Spatiotemporal Variability of Hyporheic Flow in a Losing River Section

Characterizing the spatiotemporal variability of water fluxes at the stream‐groundwater interface is extremely challenging due to the lack of methods for estimating hyporheic flows at different scales. To address this, we demonstrate the potential of Active‐Distributed Temperature Sensing (DTS) methods for measuring and mapping hyporheic flow in a lowland stream. Experiments were conducted by burying a few hundred meters of heatable Fiber‐Optic cables within streambed sediments in a large meander, where permanent stream‐losing conditions are observed along the stream reach. We propose a new methodology to filter ambient temperature variations along the heated section of the DTS cable and to extend the application of Active‐DTS to losing streams. After data processing, the results show that, along lateral and longitudinal stream profiles, both thermal conductivity and water flux values follow normal distributions with relatively small standard deviations. Hyporheic fluxes vary by one order of magnitude. The absence of correlation between water fluxes within the hyporheic zone and streambed topography variations suggests that the variability is mainly controlled by local streambed heterogeneities. This means that the spatiotemporal variability of fluxes may be used as a marker of the variability of streambed hydraulic conductivities. The relatively low spatial variability (one order of magnitude) in hyporheic flow suggests a small variability of streambed properties. This is an important result for calibrating models assessing hyporheic processes, in which the hydraulic conductivity distribution is generally assumed. Additionally, measurements made over three years yield similar estimates showing the remarkable stability of hyporheic flows through time.

Modeling (Boano et al., 2010;Cardenas et al., 2004;Gomez-Velez & Harvey, 2014;Shanafield et al., 2010) and laboratory experiments (Arnon et al., 2010;Fox et al., 2014Fox et al., , 2016;;Salehin et al., 2004) have provided a better understanding of the mechanisms controlling hyporheic fluxes.However, the models often fail to reproduce field observations adequately.For example, several mechanistic models have investigated the effects of geologic heterogeneity on hyporheic flow and of riverbed heterogeneity on stream-groundwater interactions (Brunner et al., 2017;Fleckenstein et al., 2010;Hermans et al., 2023;Singh et al., 2020;Trauth & Fleckenstein, 2017).When applied in the field, these mechanistic model poorly described field observations (Bardini et al., 2013;Cardenas et al., 2004;Laube et al., 2018).Attempting to explain such divergence, Krause et al. (2022) suggested that boundary conditions of models do not appropriately represent the mechanisms governing hyporheic flow dynamics in a real-world context.To implement realistic boundary conditions of physical models, it is crucial to use field methods with the ability to image the effect of heterogeneities at high resolution within the hyporheic zone over a range of spatial and temporal scales.
Field studies often rely on the characterization of streambed hydraulic conductivities, whose in-situ measurements are typically taken at the point-scale, leading to significant estimate uncertainty (Landon et al., 2001).Heat has also been used as a tracer to assess hyporheic flow with the development of vertical temperature profiles (Constantz, 2008) and heat pulse probes (Banks et al., 2018;Lewandowski et al., 2011;Zlotnik & Tartakovsky, 2018).However, while these approaches are efficient to assess hyporheic fluxes locally, they do not constrain spatial variability of the fluxes, unless surveys are repeated (Schmidt et al., 2006).This is time-consuming and may still yield spatial biases based on the constraints of such sensors.To overcome these problems, Distributed Temperature Sensing (DTS) technology can be used to collect high resolution temperature measurements along Fiber Optic (FO) cables.By installing FO cables at different depths, these data can then be used to estimate the spatial variability of vertical water fluxes (Mamer & Lowry, 2013;Shanafield et al., 2018).However, the installation of FO cables at different depths in the hyporheic zone is technically challenging.
In this context, the Active-Distributed Temperature Sensing (Active-DTS) technique is attractive as it can provide high-resolution measurements of saturated subsurface flows.Active-DTS methods rely on heating of a FO cable while monitoring the resulting temperature rise at high spatial (from 10 cm to meters) and temporal resolution (every 30 s).In saturated sediments, the temperature increase is primarily dependent on the thermal conductivity of the porous media and on the water flux (estimated by the Darcy flux) through the porous media (Bense et al., 2016;del Val et al., 2021;des Tombe et al., 2019;Simon et al., 2021;Zhang et al., 2023).Water flow leads to advective heat transfer that dissipates the injected heat away from the cable more quickly than conduction alone, reducing the observed increase in temperature.
The use of Active-DTS measurements for the assessment of groundwater-surface water interactions in the hyporheic zone is relatively new.The first use of Active-DTS in such context was proposed by Kurth et al. (2015), who showed the possibility of detecting lower and higher flow rates along the heated cable.These vertical flux estimates are limited to a point-scale of discharge/infiltration.Briggs et al. (2016) then proposed to quantify vertical fluxes in streambed sediments using active heating of wrapped fiber-optic sensors, but this also provides only local discharge/infiltration assessment.More recently, Simon et al. (2022) buried a heatable FO cable into the streambed sediments of a headwater stream to assess the groundwater discharge.Results showed a large variability of both thermal conductivities and upward fluxes along a relatively short longitudinal profile.Banks et al. (2022) used horizontal directional drilling for installing heated FO cables buried 5 m below a losing reach of a braided river.They found a relatively small spatial variability of river losses to the underlying aquifer system (Banks et al., 2022).
Here, we present results of a novel Active-DTS study in the hyporheic zone of a predominantly losing river section.The aim is to estimate and map the spatiotemporal variability of water fluxes and of streambed sediment properties at high resolution (with a measurement point every 12.7 cm) in a large lowland river.To do this, we designed an innovative field setup, consisting of two fiber-optic cables buried along several hundred meters within the river sediments.In addition, we present a new approach to remove ambient temperature variations from the measured temperature signal to generalize the application of Active-DTS measurements to losing streams.

