# A prescient vision of modern weather forecasting

## Methods a century old are at the heart of modern atmospheric simulation

One hundred years ago, a remarkable book was published by Cambridge University Press. It was a commercial flop: although the print run was just 750 copies, it was still in print 30 years later. Yet, it held the key to forecasting the weather by scientific means.

The book, Weather Prediction by Numerical Process, was written by Lewis Fry Richardson, a brilliant, eccentric mathematician. He described in detail how the mathematical equations that govern the evolution of the atmosphere could be solved by numerical means to deduce future weather conditions from a set of observations.

A century ago, weather forecasting used empirical methods. A less polite term would be informed guesswork, and the results were far from satisfactory. Newton’s laws of motion provided the means of predicting the motions of the planets.

Overnight, they turned astronomy into an exact science, but they had little direct or immediate impact on weather prediction. The atmospheric flow is highly complex, involving many physical processes such as turbulence, radiation, evaporation, condensation and so on.

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Richardson constructed a systematic algorithm for generating a forecast by solving the mathematical equations. He applied it to the most complete set of observations available, but the results were catastrophic, with predicted changes differing by orders of magnitude from the true changes. He was a man ahead of his time; the observations were inadequate, knowledge of atmospheric dynamics insufficient, numerical solution methods poorly understood and computer equipment non-existent.

As a result of the abysmal failure of his forecast, and the complexity and impracticality of his process, the significance of Richardson’s work went unnoticed, and his book was all but forgotten. The key cause of the unrealistic forecast was the absence of a subtle consistency between pressure and wind from his analysis. This condition, known as geostrophic balance, is what causes the winds to blow around a storm rather than straight inwards.

Over the following three decades, there were major advances on several fronts: observations, dynamics, numerics and computing. In 1950 a successful forecast was made using the Eniac computer and five years later Norman Phillips carried out the first climate simulation. These marked the beginning of practical weather forecasting and climate prediction.

#### Earth system models

The changing climate is now a cause of great concern. The best means we have of predicting future changes is by means of simulations using Earth system models. These are based on computer programs with millions of instructions and embrace not just the atmosphere but also exchanges with the oceans and the land surface, and many other processes. Richardson included so many factors that his algorithm could be regarded as the first Earth system model.

In his book, Richardson expressed a dream that “some day in the dim future”, numerical weather prediction would become a practical reality. The dream has come true: accurate forecasts based on computer modelling are now routine and are so reliable that rare forecast failures evoke a strong reaction in the media.

Progress since the Eniac forecasts has been spectacular and the useful range of forecasts continues to increase by about a day each decade. Thus, the skill of a one-day forecast in 1982 is achieved for a five-day forecast today.

While Richardson’s work had little impact in the short term, his methods are at the heart of atmospheric simulation, and we may reasonably regard the methods he described in his book as the basis of modern weather and climate prediction.

Peter Lynch is emeritus professor at UCD School of Mathematics and Statistics – he blogs at thatsmaths.com