The Thousand-Year Rains
Although most of us have been struggling with the heat, the U.S. experienced four devastating rainfalls this summer that caused flooding, mudslides, property damage, and loss of life. The areas affected include eastern Kentucky, St. Louis, central and southern Illinois, and Death Valley.
What's special about these rainfalls is that they're classified as thousand-year events. That is, scientists estimate that each one occurs only once every thousand years.
If these are 1-in-1000 year events, we might ask how four of them could happen in the same year. Are the statistics flawed? Is the messaging from experts misleading? Do people misunderstand the message? Or, are extreme weather events simply becoming more common?
I think the answer is: a little of each.
Observation vs. statistics
For thousands of years, the best method for predicting the weather was observation. Crudely speaking, what people did was to describe the precursors to each weather event of interest.
For example, 2,500 years ago, in the most influential guide to weather forecasting in European antiquity, Theophrastus wrote:
"It is a sign of storm or rain when birds which are not aquatic take a bath. It is a sign of rain when a toad takes a bath, and still more so when frogs are vocal... It is a sign of rain when swallows hit the water of the lakes with their belly..."
This might sound strange compared to 21st century weather forecasts, but Theophrastus was often right. For instance, the tiny insects eaten by swallows get swept upward when air pressure is high and rain is unlikely. When air pressure is low and rain is probable, these insects remain close to the earth's surface. As they gather above lakes, they stay so close to the water that when swallows dive down to feed on them, the swallows often get wet.
From our perspective, the observations of Theophrastus are limited because they don't tell us much about the chances of weather outcomes. Most "signs" of rain are either present or not. If you see the swallows dipping low, you may consider rain likely, but you don't know how likely it is (or how heavily it will fall).
Thanks to statistics, modern meteorologists can calculate the chances of any particular weather event. This is progress. All the same, whether you talk about a "sign" of rain or "chances" of rain, you're confronting the same problem – uncertainty about the future – and the future often surprises us.
Where does the thousand-year statistic come from?
Organizations such as the National Weather Service (NWS) describe extreme weather events as having certain probabilities of occurring – once in 500 years, for example, or once in 1,000 years. (Terminological note: There are several ways of expressing each of these probabilities. A thousand-year event is one that's expected to happen once every thousand years, which is the same as saying there's a 1-in-1,000 chance it will happen in any one year.)
Scientists calculate these statistics with help from extrapolations across space and time. Let's take a concrete example. You almost certainly live in a neighborhood where more than 5 inches of rain in a 24-hour period would be both unusual and problematic. So, what are the chances of this event happening next year? To answer that question, the NWS could look at historical data from a rain gauge in the weather station nearest to you. Let's suppose this station was built in 1971. The NWS might identify the rainiest day per year at the station for each year from 1971 through 2021. This would yield a sample of 50 datapoints – the 50 winners of the "rainiest day of the year" contest. If there'd been more than 5 inches of rain on only one of those days, the NWS would say that a daily rainfall of over 5 inches is a 1-in-50 year event in your neighborhood, because it only occurred once in 50 years. Thus, the chances of it occurring next year are estimated at 1 in 50, or 2%.
What you just read is a simplified version of what scientists actually do. Most of the complexity comes from the need to extrapolate. Weather stations aren't located right next to each other, so there must be extrapolation across space. And, even though rain gauges have been used for thousands of years, detailed records on precipitation aren't very old (and the farther back you go, the less data you find), so extrapolation is also needed across time.
As you can see, even if the past were a completely reliable guide to the future, we couldn't predict the weather perfectly, because our knowledge of the past is limited. It's limited because of the extrapolations I mentioned, and because of various sources of error, including equipment failure and the need to account for environmental conditions such as wind.
In sum, when scientists say that a rainfall of such-and-such severity is a thousand-year event, what they mean is that for the region in question (a state, a city, or whatever), historical data hints that rainfall of that severity occurs only once in a thousand years.
How could more than one thousand-year rainfall occur in the same year?
There are four ways to address this question.
1. They're not really thousand-year rainfalls.
As I mentioned, the thousand-year estimates are based on imprecise historical data. It's possible that with better data, we'd find that the chances of one or more of the four extreme rainfalls happening this year were actually greater than 1 in 1,000. (This is purely speculative. It's also possible that the true chances were less than 1 in 1,000.)
2. They really are thousand-year rainfalls, but they don't occur every thousand years.
For each of the four rainfalls, even if the 1-in-1,000 estimate were correct, the prediction is not that we'll experience such a rainfall exactly one time every 1,000 years. If 999 years have passed and we haven't experienced it, the chances of experiencing it next year are still 1 in 1,000. By the same logic, it's possible, albeit unlikely, that we could experience that rainfall, and other equally rare storms, more than once in a given year. All the thousand-year statistic tells us is that the probability of such-and-such rainfall in any given year is 1 in 1,000.
