Numerical Weather Prediction

Numerical weather prediction forecasts the atmosphere by solving its governing equations on a computer, marching the simulated air, moisture, and energy forward grid point by grid point from an observed starting state.

Definition

Numerical weather prediction is the practice of forecasting weather by numerically integrating the discretized equations of atmospheric motion and thermodynamics forward in time from an analyzed initial state.

Scope

This topic covers the formulation of atmospheric models for forecasting: the discretization of the primitive equations onto grids or spectral bases, the dynamical core that advances the resolved flow, the parameterizations representing unresolved processes such as convection, clouds, radiation, and turbulence, and the resolution and computational trade-offs involved.

Core questions

• How are the continuous governing equations turned into a computable model?
• What is a dynamical core and how does it advance the resolved flow?
• How are unresolved processes such as convection and radiation parameterized?
• How do grid resolution and numerical stability constrain forecasts?

Key theories

Primitive-equation modeling

Operational forecast models integrate the primitive equations, the hydrostatic and filtered form of the fluid and thermodynamic laws, discretized in space and time to advance temperature, wind, pressure, and moisture.

Physical parameterization

Processes too small to resolve on the model grid, such as cumulus convection, cloud microphysics, radiation, and boundary-layer turbulence, are represented by parameterization schemes that estimate their net effect from the resolved variables.

Mechanisms

A numerical model represents the atmosphere by its values at discrete grid points or spectral coefficients and steps them forward with finite-difference, finite-volume, or spectral methods, subject to stability limits that link the time step to the grid spacing. The dynamical core handles advection, pressure-gradient, and Coriolis effects, while parameterizations supply the tendencies from convection, clouds, radiation, surface fluxes, and turbulence that the grid cannot resolve. Higher resolution captures more phenomena but multiplies the computational cost.

Clinical relevance

Numerical weather prediction is the engine of modern operational forecasting, supplying the guidance behind public, aviation, marine, and severe-weather forecasts; advances in model resolution and physics have steadily extended forecast skill and now also support climate projection and environmental prediction.

History

Richardson sketched numerical forecasting by hand in the 1920s with limited success; the field became practical when Charney, Fjortoft, and von Neumann produced the first computer forecast of the barotropic vorticity equation on ENIAC around 1950, after which models grew from single-layer to multi-level primitive-equation systems with ever more sophisticated physics.

Key figures

• Lewis Fry Richardson
• Jule Charney
• John von Neumann
• Norman Phillips

Seminal works

• kalnay2003
• charney1950

Frequently asked questions

What is the difference between a weather model and a forecast?

A weather model is the computer program that solves the atmospheric equations; a forecast is the output it produces for a particular run, which a meteorologist then interprets, often alongside other models, before issuing a prediction.

Why do models have to parameterize some processes?

Important processes such as individual clouds and turbulent eddies are far smaller than a model's grid spacing, so they cannot be resolved directly; parameterizations estimate their collective effect on the resolved-scale flow instead.