Why it came out wrong

The first numerical forecast was not wrong because the physics was wrong. It was wrong because the numbers fed into it were.

The calculation that worked and the answer that didn't

In 1922, Lewis Fry Richardson published Weather Prediction by Numerical Process ↗, a book that described, in meticulous detail, how to forecast the weather by solving equations on paper. He had done it himself — a single six-hour pressure forecast for a point over central Europe, calculated by hand during spare hours while he drove ambulances in France during the First World War. The arithmetic took weeks. The answer, when it finally came, was catastrophically wrong: the surface pressure changed by an impossible 145 hectopascals in six hours, where the real atmosphere had done almost nothing.

For decades this was cited as evidence that numerical forecasting was hopeless, or at least premature. That reading was mistaken. Richardson had not misunderstood the atmosphere. He had built a machine that worked perfectly and fed it broken inputs.

What was actually in the initial data

The observations Richardson used came from a network of surface stations and upper-air soundings taken over Europe on 20 May 1910. Those observations were genuine measurements of real conditions on a real day. The problem was not that they were inaccurate in the conventional sense — the thermometers and barometers were doing their jobs. The problem was that raw atmospheric observations contain noise: small, fast pressure oscillations that exist in the real atmosphere but are effectively irrelevant to the weather anyone cares about. These are gravity waves and acoustic waves, signals that propagate through the air at speeds far greater than the large-scale pressure systems — the highs, lows and fronts — that govern whether it rains.

In the real atmosphere, these waves carry very little energy compared with the slow, balanced flow of a developing cyclone. The atmosphere is, in a sense, already filtered: the large-scale dynamics that produce tomorrow's weather evolve slowly and are kept in a kind of dynamic balance, a relationship between pressure, wind and the rotation of the Earth that meteorologists call geostrophic balance. The observations Richardson received carried both the signal he wanted and the noise he didn't, with no way to tell them apart.

Richardson had no procedure for separating the two. He took the raw numbers and differentiated them — found their rates of change — which is exactly what the equations of motion require. Differentiation is, as any calculus student learns, a noise amplifier. A small, fast wiggle in the pressure field produces a large derivative. A large derivative in the initial conditions sends the model sprinting off in the wrong direction before the first time step is complete.

The smoothing that was missing

The fix, once numerical forecasting resumed in earnest after the Second World War, was called initialisation. The idea is to adjust the observed state of the atmosphere before handing it to the model, removing the fast-moving waves that the model would otherwise amplify. The adjustment has to be done carefully: the goal is to remove the noise without distorting the signal, keeping the large-scale pressure patterns intact while suppressing the small, fast oscillations that don't matter for a twenty-four-hour forecast.

Jule Charney, working at the Institute for Advanced Study in Princeton in the late 1940s, recognised the problem clearly. His approach was to use a simplified form of the equations — the quasi-geostrophic equations — that filtered out the fast waves by design, because they assumed geostrophic balance from the start. The first successful machine forecast, produced in 1950 on the ENIAC computer with Charney and his colleagues, used this filtered formulation. It worked. Not brilliantly by modern standards, but it worked: the answer was meteorologically recognisable rather than physically impossible.

What Charney had understood, and Richardson had not had the opportunity to implement, was that the model and the observations must be consistent with each other. You cannot take raw numbers from the atmosphere and feed them directly to equations that assume a smoothly balanced state. The mismatch between the two is what destroyed Richardson's forecast in its opening moments.

Why this matters beyond one unlucky calculation

Richardson's error is sometimes presented as a curiosity, a famous failure from the heroic age of calculation. It is more useful to think of it as a demonstration of a principle that still shapes numerical forecasting today. Every operational model run at the European Centre for Medium-Range Weather Forecasts in Reading, England, or at the National Oceanic and Atmospheric Administration ↗'s Environmental Modeling Center, begins with an initialisation step that is vastly more sophisticated than anything Richardson could have contemplated — a procedure called data assimilation that reconciles millions of observations with the model's own prior estimate of the atmospheric state, using statistical methods to weight each piece of evidence by its reliability.

The core concern is the same one Richardson ran into: the observations and the model must speak the same language. Differencing raw numbers produces wrong answers, regardless of how good the underlying equations are.

There is also a subtler lesson. Richardson's equations were, in their essentials, correct. The physics he encoded — conservation of momentum, the equation of state for a gas, continuity of mass — is the physics every model still uses a century later. He failed not because he misunderstood the atmosphere but because he misunderstood what his equations would do to imperfect inputs. That distinction matters. A wrong physical model fails systematically and can sometimes be corrected by re-examining the science. A correct model fed wrong inputs fails unpredictably and in ways that can look, superficially, like a wrong model.

The smoothed, balanced initial state that a modern model receives before each forecast run is not an approximation of the atmosphere: it is a deliberate reconstruction of the atmosphere expressed in terms the model can accept without catastrophe. Getting that reconstruction right — knowing which parts of an observation to trust, how to weight a radiosonde against a satellite retrieval against a ship report — is most of the work of modern operational forecasting, and it was the work that was entirely absent from the page when Richardson sat down, in good faith, with his 1910 observations and his equations, and began to compute.