The Contributions of Lewis Fry Richardson to Drainage Theory, Soil Physics, and the Soil-Plant-Atmosphere Continuum

The English polymath Lewis Fry Richardson (1881-1953) made important contributions to many fields, including numerical weather prediction, finite difference solutions of partial differential equations, turbulent flow and diffusion, fractals, and the cause and evolution of conflicts. His first papers in 1908 concerned unconfined flow of water in saturated soil, arising in the design of required ditch spacing for draining peat. He developed and used a graphical method to solve this problem. This and other practical problems stimulated his interest in numerical methods and soon led him to the challenge of numerical weather prediction. In 1922 he published the book Weather Prediction by Numerical Process. He did the research for this book under difficult circumstances just before, during, and right after World War I. The book was received positively, but methods like those proposed in it were not successfully implemented until the invention of fast digital computers around 1950. Posthumously, most of Richardson's contributions in various fields received considerable attention. Important exceptions are his contributions to soil science and hydrology, on which we focus in this paper. In his 1922 book, Richardson formulated an elaborate model for transport processes in the atmosphere. For the lower boundary of his atmospheric model, he needed to understand the movement of liquid water, water vapor, and heat in the upper layer of the soil, and at the soil-atmosphere and plant-atmosphere interfaces. Finding little previous work on this, he first of all formulated the partial differential equation for transient, vertical flow of liquid water in soil. We argue that the resulting equation can rightly be called the Richardson-Richards equation. In addition he formulated equations for simultaneous transfer of liquid water and water vapor, for transfer of heat in soil, and for the balances of water and energy at the soil-atmosphere and plant-atmosphere interfaces. Finite difference versions of all the equations were incorporated in the numerical weather forecasting model. Unfortunately, his results were hardly noticed by soil physicists and hydrologists, likely because they were too effectively buried in an intimidating book on weather prediction.