Combining passive and active distributed temperature sensing measurements to locate and quantify groundwater discharge variability into a headwater stream

Abstract. Exchanges between groundwater and surface water play a key role for ecosystem preservation, especially in headwater catchments where groundwater discharge into streams highly contributes to streamflow generation and maintenance. Despite several decades of research, investigating the spatial variability in groundwater discharge into streams still remains challenging mainly because groundwater/surface water interactions are controlled by multi-scale processes. In this context, we evaluated the potential of using FO-DTS (fibre optic distributed temperature sensing) technology to locate and quantify groundwater discharge at a high resolution. To do so, we propose to combine, for the first time, long-term passive DTS measurements and active DTS measurements by deploying FO cables in the streambed sediments of a first- and second-order stream in gaining conditions. The passive DTS experiment provided 8 months of monitoring of streambed temperature fluctuations along more than 530 m of cable, while the active DTS experiment, performed during a few days, allowed a detailed and
accurate investigation of groundwater discharge variability over a 60 m length heated section. Long-term passive DTS measurements turn out to be
an efficient method to detect and locate groundwater discharge along several hundreds of metres. The continuous 8 months of monitoring allowed the highlighting of changes in the groundwater discharge dynamic in response to the hydrological dynamic of the headwater catchment. However, the quantification of fluxes with this approach remains limited given the high uncertainties on estimates, due to uncertainties on thermal properties and boundary conditions. On the contrary, active DTS measurements, which have seldom been performed in streambed sediments and never applied to quantify water fluxes, allow for the estimation of the spatial distribution of both thermal conductivities and the groundwater fluxes at high resolution all along the 60 m heated section of the FO cable. The method allows for the description of the variability in streambed properties at an unprecedented scale and reveals the variability in groundwater inflows at small scales. In the end, this study shows the potential and the interest of the complementary use of passive and active DTS experiments to quantify groundwater discharge at different spatial and temporal scales. Thus, results show that groundwater discharges are mainly concentrated in the upstream part of the watershed, where steepest slopes are observed, confirming the importance of the topography in the stream generation in headwater catchments. However, through the high spatial resolution of measurements, it was also possible to highlight the presence of local and highly contributive groundwater inflows, probably driven by local heterogeneities. The possibility to quantify groundwater discharge at a high spatial resolution through active DTS offers promising perspectives for the characterization of distributed responses times but also for studying biogeochemical hotspots and hot moments.


This document is proposed as a supplement of "Combining passive-and active-DTS measurements to locate and quantify groundwater discharge variability into a headwater stream". It contains three parts related to the data interpretation. The first one details the interpretation of punctual vertical temperature profiles (VTP) using the FLUX-BOT model. Associated results are compared with passive-and active-DTS measurements in the section 3.3 of the main manuscript which allows validating fluxes estimates. The second one presents a detailed example of the use of the FLUX-BOT model to interpret passive-DTS 5 measurements. Lastly, raw results of active-DTS measurements as well as the processing of these data (sorting and quality check) are presented. The main manuscript focuses on the results of fluxes estimates.
1 Interpretation of Vertical Temperature Profile Figure S1 shows the application of the FLUX-BOT model (Munz and Schmidt, 2017) to interpret temperature 10 variations collected using the vertical temperature profile VPT3. For each value of thermal conductivity tested, the temperature time series collected at 12.5 and 22-cm depth (Fig. S1a) are reproduced by the model (Fig. S1b) providing an estimation of optimized values of vertical fluxes over time (Fig. S1c). It appears that the value of thermal conductivity has a strong impact on the fluxes estimates. By varying the value of λ between 0.9 and 4 W.m -1 .K -1 , the mean estimated flux ranges between -3x10 -6 and -1.75x10 -5 m.s -1 , while the associated quality criteria remain good for each case. However, based 15 on the value of the quality criteria, an adjustment could be done to obtain the most consistent range of thermal conductivity.  Figure S2 shows the results of the application of the FLUX-BOT model on each VTP data. The model was first applied for values of λ ranging between 0.8 and 4 W.m -1 .K -1 and this range was progressively reduced to get the best-quality 3 results (NSE, R² and RMSE). Once the optimized range of value thermal conductivity was defined (Fig. S2a), associated fluxes were estimated (Fig. S2b). Apart for the VTP 1, the model presents very good results, with RMSEs < 0.07 °C. The thermal conductivity is quite variable in space despite the proximity between the different profiles (spatially distributed over a 60 m-section of stream). The range of λ is easier to optimize for lower values of thermal conductivity. Concerning the estimation of vertical fluxes (Fig. S2b), the results confirm groundwater discharge into the stream during the month of April 30 2016 (upward water flux). Groundwater inflows are however particularly variable in space, varying between 3.5x10 -6 and 8.4x10 -6 m/s at location VTP3 (green lines) and between 8.4x10 -6 and 2.4x10 -5 m/s at location VTP4 (orange lines). Note that some data interpretation, like the VTP1, led to uncertain results (blue line on Fig. S2) with lower quality results that cannot be explained. Thus, ¼ of data are not usable, which considerably reduces the probability of detecting spatial and temporal variability of exchanges. Moreover, the results highlighted a certain spatial variability of groundwater inflows. These two points confirm the interest of DTS measurements that should provide the characterization of this 40 variability at high resolution.