Experimental Site
Active-DTS measurements were conducted at the Signy experimental site located in the lowland reach of the Sélune River in Normandy, France (Figures 1a and 1b).The Sélune River drains a 1,083 km 2 catchment before flowing into Mont-Saint-Michel Bay in north-western France (Fovet et al., 2020).The experimental site is located ∼15 km from the final outlet to the sea and ∼ four km downstream of a major dam (Figure 1a).The drainage area upstream from the study site is ∼777 km 2 .In this upstream area of the catchment, the Sélune River is a high-order and large stream (15-20 m width) characterized by a floodplain and meanders, with lower streambed gradients compared to the upper reaches.The experimental site consists of a 34-ha meander with east to west flow (Figure 1b).The annual average discharge at the Signy experimental site is 9.5 m 3 .s 1 , based on data acquired from a local hydrometric station.Photos of the experimental site are provided in Supporting Information S1 (Figure S1).
The alluvial aquifer located across the neck of the meander lobe has been used for municipal water supply since the 1970s, with three pumping wells providing 1,500 m 3 of water in total per day (Figure 1b).Data from a piezometer network consisting of 10 piezometers across the meander, show that groundwater head is always lower than stream level, indicating permanent stream-losing conditions.The pumping induces significant hydraulic gradients between the stream and the aquifer (around 8-9 × 10 3 m.m 1 ), which considerably simplifies the flow complexity in the hyporheic zone.This assumption is consistent with groundwater level monitoring across the neck, which displays rapid groundwater response to stream stage variations, indicating the hydraulic connection between the stream and the alluvial aquifer.Thus, the response time between any stream water level variation and the related groundwater level variation measured in P1, which is the closest piezometer of the bank where the experiment was conducted (Figure 1b), is around 10 min.

Experimental Setup
Active-DTS experiments were performed in the southern part of the meander (Figure 1b), where three piezometers were installed to monitor groundwater level changes.This section of the meander was selected because of stream/riverbank accessibility.Electricity is also available at the hydrometric station.Figure 1c shows the experimental setup consisting of two FO cables buried within the streambed sediments at 10 cm depth.Experiments were conducted using a 3.8-mm-diameter cable (BruSens cable; reference LLK-BSTE 85°C) containing four multimode 50/125-μm fibers, protected by steel armoring and a plastic jacket.For a long-term deployment, this type of cable presents the advantage of being particularly resistant to damage induced by flood events or animals.Moreover, electricity can be injected within the steel armoring of the cable, which allows heating the FO cable.In this configuration, each FO cable can be heated along some sections of the cable, while non-heated sections can be used to monitor riverbed temperature.Moreover, the distance between the heated armoring and the fibers does not vary along the cable.
FO1 consisted of a 167 m-long buried cable with three electrical connections, F1-3, F1-2 and F1-1, which allowed for varying heat injection points along the cable.A toggle switch allowed for three sections of the cable to be heated.These sections of cable are referenced as F1-3/F1-2 (65 m length), F1-2/F1-1 (55 m length), and F1-3/F1-1 (120 m length) based on the section of the cable between electrical connections (Figure 1c).Whatever the section heated, streambed temperature variations were continuously monitored in the sections that were not heated and along the 47 m of buried cable located outside the heated sections.
The second buried FO cable, FO2, was installed in a U-shape to get three parallel heatable cable sections at different distances from the riverbank.The distance between these sections varied between 2 and 4 m.This innovative experimental setup allowed us to study both the longitudinal variability of surface water infiltration over the whole heatable section (120 m) and the lateral variability at different distances from the riverbank (Figure 1c).FO2 is a 207 m-long buried cable with four electrical connections, F2-4, F2-3, F2-2 and F2-1.The toggle switch allowed for five sections of the cable to be heated.These sections of cable are referenced as F2-4/ F2-3 (65 m length), F2-3/F2-2 (40 m length), F2-2/F2-1 (65 m length), F2-4/F2-2 (105 m length) and F2-3/F2-1 (105 m length) based on the section of the cable between electrical connections (Figure 1c).and FO2) were buried within the streambed sediments at 10 cm-depth and heated sections of the cables were connected separately to a heat pulse unit and controlled using a toggle switch.The total length of buried FO cables is about 374m.
A plow developed for the installation of FO in soils and sediments, was used to bury the FO cables within the streambed at 10 cm depth (Figure S1 in Supporting Information S1).The installation of the whole setup required one week with a team of five people.During the installation, GPS measurements were made to precisely locate the cables.The burial depth of the cables was also controlled each half meter by controlling the depth of the plow in the streambed.During the deployment, the height of the water column was also measured using a ruler all along the cable, which allowed mapping the riverbed morphology and the alternance of riffles and pools.Riffle-pool sequences were along ∼50 m of the FO1 cable (see Figure S4b in Supporting Information S1).

