# Uncritical Mass

Cliff Mass is at it again, trying to tell us that the recent extreme heat in the northwest is unrelated to man-made global warming. What’s surprising is that he actually had this to say in a recent blog post:

the more extreme the weather anomaly, the less likely it is to be caused by human-induced (anthropogenic) global warming.

The truth is exactly the opposite.

I have an idea where Cliff Mass might have gotten his wrong idea. Suppose the phenomenon is governed by the normal probability distribution, and that we choose our scale so that the mean is zero and the standard deviation is 1. Let’s say that we limit “extreme” to values which are at least two standard deviations above the historical mean.

Then we can consider what happens when we increase the mean, say, by 1 standard deviation. We won’t change the cutoff limit of “extreme,” we’ll just change the probability of its occurence. Here’s the probability of occurence for extremes from 2 to 6 standard deviations, for the unchanged mean (in blue) and after the mean increases (in red):

Increasing the mean makes all extremes more likely. But, as expected, as the extreme gets more and more extreme it gets less and less likely.

The relevant question is, when we increase the mean, by how much does the probability increase? Perhaps Cliff Mass is considering the difference in probability, i.e. the probability after increasing the mean, minus the probability before. Here’s a graph:

The more extreme the extreme, the less is the absolute increase in probability.

But that’s not what counts. What matters is the ratio of the probabilities, i.e. the probability after increasing the mean divided by the probability before:

Increasing the mean by 1 standard deviation will makes a 2-sigma extreme 7 times as likely. But it makes a 3-sigma extreme 17 times as likely, a 4-sigma extreme 43 times as likely, a 5-sigma extreme 110 times as likely, and a 6-sigma extreme 290 times as likely.

The truth is, that the more extreme the weather anomaly, the more likely it is to be caused by human-induced (anthropogenic) global warming.

But perhaps Cliff Mass suffers from another misconception. Maybe he’s so intent on denying the link between global warming and extremes that he limits himself to the narrowest possible definition of “caused by.” Maybe he actually believes that extreme heat cannot possibly be caused by global warming because we get our energy from the sun — so all extreme heat events are “caused” by solar radiation.

That seems like claiming that all lung cancer is “caused” by genetic defects of lung cells, so no lung cancer is “caused” by cigarette smoking.

I prefer a more relevant definition: that without man-made global warming it wouldn’t have happened. Clearly, without man-made global warming the majority of extreme heat events, and the vast majority of “extreme extreme” heat events, wouldn’t have happened.

### 47 responses to “Uncritical Mass”

1. Taleb pointed out that

In thin-tailed domains, an increase in uncertainty changes the probability of ruin by several orders of magnitude, but the effect remains small: from say 10−40 to 10−30
is not quite worrisome. In fat-tailed domains, the effect is sizeable as we start with a substantially higher probability of ruin (which is typically underestimated).

When you are close to the mean (1-2 sigma), you are by definition in the fat part of the tail. at 5-6 sigma you are in the thin part of the tail and the ratio is not so important. It never happens in the lifetime of the universe (OK, in the last zillion years or so), so it would be good to weight the ratio by the probability

2. kinimod

Just for clarification: Does that mean, that e.g. any 3-sigma-event, in the presence of a mean drift of 1 standard deviation, can be attributed to that drift with a share of 16/17?

[Response: If the phenomenon follows the normal distribution, 3-sigma events become 17 times as common. So essentially, yes.]

3. A corollary to Cliff’s sweeping bolded statement– suppose we retain some fixed climatology (e.g., 1951-80) and remain in the fixed distribution limit at your favorite geographic location, such that the probability of exceeding some (positive) threshold temperature anomaly increases. Then, according to Cliff’s argument, less and less anomalous events are being “caused” by the changing climate…

4. icarus62

“the more extreme the weather anomaly, the less likely it is to be caused by human-induced (anthropogenic) global warming.”

What he apparently means is this:

Suppose we have increased the mean surface temperature in a particular location by 1°C. If a particular spell of weather in that location is 1°C warmer than the climatological mean (before AGW), then we can attribute 100% of that ‘extra’ warmth to AGW.

