Numerical Weather Prediction works by converting the atmosphere into a mathematical problem that computers solve using the laws of physics. The process begins with data collection from satellites, weather stations, balloons, aircraft, ships, and radar. These observations are then combined through data assimilation, which blends them with a previous short-term forecast to create a balanced, three-dimensional snapshot of the current atmospheric state—the initial condition.

The model divides the atmosphere into a three-dimensional grid of cells and solves the primitive equations (a simplified form of the Navier-Stokes equations adapted for a rotating Earth) within each cell. These equations describe conservation of mass, momentum, and energy, along with thermodynamic relationships. The model repeatedly calculates how variables like temperature, pressure, wind, and humidity change over very short time intervals—typically minutes—stepping the forecast forward hour by hour or day by day.

Physical processes too small to resolve explicitly, such as individual clouds, turbulence, and convection, are represented through parameterization—simplified formulas that estimate their overall impact on the larger grid. Because the atmosphere is chaotic and observations incomplete, operational centers run ensemble forecasts: multiple model runs with slightly different initial conditions or physics to quantify uncertainty and show a range of possible outcomes.

Raw model output undergoes post-processing to correct known biases and translate numerical results into usable forecasts. Forecasts are continuously verified against observations to identify model errors and guide improvements. The atmosphere's inherent chaos and imperfect initial conditions and models limit forecast accuracy, with deterministic skill typically declining beyond 10–14 days, though probabilistic information from ensembles can extend further.