Comparison of heat tracer models in the estimation of upward flux through streambed sediments

Abstract. Although many studies examine the use of heat as a tracer to determine vertical infiltration of water into the streambed, few consider the case where both water and heat flow (advection and conduction) are in the upwards direction. In this study, we compare the usefulness of both a one-dimensional numerical model and two analytical solutions for the case where water movement is upwards and the (flat) groundwater temperature is greater than the diel temperatures at the surface. We first create a theoretical test case to compare expected temperature traces at various depths within the sediment column for each model both in the presence and absence of a vertical temperature gradient. These theoretical results are discussed in light of the assumptions inherent in the models. Then the models are applied to a study area located along a reach of the Truckee River in Nevada, USA, during the winter season and flux estimates both between models and between sensor depths are compared. Our results show that despite violation of some assumptions inherent in the analytical models, flux estimates over the entire vertical streambed column can be within one order of magnitude of the numerical model under some conditions. Further, predictions of downwards flux obtained using only the shallow sensors highlight the need to consider the physical processes to be measured when choosing sensor depth, especially when advection and conduction are upwards.