Evaluation and field-scale application of an analytical method to quantify groundwater discharge using mapped streambed temperatures

Summary

A method for calculating groundwater discharge through a streambed on a sub-reach to a reach scale has been developed using data from plan-view mapping of streambed temperatures at a uniform depth along a reach of a river or stream. An analytical solution of the one-dimensional steady-state heat-diffusion–advection equation was used to determine fluxes from observed temperature data. The method was applied to point measurements of streambed temperatures used to map a 60 m long reach of a river by Conant Jr. [Conant Jr. B., 2004. Delineating and quantifying ground water discharge zones using streambed temperatures. Ground Water 42(2), 243–257] and relies on the underlying assumption that streambed temperatures are in a quasi-steady-state during the period of mapping. The analytical method was able to match the values and pattern of flux previously obtained using an empirical relationship that related streambed temperatures to fluxes obtained from piezometers and using Darcy’s law. A second independent test of the analytical method using temperature mapping and seepage meter fluxes along a first-order stream confirmed the validity of the approach. The USGS numerical heat transport model VS2DH was also used to evaluate the thermal response of the streambed sediments to transient variations in surface water temperatures and showed that quasi-steady-state conditions occurred for most, but not all, conditions. During mapping events in the winter, quasi-steady-state conditions were typically observed for both high and low groundwater discharge conditions, but during summer mapping events quasi-steady-state conditions were typically not achieved at low flux areas or where measurements were made at shallow depths. Major advantages of using this analytical method include: it can be implemented using a spreadsheet; it does not require the installation or testing of piezometers or seepage meters (although they would help to confirm the results); and it needs only a minimal amount of input data related to water temperatures and the thermal properties of water and the sediments. The field results showed the analytical solution tends to underestimate high fluxes. However, a sensitivity analysis of possible model inputs shows the solution is relatively robust and not particularly sensitive to small uncertainties in input data and can produce reasonable flux estimates without the need for calibration.

Introduction

The exchange of water between surface water and groundwater has become an important subject in hydrogeological and river ecological research in the last two decades (Brunke and Gonser, 1997, Winter et al., 1998, USEPA, 2000). The interface between groundwater and surface water is often characterized by changes in geological materials, steep hydraulic gradients, high organic carbon content sediments, contrasts in redox conditions, and increased biological and microbial diversity and activity. These factors can strongly influence or alter the transport and fate of solutes, nutrients, and contaminants in water moving through a streambed or riverbed (Hedin et al., 1998, Conant et al., 2004, Laursen and Seitzinger, 2005). To understand these transport and biogeochemical processes at the groundwater–surface water interface, it is necessary to accurately characterize and assess the flow conditions in the streambed (Conant Jr., 2001). Accurately characterizing this exchange is a challenge, especially since spatial patterns of flow and discharge in a streambed have been shown to vary on a scale of meters to centimeters (Brunke and Gonser, 1997, Woessner, 2000, Brunke et al., 2003, Storey et al., 2003, Conant, 2004, Kalbus et al., 2007). Although discharge patterns in streambeds can be characterized using conventional instrumentation such as seepage meters and mini-piezometers (Lee and Cherry, 1978) or other standard methods (Kalbus et al., 2006), there is a need for methods that can quickly, accurately, and unobtrusively characterize spatial variability in discharge in a streambed on a sub-reach to a reach scale. Higher resolution measurements are needed to: (1) detect small-area high flux groundwater discharge zones that can dominate overall discharge of water and solutes along a reach (Conant Jr., 2001, Schmidt et al., 2006); (2) characterize the pattern and magnitude of discharge in order to infer the geochemical conditions or biodegradation in the streambed (Conant Jr., 2001, Kalbus et al., 2007); (3) better characterize the distribution of groundwater dependent benthic and hyporheic aquatic life (Malcolm et al., 2003, Brown et al., 2007). Moreover, recent changes in river management regulations increase the need for a better understanding of groundwater–surface water interactions. For example, the European Union Water Framework Directive requires an integrated management of groundwater and surface water bodies (European Commission, 2000) to reach a “good status” for both groundwater and surface water bodies.

Conant Jr. (2004) showed that by using heat as a natural tracer and mapping streambed temperatures in plan-view at a uniform depth, meter-scale spatial variations in flow in a streambed could be resolved along river reaches. The method can be used to quantify groundwater discharge in a way that is cost-effective, relatively quick, accurate, and robust. The concept of using subsurface temperatures to estimate the movement of water is well established and is summarized by Stonestrom and Constantz, 2003, Anderson, 2005. Temperature based methods generally rely on temperature contrasts and the fact that the horizontal and vertical temperature distribution in a streambed is a result of heat transport by the flowing water (advective heat flow) and by heat conduction through the solid and fluid phase of the sediments (conductive heat flow). While subsurface temperatures in groundwater discharge zones at depths greater than 5–10 m tend to remain relatively constant (i.e., vary less than 1.5 °C ) during the year (Lapham, 1989), surface water temperatures undergo larger changes between summer and winter. For example, in northern climates in summer when the surface water is warmer than the groundwater, streambed sediments in zones of high groundwater discharge will be colder than in the low discharge zones (Fig. 1). The Conant Jr. (2004) method of determining discharge flux patterns in a streambed was accomplished by mapping streambed temperatures and developing an empirical relationship that related measured temperatures to fluxes obtained using Darcy’s law and hydraulic data from mini-piezometers.

The success of the Conant Jr. (2004) method relied on the streambed temperatures being measured at a sufficient depth (0.2 m) that was below the zone of diurnal temperature oscillations (Fig. 1) and remained essentially constant at all locations during the time required to map the reach of stream. The observation that streambed temperatures at depths of 0.2 m or more are insignificantly altered by diurnal oscillations of surface water temperatures is consistent with the results of others (Keery et al., 2007). The mapping method provides observations at a uniform depth at many locations to determine fluxes but no time series of measurements at those locations, which is unlike previous applications of the heat-diffusion–advection equation that typically require that temperature be measured at multiple depths and (or) over time at a location (Carslaw and Jaeger, 1959, Bredehoeft and Papadopolus, 1965, Stallman, 1965, Suzuki, 1960, Turcotte and Schubert, 1982, Silliman et al., 1995, Taniguchi et al., 1999, Hatch et al., 2006, Schmidt et al., 2006). Because of the significant effort and cost of instrumenting multiple depths and collecting time series of temperatures, the approaches that rely on vertical temperature profiles tend to be limited to a few sampling locations and are not suited for mapping meter-scale spatial variations in flux over wide areas or long reaches of rivers. Recent advances using fibre optic temperature sensing equipment (Selker et al., 2006a, Selker et al., 2006b, Westhoff et al., 2007) allow characterization along lengthy cables over time with a meter-scale spatial resolution, but typically measure temperatures at the surface water/sediment interface and so can be more directly affected by surface water temperatures which can reduce the sensitivity to detect lower magnitudes of groundwater discharge.

It was hypothesized that if the success of the Conant Jr. (2004) method was because quasi-steady-state conditions occurred in the streambed then it would be possible to directly and accurately calculate discharge using a steady-state thermal-flux model and thereby negate the need and expense of installing and testing piezometers to obtain fluxes. This investigation evaluates the appropriateness of the steady-state assumption and demonstrates the effectiveness of using a one-dimensional steady-state analytical solution of the heat-diffusion–advection equation for calculating flux from plan-view streambed temperature measurements obtained from a river and also from a small first-order stream.