# Active distributed temperature sensing to assess surface water–groundwater interaction and river loss in braided river systems **Authors:** Eddie W. Banks, Leanne K. Morgan, Alice J. Sai Louie, David Dempsey, Scott R. Wilson **Published in:** Journal of Hydrology (2022) **DOI (version of record):** https://doi.org/10.1016/j.jhydrol.2022.128667 **This copy:** Accepted manuscript (peer-reviewed, author's version). Text extracted from the PDF at https://ddempsey.github.io/papers/2022-banks-active-distributed-temperature-sensing-assess/banks2022-active-distributed-temperature.pdf; equations, tables and figure placement may be imperfect, so cite the DOI. **Notice:** Accepted manuscript. © 2022. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/. The version of record is available at https://doi.org/10.1016/j.jhydrol.2022.128667 **Licence:** CC BY-NC-ND 4.0 https://creativecommons.org/licenses/by-nc-nd/4.0/ --- - 1 **Active distributed temperature sensing to assess surface** 2 **water–groundwater interaction and river loss in braided river** 3 **systems** - 4 - Eddie W. Banks_a,∗_ , Leanne K. Morgan_b_ , Alice J. Sai Louie_b_ , David Dempsey_c_ , Scott R. Wilson_d_ - 5 _a_ National Centre for Groundwater Research and Training and College of Science and Engineering, - 6 Flinders University, Australia - 7 _b_ Waterways Centre for Freshwater Management, School of Earth and Environment, University of - 8 Canterbury, New Zealand - 9 _c_ Department of Civil and Natural Resources Engineering, University of Canterbury, New Zealand - 10 _d_ Lincoln Agritech Ltd, Christchurch, New Zealand - 11 _∗_ Corresponding author. - 12 E-mail address: eddie.banks@flinders.edu.au (E.W. Banks). - 13 **Keywords:** Braided rivers; Surface water–groundwater interactions; Active distributed tempera14 ture sensing; Temperature; River geomorphology; Alluvial aquifers ### 15 # **Abstract** - 16 Braided river systems are continuously changing environments, comprising heterogeneous gravel17 forming meandering channels and bars, and dynamic surface water–groundwater (SW–GW) inter- - 18 actions. In alluvial aquifers associated with braided rivers, river leakage is volumetrically the most - 19 important source of groundwater recharge, yet neither the leakage process or recharge rates are well - 20 understood. Insights into how braided river systems recharge underlying braidplain aquifers dur- - 21 ing different hydrological conditions, and how this can be measured, is of critical concern for river - 22 management practices. Innovative field techniques using heat as a tracer can be applied to spatially - 23 map and quantify the temporal changes of SW–GW interaction and the processes and mechanisms - 24 of groundwater recharge for different flow regimes. Horizontal directional drilling was used to con- - 25 struct two 100 m long drillholes at a depth of _∼_ 5 m beneath and perpendicular to the river channel - 26 at a field site on the Waikirikiri Selwyn River, South Island, New Zealand. The two drillholes were - 27 completed with a hybrid fibre optic cable, containing four multi-mode fibres and 2x18AWG copper 1 - 28 conductors. A Silixa XT-DTS — distributed temperature sensor unit combined with a Silixa Heat - 29 Pulse System, was used to collect active distributed temperature sensing (A-DTS) measurements - 30 along both cables. Results from two A-DTS surveys showed distinct temperature changes across the - 31 active river channel indicating spatial variability in river loss and preferential groundwater recharge - 32 pathways to the shallow braidplain aquifer. The average groundwater velocity was 14 m d_−_1 . The - 33 average calculated river loss at the survey sites was 21 m3 d_−_1 m_−_1 compared to 25 – 26 m3 d_−_1 m_−_1 - 34 that was measured using differential flow gauging conducted during the same time period. The hor- - 35 izontal installation of the fibre optic cable and the A-DTS method provided valuable insights into - 36 SW–GW exchange between the Waikirikiri Selwyn River and shallow braidplain aquifer and how - 37 the river leakage rates varied spatially across the river channel. # 38 **1 Introduction** - 39 River loss to underlying aquifers (i.e., groundwater recharge) from losing rivers is the quantity - 40 of greatest interest in surface water–groundwater (SW–GW) investigations (Shanafield and Cook, - 41 2014). For braided rivers, river leakage is the most important source of groundwater recharge to - 42 the connected alluvial aquifers, yet the recharge mechanisms and pathways are not well understood - 43 (Coluccio and Morgan, 2019; Rupp et al., 2008). Insights into how these rivers recharge underlying - 44 braidplain aquifers and the SW–GW exchange during different hydrological conditions and temporal - 45 scales, and how it can be measured, is of critical concern for river management practices (Pi´egay et - 46 al., 2006). Due to the high energy of these environments, there is continuous change with the move- - 47 ment and creation of heterogeneous, gravel-forming, meandering channels and bars, and dynamic - 48 SW–GW interactions (Gray and Harding, 2007; Reinfelds and Nanson, 1993). The changing river - 49 geomorphology has been identified to impact on the spatial variability in the SW–GW exchange 50 and the recharge processes (W¨ohling et al., 2018). - 51 Temperature or heat-based methods are one of the most widely used field techniques to study - 52 and characterise SW–GW exchange and to determine the state of connectivity (Anderson, 2005; - 53 Constantz, 2008; Kalbus et al., 2006; Rau et al., 2014). Heat is an effective environmental tracer - 54 for quantifying SW–GW exchange fluxes because of its strong diurnal fluctuations in surface waters - 55 and low cost of application (Hatch et al., 2006; McCallum et al., 2012; Shanafield et al., 2010). A 2 - 56 standard application involves the use of discrete temperature sensors (e.g., i-buttons) at multiple 57 depths to evaluate and quantify the rate of exchange within the hyporheic zone and between the 58 river and the underlying aquifer systems (Rau et al., 2010), and in heterogeneous river environments 59 (Irvine et al., 2017). In the last two decades, higher spatial resolution surveys of river and riverbed 60 settings have