Generalisation of various hydrological and environmental transport models using the Fokker–Planck equation

The Fokker–Planck equation (FP) and its special derivatives, the generalised Feller equation (GF) and the advection equation (AE), have been shown to be universal in linking many hydrological and environmental transport models. A similarity solution of the GF is a hypergamma function, which is shown to generalise the various similarity solutions of different transport models. The hydrological and various transport models generalised using FP include the models for: (1) groundwater flow; (2) generalised diffusion wave with inertial effects for open-channel flows and flood waves; (3) flood waves, shock waves, kinetic overland and saturated subsurface flows; (4) solute transport in groundwater in fractal porous media; (5) isothermal gas flow through porous media; (6) moisture and solute transport in unsaturated soils; (7) transport and distribution of sediment in stream channels and movement of stream beds; (8) hillslope erosion; (9) dynamic rainfall and cloud fields; (10) transport in stream channels subject to estuarine tidal effect, and (11) transport in the atmospheric boundary layer.