DTS Measurements
Two DTS units were used for recording temperature variations (Figure 1c): one Silixa Ultima S instrument configured to collect data at a sampling resolution of 12.7 cm, with a 20 s time interval and one Silixa XT-DTS instrument configured to collect data at a sampling resolution of 25.4 cm and a 20 s time interval.Both units were configured in a double-end configuration (van de Giesen et al., 2012) and calibrated using one cold calibration bath, a box filled with wetted ice, and one warm calibration bath, equipped with a heating resistor.About 20 m of FO cable were submerged in each calibration bath.Following Simon et al. (2020), effective spatial resolutions of DTS measurements along the cable are estimated to vary between 51 and 67 cm for the Silixa Ultima S instrument and between 66 and 90 cm for the Silixa XT-DTS instrument.To heat a specific section of the buried FO cables, a Heat Pulse System was used to inject electricity in the electric cables/FO cable system.Thus, the setup of the experiment allowed heating only one section of cable at time, with heating periods varied between 4 and 52 hr.As the spatial resolution of the Silixa Ultima S unit is higher, this instrument was systematically used to monitor temperature variations along the actively heated section of the FO.Concurrently, the Silixa XT-DTS unit was used to monitor temperature variations along the second non-heated FO cable.
To study temporal variability of hyporheic flow, surveys were repeated under different meteorological and hydrological conditions.FO cables were buried before the first experimental week and have remained in place for 2 years, the entire duration of the experiment.We assume that the eight weeks time period between the cable installation and the first experiment was sufficient for the riverbed recovery as the sediment resettled around the cable.Heated sections of the FO cable were tested over four weeks, in November 2017, in April 2018, in September 2018 and in September 2019, during which all heated sections were tested.Losing conditions were systematically observed over these time periods.The first and second experimental weeks (Nov-17, April-18) experienced similar hydrological conditions and were relatively wet periods.At that time, the piezometric level in P1 and the stream water level both experienced significant fluctuations, mainly due to upstream dam releases.The groundwater level follows the stream level fluctuations.This is due to the hydraulic connection between the stream and the alluvial aquifer.Thus, despite rapid and significant changes in the river level, the hydraulic head difference between the stream and P1 (Δh) does not vary significantly over time.In contrast, the third and fourth experimental weeks  were relatively dry periods.At that time, the piezometric level in P1 was around 10.23 m and the difference between the stream and P1 (Δh) was around 7.5 cm.Details about the hydrological conditions occurring during the four weeks of experiment conducted and about heating periods (durations and injected power [W.m 1 ] are provided in Supporting Information S1 (Figure S2).

Data Acquisition and Pre-Processing
Examples of raw temperature profiles recorded along cable FO1 are provided in Supporting Information S1 (Figure S3).Data processing involved two primary steps before interpretation consisting of removing non-buried sections and verifying the consistency of measurements.The first step removed non-buried sections from temperature profiles using GPS measurements made during the burial of the cable.The non-buried sections were easily identified as the temperature increase observed during heating periods features rapid temperature stabilization, as observed by Read et al. (2014) and Simon et al. (2022).In a second step, to verify the consistency of temperature measurements, we applied the following process.The capacity of measuring small-scale temperature gradients depends on the DTS unit and the spatial resolution of measurements (Simon et al., 2020).If temperature changes occur at a scale smaller than the spatial resolution of measurements, the measured temperature may be lower or higher than the true temperature.This can then lead to an estimated water flux being overestimated or underestimated.Therefore, such measurements are not considered although they could be interpreted.such measurements, we applied the derivative method, which consists of calculating the derivative of the temperature with respect to distance to highlight abrupt temperature changes that cannot be efficiently measured by the DTS unit (Simon et al., 2020).