been undertaken using fibre optic distributed temperature sensing (FO-DTS) that 61 apply passive-DTS and active-DTS measurements (Selker et al., 2006b; Shanafield et al., 2018; 62 Tyler et al., 2009). Passive-DTS consists of measuring the natural temperature fluctuations with 63 time and the quantification of fluxes is determined together with other distributed temperature 64 measurements and outputs from energy balance models (Selker et al., 2006a). In comparison, 65 active-DTS (A-DTS) consists of measuring temperature changes in response to a continuous heat 66 source along a FO cable, which enables quantification of fluxes at a higher spatial and temporal 67 resolution (Simon et al., 2021a). Laboratory scale studies have been undertaken to validate the 68 A-DTS methodology in using heat as a tracer and to calibrate thermal properties of both the water 69 and sediment to quantify water velocities (Bakx et al., 2019; Maldaner et al., 2019; Simon et al., 70 2020; Simon et al., 2021b). - 71 At the field and river reach scale, both passive and active-DTS surveys have been utilized to 72 locate SW–GW exchange and quantify groundwater discharge into streams (e.g., Gonz´alez-Pinz´on 73 et al., 2015; Simon et al., 2021a). In these applications, the FO cable has been installed at or just 74 below (few centimetres) the riverbed surface (Mohamed et al., 2021; Slater et al., 2010). There 75 are fewer studies that have used DTS to measure seepage rates in losing streams to groundwater 76 (e.g., Vogt et al., 2010). In Trento, Italy, Busato et al. (2019) used horizontal drilling techniques to 77 install a FO-cable beneath the riverbed and applied passive-DTS to understand the interconnection 78 between surface water and groundwater in the Vermigliana Creek catchment. To the authors’ 79 knowledge, this has been the only other study and installation of FO cable beneath a river channel. 80 One of the key challenges of monitoring SW–GW exchange in braided river systems is the in81 stallation of appropriate water monitoring infrastructure, which is at risk of damage due to flooding 82 and riverbed scouring. For the first time, this study used sub-surface horizontal drilling and A-DTS 83 surveys to measure river infiltration loss (i.e., groundwater recharge) in a braided river system in the - 84 South Island of New Zealand. The novel approach using the A-DTS survey data and an analytical - 85 moving instantaneous line source solution of the heat transport equation, made it possible to quan- 3 - 86 tify groundwater velocities and thermal conductivities in the underlying shallow braidplain aquifer. - 87 The study demonstrated the advantages of this cutting-edge field technique over other methods - 88 to quantify SW–GW exchange. It provided high spatial resolution mapping of river infiltration - 89 loss across the width of the active river channel and identified the role of river geomorphology on - 90 preferential groundwater recharge pathways in the shallow braidplain aquifer. 4 Fig. 1. (a) Location map of the Waikirikiri Selwyn River catchment, New Zealand, (b) Waikirikiri Selwyn River catchment and (c) Study site and the location of the two subsurface horizontal drillholes containing the A-DTS cable and location of river level gauge and the shallow and deep piezometers completed in the braidplain and regional aquifers. Also shown are the manual differential gauging stations G3 and G6. 5 # 91 **2 Study site** - 92 The Waikirikiri Selwyn River is located on the Canterbury Plains in the South Island of New 93 Zealand (Fig. 1). It flows from the Canterbury foothills southeast across the Canterbury Plains for - 94 approximately 80 km, where it joins Te Waihora Lake Ellesmere at the coast. Surface runoff from the - 95 hills generates most of the river flow to the upstream section of the Waikirikiri Selwyn River, which - 96 has a braided morphology. The downstream section receives groundwater from the Canterbury - 97 Plains aquifers and is characterised by a meandering braided river channel. This river is a highly - 98 dynamic river system and is characterised by large fluctuations in discharge between summer and 99 winter months (Fig. 2). It has perennial, ephemeral and intermittent reaches that experience both - 100 losing and gaining SW–GW conditions. The primary mechanism of aquifer recharge is leakage from 101 the river channels (Larned et al., 2008). 102 The study site is an active channel of the Waikirikiri Selwyn River (Fig. 1c) and is located 103 approximately 210 m above mean sea level (AMSL). Here, the river comprises one to three braids 104 and is within an ephemeral losing reach. There is a gravel bar within the study site, which has two 105 clusters of piezometers (S05, S06, S07 and S08). The contemporary braidplain is approximately 400 106 m wide and is bound by river terraces that are up to 5 m high. The active riverbed is up to 60 m 107 wide. There are many paleochannels present at the site, which may act as preferential flowpaths 108 and a recharge mechanism to the underlying braidplain aquifer. 109 The geology of the area comprises two distinct hydrostratigraphic units of greywacke-derived 110 gravel, known regionally as the Springston and Burnham formations (Forsyth et al., 2008). The 111 Springston Formation was deposited during the Holocene epoch under slightly degrading deposi112 tional conditions. As a result, these gravels occur as thin lenses of postglacial fluvial channel and 113 overbank sediments associated with contemporary braided rivers. Deposition during the current 114 postglacial period with a relatively low sediment supply has resulted in a lag deposit of well-sorted 115 gravels, sands and silts (Brown et al., 1988). This unit is approximately 3.5 to 4 m thick in the 116 study area and hosts a high permeability aquifer associated with the Waikirikiri Selwyn River, 117 herein referred to as the ‘braidplain aquifer’. An aquifer test carried out for this study estimated 118 hydraulic conductivity of 75 – 250 m d_−_1 and a specific yield of 0.03 _±_ 0.01 for this unit. 119 The Burnham Formation lies beneath the Springston Formation and hosts the regional aquifer 6 120 system. Burnham Formation deposits consist of glacial and periglacial outwash gravels deposited 121 in the last glacial period (Vincent, 2005). Core sediment material recovered during drilling at the 122 study site shows fine to coarse greywacke gravels with occasional cobbles in a fine sand to clay 123 matrix interbedded with silt layers (Fig. S1). The permeability of the Burnham Formation is low 124 near the surface, but generally increases with depth. This vertical change in permeability creates 125 a zone of lower water content between the base of the braidplain aquifer at approximately 4 m 126 depth, and the potentiometric surface of the regional aquifer at approximately 20 m below ground 127 level (bgl). The regional aquifer is not the focus of this study, however, based on water level and 128 temperature data, this aquifer can be considered hydraulically disconnected from the river and 129 shallow braidplain aquifer, and separated by an unsaturated zone of _∼_ 15 m in thickness. 