Richards equation

The Richards equation represents the movement of water in unsaturated soils, and is attributed to Lorenzo A. Richards who published the equation in 1931. It is a nonlinear partial differential equation, which is often difficult to approximate since it does not have a closed-form analytical solution. Although attributed to Richards, it is established that this equation was actually discovered 9 years earlier Lorenzo A. Richards by Lewis Fry Richardson in his book 'Weather prediction by numerical process' published in 1922 (p.108). The Richards equation represents the movement of water in unsaturated soils, and is attributed to Lorenzo A. Richards who published the equation in 1931. It is a nonlinear partial differential equation, which is often difficult to approximate since it does not have a closed-form analytical solution. Although attributed to Richards, it is established that this equation was actually discovered 9 years earlier Lorenzo A. Richards by Lewis Fry Richardson in his book 'Weather prediction by numerical process' published in 1922 (p.108). Darcy's law was developed for saturated flow in porous media; to this Richardson applied a continuity requirement suggested by Edgar Buckingham and obtained a 'general partial differential equation describing water movement in unsaturated non-swelling soils'. The transient state form of this flow equation, known commonly as Richards' equation writes in one-dimension (vertical):