Profiles of temperature time series are commonly used to determine hyporheic
flow patterns and hydraulic dynamics in the streambed
sediments. Although hyporheic flows are 3-D, past research has focused on determining the magnitude of the vertical flow component
and how this varies spatially. This study used a portable 56-sensor, 3-D temperature array with three heat pulse sources to measure the
flow direction and magnitude up to 200
Application of heat as a tracer to hydrological studies has rapidly progressed in recent decades, driven by the simplicity of the methodology and low cost of sensor technology (Anderson, 2005; Rau et al., 2014). Using this method, spatial and temporal flow dynamics within the hyporheic zone, particularly hyporheic transport and exchange (e.g. longer attenuation), have been shown to enhance stream denitrification (Harvey et al., 2013; Gomez-Velez et al., 2015; Zarnetske et al., 2011), degradation of mine-pollutants (Gandy et al., 2007) and the degradation of wastewater micro-pollutants (Engelhardt et al., 2013). It is also widely used by other disciplines, e.g. ecology, where the thermal regime in river systems plays an important role in ecosystem health (Caissie, 2006; Harvey and Wagner, 2000; Brunke and Gonser, 1997; Boulton et al., 1998).
The majority of streambed heat tracer studies use vertical, ambient temperature profiles and a one-dimensional analytical solution of the heat diffusion–advection equation to estimate streambed exchange fluxes and infer hyporheic flow patterns (Constantz et al., 2002; Naranjo and Turcotte, 2015; Rau et al., 2010; Vogt et al., 2010). Series of vertical temperature profile sticks installed along transects have also be used in other studies to examine 2-D flow fields in the streambed (Constantz et al., 2013, 2016; Shanafield et al., 2010). When using ambient temperature fluctuations and one-dimensional heat transport models, several days of data are required to estimate the vertical flux. In addition, an assumption is made that the dominant exchange process is in the vertical direction only and the horizontal or lateral component of flow is considered to be negligible. There are very few investigations which have tried to capture both the vertical and horizontal component of flow, as the determination of the non-vertical component is challenging with the physical installation of sensors to measure the flow field as well as the mathematical framework to process the data (Munz et al., 2016; Briggs et al., 2012; Shanafield et al., 2016).
More recently, the suitability of active temperature sensing has been explored as an approach to characterise streambed spatial and temporal exchange dynamics in three dimensions. The injection of heat as a tracer is not new, with a number of studies using the active temperature-sensing technique to evaluate groundwater flow within wells (Sellwood et al., 2016; Read et al., 2014; Banks et al., 2014), flow in sediments (Greswell et al., 2009; Ballard, 1996; Bakker et al., 2015), surface water–groundwater exchange processes (Kurth et al., 2015) and hyporheic exchange flows in the hyporheic zone (Angermann et al., 2012a, b; Lewandowski et al., 2011).
The aim of the present study was to develop an active heat-pulse-sensing (HPS) instrument to conduct rapid assessments of the three-dimensional (3-D) flow field in the streambed from fine silt to coarse gravels across different geomorphological structures. It builds upon previous studies by Lewandowski et al. (2011) and Angermann (2012a, b), who developed an active heat pulse sensor to determine the flow direction and flow velocity in shallow sandy stream environments. In the present study we have developed a more robust field instrument and advanced the analysis of the temperature breakthrough data using the analytical solution of the heat transport equation for a 3-D array. Parameter estimation and uncertainty analysis was implemented using the differential evolution adaptive metropolis (DREAM) algorithm (Vrugt et al., 2009c), an adaption of the standard Markov chain Monte Carlo method, to determine the direction and magnitude of flow velocity patterns in the streambed at multiple depths. Laboratory tests were conducted in a sand tank using an extensive range of flow scenarios with tightly controlled hydraulic conditions to evaluate the methodology. Field tests demonstrated the active heat pulse instrument in different geomorphological structures in a small stream in the Mount Lofty Ranges, South Australia.
