QUANTIFYING GROUNDWATER FLUX USING TEMPERATURE AS A TRACER AND MOST LIKELY ESTIMATORS (MLE)

Measurements of groundwater flux can inform us of how much water is entering the subsurface in recharge basins, as well as informing where water is moving in a stream-aquifer system, allowing for better tracking of water supply and contaminants when they enter public waterways. Determining the magnitude of water moving between the ground and surface has been investigated with different tracers such as dyes, salts, and radiocarbon / isotope tracers; but a method gaining popularity is using the natural temperature changes in the groundwater as a tracer. Using different analytical models, it is possible to quantify flux using diurnal temperature changes in an aquifer; one such method that is more widely used utilizes the difference in amplitude of the temperature measurements between sensors and filtering the signal through dynamic harmonic regression to determine flux (Hatch Amplitude method) in a MATLAB program called VFLUX. Where these methods fall short is the assumption that the subsurface is homogeneous with a fixed thermal conductivity (λ₀). A homogeneous subsurface is unlikely and indicates flux magnitude does not change with depth. It is possible to take the diurnal temperature signals and use FFT to transform the data into the Frequency Domain; to then determine flux and thermal diffusivity in the subsurface through a “Local Polynomial Most Likely Estimation” (LPMLEn) method. The LPMLEn method uses temperature data at several “n” depths and will use the diurnal signal that is collected to estimate what flux and thermal diffusivity are based off their log likelihood cost functions. The cost functions solve for the most likely parameters of flux and thermal diffusivity based on the advection-diffusion equation. Using the LPMLEn method, we developed a unique instrument that collects temperature data (used at four different field sites) and processes the data to determine flux and thermal diffusivity, and we are also processing the same datasets through VFLUX using the Hatch Amplitude method. The VFLUX solutions will be treated as the “true” solution and will be compared to the instrument’ solutions. The difference in the results have been evaluated with a two sample T-Test along with their Residual errors between the two to determine if the instrument is accurate to the known good solution.