Something I have been bothered about for some time now, is how we best discuss climate change in the context of extreme events. Given the devastation from Hurricanes Harvey and Irma, damaging floods in South Asia and Nigeria, and the potential of more damage from Hurricane Jose, you’d think there would be a clear way to discuss the relationship to climate change that was also consistent with the scientific evidence.

However, there is clear pressure – from some – to avoid discussing the link to climate change because that supposedly politicises catastrophic events (FWIW, I think this argument is itself – rather ironically – political). There are also those (who I probably don’t need to name) who continually point out that the IPCC is clear that we cannot yet detect an anthropogenic climate change signal in many of these events. The problem, though, is that we have some prior knowledge as to how we expect climate change to influence these events and waiting until it is obvious that it has done so, before we take it seriously, seems rather unsatisfactory.

This has been a somewhat lengthy introduction to what I wanted to mention, which is one of James Annan’s posts in which he discusses a new paper by Michael Mann, Elisabeth Lloyd, and Naomi Oreskes called Assessing climate change impacts on extreme weather events: the case for an alternative (Bayesian) approach. Their argument is that rather than using a frequentist approach when trying to assess climate change impacts on extreme weather events, a Bayesian approach should be used.

I’m not an expert at Bayesian analysis, so I’m not going to try and explain it. Instead, I’ll try to explain what I think is wrong with the frequentist approach. This is partly based on a couple of James’s other posts. Essentially, the standard frequentist approach is to assume some kind of null hypothesis and to only reject this if you detect a statistically significant signal in your data. In the climate change context, the null hypothesis would normally be that there has been no change in some type of event. If you do detect some change, then one can try to attribute that to anthropogenic influences (i.e., detection and attribution).

In some sense, it’s a two-step process; detect some signal and then perform some kind of attribution analysis. If you do not detect any signal, then you do not reject the null hypothesis that there has been no change, and the process stops before any attempt at attribution. The problem, though, is that we know that our climate has changed due to anthropogenic influences and we can be pretty confident that this will have influenced, and will continue to influence, weather events. Therefore, the frequentist null hypothesis of *no change* is immediately wrong and the frequentist test will regularly return a result that is essentially incorrect (i.e., we will conclude that there has been no change even if we are pretty confident that there must have been some kind of change).

As you may have already noticed, though, the obvious other problem is that being confident that there must be some kind of change does not – itself – tell us anything about how it probably did change. Events could get stronger, or weaker. Events could become more, or less, frequent. Maybe they’ll move and start to occur more in regions where they were once rare.

However, in many cases we do have prior knowledge/understanding of how these events will probably change under anthropogenically-driven warming. There will probably be an increase in the frequency and intensity of heatwaves and extreme precipitation events. We expect an increase in the intensity and frequency of the strongest tropical cyclones, even though we might expect a decrease in the overall number of tropical cyclones. It seems, therefore, that we should really be updating our prior knowledge/understanding, rather than simply assuming that we can’t say anything until a statistically significant signal emerges from the data.

So, given that we are confident that anthropogenic climate change is happening and that this will almost certainly influence extreme weather, using a technique that will return *no change* until we eventually have enough data to detect changes, seems very unsatisfactory. That said, I don’t have a good sense of how to effectively, and properly, introduce a more Bayesian approach to discussing these events. If anyone has any suggestions, I’d be happy to hear them. Similarly, if anyone thinks I’m wrong, or am confused, about this, I’m also happy to hear that. I will add that this post was partly motived by Michael Tobis’s post which takes, I think, a slightly different line.

**Links:**

Assessing climate change impacts on extreme weather events: the case for an alternative (Bayesian) approach, by Mann, Lloyd and Oreskes.

More on Bayesian approaches to detection and attribution, by James Annan.

The inevitable failure of attribution, by James Annan.

Detection, attribution and estimation, by James Annan.

Neptune’s revenge, by Michael Tobis.

**Update:**

I had intended to highight this Realclimate post by Rasmus Benestad, which makes a related argument. Climate change has to impact the probability density function of weather events and, therefore, must impact the probability and intensity of those that are regarded as extreme.

I should probably have added that some people do seem to approach the discussion of extreme events in a way that both takes our prior knowledge into account and that is also careful about what we can actually say about individual events, so maybe some have already worked out how to do this. Maybe the key point is that we should – in my view – put more effort into approaching it that way and try to avoid making too strong statements based on a frequentist approach that may well regularly be leading us to draw conclusions that are probably wrong.

