Numerical modeling of thermal stratification in a lake reservoir. Methodology and case study

A numerical model of the hydrodynamic and thermal structure of an artificial lake was designed and developed as a basis for an ecological water-quality model. It allows the quantification of the vertical mixing processes that govern not only the thermal structure but also the nutrient exchanges, and more generally the distribution of dissolved and particulate matter between the different parts of the lake. The vertical temperature profiles were calculated by solving the one-dimensional heat transfer equation that takes into account the internal heat sources and sinks, advection due to inflow and outflow and the molecular and eddy diffusions. A finite-difference discretization of first-order in time and second-order in space was chosen. The numerical time-step was three hours and layers were one-meter in thickness. These time- and space-scales are well-suited to perform a precise simulation of the different processes occurring over a seasonal period. Moreover, this simulation requires only a reasonable amount of computer time. This model was used to study an artificial lake, (i.e. a reservoir), located in the high Loire valley (Roanne, France). To precisely identify the physical processes followed with an accurate numerical modeling, on-site data were acquired intensively over three years. Temperatures were monitored hourly at 11 different levels in the three main reaches of the reservoir to study the lake hydrodynamics and thermal behaviour. Meterological measurements were made every 20 minutes. One-year data were used for calibration, whereas the model was validated using the data collected over the other two years.