How a model is actually run

It is a pipeline of decisions, data, corrections and approximations — all of which have to finish before the window closes.

From observations to first guess

At a fixed time — in global operations, typically 00 UTC and 12 UTC — the pipeline opens. Observations start arriving: surface stations, ships, aircraft filing automated reports, radiosondes ascending through the troposphere, satellites, ocean buoys. No two observations are taken at the same place, the same altitude or precisely the same moment, and many arrive late. The model cannot wait indefinitely. There is a cutoff, and any observation that misses it is simply not used.

What the model needs is not a scattering of point measurements but a complete, continuous three-dimensional description of the atmosphere — temperature, wind speed and direction, humidity, pressure — at every grid point, from the surface to the stratosphere. To get from the former to the latter, forecasters use a process called data assimilation. The principle is that you already have a previous forecast covering this moment in time — called the background field or the first guess. Data assimilation adjusts that background toward the incoming observations, weighting each by its estimated reliability. A radiosonde over the ocean, where the background is poorly constrained, carries more weight than a surface thermometer in a region already dense with measurements. The result — called the analysis — is the best achievable snapshot of the atmosphere at the starting time.

The European Centre for Medium-Range Weather Forecasts ↗, based in Reading, England, runs one of the most sophisticated assimilation systems in the world, using a technique called four-dimensional variational assimilation, or 4D-Var, which fits the background field to observations spread across a twelve-hour window rather than a single moment. This is computationally expensive, and it is also genuinely better: the atmosphere does not freeze for the convenience of a snapshot.

Dividing the atmosphere into boxes

The analysis now has to be translated into the model's own language. A numerical model divides the atmosphere into a three-dimensional grid — columns of boxes stacked from the surface upward, each box assigned a single value for temperature, wind, humidity and so on. The horizontal spacing between grid points defines the model's resolution. At the finest resolutions in current operations, that spacing is a kilometre or two for limited-area models; global models operate at somewhat coarser spacing, though the gap has narrowed significantly over the decades.

Anything smaller than one grid box cannot be represented directly. A single convective shower, a small valley that channels wind, a patch of sea ice — these fall below the threshold. The model handles them through parameterisation: a set of equations that estimate the statistical effect of sub-grid processes on the larger-scale flow. Parameterisation schemes exist for clouds, convection, turbulence, radiation and the exchange of heat and moisture between the surface and the atmosphere. Each scheme contains tunable coefficients, and tuning them is as much art as science — the modeller adjusts them until the model's climatology (its average behaviour across many runs) matches observations. A scheme that works beautifully for mid-latitude frontal rain can perform poorly in the tropics, where convection organises differently.

Running the equations forward in time

With the analysis loaded and the parameterisation schemes engaged, the model steps forward in time. At each time step — which might be minutes, depending on grid spacing — it applies the governing equations of fluid dynamics and thermodynamics to every grid box, computing how the state of each box will change given the states of its neighbours. The equations descend from those that Vilhelm Bjerknes wrote down in 1904, when he stated the problem of weather prediction as one of initial-value physics: given the state of the atmosphere now, calculate its future state. Lewis Fry Richardson then demonstrated, at enormous personal cost, that the calculation was genuinely possible — if you had enough people, or eventually enough machine.

The machine arrived in 1950. Jule Charney and colleagues at the Institute for Advanced Study in Princeton ran the first successful numerical forecasts on ENIAC, producing results that were recognisably useful after roughly a day of computation. The same calculation now runs in minutes on supercomputers that would be unrecognisable to anyone from that era. The ECMWF supercomputer ↗ performs on the order of tens of petaflops — quadrillions of floating-point operations per second — and the model must finish its run in time for the forecast to be of any use to anyone. A twelve-hour forecast that takes thirteen hours to compute is worthless.

What comes out and what happens to it

The raw output of a model run is not the forecast a person sees. It is an enormous set of numbers — the state of every grid box at every output time step, typically every hour or every three hours, out to the forecast lead time. For a global model running to ten days, that is a dataset of considerable size: gigabytes, often terabytes, depending on the number of vertical levels and output variables requested.

Post-processing converts raw model output into usable products. Statistical correction schemes — sometimes called model output statistics, or MOS — adjust the model's raw numbers using a long record of how the model has performed against observations in the past. If a particular model systematically underestimates overnight cooling in valleys, MOS will correct for it. This is verification feeding back into the production chain: the record of how forecasts perform shapes how the next batch is adjusted before it reaches a user.

Most major centres now run ensembles rather than a single deterministic forecast. The model is run many times from slightly different starting analyses — each perturbed within the bounds of observational uncertainty — and the spread of results gives a measure of confidence. Where the ensemble members agree, confidence is high. Where they diverge — typically at longer lead times, or in regions of active cyclogenesis — the spread itself is informative. It tells a forecaster that the atmosphere is in a state where small differences matter enormously, a property that Edward Lorenz, working in Cambridge, Massachusetts, described mathematically and that now has a measured timescale attached to it rather than a mere philosophical reputation.

The final step before any of this reaches the public is human interpretation. A forecaster at a national centre — the Met Office in Exeter, or NOAA's operations centres across the United States — reads the model output, notes where the guidance is uncertain or where local effects the model cannot resolve are likely to matter, and applies trained judgement. The model does the physics; the forecaster does the reading. Both are necessary, and the handover between them is quieter and more continuous than the word "forecast" suggests.