How a model is computed
Grid boxes, equations, time steps and the parts of the weather that have to be approximated.
Step 1: cut the atmosphere into boxes
A model divides the atmosphere into a three-dimensional grid. Horizontally, the distance between neighbouring points is the grid spacing, for example 9 km. Vertically, the model stacks many layers from the surface to the top of the atmosphere, thin near the ground where the weather happens and thicker higher up. Every box holds a single value for each variable: wind, temperature, pressure, humidity, cloud water.
Step 2: the equations
In plain words, the model keeps track of five things for every box and how they change from one moment to the next:
- Motion: air is pushed by pressure differences, slowed by friction and bent by the Earth’s rotation (this is why wind circles around lows).
- Mass: air that flows out of one box flows into the next; nothing is created or lost.
- Heat: air warms when it sinks or is heated by the sun and the surface, and cools when it rises or loses heat by radiation.
- Water: vapour, cloud droplets, ice and rain move between boxes and change form, releasing or absorbing heat.
- The gas law: ties pressure, temperature and density together.
Step 3: time steps
The model does not jump to tomorrow. It advances in small time steps, from a few tens of seconds for the finest grids up to several minutes for global models, recalculating every box each time. A finer grid needs shorter steps to stay stable, so the cost grows quickly with resolution. A forecast to day ten means thousands of steps.
Step 4: what is too small to see
Many important processes happen on scales smaller than a grid box, and the model represents them with simplified rules called parametrisation. The main ones:
| Process | Why it needs a rule | Where you notice it |
|---|---|---|
| Convection (showers and thunderstorms) | Individual cells are a few km wide; coarse grids cannot simulate them | Squalls, local heavy rain, gusts |
| Turbulence near the surface | Eddies of tens of metres mix air close to the sea and land | Mean wind and gusts at 10 m |
| Clouds and rain formation | Droplets and ice form on micrometre scales | Cloud cover, rain amounts, visibility |
| Radiation | Sun and heat exchange between layers and the surface | Day and night temperature, sea breeze strength |
| Surface exchange | Heat, moisture and friction depend on land type and sea state | Coastal winds, fog, land-sea contrasts |
Different centres choose different rules, and this is one of the main reasons models disagree: see Why models disagree.
Step 5: the edges, and the cost
- A global model has no edges. A regional model needs boundary conditions at its edges from a global model, updated as the run proceeds.
- Halving the grid spacing doubles the number of boxes in each horizontal direction (four times as many) and needs about twice as many time steps: roughly eight times the computing for the same area and length. That is why a 1.5 km model covers a country, not the world.
- The finished run is saved as files of gridded values at hourly or three-hourly steps. Those are what you download: GRIB files.