PRACTICAL LIMITATIONS ON THE USE OF DIURNAL TEMPERATURE SIGNALS TO QUANTIFY GROUNDWATER UPWELLING

Groundwater upwelling to streams influences stream water quality and temperature; upwelling zones also serve as vectors for contamination when groundwater is degraded. Temperature time series data acquired along vertical profiles in the streambed have been applied to simple analytical models to determine rates of vertical fluid flux. These models are based on the downward propagation characteristics (amplitude-attenuation and phase-lag) of the surface diurnal signal. Despite the popularity of these models, there are few published characterizations of moderate-to-strong upwelling using field data. We attribute this limitation to the thermodynamics of upwelling, under which the downward conductive signal transport from the streambed interface occurs against the upward advective fluid flux. Governing equations describing the advection-diffusion of heat within the streambed predict that under upwelling conditions, signal amplitude attenuation will increase, but, counterintuitively, phase-lag will decrease. Therefore the extinction depth of the diurnal signal is very shallow, and phase lag is also short, yielding low signal to noise ratio and poor phase-lag model sensitivity. In contrast, amplitude attenuation over similar sensor spacing is strong, yielding greater potential signal to noise ratio and related amplitude-attenuation model sensitivity. These concepts are shown with streambed thermal time series collected over a range of moderate to strong upwelling sites in the Quashnet River, Cape Cod, Massachusetts. The predicted inverse relation between phase-lag and rate of upwelling was observed in the field data over a range of conditions, but the observed phase-lags were consistently shorter than predicted. Analytical solutions for fluid flux based on signal amplitude attenuation yield results consistent with numerical models and physical seepage meters, but the phase-lag analytical model results are generally not-comparable. Through numerical modeling we explore reasons why phase-lag may have been over-predicted by the analytical models, and develop guiding relations of diurnal temperature signal extinction depth based on site-specific diurnal signal amplitude, upwelling magnitude, and streambed thermal properties, that will be useful in designing future experiments.