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← What a Chance of Rain Means

What a Chance of Rain Means

Three short lessons on the number in every forecast: what a "30% chance of rain" is a share of, how that one number is built from two, and how you can check whether a forecaster is any good.

Spark & Whetstone · sparkwhetstone.org/learn/what-a-chance-of-rain-means · CC BY-NC-SA 4.0. Answers are at the end, so you can try each question first.

Lesson 1. Thirty per cent of what?

A forecast says "30% chance of rain tomorrow". A study that asked people in five cities what that means found at least three answers: rain for 30% of the day, rain over 30% of the area, or rain on about 3 of every 10 days like tomorrow. Only in New York did most people give the forecaster’s meaning, the third one.

The trouble is not arithmetic. A probability is a share of something, and the forecast does not say of what. The fix the researchers suggested is to name the reference class: "on days like tomorrow, it rains here on about 3 in 10".

Teenagers on Spark & Anvil meet the same question in 30% Chance of Rain, and younger children count rainy days in a week, which is where the idea of "out of how many" starts.

Question. Which reading is the forecaster’s meaning of "30% chance of rain tomorrow"?

  1. Rain at a given spot on about 3 in 10 days like this
  2. Rain will fall over 30% of the whole area around the town
  3. It will rain 30% of the day

Say it back. In your own words: what does a 30% chance of rain count, and why do people read it so differently?

Lesson 2. One number built from two

In the United States the chance of rain is worked out as the forecaster’s confidence that rain will fall somewhere in the area, multiplied by the share of the area it would cover. Half sure of rain over six tenths of the area gives 0.5 × 0.6 = 0.3, so 30%.

Certain of showers over three tenths of the area gives 1 × 0.3 = 0.3 as well. Both days print 30%, but one is "maybe a big rain" and the other is "surely some scattered showers". The single number hides how it splits.

Question. A forecaster is 80% sure of rain, and if it comes it would cover half the area. What chance of rain does the forecast give?

  1. 40%
  2. 30%
  3. 130%

Say it back. In your own words: which two numbers make up a chance of rain, and what can one printed number hide?

Lesson 3. Checking a forecaster

You can check a forecaster yourself. Keep a list of the days they said 30%, and count how many of them it rained where you are. A good forecaster is calibrated: over many 30% days, it rains on about 30 of every 100. If it rained on 60 of them, their 30% means more than they say.

Weather services score this with the Brier score: for each forecast, square the gap between the chance given and what happened (1 if it rained, 0 if not), then average. Saying 30% on a day it stays dry costs 0.09; saying 90% on that day costs 0.81. Lower is better, and hedging every day at 50% scores a steady 0.25.

WeatherForge’s Forecaster’s Confidence Ledger has children forecast, say how sure they are, and see their own Brier score.

Question. A forecaster said 90% chance of rain and it stayed dry. What is the Brier score for that day?

  1. 0.90
  2. 0.81
  3. 0.10

Say it back. In your own words: how could you find out whether a forecaster’s "30%" really means 30%?

At the table: The family forecast jar

Players: Two or more, ages 7 and up. You'll need: A jar, slips of paper, a pen, and a week or two of evenings.

  1. Each evening, everyone writes their chance of rain for tomorrow (0%, 30%, 50%, 70% or 100%) on a slip and puts it in the jar.
  2. The next evening, say whether it rained at home. Sort the slips by the chance written on them.
  3. After a week or two, look at each pile: did it rain on about as many days as the number promised?
  4. Talk about who was most often right, and who was most sure when wrong. Nobody wins; the jar keeps count.

Answers

  1. Rain at a given spot on about 3 in 10 days like this — The number counts days like tomorrow: on about 3 of every 10 of them, rain falls at a given spot. The other two readings are common but are not what the forecast means.
  2. 40% — 0.8 × 0.5 = 0.4, a 40% chance of rain at a given spot.
  3. 0.81 — The gap is 0.9 − 0 = 0.9, and 0.9 squared is 0.81. A confident miss costs far more than a cautious one.