A 56-sensor, 3-D temperature array with three heat pulse sources (also known as the Hot Rod) was developed to measure the flow direction and
magnitude up to 200
A terminal program is used to communicate with the data logger and to control the sampling routine of the Hot Rod (e.g. sampling frequency, duration and power output of the active heat pulse, selected heating element used and logging period). A sealed 12 V lead acid battery together with a power supply regulator is used to maintain a constant 12 V output to the heating elements. The power delivered to the three heating elements can be adjusted in the logger program from 0 to 100 % to provide greater flexibility to the required active heat pulse. The input current from the power supply regulator is also recorded each time the temperature is measured to ensure a tight control on the actual power being delivered through the heating elements to the surrounding material and therefore reducing uncertainty in the analysis routine.
An important aspect of the design was that it could be rapidly and easily deployed to capture large spatial data sets along a reach of
stream or across a pool–riffle sequence. Installation requires gently pushing (or lightly tapping with a shockless impact hammer) the
device into the streambed ensuring that there is a sufficient gap between the top of the sediment and the underside of the base plate
to prevent streamflow constriction (the top thermistor is set at 44
Once installed and equilibrated with the surrounding sediment, the logger program is executed and the ambient temperature is measured
at each thermistor (
The magnitude and direction of the water velocity at the observation point based on the measured temperature breakthrough curves at the
56 sensors were determined using a modified version of the heat transport equation:
An analogy can be made to the solute transport equation where the mean water velocity is replaced with
The thermal mass input was not considered in previous studies as a known parameter (Angermann et al., 2012b). The Hot Rod, however,
uses a known wattage, and the thermal mass term is given as
The requirement of Eq. (4) is that the flow component is only in the
Schematic showing the rotation of the coordinate system to determine
angles
We then substitute these new dimensions into Eq. (4) to get
Parameter estimation and uncertainty analysis was undertaken using the DREAM
algorithm (Vrugt et al., 2009a, b). The fit of the data
was performed by assessing the likelihood of each individual model run. The
likelihood is defined as
Initial parameter values for
The DREAM method is an adaption of the standard Markov chain Monte Carlo method. The technique is initialised by specifying a number of chains. Each chain receives starting parameters by randomly sampling the parameter ranges (Table 1). After calculating an initial likelihood for the starting parameters, the algorithm selects proposed parameter values using the other chains, and the likelihood of these model parameters are also calculated. If the likelihood of these parameters is greater than the current parameters, the new parameters are accepted; however, if the likelihood of the new parameters is lower, the transition probability is calculated using a ratio of the likelihoods, and the transition is determined by generating a random number. The method is explained in greater detail in Vrugt et al. (2009c). The general outcome is that the chains spend a greater amount of time in locations of more favourable parameters, and the distribution of these parameters represents the posterior distribution of the parameter probabilities, given the model, the data and the prior knowledge of the parameter distributions.
Laboratory sand tank dimensions for each of the flow scenarios:
Breakthrough curves shown of the fourth vertical thermistor
(158
The optimisation was undertaken using five parameters:
Calculated fluxes and directions for the four flow scenarios at each
of the heat injection depths:
Fluxes of the different flow scenarios, listed along the
A laboratory sand tank was used to provide a controlled environment on the
hydraulic regime to test the performance of the Hot Rod and so that the
different flux calculation methods could be compared. A total of 36
combinations of flow direction, magnitude and depth of heat pulse were used.
The dimensions of the sand tank for each of the scenarios varied slightly
according to the fixed boundary conditions (Fig. 3). Four flow scenarios were
tested: (1) horizontal flow from left to right (inflow and outflow occurred
over the entire saturated cross-sectional area of the sediment volume on the
left and right boundaries of the tank), (2) diagonal flow from the top left
to bottom right (inflow was through a 20
The Sturt River, Adelaide, Australia, is a perennial river system receiving the majority of its input from a wastewater treatment
facility. The geomorphology of the river was characterised by a narrow channel, no more than 3
Overall, the modelled breakthrough curves closely fit the observed data from
the 56-sensor array with the modelled curves capturing the rising limb, peak
and tail of the measured temperature data over the sample period (Fig. 3).
