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Richardson held a large number of posts. He worked in the National Physical Laboratory (1903-04, 1907-09) and the Meteorological Office (1913-16), and he held university posts at University College Aberystwyth (1905-06) and Manchester College of Technology (1912-13).
In addition he was a chemist with National Peat Industries (1906-07) and in charge of the physical and chemical laboratory of the Sunbeam Lamp Company (1909-12).
From 1920 to 1929 Richardson was head of the Physics Department at Westminster Training College, then from 1929 to 1940, he was Principal of Paisley College of Technology in Scotland.
Richardson was a scientist who was the first to apply mathematics, in particular the method of finite differences, to predicting the weather in Weather Prediction by Numerical Process (1922). In this work he uses data from work by Vilhelm Bjerknes published in Dynamical meteorology and hydrography.
Another application of mathematics by Richardson was in his study of the causes of war in Generalized Foreign Politics (1939), Arms and Insecurity (1949), and Statistics of Deadly Quarrels (1950).
He made contributions to the calculus and to the theory of diffusion, in particular eddy-diffusion in the atmosphere.
The 'Richardson number', a fundamental quantity involving gradients of temperature and wind velocity is named after him.
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