130 The calculated porosity values for the Springston and Burnham Formations range between 0.18 131 and 0.3 from 27 samples of recovered drillhole core material at the study site (Robb, 2021). These 132 values are consistent with other studies on the Canterbury Plains (Dann et al., 2009). # 133 **3 Methods** 134 ## **3.1 Horizontal directional drilling** 135 Horizontal Directional Drilling (HDD) was used to construct two 100 m long, 125-mm diameter 136 drillholes at a depth of approximately 5 m beneath and perpendicular to the river channel at the 137 study site on the Waikirikiri Selwyn River. The two HDD drillholes (True Right [HDD1] and True 138 Left [HDD2]; orientation looking down river) were drilled with the assistance of a xanthan gum 139 drilling mud to keep the hole open and provide lubricant during the installation process. Following 140 a successful drillhole, a 125-mm diameter poly pipe conduit was welded to the exposed drill bit. 141 This poly pipe was temporarily installed within the HDD hole via back-reaming. Hybrid FO cable, 142 consisting of multi-mode fibres and 2x18AWG copper conductors (Fig. S2) were then threaded 143 through the temporary conduit. The FO cables were then held in place, while the temporary conduit 144 was removed. This installation method enabled the drillhole to subsequently collapse, allowing the 145 riverbed material to make direct contact with the cable. The cable connector terminals were secured 146 in a buried cable pit on the riverbank to prevent vandalism and damage from river flooding. 7 Fig. 2. River discharge of the Waikirikiri Selwyn River between 15 May 2020 to 15 May 2021. Inset photos of the river conditions (looking upstream) for the dates of the A-DTS surveys for the True Right (24/02/2021) and True Left (01/03/2021). ## 147 **3.2 Active distributed temperature sensing** 148 A Silixa XT-DTS — distributed temperature sensor combined with a Silixa Heat Pulse System was 149 used to collect A-DTS measurements along both FO cables. The reported manufacturer specifi150 cations of the XT-DTS details a spatial sample interval of 0.25 m, spatial resolution of 0.54 m 151 and a temperature resolution of 0.01_◦_ C (Silixa Ltd, UK). The spatial resolution is larger than the 152 sample interval and is typically estimated by applying the 90% step change method where the true 153 temperature change occurs over a step-wise shift in distance along the FO cable (Selker et al., 2014; 154 Simon et al., 2020; Tyler et al., 2009). A double-ended configuration was used where the instrument 155 makes measurements from both directions of a looped FO cable that has its two ends connected to 156 the XT-DTS. The non-uniform differential loss along the length of the fibre is corrected by aligning 157 the forward and reverse signals that are measured from both ends of the fibre. In addition, 8 m of 158 cable reference sections were positioned in two calibration baths of different temperatures (ambient 159 river water collected at the time of survey and ice water: 0_◦_ C) that were monitored using Pt-100 8 160 temperature probes connected to the XT-DTS (Fig. S3). The temperature measurement error for 161 the ice calibration bath for the True Right was 0.068_◦_ C and 0.099_◦_ C for the True Left, over the 162 duration of the measurement period. The measurement error for the river calibration bath for the 163 True Right was 0.100_◦_ C and 0.11_◦_ C for the True Left. Each measurement cycle used the ice cal164 ibration bath temperature to correct the reported temperature value along the length of the cable 165 at a sample interval of 0.25 m. The double-ended configuration together with the calibration baths 166 greatly improves the temperature accuracy and precision along the length of the fibre (Hausner et 167 al., 2011; van de Giesen et al., 2012). 168 The measurement sequence, acquisition sampling rate, and heat-pulse duration for the surveys, 169 using the double-ended configuration, involved the following: An acquisition sampling rate of 10 s 170 (sampled at 5 s on channel 1-forward measurement) and 5 s on channel 2- reverse measurement) 171 for a measurement period of 300 s (i.e., baseline temperature conditions) prior to heating the 172 cable for 1200 s at 15 W m_−_1 of cable, followed by a post-heating measurement period of 1200 s. 173 This sampling routine was sufficient to capture subtle temperature changes along the fibre and a 174 significant increase in temperature from the baseline conditions. 175 ## **3.3 Surface water and groundwater monitoring infrastructure** 176 There is an extensive network of surface water and groundwater monitoring infrastructure at the 177 study site (Fig. 1). It includes a river level gauge recorder (station: 68007) on the western edge 178 of the main channel and a network of 27 shallow piezometers (e.g., S01, S02 etc) completed in 179 the unconfined shallow braidplain aquifer (screen intervals between 1 and 4 m below ground) and 180 deep piezometers completed in the semi-confined regional aquifer (screen intervals between 19 and 181 35 m below ground). River stage and surface water temperature are recorded at 15-min intervals. 