Scale and time effects on mathematical models for transport in the environment

The purpose of this paper is to analyse mathematical models used in environmental modelling. Following a brief survey of the development in modelling scale- and time-dependent dispersion processes in the environment, this paper compares three similarity solutions, one of which is a solution of the generalized Feller equation (GF) with fractal parameters, and the other two for the newly-developed generalized Fokker-Planck equation (GFP). The three solutions are derived with parameters having physical significance. Data from field experiments are used to verify the solutions. The analyses indicate that the solutions of both GF and GFP represent the physically meaningful natural processes, and simulate the realistic shapes of tracer breakthrough curves.