Water temperature modelling in a controlled environment: Comparative study of heat budget equations

One of the challenges when modelling a complex variable such as water temperature in rivers is that it can be difficult to determine the sources of error and to ensure that the simulations are truly representative of the reality. Therefore, a heat budget study was completed in a controlled environment, which excluded advection and bottom fluxes but enabled observation of all the other fluxes. A 21.42 m3 pool was installed and insulated to limit heat exchange through the sides and bottom. All the major energy fluxes were monitored for a 50‐day period. Different equations for individual heat budget terms were tested to determine their ability to reproduce the observations. This experiment also permitted to assess the relative importance of each component of the heat budget. Performance of each semi‐empirical equation was determined by comparing predictions and measured values. It was thus possible to choose the formulae that best represented the measured heat exchange processes, while understanding the limits of some of the semi‐empirical representations of heat exchange processes. The results highlight the importance of radiative terms into the heat budget because they controlled the major sources and sinks. The study also showed the importance of the wind function determination into the calculation of latent heat flux. The resulting water temperature model returned simulated hourly water temperature with an overall root mean square error of 0.71 °C/h and a modified Nash–Sutcliffe coefficient of 0.97.