Dr. Falk is a research professor in computer and Information Sciences at the University of Pennsylvania and director of the Crypto and Society Lab. He is the author of a recent CHANCE article "Why Will a Small Increase in Global Temperature Lead to a Large Increase in the Number of Heat Waves? Truncation and Extreme Events".
Episode Description
More than 15 years ago, Thomas Friedman wrote, “I prefer the term “global weirding,” because that is what actually happens as global temperatures rise and the climate changes. The weather gets weird. The hots are expected to get hotter, the wets wetter, the dries drier and the most violent storms more numerous.” Today’s Stats+Stories episode will be a conversation about how a small shift in temperatures can lead to large changes in extreme weather events with guest Brett Falk.
+Full Transcript
John Bailer
I more than 15 years ago, Thomas Friedman wrote, and I quote, I prefer the term Global Weirding, because that is what actually happens as global temperatures rise and the climate changes. The weather gets weird. The hots are expected to get hotter, the wet sweater, the dries drier, and the most violent storms more numerous. End quote. Today's stats and stories episode will be a conversation about how a small shift in temperatures can lead to large changes in extreme weather events. I'm John Bailer. Stats and stories is a production of the American Statistical Association and Miami University's departments of statistics and media, journalism and film. I'm joined in the studio by Rosemary Pennington, chair of the department of media, journalism and film. Our guest today is Dr Brett H. Falk, research professor in the Department of Computer and Information Sciences at the University of Pennsylvania, and director of the crypto and society lab. He is the co author of a recent chance article. Why will a small increase in global temperature lead to a large increase in the number of heat waves, truncation and extreme events. Brett, thank you so much for being here today.
Brett Falk
Thanks. I'm really glad to be here.
John Bailer
Well, you know, before we get into this, this article, hey, what can what can you tell us about your co author?
Brett Falk
So, so this is a paper that I wrote with my dad, who's director of the Harvard Injury Research control center. And I'd say, about 10 years ago, when we moved to Philadelphia to start my job in the computer science department at Penn, we had to renovate our house, and we had this contractor team, and it was a guy, Willie, and his sons, Shannon, and they were having so much fun working together. And so I called my dad, and I was like, we're not quite in the same field, but we should try to work together. And so we started trying to come up with ideas that sort of overlapped our skills. And so I have a PhD in math, and he has a PhD in econ, and we're kind of doing slightly different stuff, but there's some overlap there. And so we managed this is our third paper together.
Rosemary Pennington
Oh, wow. How did you land on this topic for this paper?
Brett Falk
so this was my dad's idea, originally, that he does a lot of work around gun violence, and I think he was looking at mass shootings. And so a mass shooting is defined to be, you know, a shooting event where there's a certain number of fatalities and it's really an outlier, right? It's when there's an extreme number of fatalities. And then you want to look at, I think he was looking at large capacity magazines, so, you know, guns that hold a lot of bullets, and how much those affect the pale distribution, this, these mass shooting events. And he was noticing some sort of weird statistical behavior. And so then we started talking about, you know, why might this occur, sort of in general, outside of this one specific context?
John Bailer
So you're talking about tail behavior, and I think it's, it's helpful to kind of paint this story for for for kind of listeners that maybe don't play in in the probability world as much so. So in your motivating example for your article, you, you talked about marathon times. Could you talk us through a little bit about how just sort of a small increase can lead to some unusual observations? Sure,
Brett Falk
sure. So imagine if you think about people running a marathon, and you know, most people who run it run it take a long time, and there's a very small number of people who can run it really fast, say, you know, sub two hours, or even sub three hours is really pretty fast, but sub two hours, there's very few people who can run a marathon in under two hours. And now, if you imagine something like, like a new shoe technology that makes everybody 5% faster, right? That's not going to have a big effect on the average speed. The average speed, the average speed of everybody gets 5% faster. But now, if you look at how many people can run now in some really fast speed, at sooner, the sub two hour speed, you might double, or even triple, the number of people who actually run in, you know, under two hours and five minutes or something, whatever is the cut off, and this is because so few people did this to begin with. If originally you had only the very best person could do this. But you know, a lot of people could run 5% slower than the best person, but now, if you made them 5% faster, all those people who were 5% slower than the best person are now running as fast as the best person was, and there was a lot more of those people that you kind of shifted outward on the distribution.
John Bailer
Yeah, I noted that in your in your motivating example, you talked about that, that that sub 230 marathon pace could increase more than 160% increase in the number of people that would run that fast if there was this 5% increase. Yeah.
