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Theory, tools, and multidisciplinary applications for tracing groundwater fluxes from temperature profiles

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Quantifying groundwater fluxes to and from deep aquifers or shallow sediment is a critical task faced by researchers and practitioners from many environmental science disciplines including hydrology, hydrogeology, ecology, climatology, and oceanography. Groundwater discharge to inland and coastal water bodies influences their water budgets, thermal regimes, and biogeochemistry. Conversely, downward water flow from the land surface or from surface water bodies to underlying aquifers represents an important water flux that must be quantified for sustainable groundwater management. Because these vertical subsurface flows are slow and typically diffuse, they cannot be measured directly and must rather be estimated using groundwater tracers. Heat is a naturally occurring groundwater tracer that is ubiquitous in the subsurface and readily measured. Most of the academic literature has focused on groundwater temperature tracing methods capitalizing on the propagation of diel temperature sine waves into sediment beneath surface water bodies. Such methods rely on temperature–time series to infer groundwater fluxes and are typically only viable in the shallow subsurface and in locations with focused groundwater fluxes. Alternative methods that utilize temperature–depth profiles are applicable across a broader range of hydrologic environments, and point‐in‐time measurements can be quickly taken to cover larger spatial scales. Applications of these methods have been impeded due in part to the lack of understanding regarding their potential applications and limitations. Herein, we highlight relevant theory, thermal data collection techniques, and recent diverse field applications to stimulate further multidisciplinary uptake of thermal groundwater tracing methods that rely on temperature–depth profiles. This article is categorized under: Water and Life > Methods Science of Water > Methods Water and Life > Nature of Freshwater Ecosystems
Diverse environments for using temperature–depth (TD) profiles to trace groundwater fluxes with the scale of the vertical TD profiles increasing and the minimum detectable groundwater flux decreasing from left to right. Potential environments include (a) streambeds separated into transient and steady‐state zones, (b) offshore submarine applications (deep or shallow) for thermal groundwater tracing with concave‐upward profiles indicating recharge zones and convex‐upward profiles indicating discharge zones (note this implies the thermal profiles are at steady‐state, but this is often not the case in very shallow coastal zones), and (c) deeper aquifer‐scale applications in recharge and discharge zones with seasonal and climate impacts
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(a) Methods for temperature–depth (TD) profile recording in shallow sediment include (from left to right) progressively lowering a probe with a single temperature sensor, stakes with embedded, multidepth temperature loggers, self‐contained thermal logging instruments, and high‐resolution temperature sensors. (b) Methods for TD profile recording in wells include slowly lowering a temperature probe (including continuous logging and the stop–go method) or installing a fiber optic table cable to conduct distributed temperature surveys
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(a) Measured 1978 temperature–depth (TD) profiles for three sites in the Netherlands representing recharge (Deelen, blue), intermediate (Wenum, black) and discharge (Terwolde, red) conditions (data from Bense & Kurylyk, ). Symbols show inflection points in the TD profile (see text). (b) Data from the same boreholes reprofiled in 2016 with inflection points that have migrated downwards. Inflection points appear earlier and migrate more deeply in recharge zones (Deelen) than in discharge zones (Terwolde). (c) Thermal difference between (a) and (b). The Deelen profile was analyzed in FAST (see Figure ) since this profile was characterized by homogeneous conditions
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(a) Air temperatures from the Netherlands (gray) used to generate the Flexible Analytical Solution using Temperature (FAST) surface temperature boundary condition (BC). These air temperatures are represented using 5‐year steps. The influence of the offset (Section 4.2), which was determined to be 0.28°C for this site, is apparent in the upward shift from the gold to the green BCs. (b) Measured temperature–depth (TD) profiles in Deelen, the Netherlands, in 1978 (blue dashed line) and 2016 (red dashed lines). The 1978 profile was used as the FAST initial condition (blue solid line), and the forward model (forced by the green BC) produced the optimal 2016 modeled TD profile (red solid line) with a downward q of 0.3 m/year. Data underlying this figure are from Bense et al. ()
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Temperature–depth (TD) profiles simulated over 100 years by the CJT method (Equation ) for (a) discharge, (b) intermediate, and (c) recharge conditions. In (a) and (c), q has a magnitude of 0.4 m/year. Thermal properties represent those for saturated sand. Black circles represent theoretical, present‐day (i.e., 100 years from the IC) measured TD profiles that are the fitting objective for the CJT method
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(a) Measured deep temperature–depth (TD) profiles (gray) at the Willunga Super Science Site, South Australia (data from Irvine, Kurylyk, et al., ) and the optimal Bredehoeft and Papadopulos fits (red series), that yielded q values of 366 and 352 mm/year upward flow for Sites 4 and 5, respectively. (b) A measured, daily average, streambed TD profile in the Quashnet River, Massachusetts, USA (gray) and the optimal fit using the two‐layer Shan and Bodvarsson () algorithm (red). In this example (data from Kurylyk et al., ), a low‐λ organic mud layer overlies a high‐λ sand layer. The blue line in (b) denotes the interface between the two layers. Vertical ranges for the analyses in (a) and (b) are explained in the original papers
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General approach for using heat as a groundwater tracer
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Different boundary conditions (BCs) and initial conditions (ICs) for the steady‐state (a) and transient (b–e) solutions described in Sections 3 and 4, respectively. Citations and equations for each BC and IC are presented in the left column. Parameters are defined in Table
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