Wind Mixing in Temperature Simulations for Lakes and Reservoirs

A one-dimensional mathematical formulation for simulating the wind mixing of the surface layers in reservoirs and lakes is developed. Emphasis is placed on the estimation of the net available wind-supplied energy for mixing by taking into consideration the variability of the wind in time. The formulation of the dynamics of the wind-mixed layer presented in this paper is implemented in a modified version of the one-dimensional Massachusetts Institute of Technology reservoir model. The model was used to predict the annual cycle of the thermal structure of Spada Lake in northwestern Washington State. A complete record of inflow and outflow water temperatures, temperature profiles in the reservoir, and meteorological data at the site over a 16-month period provided the basis for verifying the model. Special effort was made to screen and analyze these data to assure their quality. The application of the temperature model in Spada Lake produced good agreement between simulated and observed temperature profiles. Noticeable features of this application are the accurate simulation of the growth of the wind-mixed layer in the fall and the prediction of the exact time of formation and melting of the ice cover in the winter. These features could not have been predicted accurately without accounting for the variability of the wind pattern and its effect on the net available energy for mixing, as it was found in earlier simulations with simpler formulations of the wind-mixing effect.