowing the available space. There’s no great solution and I am coming round to the idea that a slight discouragement towards throwing in too many abstracts might be the least-worst approach. There are of course ways round the one-abstract-per-first-author for anyone sufficiently motivated (like jules and I might be) but people who chuck in virtual duplicates to several sessions might be dissuaded which would be a good thing in terms of conference quality as well as freeing up space. I’m not sure it will make much difference overall though as surely there can’t be all that many of these cases. Some audience members also made the case for more remote participation and I don’t think the EGU can continue to resist this indefinitely. Attending in person brings greater benefits, but also costs, and allowing people to participate without the massive investment of time and money involved in travel could surely only be a good thing.

The afternoon sessions contained some advanced and high resolution modelling – a mix of future plans and existing results. Bjorn Stevens gave a well-received talk extolling the benefits of 1km resolution modelling. Mind you a bunch of high-resolution modellers is perhaps not the toughest crowd for that topic! There were some very truthy images of modelled clouds looking like reality. A particular goal of the highest resolution modelling is to resolve tropical storms and some of our past Japanese colleagues had some impressive results here too.

Previously the Friday afternoon slot has usually been a bit of a graveyard with lots of conference-goers leaving early for flights home, but now the schedule is so full there was even a busy poster session in the evening, including more of both the paleo and advanced numerical modelling. We hung around for the start of the convenors’ party but left quite early.


And now for the final score: jules says she had 9 free meals during the week, which were much higher quality than previously (so that’s where the EGU budget disappears to). As for myself, I attended 7 of the 3 meals to which I was actually invited. It seemed a particularly good week this time, perhaps partly due to our long absence. We last came 2 years ago when we were so ill and tired we only attended a fraction of the week, so this time there was rather a lot of new stuff. Jules was also involved in three sessions and we had a total of 4 presentations between us, which kept us busy across a wide range of topics. There was also an element of escapism for us in getting away from home for a bit, which we can now return to feeling (I hope) somewhat rejuvenated.

As for Day 6, we started off with a lovely sunny jog along the Donau Insel, and I’m pleased to report that my legs are now just about working properly after the marathon.


Some gentle sightseeing in town (see Belvedere above) was rounded off by a fabulous concert from the Vienna Philharmonic. I always check their schedule when we are at the EGU – more often than not they are either absent or sold out but this time we got prime seats for a concert including Elgar’s Cello Concerto by Sol Gabetta. We were so worn out by this stage that we forgot to check the venue and went to the wrong place, but fortunately the right place is only a short walk away. jules and I were amused to see a prominent EGU committee member taking photos in the concert hall just after the announcer had clearly forbidden such behaviour 🙂 It looked rather like this:


Saturday, April 14, 2018 EGU 2018 Day 4

Four days in and the fog is descending…not the weather which remains resolutely warm and sunny, but my mental state after on overload of science, food, drink, and long days. Nothing compelling at 8:30 so we had a morning jog and breakfast at the excellent cafe just outside our apartment. Possibly the best almond croissant ever, feeling a bit stupid for not discovering this place before as we’ve stayed in the same airbnb three times now. We’ve got some catching up to do!


There was a mathematical session at 10:30 covering a huge range of ideas. I was particularly looking forward to a talk that promised to explore the mathematics of emergent constraints. However it turned out to be a little more specialised than I had hoped, focussing in detail on the relationship of variability to long-term changes motivated by the recent Cox et al paper. Still lots of room for more to be done here.

Lunch was the GMD editorial board meeting. I’m happy to see GMD charging on successfully and jules will be stepping down from her Chief Exec position in due course. It’s no longer growing rapidly but seems to have stabilised at a reasonable level. I don’t think there is anything of great public interest to report. There will be a mobile version of the journal website launched soon.

