A mathematical model for biological polishing

Abstract

The object of the dynamical model of biological polishing presented herein is to simulate the biogeochemical processes operating in the removal of heavy metals from mine drainage by means of periphytic algae. The model describes the growth of periphyton, and the interactions between periphyton, effluent, and fertilizer. Eventually it is hoped that it will serve as a management tool in that it will allow the user to determine the number of trees (or other substrate) and the amounts of nutrient to put into an effluent pool to maintain the metal concentrations below some legislatively set value year round. There are two markedly different approaches to modelling ecosystems in the scientific literature. In the “top down” approach, models are constructed which call for a comprehensive and detailed description of ecosystem components. These models are typically empirical in nature, and based on on-site observations. The “top down” approach is the methodology generally favoured by field biologists probably due to the the great complexity of natural systems they study. In contrast, the “bottom up’’ approach relies on careful quantification of key inputs, outputs, and internal processes for simulation of system dynamics. This approach is generally favoured by physical scientists and engineers, largely because it has been successful in their respective disciplines for several centuries. The models constructed in this approach are typically mechanistic and mathematical. The model which I will construct is an attempt to bridge the two ways of doing things. I will adopt a mechanistic theoretical perspective and identify the key biogeochemical processes operating in polishing ponds. However, I will use an empirical approach to quantify these complex processes first in the laboratory and then in the field on a site-specific basis. Finally, the mechanistic/empirical model constructed must be calibrated and verified in the field.