Richardson's Marvellous Forecast

Peter Lynch

Met Éireann, Dublin.


While Vilhelm Bjerknes and his team were developing their synoptic models in Bergen, a radically different approach to forecasting was being pursued by Lewis Fry Richardson. Richardson's starting point was the system of fundamental physical principles governing atmospheric motion. He assembled the set of mathematical equations which represent these principles and formulated an approximate algebraic method of calculating their solution. Starting from the state of the atmosphere at a given time - the initial conditions - the method could be used to work out its future evolution.

Using the most complete set of observations available to him, Richardson applied his numerical method and calculated the changes in the pressure and winds at two points in central Europe. The results were something of a calamity: Richardson calculated a change in surface pressure over a six-hour period of 145 hPa, a totally unrealistic value. As Sir Napier Shaw remarked, the wildest guess would not have been wider of the mark! Despite the ``glaring errors'' in his forecast, Richardson was bold enough to publish his method and results in his remarkable Weather Prediction by Numerical Process (LFR; Richardson, 1922). This profound, and occasionally whimsical, book is a treasure-store of original and thought-provoking ideas and amply repays the effort required to read it.

The application of Richardson's forecasting method involved an enormous amount of numerical computation. Even the limited results he obtained cost him some two years of arduous calculation (Lynch, 1993). This work was carried out in the Champagne district of France where Richardson served as an ambulance driver during the Great War (Ashford, 1985). His dedication and tenacity in the dreadful conditions of the war are an inspiration to those of us who work in more genial conditions.

In this paper the results obtained by Richardson will be examined and the causes of the errors in his forecast will be explained. It will be shown how a realistic forecast can be obtained by modifying the initial data. The study is based on the original observations for 20 May, 1910, originally compiled by Hugo Hergessel and analysed by Vilhelm Bjerknes. These are used to extend the table of values published by Richardson, to cover most of Europe. A numerical model is then constructed, keeping as close as possible to the method of Richardson, except for omission of minor physical processes. When the model is run with the extended data, the results are virtually identical to those of Richardson. In particular, an initial pressure tendency of 145 hPa in 6 hours is obtained at the central point, in agreement with Richardson. The tendency values are unrealistic, being generally about two orders of magnitude too large.

The reasons for the spurious tendencies will be discussed. They are essentially due to an imbalance between the pressure and wind fields resulting in large amplitude high frequency gravity wave oscillations. The `cure' is to modify the analysis so as to restore balance; this process is called initialization. An initialization method based on a digital filter will be outlined, and its application to Richardson's problem described. The forecast tendency from the modified data yields reasonable results. In particular, the tendency at the central point is reduced to 3 hPa per 6 hours - a realistic value! The chapter will conclude with some speculations about what-might-have-been had Richardson been able to initialize his data.

Reference: Lynch, Peter, 1999: Richardson's Marvellous Forecast. Pp 61-73 in The Life Cycles of Extratropical Cyclones, M A Shapiro and S Grønås, Eds., Amer. Met. Soc., Boston, 355pp.

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