However, if a particular spell of weather is 4°C warmer than the climatological mean (before AGW), then we can only attribute 25% of that ‘extra’ warmth to AGW. His reasoning is that we can’t possibly have caused more ‘extra’ warmth than the 1°C of AGW, so the greater the severity of the heatwave, the less we can possibly have contributed to its severity.

His argument seems… well, not so much wrong as “not even wrong”. Any climate change is by definition a change in long term statistics, rather than being a property of individual weather events. It’s meaningless to talk about how much of a particular heatwave is ‘due to AGW’ and how much is ‘natural’. We can only say that (for example) in a 1°C warmer world, we can now expect to see temperatures of 35°C in the UK on average every 5 years instead of every 50 years before AGW, or something like that. It’s valid to say that a particular severity of heatwave is now 10 times more frequent than before AGW, but we can’t attribute the likelihood or the severity of a particular heatwave to AGW, as that would be nonsensical.

• Horatio Algeranon

That’s also how I interpret Mass’ statement. It’s very much in keeping with his original logic on the subject which was that because human caused global warming was only a small fraction of the temperature swing for heat waves, it could not have made much difference.

But, from my understanding, it’s not necessarily nonsensical to “attribute the likelihood or the severity of a particular heatwave to AGW”

See “Russian heat Wave statistically linked to Climate Change” for example.

“With climate change, it’s going to happen five times more often than without,” said climatologist Stefan Rahmstorf of Germany’s Potsdam Institute for Climate Impact Research.

After running the simulation 100,000 times, “we could see how many times we got an extreme temperature like the one in 2010,” said Rahsmtorf.

“For every five new records observed in the last few years, one would happen without climate change. An additional four happen with climate change,” said Rahmstorf. “There’s an 80 percent probability” that climate change produced the Russian heat wave.

• Only works if the distribution is linear.

5. Joseph Ratliff

Sorry Tamino, based on what I have read on Cliff’s blog (the post you are referencing), he has explained his position in a way that seems more “correctly applied” to our specific anomaly here in WA.

This is the specific comment written by Professor Mass that “tipped” my opinion of this recent event towards what Cliff was offering as an explanation of this “heat wave” (bolding and italics, if it is allowed, is mine)…

“I will tell you precisely what is wrong. You are thinking about frequency and not magnitude. If you assume a gaussian distribution (PDF), consider a specific threshold, and then shift the mean of the distribution, you will get much higher frequency of events exceeding that threshold, particularly if it on the extreme end. No doubt about it. But that is really not the issue. The issue is how MUCH of a specific extreme event is caused by human emissions. That is an entirely different question…that is the one I am dealing with. And the truth is that very little of the current event is caused by additional greenhouse gases…it was almost entirely natural. So PLEASE think about magnitude and not frequency above a threshold and you will understand what I am trying to say…cliff”

The rest of his comments provided by Professor Mass are actually quite instructive. Also, one of the other commentators included the link to a Nature paper that seems to show more agreement between Tamino and Professor Mass than indicated in Tamino’s blog post here.

Interesting discussion indeed.

• I was the other commentator. For convenience, I’ll include here the same quote from the Nature Climate Change “News and Views” article:

The study of Fischer and Knutti does not directly address the attribution question asked by individuals facing the brunt of a specific damaging storm or heatwave. While the authors do provide maps of how probabilities of extreme temperatures and precipitation have changed across the globe, the framework they use means that such probabilities cannot be applied to specific individual extreme weather events. The effects of natural and human-induced climate change can vary from place to place and from year to year, increasing or decreasing the FAR [“fraction of attributable risk”] relative to the averaged global numbers calculated in this study. Further work is therefore needed to refine regional estimates and to unpick the effects of anthropogenic influences on climate from natural influences, such as changes in solar output and internal variations in the climate system (the El Niño/Southern Oscillation, for example).

Mass seems to be saying that the FAR for this summer’s PNW heat wave is low relative to global probability of extreme temperature.

• Horatio Algeranon

Risk is based on the “consequences” of the extreme event (related to the magnitude of the temp change in this case) times the probability of occurrence.

Considering one without the other makes no sense.

• jgnfld

If I am to parse what Mr. Ratliff is quoting, the “magnitude” of any couple of degree temperature rise directly attributable to the additional CO2 we put into the air is, in fact, small relative to the entirety of 33C that makes the Earth inhabitable. That is hardly the important issue, however, but rather a really disinformational sophistry.