Theoretical Background for Data Interpretation
Previous studies validated the use of heated FO cables for estimating water fluxes in porous media (del Val et al., 2021;des Tombe et al., 2019;Simon et al., 2021).The principle of the method consists of injecting an artificial heat source in a saturated porous media and continuously monitoring the associated temperature increase (ΔT) over time (Figure 2a).Conduction and advection are the two main heat transfer processes that control the temperature evolution during heat injection.Initially, the temperature rise is mainly controlled by conduction, which depends on the thermal conductivity of the material that controls the diffusion of thermal energy within the solid matrix.In a semilogarithmic plot (Figure 2b), the "induced" temperature evolution follows a gradual and continuous increase of temperature during this conduction-dominant period.Subsequently, the emitted heat is mainly dissipated by advection (Diao et al., 2004;Simon et al., 2021).The dissipation of the heat produced by flowing water through the porous media results in the temperature stabilization for late time (Figure 2b).Therefore, the magnitude of the temperature increase at steady-state conditions depends on water flow: the higher the water flux, the higher the heat dissipation by advection and thus the lower the temperature increase.
The interpretation of the induced temperature evolution consists of a two-steps reflecting the two heat transfer mechanisms controlling the thermal response.Here, we briefly recall the main steps to infer the flux from the temperature signal.The first step is to estimate the thermal conductivity of the porous media by analyzing the temperature increase measured during the conduction-dominant period.During this period, the slope of the linear regression between ΔT and ln(t) (Figure 2b) mainly depends on the thermal conductivity of the porous media, meaning that its value is independent of the flow velocity.Thus, the temperature increase measured during the conduction-dominant period can be simulated using the 1-D MILS (Moving Instantaneous Line Source) analytical model, initially introduced by Carslaw and Jaeger (1959), by considering q = 0 m.s 1 .Once thermal conductivity (λ) is estimated, the MILS model can be used to reproduce the subsequent temperature evolution.Groundwater flux can be determined based on the late-time temperature behavior and temperature stabilization, derived from the independent variable of thermal conductivity.Long heating periods (>4 hr) were used to ensure stable temperatures and accurate flux estimates.Finally, as Simon, Bour, Lavenant, et al. (2023) showed that water fluxes variations over time may be monitored through Active-DTS measurements, we used longer heating periods (up to 52 hr) to monitor the possible effect of dam release, which induced rapid changes in stream level, on hyporheic flow.Further details about the method used for data interpretation can be found in Simon et al. (2021) and Simon and Bour (2023).
The ADTS toolbox can be used to automatically interpret temperature increases recorded in all heated sections from Active-DTS measurements (Simon & Bour, 2023).This toolbox estimates both the thermal conductivity of the surrounding material and the water flux and their uncertainties for each measurement point.Note also that the data interpretation considers that the electricity injection through the steel armoring of the FO cable induces a significant temperature increase in the first minutes of the experiment (del Val et al., 2021;Simon et al., 2021).This temperature elevation due to heat conduction through the FO cable was calibrated with lab experiments (Simon et al., 2021) and adjusted for each heating period depending on the electrical power injected.Thus, the temperature increase due to the cable heating was estimated 3.32°C at 7 W.m 1 and 11.8°C at 24.96 W.m 1 , which is in good agreement with the results of Simon and Bour (2023) using similar FO cables.

Application of Active-DTS in Losing Streams
Water flux estimates from Active-DTS experiments rely on the interpretation of induced temperature variations (Figures 2a and 2b) that are temperature increases resulting from the artificial injection of heat into the porous media.This means that ambient temperature variations must be negligible to correctly interpret the results of the heating experiment.In gaining streams, sediment temperature shows negligible diurnal variations indicating the temperature of the water discharging into a stream is generally relatively constant (Constantz, 2008).In such cases, temperature variations recorded during heating experiments may be exclusively due to heat injection as demonstrated by Simon et al. (2022).
For losing streams, downward water fluxes controlling advective heat transport lead to the depth propagation of diurnal fluctuations (Constantz, 2008).In such cases, as illustrated in Figure 2, the temperature signal recorded in the streambed (Figure 2d) is expected to be a combination of the induced temperature variations (Figure 2a) resulting from the artificial heat injection and the ambient (or natural) temperature variations due to stream water infiltration (Figure 2c).Since heating periods can require several hours or more to reduce uncertainties in flux estimates, both temperature variations (induced and ambient) may occur during heating.Therefore, for Active-DTS conducted in losing conditions, estimating water fluxes requires processing the raw temperature signal recorded to filter and remove ambient temperature variations resulting from the propagation of stream temperature fluctuations.
The temperature signal recorded at a certain depth in streambed sediments displays a phase shift and an amplitude difference compared to stream water temperature signal (Constantz, 2008).The analytical models used for modeling stream temperature propagation into streambed sediments (Anderson, 2005;Constantz, 2008;Goto et al., 2005;Hatch et al., 2006;Stallman, 1965) could have been used to model the natural temperature signal at the FO cable depth.However, these analytical models rely on the values of the thermal conductivity of sediments and the downward water flux to model the temperature signal at a certain depth.As these values are unknown at this point of the data processing, it is not possible to use them to filter data recorded during heating periods.Consequently, we developed a new methodology to process raw temperature signals.
The new approach uses temperature measurements collected along FO cables located outside heated sections to filter ambient temperature variations from raw temperature signals measured within heated FO sections.The principle consists of finding, for each measurement point located within heated sections, a "matching" measurement point located outside heated sections which experienced similar ambient temperature variations during the non heating periods.The illustrative example presented in Figure 3 shows the approach applied to temperature signal recorded in one measurement point located in a heated section.The first step consists of delimiting reference periods (Ref) corresponding to periods during which only ambient temperature variations are recorded (outside heating (H) and recovery stages).Note that, although it is reasonable to consider that heating and recovery stages have equal durations, we added 30 min to the recovery as a precaution.Then, an automated routine is used to calculate Root-Mean-Square Errors (RMSEs) between the measured temperature recorded during reference periods (red bars) and the temperature recorded for the same period outside heated sections (gray bars).We use the lowest RMSE value to associate each measurement point recorded within the heated section with a Water Resources Research 10.1029/2023WR035475 point located outside the heated sections.Then, the parameters controlling the ambient temperature variations (thermal conductivity of sediments, the downward water flux, stream temperature and the depth of the FO cable) are assumed to be identical for the heated and non-heated measurements, or at least that the combination of these parameters lead to similar ambient temperature variations.Thus, the temperature signal recorded during heating and recovery periods at the non-heated point is removed from the signal recorded at the heated point to isolate the thermal response to the artificial heat injection.This routine was applied to each measurement point location in the heated sections of the FO cable.

