Rhett Allain

No. Why is this even a question? You can’t just go and alter the predictions of a model because you expected something different. I’m talking, of course, about that famously doctored map of Hurricane Dorian’s projected path. The chart, dated August 29, included a white “uncertainty cone” around the storm’s anticipated path, which someone later clumsily extended with a Sharpie to include Alabama—quite contrary to actual Weather Service forecasts.

But hey, someone might say, “It’s a cone of uncertainty, so who knows? One person’s guess is as good as another’s.” Look, I’m no meteorologist, but I think I have a pretty good grasp of this whole science thing. So maybe I can help explain what uncertainty means in the context of model predictions.

Photograph: Chip Somodevilla/Getty Images

To do that, I’m going to use a much simpler problem—predicting the path of a tennis ball tossed into the air. In this case, once the ball leaves my hand, there are only two main forces working on it: the downward gravitational force and an air-drag force resisting the ball’s forward motion.

Actually, when you dig into it, it turns out that air drag itself is pretty complicated. It depends on the density of the air and the size, shape, and surface texture of the ball. It also depends on the ball’s velocity, which means it keeps changing as the ball moves. That’s a tough problem, but if I break it into tiny steps, it’s not too bad. This is called a numerical calculation.

So let’s say we want to predict where the ball will land. We can build a mathematical model, input some initial values and the results of our numerical calculations, and get an answer. Is it going to be perfectly accurate? No, because we don’t know everything about the situation. Our estimate of launch velocity and launch angle will have a margin of error, and in reality there are even more factors that affect air drag. (This stuff matters. Just look at the debate raging in baseball this summer about the sudden increase in home runs.)

Let me demonstrate this by calculating the trajectory of three tennis balls. These balls are about the same, but all slightly different. They have different initial conditions with different drag forces. Here’s what happens. (This is real code. If you click the pencil icon, you can view and edit the code. Jump in, it’s fun!)

Now imagine there are a bunch more parameters. Maybe there’s some wind pushing to the side. It’s possible I don’t even really know where the ball starts from. You could imagine that with many different runs of this model it could get weird. That’s exactly what happens with hurricane predictions. That’s why you get something with a bunch of lines that looks like spaghetti.

In our model above, the ball lands between 7.93 and 8.06 meters. Is it possible for it to land at 8.7 meters? Sure, with a slight change to the initial conditions. What about 11 meters? Hmmm … that’s a bit far. Twenty meters? OK, it’s technically possible but extremely unlikely.