So at some point does a warming climate – or rate of warming – become the null hypothesis against which “change” is compared?

I don’t have the grounding to debate the relative merits of Bayesian or frequentist methodology but my instinct is always to look deeper into the physical processes themselves.

Ken,

I think that is one of the problems with the frequentist approach. Consider the so-called “pause”. This was often based on not being able to reject the null hypothesis that there had been no warming (i.e., 0K/decade). However, there is nothing special about this null, so one could have equally chosen a null of warming at 0.2K/decade, which we would also not have been able to reject.

Another issue is that there is no consensus in our understanding of the fundamental behaviors that drive extreme climate behavior — ENSO for temperature extremes and QBO for hurricane formation.

If we understood these perfectly we could discriminate their impact on extremes from the impact due to AGW. But since we don’t understand much at all we can’t do the attribution, and neither can we say how AGW impacts ENSO and QBO.

Repeat that for the other quasiperiodic processes like PDO, AMO, etc.

That’s why it will be a big deal for climate science when the underlying patterns for ENSO and QBO are solved and the driving mechanisms are determined for their behaviors. Then the impacts due to AGW can be more easily isolated.

Consider the case of ocean tides. This may sound ridiculous, but if we didn’t have a clear understanding of their origin, every time the seas start rising we might attribute that to global warming. And over the long term we wouldn’t be able to distinguish a trend from a cycle of unknown origin. But fortunately we do have a handle on tides and so can easily discriminate their contribution to sea level variations. HINT HINT

geo,

With all due respect, you’ve bombarded an earlier thread with your ENSO model comments. Maybe you could avoid doing so on this thread too.

There is an interesting exchange between Cliff Mass and one of his former graduate students, SharplyFocused, in the comments section of the Cliff Mass blog about Harvey and global warming.

JCH,

That is interesting. I tried to leave a comment on that post about the SST baseline (which may still appear) but have just seen that others have made the same point (using a 1981-2010 baseline is hardly a reasonable definition of “normal”).

Sounds like you are making excuses for thinking what you were already thinking. It’s always easy to fit anything and everything into any narrative IF it has already happened.you smart people are supposed to be able to tell us what is going to happen going forward. In 2013 there were no major hurricanes, all the smart people were predicting the worst year ever. Now you seem to be saying that you know it’s getting warmer but you don’t know if it will cause more or less of this or that,

[

Snip. Chill, dude. – Willard]Gm,

This is kind of the point I’m making. We do have good ideas of what will happen if we continue to pump CO

_{2}into the atmosphere and we should – in my view – be discussing this and should not feel obligated to avoid doing so until a signal has emerged from the noise.No, I didn’t say this. Try reading the

wholepost.[But ENSO. – Willard]I think the argument/discussion that makes the most sense is to compare global warming to loaded dice. If you go to a game of dice and lose everything and then found out that the dice were loaded, can you be certain that you would not have lost if the dice had been fair? No, a person can lose with standard dice, but the evidence is clear that a person will lose more if the dice are loaded. That is exactly the situation with global warming and extreme events. The risk of losing everything is amplified by global warming. It’s not a cause, it’s an enhancement, a change in background conditions that is likely to amplify destruction.

Geo,

One more time. Please don’t hijack this thread.

Climate Code Red has discussion about the climate factor in Syrian instability. Good read and fits with the discussion of climate factor with hurricanes and other extreme weather event. This piece talks about conflation of causality and contribution. http://www.climatecodered.org/2017/09/the-climate-factor-in-syrian-instability.html?utm_source=feedburner&utm_medium=email&utm_campaign=Feed%3A+ClimateCodeRed+%28climate+code+red%29

on the money imho

The below article has been repeatedly cited and linked to by more than one mainstream climate scientist who has been interviewed by the media about the climate change-hurricane* connection in recent articles about Hurricanes Harvey, Irma, Jose, and Katia.

Global Warming and Hurricanes: An Overview of Current Research Resultsposted on the website of NOAA’s Geophysical Fluids Dynamics Laboratory (GFDL). It was last revised on Aug 30, 2017.*North Atlantic basin only.

Anders –

Thanks for the post.

