A Nutrient Model for a Lake with Time-Variable Volumes

Abstract

A total nutrient model for a completely mixed water body is often used for lake eutrophication analysis. In the model, the assumption of constant volume of a lake is usually made, i.e. the inflow to the lake is equal to the outflow. However, for some lakes which have significant difference between inflow and outflow during a studying period (usually larger than the detention time), the assumption of constant volume is no longer valid and could cause error in solution. This research has developed a more general model which solves the nutrient mass balance equation for the lake with time-variable volumes. In the model, the method of power series is used to obtain the solution. By merely taking the first few terms in power series (e.g. fewer than 15 terms), the approximate solution is very close to the exact solution. In this way, both computer time and numerical error can be minimized compared to the numerical solution. This newly developed nutrient model is applied to Chen-Chin Lake in southern Taiwan for phosphorus modeling in eutrophication study.