Straight after lunch was jules’ climate sensitivity session. I’ve struggled to organise similar sessions in the past so it was great to see that this was packed with great talks and well attended too. Andrew Dessler gave a particularly good presentation on some of his work on interannual variability and also included the below graphic which is perhaps my biggest contribution to science this year. Perhaps I should have made a slightly less fuzzy green camera, it’s a bit low-resolution but never mind.
There is still a general prohibition on photography “unless the presenter authorizes it. Presenters are encouraged to inform the audience if they welcome photos.” Baby steps when compared to the blanket prohibition that has been in place in earlier years. People take photos all the time of course, it’s easier than writing a note these days if you want to take down a name/reference/idea/… Maria Rugenstein also gave a nice summary of er Longrun MIP analysis which I’ve seen some of before but which seems more complete now.

After tea I listened to Tim Palmer’s medal lecture. Tim sometimes gives interesting-but-controversial talks about wild idea relating to stochastic parameterisations, stochastic computing or his aims for a global climate centre, but this was more of a standard didactic history lesson on the growth of probabilistic prediction in numerical weather prediction. As such I knew most (but not all) of it and it was probably of wide interest but not hugely stimulating to me personally. The main message is that we should make probabilistic weather forecasts, and we already do, so that’s alright then.

jules and I had three posters to defend between us, slightly inconveniently arranged on three different (but at least neighbouring) rows. We had however discovered the best strategy for dealing with the 5:30 beer queue (thanks to a fortuitous coincidence on Monday) so at least were well fuelled for the occasion. Lots of interesting conversations ensued, at least that’s how I remember it. As well as taking about our own work there was time to visit the others in the sessions."Oh look here’s James to tell you why your poster is wrong" said one person as I wandered along which raises the question of how many others were thinking it 🙂

After posters we had the Copernicus 30y Birthday Party to attend. Copernicus is the admin/meetings/publications wing of the EGU (which was the EGS back then, if it wasn’t something else previous to that). To be honest I’m not sure exactly how it all fits together but it seems to work very well so I’m not too bothered. It was up on the top floor of one of the local office blocks close to the conference centre. There was plenty of food and drink to go round.

(Not sure why these last two pics are so fuzzy - something to do with how they originally appeared on the blueskies blog.)

Thursday, April 12, 2018


Another year, another PB.

This year the marathon was scheduled for the Sunday immediately before the EGU. However we weren't committed to that so I entered anyway when they sent me an early bird discount offer. The Vienna marathon was also a week too late for a combined work/run trip.

Later on we started to think about the EGU trip, and realised that it was actually possible to run the marathon, go straight to the airport, and hop on a plane to Vienna. The marathon is on the south side of Manchester and really very close to the airport. Parking the van in the city centre can be difficult due to height barriers so rather than a hotel we found an airbnb in a residential area a couple of miles south of the race start which proved to be very convenient. There was even a fabulous pizza just down the road. Probably the best we've had this side of the Japan Sea, in fact. A proper soft chewy crust with a few crispy bits and plenty of topping.

Under usual circumstances, one between two would have been reasonable, but these were not usual circumstances! We staggered back and collapsed into bed.

Sunday morning dawned cold, cloudy and still. It would be hard to imagine a better day for a marathon. I forced down a bit more breakfast before packing up and heading off to the start. Didn't see anyone I recognised, but I hadn't really expected to. There was a club-mate somewhere a bit further back in the field but as I had last time I hopped the barrier close to the front and tried to position myself among other people aiming for a similar time. After a good winter of training I'd been starting to dream of the magic 2:45 (the threshold at which I could enter the Championship race at London and line up alongside people such as Bekele and Mo Farah etc) but didn't think it was that likely. 2:50, on the other hand, I was confident of beating, having come reasonably close to it last year. During training I had beaten my half marathon PB by about 100 seconds, which logically should be worth comfortably than 3 mins over a marathon. However, while the running had been going well, there had been a lot of other stuff happening that had meant I hadn't been sleeping well for a while. You never quite know what's going to happen on the day either.

