As others said, the “40%” means they think that 40% of an area will get rain. They cannot be certain if it will be one neighborhood or another though.
And as for what goes into that, weather predictions are based almost 100% on taking the current weather conditions that you have, and comparing it to past data and what happened in the past.
That is how weather models on computers work, they take the current weather data and compare it to DECADES of data that has been collected. So if the computer sees that condition XYZ is happening now, and that if the past 10 times XYZ happened it rained 8 of those 10 times, well it’s probably gonna rain again then.
And removed that the “XYZ” condition involves taking multiple kinds of data from multiple sources.
Models to predict weather rely on historic weather data. The models will look for times when conditions today are similar to conditions seen in the past. Now, weather has a lot of factors that play into it. Local temperature, pressure, and humidity as well as the factors of nearby regions that may cause weather fronts to move and change. As such, conditions today are likely not to be exactly like those seen in the past. So models will take the closest examples and examine how often those examples resulted in precipitation. For example, if 40% of similar conditions in the past resulted in rain, the weather prediction will report a 40% chance of rain.
From Weather.gov:
>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…
>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.
[Source](https://www.weather.gov/media/pah/WeatherEducation/pop.pdf)
Weather is basically the physics of the atmosphere. Precipitation is when certain conditions are met. So the idea behind prediction is that if we know the current state of the atmosphere, we can predict the next state.
Imagine a billiards game with several balls moving. If you have a fast enough computer, you can tell what’s going to happen, which balls will hit each other etc, before it’s happening. This is the goal with weather forecasting: tell what’s going to happen before it happens.
To do that on a billiards table, you have to measure the position and the speed of each ball. Maybe it’s and old table, has some uneven spots, you have to take that into consideration.
With the weather, you also have to measure things such as temperature, air pressure, humidity, wind speed. Here comes the first challenge: you cannot measure everything and everywhere. You can have a grid of measurement system and blind holes in between. At some points you have more data points because you have a better station that also measures dust concentration for example. And no matter how good your measurement grid is, it will end somewhere, at the country border or at the ocean. There will be always something coming into your grid that you cannot foresee.
So now you have a lot of data, and we also have a lot of knowledge. The knowledge is basically a set of mathematical equations that can tell if these are the measurements then the air will do this. Will it go up and form clouds? Will it go sideways? Will two blocks of wet air collide or they miss each other?
Now the problem is that these equations are very very difficult to solve even for a supercomputer. You see there’s a time constraint, you measure the data today and by the evening you want tomorrow weather. So the equations must be simplified a bit.
And because of the imperfect measurement and the imperfect math equations you use, the results will also be imperfect. It’s like: we calculated rain, but we’re not very certain about it, because in these calculations those imperfections matter a lot. The reason is that in some cases a little difference in the raw data multiplies by a lot, so when you calculate the best case scenario and the worst case scenario, the two results are very far away. One calculation says the air goes up, the other say the air goes to west. On better days when all your raw measurements tend to point in the same direction, all your calculations are similar so you are more sure.
So that’s why you have these percentages, and what they exactly mean, depends on what the uncertainty was. It can be an uncertainty of whether the precipitation forms at all, but also where and when it goes. So if an area is either hit or not, then it’s kind of a 50% rain at that spot. Maybe it will be hit but only tomorrow which is translated as 50% today.
And of course the longer time span you want to predict, the more uncertainties you will have.
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