There are many reasons why the frequentist approach to null hypothesis testing is not only statistically unsound, but logically unsound. Interested readers can inspect:

* E. T. Jaynes,

Probability Theory: The Logic of Science, Cambridge University Press, 2003* D. V. Lindley,

Bayesian Statistics, A Review, 1970.Jaynes is very much a champion of the robustness of the Bayesian approach. Lindley, while Bayesian, is much more self-critical. It’s possible the 30 intervening years of experience would have changed his mind, but I’m not convinced that’s necessarily so.

The basic unsoundness comes from several problematic features. A big one is that, in the classical significance test formulation, the

p-value is a probabilityconditional upon assuming the null hypothesis is true. Most nulls are straw men, and are often outrageously simple. In fact, it’s possible to contrive matters so that the null is rejected assuming the null itself is true. That’s becausep-values themselves are random variables. So a rejection of a null might happen, or it might not: Repeatedt-tests between pairs of samples drawn from thesame theoretical Gaussian populationshows that the distribution ofp-values is nearly uniform on the unit interval.Cornfeld, in 1976, reviewing use of significance tests in medicine observed:

And Goodman wrote:

Repeated observations of this kind and the continuing practice of using significance tests led the

American Statistical Associationto recently state, in part:There are alternatives, ranging from the proposed Bayesian approaches to likelihood ratio tests … although the latter need to contend with paradoxes like

Stein’s, which has been known since 1955.In short, I opine Mann, Lloyd, and Oreskes are being unnecessarily kind. The problem is that Geophysics — and some Meteorology — have not woken up to the problems with approaching things this way, including the incredibly offensive idea — often and recently repeated as the following:

That’s from a peer-reviewed publication in

Nature.It’s also important to not fall into the trap of assuming other statistics like AIC or BIC can automatically replace

p-values. After a degree, they aren’t any better.The canonical Bayesian approach to these questions is well-illustrated by the paper,

N. M. Urban, P. B. Holden, N. R. Edwards, R. L. Sriver, K. Keller, “Historical and future learning about climate sensitivity”,

Geophysical Reserarch Letters,41, 2543–2552,doi:10.1002/2014GL059484, 2014.An example of a Bayesian critique of a frequentist studies is available in

N. M. Urban, K. Keller, “Complementary observational constraints on climate sensitivity”,

Geophysical Research Letters,36, L04708, doi:10.1029/2008GL036457, 2009.where the IPCC consensus on climate sensitvity from 2007 is the subject:

Urban and Keller’s Figure 2e is

sobering.veryATTP:

“…so one could have equally chosen a null of…”Using the classical t-test, the formulation is usually expressed as “observed – expected”, with “expected” being the null hypothesis. That raises two questions:

1. What did you expect?

2. Why did you expect it?

Too many blind statistical tests are carried out without really contemplating the implications of those two questions. I won’t go into detail on the people that present statistical results knowing full well that they have done an intentional bait-and-switch on what they claim the test shows and what they actually used as “expected”.

as I think abo8ut this more, this arises:

Since we can determine

1. the amount of ocean warming with some precision and

2. physics indicates that for every degree of ocean temp over the preindustrial ocean temp a hurricane can derive a certain amount of power

3. the energy load of a specific hurricane

can’t we do a pretty simple calculation to determine the percentage contribution of global warming to a specific hurricane over a certain time frame?

OP:

This is the position I’ve taken in online exchanges about Hurricane Harvey. Heavier rainstorms over Houston, and a higher proportion of hurricanes in the upper categories, are predicted consequences of AGW. Of course AGW didn’t ’cause’ Harvey, but warming at the surface of the Gulf of Mexico, and in the air column above SE Texas, made Harvey’s extreme rainfall more likely to occur. It can’t be that hard to understand (a hollow sound may be heard as Mal knocks on his head in lieu of wood).

aTTP comment:

This is in fact the null condition chosen for change point analysis of the alleged ‘pause’. Stefan Rahmstorf and Tamino discussed change-point analysis in depth a couple of years ago. They both showed that the hypothesis “the slope of dGMST/dt was lower during the eyeball interval of the ‘pause’ than during the previous longer interval” is not supported; that is, no change in the long-term warming rate is detected.

Main thing about the Bayesian approach is that you need to justify your prior. Climate model output could be used as a prior, although it is a bit questionable. Maybe use climate model output to justify a hyperprior? You could start with some sort of not very informative uniform prior, but I think Nic Lewis showed that such priors can strongly influence the conclusions. An alternative is to use some non-informative prior (Jeffery’s prior), but I think people complain that such a prior is unphysical. Maybe a Jeffery’s prior over only an interval that is physical?