So I set off around 2:47 pace, feeling ridiculously comfortable as you do when your legs are fresh after a gentle couple of weeks tapering. Settled into a comfortable pace, trying to stay in groups of similar speed. Seemed to be going well, I had dreams of a fast second half but made sure not to try too hard too early. I't do 20 miles or so, then sprint past everyone with a fast last 10k.

Around half-way there's a section where the course doubles back on itself and we saw the leaders coming back. Two Kenyans glided effortlessly past.

and then after what seemed like an age but was probably less than 30 seconds, a bunch of brits appeared. One of the Kenyans appears to have dropped out later but the other won by a few minutes. Only 2:21, the best runners aim for London of course.

Somewhere around this point I caught up with one of the elite female runners, and we ran together for a few miles. I later discovered that she had a best time of 2:37 and ran in both the Commonwealth Games and European Champs back in 2010. Not bad company to be keeping. Up to mile 20 and even a little beyond I was doing fine, but gradually things started to hurt - especially my left hip and leg which have been the weak spot before, so either I'm slightly weak on that side or slightly lopsided in running. The planned fast last 10k became a fast 4 miles then a fast 5k and although I did try pushing on the pace just a little bit at that point ("it's just a parkrun!"), I soon reverted to damage limitation and decided to just keep on plodding on in the hope that I wouldn't fall apart too badly. This worked pretty much ok, I did lose a minute over this section to Holly who kept on at a steady speed but that's not too bad in the great scheme of things. The two halves were 1:23:28 and 1:25:16 which is only a positive split of 1:48, a touch higher than ideal but hardly shameful. Despite this slowdown I did move up over 40 places in the second half.

Food and water worked fine again with my own bag of jelly babies and kendal mint cake washed down by the supplied bottles. I really wasn't hungry or under fuelled at all after the pizza though. Perhaps with hindsight I could have splashed on a bit more water towards the end of the race when I wasn't interested in drinking. Fixing the left leg problem might have the biggest impact. It isn't causing a problem now three days later so there isn't a real injury problem, it's just not quite as good as the other one. Oh, and a pair of magic nike sub-2 shoes though even finding a pair would be a bit of a miracle. A 3 min PB is a pretty big improvement at this stage in my running career and at this age, but one disappointment with my result is that I didn't get quite as much as half-way to 2:45. That still seems like it may be a step too far for me. We'll see...

Anyway, here is my official result and here it is on Strava: EGU 2018 Day 3

jules was talking in the first session this morning (paleo data assimilation) so had to rush in a bit early. She was talking about our plans for reconstructing the last deglaciation (21ka to present). It seems to have gone ok, I was sitting in on the proper data assimilation session so didn’t get to hear it 🙂 In a bizarre blast from the past, someone was talking about orthogonality of bred vectors and even mentioned that I’d done some work on that many years ago! I suppose that sort of makes up for when other people ostentatiously omit our work from their list of references despite it being one of the most obvious and seminal sources for the topic under discussion. Not that I’m bitter or anything. I expect it’s accidental some of the time.

Another free lunch thanks to an important discussion on policy matters at GMD. Not that I was part of the policy-making process, but I sneaked in along with the proper executive editors and ate all the food while they were talking 🙂 I then went for a very gentle and slow run for reasons that will be made obvious in a future blog. Well, I mean the reasons for it being gentle and slow (other than being straight after lunch). The reason for doing the run at all is just that I wanted a bit of fresh air and there was nothing compelling in the program. We’ve always found it is impossible to do 5 full days anyway at such a big conference as this, no human brain can reasonably be expected to cope with that much science. I returned for some more paleoclimate stuff including a medal lecture from yet another old white man. I especially liked the way he managed to open by telling us all about the other medal he’d just been awarded by That Other Organisation. It was a good talk though and it’s not really fair to blame recipients for the limitations of the process. His talk concerned Dansgaard-Oeschger events, the massive rapid changes in climatic conditions that happened irregularly through colder periods in Earth’s recent paleoclimatic past. It’s still unclear exactly how and why they happen.

