Observing temporal patterns of vertical flux through streambed sediments using time-series analysis of temperature records

Rates of water exchange between surface water and groundwater (SW-GW) can be highly variable over time due to temporal changes in streambed hydraulic conductivity, storm events, and oscillation of stage due to natural and regulated river flow. There are few effective field methods available to make continuous measurements of SW-GW exchange rates with the temporal resolution required in many field applications. Here, controlled laboratory experiments were used to explore the accuracy of analytical solutions to the one-dimensional heat transport model for capturing temporal variability of flux through porous media from propagation of a periodic temperature signal to depth. Column experiments were used to generate one-dimensional flow of water and heat through saturated sand with a quasi-sinusoidal temperature oscillation at the upstream boundary. Measured flux rates through the column were compared to modeled flux rates derived using the computer model VFLUX and the amplitude ratio between filtered temperature records from two depths in the column. Imposed temporal changes in water flux through the column were designed to replicate observed patterns of flux in the field, derived using the same methodology. Field observations of temporal changes in flux were made over multiple days during a large-scale storm event and diurnally during seasonal baseflow recession. Temporal changes in flux that occur gradually over days, sub-daily, and instantaneously in time can be accurately measured using the one-dimensional heat transport model, although those temporal changes may be slightly smoothed over time. Filtering methods effectively isolate the time-variable amplitude and phase of the periodic temperature signal, effectively eliminating artificial temporal flux patterns otherwise imposed by perturbations of the temperature signal, which result from typical weather patterns during field investigations. Although previous studies have indicated that sub-cycle information from the heat transport model is not reliable, this laboratory experiment shows that the sub-cycle information is real and sub-cycle changes in flux can be observed using heat transport modeling. One-dimensional heat transport modeling provides an easy-to-implement, cost effective, reliable field tool for making continuous observations of SW-GW exchange through time, which may be particularly useful for monitoring exchange rates during storms and other conditions that create temporal change in hydraulic gradient across the streambed interface or change in streambed hydraulic conductivity.