Data Pre-Processing
The first step of data pre-processing consisted of removing data from non-buried sections of cable from raw temperature profiles.These were only located along F1-3/F1-2 and along F2-2/F2-1, where non-buried points represent 20% and 36% of the points collected respectively.The locations of non-buried sections found through the data analysis agrees with sections georeferenced during the installation of the cables.The second step consisted of verifying the consistency of temperature measurements.Along the section F2-4/F2-3, 62% of temperature measurement can be considered as non-representative, which means that the scale of temperature changes is certainly smaller than the spatial resolution of the DTS unit.Along other sections, temperature profiles are relatively uniform in space and only few points (<26%) are considered as "non representative."Table S1, provided as Supporting Information S1, summarizes results of data pre-processing for each heated section.

Removal of Ambient Temperature Variations
Figure 4 shows an example of data processing following the new method described in Section 3.3.The blue curves show examples of raw temperature signals recorded along heated sections and the red curves correspond to the temperature variations at a point outside the heated section which show the lowest RMSE.The black lines correspond to the processed temperature signal, once ambient temperature variations (red lines) were removed from raw temperature signal (blue lines).While the data processing is efficient (Figures 4a and 4b), the RMSEs between the heated measurement point and its associated measurement point located outside the heated section are low (≤0.1°C).In these cases, the processed temperature signal (black lines) is smooth and periodic variations induced by stream temperature variations are removed.The efficiency of the data processing is particularly obvious when heating periods are longer than 8 hr as in Figure 4b.For shorter heating periods (Figure 4a), it appears that ambient temperature variations can still impact the temperature signal (see the difference between the blue and black lines) and thus lead to a potentially large difference in the flux estimate.For instance, the interpretation of the blue curve of Figure 4a (raw temperature signal) leads to estimate q ≈ 8 × 10 6 m.s 1 while after data processing q ≈ 1 × 10 5 m.s 1 , that is, a difference of 20% on flux estimate.
For larger values of RMSE (Figure 4c), the data processing may not be productive as the resulting temperature signal (black lines) can show abnormal temperature variations.For such examples, it is not possible to define a matching point in non-heated sections that shows similar ambient temperature variations.In practice, it appears that for RMSE greater than 0.2°C, measurement points could not be considered and should be removed from the data set.Despite this limitation, the number of discarded data points was negligible (less than six percent for this study).Table S1 in Supporting Information S1 provides further details on data that could not be reliability filtered.

Example of Data Interpretation
Figure 5 shows an example of data interpretation for flow estimates.Figure 5 corresponds to the normalized temperature profiles (∆T/Q) obtained along the heated sections of the cable FO1 after 4 hr of heat injection.These data correspond to those processed as described previously (293 measurements points).The gaps correspond to location of measurement points that were not interpreted because of non-buried sections, small-scale temperature gradient or the difficulty in removing ambient temperature variations.It is worth noting that these points are generally grouped over a few meters sections and not isolated in space (see Figures 6 and 8).Thus, although some sections are not interpreted, the method provides an excellent overview of the variability at high spatial resolution of water fluxes along the 120 m stream reach.
The ADTS Toolbox (Simon & Bour, 2023) was used to interpret evolution curves and to estimate groundwater flux and thermal conductivity.Figure 5 shows several examples of interpreted thermal response curves.Along the heated section, some measurement points show similar temperature increases (a 1 and a 2 ), which reflect similar values of thermal conductivities and water fluxes (Figure 5b).Other locations show similar temperature evolution during the conduction-dominant period but show different temperature stabilizations for later time, during the advection-dominant period (b 1 , b 2 and b 2 ).These points are therefore characterized by similar thermal conductivities, but different groundwater fluxes (Figure 5c).Results also show that measurement points (c 1 and c 2 ) can be characterized in terms of different thermal conductivities and similar groundwater fluxes.The ADTS Toolbox can further efficiently reproduce the measured temperature increases (Figures 5b-5d).Having interpreted each measurement point, we obtain the profiles of thermal conductivities and water fluxes (Figure 5e).The uncertainty on estimates is calculated considering the data noise of the temperature signal as the dominant influence (Simon & Bour, 2023).

