Building a mathematical model for simulating river water quality, a case of study applied to the Tatara river in Fukuoka City

From an advection-dispersion equation based on the mass conservation law, I developed a theoretical model for simulating the alteration of the Tatara river's water quality according to time. This equation has been solved for water quality variables by method of finite-difference approximations for the derivatives in the equation. To solve this equation effectively, an algorithm has been developed and a software program has been coded in Fortran language 90 (Nyhoff and Leestma, 1997, 1999) to implement this algorithm. As a case of study, the Tatara river's water quality parameters, hydraulic parameters such as discharge, velocity as well as cross-sections of the river and meteorological data of the river area have been observed and used as initial and boundary conditions for the model. The calibration of the model has been made by the trial-by-error method to find a reasonable dispersion constant that helps to obtain an optimal agreement between the model calculations and the set of observed data.