Quantifying downflow through creek sediments using temperature time series: one-dimensional solution incorporating measured surface temperature

Several authors have addressed the question of identifying the location of and quantifying the volume of groundwater/surface water interaction. Utilizing measurement of temperature within the sediments has been suggested as a means of estimating water flux through the sediments. A qualitative version of this method has been applied to identifying locations of communication between a creek and groundwater based upon temperature time series measurements in the water column and the sediments. The discussion presented earlier is extended to a more general solution which allows for incorporation of measured surface temperature (rather than an assumed surface temperature). The mathematical formulation presented is targeted on the quantification of flux across the sediment for conditions of one-dimensional downflow with a constant flux over periods of days to weeks. This technique, based on the assumption that the temperature of the surface water is the primary thermal influence on sediment temperature, is shown to provide an estimate of fluid flux (volume of water per area per time) for flux rates above a critical threshold. The flux threshold depends on a number of factors including thermal diffusivity of the sediments and depth of burial of the temperature measuring device. Based on use of three simple forcing functions for temperature at the surface of the sediments, it is shown that the amplitude of the temperature response in the sediments to a change in temperature in the overlying water column decreases with increasing depth and decreasing flux. Further, the timing of the peak response in the sediments becomes increasingly delayed as depth increases and flux decreases. These observations, combined with consideration of the assumption of one-dimensional flow, lead to suggesting that field design be based on relatively shallow burial (e.g. 5–15 cm) of the device to measure sediment temperatures. Based on these observations, one of the data sets presented earlier is reanalyzed to derive flux estimates. It is shown that a reasonable fit is obtained with a downflow flux of less than 0.03 cm day−1. Independent measurement of hydraulic gradient and hydraulic conductivity provide a range of flux estimates for the same site (although measured in a different year) which are consistent with this value. Based on these results, it is argued that this technique is a reasonable screening tool for use in situations where relatively inexpensive, point estimates of water flux are required within losing reaches of a creek.