Quantifying streambed advection and conduction heat fluxes

Groundwater and accompanying heat fluxes are particularly relevant for aquatic habitats as they influence living conditions both within the river and streambed. This study focuses on the theory and the development of new equations to estimate conduction and advection heat fluxes into and out of the bed, correcting some earlier misunderstandings and adding parameterizations that extend our understanding of timing of heat fluxes. The new heat flux equations are illustrated using Catamaran Brook (New Brunswick, Canada) stream/streambed temperature data. We show important relationships between fluxes when the surface water temperature (1) follows a sinusoidal function superimposed on a steady state condition (constant deep streambed temperature) and (2) when sinusoidal variations in stream temperature at two frequencies (annual and diel) are superimposed. When the stream temperature is used as a prescribed boundary condition, the contribution of bed fluid fluxes to stream temperature occurs through the effects of conductive thermal gradients, not through direct contribution/mixing of cold/warm water. Boundary conditions can be modified, however, to account for direct contribution of cold/warm water (e.g., localized upwelling) and consequences for the conduction heat flux. Equations developed allow for prediction of conductive fluxes to the bed during summer driven by diel and annual temperature fluctuations of the stream water and good agreement was observed between analytic solutions and field data. Results from this study provide a better insight into groundwater and heat fluxes which will ultimately result in better stream temperature models and a better management of fisheries resources.