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

• Published in: Journal of hydrology (Amsterdam) 2007-12, Vol.347 (3), p.292-307
• Main Authors: Schmidt, Christian, Conant, Brewster, Bayer-Raich, Martí, Schirmer, Mario
• Format: Article
• Language: English
• Subjects: Analytical solution; aquifers; Earth sciences; Earth, ocean, space; equations; Exact sciences and technology; Field methods; Freshwater; Groundwater discharge; groundwater flow; Groundwater–surface water interaction; Hydrogeology; Hydrology; Hydrology. Hydrogeology; mathematics and statistics; seepage; spatial variation; stream channels; Streambed temperature; streams; surface water; Temperature modeling; water temperature
• ISSN: 0022-1694; 1879-2707
• DOI: 10.1016/j.jhydrol.2007.08.022

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.