Brett Falk
Yeah, yeah. So just even to get concrete numbers on this right, I don't remember the times off the top of my head, but you can get the historical data. So we grab the historical data from a bunch of different marathons, and then you can just run a hypothetical experiment. What if we push everybody speed up by 5% what would happen there? And how many people run, you know, sub three hours, or sub 230 or some thing and and you know, the number of people who run sub four hours doesn't change that much, but the number of people who run sub 230 changes by a huge amount because there were so few of them to begin with.
Rosemary Pennington
So in this article, you use this framework of truncation. And as I, you know, a journalist. I'm not a statistician. I'm thinking of truncation in the in the sense that I know it, which is like this shortening or quickening of something. And I was really trying to wrap my brain around kind of how truncation was working in this, this statistical sense. So could you talk us through that?
Brett Falk
Sure. So we're using that term basically to think of, if you think of a distribution, if you think of like a normal distribution, like a bell curve, and if you just now throw out most of it, you truncate it, so you just say, we're only going to consider this tail end. And now if you've thrown out sort of the bulk of the distribution, you're left with this kind of weird behavior at the end. And these small changes can have big effects on this the edges, the part that you didn't truncate, right? And so, again, you can think of it like, I think sports are a reasonable example, if you think of like, you know, an all star game or something, if you say that, here's all the best people in the world, and now we're going to truncate, we're going to only consider the, you know, the 20 best basketball players, and they're going to play on some game, right? Like this is the sort of truncated part of the distribution that you're thinking about. Any small change to the whole population will have a huge effect on this sort of small sub population at the extremes.
John Bailer
So let's transition a bit into kind of thinking about the environment, you know. So, so you've there's a lot of discussion of temperature change and and warming around the globe and what that might mean. So what are some of the kind of extreme events that that you start to worry about as as you have these shifts in the actual observations across the globe?
Brett Falk
Sure, sure. So one thing I want to caveat right is, I'm not a meteorologist, and this is actually just a general statistical phenomenon that you'll see kind of all the time outside of specific weather events. But in the paper, we looked at a couple of different types of weather events. So one is extreme temperatures. And I thought this was sort of really relevant, because you hear these goals of, you know, to keep warming under two degrees centigrade. And two degrees really doesn't seem like that much, right? Like, I can't tell the temperature of my room to two degrees. If you made my room here two degrees warmer, like, I would feel pretty comfortable. That doesn't matter to me. And so I think a lot of people are inclined to say, Well, what's two degrees, right? What does that really matter? But you can understand, these sort of heat waves are extremely deadly. When there's the heat reaches some temperature, right? It becomes really dangerous to people, to animals, to plants, and so you want to really minimize these heat waves. And I think people do understand that. And so then we said, well, let's just imagine, sort of the simplest kind of model you can imagine, let's take the historical temperatures. And we grabbed historical temperatures from a lot of places, but say I'm from Boston, so we grab some historical temperatures from Boston, and you imagine what happens if the average temperature goes up by two degrees. So just take this historical data and just add two to every observation that you have. Now, how many days above, you know, 100 Do you have? How much does that increase? And that increases, like, five fold or something, and maybe even more than that. And if you ask for even more extreme days, how many days over 104 which is actually like a pretty dangerous temperature, those go up by, you know, 600% or something like that, or even more. And because those were already more extreme, and those are so rare in Boston. But the way to think about this, I think, is that, you know, they're actually there are a lot more 98 degree days than there are 100 degree days. And so if you now take all of those 98 degree days and add two, and they become 100 degree days, now you have a lot more 100 degree days. And also this to be a little Danica. I'm also, you know, 100 degree days. We're talking about 100 degree Fahrenheit, whereas the goals are, you know, two degree range in centigrade. So it would be like in a 3.6 degree increase in Fahrenheit. But, but you see this tail behavior in in this data a lot,
Rosemary Pennington
given this work that you've been doing, how would you suggest journalists go about reporting on some of this right? Because I am always kind of concerned about that, and we are experiencing these very severe thunderstorms and flooding events in the Midwest right now. We just have lived through a very. Hard one this weekend. How should journalists cover this? Do you think, based on kind of the work you've been doing?
