Hydrodynamics of the Lake Livingston, Texas, headwaters.

In Part I of the present study, an empirical model is developed to describe typical temperature conditions in the headwaters of Lake Livingston, Texas, (see Figure 1). The purpose of this empirical description is to provide a reasonable, but surely preliminary, description of temperature conditions in the Lake Livingston headwaters for use in exploratory eutrophication studies currently (1974) being conducted by the Trinity River Authority. In view of the exploratory character of this eutrophication study, the formulation of the empirical description had the following guidelines for its development: a. Actual measured temperatures in the lake itself should form the basis of the empirical description; b. The description should be relatively simple; c. The empirical model should be able to be used for temperature prediction with only desk top type of calculations; and d. Consideration should be limited to in-bank flow periods associated with low flow summer conditions. The empirical model developed according to these guidelines consists of a series of graphs supplemented by a few simple algebric equations which permit prediction of the vertical temperature profile (and associated parameters) at various longitudinal stations in the headwaters of Lake Livingston. Because of the intended use of the empirical model, only the summer season of mid-May through early September is considered. In Part II of the present study, an analytical predictive model is developed to approximately describe the macroscopic behavior of the flow and velocity conditions in the Lake Livingston headwaters (Figure 1). Inputs into the model are the geometric characteristics of the headwaters and the temperature description developed in Part I. As opposed to the empirical temperature model, this hydrodynamic model, except for the temperature data, is completely predictive and does not require inclusion of empirical fitting constants. As such it is well suited to exploratory studies where field data available for empirical adjustment are limited. However, since it is to be used in a predictive manner for exploratory eutrophication studies, it is approximate and describes only gross flow characteristics of the headwaters during the summer season. For its formulation, the hydrodynamic model had the following guidelines: a. The results of the empirical temperature description could provide an input into the hydrodynamic model; b. Beyond temperature information, the hydrodynamic model should be predictive; c. Predictions should be able to be made with only desk top type of calculations; and d. Consideration should be limited to in-bank flow periods associated with low flow summer conditions. The predictive model in its simplest form consists of two couple equations which, when solved with the appropriate temperature information from the empirical temperature model, permits destination of the relative flow velocities in a two layer stratified flow in the Lake Livingston headwaters.