Lake Decay Modeling*

Introduction

Understanding and predicting the impact of various sources are essential components of a typical course on Analysis of Stream and Estuary Pollution in an engineering curriculum. Dispersal and decay of contaminants in lakes, streams, estuaries, and oceans. Effects of pollutants on chemical quality and ecology of receiving waters.

Completely Mixed Systems

It is often useful to describe lakes and reservoirs under the assumption that the body of water is completely mixed horizontally and vertically. The substance decays is assumed with a first-order decay coefficient and with constant parameters of flow Q, decay K, over time. A mass balance for the lake is then given by

Case I : No Input Concentration

If W is zero, that is, there are no inputs of the concentration, and the solution is

Figure 1 shows the "flushing" of a lake initial condition.
Case II : Step Input Concentration

Consider the buildup of concentration due to the load W. An important form of W is when the input changes from one constant level (or a zero level) to another load level. This is the step input. The solution, which is called the step response, is

Figure 2 shows the buildup in time.
Model Example * Contents and Pictures are from "Principles of Surface Water Quality Modeling and Control" by Robert V. Thomann and John A. Mueller, Harper-Collins, 1988
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