(If that seems unclear, just imagine tossing a normal coin. The chances of heads are 1 in 2. But if you toss the coin 10 times, you won't always get exactly 5 heads. And, if you've tossed it 9 times already and gotten 4 heads, the chances that the next toss will turn up heads is still 1 in 2. You can think of probability statements such as "1 in 2" or "1 in 1,000" as generalizations about what would happen across infinite tosses of the coin or measurements of annual rainfall.)
3. They used to be thousand-year rainfalls, but not anymore.
The thousand-year estimates are derived from historical data, but the past can't perfectly predict the future. Weather is very complex. Even if the historical data were accurate, we'll never understand the minutiae well enough to make forecasts with 100% certainty. You've probably heard of the "butterfly effect" – the idea that the flapping of a butterfly's wings may ultimately cause a tornado many miles away. MIT meteorologist Edward Lorenz created this metaphor to illustrate his finding that future weather is sensitive to surprisingly small changes in current conditions.
Prior weather data is actually becoming less and less successful at predicting extreme weather events, owing to climate change. According to one study, the effects are especially strong for rain forecasting. In short, even if the historical data were perfectly accurate, as time goes on the predictive power of the data is diminishing. One might say that with respect to the weather, the past is increasingly a thing of the past.
The problem with current NWS models is that they assume "stationarity", a statistical term meaning that the prevalence of extreme events will remain constant over long periods of time. You can see stationarity in the simplified example I gave earlier: If your neighborhood experienced more than 5 inches of rain per day only once over the past 50 years, NWS models would say that the chances of that much rain in the future will continue to be 1 in 50.
Climate change is causing a rapid uptick in more extreme weather events, and thus we need better models that don't rely on stationarity. The NWS is currently collaborating with several research teams to incorporate climate change models into their extreme precipitation forecasts, but at this point it looks like a race to see whether the modeling can keep up with the effects of climate change (as well as some hoped-for benefits stemming from the Inflation Reduction Act signed on Tuesday).
Problematic messaging
It's not the fault of the NWS that weather is complex and prior data are limited. However, one could fault the NWS for its messaging, such as the very user-unfriendly sections of its website that concern precipitation. Here's a striking example: One of their FAQ pages contains the question: "Why do 1000-year (100-year) events happen so often?" The answer provided in the FAQ is so incomplete and poorly worded that the only people who could understand it are those who already do. And, at the end of their answer, the NWS refers the reader to an Australian Bureau of Meteorology article that "explains well". I found it sad (and funny) that after mangling the answer to a straightforward question, the NWS points us to Australia for help. (The NWS is a federal agency, so I would say that this FAQ entry was not a good use of our tax dollars.)
As for news and social media, a key problem with the messaging is that it doesn't emphasize strongly enough that the thousand-year statistics represent cumulative probabilities. If the chances of some event occurring next year next year are 1 in 1,000, then there's a 2-in-1,000 chance that it will occur sometime in the next two years, and so on.
Why should people care about the "cumulativeness" of cumulative probabilities? For one thing, it tells us that the longer the stretch of time we consider, the greater the chances of an extreme event occurring. Failure to appreciate this has led property owners to underestimate the risks of extreme rain and flooding. Some people who decline to purchase flood insurance, for example, misunderstand the statistics on precipitation and flooding in their area. Specifically, they don't realize that if flooding is a 1-in-100 year phenomenon, then the chances that it will occur during the time span of, say, a 30-year mortgage are 30%. Again, because we're looking at cumulative probabilities, the chances of flooding within the first year are 1%, the chances of flooding within the first two years are 1 + 1 = 2%, and so on up to however many years one owns the house. (A separate issue, which exacerbates the problem, is that some property owners underestimate the single-year risk of extreme precipitation events.)
Conclusion
Here are my original questions, followed by my boiled-down, bottom-line answers:
--If these rainfalls are 1-in-1,000 year events, how could we have four of them in the same year?
They might not be 1-in-1,000 year events, at least not anymore. In any case, thousand-year events can occur more than once every thousand years.
--Are the 1-in-1,000 statistics flawed?
Yes, although this isn't anyone's fault. The statistics are based on extrapolations from imperfect historical data, and they haven't fully incorporated climate change modeling yet.
--Is the public messaging misleading?
Yes, in some cases the messaging seems to be incomplete and/or misleading. Examples include the NWS website and the treatment of thousand-year rains in some news and social media reports.
--Do people misunderstand the message?
Some people don't seem to grasp one or both of the following statistical ideas: A thousand-year event doesn't necessarily occur exactly once every thousand years. However, the probability of such an event increases as one examines increasingly lengthy stretches of time, because it's a cumulative probability.
--Are extreme weather events becoming more common?
Yes. Climate change has contributed to a variety of extreme weather events that are increasing in prevalence and severity. For this reason, we've experienced four thousand-year rains this summer in a year marked by extreme heat, severe wildfires, and drought.
To learn more about the impact of climate change on weather and other phenomena, see here or here.) Thanks for reading!