Modelling the Role of Fluctuations in Volume on Self-purification of Natural Water Bodies

We present a simple mathematical model for examining the role of seasonal fluctuations of volume on self-purification of natural water bodies such as a lake ecosystem. The evolution of self-purification process, activated by natural mechanisms of flushing by clean water and degradation of pollutants by aeration, is influenced by a number of parameters depending on lake-specific characteristics. These parameters have been identified in the formulation of the model. The model consists of an initial value problem which has been solved analytically. Numerical results are presented graphically to highlight the effect of these parameters on clean-up time corresponding to all pollution levels. Results for a few simpler situations derived as particular cases from the general solution are also included and discussed.