“A butterfly flaps its wings in China, and we get a tornado in Texas.” That’s the thought behind the butterfly effect, and, interestingly enough, it’s why our weather forecasts for tomorrow are excellent, and why the same ones for 10 days are essentially guesses. 

Chico State physics professor Nick Nelson explains the chaotic business of weather prediction on planet Earth. 

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A heavy layer of hail gives the appearance of a snowy scene in front of the Kendall Hall walkway
A white, wintry setting is rare at Chico State, but within the realm of certainty in models deemed “chaotic”—such as the weather. (Jason Halley/University Photographer)

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SOUNDBITE OF PROFESSOR NICK NELSON: A lot of times what gets lost in the political debate is it become this binary thing, right? It becomes this, “yes, climate change,” “no, climate change,” “yes, climate change,” “no, climate change.” Which is, from a scientific standpoint, really frustrating, because the answer isn’t “yes” or “no.” The answer is “how much, and how certain are we?”

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KATE POST, HOST: This is Out of Curiosity, a podcast driven by the wonder of lifelong learning from California State University, Chico.

TRAVIS SOUDERS, HOST: Welcome to Out of Curiosity. I’m Travis Souders.

POST: And I’m Kate Post. Today’s guest is Chico State physics professor Nick Nelson, who’s going to tell us a little bit about how weather forecasts work—or sometimes don’t.

Travis, it’s coming up on the end of the workday today, so do you know what you’re planning on doing after work today?

SOUDERS: Yeah, pretty good idea. Maybe a bike ride, maybe some dinner.

POST: OK! How about a week from today?

SOUDERS: Um, a lot of things can change in a week. Not sure!

POST: Yeah, it seems like it’s not too hard to predict where you might be in an hour, but it’s a lot harder to figure out where you’re gonna be in a week.

SOUDERS: Yeah, I think a great example of where we see that all the time is trying to figure out just what we’re going to wear tomorrow, because we can’t always be sure what the weather’s going to be like.

POST: It’s relatively easy to predict something in the short term, but it’s way harder to know with any certainty the further away you get from this point in time right now. Because there’s so many things that can happen between now and then, and we see this all the time when we look at the weather forecast, right? Sometimes those forecasts are like, up to the minute or up to the hour and they’re pretty accurate, but the further you go out—tomorrow, the next day—by the time you get to a 10-day forecast, who knows what the weather’s going to be like? It could change four times between now and then.

SOUDERS: Yeah. As much as we like to play around with the idea of predicting the future and we look seven days in advance and think that we know what’s happening, it’s still the case that the best weather forecast is sticking your head out the window.

NELSON: For most of human history, we knew what the weather was going to be like for about five minutes, and then it changed, and it was different, and you never saw anything coming, and now we can’t hardly think about, you know, looking at the weather and figuring out if it’s going to be sunny this weekend and trying to plan our lives around some of these things. But this idea of predictability is fascinating. The simplest example you can take is, if you just take an object and drop it, right, just drop it, you can predict the motion of that object really, really well. We do this with all of our intro physics students. We have them drop basketballs and baseballs and things and it’s extremely predictable. As you start to make your system more complicated—instead of thinking about just dropping a ball, now let’s think about, oh, a pendulum swinging back and forth, or some more complicated system, it seems like we should be able to just, it might be harder to do, but we should be able to do the exact same thing, is predict. If we know how the thing started, we should be able to predict what it’s going to do. And interestingly enough, that is true for the weather, even though it’s this incredibly complicated system, where you have fluid dynamics, and you have to deal with chemistry, and you have to deal with the sun, and the moons, and the tides, and all sorts of variables, if you know exactly how it started, you should be able to predict what’s going to happen, and you should be able to predict what’s going to happen forever.

POST: But we know from weather forecasts, that’s not really the case. You get a three-day forecast, or sometimes a seven- or 10-day forecast if they’re feeling really ambitious.

SOUDERS: Yeah, and professor Nelson says that the 10th day is basically just guessing at that point. So, what’s going on?