• Joseph-

The problem is that the climate change signal (the mean) that we’re talking about will never be larger than the local synoptic variability leading to a modern NW anomaly like those being discussed.

Even if you go back in time over 50 million years ago to an Eocene hothouse climate, you’d have to say something like “well, it’s only 5 degrees C warming, maybe half as large as natural variability, so it didn’t cause the heatwave.” In any case, if we follow this reasoning, what is the threshold for “caused.” What if global warming were 15 degrees C and everything was going extinct, and there was some anomalous ridge pattern over the Pacific Northwest leading to anomalies of 5 degrees C. Do we, then say, that global warming “caused that ridging pattern? That doesn’t really make sense either.

Cliff is obviously right, that to first order global warming isn’t changing synoptic meteorology (putting aside issues about how wave dynamics, etc might be modified under external forcing. There are ideas out there but not particularly robust). But his framing makes little sense to me if the metric is always magnitude of unforced synoptic variation on an event-by-event basis relative to the global (or local) mean temperature anomaly.

6. jgnfld

Well here in Newfoundland it was 47.3F on Mon. A bit colder than Alert Nunavut I might add. I think that totally disproves global warming right there, does it not?

7. “the more extreme the weather anomaly, the less likely it is to be caused by human-induced (anthropogenic) global warming.”

Dumbmass.

8. Tamino:

Maybe he’s so intent on denying the link between global warming and extremes that he limits himself to the narrowest possible definition of “caused by.”

When I suggested that to him, he doubled down:

…magnitude counts. This event is MUCH larger than the shift of the probability distribution. To put it another way, the 1-degree shift of the probability distribution does not explain a 10-20F anomaly. Yes, perhaps a degree of it is associated with human-induced global warming. But with or without increasing greenhouse gases there would have been a huge heat wave.

• It seems like arguing about just the mean is a way to avoid arguing about state change- i.e. blocking events.

9. If any effect on frequency of events is discounted as suggested by Cliff Mass, so that any extreme weather event is treated as a unique and isolated circumstance then within that constrained atemporal scenario there is a certain logic to ascribing no more than the rise in the long term mean to the magnitude of an extreme event.

In that context a heatwave with a 20F anomaly would have been a heatwave with a 19F anomaly if climate change has changed the local mean by 1F.

But that is perhaps unintentionally discarding the real impact the change in frequency can have on the magnitude of the anomaly experienced.
If the 20F anomaly is a 3 sigma event then it is 17 times more likely to occur. That increase in incidence holds for 19F and lower extremes down to the 2sigma level. The impact of a 1F increase in the mean has increased the chance of extreme anomalies by much more than just a magnitude of 1F.

If an area experiences a 20F heatwave instead of a 10F heatwave, the chances are that climate change is responsible for at least half that extra 10F BECAUSE of the frequency effect.

If the change in mean and distribution makes a very large extreme weather event twice as likely, then when it does happen it is 50% caused by the warming climate, not just the amount of shift in the mean.

• Magma

If the 20F anomaly is a 3 sigma event then it is 17 times more likely to occur. That increase in incidence holds for 19F and lower extremes down to the 2sigma level.

No, because in your scenario 1 sigma is 6.67°F, so the difference between the 19°F and 20°F anomalies is that between a 2.85 sigma and a 3 sigma event. By my calculation, a CDF of 0.00219 vs. 0.00135, or ~1.6x more likely. (All assuming a Gaussian distribution.)

10. Tamino,
You really are not understanding what I am trying to say, but before I comment on that, let me note that your snarky, ad hominem tone is inappropriate and non-professional. You may not agree with me, but some civility would be appreciated.

My points are really quite simple, but based on your comments, frequently misunderstood. OF COURSE, the frequency of heat waves increase under global warming. I totally agree with that. But step back for a second and think about physical contributions, of magnitudes, and not frequency. For most locations, the more severe the event, the greater the percentage of the anomaly is due to natural variability and not the global signal. Here in the NW the long-term warming over the region is about 1F during the past 60-70 years. The temperature anomaly has been 15-20F over most of the region. Yes, global warming is contributing to the heat wave, but it is a minor contribution. We would have had a heat wave with our without global warming. And don’t start arguing about non-linearities. I know about that..I have written papers in the peered review literature about it. That is not what is going on here.
The other thing you don’t seem to know about is the literature explaining what IS happening. We have a very perturbed long wave pattern. There is no reason to expect that is caused by global warming. In fact, the causality of the pattern has been explained by the North Pacific Mod and its connecting with a SST anomaly in subtropics. And the east coast is way cooler than normal as a result.
Anyway, my profession has a lot of work to explain to the lay audience, such as yourself, about natural variability and the causal links that cause major anomalies like this.