Interpretation of the four VTP
The fluxes estimated from VTP are compared with estimates made with both passive and active experiments in the section 3.3 of the main manuscript. The high uncertainties induced by the ignorance of the value of the thermal conductivity are discussed in the main manuscript.
2 Interpreting passive-DTS measurements 45 Figure S3 shows the results of the application of the FLUX-BOT model on passive-DTS measurements collected in streambed sediments in the wetland area at d = 5.08 m. The model was applied for 3 values of thermal conductivity (1, 2.5 and 4 W.m -1 .K -1 ). For each case, the model provides optimized values of fluxes (Fig. S3b) that allow reproducing the more efficiently the streambed temperature variations over time (Fig. S3a). As shown in Fig. S3b, the setted value of the thermal conductivity has a strong impact on fluxes estimates, especially from January to May when groundwater inflows are higher. 50 For instance, the 01/04/2016, the discharge is estimated at 7.25x10 -6 m.s -1 for λ=1 W.m -1 .K -1 and at 2.65x10 -5 m.s -1 for λ=4 W.m -1 .K -1 . Despite such variability, the quality of estimates are similar for each value of λ tested, as highlighted by quality criteria (NSE, R², RMSE) and by the Fig. S3c showing the difference between the experimental and the modelled data.
These results confirm the assumption of groundwater discharge into stream. The temporal dynamic of exchanges can clearly be identified: higher groundwater discharge occurs from January to May, during high water table conditions. 55 During this period, the mean value of groundwater inflows is estimated ranging between 6.47x10 -6 to 2.62x10 -5 m.s -1 with associated standard deviations respectively equals to 1.47x10 -6 and 4.2x10 -6 m.s -1 . Differences between measured and simulated temperature variations are more important at the beginning and the end of the experiment (see the calculation of RMSEs for each period in Fig. S3c), showing that the model performs better for larger groundwater inflows, although the range of estimated fluxes is larger. 60

3 Interpreting active-DTS measurements
The following presents the data collected during this active-DTS experiment as well as the data processing. The data interpretation is presented in the main manuscript. Figure S4a shows the temperature increase monitored during the heating period along the heated FO cable section.

Increase of temperature along the heated section 70
The blue line corresponds to the initial temperature profile (T0) measured along the cable before the start of the heating period. This profile is uniform with a mean temperature at 11.7 °C (± 0.2 °C). Upon heating, the temperature increases very rapidly and reaches at least 15 °C in less than 2 minutes. While temperature levels off immediately around 27 °C in some sections, temperature kept on increasing up to 29 to 47 °C in others sections. This spatial variability in the thermal response 75 is in perfect consistence with the installation of the FO cable on the field. For sections where the deployment of the cable in the streambed was not possible, the cable lies at the water/sediments interface. The associated thermal response is fast and the steady state is reached in less than 2 minutes as shown in Fig. S4b. In such case, the temperature increase is mainly controlled by convection in the stream with a temperature that increases rapidly before reaching steady-state in one or two minutes (Read et al., 2014). Elsewhere, the cable is buried into the sediments and the temperature increases gradually over 80 time before eventually stabilizing as shown in Fig. S4c. In this case, heat dissipates thanks to conduction through the porous media and advection when groundwater flows (Simon et al., 2021). Particularly noteworthy is the response variability along the heated cable section: while initial recorded temperature (around 12 °C) is relatively uniform along the section, temperature reaches between 29 and 47 °C after 4 hours of heat injection. During this period, temperature has been also recorded in sediments with the non-heated FO cable and shows an average temperature of 12.1 °C and a standard deviation 85 of 0.12 °C. This shows that i) the streambed temperature is not affected by potentials air/stream variations during the experiment duration, meaning that the temporal variations are exclusively due to the heat experiment and ii) the heat experiment induces only a small and local thermal perturbation of the streambed around the buried FO cable.

Data processing
The first step of data processing was to remove unburied sections from the initial data set. In order to take into account the spatial resolution of the DTS unit (29 cm), temperature samples collected 37.5 cm before and after each exposed section have also been removed. This led to remove 126 measurement points from the data set but ensures that thermal 100 response observed in the streambed is not affected by edge effects due to these unburied sections. Then, the derivative method proposed by Simon et al. (2020) to evaluate the representativeness of DTS measurements was applied on the data set. They showed that the effective spatial resolution of DTS units could actually be higher than the one provided by the manufacturers, especially during active-DTS experiments because of heat conduction occurring along the FO cable. The derivative method consists in calculating the derivative of the temperature with respect to distance measurements all along 105 the measurement length. It allows localizing sections where measurements are actually representative of the effective temperature and thus validating consistency of temperature variations detected over small scales. Here, seeing the important spatial variability of data, this step is essential before the data interpretation. This step led to remove 185 additional points from the data set. It should be noted however that the removal of data does not mean that there is no flow at these locations.
It just implies that, considering the effective spatial resolution of measurements, their interpretation would not be significant. 110 Once the significant data identified, the increase of temperature measured over time (ΔT) induced by the heat injection was calculated as the difference between the rise in temperature at each point along the heated cable and the starting temperature T0. The value of T0 has been calculated as the average of the last two minutes taken immediately prior to heating. Different tests showed that T0 could be chosen as the average of the up to last twenty minutes taken immediately prior to heating without significant impacts on the calculation of ΔT (no data available earlier). 115 In the end, 172 measurements points were fully validated along the heated section and used for fluxes estimates as described in the section 3.2.2 of the main manuscript.