Spatial Variability
Figure 6 shows profiles of thermal conductivities (a) and of water fluxes (b) as a function of distance along the cable.Thermal conductivities of sediments vary between 2.1 and 2.9 W.m 1 .K 1 , with an uncertainty regarding the data interpretation on estimates of 0.1 W.m 1 .K 1 .This result is consistent with values of thermal conductivity commonly measured in saturated sand, that is, 1.5-4.0W.m 1 .K 1 (Stauffer et al., 2013).Downward water fluxes along each of the three sections vary between 5 × 10 6 and 3.5 × 10 5 m.s 1 , with an uncertainty <10%.The mean water flux for all sections is 9.7 × 10 6 m.s 1 and the standard deviation 3.8 × 10 6 m.s 1 .
Figure 7 shows the distributions of thermal conductivities (a-d) and of water fluxes (e-h) obtained for each heated section.Based on Kolmogorov-Smirnov tests, the values of estimated thermal conductivities follow normal distributions (red curves) with similar means (2.47-2.69W.m 1 .K 1 ) and small values of standard deviations (<0.2 W.m 1 .K 1 ).Kolmogorov-Smirnov tests also show that the values of fluxes estimated along F1-2/F1-1 (Figure 7h) also follow normal distributions.Along other sections, the values of estimated water fluxes are tightly distributed with relatively small values of standard deviations (between 2.9 × 10 6 and 5.5 × 10 6 m.s 1 ), but are not statistically normally distributed.This is not surprising since water flux estimates are more variable along this latter section (see blue line in Figure 6b).Note that no clear correlation appears between the profiles of downward water flux estimated and the streambed topography profile (see Figure S4 in Supporting Information S1).This suggests that water flux variations do not depend here on the streambed topography.
GPS measurements made along the FO cable facilitate the spatial mapping of hyporheic flow across the stream at the study site (Figure 8).Despite the small values of standard deviation of water fluxes estimated, water fluxes seem to be slightly higher in the middle of the stream.This was confirmed by a Mood's median test, which highlighted that water fluxes along these two sections are statistically distinct (p-value < 0.001 with an observed critical value of 62.86, higher than the critical value = 3.84).

Temporal Variability
Figure 9 shows thermal conductivities (a) and water fluxes (b,c,d) estimated along the cable FO1 at different times.Despite the different hydrological conditions, the estimates of thermal conductivity and the estimates water flux estimates vary little over time.Nevertheless, water fluxes appear slightly lower when estimated during the last field campaign in September 2019, specifically along the section between 0 and 70 m.Apart from this outlier, the data show remarkable reproducibility, with excellent accuracy in determining thermal conductivities and water fluxes.

Applicability and Limitations of the Method
In this study, we demonstrated the feasibility of performing Active-DTS in the hyporheic zone of a large lowland river.Despite some difficulties in burying the FO cables, sediment thermal conductivities and hyporheic flows were successfully estimated along large, continuous sections of the river.This highlights the primary advantage of the method, as existing methods (i.e., seepage meters, VTPs, etc.) are unable to make such estimates with similar spatial resolution.Moreover, by providing water flux estimates with low uncertainties, the approach provides higher quality data than conventional methods dependent on hydraulic conductivity estimates.The measurements collected over varying sampling periods within the same spatial bounds show excellent reproducibility, confirming the accuracy of the method.This study also highlights the utility of Active-DTS methods in a losing river environment.We have shown how to efficiently remove ambient temperature variation from the majority of raw data.The method presented here to filter ambient temperature variations could also be useful in gaining streams, since stream temperature may also propagate with depth when upward fluxes are small.The data filtering relies on identifying two measurement points displaying similar ambient temperature variations, which may be difficult in highly heterogeneous conditions.In this case, monitoring temperature along longer non-heated sections should increase the probability of finding a matching point.
The deployment of the FO cable in large streams is challenging due to high stream water levels preventing the burial of the FO cable.Here, the use of a plow solved that problem and ensured the cable depth was relatively consistent.This also helped to protect the streambed, which is important since burying a cable in a streambed may impact sensitive ecosystems.To illustrate that the plow limits the destruction of the streambed, a movie showing the cable installation within the streambed is provided as Supporting Information S1.However, even with the use  of the plow, it was not possible to bury the FO cable everywhere because of impenetrable streambed substrate areas.Likewise, even if the cable burial was controlled during the installation, the burial depth may slightly vary in space.This is not critical as the data interpretation does not depend on burial depth.However, if the burial depth of the cable is less than 3 cm, the induced heat is expected to be partly dissipated in the stream, which would affect the temperature increase.In our study, the burial depth of the cable seems acceptable since significant temperature increases were recorded along the heated sections.Once installed, the armored FO cable can remain in the river without being impacted.This allowed long-term monitoring for different hydrological conditions or for variations in streambed properties caused by clogging for instance.At Signy, the streambed is stable, and then burying the FO cable at 10 cm-depth is enough.However, if the geometry and the geomorphology of the stream change rapidly, as observed for instance in braided rivers, the burial depth of the cable may become an issue.
The main limitation of the method is the inability to determine the flux direction.Here, measurements were performed in a predominantly losing river section.Pumping in the aquifer close to the stream induces a significant hydraulic gradient between the stream and the aquifer with permanent losing conditions.Because of this, it is assumed that fluxes are mainly downward and that the flow paths in the hyporheic zone are simple, in comparison to natural flow conditions.This means that a 1D heat model is sufficient for data interpretation.In the case of natural flow conditions, the flow paths in the hyporheic may be more complex, meaning that complementary methods, such as seepage meters (Humphrey et al., 2022;Rosenberry et al., 2020) or heat-pulse probes (Banks et al., 2018;Lewandowski et al., 2011;Zlotnik & Tartakovsky, 2018), should be used to characterize flow direction.Indeed, studies assessing the effect of non-perpendicular fluxes on the thermal response suggest that the magnitude of temperature increase is significantly affected as soon as the angle between the fiber-optic cable and the water flux is less than 60°(at 90°the cable and the flow being orthogonal) (Aufleger et al., 2007;Chen et al., 2019;Perzlmaier et al., 2004).In natural conditions (no pumping), this assumption may not be fulfilled since local streambed topography may induce complex flowpaths within the hyporheic zone (Tonina & Buffington, 2011).

