Corresponding author: G. Liu, Kansas Geological Survey, University of Kansas, 1930 Constant Ave., Lawrence, KS 66047, USA. (firstname.lastname@example.org)
 The rate of groundwater flow has long been recognized as a critical control on solute transport in the subsurface. However, information about groundwater flux and its variability in space is rarely available, especially at the resolution required for investigations at sites of groundwater contamination. Recently, high-resolution information about vertical variations in groundwater flux was obtained using fiber-optic distributed temperature sensing technology to monitor the temperature response to active heating in a well. A series of vertical thermal profiles were acquired at a 1.4 cm resolution in a sand and gravel aquifer. These high-resolution profiles, which display many of the same general features as hydraulic conductivity (K) profiles obtained using multiple techniques at the same well, provide new insights into site hydrostratigraphy. In particular, the near-continuous profiles reveal the existence of thin zones of relatively high or low velocity that would be difficult to detect using other methods. These profiles also demonstrate that vertical variations in K may not be an accurate indicator of vertical variability in groundwater flux in highly heterogeneous aquifers.
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 The rate of groundwater flow is a critical control on solute transport in the subsurface [e.g., Dagan, 1989]. Information about groundwater flux and its spatial variability is essential at sites of groundwater contamination for reliable risk assessments and design of effective remediation systems. In recent years, contaminant mass discharge, the product of groundwater flux and contaminant concentration, has received increasing attention as a metric for site characterization and remediation activities [e.g., Suthersan et al., 2010]. Although this metric is highly appealing, the characterization of groundwater flux has proven to be a significant challenge.
 Many different approaches have been used to estimate groundwater flux. The most common method is based on Darcy's law, q = K × i, where q is the Darcy velocity, K is the hydraulic conductivity, and i is the hydraulic gradient. Water levels in a minimum of three wells are used to estimate i, and hydraulic tests are used to estimate K. The flux estimate typically represents an average value over a relatively large volume and thus rarely provides information at the resolution needed for site characterization and remediation.
 There are a number of other approaches for estimating groundwater flux (e.g., Ballard , Hatfield et al. , and Devlin et al. ; see summary in Bayless et al. ). Most of these are based on introducing a tracer (e.g., heat or solute) into the subsurface and monitoring the subsequent response. The underlying assumption is that groundwater flow is the primary mechanism for tracer movement. A major disadvantage of most of these approaches is that only a limited number of measurements, whether at a few points or averaged over a discrete interval, can be acquired at a single time. The result is that selection of measurement locations becomes a critical issue; thin layers that act as preferential flow pathways or barriers may often go undetected. Clearly, an approach that provides more continuous information on the flux distribution is needed. Such an approach and the insights that it can provide are described here.
 In this paper, we present a new method for the near-continuous, high-resolution characterization of relative variations in horizontal groundwater flux. This method couples the proven concept of using a heat tracer to track groundwater movement with distributed temperature sensing (DTS) technology. DTS technology, which is based on analyzing the Raman backscatter after a laser light pulse is transmitted down a fiber-optic (FO) cable, yields high-resolution temporal (subminute) and spatial (meter-scale) temperature measurements along the FO cable [Selker et al., 2006; Tyler et al., 2009]. It has been increasingly utilized for measuring and monitoring various hydrologic processes [e.g., Lowry et al., 2007; Moffett et al., 2008; Henderson et al., 2009; Leaf et al., 2012; Striegl and Loheide, 2012]. As shown here, the high resolution possible with DTS enables us to glean new insights into hydrostratigraphic controls of groundwater flow.
 The method developed for groundwater flux characterization (henceforth, GFC) is based on the temperature increase produced by heating in the presence of flowing groundwater (Figure 1a). While the spatial resolution of DTS temperature measurements obtained with a FO cable is typically on the order of a meter, previous work for other applications has shown that cable wrapping can greatly increase the resolution of DTS measurements [Vogt et al., 2010; Briggs et al., 2012]. In this work, a 1.4 cm vertical resolution is obtained by wrapping the cable around an 8.9 cm outer diameter (OD) PVC (polyvinyl chloride) pipe (Figure 1b; see Figure S1 in the Supporting Information for a photo of the prototype tool). The FO cable used in this study (AFL LSZH (low smoke zero halogen) FD-3690, 0.4 cm diameter) has two fibers encased in a hydrophobic-gel-filled tube that are spliced together at the bottom of the tool. A resistance heating cable (0.1 cm diameter) is wrapped tightly along the outside grooves of the FO cable, giving the tool a 9.8 cm OD. The wrapped PVC pipe is 3.05 m long (total length of the wrapped FO cable is 219 m) and sealed at both ends. In this configuration, the amount of thermal mass inside the 10.2 cm inner diameter (ID) test well (including the well, water, heating and FO cables, and air-filled PVC pipe; see Figure 1c) is kept small, thus enhancing the sensitivity to groundwater flux in the aquifer. The temperature along the FO cable was measured with a Sensornet Oryx DTS unit. The power for the heating cable was controlled by a variable-output transformer.
