Most of us check the weather report most days. We want to know if its going to be rainy, snowy, windy, or sunny. I tend to check the weather report when I'm due to travel because if its bad, I won't be able to get out of the village.
Yes, it has happened when a storm blew in faster than expected and visibility dropped to nothing.
The type of math used in predicting weather is called numerical weather prediction. This is actually a branch of atmospheric sciences and was pioneered since World War II.
This type of math really took off in the 1980's when computing power reached a certain level. In addition, accuracy has improved with the better computing abilities.
Numerical Weather Predictions is composed of equations, numerical approximations, boundaries, domains and a couple of other things. What is most interesting are the equations they use in weather predicting.
1. Conservation of Momentum - 3 equations
2. Conservation of Mass for both water and air.
3. Conservation of Energy using the first law of thermodynamics
4. The relationship among density, pressure, and temperature.
The form of the equations vary slightly due to where in the world weather is being predicted. Wind patterns are different, humidity changes, pressure changes slightly due to elevation, and other factors. In addition all equations have to be converted to algebraic equivalents because computers can only do arithmetic, not calculus.
In addition, Reynolds Averaging is used to separate out the resolvable and unresolvable scales of motions in the equations themselves. This is accomplished by splitting the dependent variables into resolvable (mean) or unresolvable (turbulent) components.
If you noticed both physics and numerical calculations are heavily involved in predicting the weather. There are more factors involved in this process than I mentioned but if you check out
this presentation, it gives a good explanation of Numerical Weather Predictions and provides some excellent detail. It shows the actual math and provides detailed examples of all facets used in the process of predicting weather.