Evening posters were (as usual) related to the daytime talks, so more data assimilation of modern and paleo flavours, which kept us busy until it was time for dinner.


Over the years we’ve discovered some nice restaurants outside the most touristy bits which are reasonably quiet. Yesterday was the schnitzel, tonight was the turn of the Chinese. This pic is just the walk home though.

Wednesday, April 11, 2018 EGU 2018 Day 2

jules had a a 7:30 breakfast meeting today which didn’t seem very civilised to me. But it looks like it was worth getting up for.


A perk of being Executive Editor, but very little recompense really for the hours of work she puts into running GMD. I am pleased to confirm that the croissant that she smuggled out for me was excellent.
The day proper started with general paleo data/modelling stuff in a session that jules was co-convening. This was a little thin this year, especially on the modelling front, probably due to the forthcoming CMIP/PMIP experiments which will be underway around the world but which are not yet ready to report on. I probably should have paid more attention but was distracted by croissant crumbs.

Today’s free lunch was at the CL (climate) Division meeting. All seems to be sailing on fairly smoothly though the EGU is heading towards full capacity of the meeting venue and it’s not clear how best to address this. One new policy initiative that jules and I are not particularly keen on is the imposition of a limit to one submission per person as first author (a second submission would be allowed if you are actually invited to talk, but that’s fairly rare). We have 4 between us this year and rarely if ever have come with a bare one each – though to be fair last time we came 2 years ago jules had a invited talk and we only submitted one more one more each on top of that, so it’s not always going to be a huge problem. Also, the limit could be easily evaded by author padding which seems like an open invitation to ethically dubious behaviour. Another issue that generated some discussion is the prevalence of stale pale males in the higher echelons of the division hierarchy. Hard to blame the maleness of the president in particular on any institutional bias though, since they are elected by the members and there have certainly been female candidates for this position. The medal winners on the other hand…enough said.

Amazingly, the weather/climate sessions contained yet more discussion of the good performance of the ensemble mean. Apparently its good performance (relative to ensemble members) is due to nonlinear filtering? Not really, it’s just Euclidean geometry and simple algebra. Ho hum. See these three posts and the associated paper for more details. Not much point writing it down if people aren’t going to read it though! There was also "decadal" forecasting of the next 2-5 years but to be fair someone had actually done a full 10. It doesn’t work, but at least they tried.

A PICO session on the use of econometric methods in climate science is the sort of thing I really appreciate being able to see at the EGU. Nothing stood out as particularly important but it covered a wide range of methods and applications. I must admit I was a little bit suspicious of someone fitting an inherently unstable time series model to 20 years of ice sheet volume data and concluding as a result that the ice sheets are terribly unstable though 🙂 His argument was that the unstable model fitted the data better than any simpler version. My counter-argument was that we’ve actually had 10,000 years of stable ice sheets prior to the reduction in recent decades! I think the underlying problem is that the recent accelerated loss is externally forced which his model doesn’t explicitly account for. This is a typical failure of econometric methods in my view, that they do not always take account of background knowledge that is implicit in the fundamental physics of the systems they are attempting to model. All good fun stuff again though. Last thing today was paleo posters (from the morning session) which we are not contributing to this time round. Lots of people to meet and chat to, after not attending last year.

Tuesday, April 10, 2018 EGU 2018 Day 1

Going to try a mini-blog straight away to avoid a big backlog. Arriving late on Sunday to a self-catering apartment meant a quick shop on Monday morning and missed session. As I said to Didier when he complained that I missed his 8:30 session (with a sceptic talk first up), I had something else more important already scheduled – breakfast! There was a brief moment of excitement later on when I asked a hostile question and the speaker accused me of being Jonty Rougier. No, he’s the other one who does that 🙂 The presentation in question was something that basically reproduced our results from several years ago, only less completely and correctly. Well, that’s my side of the story anyway. I presume Jonty has yet another side. To be honest we agree far more than we disagree but of course it’s the disagreements that make it fun.

