Six Weeks of Arithmetic for Six Hours of Weather

The first numerical forecast took one man, sixty-four thousand hypothetical assistants, and a result so wrong it almost buried the method.

The Problem Richardson Set Himself

In 1922, Lewis Fry Richardson published a book called Weather Prediction by Numerical Process that contained, as an appendix, the first attempt to calculate a weather forecast from physical equations rather than pattern-matching or intuition. The calculation covered a single point over central Europe and a single six-hour interval. It produced a forecast of surface pressure change that was wrong by two orders of magnitude — the computed change was roughly a hundred times larger than what actually happened. Richardson knew it immediately. He published anyway.

The reason that decision matters is that the method was not wrong. The equations Richardson used — derived from the work of Vilhelm Bjerknes ↗, who had argued in 1904 that weather forecasting was in principle a problem of mathematical physics — were the right equations. Richardson had simply inherited data that had not been smoothed before he started. Unbalanced initial pressure gradients drove fictitious winds in his calculation, and those winds amplified the error rather than correcting it. The atmosphere starts from a state of near-balance; his starting numbers did not, and the mathematics dutifully told him so at full volume.

He was not discouraged, or at least not publicly. The book includes his famous estimate of sixty-four thousand people with slide rules working in a vast circular hall to keep pace with the real atmosphere in real time — a fantasia of parallel human computation that gestures, without knowing it, at what electronic computers would eventually make routine.

The Calculation Itself

Richardson divided the atmosphere above a point in Bavaria into five layers and wrote down the governing equations for each: conservation of momentum, conservation of mass, the thermodynamic equation. These are the same equations at the core of every operational forecast model running today. He then discretised them — replaced the smooth mathematical derivatives with finite differences, meaning small changes over short intervals — and turned the crank by hand. Or rather, he turned it during whatever quiet hours he could find while working as an ambulance driver near Champagne during the First World War. Parts of the manuscript were lost in the chaos of the battle of Champagne and later recovered under a heap of coal.

The arithmetic was meticulous. The book reproduces the working in columns, with the intermediate results visible. Reading it now, you can watch a mind trying to build a machine out of pencil and patience. Each step is correct. The accumulation of steps produces something that, as verification against the actual record shows, has no predictive value for that interval. The failure is not in the algebra; it is in the initial condition — the snapshot of the atmosphere he was handed to start from.

This distinction — between the model being wrong and the starting data being wrong — would take several more decades to be fully worked through. Edward Lorenz ↗ at MIT would later show, in the early 1960s, that the atmosphere's own dynamics impose a fundamental limit on how long any forecast can remain useful, regardless of how good the initial data are. Richardson's problem was upstream of even that: he did not yet have the technique of data assimilation, the process by which raw observations are reconciled with the model's own internal state before a forecast run begins.

What Went Wrong, and What It Eventually Fixed

The specific failure was understood relatively quickly, at least in principle. The governing equations contain several types of wave solution, and not all of them matter for weather. Fast-moving acoustic and gravitational waves are real physics but meteorological irrelevances; they do not carry the weather patterns that forecasters care about. Richardson's unsmoothed initial data excited these fast waves energetically, and they swamped the slower, meteorologically interesting solution. Later workers called this problem "initialisation," and solving it — finding ways to suppress the spurious fast waves before the forecast run starts — occupied numerical meteorologists for decades.

The practical breakthrough came after the Second World War. Jule Charney, working at Princeton with John von Neumann's group and later at MIT, led the effort to produce the first successful machine-computed forecast in 1950. Charney's crucial move was to filter the equations — using a simplified form called the barotropic vorticity equation — so that only the slow, weather-relevant waves survived. The computation ran on ENIAC and produced a twenty-four-hour forecast of upper-atmosphere pressure patterns that was, for the first time, recognisably like what actually happened. Richardson's equations, Charney's filtering, von Neumann's machine: the lineage is clean.

From there the field expanded rapidly. Primitive equations — Richardson's fuller set, not Charney's simplification — were reintroduced as computers grew capable of handling them. Resolution increased. Initialisation techniques improved through the 1960s and 1970s until the modern practice of data assimilation, which absorbs millions of observations from radiosondes, satellites, aircraft and ocean buoys into a dynamically consistent model state before each forecast begins, replaced the crude hand-smoothing Richardson never had available.

Why It Deserves More Than a Footnote

The story tends to get told as a curiosity — the eccentric Quaker ambulance driver who computed a terrible forecast in a warzone — and the wrong answer is treated as the punchline. That framing misses what Richardson actually demonstrated. He proved that the calculation was completable by a single person with finite time, which settled a question that had not been settled before: were the equations tractable at all, given the complexity of the atmosphere? The answer was yes, at enormous cost, and the wrong answer told you precisely where the cost lay. Bad data, not bad mathematics.

Every operational centre running forecasts today — the ECMWF ↗ in Reading, the Met Office in Exeter, NOAA's Environmental Modeling Center in the United States — begins each forecast cycle with a data assimilation step whose entire purpose is to produce the smoothed, balanced initial state that Richardson lacked in 1922. The first-run failure, properly understood, is the specification for everything that followed.

Richardson himself went on to other things — mathematical studies of conflict and the geometry of borders — but the 1922 book did not disappear. It was reprinted, studied and eventually recognised as the document in which numerical weather prediction was born, wrong answer and all. The forecast was off by a factor of roughly a hundred. The method was off by roughly zero.