182 Regular manual flow gauging has been undertaken to create a flow rating curve to calculate surface 183 water discharge at the level gauge and differential flow gauging to determine water loss along the 184 river reach within the study site. Water levels and temperature in the shallow and deep aquifers 185 are recorded at 15-min intervals. 9 ## 186 **3.4 Mathematical model for estimating thermal conductivity and groundwater** 187 **velocity** 188 The evolution of temperature in saturated porous media due to advection and conduction is de189 scribed by the 2D heat transport equation (Bakker et al., 2015; Domenico and Schwartz, 1998): 190 where _T_ (_◦_ C) is temperature, _t_ (s) is time, _D_ (m2 /s) is thermal diffusivity, _u_ is groundwater velocity 191 (m/s) in the positive _x_ -direction and _R_ (-) is a thermal retardation coefficient. 192 The porosity-weighted thermal diffusivity and thermal retardation coefficients are defined as: 193 194 where _n_ (-) is porosity, _λ_ (W/m_◦_ C_−_1 ) is thermal conductivity, _c_ is specific heat capacity (J kg_−_1_◦_ C_−_1 ) 195 and _ρ_ (kg m_−_3 ) is density. Subscript _w_ refers to water, _s_ refers to solids and no subscript indi196 cates the combined rock-fluid matrix. It is assumed that the temperature of water and solids are 197 at instantaneous equilibrium and the effect of temperature on density and viscosity is negligible 198 (Anderson, 2005). 199 In this study, A-DTS survey temperature data and the analytic moving instantaneous line source 200 (MILS) solution of Zubair and Chaudhry (1996), as detailed in Bakker et al. (2015), are used to 201 estimate thermal conductivity and groundwater velocity (i.e., average linear or pore fluid velocity; 202 _u_ ) along the A-DTS cable at a spatial sample interval of 0.25 m. It is assumed that the estimated 203 groundwater velocity represents the magnitude of the dominant groundwater flow vector across the 204 cable, although the direction of flow cannot be determined by the method and remains unknown. 205 In the MILS model, an infinitely long source of constant heat, _Q_ (W/m) is located at the origin, 206 normal to the plane of constant groundwater flow. The change in temperature ∆ _T_ (_◦_ C) since the 10 207 start of heating _t_ (s) at a radial distance _r_ (m) from the line source is given by: 208 where _W_ is the Hantush Well function defined as: 209 Observations of temperature change during the heating period were used to fit Equation (4) using 210 a non-linear least squares algorithm implemented in Python. The output was best-fitting values of 211 thermal conductivity, groundwater velocity and thermal diffusivity optimised using the temperature 212 change at each individual measurement point along the cable. The root mean square error (RMSE) 213 was calculated from the residuals between the best-fitting model and the data, which gives a measure 214 of the goodness of fit. Additionally, a covariance matrix was calculated, and the parameter standard 215 deviations used to construct error bars. In this context, a small error bar indicates a good fit was 216 achieved between measured and modelled data over a small range of parameter values during the 217 non-linear least squares estimation procedure. 218 The thermal retardation value, _R_ , is calculated as 3.1. This is calculated using a porosity of 0.2 219 as measured by Robb (2021) in the vicinity of the A-DTS cable. Values of density and specific heat 220 capacity for water were taken from Bakker et al. (2015) as follows: _cw_ of 4,100 J kg_−_1_◦_ C_−_1 , _ρs_ of 221 2,650 kg m_−_3 and _ρw_ of 1,000 kg m_−_3 . Specific heat capacity for the solid, which is a greywacke 222 derived material, was taken from average values reported by Mielke et al. (2016) as _cs_ of 800 223 J kg_−_1_◦_ C_−_1 . This value is slightly lower than the 860 J kg_−_1_◦_ C_−_1 used by Bakker et al. (2015). 224 The copper heating conductor and optical fibres are contained within a composite FO cable, as 225 shown in Fig. S2. The manufacturer specifications indicate that the distance between the copper 226 heating conductor and optical fibre is within the range of 1.8 mm and 3.7 mm. In order to estimate 227 this distance, we used Equation (4) with _u_ = 0 (and other values as listed above) and iteratively 228 altered the value of _λ_ and _r_ to optimise the match (i.e., minimise the RMSE) between the modelled 229 and measured heating curves along the cable during the conduction dominant period of the heating 230 curve. Using this approach, _r_ values of 2.9 mm and 3.1 mm were estimated for the true right and true 11 - 231 left cables, respectively. For the modelling, 3.0 mm was used for the base case scenario. The impact - 232 of uncertainty associated with this parameter is explored as part of a sensitivity analysis. A key 233 assumption in our interpretation of the data is that the drillhole annulus has collapsed around the 234 FO cable. This assumption is needed to consider that the A-DTS measurements are representative 235 of perpendicular flow across the cable from the surrounding sediments. # 236 **4 Results** ## 237 **4.1 Surface water and groundwater time series** - 238 Groundwater levels in the shallow aquifer (piezometers: S02, S04, S06, S08 and S21) show very 239 similar temporal trends to river stage (Fig. 3a). The direct response in the groundwater to changes 240 in river stage indicates that the river and shallow braidplain aquifer are intimately connected. 241 Although the True Right and True Left surveys were conducted 1-week apart, the river level and 242 the shallow groundwater level conditions were similar. The hydraulic head gradient between the 243 river and the observed shallow piezometers ranged from _−_ 0.15 to _−_ 0.76 (average = _−_ 0.5) confirming 244 that the local flow field at the cable locations was from the river to groundwater (Fig. 3b). 245 Similar temporal trends are observed in the temperature time series data between the river and 246 shallow groundwater (Fig. 3c). At the daily timescale, there is a clear diurnal temperature response 247 in the river, where the surface water temperature increases from early morning and peaking mid248 afternoon before decreasing again in the evening (Fig. 3d and Fig. 3e). The diurnal temperature 249 signal in the shallow groundwater is dampened compared to the river. An exception is piezometer 250 S21, which is located on the inside of the river meander bend and shows a similar diurnal temperature 251 signal to the river but there is a clear phase shift (lag), and its amplitude is also slightly dampened. 