numerical forecasting

(Also called mathematical forecasting, dynamical forecasting, physical forecasting, numerical weather prediction.) The integration of the governing equations of hydrodynamics by numerical methods subject to specified initial conditions.

Numerical approximations are fundamental to almost all dynamical weather prediction schemes since the complexity and nonlinearity of the hydrodynamic equations do not allow exact solutions of the continuous equations.
See numerical integration, numerical simulation.
Haltiner, G. J., and R. T. Williams 1980. Numerical Prediction and Dynamic Meteorology. Wiley, New York, . 477 pp.

See numerical weather prediction, climate prediction;

1. The study of the physics, chemistry, and dynamics of the earth's atmosphere, including the related effects at the air–earth boundary over both land and the oceans. Fundamental topics include the composition, structure, and motion of the atmosphere. The goals ascribed to meteorology are the complete understanding and accurate prediction of atmospheric phenomena.