“Consider the so-called “pause”. This was often based on not being able to reject the null hypothesis that there had been no warming (i.e., 0K/decade). However, there is nothing special about this null”

To be fair, shouldn’t some preference be given to simpler models? Isn’t that why things like the Akaike Information Criterion are used?

All else being equal, maybe, but I don’t think this necessarily applies if you have some reason to think that the simpler model is not as good a representation of reality as something more complex. People often talk about Occam’s Razor, and use it to suggest that a simple model is somehow better than a more complex one. However, Occam’s Razor is really just a general guideline that suggests that one shouldn’t make something more complicated than you need to, not a method for distinguishing between different models.

Bob,

Indeed, that are certainly plenty who naively (or, maybe, not naively) apply some kind of statistical test and then draw all sorts of strong conclusions without considering if the test they applied was actually appropriate.

ATTP:

There is also the tendency in some disciplines to do naive statistical testing starting with the premise that nothing is known. It’s “collect some data, throw it at a stats package, and see what kind of sausage comes out”. Arguments of “…but I already know that…” are met with “…but you need a random sample…” as if “random” is the only possible kind of sample design.

Not as bad as the people that intentionally use statistics to obfuscate their game of three-card Monte, though.

@-1,

Modern inference does not use a single prior. Generally priors are arranged in a hierarchy, connecting the scaffold of parameters which determine an outcome. Uninformative priors tend not to be terribly useful. See Kruschke’s [url=https://sites.google.com/site/doingbayesiandataanalysis/][i]Doing Bayesian Data Analysis[/i][/url], or any of the other modern Bayesian practice books, e.g., by Congdon.

@-1,

(Oh well: Wrong syntax)

@-1,

Modern inference does not use a single prior. Generally priors are arranged in a hierarchy, connecting the scaffold of parameters which determine an outcome. Uninformative priors tend not to be terribly useful. See Kruschke’s

]Doing Bayesian Data Analysis, or any of the other modern Bayesian practice books, e.g., by Congdon.@-1,

(Here’s hoping I can type this time)

— S. N. Wood,

Generalized Additive Models, 2nd edition, 2017.See also, Gelman, Hwang, Vehtari, “Understanding predictive information criteria for Bayesian models”, 2013.

Best of all, from Penny’s 2015 short course on

Bayesian Model Selection and Averaging, based upon Bayesian model probabilities andnegative free energyas an approximation to thelog model evidence. See also Skilling’s work on model evidence and a review of the same.@ATTP,

On Occam’s, yeah, but there should be some

quantitativeway of doing the tradeoff. Despite the limitations of AIC, BIC, WAIC, DIC, and the like at least they have a way of trading off increased model complexity against improvement in likelihood. Still, it’s possible to overfit, even with IC-type methods. That’s another reason Bayes issovaluable.You can do all this with generalized cross validation and specific forms of the bootstrap, although these are expensive evaluation methods. What really wants to be evaluated is out-of-sample performance, just like every other field.

Here are some better references than what I gave above, particular to geophysics:

* Berliner, Cressie, Tutorial on Bayesian Statistics for Geophysicists

* Berliner, Milliff, Wikle, “Bayesian hierarchical modeling of air-sea interaction”

* Campbell, “Introduction to physical-statistical modelling using Bayesian methods”, 2004

On a different question I had success using just the Bayes factor, no priors, plus AIC for model complexity.

It is also important what you do with the result that something is statistically significant or not. Many treat it as answering the question whether something is true or not. I would argue to use it in to indicate whether there is something worthwhile to study. (In medicine you may not have the luxury to wait and need to use the result for a provisional assessment.)

If something is statistically significant that is a green light for further research. Especially if the significance level is low (the effect is unlikely to be due to chance under the null hypothesis) and the number of ways the data could be analyzed is limited. In the end it is the understanding from the further research that is important.

If it is not significant, I would say that is a yellow light. There may well still be something there and especially if you have physical reasons to expect a relationship, you may still want to continue and do further research. Or if the consequences would be large that would be a reason to continue research anyway.

I had no problem with people studying reasons for the “hiatus” for example even if the right statistical test (for a trend break at an unknown position) showed no statistically significant change in the trend. But if you have a reason (El Nino, coverage bias, volcanoes) why not study it. If you do not have a reason: you are free to use your limited time on Earth on anything.

