Richardsons Forecast the Dream and the Fantasy Peter Lynch1

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Richardson’s Forecast:

the Dream and the Fantasy

Peter Lynch1

School of Mathematics and Statistics, University College Dublin.

Perhaps, some day in the dim future it will be possible to advance the computations

faster than the weather advances . . . . But that is a dream [WPNP, p. vii].

Introduction

A remarkable book on weather forecasting was published just one hundred years ago. Writ-

ten by the brilliant and prescient applied mathematician, Lewis Fry Richardson, Weather

Prediction by Numerical Process was published by Cambridge University Press and went on

sale in 1922 at a cost of 30 shillings (£1.50). With a print run of just 750 copies, it was not

a commercial success and was still in print thirty years after publication. It was re-issued in

1965 as a Dover paperback. Cambridge University Press reprinted the book in 2007, with a

foreword by Peter Lynch. Described as a second edition, it diﬀers in no essential way from

the 1922 edition.

Weather Prediction by Numerical Process (denoted WPNP) is a strikingly original scientiﬁc

work, one of the most remarkable books on meteorology ever written. In it, Richardson

described a systematic mathematical method for predicting the weather and demonstrated

its application by carrying out a trial forecast. Richardson’s innovative approach was fun-

damentally sound, but the method devised by him was utterly impractical at the time of its

publication and the results of his trial forecast appeared to be little short of outlandish. As

a result, his ideas were eclipsed for decades. For a brief biographical sketch of Richardson,

see the Benchmark article by Lea (2012) and for a full biography, see Ashford (1985).

Background to Scientiﬁc Forecasting

The basic ideas of numerical forecasting and climate modelling were developed more than a

century ago, long before the ﬁrst electronic computer was constructed. American meteorolo-

gist Cleveland Abbe and Norwegian physicist Vilhelm Bjerknes recognized that predictions of

meteorological phenomena could be based on the application of hydrodynamics and thermo-

dynamics to the atmosphere (Abbe 1901; Bjerknes 1904). They each speciﬁed the required

process: analysis of the initial state and time integration of the governing equations from

that state. They listed the system of mathematical equations needed and outlined the steps

required to produce a forecast. Realizing the numerous practical diﬃculties, neither Abbe

nor Bjerknes attempted to implement their techniques.

1Peter.Lynch@ucd.ie

arXiv:2210.01674v1 [physics.hist-ph] 27 Aug 2022

A ﬁrst tentative trial to produce a forecast using the laws of physics was made by Felix Exner

(1908), working in Vienna. His eﬀorts yielded a realistic forecast for the particular case that

he chose. Despite the restricted applicability of his technique, his work was a ﬁrst attempt at

systematic, scientiﬁc weather forecasting. However, it involved some drastic simpliﬁcations

and was far from providing anything of use for practical forecasting.

Weather Prediction by Numerical Process

Lewis Fry Richardson ﬁrst learned of Bjerknes’ plan for rational forecasting in 1913, when

he took up employment with the Meteorological Oﬃce. Richardson’s forecasting scheme

amounts to a precise and detailed implementation of the prognostic component of Bjerknes’

programme. It is a highly intricate procedure: as Richardson observed, “the scheme is

complicated because the atmosphere is complicated.” It also involved an enormous volume

of numerical computation and was quite impractical in the pre-computer era. But Richardson

was undaunted, expressing his dream that “some day in the dim future it will be possible to

advance the computations faster than the weather advances.”

Earlier, Richardson had applied an approximate numerical method to the solution of par-

tial diﬀerential equations to investigate the stresses in masonry dams. He realized that this

method had potential for use in a wide range of problems. The idea of numerical weather

prediction appears to have germinated in his mind for several years. Around 1911, Richard-

son had begun to think about the application of his approach to the problem of forecasting

the weather. He stated in the Preface of WPNP that the idea “grew out of a study of ﬁnite

diﬀerences and ﬁrst took shape in 1911 as a fantasy.” The fantasy was that of a forecast

factory, which we will discuss below.

Upon joining the Met Oﬃce, Richardson was appointed Superintendent of Eskdalemuir

Observatory in the Southern Uplands of Scotland and began serious work on numerical

forecasting. In May 1916 he resigned from the Met Oﬃce in order to work with the Friends

Ambulance Unit in France. By this time, he had completed the formulation of his scheme

and had set down the details in the ﬁrst draft of his book. But he was not concerned merely

with theoretical rigour and wished to include a fully worked example to demonstrate how

the method could be put to use.

Richardson assumed that the state of the atmosphere at any point could be speciﬁed by seven

numbers: pressure, temperature, density, water content and velocity components eastward,

northward and upward. He formulated a description of atmospheric phenomena in terms of

seven partial diﬀerential equations. To solve them, he divided the atmosphere into discrete

columns of extent 3 degrees east-west and 200 km north-south, giving 120×100 = 12,000

columns to cover the globe. Each of these columns was divided vertically into ﬁve cells. The

values of the variables were given at the centre of each cell, and the diﬀerential equations

were approximated by expressing them in ﬁnite diﬀerence form. The rates of change of the

variables could then be calculated by arithmetical means. These rates enabled Richardson

to calculate the variables at a later time.

Richardson calculated the initial changes over a six hour period in two columns over central

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Richardson'sForecast:theDreamandtheFantasyPeterLynch1SchoolofMathematicsandStatistics,UniversityCollegeDublin.Perhaps,somedayinthedimfutureitwillbepossibletoadvancethecomputationsfasterthantheweatheradvances....Butthatisadream[WPNP,p.vii].IntroductionAremarkablebookonweatherforecastingwaspublishedju...

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