252 The dampened amplitude and phase lag signals can be used to infer the losing river conditions. 253 We assume that these diurnal temperature variations do not have a significant effect on the ADTS 254 measurements given the overall duration of the experiment (approximately 45-min). The surveys 255 were also undertaken before the highest daily temperatures that are typically experienced by mid256 afternoon. 12 ## 257 **4.2 Active distributed temperature sensing** 258 The baseline and peak heat-pulse temperature measurements for the True Right (24/02/2021) and 259 True Left (01/03/2021) surveys are shown in Fig. 4 and Fig. 5, respectively. For the True Right 260 survey from 0 to 32.1 m, the cable is located within the unsaturated zone and above the water 261 level of shallow piezometer S02. This is also the case at 100 to 105 m, where the cable is above 262 the water level of piezometer S04 (Fig. 4a). The river temperature (21_◦_ C) at the time of the True 263 Right survey was higher than the measured temperature of the shallow groundwater in piezometers 264 S02 (17.1_◦_ C), S04 (16.6_◦_ C) and S21 (15.1_◦_ C), and the measured baseline temperature along the 265 A-DTS cable that was located below the shallow watertable (Fig. 4b). 266 For the True Left survey from 0 to 46.1 m and from 98.7 to 106 m, the cable is within the 267 unsaturated zone and above the water levels of shallow piezometers S06 and S08, which are located 268 on the gravel bar between two of the braided river channels (Fig. 5a). The river temperature 269 (17.6_◦_ C) at the time of the True Left survey was higher than the measured temperature of the 270 shallow groundwater in piezometers S06 (15.8_◦_ C) and S08 (15.6_◦_ C), and the measured baseline 271 temperature along the A-DTS cable that was located below the shallow watertable (Fig. 5b). 272 For the A-DTS cable that is located below the watertable in both surveys, there is some visible 273 spatial variability in the measured baseline and peak heat-pulse temperature measurements that 274 suggest zones beneath the river that have greater or less advective flow. For example, at a distance 275 between 62 and 68 m for the True Right there is an abrupt change in the temperature profile. The 276 measured baseline temperature at this low-point is similar to the measured groundwater temperature 277 of S021 at the time of the survey (Fig. 4b) and the river temperature measured early that morning 278 on the 24/02/2021 (Fig. 3d). Similar comparisons can be made for the True Left survey where the 279 measured early morning river temperature on the 01/03/2021 is close to the baseline A-DTS survey 280 and the shallow groundwater. 281 Temperature breakthrough curves at selected locations along the saturated sections of the FO 282 cable are shown for the True Right survey in Fig. 6 and for the True Left survey in Fig. 7. When 283 the heating cable is turned on, there is a temperature increase from the baseline, of about 4_◦_ C, 284 where it reaches an asymptotic plateau. Once the heating is turned off, the temperature returns to 285 the baseline (Fig. 6a and Fig. 7a). The sections of the cable that are located within the unsaturated 13 286 zone and above the watertable of the shallow braidplain aquifer (True Right: 0–32.1 m; 100–105 m 287 and True Left: 0–46.1 m; 98.7–106 m), show greater increases in temperature (8–10_◦_ C) immediately 288 after the heating is turned on (Fig. 6b and Fig. 7b). For the groundwater velocity calculations 289 these measurements are not considered due to the partially saturated conditions of the unsaturated 290 zone. 291 Other noticeable features in the temperature heat maps (Fig. 6c and Fig. 7c) are locations 292 along the FO cable where there is more rapid cooling (or where the temperature increase is not as 293 high) compared to adjacent locations. These features of rapid cooling are likely to be locations of 294 higher groundwater velocities created by the spatial variability in the hydrogeological conditions of 295 the braidplain aquifer. 296 For the True Right survey on 24/02/2021, fitting Equation (5) to the temperature data suggests 297 an average groundwater velocity of 12.0 m d_−_1 , with values along the length of cable (at a spatial 298 sample interval of 0.25 m) ranging between 10.8 and 13.6 m d_−_1 (Fig. 8a). The average thermal 299 conductivity is 0.56 W m_−_1_◦_ C_−_1 with a range in values from 0.48 to 0.62 W m_−_1_◦_ C_−_1 . The clear 300 change in the baseline temperature at a distance between 62 and 68 m is also the location of the 301 calculated highest velocity. 302 For the True Left survey on 01/03/2021, the average groundwater velocity is 15.8 m d_−_1 and 303 along the length of cable, the velocities range from 12.4 to 19.4 m d_−_1 (Fig. 8b). The average 304 thermal conductivity is 0.74 W m_−_1_◦_ C_−_1 with a range in values from 0.66 to 0.80 W m_−_1_◦_ C_−_1 . 305 RMSE for the surveys conducted on the 24/02/2021 and 01/03/2021 are less than 0.07_◦_ C, indicating 306 a good fit between modelled and measured temperature change along the cable. 14 Fig. 3. (a) Selected water level time series data of the Waikirikiri Selwyn River and monitored piezometers in the shallow braidplain aquifer (S02, S04, S06, S08 and S21). Daily rainfall is also shown. (b) Water level time series data at time of surveys. (c) Selected temperature time series data of the Waikirikiri Selwyn River and shallow braidplain aquifer (15 May 2020–15 May 2021). (d) Temperature at time of True Right survey 24/02/2021. (e) Temperature at time of True Left survey 01/03/2021. 307 A simple sensitivity analysis of the input parameters that were used in the MILS flow and heat 308 transport model was undertaken on the TR survey data. The derived groundwater velocity and 15 309 bulk thermal conductivity values as a result of increasing and decreasing the input parameters of 310 porosity, specific heat capacity and _r_ by 20 % are shown in Table 1. Changing the porosity from 311 the base case of 0.2 to 0.16 increased the groundwater velocity from an average of 12 to 14.4 m d_−_1 . 