Use of heat-based vertical fluxes to approximate total flux in simple channels

Heat flux through shallow streambed sediments is often used to quantify streambed water exchange with groundwater. Although two-dimensional (2-D) and three-dimensional (3-D) models are available, one-dimensional (1-D) models still have advantages in terms of ease of use and cost effectiveness. This study investigated error associated with the vertical flow assumption for a lateral section of a synthetic channel of varying geometry, hydraulic gradient, and stage using 1-D and 2-D models. Hydraulic gradient had the greatest influence on total channel flux. Flux at the lateral edge of the channel was up to 8.3 times higher than at channel center, and seepage from the channel banks accounted for up to 50% of total flux. Despite this variation along the channel boundary, the difference between channel flux estimates using 1-D and 2-D models was less than 30%. The models were applied to data from a large irrigation canal, and 1-D channel flux estimates were 30% greater and 81% lower than from the 2-D model, using temperatures collected at channel center and at the left edge of the channel, respectively. These results stress the importance of placing probes to best capture water flux direction when using 1-D, temperature-based methods.