…cliff mass, university of washington

• Cliff,
Let me see if I understand what you’re trying to say. You seem to agree that AGW will increase the likelihood of extreme heatwaves. However, what you seem to be suggesting is that the more extreme an event, the bigger the natural variability contribution to that event. Is that about right?

Firstly, I would argue that we can’t actually do what you seem to trying to do. We can’t attribute a natural and anthropogenic component to an individual event. What we can do is consider whether the likelihood/probably of certain events has changed due to anthropogenic influences.

Secondly, it seems to be a bizarre argument. Taken to the extreme, if we increase anthropogenic forcings to the point where we have many more extreme heatwaves in a particular region, you would seem to be arguing that the biggest contribution to those heatwaves is natural variability, rather than the underlying long-term anthropogenic trend. So what? That extreme events are a consequence of variability about some mean, doesn’t change that the reason more such events are happening is a consequence of the increased anthropogenic influence.

In a sense you seem to be addressing a completely different question to what most people think you’re addressing. The relevant question – IMO – is how does AGW change the likelihood/probability of extreme events, not what fraction of an extreme event can be attributed to AGW.

• Horatio Algeranon

“Here in the NW the long-term warming over the region is about 1F during the past 60-70 years. The temperature anomaly has been 15-20F over most of the region. Yes, global warming is contributing to the heat wave, but it is a minor contribution. We would have had a heat wave with our without global warming.”

Tell that to the people at Munich-RE.

In the context of risk (which is the important thing) you must take into account both the magnitude and the probability of the extreme event (and in the particular case of climate change how that probability has increased)

When that probability (in this case of a heat wave) increases substantially due to even a relatively small change in mean temperature, it has a large impact on the expected cost.

The implication that only a small fraction of the extreme anomaly is due to climate change and therefore the “contribution” of the latter to the heat wave is minor is misguided.

• Horatio Algeranon

After saying
“The more extreme the weather anomaly, the less likely it is to be caused by human-induced (anthropogenic) global warming”

which is about (can you guess?) “probability”, Mass encourages us to

“think about physical contributions, of magnitudes, and not frequency.”

• Martin Smith

Cliff, Isn’t some of the magnitude of the WA heatwave due to its duration? And isn’t the duration due to the stability of the bunched up jet stream, which is dues to the reduction in the temperature difference between the Arctic air and the air at the lower latitudes, which is due to the reduction in Arctic sea ice?

• Jim Eager

In addition to the possibility (increasing in probability based on the most recent research) that the perturbed long wave pattern may itself be at least partly caused by AGW, as Martin noted, given that ~70% of earth’s radiative energy imbalance is absorbed by the ocean surface layer then AGW is also responsible for some part of the SST anomaly in the subtropics as well. The new reality is now that we have changed the composition of the atmosphere, and thus altered earth’s radiative balance, we have also changed earth’s climate regime, meaning there is no longer any purely “natural” variation. There is now an AGW fingerprint of some lesser or greater size in every weather event.

• Cliff Mass writes:

Here in the NW the long-term warming over the region is about 1F during the past 60-70 years. The temperature anomaly has been 15-20F over most of the region. Yes, global warming is contributing to the heat wave, but it is a minor contribution. We would have had a heat wave with our without global warming.

…. and later states:

We have a very perturbed long wave pattern. There is no reason to expect that is caused by global warming. In fact, the causality of the pattern has been explained by the North Pacific Mod and its connecting with a SST anomaly in subtropics. And the east coast is way cooler than normal as a result.