312 Whilst modifying the distance between the line heat source and the fibre ( _r_ ) from 2.4 to 3.6 mm 313 changed the estimated groundwater velocity from 9.6 to 14.4 m d_−_1 . There was no change to the 314 estimated bulk conductivity with the range of input parameters that were tested. # 315 **5 Discussion** 316 Assuming that the measured groundwater velocity is in the vertical direction, the average specific 317 discharge ( _q_ ), i.e., river loss to the shallow braidplain aquifer, is 2.8 m d_−_1 (ranged from 2.3 to 3.3 318 m d_−_1 ). This was determined using the calculated average groundwater velocity ( _u_ ) of 13.9 m d_−_1 319 (ranged from 11.6 to 16.5 m d_−_1 ) for the True Right and True Left surveys and a measured porosity 320 of 0.2 from the drillcore material. The groundwater velocities do not vary significantly beneath the 321 width of the active river channel (as defined by the wetted footprint of the channel). In a previous 322 study by Vincent (2005) of the upper reaches of the Waikirikiri Selwyn River, it was suggested that 323 the groundwater movement within the shallow braidplain aquifer would be influenced by remnant 324 paleochannels that have formed by progressive shifting and abandonment of river channels on the 325 alluvial fan surfaces. Furthermore, preferential groundwater flow would occur where there is a 326 complex network of interconnected channels of more permeable gravels surrounded by less permeable 327 sediments and would also be influenced by the heterogeneity of the aquifer material. This does not 328 appear to be a significant controlling factor on the groundwater velocities beneath the active river 329 channel at the study site. However, the measurement scale (0.25 m sample interval) compared to 330 the potential scale of macropore flow ( _∼_ 1–2 cm) needs to be taken into consideration. 331 The calculated groundwater velocities are dependent on the derived thermal conductivities. In 332 this study, there was not a large variation in the values along the length of the cable for the two 333 surveys and the uncertainty in thermal conductivity was relatively low (Fig. 8). However, we note 334 that Simon et al. (2021b) and del Val et al. (2021) found that calculated thermal conductivity 335 uncertainty increases when the conduction dominant period is short, as occurs under high flux 336 conditions, such as those found in our study. The effects of homogeneous and heterogeneous dis- 16 337 tributions of sediment thermal conductivity on vertical groundwater flux estimates in a high-flux 338 stream and low-flux lagoon was studied by Sebok and M¨uller (2019). Their study found that the 339 vertical heterogeneous distribution of thermal conductivity did not significantly change the modelled 340 versus observed temperature data compared to the homogeneous distribution. However, it was crit341 ical that spatially representative thermal properties are used to obtain more precise flux estimates 342 rather than using standard textbook values. In our study, the best-fit values (lowest RMSE, which 343 was less than 0.07_◦_ C for both surveys) for the bulk thermal conductivity of the saturated fluid-rock 344 matrix for the True Right and True Left A-DTS transects are contained within a narrow range from 345 0.48 to 0.8 W m_−_1_◦_ C_−_1 . Reported thermal conductivity for greywacke basement rock (porosity 346 = 0.03) is 1.7 W m_−_1_◦_ C_−_1 (Mielke et al., 2016). The variations to the geometrical arrangement 347 of layers, mineral grains, and pores will also affect the bulk conductivity, in particular, changes 348 in porosity (Clauser, 2011). Therefore, the derived low bulk thermal conductivities from the two 349 surveys are reasonable for the saturated fluid-rock matrix of the greywacke aquifer material that 350 has an average porosity of 0.2. When the porosity values were changed from 0.16 to 0.24 compared 351 to the base case ( _n_ = 0 _._ 2), the calculated groundwater velocities decreased from 14.4 to 6.3 m d_−_1 . 352 Another consideration as to why the derived bulk thermal conductivities are low for the saturated 353 aquifer material in this study is how the subsurface gravels and fines have collapsed and repacked 354 around the FO cable after horizontal drilling and cable installation. This re-packing, settling of 355 heavier gravels and infill of finer material would change the proportion of water filled voids to solid 356 material. Unfortunately, there is no way to physically measure this change in-situ but repeat A- 357 DTS surveys may be able to identify if there is any notable change to the derived bulk thermal 358 conductivities along the length of the cable with time. Physical measurements of drillcore material 359 using a thermal properties analyser would also help constrain the range in plausible values for the 360 aquifer material under different saturated conditions. 17 Fig. 4. (a) True Right FO cable transect and measured river and shallow groundwater levels. (b) Measured baseline and peak heat pulse temperatures on 24/02/2021. The coloured symbols are the observed temperature at the time of the survey from the river and shallow groundwater from piezometer S02, S04 and S21. Vertical arrows show locations along the FO cable where temperature breakthrough curves are presented in Fig. 6. Grey shaded area is where the FO cable is located within the unsaturated zone. 361 One of the more sensitive parameters in the MILS flow and heat transport model was associated 362 with knowing the exact start time of the heating input (s) and the value of _r_ , as the distance between 363 the heating line source and the observing fibre (refer to equation (5)). A simple sensitivity analysis 364 of the TR survey showed that the effect of changing the start time from 240 to 252 s changed the 365 calculated groundwater velocity from 12.0 to 15.4 m d_−_1 and the bulk thermal conductivity from 366 0.56 to 0.69 W m_−_1_◦_ C_−_1 . The results presented here indicate that a higher temporal resolution 367 in the early time measurements is important to capture the rapid temperature change in response 368 to the line source heating. Whilst changing the distance between the line heat source and the fibre 369 ( _r_ ) by 0.8 mm was very sensitive to the derived groundwater velocities, implying that knowing the 18 370 cable specifications is critical to the survey results. - 371 The main challenge with interpreting the A-DTS data is that the inferred direction of water flow 372 is assumed to be 1D and does not account for flow in the two other directions. Multi-direction, 3D373 flow fields in the shallow streambed have been evaluated for hyporheic exchange using other active 374 heat pulse temperature methods (e.g., Banks et al., 2018), however, there are no known studies 375 that have been undertaken at depths greater than a few metres within river channels. It is assumed 376 that the longitudinal flow component in the near surface of the riverbed in the direction of river 377 flow would be greater than the vertical and lateral flow components because of the permeability 378 structure in riverbed environments. 