Transient or steady‐state? Using vertical temperature profiles to quantify groundwater–surface water exchange

Abstract

Abstract:Heat is recognized as a natural tracer to identify the exchange of water between the groundwater and surface water compartment. One-dimensional (1D) heat transport models have the ability to obtain quantitative estimates of vertical fluxes through the sediment matrix. Input to these models can come from temperatures observed in the surface water and in the bed material of rivers and lakes. The upper thermal boundary condition at the groundwater-surface water interface is affected by seasonal and diurnal temperature variations. We hypothesize that effects of these transient influences are negligible at certain times of the year, such that the vertical temperature distribution can be approximated to be at steady state. Temperature time series observed over a year in the surface water and at several depths below a river in Belgium and in sediments of an acid mine lake in Eastern Germany were simulated with a heat balance model implemented in FEMME and the water and energy model VS2DH to obtain seepage fluxes. Temperature variations throughout the year at all depths could be adequately reproduced with the transient models. Vertical temperature profiles at several measuring times during the year were also fitted with an analytical, steady-state solution for 1D heat transport and the obtained fluxes compared to the results from transient simulations. Fluxes obtained from the much simpler steady-state solution were compared well with the flux rates from transient simulations for moments between mid and late summer, as well as during the winter. During transitional seasons (fall and spring), the fluxes from the steady-state solution deviated significantly from the transient estimates with a tendency to underestimate at the beginning and to overestimate towards the end of those seasons. We conclude that fitting a simple analytical solution for 1D vertical heat transport to temperature data observed at particular well-selected times of the year can provide an inexpensive, simple method to obtain accurate point estimates of groundwater-surface water exchange in rivers and lakes.

Upscaling lacustrine groundwater discharge rates by fiber-optic distributed temperature sensing

“…Further indirect methods for quantifying LGD rates are based on Darcy's law and require detailed observations of pressure head gradients (e.g., in piezometers) and hydraulic conductivity of the local aquifer [Stauffer, 1985;Kishel and Gerla, 2002]. Sediment depth profiles of temperature [Schmidt et al, 2006;Stonestrom and Constantz, 2003;Anibas et al, 2009;Meinikmann et al, 2013] or conservative ions [Mortimer et al, 1999;Schuster et al, 2003] at the sedimentwater interface have been successfully analyzed for indirect determination of water fluxes at the groundwater-surface water interface. However, the application of these methods is subject to certain assumptions (see sections 2.2.2 and 4.1) and requires the existence of distinct differences in the respective characteristics of the groundwater and surface water end-members.…”

Investigating patterns and controls of groundwater up-welling in a lowland river by combining Fibre-optic Distributed Temperature Sensing with observations of vertical hydraulic gradients

“…Schmidt et al, 2007;Anibas et al, 2009;Hannah et al, 2004Hannah et al, , 2009Constantz et al, 2003;Cardenas and Wilson, 2007;Krause et al, 2011b). Streambed heat transfer is controlled by three processes: (i) advective heat transfer, (ii) conductive heat transfer, and (iii) radiative heat transfer (Constantz, 2008;Hannah et al, 2004;Webb et al, 2008).…”

“…Streambed temperature patterns have been frequently reported to be dominantly controlled by advective heat fluxes from down-welling surface waters or up-welling groundwater (Cardenas and Wilson, 2007;Hannah et al, 2004;Malcolm et al, 2002). By measuring streambed temperatures in an environment with significant differences in groundwater and surface water temperatures, the propagation of a heat signal can be used as proxy, indicating exchange flow directions (Hatch et al, 2010;Keery et al, 2007;Anibas et al, 2009;Schmidt et al, 2007;Anderson, 2005) or even to quantify exchange fluxes (Hatch et al, 2010;Westhoff et al, 2007).…”

Investigating the spatio-temporal variability in groundwater and surface water interactions: a multi-technique approach

“…As groundwater temperature is commonly higher than that of surface water in winter and lower in summer (Anibas et al, 2009), measurement of temperature in rivers and streambeds can be used to identify the gaining and losing…”