The thermal regime of rivers: development, verification and application of a numerical model

Abstract

The finite volumes method is applied and the ultimate strategy is generalized to solve the advection-diffusion-reaction equation with variable parameters, in order to obtain results with negligible numeric diffusion. The model is verified through calculations with known analytical solutions, showing its capability to simulate diffusive and advective transport of scalar properties in water. The model is used to calculate temperature in a 32 km section of the lower Itata River, located in Central Chile, measuring the river's temperature and variables controlling the thermal regime at several points. Results are presented for four 12-day periods, corresponding to winter, spring, summer and autumn scenarios. The mean temperature measured during the winter and summer scenarios are constant, at 9.6 and 24.0 °C, respectively, and do not change throughout the section. In the autumn and spring scenarios, a slight increase throughout the section is observed, of 0.45 y 0.74 °C, respectively. The amplitude of the daily thermal oscillation measured for the winter scenario (0.7 °C) is negligible, and very significant (8.4 °C) for the summer scenario. The amplitude is observed to increase in the section studied only for the summer scenario, at a rate of 0.175 °C/km. The model developed adequately predicts the complex behaviour of the river's temperature for the four scenarios analyzed, constituting a simulation tool with prediction capability.