Brett Falk
Yeah, I mean, I, I do think that focusing on these extreme events, right? This thing of two degrees centigrade really doesn't sound like much, but the types of extreme weather events that we see, of, you know, hurricanes and tornadoes and flooding, right? These seem these are very visceral, and they're very scary. And, you know, we looked at a couple of examples in the paper of temperatures. So if you think of heat waves, we also looked at hurricanes. If you imagine that, you know, wind speeds increased by 5% or something. How many more, you know, Category Five hurricanes would you have? And again, a small like a 5% increase in wind speed will end up with, you know, five times as many Category Five hurricanes. Because, again, these are the real outliers, but you can think of we didn't specifically analyze this in the paper, but this type of statistical behavior happens all the time. You can imagine it with rainfall, right? There has been so many scary flooding events, right? And if you say we, you know, if rainfall increases by a small amount, you would expect a lot more of these really kind of dangerous rainfall events. And so I do think the sort of focusing on the extreme and saying these extremes just are going to happen more. And it's not. They may happen more because of complex interactions in the, you know, in the weather systems, but even if there were none of that, basically, the basic statistics say that they're going to happen a lot more, even if you just have this small increase, say, in temperature.
John Bailer
Yeah, I think that makes it a really hard message to communicate, because, for the reason that that Brent was Brent was mentioning that, that, you know, you have this, this small shift. And, like you said, Well, what the heck? I mean, 1.5 degrees centigrade, two degrees centigrade, what's the big deal, but, but then, you know, defining this in terms of numbers of these extreme events that have these tremendous, this tremendous consequence. I mean, how do you you have to first process that, what that, what that is as a if you're covering it, so you know what? What I mean, ask Rosemary question. No, don't ask. It's not that kind of shows, yeah,
yeah. Come on, Brett, you can join the panel. So,
you know, I'm just curious, you know, I am curious as you think about this, and you know, because you're talking about kind of a distribution shifting some. So that's all the observations shifting some. But kind of, you know, looking at what happens is sort of the number in the tales increasing, yeah. Can you think of other stories like that? I'm just trying to
Rosemary Pennington
just curious. Climate change is the big one that I can think of off the top of my head. I mean, economics data sometimes, I think, gets covered, not quite the same way, but it's similar kinds of processing, of like these minute changes that actually have very large impact. And I think for journalists, we're often trying to find like, a concrete example of the impact to explain why it matters, right? Because people don't care if it stays in the abstract, which is why I enjoy this article so much, is because you're taking this abstract concept and trying to apply it to these concrete things, like obesity, like running, like climate change, that allows for people to understand why this small shift in these various contexts matter and how they impact people. And then you can start thinking about that in other things.
John Bailer
Well, Brad, I thought that you, you know, by starting out with the marathon times you were kind of, it seems like you were sort of anchoring the story in something that that maybe was easier to process, you know, when you then, then think, than trying to do, you know, start immediately with the temperature change and its impact. Was that kind of, was that sort of, as you were, were framing the story? Was that one of the considerations,
Brett Falk
yeah, I mean, I think a lot of the sports examples are sort of easier to think about. And I think part of this is, again, because, you know, weather systems are very complicated, and this isn't, this isn't a result about, sort of the interaction between weather patterns or something, right? This is really about distributions, and you do kind of see it everywhere, yeah, so I think sort of anchoring to things that people have maybe thought about is very useful,
John Bailer
all right. Well, you're listening to stats and stories, and our guest today is Brett Falk, research professor in the Department of Computer and Information Sciences at the University of Pennsylvania,
Rosemary Pennington
so I'm interested. So you chose running and then climate change, and the other example you talk through is obesity. So can you talk us through what you and your father found in that analysis and what people maybe should take away from that?
Brett Falk
Yeah. So again, this is something where, I think with news stories you hear about sort of an obesity epidemic, and you can have a very there are very. Of you know, concrete definitions of obesity, of above a body mass, of you know, some threshold, and you think this is kind of an outlier, like, this is an extreme event or not an event, but there's an extreme value in body mass, if that's how you're defining obesity. And now, if you imagine if everyone to body mass increased by 5% sort of, what would that do to the rate of obesity in the population? And again, because there the by definition, sort of obesity starts out as an as a rare phenomenon, once you push the distribution out a little bit toward, more towards the extreme, sort of dense part of the distribution now lands in what was the tail, basically in what was this extreme notion of, you know, obesity, or morbid obesity, or whatever is the sort of outlier event that you're considering. And so if you push everybody by about 5% then all of a sudden the rate of obesity will again, double or triple or something, depending on how rare it was to begin with. And so this is something we could also get nice data on. And you could run this kind of very, very simple hypothetical experiment. Is, what if everybody's body mass increased by 5% or what if everybody's, you know, weight increased by 5% what would that do to the tail of the distribution, to the the rate of obesity in the population, and it grows enormously.