379 The installation depth of the horizontal FO cable at the study site is several metres below the 380 influence of hyporheic zone exchange (Lewandowski et al., 2019), and therefore the derived ground381 water velocities represent the dominant direction of flow within the shallow braidplain aquifer. 382 Based on the observed hydraulic head gradient between the river and water level of the shallow 383 braidplain aquifer as well as the measured differential river flow gauging, we can be confident that 384 the calculated specific discharge over this river reach represents river loss. 385 The hydraulic conductivity of the aquifer material of the shallow braidplain aquifer was esti386 mated to be in the range of 23 to 33 m d_−_1 . This was determined based on the range of calculated 387 groundwater velocities (11.6 and 16.5 m d_−_1 ) and the measured average hydraulic head gradient 388 between the river and shallow braidplain aquifer, which at the time of the surveys was 0.5 m. These 389 hydraulic conductivities are less than the values based on aquifer tests that were done at the site, 390 which ranged from 75 to 250 m d_−_1 . The permeability of riverbed materials are known to vary over 391 eight orders of magnitude (9 _×_ 10_−_6 to 9 _×_ 102 m d_−_1 ) (Calver, 2001), and because of the signif392 icant spatio-temporal variability, this can strongly control river loss to groundwater. Aquifer tests 393 results primarily represent horizontal flow, whereas river leakage is controlled by vertical hydraulic 394 conductivity, which is expected to be lower because of stratification and imbrication. 19 Fig. 5. (a) True Left FO cable transect and measured river and shallow groundwater levels. (b) Measured baseline and peak heat pulse temperatures on 01/03/2021. The coloured symbols are the observed temperature at the time of the survey from the river and shallow groundwater from piezometer S06 and S08. Vertical arrows show locations along the FO cable where temperature breakthrough curves are presented in Fig. 7. Grey shaded area is where the FO cable is located within the unsaturated zone. 395 Manual differential flow gauging that was undertaken on the 24/02/2021, using an Acoustic 396 Doppler Velocimeter by hydrographers from NIWA, measured a river infiltration loss of 8,640 m3 d_−_1 397 (average point measurement uncertainty of 3%) over a river reach length of 333 m (equivalent to 398 26 m3 d_−_1 m_−_1 ) that encompassed the True Right and True Left A-DTS transect locations (Fig. 399 1). In comparison, the measured river infiltration loss over the entire 888 m long river reach of 400 the study area was 22,464 m3 d_−_1 (equivalent to 25 m3 d_−_1 m_−_1 ). Using a wetted footprint width 401 of the active river channel of 60 m and an effective distance over which the ADTS measurement 402 can be applied that is equivalent to the diameter of the drillhole (0.125 m) and combined with the 20 403 calculated specific discharge from the A-DTS surveys (2.8 m d_−_1 ), the river infiltration loss at the 404 transect locations is 21 m3 d_−_1 m_−_1 . 405 The calculated river losses using the A-DTS survey data and differential flow gauging are similar, 406 which is an encouraging result. The scale of investigation between the two techniques is the most 407 likely contributing factor to the different river loss calculations. Despite the low measurement 408 uncertainty, the differential flow gauging provides a net loss of surface water over a river reach that 409 is 100_′_ s of metres long. Whilst the A-DTS survey is measuring the groundwater velocities within 410 the braidplain aquifer at a local scale, directly beneath the active river channel but also at a high 411 spatial resolution along the length of the transect that is perpendicular to the river channel. # 412 **6 Summary** 413 The novel approach that has been used in this study provides an improved understanding of the 414 complex SW–GW exchange processes in braided river systems. The FO cable installation beneath 415 the riverbed has demonstrated the value of A-DTS to quantify river infiltration losses at a high 416 spatial sample interval (0.25 m) and over the entire width of the active river channel. There was 417 some spatial variation in the calculated groundwater velocities beneath the active river channel, 418 which ranged from 11.6 to 16.5 m d_−_1 (average = 13.9 m d_−_1 ). These findings suggest that changes 419 in the riverbed geomorphology or the presence of more transmissive paleochannels are, to a small 420 degree, influencing preferential groundwater flowpaths in the shallow braidplain aquifer at the survey 421 sites. The calculated average infiltration loss of 21 m3 d_−_1 m_−_1 from the A-DTS surveys was similar 422 to values derived from differential flow gauging across the study site (25 to 26 m3 d_−_1 m_−_1 ). 423 The buried permanent installation of the FO cable allows for repeat surveys at different river 424 stage and aquifer conditions to be conducted more frequently to evaluate how hydrologic conditions 425 may affect groundwater velocities and recharge rates. A higher frequency of monitoring has potential 426 to be used to identify critical river flow conditions when the highest groundwater recharge occurs, 427 thus providing valuable information to water management decisions. 