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Show 1973). These models are structured generally in accordance with the hydrologic flow diagram of Figure 10. In a subsequent study, the salinity dimension was added to the hydrologic model of the Bear River system ( Hill et al., 1973). Under two current projects at the UWRL, multi- dimensional hydrologic- quality simulation models are being developed for parts of the three river drainage basins. These models cover the We- ber- Ogden system from Park City and Kamas to the Great Salt Lake, the Jordan River from the Jordan Narrows to Great Salt Lake, and the Bear River from the Utah- Idaho border to Great Salt Lake. Lake and near shore submodels The immediate objective of this study, then, is to complete the submodel components of the first layer shown by Figure 7 by developing hydrologic and water quality models of the near shore and lake areas. The near shore area is envisioned as being the transition zone between the watershed and lake areas. Depending upon circumstances, this transition zone might be included in either one of the other two components. For example, the benchlands situated west of the mouth of the Weber River Canyon might be included in the watershed submodel, while the Willard Bay reservoir might be contained in the lake submodel. The near shore area also contains the mineral extraction industries. Effects which are introduced by this kind of activity can be considered as point inputs to the lake submodel. The computer model of the hydrologic and water quality components of the lake subsystem will be developed by applyinga finite difference technique, and employing a steady- state solution which will allow long- term ( seasonal) gradients to be simulated. A model structure based on a linked node system developed by Chen and Orlob ( 1972) is shown by Figure 11. This structure has been used for modeling numerous lakes and estuaries. Dailey and Harleman ( 1972) and Hann and Young ( 1972) also have reported on similar models. The advantages of using the finite difference technique for the lake submodel in this case are as follows: 1. The method is now developed to the point where it is applicable as a practical tool for simulation. 2.' The model will allow vertical and horizontal stratification to be investigated which is not possible if complete mixing is assumed. This will allow the refinement necessary for a management model. 3. The steady- state model is relatively inexpensive in computer time as compared with dynamic or time varying models, but is still of sufficient resolution ( accuracy) to be a useful management tool. 4. The finite difference grid is sufficiently flexible to incorporate proposed as well as existing man- made barriers. 5. A two- dimensional grid of this type is superimposed upon the lake. The grid has the flexibility to be able to incorporate islands and natural and man- made barriers. Concentrations of various water quality constituents are predicted at the nodes and transport among adjacent nodes is accomplished by the " linking- equations" which connect the nodes. Because of the importance of modeling the vertical stratifications of the lake, three horizontal grids will be applied: 1. A top grid to represent the less dense layer of water. 2. A lower grid to represent the dense layer of water. 3. A grid to represent the bottom characteristics. Linking- equations will be provided for the vertical dimension as well as the horizontal dimension so that a three- dimensional modd will result, as shown in Figure 12. Linking- equations in the horizontal grid will simulate advection, dispersion, and biochemical reactions occurring among constituents as follows: 9AQ _ dQCj + 0 3t 3x 3x AD^ j+ Ri + Si. . ( 1) ox in which Cj = concentration of the im water quality constituent t = time x = horizontal distance between nodes A = cross- sectional area of a hypothetical channel between nodes Q = flow between nodes D = longitudinal dispersion coefficient R| = a function representing the rate of loss or gain of constituent i due to biochemical reactions Sj = the rate of loss or gain of constituent i due to external sources and sinks The linking- equations in the vertical dimension will simulate dispersion as follows: 8t 9z 9z ( 2) in which z = distance in the vertical dimension 39 |