A Linear Systems Model of a Lake Cove
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The Lake Texoma Model was developed at an eight week summer institute sponsored by the National Science Foundation. Bernard Patten of the University of Georgia coordinated the program. Lake Texoma is a reservoir between Texas and Oklahoma. Since it was thought that modeling the entire lake was a formidable project for an eight-week course, the researchers chose to model only a single cove of the reservoir. The cove was chosen because of the presence of a biological station of the University of Oklahoma. Lake Texoma is regularly used for flood control and as a city water supply, consequently water level fluctuations are an important aspect of cove the dynamics. Research done on Tennessee River Valley reservoirs have demonstrated that water level fluctuations have a tremendous impact on marginal plants. (Penfound, et.al., 1946) Eugene Odum visited the modeling site during the institute and conjectured that the water level fluctuations constituted an extremely important driving function on the cove's organisms. Although the simulation of the effects of water level fluctuations was given rather high priority in the modeling effort, it has not been accomplished with any degree of satisfaction. The model is a compartmental model, described by a network of first-order, linear, differential equations. Components with similarly behaving features were grouped together as compartments. There are 33 compartments in the model, a fact which makes it one of the largest ecosystem models that has been developed. The model depicts the behavior of the cove over a year. Most of the flow rates are described in weekly terms. The iteration step, during which changes in the variables are calculated, has a length of one-half day. Euler's method is used to approximate the differential equations.