Comment by cubefox

Expected value is already what most forecasts show. Expected value conveys information poorly in some common cases, like thunderstorms in the summer. It is very different to hear there's a 20% chance of a thunderstorm, dropping an inch of rain, vs. a 100% chance of .2" rain - the former needs a backup plan to deal with rain, the latter needs to plan for rain. Hence I prefer the text forecasts from the NWS, which list an amount possible, plus more in thunderstorms, rather than a bare number.

Meanwhile the 'probability' listed in forecasts is also well defined as an expected value - it's (probability of X% rain coverage) * (X %), over all X. (Rain is defined as > .01")

I tend to use probability more for decision making - usually trying to determine whether I need to bring an umbrella or rain gear with me on a given day. If the probability is low I can usually just look out the window and time my trips outside when it’s not raining and probably get by without rain gear. Whereas a high probability means I’m probably going to need to go out in the rain at some point, and need to pack appropriately.

I also do a lot of cycling, and total duration spent in the rain tends to matter more to me than the amount of rainfall. I don’t mind riding through a quick downpour or two on a ride if I can dry out in between, but spending several hours in constant rain can be miserable (and hypothermia becomes a concern) - even if it’s light rain.

Of course expected amount definitely has uses, too. For example if there is rain forecast for tonight, and I’m trying to determine the probability that a field will be usable for practice in the morning.

Anyway I would say that both probability and expected amount are important, and any competent weather app should offer both. The Apple Weather app only shows hourly forecasts for expected amount, and that alone would be enough to be a dealbreaker for me.

Not a meteorologist, just a computer science guy that read a couple of papers.

My understanding is that the probabilities in weather forecasts aren't a probability at all, but rather a coverage measure. Local weather models are computed in discrete grid coordinates of say 10km. Every grid cell of 10km^2 has a single set of computed forecast data. The percentage is a measure of how much of that area received rain in the timeframe, not of probability of rain, but of coverage of rain.

Author here -- I wholeheartedly agree. I recommend reading up on some of the research in uncertainty visualization. There's a good example of visualizing the probability that a bus will arrive in the next X minutes that feels similar.

https://www.youtube.com/watch?v=E1kSnWvqCw0

Relatedly, I'm fasinated by how much human judgement goes into those numbers. A meteorologist with local expertise looks at a few different models, decides which are more likely to be accurate, and then fills out a grid.

Just to hop on this, the standard is counter intuitive for rain probability. I'm annoyed, but also fascinated by how much it "makes sense" when I have read about it, but it also "makes no sense" when I just want to know: should I get my jacket? :)

Loose definition (with errors and assumptions, but helps some without getting into actual probability math):

If it says "30%" - many of us have heard "30% chance of showers". It is NOT "30% chance of showers"; it actually is "100% percent chance of rain, over 30% of the area, within a given time, of a particular amount of rain."

Which is STILL (to me), difficult for the average person to comprehend.

Copying and pasting from Weather.com (linked PDF - https://www.weather.gov/media/pah/WeatherEducation/pop.pdf)

PRECIPITATION PROBABILITY The probability of precipitation forecast is one of the most least understood elements of the weather forecast. The probability of precipitation has the following features: ..... The likelihood of occurrence of precipitation is stated as a percentage ..... A measurable amount is defined as 0.01" (one hundredth of an inch) or more (usually produces enough runoff for puddles to form) ..... The measurement is of liquid precipitation or the water equivalent of frozen precipitation ..... The probability is for a specified time period (i.e., today, this afternoon, tonight, Thursday) ..... The probability forecast is for any given point in the forecast area To summarize, the probability of precipitation is simply a statistical probability of 0.01" inch of more of precipitation at a given area in the given forecast area in the time period specified. Using a 40% probability of rain as an example, it does not mean (1) that 40% of the area will be covered by precipitation at given time in the given forecast area or (2) that you will be seeing precipitation 40% of the time in the given forecast area for the given forecast time period. Let's look at an example of what the probability does mean. If a forecast for a given county says that there is a 40% chance of rain this afternoon, then there is a 40% chance of rain at any point in the county from noon to 6 p.m. local time. This point probability of precipitation is predetermined and arrived at by the forecaster by multiplying two factors: Forecaster certainty that precipitation will form or move into the area X Areal coverage of precipitation that is expected (and then moving the decimal point two places to the left) Using this, here are two examples giving the same statistical result: (1) If the forecaster was 80% certain that rain would develop but only expected to cover 50% of the forecast area, then the forecast would read "a 40% chance of rain" for any given location. (2) If the forecaster expected a widespread area of precipitation with 100% coverage to approach, but he/she was only 40% certain that it would reach the forecast area, this would, as well, result in a "40% chance of rain" at any given location in the forecast area.