Practical limitations on the use of diurnal temperature signals to quantify groundwater upwelling

Abstract

Groundwater upwelling to streams creates unique habitat by influencing 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. We attribute this limitation to the thermodynamics of upwelling, under which the downward conductive signal transport from the streambed interface occurs opposite 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 (measurable) depth of the diurnal signal is very shallow, but phase lag is also short, yielding low signal to noise ratio and poor model sensitivity. Conversely, amplitude attenuation over similar sensor spacing is strong, yielding greater potential model sensitivity. Here we present streambed thermal time series over a range of moderate to strong upwelling sites in the Quashnet River, Cape Cod, Massachusetts. The predicted inverse relationship 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 return results consistent with numerical models and physical seepage meters, but the phase-lag analytical model results are generally unreasonable. 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 stream diurnal signal amplitude, upwelling magnitude, and streambed thermal properties that will be useful in designing future experiments.