Experimental evaluation of the applicability of phase, amplitude, and combined methods to determine water flux and thermal diffusivity from temperature time series using VFLUX 2

Vertical fluid exchange between surface water and groundwater can be estimated using diurnal signals from temperature time series methods based on amplitude ratios (A_r), phase shifts (δϕ), or combined use of both (A_rδϕ). The A_r, δϕ, and A_rδϕ methods are typically applied in conditions where one or more of their underlying assumptions are violated, and the reliability of the various methods in response to non-ideal conditions is unclear. Additionally, A_rδϕ methods offer the ability to estimate thermal diffusivity (κ_e) without assuming any thermal parameters, although the value of such output has not been broadly tested. The A_r, δϕ, and A_rδϕ methods are tested under non-steady, 1D flows in sand column experiments, and multi-dimensional flows in heterogeneous media in numerical modeling experiments. Results show that, in non-steady flow conditions, estimated κ_e values outside of a plausible range for streambed materials (0.028-0.180m²d^-1) coincide with time periods with erroneous flux estimates. In heterogeneous media, sudden changes of κ_e with depth also coincide with erroneous flux estimates. When (known) fluxes are variable in time, poor identification of δϕ leads to poor flux estimates from δϕ and A_rδϕ methods. However, when fluxes are steady, or near zero, A_rδϕ methods provide the most accurate flux estimates. This comparison of A_r, δϕ and A_rδϕ methods under non-ideal conditions provides guidance on their use. In this study, A_rδϕ methods have been coded into a new version of VFLUX, allowing users easy access to recent advances in heat tracing.