COMPARISON OF THE HATCH, KEERY, MCCALLUM AND LUCE METHODS UNDER NON-IDEAL CONDITIONS: WHICH MODEL SHOULD I USE, AND WHEN?

Pairs of temperature time series can be used to calculate fluid fluxes between surface water bodies and groundwater using amplitude ratios (Ar), phase shifts (Δϕ), or methods which simultaneously use both (denoted here as ArΔϕ). Newer ArΔϕ methods also offer the ability to compute thermal diffusivity, a parameter that is expected to be relatively homogeneous spatially and temporally. These temperature time series methods assume one-dimensional flows that are constant in time, that the properties of the porous medium are homogeneous and that the temperature signal at the surface is sinusoidal. While the influences of non-ideal conditions have been extensively investigated for the Ar or Δϕ approaches, the impacts of non-ideal conditions on ArΔϕmethods are not as well understood.

In this study, the influences of a non-sinusoidal upper temperature boundary and temporally variable fluxes on model results are assessed from controlled sand column experiments. The influence of multi-dimensional flows and streambed heterogeneity are assessed through the use of 3D numerical simulations. These experiments provide the opportunity to evaluate the performance of different analytical solutions where fluxes are known.

Fluxes and thermal diffusivities are calculated using the VFLUX MATLAB scripts, which have been extended to include ArΔϕ methods. Results confirm that calculated thermal diffusivities can be used to identify periods where flux calculations are unreliable due to unsteady flow rates. In addition, sudden changes in calculated thermal diffusivity with depth correlate with clearly erroneous flux calculations. Results from Monte Carlo analyses show that uncertainties in calculated fluxes caused by uncertainties in thermal parameters are generally greater for equations that use Ar or Δϕ, relative to ArΔϕ methods, but also that flux calculations are not necessarily more accurate using ArΔϕ methods. Of the three potential methods (Ar, Δϕ or ArΔϕ), Δϕ typically performs the worst, and given the inability to determine flow direction from this method, Ar or ArΔϕ methods are better alternatives.

The extended capabilities of VFLUX will allow practitioners access to updated techniques, and the ability to calculate thermal diffusivities will be useful in determining whether flux calculations are reliable.