Use of heat as tracer to quantify vertical streambed flow in a two-dimensional flow field

Analytical solutions to the heat transport equation in porous media have been developed in the past to estimate surface water-groundwater interactions. These solutions, however, are based upon simplifying assumptions that are frequently violated in natural systems. A nonvertical flow field, inherent to most field settings, can violate the one-dimensional (1-D) flow assumption and lead to erroneous velocity estimates. In this study, we have developed a 2-D heat and mass transport finite element-based numerical model for a stream aquifer cross section experiencing flow-through. Synthetic multilevel streambed temperature time series were generated with the model using a sinusoidal temperature boundary. The temperature data was used to quantify the vertical flow velocity with a 1-D analytical solution based on the amplitude decay and phase shift of temperature with depth. Results demonstrate that erroneous vertical components of fluid velocity can be obtained by the 1-D analytical solution when the true vertical velocity approaches zero and the flow regime becomes almost horizontal. The results also illustrate that the amplitude ratio method performs quite poorly on the gaining side of the stream where the only reliable method is phase shift. On the losing side of the stream, both methods can be employed but a better estimation is obtained from the amplitude ratio method. In general, amplitude ratio and phase shift data should be used in conjunction to maximize the information of the system.