The Probability of Precipitation: What Does it Mean?

My father-in-law runs a fruit farm, and made an interesting observation one day about weather prediction:

If the weather report says 40% chance of rain, it never rains. If it says 50%, then maybe it rains, maybe not. But if it says 70%, then it rains for sure.

This may seem self-contradictory, but it raises an interesting question: What do the predictions about the probability of rain in the weather reports even mean? How can you tell if the predictions are correct or not? If the weather report says there is a 60% chance of rain, and it actually rains, was the prediction correct? What if it doesn’t rain; does that mean the prediction is incorrect?

These are all very good questions, and are worth discussing with students in elementary probability classes. The easiest way to make sense of them is to adopt a relative-frequency interpretation of probability (see here or here); that is, to interpret “40% chance of rain” to mean that in an ensemble of many, many similar days, it will rain on 40% of those days.

This makes it straightforward to test such claims, and this would make a good project for children of a certain age. Collect daily data for a long period of time (at least a year, preferably longer). It is possible to collect historical data on amount of precipitation, although I am not sure that predictions are recorded. (The Weather Network does not seem to have them.) In any case, eventually students will be able to check on the reliability of the predictions after accumulating sufficient data. (And how much data is enough? This is a very good question, and leads to another teachable moment!)

Surely this kind of testing is done among meteorologists, right? It would be unwise to be making predictions for many years without checking them systematically to see if they have any validity, and indeed, this is an area of active research.

I have located an old academic paper in which the authors construct a formula for assessing weather predictions; it can be found here. A more recent example is here; since this is way outside my area of expertise, I’ll let interested readers follow up from these two references to search for more.

For some other relevant links, see the following:

• here is an attempt by the BBC to assess weather prediction by various UK  meteorologists
• an online tool for forecasting the weather yourself (students can do this as a class) using the dame data that professional meteorologists use
• Canadian National Climate Data and Information Archive is here
• Environment Canada criteria used in reporting predictions are here

(This post first appeared at my other (now deleted) blog, and was transferred to this blog on 25 January 2021.)