Main event of the day – apart from me blagging my way into a free lunch –


– was the GMD 10th anniversary celebrations. A mixed session of short talks and a reception at the end of the day. When we set it up 10 years ago I never really imagined it would be so successful. So that’s really been (and continues to be) a lot of fun. Rolf Sander had a small puzzle that computing experts might like to consider: firstly, what does this Fortran 77 code output, and secondly, why? I answered the first part easily enough, the second was more challenging.

This is the code:

 Screenshot 2018-04-09 21.48.20

which can be found here if you want to download it and try it yourself. I should however warn you that some have found it either does not compile or does not generate the correct result depending on compiler. But I have it on (reasonably) good authority that it is acceptable code that should work (though not necessarily how you would expect…) according to the formal standard.

Here are our merry band of intrepid executive editors. Well, the 4 of them (out of 6) who could attend. One of them is jules and three of them are not. They all have feet really, just imagine 8 open-toed sandals and you won’t be far wrong.


And so to bed. Jules has a 7:30 meeting to look forward to. I have breakfast again 🙂

Wednesday, January 31, 2018

Trip to the 21st(?) Century

Went to Reading University last week, to do a lecture as part of a course for PhD students. The course was aimed at teaching paleodata students about models and how they might be useful for their research. A very good idea! Here are some students, and Joy (at the end of the bench) who was in charge, doing a lot of the teaching and most of the lecturing (a lot of work!) all while living up to her name!

Luckily, frothy coffee (a necessity for this travelling lecturer!) is as plentiful outside of Yorkshire as it  is inside. 

The main feature of Reading University campus is the pond which, at this time of year, is chock full of birds. I managed a couple of trips to inspect it, but I only had my iPhone so no point posting the bird pics. Here instead is some pond and trees.

Railway Britain does not seem to have advanced much since the 1980 and 1990s. Biggest difference is that the announcements at the stations are now audible. People also look at phones a lot more, and thankfully they shout into them a lot less. There are also places on the trains to plug your phone in to charge up its failing battery. 

Birmingham New Street station. Dangerously narrow platforms, with crowds standing well over the yellow line! ("Abunai desu kara kiiroi sen made osagari kudasai" - standard train announcement at all Japanese railway stations - because it is dangerous, stay back from the yellow line)

Reading station, however, was redeveloped THIS CENTURY! It's a sort of curvier, blue, dirty version of a late 20th century Japanese station. But at least it has nice wide platforms.

Settle-Reading is about 240 miles, taking about five and a half hours. I suppose this is an improvement over the seemingly endless period in the mid-1990s when all journeys took at least 10 hours due to every inch of track having to be inspected with a fine tooth comb. But it seemed like a lot of travelling for my 1.5 days in Reading. Trains back to the safety of the 19th century are rare and there was a long wait on an empty platform at Leeds station on Friday, but one can gain a little encouragement from the flavour of Victoriana emerging on the painted pillars.

Eventually... Ahhh, Settle station - back in the 19th century at last!

Monday, January 29, 2018 Cox et al part 3

As promised some more on this. The first thing I thought, on seeing this paper – a feeling that others apparently shared – was, why had no-one else already thought of this? Had we all just behaved like the fabled economist who, when their companion points out a £10 note lying on the pavement, ignores it, saying "If there really was a £10 note, someone would have picked it up already"?

Certainly the Schwartz fiasco will have put people off from pursuing this approach, as many of us had shown via a variety of arguments that the theoretical relationship in the simple 1-box climate model that directly links the autocorrelation of internal variability to equilibrium response, cannot be directly used for diagnosing the latter from the former in more complex climate models. Of course, this is not quite what Cox et al do, rather they show a strong correlation between their measure of variability and the sensitivity, across the ensemble of CMIP5 models. One complication in their analysis is that they measure variability via the 20th century simulations. Most of the variation in temperature seen in the 20th century is actually the response to external forcing and this forcing is far from the white noise assumed by Cox et al’s analysis (even after detrending, the variation about the trend is not white noise either). This would seem to undermine the theoretical basis for their relationship.

