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

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.

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