Wouldn’t the extremity of sea surface temperature anomalies have something to do with man-made global warming? Kevin Trenberth would seem to think so. Would you give the same sort of explanation for the California drought? The evidence argues against this, pointing not to the El Niño Southern Oscillation or Pacific Decadal Oscillation:

Why did this “anomalous” ridge become both so persistent and so robust? While the winter climate in the West Coast is known to respond to the El Niño–Southern Oscillation (ENSO), and the Pacific Decadal Oscillation (PDO) [Cayan et al., 1999; Dettinger et al., 1998; McCabe and Dettinger, 1999], the winter circulation anomalies did not correspond with either of these oscillations, as ENSO was in a near-neutral state and the PDO was not strong in either phase.

Open Access: Wang, S‐Y., et al. Probable causes of the abnormal ridge accompanying the 2013–2014 California drought: ENSO precursor and anthropogenic warming footprint. Geophysical Research Letters 41.9 (2014): 3220-3226.

… or even the North Pacific Oscillation, but to a recently identified dipole:

… a distinct, east-west circulation “dipole” comprising an abnormal ridge over the Gulf of Alaska and a deepened trough centered north of the Great Lakes. Hereafter this circulation feature will be referred to as “the dipole.” …. The dipole index and associated circulation pattern were compared to an empirical orthogonal function (EOF) of Z250, shown in the supporting information Figure S1. It appears that the dipole index corresponds (r > 0.6) to EOF2, while EOF1 and 3 correspond respectively to the PDO and the North Pacific Oscillation (NPO)…. we did not find any of the climate modes that correlate significantly (p < 0.05) with either the dipole index or EOF2….

ibid.

Given the unusual severity of the drought, the study asks whether there might be any relation to recent man-made global warming, beginning with whether the dipole has become more pronounced in recent years. They find the dipole has become more pronounced:

The record-breaking quality of the extreme drought and the dipole in 2013–2014 brings up the role of human influence on climate. For this reason, we examined further whether the dipole has been more active in recent years. Figure 4a shows the running variance of the dipole index over a 30 year window, using the 20CR data. The results reveal an increase in the variance during the 1940–1960 period followed by a decrease in the 1970s, accompanied later by an amplification after 2000; this result was robust regardless of which reanalysis was used.

… and that the increasing strength of the dipole bears the human fingerprint:

The CESM1 single-forcing simulations were subject to the same variance analysis. It is interesting to note that the CESM1-GHG run simulated a persistent increase in the dipole’s variance whereas the CESM1-NAT run produced a decrease after 1970. Such a feature is in concert with recent findings that atmospheric waves in the middle to high latitudes have amplified leading to increased extreme events [Screen and Simmonds, 2013; Wang et al., 2013a]. What is more, Figure 4a further suggests that GHG did play a role in the amplification of the dipole.

As suggested by their citations, numerous studies are finding increased amplitude in Rossby waves that likewise appear to bear that fingerprint.
Cliff Mass writes:

And don’t start arguing about non-linearities.

Don’t bring up feedbacks when discussing weather or the climate system? Wouldn’t dream of it!

Cliff Mass writes:

That is not what is going on here.

There is a growing body of literature that suggests otherwise.

• Alliecat

Polite nonsense is still nonsense.

If, to first order, the probability of the event was zero without GW, then *all* of the impacts are attributable to GW. I think most people could understand that.

More generally, if the event was much more likely to occur due to GW, then most of the impact is reasonably attributable to GW. (Imagine if the probability of the event went from 1% to 10% due to warming – a reasonable approach would be say 10/11 of the impact is attributable to the warming.)

In other words, despite Cliff’s protestations, the relative probabilties matter in assigning “blame” to GW.

• Nick A

It seems like everybody accepts that the frequency of extreme heat events will increase significantly with a relatively small increase in mean temperature. So, if we are to accept that the contribution of glogal warming to any single event is only equal to the (average) temperature increase due to global warming and that as this is only a tiny fraction of the total temperature anomaly during the event (which would therefore have been an extreme event anyway), where does the increase in frequency of extreme events come from?

11. Andre

In the book “Six Sources of Collapse” there is a discussion of the probability of extreme events and the need to be careful of fat tails. He also mentions the use of the Generalized Extreme Value theorem and how the extreme value index can be useful in understanding the tails. Is the data being discussed amenable to this type of analysis?

