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The application of heat as a hydrological tracer has become a standard method for quantifying water fluxes between groundwater and surface water. The typical application is to estimate vertical water fluxes in the shallow subsurface beneath streams or lakes. For this purpose, time series of temperatures in the surface water and in the sediment are measured and evaluated by a vertical 1D representation of heat transport by advection and conduction. Several analytical solutions exist to calculate the vertical water flux from the measured temperatures. Although analytical solutions can be easily implemented, they are restricted to specific boundary conditions such as a sinusoidal upper temperature boundary. Numerical solutions offer higher flexibility in the selection of the boundary conditions. This, in turn, reduces the effort of data preprocessing, such as the extraction of the diurnal temperature variation from the raw data. Here, we present software to estimate water fluxes based on temperaturesFLUX-BOT. FLUX-BOT is a numerical code written in MATLAB that calculates vertical water fluxes in saturated sediments based on the inversion of measured temperature time series observed at multiple depths. FLUX-BOT applies a centred Crank-Nicolson implicit finite difference scheme to solve the one-dimensional heat advection-conduction equation. FLUX-BOT includes functions for the inverse numerical routines, functions for visualizing the results, and a function for performing uncertainty analysis. We present applications of FLUX-BOT to synthetic and to real temperature data to demonstrate its performance.
Flow patterns in conjunction with seasonal and diurnal temperature variations control ecological and biogeochemical conditions in hyporheic sediments. In particular, hyporheic temperatures have a great impact on many temperature-sensitive microbial processes. In this study, we used 3-D coupled water flow and heat transport simulations applying the HydroGeoSphere code in combination with high-resolution observations of hydraulic heads and temperatures to quantify reach-scale water and heat flux across the river-groundwater interface and hyporheic temperature dynamics of a lowland gravel bed river. The model was calibrated in order to constrain estimates of the most sensitive model parameters. The magnitude and variations of the simulated temperatures matched the observed ones, with an average mean absolute error of 0.7 degrees C and an average Nash Sutcliffe efficiency of 0.87. Our results indicate that nonsubmerged streambed structures such as gravel bars cause substantial thermal heterogeneity within the saturated sediment at the reach scale. Individual hyporheic flow path temperatures strongly depend on the flow path residence time, flow path depth, river, and groundwater temperature. Variations in individual hyporheic flow path temperatures were up to 7.9 degrees C, significantly higher than the daily average (2.8 degrees C), but still lower than the average seasonal hyporheic temperature difference (19.2 degrees C). The distribution between flow path temperatures and residence times follows a power law relationship with exponent of about 0.37. Based on this empirical relation, we further estimated the influence of hyporheic flow path residence time and temperature on oxygen consumption which was found to partly increase by up to 29% in simulations.
The functioning of the surface water-groundwater interface as buffer, filter and reactive zone is important for water quality, ecological health and resilience of streams and riparian ecosystems. Solute and heat exchange across this interface is driven by the advection of water. Characterizing the flow conditions in the streambed is challenging as flow patterns are often complex and multidimensional, driven by surface hydraulic gradients and groundwater discharge. This thesis presents the results of an integrated approach of studies, ranging from the acquisition of field data, the development of analytical and numerical approaches to analyse vertical temperature profiles to the detailed, fully-integrated 3D numerical modelling of water and heat flux at the reach scale. All techniques were applied in order to characterize exchange flux between stream and groundwater, hyporheic flow paths and temperature patterns.
The study was conducted at a reach-scale section of the lowland Selke River, characterized by distinctive pool riffle sequences and fluvial islands and gravel bars. Continuous time series of hydraulic heads and temperatures were measured at different depths in the river bank, the hyporheic zone and within the river. The analyses of the measured diurnal temperature variation in riverbed sediments provided detailed information about the exchange flux between river and groundwater. Beyond the one-dimensional vertical water flow in the riverbed sediment, hyporheic and parafluvial flow patterns were identified. Subsurface flow direction and magnitude around fluvial islands and gravel bars at the study site strongly depended on the position around the geomorphological structures and on the river stage. Horizontal water flux in the streambed substantially impacted temperature patterns in the streambed. At locations with substantial horizontal fluxes the penetration depths of daily temperature fluctuations was reduced in comparison to purely vertical exchange conditions.
The calibrated and validated 3D fully-integrated model of reach-scale water and heat fluxes across the river-groundwater interface was able to accurately represent the real system. The magnitude and variations of the simulated temperatures matched the observed ones, with an average mean absolute error of 0.7 °C and an average Nash Sutcliffe Efficiency of 0.87. The simulation results showed that the water and heat exchange at the surface water-groundwater interface is highly variable in space and time with zones of daily temperature oscillations penetrating deep into the sediment and spots of daily constant temperature following the average groundwater temperature. The average hyporheic flow path temperature was found to strongly correlate with the flow path residence time (flow path length) and the temperature gradient between river and groundwater. Despite the complexity of these processes, the simulation results allowed the derivation of a general empirical relationship between the hyporheic residence times and temperature patterns. The presented results improve our understanding of the complex spatial and temporal dynamics of water flux and thermal processes within the shallow streambed. Understanding these links provides a general basis from which to assess hyporheic temperature conditions in river reaches.