(And, yes, in case of the “hiatus” the null hypothesis of continued warming would have been more appropriate given our understanding of the climate system.)

@VV,

Regarding,

As indicated previously, I have severe problems with the notion of

significance. Something which arises in medicine and engineering which, for whatever reason, seems passed over in other sciences, is use of aneffect sizeas a criterion for whether or not a finding is important. This is related tostatistical power, at least in frequentist work. While specify effect size and doing power analysis seems completely and logically necessary in hypothesis testing approaches, in practice, there are problems doing this. Without sufficient power, a statistical experiment might return a significant result and yet be meaningless. Ironically, it seems apost hocBayesian analysis can sometimes rescue frequentist experiments done without regard to effect size. (I think this might be applicable to cross-validation used in machine learning work, but I haven’t done the calculations to see.)This article describes how to do something like hypothesis testing from a purely Bayesian perspective. Kruschke discusses effect sizes further here.

However they are set up, having an idea what the minimize such of an effect should be in order to be important seems critical for any experiment. How would you ever otherwise know what sample size to take, or how to design the experiment?

There are no conventional conservation laws in statistics (e. g. mass energy momentum). All this BS about statistical methods is just that, BS. All statistical methods are wrong, none are useful (unless they include real physical laws).

Note to self: Where I worked, we had this debate like 30 years ago. Go hard or go home.

@EFSargent,

Okay. So, then, how does one establish that there is such a thing as a Higgs boson?

Okay. So, then, how does one establish that there is such a thing as a Higgs boson?

It’s defined as five sigma above the background noise, but I use To Infinity and Beyond, because one can never be too certain.

https://blogs.scientificamerican.com/observations/five-sigmawhats-that/

CERN physicists are just another bunch of Frequentists! Boo, CERN, Boooooo! Boo CERN.

I’m not booing your opinion, I’m booing your report topic. No one even knows what a frequentist is. Boo, booben, boo.

A Bayesian would stop counting after the first Higgs boson!

ATTP,

You missed a link. It’s in the POS paper by Mann, et. al. (IMHO anything with Oreskes name on it is, by definition, a biased POS) …

Is the choice of statistical paradigm critical in extreme event attribution studies?

https://link.springer.com/article/10.1007%2Fs10584-017-2049-2

https://link.springer.com/content/pdf/10.1007%2Fs10584-017-2049-2.pdf

“We have three points to make about the choice of statistical paradigm for event attribution studies. First, different approaches to event attribution may choose to occupy different places on the conditioning spectrum. Providing this choice of conditioning is communicated clearly, the value of such choices depends ultimately on their utility to the user concerned. Second, event attribution is an estimation problem for which either frequentist or Bayesian paradigms can be used. Third, for hypothesis testing, the choice of null hypothesis is context specific. Thus, the null hypothesis of human influence is not inherently a preferable alternative to the usual null hypothesis of no human influence.”

We now return you to your regular scheduled programming. 😉

Who wrote this?

“Given, for example, that the rate of record-breaking warmth has doubled (i.e., exhibited a 100% increase) over the past half century (Meehl et al. 2007), our use of a 20 and even 50% increase is, at least for some extreme weather phenomena, conservative.”

Meehl et al. 2007 is here …

Contributions of natural and anthropogenic forcing to changes in temperature extremes over the United States

https://pdfs.semanticscholar.org/7e2a/deb62b7da170e641ccdfcbb373dd37429985.pdf

Everything in the Meehl paper is baselined to ZERO means! Getting out my four function calculator and … wait for it … any change divided by ZERO = infinity!

From Meehl …

“An 1890 – 1919 mean is not available for the observations, so they are instead centered on the 1960– 1999 mean of the anthropogenic runs from the models, the models are interpolated to the HadEX grid and only grid points with valid observations are used … (see Figure 2).

I need some help. Can anyone find a “so called” 100% increase in the Meehl paper? Other than the trivial one frost day per year is now zero frost days per year (e. g. a 100% decrease in frost days per year. D’oh!). Meehl is, more or less, a CMIP3 modelling paper.

hypergeometric, yes I should also have mentioned statistical power and the size of the physical effect as considerations whether one would pursue further research.

Not quite sure if you’re joking, or not, but – FWIW – I am an author of one paper with Naomi Oreskes.

