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Ken Thompson: why forecasts of rain are most likely to be wrong

August rain in Regents Park, London - PA
August rain in Regents Park, London - PA

We’re all obsessed by the weather, and gardeners more than most. Half the time we are hoping it will rain so we don’t have to water the veg plot, the other half we are hoping the rain will stop so we can get out and mow the lawn. So how useful are weather forecasts in helping us decide what to expect – specifically, whether it’s going to rain or not?

Helpfully, the Met Office has a web page that asks ‘How accurate are our public forecasts?’. Less helpfully, it reports their rain-forecasting accuracy as follows: ‘0.589 Equitable Threat Score (ETS) of three hourly weather is correctly forecast as ‘rain’ on the current day’.

Pardon? Equitable what? Don’t worry, they really are trying to be helpful, they just aren’t trying very hard. The problem is that just reporting how often it rains when the weather man says it will isn’t very useful, because that ignores the underlying probability of rain. To take an extreme example, in an equatorial rain forest I can say with complete confidence that it will rain tomorrow. But that tells you precisely nothing about my rain-forecasting skills, because it rains every day.

Vadim Turnov snail  - Credit: Vadim Trunov/ Barcroft Media
Credit: Vadim Trunov/ Barcroft Media

A legendary example of the opposite extreme is forecasting of tornadoes in the American Midwest in the late 19th century by one sergeant John Finley. Finley claimed his twice-daily tornado forecasts were 96.6 per cent correct. Which sounds terrific, until you consider that tornadoes are actually rare. Essentially, Finley arrived at such a high success rate by being very good at forecasting the non-appearance of a non-tornado. In fact, as critics pointed out, tornadoes are so rare that Finley could have increased his forecasting accuracy to 98.2 per cent by simply forecasting no tornado every time.

What we want is a forecasting measure that takes account of the underlying probability of whatever is being forecast. The Equitable Threat Score is one such measure. I’ll spare you (and me) the maths, but the ETS is ‘equitable’ because it adjusts for the ‘cheating’ that occurs if we just forecast more of whatever happens most often. It’s answering the question ‘how often did it rain when the Met Office said it would, after allowing for forecasts that would have been right by chance?’.

So is an ETS of 0.589 any good? Actually it’s not bad at all, and the Met Office is one of the world’s best weather forecasters. But there’s no getting around the problem that although rain is a lot more likely than a tornado, it still doesn’t rain all that often, even in Britain.

Obviously there’s a lot of regional variation, but the average for the whole country, on an hourly timescale, is that the probability of rain is about 8 per cent. In other words, if you choose 1000 hours of weather at random, about 80 of them will be wet.

Let’s assume, for the sake of argument, that the Met Office forecasts rain with about 90 per cent accuracy, which sounds pretty good to me. That means that 90 per cent of those 80 wet hours (72 hours) would be forecast correctly. Similarly, the forecast for 90 per cent of the remaining 920 dry hours would also be right; these 828 hours would be correctly forecast to be dry. So far so good, but that leaves 92 hours (920-828) of dry weather that would be forecast to be wet.

Which means that rain would be forecast for 164 hours (92+72) in every thousand, but rain would actually fall in only 72 of those hours. In other words, forecasts of rain are right less than half the time, even if rain really is forecast with 90 per cent accuracy.

What does all this mean for gardeners? Looking on the bright side, it’s forecasts of rain that are most likely to be wrong, so such a forecast should not deter you from getting out either the watering can or the lawnmower.

Ken Thompson is a plant biologist with a keen interest in the science of gardening. He writes and lectures extensively and has written five gardening books. His most recent is Where do Camels Belong? The Story and Science of Invasive Species.