21 Fig. 6. (a) Temperature breakthrough curves from FO cable locations: 40, 50, 60, 70, 80 and 90 m of the True Right transect for the survey conducted on 24/02/2021. (b) Temperature change heat map along the full length of the FO cable. (c) Temperature change heat map between 32.1 and 100.0 m where the FO is below the standing water level of the shallow unconfined aquifer. Note the different temperature scale in b and c. 22 Fig. 7. (a) Temperature breakthrough curves from FO cable locations: 50, 60, 70, 80 and 90 m of the True Left transect for the survey conducted on 01/03/2021. (b) Temperature change heat map along the full length of the FO cable. (c) Temperature change heat map between 46.1 and 98.7 m where the FO is below the standing water level of the shallow unconfined aquifer. Note the different temperature scale in b and c. 428 ## **6.1 Future recommendations** 429 To improve the conceptualisation of river infiltration loss in braided river systems, the significance of 430 1D versus 2D flow components beneath the river needs to be addressed. To address the uncertainty 431 in the derived groundwater velocities and to explore the phenomena of multi-directional flow, two 23 432 vertical A-DTS FO cables have recently been installed on the riverbank adjacent to the horizontal 433 drillholes to a depth of 30 m. Planned future surveys will hopefully provide greater insight into the 434 complex flow fields beneath the river and resolve whether the vertical or lateral flow component is 435 more dominant at this study site. 436 Further work is required to compare the different analytical approaches of Bakker et al. (2015) 437 to those of other studies, including the ADTS Toolbox by Simon and Bour (2022) and how they 438 align to different fibre and heating cable configurations. Furthermore, how this approach relates to 439 the analytical solutions described by others, including Diao et al. (2004) and del Val et al. (2021). 440 The installation of the horizontal FO cables was a very costly field investigation method. How441 ever, this type of installation provided very high spatial resolution of groundwater velocities beneath 442 a complex braided river system. It has also allowed for multiple surveys to be conducted during dif443 ferent flow conditions with a reduced risk of losing equipment due to changing river flow conditions. 444 This was demonstrated in June 2021, when the installation survived a significant 1/50-year flood 445 event where the river level gauge station and eight piezometers were damaged and lost. Time series 446 data from a high-resolution vertical DTS profile used in the study by Vogt et al., (2010) observed 447 sporadic high infiltration rates at times of high water tables. The installation described in our study 448 is of considerable benefit to being able to measure the dynamic behaviour of groundwater recharge 449 beneath complex braided river systems and improve modelling efforts of SW–GW exchange. Future 450 planned research activities will provide new insights to how the controlling factors of river stage 451 and channel elevation relative to watertable elevation of the shallow braidplain aquifer changes river 452 infiltration loss prior to and after a large flood event. 24 Fig. 8. Calculated groundwater velocities and thermal conductivity values for the (a) True Right on 24/02/2021 and (b) True Left on 01/03/2021. Error shading is based on standard deviation of the fitted parameter values determined by the linear least-squares fitting algorithm. 25 Table 1 Sensitivity analysis of input parameters used in the MILS model for the True Right survey only. ||Input p|aram|eters||||Results|| |---|---|---|---|---|---|---|---|---| |Scenario|_r_|_n_|_cs_|_ρs_|_cw_|_ρw_|_u_ (m d_−_1)|_λ_ (W_−_1 m_−_1 _◦_C)| ||(m)|(-)|(J_−_1 kg_−_1 _◦_C)|(kg m_−_3)|(J_−_1 kg_−_1 _◦_C)|(kg m_−_3)|average (range)|average (range)| |Base case|0.003|0.2|800|2650|4100|1000|12.0 (10.8, 13.6)|0.56 (0.48, 0.62)| |Low _n_|0.003|0.16|800|2650|4100|1000|14.4 (13.0, 16.3)|0.56 (0.48, 0.62)| |High _n_|0.003|0.24|800|2650|4100|1000|6.3 (5.6, 7.1)|0.56 (0.48, 0.62)| |Low _cs_|0.003|0.2|640|2650|4100|1000|10.3 (9.3, 11.7)|0.56 (0.48, 0.62)| |High _cs_|0.003|0.2|960|2650|4100|1000|13.5 (12.2, 15.3)|0.56 (0.48, 0.62)| |Low _r_|0.0024|0.2|800|2650|4100|1000|9.6 (8.7, 10.9)|0.56 (0.48, 0.62)| |High _r_|0.0036|0.2|800|2650|4100|1000|14.4 (13.0, 16.3)|0.56 (0.48, 0.62)| 453 Other types of installation of FO cable or individual temperature sensors at an oblique angle 454 beneath the river channel are also being considered to provide a simpler solution to be able to 455 measure river infiltration losses during different flow events at several locations and at a reduced 456 cost. ### 457 # **Declaration of Competing Interest** 458 The authors declare that they have no known competing financial interests or personal relationships 459 that could have appeared to influence the work reported in this paper. ### 460 # **Data availability** 461 Data will be made available on request. ### 462 # **Acknowledgements** 463 This research has been financially supported by MBIE grant LVLX1901 and supported by the Can- 464 terbury Regional Council and the Waterways Centre for Freshwater Management. Field work assis- 465 tance and technical support was provided by Aaron Dutton and Blair Miller from Lincoln Agritech, 26 466 NZ. Special thanks to the National Centre for Groundwater Research and Training, Flinders Uni- - 467 versity for field equipment and technical support. ### 468 # **Appendix A. Supplementary data** 469 Supplementary data to this article can be found online at `https://doi.org/10.1016/j.jhydrol.` 470 `2022.128667` . ### 471 # **References** 472 Anderson, M.P., 2005. Heat as a ground water tracer. Ground Water 43 (6), 951–968. 473 Bakker, M., Calj´e, R., Schaars, F., van der Made, K.-J., de Haas, S., 2015. An active heat tracer 474 experiment to determine groundwater velocities using fiber optic cables installed with direct push 475 equipment. Water Resour. Res. 51 (4), 2760–2772. `https://doi.org/10.1002/2014WR016632` . 476 Bakx, W., Doornenbal, P.J., van Weesep, R.J., Bense, V.F., Oude Essink, G.H.P., Bierkens, 477 M.F.P., 2019. 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