So, rather than using the 20th century simulations, I’ve had a quick look at the pre-industrial control simulations in which models are run for lengthy periods of time with no changes in external forcing. In all the following analyses I have restricted my attention to the models for which I had at least 500y of P-I control simulation, in order that the behaviour of each model would be well characterised (it is well known that the empirical estimate of the lag-1 autocorrelation tends to be biased low to a substantial degree for short time series). This restricted my set to 13 models. In this set of 13 models I  included both the MIROC models (5 and ESM) which Cox et al used as alternates, as I happen to know that the changes between the two generations here are substantial and were specifically made to affect the climate sensitivity-relevant processes as can be seen in their widely differing equilibrium sensitivities. It may however be that my results are themselves somewhat sensitive to the choice of models.

So, firstly, here’s a quick look at whether the lag-1 autocorrelation of annual mean temperature is related to the equilibrium sensitivity across this set of models:

Screenshot 2018-01-25 17.11.56
Nope. The regression line is nearly flat and nowhere near significant.

However, this isn’t quite what Cox et al presented. They actually calculated a function psi which depends also on the magnitude of interannual variability as well as its persistence. In fact their psi is defined as sd/sqrt(-log(alpha)) were sd is the standard deviation of interannual variability and alpha is the lag-1 correlation coefficient. They argue that this is the most relevant diagnostic as it is linearly related to sensitivity in their theoretical case. Sure enough when we calculate psi for the control simulations and correlate this with sensitivity we see:

Screenshot 2018-01-25 17.12.11

There is a significant correlation at the 5% level! Just to be clear, the values of psi here are not the same ones that Cox et al calculate, instead I’ve applied their formula to the model data from the control simulations in order to eliminate the effect of external forcing. So why does this work whereas the lag-1 autocorrelation is not useful?

Well the answer is found by checking the relationship between standard deviation (the numerator in their psi function) and sensitivity, and here it is:

Screenshot 2018-01-25 17.12.24

This is actually a much stronger correlation than the previous one, now significant at the 1% level. Of course we have no direct measure of the magnitude of internal variability of the real climate system, but this could be reasonably estimated by subtracting the forced response from the observations (by some combination of statistical and/or model-based calculation). So this relationship could in principle also be used as an emergent constraint (without prejudice as to its credibility).

In terms of the simple one-box climate model, the differing magnitudes of interannual variability across the ensemble could be due to the variation in (internally-generated) radiative imbalance on the interannual time scale, or the effective heat capacity of the thin layer that reacts on this time scale, or the radiative feedback lambda = 1/sensitivity. I suppose more detailed examination of model data might reveal which factor is most important here. I would be very surprised if people haven’t already looked into this in some detail, and don’t propose to do so myself at this point. Certainly many people have looked at variability on various space and time scales and tried to relate this to equilibrium sensitivity. Anyway, at this point I think I should call a halt and "reach out to" (don’t you hate that phrase) Andy Dessler and perhaps one or two others to ask if this strong correlation makes sense to them. I can’t help but think it would have been noticed previously if it’s actually robust (eg if it exists across CMIP3 as well as CMIP5). And if not, maybe it’s just luck.

Friday, January 26, 2018 More about Cox et al.

Time to move this discussion onto the BlueSkiesResearch blog as it is, after all, directly related to my work. Previous post here but I might copy that over here too.

Conversations about the Cox et al paper have continued on twitter and blogs. Firstly, Rasmus Benestad posted an article on RealClimate that I thought missed the mark rather badly. His main complaint seems to be that the simple model discussed by Cox et al doesn’t adequately describe the behaviour of the climate system over short and long time scales. Of course that’s well known but Cox et al explicitly acknowledge this and don’t actually use the simple model to directly diagnose the climate sensitivity. Rather, they use it as motivation for searching for a relationship between variability and sensitivity, and for diagnosing what functional form this relationship might take. Since a major criticism of the emergent constraint approach is that it risks data mining and p-hacking to generate relationships out of random noise, it’s clearly a good thing to have some theoretical basis for them, as jules and I have frequently mentioned in the context of our own paleoclimate research.