NELSON: What happened is something that we call chaos. When mathematicians and physicists use that word, we don’t mean what happens when I try to put my children to bed. What we mean is that the system is extremely sensitive to its initial state. So, if you knew exactly what the weather was doing, and you knew everything exactly about how it was interacting with the sun, and the moon, and the plants on the ground and all these sorts of things, then you could predict what the weather was going to do forever. But let’s say you don’t know it exactly. Let’s say you only know it roughly, because you don’t have thermometers everywhere throughout the entire atmosphere, or because your thermometer’s only good to, I don’t know, a tenth of a degree instead of an infinite-precision thermometer. Then you can’t predict what it’s going to do forever, and the reason for that is what we call dynamical chaos, this idea that if you bump the system just a little bit to start off with, initially it’s going to look like you haven’t bumped it. It’s going to keep happily progressing. But over time, that difference is going to grow. That little teeny bump in one spot is going to change and it’s going to produce dramatically different weather over the course of, in the case of our atmosphere, five to seven days.

POST: Imagine you’re at the bowling alley and you toss your ball down the lane, and it looks like it’s going dead-center toward the pins. But it turns out, there’s a little bump in the lane you didn’t know about, and it knocks your ball slightly off-course. It’s still going mostly straight, but the further it goes down the lane, the more it veers to the left, and by the time it gets to the end, it’s a gutter ball.

SOUDERS: One tiny deviation at the beginning of your roll ended up being an enormous change at the very end.

POST: When you’re describing chaotic systems, is that the same thing as what we call the butterfly effect?

NELSON: Yeah, it’s often described as the butterfly effect. The idea is that you can make an imperceptible change, right—so the butterfly effect, is sort of a thought experiment. The idea is you have a butterfly flap its wings. That changes the atmosphere a little bit, right? It changes the wind speed in one spot somewhere on the globe by some incredibly small amount. Well, over time, that incredibly small change changes other things, and changes other things, and changes other things, and the growth of that difference between butterfly flapped its wings vs. butterfly didn’t flap its wings becomes huge. And the butterfly effect is often stated as, “A butterfly flaps its wings in China and you get a tornado in Texas.” But this idea that a very small change dramatically changes what’s going to happen in the future, is the right idea.

SOUDERS: What Professor Nelson stresses over and over again with his students is noting the certainty of a prediction.

POST: Yeah, how certain you are that the prediction you’re making is accurate. That’s the key for weather forecasts.

NELSON: When we use chaos in a technical sense, in a mathematical sense, it doesn’t mean anything can happen. It doesn’t mean the system is completely unpredictable or that we can never know anything about this. What a chaotic system means is that over time, our predictions will become less and less reliable. So your forecast for tomorrow is really very, very good—I mean, we all complain about, “Well, it said it was a 40 percent chance of rain and now it’s raining”—but your weather forecast for tomorrow is really, really good. Your weather forecast for four days from now is pretty good, and your weather forecast for seven days is decent-ish. And when you get out to 10 days, what you’re basically projecting is the average weather for that time of year. So these projections, they’re not all equally bad. It’s just that they get harder and harder to do the further and further you move down the line in time.

SOUDERS: So he’s saying our predictions can vary in accuracy. But just because a system is chaotic, doesn’t mean it’s random.

NELSON: When we say a chaotic system, we don’t mean it’s gonna do some random thing. These models are going to predict a whole bunch of different things. So right now, it’s a rainy March day, right? If you run a 10-day weather forecast, you can run thousands of them, it’s not gonna predict snow 10 days from now. None of them are, because the chances of snow are extremely small towards the end of March. And so it’s not that the weather can do anything it likes, it’s that what it can do is bounded in some way. There’s some range of possibilities, and what you really want to know is, where in that range are we likely to be?

POST: We’ve been talking about weather and short-term forecasts, but what about long-term climate?

NELSON: Climate models are also chaotic, meaning that small changes in your initial conditions, what you think the climate is today, are going to create less and less certain models as you move forward. The trick here is that the details of these models are chaotic, but remember, chaos doesn’t mean “random.” It doesn’t mean anything can happen. It means that it’s hard to tell exactly what’s going to happen.

SOUDERS: Professor Nelson says climate models work similar to weather ones—you start with the best measurements you have about the climate today, and then you project them forward.

