Simulating the effects of geologic heterogeneity and transient boundary conditions on streambed temperatures — Implications for temperature-based water flux calculations

Analytical solutions to the one-dimensional heat transport equation for steady-state conditions can provide simple means to quantify groundwater surface water exchange. The errors in exchange flux calculations that are introduced when the underlying assumptions of homogeneous sediments and constant temperature boundary conditions are violated were systematically evaluated in a simulation study. Temperatures in heterogeneous sediments were simulated using a numerical model. Heterogeneity in the sediments was represented by discrete, binary geologic units. High contrasts between the hydraulic conductivities (K) of the geologic units were found to lead to large errors, while the influence of the structural arrangement of the units was smaller. The effects of transient temperature boundary conditions were investigated using an analytical equation. Errors introduced by transient boundary conditions were small for Darcy-velocities > 0.1 m d^− 1 in the period near maximum and minimum annual surface water temperatures. For smaller fluxes, however, errors can be large. Assuming steady-state conditions and vertical flow in homogeneous sediments is acceptable at certain times of the year and for medium to high exchange fluxes, but pronounced geologic heterogeneity can lead to large errors.