12. Gavin

Cliff, Your reasoning here is fallacious. Your claim is that the GW contribution to anomaly is equal to the local GW trend in the region, and therefore the bigger the anomaly the smaller the % contribution. But think about this more carefully and you should realise that the ‘% contribution’ is very poorly defined. Specifically, what is the baseline from which the anomaly is defined? Start with the monthly climatology, that will give a particular number – perhaps 20ºC. But what about the daily climatology, that will give another (maybe 18ºC – I’m just making these up for the sake of argument so feel free to do the calculation and let me know). And if we condition the event on the phase on ENSO? (maybe 15ºC) Or the SST pattern in the North Pacific? (maybe 10ºC) And what if we additionally condition it on the phase of the Rossby wave? (maybe 5ºC) Or the the phase and amplitude of the wave? (maybe 2ºC)…. etc.

As you get closer and closer to conditioning your baseline to the analogous weather pattern/season/large scale environment, the magnitude of the anomaly will decrease, and the ‘contribution’ of GW will increase. And for truly ‘novel’ warm extremes, it will become clear that the conditional anomaly will be almost entirely GW. It should therefore be clear that your framework gives a totally arbitrary ‘% contribution to GW’ and isn’t much good for anything, except perhaps in the final limit, where it will give something similar to the approach based on return times or excedences.

Thus there is a really good reason why looking at odds ratios or return times is a better way of doing fractional attribution. They do not depend on an arbitrary baseline! They also has the advantage of being much more useful in terms of assessing impacts (which even you will admit are a non-linear function of the extremes).

13. Susan Anderson

Taking this down to layperson sloppy language, let me see if I get this straight.

The more serious the change in climate, the less likely it is mostly due to the change in climate …

Thanks, I’ll take reality, thank you.

Meanwhile, the artful encouragement of apathetic laziness on behalf of the entire global population in the face of extreme risk is imnsho immoral and dangerous.

• Susan Anderson

Tamino is knowledgeable and I mostly have to infer, but the redaction of what I wrote does make it look odd. I hope it will be acceptable to try removing “climate”, restate, and see how that works:

The more serious the change … the less likely it is due to the {words removed about the probable cause of that} change.

I’m sinning above my station on these boards, but when I took another look it seemed to be confusedly tautological. If I have it wrong, I would appreciate any hints on offer.

Horatio, it is so fine to see you back.

14. Horatio Algeranon

Not only is global warming responsible for just 1 degree out of 20 in the NW heat wave (according to Massean Logic), it is also only responsible for just the very first (least impacting) degree above the norm

So, just relax. Kick back by the pool and sip an ice cold glass of lemonade (climate lemonadagation)

• Horatio Algeranon

….because without the very first degree deviation from the norm, we would never get to a second degree…and a third..and a 15th …and so forth.

So maybe the first is actually the most important of all.

As Highsick Heatwave once said, “If I have reached higher degrees, it is by standing on the shoulders of the Global E. Warming”

15. Philippe Chantreau

I’m really not very learned on this subject, nor the statistics of it, so have mostly questions, hope some will help me out. I’m assuming that there is a history of previous heat waves that allows to establish what natural variability used to be. Is this one really far out of those previous bounds? If that is the case, am I to interpret Mr. Mass’ explanation as showing that we now have an event that essentially redefines natural variability? If no previous event is comparable in magnitude, then it seems that would have to be the case. It happens to be caused by another event having to do with sea surface temperatures. Is that event also attributed to natural variability? How is the literature on attribution of heat waves? Could this also be said of the heat waves in Russia and India, all recent and all of extraordinary magnitudes? Is there any literature showing that only the increase in average temp at a specific location can be applied to extremes as contribution from the overall trend? Is it not possible that the increased heat in the system increases variability and the position of extremes? Some often harp on the complexity of climate and how much we don’t know. De we have any idea of what is the effect on heat waves magnitude of the extra heat that has already be accumulated in the system?

16. Bernard J.

…the more extreme the weather anomaly, the less likely it is to be caused by human-induced (anthropogenic) global warming.

The corollary to this is that we should emit as much CO2 as we possibly can…

After all, any warming that resulted would be more attributable to natural causes until, once we’ve absolutely minimised the probability that humans are warming the planet by emitting as much CO2 as we can, we can be sure that there is no harm at all from burning fossil fuels and nothing need be done to mitigate any human contribution to global warming.