And more recently, Tapio Schneider has posted an article arguing that Cox et al underestimated their uncertainties. Unfortunately, he does this via an analysis of his own work that certainly does underestimate uncertainties, but which does not (I believe) accurately represent the Cox et al work. Here’s the Cox et al figure again, and below it another regression analysis of different data from Schneider’s blog.
Screenshot 2018-01-18 10.17.32
Screenshot 2018-01-25 10.45.40
It’s clear at a glance that the uncertainty bounds on the Cox et al regression basically include most of the models whereas the uncertainty bounds of Schneider exclude the vast majority of his (I’m talking about the black dashed lines in both plots). I think the simple error here is that Schneider is considering only the uncertainty on the regression line itself whereas Cox is considering the predictive uncertainty of the regression relationship. The theoretical basis for most of the emergent constraint work is that reality can be considered to be "like" one of the models in the sense of satisfying the regression relationship that the models exhibit, ie it follows on naturally from the statistically indistinguishable paradigm for ensemble interpretation (I don’t preclude the possibility that there may be other ways to justify it). The intuitive idea is that reality is just like another model for which we can observe the variable on the x-axis (albeit typically with some non-negligible uncertainty) and want to predict the corresponding variable on the y-axis. So the location of reality along the x-axis is constrained by our observations of the climate system, and it is likely to be a similar distance from the regression line as the models themselves are.

Schneider then compares his interpretation of the emergent constraint method with model weighting, this being a fairly standard Bayesian approach. We also did this in our LGM paper, though we did the regression method properly so the differences were less marked. I always meant to go back and explore the ideas underlying the two approaches in more detail, but I believe that the main practical difference is that the Bayesian weighting approach is using the models themselves as a prior whereas the regression is implicitly using a uniform prior on the unknown. The regression has the ability to extrapolate beyond the model range and also can be used more readily when there is a very small number of models, as is typically the case in paleo research.

Here’s our own example from the paper which attempts to use tropical temperature at the Last Glacial Maximum as a constraint on the equilibrium sensitivity.
Screenshot 2018-01-25 11.01.56
The models are the big blue dots (yes, only 7 of them, hence the large uncertainty in the regression). I used the random sampling (red dots) to generate the pdf for sensitivity, by first sampling from the pdf for tropical temperature and then for each dot sampling from the regression prediction. The broad scatter of the red dots is due to using t-distributions which I think is necessary due to the small number of models involved (eg even the uncertainty on the tropical temp constraint is a t-distribution as it was estimated by a leave-one-out cross validation process). But this is perhaps a bit of a fine detail on the overall picture. It is often not clear exactly how other authors have approached this and to be fair it probably matters less when considering modern constraints when data are generally more precise and ensemble sizes are rather larger.

We also did the Bayesian model weighting in this paper, but with only 7 models the result is a bit unsatisfactory. However the main reason we didn’t like it for that work is that by using the models as a prior, it already constrains the sensitivity substantially! Whereas if the observations of LGM cooling had been outside the model range, the regression would have been able to extrapolate as necessary.
Screenshot 2018-01-25 15.06.47
Here’s the weighting approach applied to the same question, with the blue dots marking the models, the green curve is the prior pdf (equal weighting on the models) and the thick red is the posterior which is the weighted sum of the thinner red curves. Each model has to be dressed up in a rather fat gaussian kernel (standard techniques exist to choose an appropriate width) to make an acceptably smooth shape. It’s different from the regression-based answer, but not radically so, and the difference can for the most part be attributed to the different prior.

Having said all that, I’m not uncritically a fan of the Cox et al work and result, a point that I’ll address in a subsequent post. But I thought I should point out that at least these two criticisms of Schneider and Benestad seem basically unfounded and unfair.