Weather Math
I have backed myself into a corner, where my understanding of weather forecasts and of statistics collide. I've never been really wild about statistics; it's a numbers-dance that I understand the purpose of, and as a scientist have had to use, but am just as likely to be bamboozled by numberical hand-waving as the average citizen.
So here's my conundrum, straight off of weather.com:
Tomorrow, for example, there's a 20% chance of rain.
I click for the hourly forecast, and see the day broken into 3-hour chunks: 10%, 10%, 10%, 20%, 20%, 20%, 20%, 10%.
Wait, how is that supposed to add up??
What I'd always blithely assumed was that "20% chance of rain on Thursday" means that if I put a bucket out at 12:01am, there's a 1 in 5 chance that it will have water in it by 11:59pm. I would still tend to believe that this is what it's supposed to mean, but I would also like to believe that "20% chance of rain on Thursday early-evening" means that if I put a bucket out at 5:01pm, there's a 1 in 5 chance that it will have water in it by 7:59pm. If both those definitions were true, then adding up hourly forecasts to make a daily forecast can't possibly be straightforward - the more frequently you measure, the more chances you have to turn up rain.
Say the 20% applies once per hour, then for a 24-hour period that's (.2)^24=~1.7x10^-17 that it's raining all day long, or (.8)^24=~0.5% that it's dry all day long, meaning a 99.5% chance that it rains at least once during the day. For the 3-hour timeblocks as above, chance of at least one rainy segment drops to 70% - it got much drier simply by measuring less often.
Maybe the issue is with "rain". Maybe "rain" doesn't mean that there was a drop of water, but that the time period in question is considered "rainy", i.e. actively precipitating for some percentage of the time segment involved... or maybe not a percentage, but "for at least 5 minutes of"... or maybe requiring some amount of water rather than some length of time... This is the point at which I get too irritated to actually try to figure this out, and resort to whining on the internet. I have a feeling there's a website out there that would explain this, but also that I'd probably have to slog through a lot of bad explanations (incorrect explanations?) and way-more-technical-than-I-wanted explanations to get the right sense of what's going on, and I honestly don't have the patience.
In general, I've been going with the idea that it doesn't matter how I interpret a forecast, it's still not so likely to be correct, so maybe it doesn't much matter.
So here's my conundrum, straight off of weather.com:
Tomorrow, for example, there's a 20% chance of rain.
I click for the hourly forecast, and see the day broken into 3-hour chunks: 10%, 10%, 10%, 20%, 20%, 20%, 20%, 10%.
Wait, how is that supposed to add up??
What I'd always blithely assumed was that "20% chance of rain on Thursday" means that if I put a bucket out at 12:01am, there's a 1 in 5 chance that it will have water in it by 11:59pm. I would still tend to believe that this is what it's supposed to mean, but I would also like to believe that "20% chance of rain on Thursday early-evening" means that if I put a bucket out at 5:01pm, there's a 1 in 5 chance that it will have water in it by 7:59pm. If both those definitions were true, then adding up hourly forecasts to make a daily forecast can't possibly be straightforward - the more frequently you measure, the more chances you have to turn up rain.
Say the 20% applies once per hour, then for a 24-hour period that's (.2)^24=~1.7x10^-17 that it's raining all day long, or (.8)^24=~0.5% that it's dry all day long, meaning a 99.5% chance that it rains at least once during the day. For the 3-hour timeblocks as above, chance of at least one rainy segment drops to 70% - it got much drier simply by measuring less often.
Maybe the issue is with "rain". Maybe "rain" doesn't mean that there was a drop of water, but that the time period in question is considered "rainy", i.e. actively precipitating for some percentage of the time segment involved... or maybe not a percentage, but "for at least 5 minutes of"... or maybe requiring some amount of water rather than some length of time... This is the point at which I get too irritated to actually try to figure this out, and resort to whining on the internet. I have a feeling there's a website out there that would explain this, but also that I'd probably have to slog through a lot of bad explanations (incorrect explanations?) and way-more-technical-than-I-wanted explanations to get the right sense of what's going on, and I honestly don't have the patience.
In general, I've been going with the idea that it doesn't matter how I interpret a forecast, it's still not so likely to be correct, so maybe it doesn't much matter.