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Earth Science 1922

Weather Prediction by Numerical Process

Lewis Fry Richardson

Predict the weather by solving the equations of the atmosphere, one time-step at a time.

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In depth · the introduction

In 1922 a Quaker mathematician worked out how to predict the weather from nothing but the laws of physics and arithmetic — and got an answer that was wildly, instructively wrong.

The idea, unpacked

The weather is not magic; it is air obeying physics. If you know the air's pressure, temperature, humidity and motion everywhere right now, the equations of physics tell you how each of those will change over the next few minutes. Do that arithmetic, step a few minutes forward, then repeat — and you have computed the future.

Richardson's leap was to take that literally. He laid a grid of cells over the map and, cell by cell, ground the equations forward by hand. No folklore, no “red sky at night” — just numbers marching the atmosphere into the future. Every weather forecast you have ever seen works this way.

Where it came from

Lewis Fry Richardson was a Quaker and a pacifist who, during the First World War, served as an ambulance driver on the Western Front. Between casualties he did his weather sums by hand — a single six-hour forecast over Germany that took him the better part of two years. The manuscript was once lost in the chaos of a retreat and turned up months later beneath a heap of coal.

When he finally finished, the answer was nonsense: his calculation said the surface pressure would leap by an amount never seen in nature. He published the failure anyway, in full, in 1922 — convinced the method was right even though this attempt was not.

Why it mattered

He was right. The forecast failed only because the starting measurements were very slightly out of balance — not because the idea was wrong, a subtlety untangled decades later. The method itself is exactly what every national weather service now runs on supercomputers. Richardson simply tried to do it, by hand, eighty years too early.

An analogy

Think of a film of the sky played forward one frame at a time. Each frame is the whole atmosphere — the pressure and wind in every square of a grid. The laws of physics are the rule that draws the next frame from the current one. Richardson drew those frames with a pencil and a slide-rule; today a computer draws millions a second. The catch: if your very first frame is even slightly off, the error can grow with every new frame — which is exactly what tripped him up.

A bump of weather sits on a row of grid cells. One slider sets the size of each forward time step; another sets how many steps to take. With small steps the bump glides smoothly along the grid, close to the faint dashed curve that marks the true answer. Make the step too large and the forecast curve turns red and explodes into wild zig-zags — just like Richardson's calculation did.

Where it sits

The dream of forecasting from physical law was Vilhelm Bjerknes', in 1904; Richardson turned it into an actual recipe. It came true in 1950, when one of the first electronic computers, the ENIAC — guided by John von Neumann and Jule Charney — produced the first successful numerical forecast, this time filtering out the fast disturbances that had wrecked Richardson's attempt. The same lineage runs on to Edward Lorenz, whose 1963 discovery of chaos (also in this Library) showed why even a perfect version of Richardson's machine can see only a week or two ahead.

The original document
Original source text
Lewis F. Richardson · Cambridge University Press · 1922 · xii + 236 pp.
The aim
the scheme is complicated because the atmosphere is complicated.
Richardson sets out to forecast the weather by numerically integrating the governing differential equations of the atmosphere. He divides the air into a horizontal lattice of cells and several vertical layers, tabulates pressure, temperature, density, water content and the two horizontal winds, and replaces the equations' space- and time-derivatives with finite differences so the future can be computed by arithmetic alone.
The trial forecast
He demonstrates the method on a single example: a six-hour forecast of the change in surface pressure and wind over central Europe for 20 May 1910, using Vilhelm Bjerknes' observational data. Much of the hand computation was done in France, where Richardson served as a wartime ambulance driver; the manuscript was once lost in the retreat at the Battle of Champagne and recovered months later under a heap of coal.
[ … ]
The forecast-factory — a fantasy
After so much hard reasoning, may one play with a fantasy?
Richardson imagines a vast theatre-like hall, its walls painted as a map of the globe, filled with tens of thousands of human “computers,” each solving the equations for one patch of the world, coordinated from a pulpit at the centre.
In this respect he is like the conductor of an orchestra in which the instruments are slide-rules and calculating machines.
But instead of waving a baton he turns a beam of rosy light upon any region that is running ahead of the rest, and a beam of blue light upon those who are behindhand.
He estimates the staff required: a roughly 200-km grid gives about 3,200 columns over the globe, some 2,000 of them active at once, about 32 computers to a column — some 64,000 people working in concert merely to keep pace with the weather as it happens.
The dream
Perhaps some day in the dim future it will be possible to advance the computations faster than the weather advances and at a cost less than the saving to mankind due to the information gained. But that is a dream.
Cambridge · 1922