Transport phenomena, such as fluid flows, solute dispersion, and migration of aquatic species, are ubiquitous in surface water bodies. These transport phenomena are inherently nonlinear and stochastic, and analyzing their dynamics requires using mathematically and physically sophisticated knowledge. Numerical analysis assisted by firm mathematics can serve as an effective tool for comprehending the transport phenomena; however, there exist only a limited number of such kinds of approaches in regional environment science and related research areas. This paper provides a brief summary of our previous researches on mathematical and numerical modelling of the transport phenomena for promoting the use of the modelling techniques. Their applicability to the problems specific to the Hii River system, Japan, is also discussed in this paper.