Weather forecasting estimates future meteorological conditions from observations and physical models. Numerical models use an approximate initial condition and equations of fluid mechanics to simulate future conditions; forecasters also compare model outputs and apply experience and research.[ref]
https://www.weather.gov/rah/virtualtourforecast. National Weather Service, The forecast process
The forecast horizon describes how far ahead a prediction remains useful at a specified accuracy; sensitive dependence on initial conditions can limit detailed predictions under deterministic evolution.An ensemble runs multiple forecasts with perturbed initial states, model parameters or physical formulations to represent uncertainty. Its distribution can indicate probabilities and sensitivity, but finite sampling or shared model errors can make the ensemble underdispersive. Growing initial perturbations can be selected using right singular vectors of a finite-time propagator.
Combining observations with a dynamical prior estimates an initial atmospheric state and its uncertainty. In a linear Gaussian update, analysis increments are with , where and are prior and observation error covariance matrices. Observation noise, sparse coverage and incorrect model or covariance assumptions can all leave forecast errors.
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Weather forecasting is the practice of predicting atmospheric conditions at a specific location over a set time period. This involves analyzing various meteorological data, including temperature, humidity, precipitation, wind speed and direction, atmospheric pressure, and cloud cover, among other factors. Forecasting utilizes a combination of observational data from weather stations, satellites, and radars, as well as computer models that simulate the atmosphere's behavior.