a retrospective view of Richardson's book on weather prediction*

Abstract

In 1922 Lewis F. Richardson published a comprehensive numerical method of weather prediction. He used height rather than pressure as vertical coordinate but recognized that a diagnostic equation for the vertical velocity is a necessary corollary to the quasi-static approximation. His vertical-velocity equation is the principal, substantive contribution of the book to dynamic meteorology. A comparison of Richardson's model with one now in operational use at the U. S. National Meteorological Center shows that, if only the essential attributes of these models are considered, there is virtually no fundamental difference between them. Even the vertical and horizontal resolutions of the models are similar. Richardson made a forecast at two grid points in central Europe and obtained catastrophic results, in particular a surface pressure change of 145 mb in 6 hours. This failure resulted partly, as Richardson believed, from inadequacies of upper wind data. Underlying this was a more fundamental difficulty which he did not seem to recognize clearly at the time he wrote his book: the impossibility of using observed winds to calculate pressure change from the pressure-tendency equation, a principle stated many years earlier by Margules. However, he did point in the direction in which a remedy was later found: suppression or smoothing of the initial field of horizontal velocity divergence. The 6-hr time interval used by Richardson violates the condition for computational stability, a constraint then unknown. It is sometimes said that this is one of the reasons his calculation failed, but that interpretation is misleading because the stability criterion becomes relevant only after several time steps have been made. Since Richardson did not go beyond a calculation of initial tendencies—in other words, he took only one time step—violation of the stability criterion had no effect on the result. Richardson's book surely must be recorded as a major scientific achievement. Nevertheless, it appears to have had little influence in the decades that followed, and indeed, the modern development of numerical weather prediction, which began about twenty-five years later, did not evolve primarily from Richardson's work. Shaw said it would be misleading to regard the book as “a soliloquy on the scientific stage,” but in fact that is what it proved to be. The intriguing problem of explaining this strange irony is one that leads beyond the obvious facts that when Richardson wrote, computers were nonexistent and upper-air data insufficient.

Margules's tendency equation and Richardson's forecast

“…In a note inserted in a manuscript version of his book, he wrote``Perhaps the most important change to be made in the second edition is that the equation of continuity of mass must be eliminated'' (Richardson's underlining). Unfortunately, this note, which is reproduced in Platzman (1967), is undated so we cannot say when Richardson reached this conclusion. He went on to speculate that the vertical component of vorticity might be a suitable prognostic variable.…”

“…As pointed out by Platzman (1967), Margules's results were summarised by Exner (1917) I +1800 +8 000 0 +2 700 II +6200 +4 100 +16 600 ± 32 800 III ± 2900 +15 000 +9 500 ± 13 600 IV ± 5800 +8 000 +1 900 ± 3 300 V ± 5500 +4 000 +6 500 +4 800 Total ± 6200 +39 100 +34 500 ± 42 200 At some later stage, Richardson did come to a realisation that his original method was unfeasible. In a note inserted in a manuscript version of his book, he wrote``Perhaps the most important change to be made in the second edition is that the equation of continuity of mass must be eliminated'' (Richardson's underlining).…”

“…This explanation, while incomplete, is consistent with the analysis of Margules. Had Richardson been aware, at an earlier stage, of Margules's results, he might well have decided not to proceed with his trial forecast, or sought a radically different approach (Platzman 1967).…”

An Introduction To Lewis Fry Richardson and His Mathematical Theory of War and Peace

“…His weather prediction experiment used a very sophisticated physical model for the calculations (a number of contemporary reviewers of his book, in fact, criticized him for the amount of detail, see for example the survey by Platzman, 1967). This experiment was performed before the age of computers, and since all the calculations had to be done by hand, the enterprise was very time-consuming and took longer than the passage of actual weather.…”

“…However, by this time Richardson had turned away from meteorology to devote all of his time to the study of the causes of war. By the mid-to late 1960s understanding and technology had advanced to the point where the leading national weather services were using models virtually identical to Richardson's to predict the weather (Platzman, 1967(Platzman, , 1968 Ashford, 1985, pp. 246-…”