Limits on Groundwater-Surface Water Fluxes Derived from Temperature Time Series: Defining Resolution-Based Thresholds

Heat as a tracer is frequently used to quantify Darcy fluxes across the groundwater-surface water interface. Often quantified through the analysis of diurnal or annual periodic temperature signals, these temperature time series methods rely on the advective transport of heat by flowing water perturbing the periodic conducted heat signal. Multiple methodologies have been developed that rely on temperature time series data collected from at least two unique depths a set distance apart. However, the lower limits at which these methods can no longer reliably quantify a Darcy flux are not well established. To examine these lower limits, synthetic temperature time series data were generated using a numerical model for various combinations of head gradients, sensor spacing, and thermal properties of the sediment. Darcy fluxes were subsequently quantified using the combined method and directly compared to prescribed Darcy fluxes. The dimensionless Peclet number, representing the ratio of advective to conductive heat flux, was used to establish threshold values at which the combined amplitude ratio and phase shift method was no longer able to reliably quantify a Darcy flux. The lowest recharge Darcy flux that can be quantified ranges from 0.07 to 0.2 m/day, dependent on the resolution of the sensor used to collect data, a narrower range than previously reported. When transitioning to a field setting, where the accuracy of Darcy fluxes is not known, a newly developed relationship between the true and inferred Peclet numbers can be used to evaluate quantified Darcy fluxes for accuracy.