Definition
Modern weather forecasting is fundamentally probabilistic. Meteorological services run ensembles of atmospheric simulations — each starting from slightly perturbed initial conditions — and report the distribution of outcomes as the forecast. A '70% chance of rain' is not a guess but the fraction of ensemble members that produce rain at the location.
The shift to ensemble forecasting in the 1990s, combined with massive supercomputing and data assimilation, turned weather prediction into a leading example of operational probability.
Why it matters
How it works
A weather model is a system of partial differential equations describing fluid dynamics in the atmosphere, discretised on a grid covering the globe. The model is initialised from observations (satellites, balloons, ground stations), integrated forward in time, and the output is the forecast. Because initial conditions are imperfect, an ensemble of perturbed initial states is run; the resulting spread is the forecast uncertainty.
Probabilities are then read off the ensemble or post-processed with statistical corrections that account for known model biases. The output is what we see on weather apps — temperature distributions, precipitation probabilities, severe-weather risks.