Impacts of three-dimensional nonuniform flow on quantification of groundwater-surface water interactions using heat as a tracer

Use of heat-as-a-tracer is a common method to quantify surface water-groundwater interactions (SW-GW). However, the method relies on assumptions likely violated in natural systems. Numerical studies have explored violation of fundamental assumptions such as heterogeneous streambed properties, two-dimensional groundwater flow fields and uncertainty in thermal parameters for the 1-D heat-as-a-tracer method. Few studies to date have modeled complex, fully three-dimensional groundwater flows to address the impacts of nonuniform, 3-D flow vectors on use of heat-as-a-tracer to quantify SW-GW interactions. COMSOL Multiphysics was used to model scenarios in a fully three-dimensional flow field in homogeneous, isotropic sand with a sinusoidal temperature upper boundary where vertical flows are deliberately disrupted by large and varied horizontal flows from two directions. Resulting temperature time series from multiple depths were used to estimate vertical Darcy flux and compared with modeled fluxes to assess the performance of the 1-D thermal methods to quantify multidimensional groundwater flows. In addition, apparent effective thermal diffusivity was calculated from synthetic temperature time series and compared to model input diffusivity. Both increasingly nonuniform and nonvertical groundwater flow fields resulted in increasing errors for both the temperature-derived flux and temperature-derived effective thermal diffusivity. For losing (downward) flow geometries, errors in temperature-derived effective thermal diffusivity were highly correlated with errors in temperature-derived flux and were used to identify how and when underlying assumptions necessary to use heat-as-a-tracer for quantifying groundwater flows were violated. Specifically, nonuniform flow fields (with flow lines that converge or diverge) produced the largest errors in simulated fluxes.