On the subject of expecting the unexpected, a recent piece “It’s Later Than You Think: Climate Fueled Extreme Weather, Part 3” by Roger Pielke Jr. addresses the somewhat recondite mathematical point that if the weather is becoming more unusual we might not notice it at first. But there are ways of looking at how unusual it has to get and for how long in order to detect a meaningful change in typical conditions rather than just the usual random incidents of wet or dry, calm or windy, cold or hot and so on that have made weather forecasting the butt of jokes beyond number. Specifically, Pielke notes, scientists are asking about “the concept of the ‘time of emergence’ for the detection of a signal of a change in climate in observations and projections.” And the answers suggest it isn’t going to happen any time soon for most types of extreme weather. So once again, even if we really wish we did know it, even if we really need to, we just can’t. And making stuff up is no substitute for knowing it.

Statistics can be challenging. But there are good and bad ways to tell whether a cluster of odd occurrences represent a change in a trend, or just typical fluctuations within it. Including when you get a bunch of odd weather. Including the good kind as well as the bad.

Suppose that you had a coin you suspected might not be equally weighted, and you were going to toss it until you determined either that it really did produce tails or heads at random or was biased toward one or the other. How many tosses would it take?

Well, if the thing were actually rigged to come up heads every time, not a whole lot. Yes, a proper coin can generate long runs of heads or tails, but round about 20 you smell a rat. Such an outcome is, roughly, a one-in-a-million shot (one in 1,048,576). But what if you toss it 10 times and get 8 heads or more. Crooked or not?

Hard to say. That happens roughly 5% of the time. And Atlantic hurricane seasons are a lot more variable than coins. For instance, in the 1930s (defined as 1930-1939) the number of hurricanes during the Atlantic season was 2, 3, 6, 11, 7, 5, 7, 4, 4 and 3, for a total of 52, and the number of major hurricanes (Category 3 or higher) was 2, 1, 4, 6, 1, 3, 1, 1, 2 and 1 (total 22). So what would you predict for the 1940s if there was no “climate change” worth discussing?

Well, the actual numbers are 6, 4, 4, 5, 8, 5, 3, 5, 6 and 7 for total hurricanes (53), and 0, 3, 1, 2, 3, 2, 0, 2, 4 and 3 for major ones (total 20). Very similar overall. What are the odds?

Who knows? The 1950s totals are 68 and 29. Is it a rising trend? Then why were there 11 in 1950, and not another year in double digits until 1969? Why did the 1960s see 64 total and 23 majors, but the 1970s only 51 total and 16 majors? And why was there no double-digit year in the 1970s or 1980s, but two in the 1990s (1995 and 1998)? Well, you may say, that’s because climate change was changing the climate by the 1990s. But only one year in the 2000s was in double digits, 2005. Still, that decade saw 75 total hurricanes (and 36 major ones) versus just 64 and 25 in the 1990s. And then the 2010s had three years in double digits… but fewer overall, at 72, and fewer majors, at 30.

Detecting a genuine change or trend is harder than it sounds, and “when I was a kid” or “we’re all going to die” aren’t good lead-ins to the reliable kind of analysis. Suppose for instance that something genuinely is a “thousand-year event”, some kind of storm or disaster or for that matter an absolutely ideal summer for crops that would typically happen once in a millennium, meaning that if you had data for many, many thousands of years you could state with confidence that it happens once per 1,000 years. And then you get two of them in a decade. Has the planet gone nuts or, alternatively, become Eden again? Or was it just a fluke? How would you tell?

Well, for fun Pielke Jr. went and looked at a variety of standard computer models that project hurricane frequency, strength and damage under various scenarios. And in case someone told you the science is settled, the models disagree among themselves as well as not exactly predicting actual results well. But here’s the key point.

One characteristic scenario, in which there’s a near-doubling of Category 4 and 5 Atlantic hurricanes between now and 2100, specifically an 81% increase, would require more than two centuries to verify. And the model that predicts the smallest change (which is actually a decrease in number) would take over 500 years. Meanwhile “The IPCC AR6 projection of a 1% or no decrease in the global incidence of Category 4 and 5 storms would never be detectable in observational data.”

If you go back a long way the records are less reliable because regular surveillance plane flights only began in the mid-1930s and satellite records in the late 1970s. Despite which 63 hurricanes were counted in the 1880s, including two years in double digits, and 15 majors. Which is almost certainly an undercount; the 1860s, for instance, only show four major hurricanes.

Then again, who knows? Maybe it was a quiet decade. Maybe they happen. We don’t know. And since we don’t, estimating whether a modern quiet season was a trend or an anomaly would be hard. (That example is not fanciful. Some models actually do predict fewer hurricanes though generally, to keep things dismal, they say the ones we do get will be more powerful and destructive.)

Now look at the way media casually assert that a “hundred-year event” has become annual or is about to or some such. (Or if you’re Michael Mann, “it’s no longer a thousand years uh event it’s maybe a five or ten year event…”) As those who work professionally with statistics can tell you, a “thousand-year event” without thousands of years of reliable records is essentially a guess. You create a probability curve, construct a very flat very high end and go well, could be unless it’s not.

It's one thing to calculate coin tosses and quite another to try to detect trends in complex naturally fluctuating weather events then try to determine what would lie outside the trend line and by how far. As Pielke Jr. observes, “There exist a very wide range of projections for the future behavior of tropical cyclones” which he demonstrates graphically before warning:

“If you tell me what result you want, I can find you a study in support of that result. The very long emergence timescales mean that it will be very difficult, perhaps impossible, to identify with evolving experience which projections may be more accurate than others.”

So don’t let the “mathiness” intimidate you. On the contrary, when someone makes a highly improbable statement about probability, assume they’ve already confused themselves and are now working on you.