John Bailer
Yeah, I really liked how, how you could, you could structure this, you know, if you're willing to assume this distribution and these observations, whether it's the obesity or the times and or temperature, and you shift every observation by a small amount, what does that mean to the tail? And you know, it's that's not a huge number of assumptions structurally to tell this story. And
Brett Falk
and we don't even have to assume the original distribution, because that we can actually get, like from the CDC, we can get the distribution of body mass. And so the only assumption we're making is this sort of hypothetical shift. We imagine, what if the body mass increased by 5% or what if temperatures increased by two degrees or something? So we're just running this one experiment. That's really kind of the only sort of assumption we have to make there. And the other thing, though, that you can think about, that I think is maybe clearer in the body mass example, is that this could be a positive thing too, if you're thinking about this, like, from a public health standpoint, if you say you want to reduce obesity, if you could reduce everybody's body mass by 5% it would, you know, have the amount of obesity or reduce it by 80% or something just like, increasing by 5% would dramatically increase the amount of Obesity. Decreasing by the same amount would actually dramatically reduce the amount of obesity. So if you're thinking about sort of public health interventions, you actually don't have to move the needle that much to improve things.
John Bailer
So, you know, there was this takeaway that that some of the human induced climate change could be associated with these more extreme weather events. That's kind of a big part of the focus of this. And you linked to the some of these shifts, like a two degree centigrade shift and a one degree one and a half degree centigrade shift, to some of the data from the World Economic Forum. So could you know, could you you talk about some of those outcomes, and how much that just that simple half of a degree difference plays out in terms of more adverse events being observed.
Brett Falk
Yeah. So I think you know, one of the things that we as a society are trying to reduce the most are these really adverse event events, again, like, you know, on a normal day, whether the temperature is 62 or, you know, 64 degrees, like, is not going to matter that much, but once you get to these extremes, you actually, like, a small increase actually has big effects in terms of people dying and plants dying and animals dying and really sort of ecosystem collapse. And so you really want to minimize these really extreme events. And the thing that happens is that even a small shift really dramatically increases these extreme events. And this is what you're kind of hoping to to avoid, right? These things that cause that kind of collapse, or right cause some kind of, you know, the number of deaths from heat waves is actually enormous, right? And this happens only when the temperature is really very high, right? But if a small increase will actually increase the number of, you know, days over 104 degrees by, you know, a factor of five or something,
Rosemary Pennington
I wonder what questions you were left with after you did this work. Did it open up other areas that you are curious about exploring?
Brett Falk
Um, yeah, I mean, so I think there's a lot of, there's sort of a lot of places where you can see this happening, and there's a lot of different ways this can manifest itself. So even to be, like, a little bit nerdy about this, right, you could say, like, imagine there's a. Fixed shift of, like, two degrees. Or imagine there's like a percentage shift of we said, you know, shoes would make people 5% faster or something, right? These actually have slightly different mathematical effects, and you can look at them a little bit like that. Another thing, though, I think is really interesting about this is we've been talking about, like a sort of a hypothetical change of like, what if the temperatures increased a little bit, or what if people, sort of, you know, on the whole, got a little bit faster running. But you can also imagine doing this when you're comparing populations. And so you can think of things like, you know, in Brazil, people play more soccer than they do in the US. And if you imagine now that we make up some number that people in Brazil are, you know, 5% better at soccer than the US. And now, if you look what fraction of the you know, top 100 soccer players in the world would you expect to be from Brazil? And the answer is basically, like all of them, right? And that's not necessarily because they are just so, so much better, even if that every person in Brazil sort of was, on average, about 5% better. Once you start looking at the very extremes of the, you know, top 100 people in the world, well, then you would expect this much higher prevalence from, you know, one population versus another. And so this is another way to see it's the same basic phenomenon, right? You could imagine back to the like running and shoe example, right? If I say, say, I gave some people these magical shoes that make you 5% faster, and now I asked, what percent of people who ran sub 230 marathons had these shoes on? It's going to be basically everybody, even though, if I gave them to only half the people, and it's because, yeah, they just got that little bump, which doesn't matter most of the time, but it really matters, sort of in these tales.
John Bailer
You know, the when I was looking at some of the summaries again, about some of the impact of kind of the globe, the temperature change, the ones of the half degree difference between the one and a half degree centigrade, degrees centigrade and the two two degrees centigrade shift tied to an earlier episode we had, which is about coral reefs. So we had a we had a conversation with someone that would talk about all these dramatic changes. And you know, now it's, you know, you that with a one and a half degree you're looking at 70% of the reefs destroyed. But then you that you reported, I guess this was also from World Economic Forum data, that the it's anticipating that 99% of the coral reefs will be destroyed if there was a two degree shift in in temperature. And I just that that was one of the ones that really sort of struck, struck me. And I just thought of these. You know that the impact of these, these changes cascading through and I Yeah, were there other, were there other kind of outcomes that were the most, what was the most surprising of the outcomes? As you looked at this and thought about this,
Brett Falk
I don't know. I think they're, they're all kind of surprising, right? It's, you get such big effects on the tails. It's like almost unbelievable, these things of saying that, you know, if we increased temperature by, you know, two degrees centigrade, or 3.6 degrees Fahrenheit, that you would have, you know, five times as many 100 degree days, or something like that. That's such a big change coming from such sort of a small change to the distribution. Every time you see that it's always like, a little bit surprising.
