Exceedance Risk over a Design Life

A return period is not a schedule. It is the reciprocal of an annual exceedance probability, and nothing more: a 100-year storm is a storm with a 1 percent chance of being equalled or exceeded in any given year. It does not arrive every hundred years, it is not "due", and having had one last year changes the odds this year by exactly nothing. Two 100-year storms in consecutive years at one gauge is a 1-in-10,000 coincidence, which sounds impossible until you remember how many gauges there are — an event with those odds happens somewhere every single year, and it is not evidence of anything at all until a frequency analysis says otherwise. The name is most of the problem. A hundred-year storm sounds like a calendar entry and reads to a homeowner as a promise, which is why a growing number of agencies now publish the annual exceedance probability instead: a 1 percent AEP storm is the same number and invites none of the same misreading.

What people actually want to know is the risk over a period they care about, and that is what $R = 1 - (1 - 1/T)^n$ gives. The logic is one line: the chance of surviving any one year is $1 - 1/T$, the years are treated as independent, so the chance of surviving $n$ of them is that raised to the $n$, and the risk is what is left over. Run it on the case everyone quotes and the answer is bracing. A 100-year storm over a 30-year mortgage: $1 - 0.99^{30} = 0.26$. Twenty-six percent. Over a 50-year building life, a 100-year design gives 39 percent, and to get the odds down to even over that life you need roughly a 73-year event — the arithmetic runs the other way from intuition, and designing to a 50-year storm for a 50-year life is already a losing bet at 64 percent.

Two honest limits. The independence assumption is doing real work here, and it is only approximately true: rainfall shows serial correlation, and a wet regime that persists for several years raises the odds above what this returns. And $T$ itself is an estimate with a confidence interval around it that is usually much wider than anyone admits — a 100-year value from a 40-year record is an extrapolation, and its uncertainty dwarfs the difference between a 26 percent and a 30 percent answer. Use this to make risk legible to a client or a council, which is what it is genuinely good for, and not to argue over the third digit. It is also the cleanest way to explain why a jurisdiction that has updated its IDF curves is not being alarmist. If the underlying frequency has shifted, every number on this page shifts with it, and the current published curves are the design basis rather than the ones in the old manual.