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What a 60% chance of rain means

The morning forecast says "chance of rain in Seoul today: 60%". Should you take an umbrella? The answer splits the moment you ask how exactly to read the number. Some read it as "60% of Seoul gets rain", others as "it rains for 60% of the day", others as "it will rain a lot". All three differ from the Korea Meteorological Administration's (KMA) definition. This page first sets out the definition the KMA has given, then explains how it serves everyday decisions.

The KMA's definition of rain probability

Answer 12 in the FAQ of the big-data contest site run by the KMA defines rain probability as "the possibility, expressed as a probability, that precipitation falls at a designated place during the forecast period, in an atmospheric state similar to the present". The same answer explains that it is an empirical probability and that it means the probability of 0.1 mm or more of precipitation regardless of intensity or amount. Its example reads: with a 40% rain probability, it rained on about 4 of 10 days with weather conditions like today's.

We read this definition in the FAQ of a KMA-operated site. We also opened the KMA's forecast terminology page, but it describes only rainfall intensity (light rain, heavy rain and so on) and frequency words such as "at times" and "occasionally", and does not define rain probability. We could not confirm the same sentence in the KMA's official glossary, so the explanation below rests on this FAQ.

Three common misreadings

  1. It does not mean 60% of the area gets rain. The probability is the chance of rain at one place (a designated location). It is not the proportion of Seoul's area that is rained on.
  2. It does not mean it rains for 60% of the day. It is the chance of whether it rains at all, not the length of time. At 60% rain may last five minutes or half a day.
  3. It does not mean heavy rain. As the definition shows, 0.1 mm or more counts as rain whatever the amount. A 90% chance can be light rain, and a 30% chance can mean a downpour if it does come. The amount of rain must be read separately, from the expected rainfall rather than the probability.

All three arise from missing that the probability refers to a single event: "does 0.1 mm or more of rain fall at a particular place?"

What "6 out of 10" means

The frequency reading goes like this: a 60% rain probability means that if there had been 100 days with atmospheric conditions like today's, it rained on about 60 of them. Today does not "rain 60%"; today either rains or does not. The 60% is a figure drawn from the record of similar days. That is why one cannot judge a forecast right or wrong just by whether it rained afterwards. A day forecast at 60% that stayed dry is not a wrong forecast, and a day forecast at 40% that rained is not a wrong forecast either. Whether forecasts are good is judged by collecting hundreds of them and asking whether about 60% of the days forecast at 60% really had rain. This property is called the reliability (calibration) of probability forecasts. We did not verify any figure for the actual reliability of KMA forecasts and say nothing about it.

So should you take the umbrella?

The use of the number comes in decisions. Compare the inconvenience of carrying an umbrella with the cost of getting wet. Call the inconvenience c and the cost of getting wet L; if the chance of rain p is greater than c ÷ L, carrying the umbrella pays off on average. If, for example, you feel the inconvenience as 1 and being soaked as 5, carrying is better above 20%. The same person has a different L in different situations: on the day of an important interview, L is larger than usual and the threshold drops. Enter your own values in the calculator below. (The units for inconvenience and loss are arbitrary points.)

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What this shows is that "60%, so take it" or "30%, so leave it" is not one correct answer; at the same probability the right choice differs between people. A weather forecast does not make the decision for you; it supplies material for the decision.

Combining several days

If the chance of rain is 60% on each of three days in a row, what is the chance that at least one of the three days has rain? Assuming the days are independent, 1 − 0.43 = 93.6%. For five days, 1 − 0.45 = 99.0%. Weather is not independent from day to day, however: a rainy day makes a rainy next day more likely, so the real value can differ from the independent calculation. Treat it as a rough sense of how unlikely a run of dry days is, under the independence assumption. It is the same structure as "with many tries, at least one succeeds" in the earlier article on probability illusions.

How to read 0% and 100%

A 0% rain probability is better read as "it hardly ever rained on similar days" than as a promise that rain is impossible. We did not verify by what criteria the KMA displays 0% or 100%, so please check the KMA's guidance on that point. In probability forecasts 0% and 100% are edge values, used in practice when uncertainty is very small.

Link to lotteries

The structure of rain probability shows the same kind of difficulty as lottery probability: a probability is a figure about "the proportion among similar cases", not about a single event. The 1 in 8,145,060 chance that a Lotto ticket wins the jackpot does not foretell what happens to one game; it means one in eight million similar games. Reading a probability as a guarantee about a single event produces reactions such as "it said 60%, so why didn't it rain?" or "the odds are so low, so why did someone win?". Both come from reading probability wrongly.

A way to check for yourself: a forecast diary

If you wonder how trustworthy rain probabilities are, you can keep a record. For a month, write down each morning's forecast probability and whether it actually rained (rain that looks like 0.1 mm or more) that day, then take only the days forecast at 60% and count how many had rain. If 30 days were forecast at 60%, the average is 18 rainy days with a standard deviation of √(30 × 0.6 × 0.4) ≈ 2.7 days, so a 95% range is roughly 13 to 23 days. Inside that range, the forecast is not at odds with its 60% claim. Only if rain came on 10 days or on 26 would you have grounds for doubt. A month of records is often too little to judge, because the sample is small.

What the method teaches is important: evaluating a forecast is done not on one day but by collecting many days with the same probability. We did not keep such a diary, so we say nothing about what it would show.

Thinking by situation

Umbrella thresholds in invented situations (inconvenience = 1)
SituationCost of getting wet LThreshold 1 ÷ L
A short walk nearby250%
The usual commute520%
Going to an important meeting in a suit205%
Carrying outdoor filming equipment502%

At the same 30% chance of rain, leaving the umbrella is right in the first situation and taking it is right in the third. The larger the loss, the more reasonable it is to prepare even for a small probability. These numbers are invented values that turn feelings into numbers.

Limits

Sources and verification