Spatial Variability of Fluxes
Perhaps surprisingly, our results show that thermal conductivities and water fluxes are relatively homogeneous along or across the streambed sediments.As shown by their distribution (Figure 7), water fluxes vary over less than an order of magnitude with a mean value around 1 × 10 5 m.s 1 .At Signy, the mean hydraulic gradient between the stream level and the groundwater level at pumping boreholes is around 8-9 × 10 3 m.m 1 , which implies that the hydraulic conductivity is around 1.2 × 10 3 m.s 1 .This is in good agreement with values commonly encountered in sand (10 3 -10 5 m.s 1 ) and gravel (10 2 -10 3 m.s 1 ) materials (Shackelford, 2013), which shows the consistency of flux measurements.The high value of hydraulic conductivity is also consistent with a rapid groundwater response to stream stage variations observed.In contrast, Simon et al. (2022) found larger ranges of water fluxes and thermal conductivities at the stream-groundwater interface in a headwater stream, with thermal conductivities varying between 0.8 and 3.14 W.m 1 .K 1 and fluxes varying between 2 × 10 4 and 5 × 10 5 m.s 1 .
Our experimental setup allows for high resolution mapping of both the longitudinal and lateral variability of water flux, which is a major advance (Figure 8).Most of the data suggest stream water infiltration is slightly higher in the middle of the river than close to the riverbank.This could have an effect on the thermal stratigraphy or on biogeochemical processus in this section of the river, but this result warrants further investigation.Regardless, the flux variability remains small.It may be that the low variability is due to the data processing, which removed a significant percentage of the data (between 24% and 65% depending on the section) before the interpretation.However, as shown in Figures 6a and 8, there are several long sections of cables (up to almost 40 m length) where data are continuous in space.This suggests that thermal conductivities and hyporheic fluxes are truly homogeneous at such scale, which is a significant conclusion for describing the properties of the hyporheic zone.
The spatial variability of hyporheic flow is potentially due to heterogeneities induced by streambed hydraulic conductivity and/or to streambed topography variations inducing differences in hydraulic gradients.When the stream water level varies by 0.4 m, consistent with streambed topographic variations, the hydraulic gradient, and therefore water fluxes, should vary by 10%-15%.Variations of this scale should be detectable given the sensitivity of the method, implying that, streambed topography variations should partly control hyporheic flow.However, results do not show a clear correlation between water flux distribution and the bedform topography (Figure S4 in Supporting Information S1).In practice, the significant hydraulic gradient imposed by pumping is probably larger than the potential effect of streambed topography variations on flow paths.Consequently, the water flux variability in the streambed is likely to be controlled by local geological heterogeneities.This means that, in our case, the water flux variability may be used as an indicator of hydraulic conductivity variability.By considering a uniform average hydraulic gradient along the profile and as water fluxes vary over one order of magnitude it can be inferred that hydraulic conductivities also vary within one order of magnitude.This result could help in calibrating hydrological models, in which hydraulic conductivity is generally assumed.This approach could provide hydraulic conductivities with high spatial resolution and the added benefit of low uncertainties.However, under natural conditions, without any pumping in the alluvial aquifer, the effect of streambed topography variations may be more important.In this case, both streambed variations and heterogeneities would control hyporheic flow variations and direction and it would be more difficult to make reliable inference about streambed heterogeneities.However, if streambed topography is well-characterized, with airborne LiDAR for instance (Lague & Feldmann, 2020), as well as the local hydraulic gradients within the streambed (Cucchi et al., 2018), it would be possible to clearly identify the impact of both effects.

Temporal Variability of Fluxes
Despite temporal variations in groundwater levels measured at the field site, water infiltration in the riverbed was nearly constant over time.This can be explained by the high permeability of the stream bed.The recording of temporal variations in stream level and in hydraulic head in the sediments shows that the local hydraulic head is quasi-constant over time.Likewise, on a larger scale, the hydraulic gradient between the stream and the wells used for water supply changed less than eight percent between 2017 and 2020 at the site.This suggests that the hyporheic flow is mainly controlled by the large-scale hydraulic gradient imposed by groundwater pumping for local water supply.Therefore, hyporheic flows seem to remain mostly stable over time.In other hydrogeological conditions, Active-DTS experiments could be very well suited for monitoring hyporheic fluxes variations at different time scales.The method could be used to monitor the seasonal variability of water fluxes by repeating the surveys under different hydrological conditions.It could also be used for assessing diurnal variations of fluxes, because of evapotranspiration, or the effect of rainfall/flooding events on hyporheic fluxes (Simon, Bour, Lavenant, et al., 2023).
Another interesting observation is that between 20 and 35m and between 45 and 62 m along FO1 (Figures 9b and  9c), calculated water fluxes in September 2019 are less than half the calculated fluxes during other periods (while thermal conductivities estimates are similar).This change in flow over time may be due to a decrease of hydraulic conductivity of the streambed, due to local clogging, itself likely caused by the removal of the Vezin dam, a few kilometers upstream.This dam was destroyed in spring 2019 and this leads to a large increase in the river turbidity.Variations in hydraulic conductivity of this magnitude commonly result from erosion and deposition processes (Gianni et al., 2016).However, it should be noted that no temporal changes of water fluxes were observed along the FO2 cable showing that, if clogging occurred, it only affected a part of the river.Note also that such variations with time could also be due to local deposition of sediments that may induce some changes in groundwater fluxes, but this point goes beyond the scope of our study.