NELSON: What you do is start with the best measurements you have of what the climate is doing today. And then, you project them forward in time, for as far as you want to go, right? A hundred years, maybe. And you say, what’s the climate going to do over the next hundred years? And you get a measurement, and it says, ‘OK, the average temperature’s gonna go up by 2.5 degrees Celsius, right—which would be bad news. And OK, you go back and say OK, let’s run it again. Let’s assume we got the average precipitation in Madagascar wrong by two-tenths of a percent. Run the model again. And you find, ‘OK, oh this one says the temperature’s gonna go up by 2.4 degrees Celsius. And you keep doing this, and you run thousands of these models, and what you find is, that these models consistently predict warming. Now, the exact amount of warming and the exact distribution of how that warming is gonna spread around the planet, and exactly what that’s gonna mean for precipitation, changes a little bit in these models. But as a whole, they produce a probabilistic assessment of what’s going to happen in the future.

POST: I think that’s scientist speak for global warming or climate change, right?

SOUDERS: Uh, yeah.

NELSON: This is really crucial, because what that means is, with this effect from anthropogenic CO2 emission, right, the fact that we’re burning fossil fuels and other things that increase the level of CO2 in the atmosphere, the models all agree that that raises temperature. The models also roughly agree on how much temperature increase you’re going to get, with some uncertainty, right?

SOUDERS: So you’re saying there’s a range.

NELSON: There’s a range. And this is a valuable thing, because a lot of times what gets lost in the political debate is it becomes this binary thing, right? It becomes this, “yes climate change, no climate change, yes climate change, no climate change,” which from a scientific standpoint is really frustrating, because the answer isn’t yes or no. The answer is how much, and how certain are we? And the answer in the case of climate change is, we’re quite certain, and we have a good estimate of how much. Now, that estimate becomes less and less certain the further you go. And not just for physical reasons, it also matters what people do, right? And I’m a physicist—I have a hard enough time trying to predict what nature’s gonna do. Predicting what people are gonna do is infinitely harder, because people are weird and they do all kinds of weird things you wouldn’t predict.

SOUDERS: Right. People are chaotic.

NELSON: Yeah, people are chaotic in a whole different way. So this idea that you can’t predict the climate is completely wrong. The answer is, of course, you can predict the climate. How well you can predict the climate depends on a number of things. But the answer is really to look at what do the models predict, and what’s the range of possibilities? And the answer of course, with climate change, is there’s a range of possibilities, they range from bad to worse, and they’re all consistent in their prediction that as time goes forward, we’re going to see increasing changes to the earth’s climate. Then of course, it’s a whole other question to figure out, what should people do about them?

SOUDERS: The question there is, what variable can people introduce to change things?

POST: Yeah—what’s our butterfly effect? Or, which butterfly wing do you want to flap, as Professor Nelson said.

NELSON: You know, weather and climate are interesting things. Climate is kinda what happens when you average the weather over years or decades. But the important thing to think about with climate change is what we’re really talking about is a change in the average over time. And then, the weather is gonna vary all around that, right? Now, I should also point out, that the variability of weather is also an effect of change in the climate, right—most of the models you get into will say that as the warmer the climate gets, the more variability you’re going to get in weather, so the more likely it is to get extreme heat or extreme rain or extreme cyclones or extreme tornadoes or extreme whatever. And from a physics standpoint, you can kinda understand that, because what you’re basically saying is, you’re putting more energy into the system, right? Heat is energy. More energy means you can do more stuff. And so this idea that you’re going to get more dramatic events certainly goes along very well with the whole picture.

POST: So as we look ahead, scientists are trying to figure out new and better models for prediction.

NELSON: As the climate changes, and it changes the whole planet along with it, how do all of those models change? And it’s not just weather—this is a question that people are asking any time you start thinking about trying to predict out the future, is: OK, you build a model that works well for everything you have data on, right, the past? Well, what if you change the conditions, right? What if you change the underlying assumptions that your model was built on? Well, it’s gonna have problems. How many problems? Well, that’s a good question.

SOUDERS: So the short way to explain why it’s so tough to predict the weather is because the models we use to do that are changing all the time.

POST: It seems like predicting the future is a little more difficult than the app on our phones makes us think.

SOUDERS: Thank you to our guest, Nick Nelson. This has been Out of Curiosity. I’m Travis Souders.

POST: And I’m Kate Post. This show is produced by Chico State’s University Communications. Make sure you never miss an episode by subscribing wherever you listen to podcasts.

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