Producing a weather forecast

How computers predict weather

The significant improvements in Australian weather forecasting in recent decades have been largely due to enhanced weather analysis and prediction. This has been made possible from refinements in numerical weather prediction supported by progressively more powerful computers.

Day-to-day weather comes from the interactions of eddies or circulations which may range from a kilometre or less to thousands of kilometres. The eddies that will produce next week's weather may not yet exist.

Before we can predict the future state of the atmosphere we need to know its present state.

So the immense daily data from the world's national meteorological services (from ground stations, upper air observations, satellites, ships, buoys) is fed into computers, checked for accuracy, and mapped onto a three-dimensional grid. Each grid point represents a snapshot of atmospheric pressure, temperature,moisture and wind speed. These mathematical grid points do not necessarily coincide with observation points. Data allocated to each grid point is an interpolation of data from observation locations.

We can then predict the weather by solving very accurately the mathematical equations that represent the laws governing the way the atmosphere behaves.

These laws are expressed as mathematical equations ('primitive equations'), which must be integrated over time. They are the three equations of motion (derived from Newton's laws), the thermodynamic equation (representing conservation of energy), the gas laws (or equations of state), and the continuity equation (one for atmosphere, the other for water substance) which express the fact that mass is neither created not destroyed.

These form a set of simultaneous non-linear partial differential equations, which are extremely difficult to solve. No analytical method has been discovered for the full set of primitive equations, so we have to integrate them numerically: a complex task at the core of numerical weather prediction.

In the 1970s, meteorological modellers simulated southern hemisphere atmospheric processes using a grid size of 500 km. That fell to 200km in the mid-1990s, and 75 km today. Calculations were once performed at nine levels of the atmosphere; today around 30 layers are incorporated.

(right) A representation of surface and atmospheric grid points central to weather computing.