The reservoir and the dry year

A reservoir designed for a one-in-fifty-year drought failed in its thirty-first year. The engineering was sound. The statistics had quietly stopped applying.

'One in fifty years' is a statement about a probability distribution, and the distribution was estimated from the record available when the dam was designed: sixty years of rainfall, treated as draws from a stable process. Both assumptions were reasonable at the time and neither survived. The record was short enough that the worst drought in it was not necessarily close to the worst possible, and the process was not stable, because the pattern of rainfall in the catchment shifted over the following decades.

Engineers call the first problem the limit of the record and the second non-stationarity. They have different remedies. The limit of the record is handled by modelling the physical process rather than only the history, which produces wider intervals and a less comfortable design figure. Non-stationarity is handled by abandoning a single design storm and planning for a range of futures, accepting that some of the capacity built will turn out to have been unnecessary.

What both remedies share is that they make the uncertainty explicit, and explicit uncertainty is politically expensive. A figure of one in fifty years sounds like knowledge. 'Somewhere between one in twenty and one in a hundred, and moving' sounds like evasion, although it is the more honest statement and the one that supports a sensible decision about how much margin to buy.

The reservoir was eventually raised and a second source connected. The more useful change was to the paperwork: the design document now records the length of the record it rests on, which means the next engineer begins by knowing what the number does not include.