Mass’s logic is impeccable. Or something.

17. Like Susan, I’m perhaps ‘sinning above my station’ here, but I’m bothered by the conceptual framing.

“Anthropogenic global warming” or the various similar formulations used seem to be anchored in the measured warming trend in GMST–which is essentially something of an epiphenomenon, in that it’s a statistical measure. Thus, it’s not directly causative (if that’s a word.)

Trends in GMST result from specific measurements, made over specific times and in specific places, and each reflects a larger synoptic weather picture. Those are the phenomena–they drive the calculated trend, just as they are driven by specific factors, including, you know, radiative forcings from greenhouse gases.

Where this causative reversal may be a bit misleading is that the variance of a time series of global means is *always* going to be less than the variance of the largest outliers among the ‘station data’ going into that mean–which we’ve *all* happily cherry-picked for purposes of having an interesting discussion.

On an unrelated note, I must say that I have no idea why Cliff thinks the East Coast has been cooler than normal; that’s not what NCDC says, and it hasn’t been my experience here in Georgia:

http://www.ncdc.noaa.gov/news/june-2015-us-climate-report

• Susan Anderson

re East Coast “cooler” it seems to me people miss that it’s a big area, and is normally split between (to simplify) south and north of the jet stream. Princeton (family) is roughly similar to Delmarva (Delaware, Maryland, Virginia) and I find it “torrid” – hot and humid, and recently almost unbearably so. Boston (home), OTOH, has been delightful. (And to complicate matters, 40 miles north in NJ is different and much more comfortable. Dad (PWA) tells me the Princeton area used to be under the sea; north gets hilly.)

So indeed, as you go east towards Cape Cod and north towards Maine, it has been a good bit colder and the ocean is cold this year as well. There has been some suggestion that the thermohaline is changing, though the rate is still much under discussion. Arctic melt is having some unexpected counterintuitive effects, it appears.

Mass is skilled at weather, and imho not so much on “climate”. What is it with people and the inability to see that trends and local short-term weather are both similar and different?

• Very likely you are right; he’s saying “East Coast” and meaning “New England.” But one really should look at the map once in a while… the difference in area is non-trivial on the scale of CONUS.

18. In this and the previous posts, it is a basic point which gets lost that heat waves, droughts and floods are defined by the damage they do not by the nature or the width of some distribution. The damage threshold depends on the local biology and infrastructure and there are some absolute limits when it comes to humans and crops.

Because distributions are generally non linear, the shift in one parameter (say the mean) has little to do with shifts in the wings. In fat tailed domains a small shift in the mean can lead to a large shift in the probability of exceeding some fixed boundary, esp if the distribution changes at the same time. Points that have been hammered here recently

19. Horatio Algeranon

“Inertial Mass”

Inertial Mass keeps going
At speed and in a lane
Unless a force is blowing
That moves it from its line

20. icarus62

Probability is really a measure of frequency over time, or over a number of trials. It’s inherently a property of multiple events or instances, like an average. One specific event or instance cannot have a probability, any more than it can have an average. The correct way to talk about climate events such as heatwaves is to say how we have observed the frequencies of these events to change as the planet has warmed up, and how we expect them to change in the future.

It’s misleading (and physically meaningless) to say that a particular heatwave was x% ‘likely’ to have been caused by AGW, or that x% of the severity of a particular heatwave was caused by AGW and the rest was ‘natural’. What we should say is that heatwaves of this severity are now occurring, for example, 10 times more frequently than 50 years ago, or that we expect them to occur 100 times more frequently with 2°C of global mean warming.

I don’t think I’m just being pedantic. It’s impossible to defend a claim such as “ ‘There’s an 80 percent probability’ that climate change produced the Russian heat wave”. An individual event cannot have a probability, and AGW cannot be the cause of one particular heatwave and not of another. The climate doesn’t work like that, and it gives deniers a chance to demand proof of the claim, which is impossible, whereas if your claim is that “Heatwaves of this severity are now occurring 10 times more frequently than they were 50 years ago” then you can prove that simply by presenting the data. That also defuses the nonsense about x% of the severity of a heatwave being ’caused’ by AGW and the rest being ‘natural’.

• Cough! Cough! Nuclear decay. Cough! Cough!