Namesake is a treatise on applying stochastic math models to energy-related geosciences. Some characteristics, such as distribution of wind speeds collected at wind farms, follow concise statistical distributions. Other behaviors are essentially singletons and are described by a single deterministic mechanism, such as the standing waves of ENSO and QBO. The key is to identify what is stochastic and what is deterministic.

Side with Everett, lol, but I would phrase it that we are more dependent on statistical mechanics (physics) than on generic statistics. Agree with Jan that everyone should read Jaynes book on probability (The Logic of Science)

“

The key is to identify what is stochastic and what is deterministic.”Turbulence is deterministic, but a stochastic description is often more useful.

One persons noise is another persons signal.

The operation of a transistor is also deterministic, but the description is completely stochastic, as it requires statistical mechanics to make any sense of it, i.e. Fermi-Dirac, Fokker-Planck equation, etc. Computers therefore operate essentially on controlled noise.

This is a chart I did on wind speed distribution, which uses a novel Boltzmann derivation and Jaynes’ idea of MaxEntropy. About 2.5 million data points collected at 5 minute intervals at all the sites BPA in Oregon

The effects of turbulence will allow all states to fill the state space according to their energy levels. That’s statistical mechanics applied on a macro scale.

Courses on renewable energy use the probability distributions to explain what kind of power they should expect in a statistical sense.

@VV,

Moreover, structured sampling is sometimes better than random sampling, even unequal probability random sampling. Depends.

EFF:

FWIW, she’s third author ;^).

Everett, your penchant for humorous hyperbole is known (and often appreciated 8^D), thus your judgement of Oreskes may be have been intentionally histrionic; but I doubt you’ll get any argument from Russell Seitz,

inter alia.The question is always “How do you know X is biased?” You might answer “I’m not the only one who thinks X is biased!”, begging the question “How do you know X’s other critics aren’t biased?” AFAICT, the climate-science types who’re criticizing Bayesian climate statistics so far are biased either against one or more of MLO’s authors, or against “catastrophic” AGW.

I think you see where I’m going with this. I’m not an expert in climate statistics, but if a consensus of actual experts emerges that MLOClimateChange17 is a POS after a few rounds of post-publication peer review, I expect to hear of it eventually. For now, IMHO a Bayesian approach seems intuitively superior to the conventional frequentist one, because it’s more explicitly aware of anthropogenic climate change as a dynamic process with well-quantified forcing.

I mentioned somewhere above that there was a connection between hurricanes and the QBO cycle. At one time the renowned hurricane expert and crazy AGW denier William Gray asserted that frequency of hurricanes were statistically linked to the QBO cycle, but I looked at a Wikipedia chart of hurricane activity per year and I see no obvious correlations. Gray had a hurricane predictor that gave correlations above 0.8, but according to citations of his work, this algorithm stopped working after more recent data became available. It’s still the #1 citation but that’s because people citing it are simply pointing out that it’s wrong.

Bayes update required here. Sorry.

MA,

I was kind of rushed. So I’ll backpedal on the POS part.

The most prescient part of the reply paper I linked to?

“Providing this choice of conditioning is communicated clearly, the value of such choices depends ultimately on their utility to the user concerned.”

MLO17, IMHO is not communicated clearly. The above sentence also grossly and strongly hints at circular reasoning or a tautology or begging the question.

The reply authors are playing nice though as would be normally expected.

The bounded at both ends binary distro (0-1) has no immediate utility (AFAIK) to the more complex problem of objectively defining (or binning) extreme events as a function of time.

In fact, MLO17 suggests that as p approaches 0.5 neither method will converge to the correct solution quickly. The Bayesian approach has to lead to ambiguities as its PDF will contain the p = 0.5 solution, leading to false positives for reasonably small N (say N = 100 as they do in their paper). This I find very alarming. Their hypothesis is to assume that the coin is biased (implicitly by setting p above 0.5)!

And IMHO that’s the current state space we all are in at the moment, to date, there is no consensus on a single objective method to clearly define extreme event selection as a function of time.

Picking p = 0.6 (20% increase) or p = 0.75 (50% increase) on the 0-1 doubly bounded state space IMHO has very low utility.

MLO17 even states Meehl as 100% increase (BTW, still looking for that one, the “so called” 100% increase in extreme events, that one, a 100% increase would be front page headlines all over the world and I’m NOT being hyperbolic on that one) so why didn’t MLO17 use 100% increase or 200% increase (on or outside the predefined upper bound)? Rhetorical question, don’t answer.

@geoenergymath,

Very cool.