The variance of each parameter is included in the modelled temperature
breakthrough curves; however, the uncertainty is so small that it cannot be
seen without zooming in on the individual curves. Selected breakthrough curve
plots are shown of the fourth vertical thermistor (158
Overall, the 3-D flow fields calculated from the HPS Hot Rod in the laboratory sand tank for the four flux scenarios and heat injection
depths (65, 140 and 215
Results from the other three scenarios showed that the modelled flux direction is close to parallel to the flow conditions established in the tank and the magnitude of the flux was similar at each of the heat injection depths (Fig. 5c–h). Reviewing the time series data in the 3-D plots (Supplement), the spreading of the heat pulse from the heat injection depth can be clearly detected, indicating how the heat pulse moves along the established flow line. The thermistor highlighted in blue in the 3-D plot was the sensor that showed the maximum temperature breakthrough curve and clearly shows a different orientation to the most likely flux direction (black arrow) as determined by the DREAM algorithm.
Some discrepancies in the direction of the modelled flow and differences in flux magnitude at each heat injection depth may be attributed to (1) placement orientation and the angle of the sensor positions of the Hot Rod relative to the flow conditions established in the tank, (2) boundary conditions in the tank to establish flow and (3) the fact that the optimisation routine determines the best fit of all the observed data in a 3-D volume around the heat injection depth rather than at a specific point.
The difference in flux magnitude at each heat injection depth may be attributed to the number of sensors that were used in the
optimisation routine. For example, at the heat injection depth R2 (140
Comparison of the observed (blue line) and modelled breakthrough curves for selected temperature sensors (
Calculated fluxes and flux directions at the three heat injection
depths from two of the stations at the experimental field
site.
In the case of no-flow conditions established in the sand tank (Fig. S2), the
optimisation routine fitted the measured temperature breakthrough data;
however, on closer inspection of the 3-D time series plot it was evident
based on the uniform heat plume around the heat injection point during the
injection period that heat transport was by conduction only. Absence of clear
advective movement of the heat pulse and a calculated flux less than about
The flux magnitude (
The measured saturated hydraulic conductivity according to the KSAT meter for the sand tank sand was
Histograms of the flux magnitude (
Constraining the range of the thermal conductivity values used in the optimisation routine to the known measured thermal conductivity
of the sand from the KD2 Pro instrument showed little impact on the calculated flux magnitude. However, comparing the modelled
breakthrough curves from two optimisations when the range in thermal conductivity was limited to the measured known thermal
conductivity (3
Our study found that the inclusion of longitudinal and transverse thermal dispersion had less than a 2 % difference on the mean calculated fluxes. The study by Rau et al. (2012) determined Darcy velocities derived from heat experimentation that included the thermal dispersivity term differed by up to 20 % when compared to solute experimentation. However, other studies in the literature have shown that there is considerable uncertainty on the magnitude of the thermal dispersivity (Anderson, 2005). Thermal dispersivity has also been found not to be scale-dependent such as solute dispersivity because heat transport happens through the pore water and through the sediment matrix (Vandenbohede et al., 2009). Therefore, given the scale that we are working at (few centimetres) and also the low velocities, the effect on the calculated flux is likely to be negligible.
The measured 3-D flow fields at the experimental site showed considerable variability in the direction of flow and flux magnitude over
Measured
Despite the early pioneering work of Lewandowski et al. (2011) and Angermann et al. (2012b) for the concept of a 3-D active heat pulse sensor to determine flux and direction in the shallow streambed, their studies experienced a number of shortcomings that are related to the design of the instrument and the analysis of the data. This included (1) a limited number of sensors and spatial positions around the heating element; (2) weakness with the sensor sticks wobbling and therefore poorly constrained sensor positions in relation to the heating element; (3) limited constraint on the input functions to the heat transport equation, i.e. not knowing the current input; and (4) lack of a suitable optimisation routine to determine the most likely set of parameters to constrain the data and an uncertainty analysis on the flux magnitude and its direction.