There may be different types of probabilities–subjective and objective being two. Kolmogorov tried to develop a formal frequentist definition of probability in terms of measure theory. However, this foundered over the difficulty of defining the term “random”. The best he got was probably saying that if you cannot represent a series in fewer bits than are contained in the series, that series can be thought of as random. Possibly true, but a pretty cumbersome and not very useful definition.

• kinimod

This is really an interesting point having puzzled me for quite a while.
To me probability is the state of information about what will happen in the future under such and such circumstances. (More precise, this is a conditional probability, but all r e a l probabilities are conditional.)
An important piece of information to base probability on is the frequency, with which an event out of a certain class happened under circumstances of a certain class in the past.
As a thaught experiment, if we have two criminals and one crime, and we know, that A commits this kind of crime once and B 16 times a year, and there are no other possible suspects, we can formulate a probability, that if we incarcerate B, we got the right one with a probability of 16/17. So the event we predict is that of avoidance of a miscarriage of justice.
There is a difference, though, to the climate case. In the judicial case, we can hopefully corroborate our guess by additional evidence, like witnesses, finger prints, genome analysis and the like. In the climate case, we have no possibility to distinguish GW as cause of an event other than model based statistics, it all depends on the model. (Actually, is this true? Would be interesting to distinguish GW related events by their nature!) If we observe an increase of events of a certain kind parallel to GW, we cannot attribute the latter to the former, because it could well be a coincidence, a common cause or the causality could theoretically run the other way around.
The other question is: why should we attribute a culprit-probability to a certain event in the first place? IMO, it doesn’t make things really clearer. It is part of the media sickness to bring too much event based information. It would be better to just write: This kind of events has got a so-and-so-fold increase in rate because of GW.

• jgnfld

Aah. So you are a frequentist. That’s probably the closest to where I am in many respects, but there are problems with that approach. In particular there are problems with how to describe the probability of intrinsically singular, or near singular, events. So, there are other views. If you have not already read it, I suggest for starters reading Hacking, Ian, The Emergence of Probability, Cambridge University Press, Cambridge 1975. I commend that book to all who want to understand the underpinnings of probability.

• Horatio Algeranon

“It’s impossible to defend a claim such as “ ‘There’s an 80 percent probability’ that climate change produced the Russian heat wave”. An individual event cannot have a probability, and AGW cannot be the cause of one particular heatwave and not of another. “

Rahmstorf actually did not claim that an individual event (the Russian heat wave) had a specific probability nor did he claim that it was the “cause” of the Russian heat wave or any other (and not of another)

What he said (which is entirely in keeping with a frequency of occurrence interpretation) is that “With climate change, it’s going to happen five times more often than without,”
“For every five new records observed in the last few years, one would happen without climate change. An additional four happen with climate change,” said Rahmstorf. “There’s an 80 percent probability” that climate change produced the Russian heat wave.

Part of your confusion may arise from the fact that the second part of the last sentence (after “There’s an 80 percent probability”) was written by the interviewer (not Rahmstorf)

But it’s clear from what preceded it that the ““There’s an 80 percent probability” refers to a relative (not absolute) probability.

Finally, your statement — about probability and events in general — that
One specific event or instance cannot have a probability, any more than it can have an average.

is simply puzzling

So, if I throw a die, a single event (a “six”, for example) does not have a probability of occurrence? or if I toss a coin, a specific event (heads, for example) does not have a probability of occurrence?

Correct me if misinterpret, but is that what you are saying?

If it were indeed true in general that “one specific event cannot have a probability”, then I’d have to say that someone should inform the casinos (and poker players) in Las Vegas and Monte Carlo (and everywhere else) because they are apparently under a fundamental misapprehension.

21. It is difficult for me to attribute abnormal weather events to “natural variability” when we no longer have “natural” preconditions. We have both increased average temperatures and increased water content compared to the “natural” conditions pre-1860.

If we record a fine spring day in June, 2015 which enjoys a temperature identical to an average fine day in June, 1860 the two events are not equally “natural”. Without the new 2015 preconditions, that day in June, 2015 would have been cooler and drier, would it not?

22. It seems to me that Mass has produced (an extreme) lower bound on the attribution factor, if he has said anything at all.

• Horatio Algeranon

I’m not so sure.

He might be playing climate limbo.