Rosemary Pennington
So this was the third paper that you've worked on with your dad. What's next for you guys? Where are you going to go?
Brett Falk
I don't know. We keep you know, kind of brainstorming these stats is kind of a nice overlap of things we like to think about. And so yeah, most of their discussions are around sort of statistical or basic economic phenomena.
John Bailer
How does the rest of the family think about those dinner conversations?
Brett Falk
Yeah, they, you know, they indulge us.
John Bailer
Yeah, I'm not sure I'd get away with that, but that's
so what were the first two papers you did together?
Brett Falk
So the first paper was why everyone dies before they expect to. Oh, this was a thing that is, if you look at life expectancy charts, everybody, all the life expectancy charts. Condition your life expectancy on where you are now. So I'm 43 and so you conditioned on making it to 43 you know, you're expected to make it to 78 or something. But if once I make it to 75 conditioned on making it to 75 I am supposed to make it to, you know, 85 or whatever is the thing. So every, every age you get to, if you recondition, you have a bunch of years left, right, and so now this is kind of funny, because at the moment you die, conditioned on making it to, you know, one. Minute before you had a couple years left and and so you can go through and you can look at the death data, and you can look at the conditional data. And so if you look at everybody at the moment they die, how much time did the you know, IRS website say you had it left in expectation, and the average person had 11 years left, oh, wow, at the moment they die, this conditioning really has, like, a big effect. And so it's a sort of funny thing. And anyway, it was just a sort of funny statistical observation that if you keep reconditioning on how much time you have left at the moment you die, that conditioning is wrong, right? And it's always wrong for everybody at the moment they die. So that was the first paper we wrote that was little, you know, funny, statistical observation. And then the second paper was actually kind of almost a follow up to a paper my dad wrote, I don't know, maybe 40 years ago about why your classes are larger than average. And so this is a phenomenon, I think that's like, fairly well understood now. But if you go to a, you know, you go to some school and they want to advertise how small their class size are, and they say the average class has, you know, only 10 people in it or something, right? And now the question you want to ask is, from whose point of view are you taking that average right? So you can say, from the point of view of the school, they take all of the classes and they divide by the number of classes. So imagine you have 10 classes, and they each have 10 students. Well, then you know, the students see 10 classes and the average class sizes 10. But now suppose you had a school where there's one class that is 100 students, and there's nine classes that have one student each. Right from the the from the school says, we have 10 classes. We have, you know, 109 students. We have, like 10.9 students per class. But if you ask the students, 100 of the students, so you know 90% of the students, basically, are in a class of size 100 and a few people are in classes of size one. So if you ask the students, and you average how many people are in your s, you're gonna get something that's much, much higher, right? Because 100 out of the 109 students say we have a class of size 100 and only nine people say we have a class of size one, right? And so now you have the class side. The average class side, from the students perspective, is like much closer to 100 and so this is this phenomenon that's sort of well documented in a lot of areas about sort of who's averaging Right? Like, if you you can see this with restaurants, if you say how many people on average are at this restaurant, from the restaurant owners perspective, most of the time, maybe the restaurant's not that full, but when you go, it's always full, because you're going at a time when it's popular, and that's what everybody sees anyway. So we had a follow up to this about why your classes are sort of less diverse than average. And so if you imagine, um, sort of different populations are spread out between classes in different ways. Most people are in an imbalanced group, not even if they're distributed randomly. Most people, sort of by chance, are in the group where they are the majority,
John Bailer
very good. Well, I'm afraid that's all the time we have for this episode of stats and stories. Brett, thank you so muchfor joining us today. Thank you so much for being here.
Brett Falk Thanks. It's great to be here.
John Bailer
Stats and Stories is a partnership between the American Statistical Association and Miami University departments of statistics and media, journalism and film. You can follow us on Spotify, Apple podcast or other places where you find podcasts. If you'd like to share your thoughts on the program, Send your email to statsstories@amstat.org or check us out at statsandstories.net and be sure to listen for future editions of stats and stories where we discuss the statistics behind the stories and the stories behind the statistics.