The rigidity and robustness of the Hot Rod and use of heating elements at three different vertical positions provided a method to examine how the flux and its direction varied vertically with depth beneath the streambed interface at individual locations in a range of different environmental settings and sediment types. The use of two horizontal spacings between the heating elements and thermistors as well as additional thermistors at multiple angles to the heating elements increased confidence in the measurement of heat transport processes and tightened the optimisation routine of the temperature data. The addition of the measured input of energy at the heating element in the heat transport equation as a series of discrete heat pulses over the injection period provided one less unknown variable to calibrate against. In many of the experiments conducted in the sand tank and at the experimental site, the optimisation routine using the DREAM algorithm showed that the most likely flux direction from the heat injection depth was not towards the sensor that showed the maximum temperature breakthrough because it uses all of the sensor temperature breakthrough curves in the analysis. The 3-D time series plot was a valuable tool in assessing this result and it also showed whether heat transport was dominated by diffusion and/or conduction with radial symmetry around the heating element or whether there was convective heat flow. This interrogation process was found to be critical in the data assessment to ensure that the model did not overfit the measured data with unrealistic physical values for the sediment and heat transport conditions.
The laboratory and experimental field site applications using the DREAM algorithm for parameter estimation and uncertainty analysis demonstrated the performance of the active heat-pulse-sensing instrument (the Hot Rod) to measure the multi-directional 3-D-flow fields and fluxes in the near-surface streambed. Active heat pulse sensing provides a number of advantages over other approaches that have investigated hyporheic exchange, including the low cost of data collection and the rapid assessment of small physical processes that can be undertaken on a reach scale. Marzadri et al. (2013) showed that the hyporheic residence time, which is influenced by the streambed physical morphology and in-stream flow discharge, ultimately determines the spatially complex patterns of the time-varying thermal regime within the hyporheic zone. The short-duration active heat pulse sensing helped overcome some of the challenges in measuring the water temperatures because of the stronger signal from the heat pulse.
Most other studies that use heat as a tracer assume 1-D flow only and the lateral or horizontal component is not considered. Studies that have identified the geometry of the subsurface flow field using a polynomial model fitted to the amplitude ratio of the vertical temperature profiles were only able to determine the deviation from one-dimensional vertical flow (Munz et al., 2016). Errors in the vertical component of flow have been shown to progressively increase with the magnitude of the horizontal flow component (Lautz, 2010). The 3-D analysis routine and sensor arrangement applied in this study were able to capture all three components of the flow field around the point of observation. The importance of capturing the multi-directional flow field was clearly demonstrated in the sand tank under an extensive range of flow conditions that would be anticipated in a dynamic stream environment. Measurements of the hydraulic gradient and characterising the physical properties of the streambed sediment are also important in understanding the dynamic exchange processes within the hyporheic zone and the very transient nature of such environments.
The concept and design of the active heat-pulse-sensing instrument could also be adapted to other hydrological research areas, including the measurement of shallow interflow along hillslopes and discharge from groundwater seeps and springs.
Data are available at
The supplement related to this article is available online at:
The authors declare that they have no conflict of interest.
We are grateful to Flinders University South Australia for a small grant to develop the HPS Hot Rod and all Faculty of Science and Engineering technical workshop staff for their assistance in hardware development and construction. Funding support from the Australian Research Council (ARC) Linkage Project LP150100588 is acknowledged. Additional funding through the Australia–Germany Joint Research Cooperation Scheme of Universities Australia and the German Academic Exchange Service (DAAD, grant no. 57216806) provided support for fieldwork collaboration between the research institutes. Edited by: Thom Bogaard Reviewed by: Jim Constantz and Bas des Tombe