The Grid, and What Falls Between

A model carves the atmosphere into millions of boxes. Anything smaller than a box cannot exist inside it.

The geometry of a forecast

Every numerical weather model begins with a choice that shapes everything else: how fine a mesh to lay over the atmosphere. Longitude lines, latitude lines, and a stack of pressure or height levels create a three-dimensional grid of cells. At each intersection sits a single number for temperature, a single number for humidity, a single vector for wind. The atmosphere at that point, in all its turbulent complexity, is reduced to a column of values. The model then advances those values forward in time, cell by cell, step by step, and what emerges is a forecast.

It sounds like bookkeeping, and in a sense it is. But the grid is not merely an administrative convenience — it is a fundamental statement about what a model can and cannot know. A feature smaller than the distance between two grid points is invisible to the model. It does not blur; it does not simplify; it simply does not exist. The gap between grid points is called the model's resolution, and that word carries more weight than it first appears.

The European Centre for Medium-Range Weather Forecasts ↗, based in Reading, England, runs one of the highest-resolution global forecast models in the world. Its global model has operated at horizontal resolutions that have shrunk from roughly 200 kilometres in the 1980s to around 9 kilometres today for its highest-resolution deterministic run. Each halving of grid spacing multiplies the number of cells by four and the computation required by roughly eight, because you also need finer time steps to keep the mathematics stable. Resolution is expensive in every sense.

National meteorological services operating at the regional scale push finer still — 1 to 4 kilometres over a limited area — and at those scales individual thunderstorm cells begin to be resolvable. But no operational global model can resolve a street, a valley, or a single cumulus cloud. The grid is always coarser than the weather.

What the grid cannot hold

Rain begins as updrafts inside clouds. A cloud forming over a heated hillside might span a kilometre. A vigorous convective cell might span ten. The grid spacing of even a high-resolution regional model may be comparable to, or larger than, the cloud itself. The model cannot represent the updraft directly. It can only see that a column of air is warm and moist and unstable, and infer from that observation — through a set of equations called a parameterisation scheme — that convection probably occurs, and estimate how much precipitation probably results.

Parameterisation is a kind of organised guesswork. It takes a physical process too small to resolve and replaces it with a formula that approximates the statistical effect of that process on the grid-scale variables we do track. Turbulence in the boundary layer — the lowest kilometre or two of the atmosphere — is parameterised. The formation of cloud droplets is parameterised. The radiative effect of aerosols is parameterised. Each scheme embeds empirical constants tuned against observations, and each introduces a margin of error that propagates forward through the forecast. The schemes interact, too: a slightly wrong boundary-layer turbulence scheme affects how much moisture reaches the level where clouds form, which affects precipitation, which affects the surface energy budget. Errors compound.

Hills compound them faster. Orography — the shape of the terrain — matters enormously: a ridge forces air upward and triggers precipitation on its windward flank while leaving a rain shadow on the lee. The Alps, the Rockies, the Scottish Highlands all impose their geometry on the atmosphere in ways that models must represent. At coarse resolution, a model might see the Alps as a broad, gentle swell rather than a jagged wall, and the rain shadow it produces will be in the wrong place, or too weak, or too diffuse. This is not a flaw in the mathematics. It is a flaw in the geometry — the grid simply cannot hold the true shape of the land.

The choices that propagate

Grid design is not a single decision but a cascade of them. Vertical resolution matters as much as horizontal: a model with too few layers in the lower troposphere will misrepresent the temperature inversions that trap fog, or the thin stable layers that govern where a front stalls. Most operational models now use somewhere between 60 and 140 vertical levels, with finer spacing near the surface where gradients are steepest and coarser spacing higher up where the atmosphere is more homogeneous. That spacing is itself a choice shaped by computational budget.

Time step — the interval at which the model advances — is constrained by the grid spacing through a mathematical condition worked out in the 1920s by Richard Courant, Kurt Friedrichs, and Hans Lewy. Reduce the grid spacing and you must reduce the time step or the arithmetic becomes unstable. A model with a 9-kilometre grid might use a time step of a few minutes; a model at 1 kilometre may need one measured in seconds. More steps, more computation, more time before the forecast is ready — and a forecast ready after the weather has passed is no forecast at all.

The question of what to resolve and what to parameterise is therefore partly physical and partly economic. Jule Charney, who led the team that produced the first successful numerical weather forecast in 1950 ↗ on the ENIAC computer at the Aberdeen Proving Ground in Maryland, understood early that the grid is a constraint to be designed around rather than a problem to be eventually solved. His team filtered out small-scale features deliberately, not because they lacked ambition but because they understood that premature resolution of processes you cannot yet parameterise correctly will degrade the forecast, not improve it. Adding detail too fast, before the physics is ready, introduces noise rather than signal.

When finer is not better

It might seem that more resolution is always preferable — that the path to better forecasting is simply to wait for faster computers and shrink the grid. History partly supports this: forecast skill at medium range has improved substantially over the past four decades, and better resolution is one reason. But resolution is not the only reason, and it is not always the binding constraint.

Data assimilation — the process of ingesting millions of observations and reconciling them with the model's prior state — becomes harder, not easier, at finer resolution, because errors in the observations project onto smaller scales where they are harder to identify and smooth. A grid that can resolve a 2-kilometre shower is only useful if you actually know what the atmosphere looks like at 2-kilometre scales when the forecast starts. Observations are sparse. The ocean is observed far less densely than the land. The upper atmosphere is sampled at balloon launch sites that are hundreds of kilometres apart in many regions. The model knows what it knows, and what it knows is interpolated into cells whose contents are averages, not measurements.

The grid, in the end, is a negotiation between ambition and reality. It is as fine as the physics understanding, the observation network, and the available computation jointly allow. What falls between the grid points is not lost — it is represented, approximated, parameterised, tuned — but it is never quite the same as being there. Every forecast carries the ghost of the boxes that made it.