Conclusions
Active-DTS measurements were conducted along a 120 m reach of a lowland river to demonstrate the feasibility of our method to characterize and map the spatiotemporal variability of fluxes in the hyporheic zone.The DTS technology provides profound spatiotemporal insights, well beyond the fluxes provided by any other method.The approach provided estimates of thermal conductivities and water fluxes along the two FO cables buried within the streambed sediments at a depth of 10 cm.Repeating surveys in 2018 and 2019, under different hydrological conditions provided an assessment of the change in flux with time and their temporal variabilities.The ability to quantify and monitor water fluxes within the hyporheic zone at high resolution and with low uncertainties is an important outcome for characterizing flow in the hyporheic zone.
Our results show that thermal conductivities and water fluxes present minor variations in space and in time for our study site and river setting.Due to pumping in the alluvial aquifer near the stream, the absence of a clear relationship between water flux variations and streambed topography suggests that the observed spatial variability of hyporheic flow is primarily due to streambed heterogeneities.Therefore, in this case, an advantage of the approach is that the variability of water fluxes can be considered here as an indicator of heterogeneity within the streambed.Thus, we expect the water fluxes and the hydraulic conductivities to have the similar distribution, meaning that sediment hydraulic conductivities are expected to vary only over one order of magnitude.This unique insight should serve to improve understanding of flow paths in the hyporheic zone.Further, our novel deployment enhances the spatial resolution applied to characterizing stream bed heterogeneities.Furthermore, in most sections, the thermal conductivity and water flux show negligible variations over time.The measurements were found to be remarkably stable and reproducible during few years, implying that fluxes in the hyporheic zone may be stable over time at the field site.

Figure 1 .
Figure 1.(a) Map of the Sélune catchment indicating the location of the experimental site of Signy [modified from Fovet et al. (2020)].The inset map shows the location of the Sélune catchment in France.(b) Map of the experimental site of Signy.Active-DTS measurements were made in the southern part of the meander (red line).Seven observation wells and three pumping wells are found within the meander.In addition, three piezometers were installed near the riverbank (P1 being the closer of the bank).(c) Experimental setup of the Active-DTS experiments conducted in Signy.Two FO cables (called FO1and FO2) were buried within the streambed sediments at 10 cm-depth and heated sections of the cables were connected separately to a heat pulse unit and controlled using a toggle switch.The total length of buried FO cables is about 374m.

Figure 2 .
Figure 2. (a) Theoretical curve of temperature variations induced during Active-DTS experiments.(b) Data interpretation of the temperature increase in semi-log scale to estimate both thermal conductivity of sediments (λ) and water flux (q).(c) Example of ambient temperature variations which could be observed in streambed sediments under losing conditions.(d) Resulting temperature variations that could be recorded while conducting Active-DTS experiments in losing conditions.

Figure 3 .
Figure 3.The principle of the method used to process temperature variations recorded along heated sections and remove ambient temperature variations, which occur predominantly in losing streams, due to the propagation of stream temperature variations in depth.

Figure 5 .
Figure 5. Interpretation of temperature elevations measured along section FO1 in April 2018 (F1-3/F1-2 heated at 20.12 W. m 1 and F1-2/F1-1 heated at 30.13 W.m 1 ).(a) Normalized temperature profiles (ΔT/Q) obtained four hours after start of heating.Q is the constant linear heating power [W.m 1 ] (b-d) Examples of temperature increase recorded along heated sections.Indexes (a 1 , a 2 etc.) refer to the location of each measurement point along the profile (a).(e) Profiles of thermal conductivities (above) and of water fluxes (below) estimated from temperature elevations and interpreted through the ADTS toolbox.Gray bars represent uncertainties.

Figure 7 .
Figure 7. (a-d) Distributions of thermal conductivities λ [W.m 1 .K 1 ] estimated for each heated section.(e-h) Distributions of water fluxes q [m.s 1 ] estimated for each heated section.Red curves correspond to normal distributions fitted to the estimates with associated mean values (μ).

Figure 8 .
Figure 8. Map of hyporheic fluxes estimated along heated FO cables (April 2018).The blue curves correspond to the banks of the Sélune river.

Figure 9 .
Figure 9. Profiles of thermal conductivities (a) and of water fluxes (b) obtained along the FO1 from Active-DTS measurements conducted in April 2018 (brown lines), in September 2018 (pink lines) and in September 2019 (green lines).Plots (c) and (d) are zoomed sections of profiles shown in (b).
To identify SIMON ET AL.