 For flux profiling, the GFC tool is moved to a measurement interval, and temperature is monitored for at least 30 min. Once the background temperature indicates that the thermal disturbance from tool deployment has dissipated, the heating period (5 h) begins. The power output for heating is preset to a constant level (22 W) at which the temperature increase is sufficiently large to be above the noise level but not large enough to initiate density-driven flow in the small annular space (~0.2 cm) between the tool and the ID of the well. After the heat is turned off, the tool can be moved to another interval within the screen and the process repeated.
 Under a horizontal gradient, groundwater flows from the aquifer through the filter pack (materials in the borehole annulus) and well screen and then into the well where it moves around the GFC tool. The heat is transported away from the tool primarily through advection of water and thermal conduction. Although the velocity of the annular flow is different from that of the flow in the aquifer due to the distortion of the flow field produced by the well and tool, the two velocities are directly correlated with each other. Thus, when vertical variations in the rate of thermal conduction can be neglected, vertical variations in the horizontal groundwater flux in the aquifer can be characterized by the average temperature increase during heating,
where T0 is the background temperature before heating starts at time t0 and t1 is the time when heating ceases. Equation ((1)) was chosen over other metrics because of its integrated (cumulative photon count) form [Sayde et al., 2010]. To facilitate comparisons, the duration of heating (t1 − t0) is kept constant for all profiles within a well. ΔTave is used here as a relative indicator of groundwater flux variations; further work would be needed to establish a quantitative relationship between ΔTave and groundwater flux.
 Two key assumptions are invoked when using ΔTave to characterize relative variations in horizontal groundwater flux. First, the vertical component of groundwater flow is assumed negligible, as vertical flow can move heat between depths and distort the temperature responses produced by horizontal flow. Vertical flow is driven by thermally induced density differences and by background head differences. Density-driven flow can be kept small through tool design (minimal annular space) and control of the power output. Head differences, however, will invariably produce some amount of vertical flow. In the work described here, test results indicate that vertical flow is insignificant, most likely as a result of the large distances to the closest pumping wells and recharge/discharge areas. Although vertical flow may impact temperature responses at other sites, a zoned heating system can be readily incorporated into the tool to allow discrete sections of the tool to be heated while the temperature along the probe is monitored for vertical movement.
 The second key assumption is that vertical variations in the thermal conductivity (κ) of materials in the vicinity of the well are negligible, so that differences in ΔTave are primarily a result of horizontal groundwater flow. Numerical simulations (Figure S4 in the Supporting Information) show that ΔTave for a 5 h heating period is primarily sensitive to the κ within 7 cm of the well screen, i.e., materials within the filter pack. This assumption thus appears reasonable for wells with filter packs because the filter pack is typically composed of a relatively homogeneous mixture of sands and gravels. Artificial filter packs (emplaced from the surface during well installation) have this characteristic by design, while this condition is often created in natural filter packs through formation collapse and systematic development (removal of near-well fine materials) of discrete intervals along the well screen.
 The current GFC tool obtains a temperature measurement every minute for each 1.43 cm vertical interval along the tool. In contrast to previous studies [e.g., Vogt et al., 2010; Briggs et al., 2012] where a similar resolution was obtained with FO cable wrapping, active heating is incorporated here so that relative variations in groundwater flux can be characterized at a high resolution by tracking temperature responses. When groundwater flux is not present, heating-incorporated DTS (no high-resolution cable wrapping) has been used to estimate soil moisture [Sayde et al., 2010] and κ of wellbore materials [Freifeld et al., 2008].
 In this work, the measured temperature is an average over the entire circumference of the probe, so information on flow direction cannot be obtained. Although the current tool is designed for a 10 cm well, a similar tool could be used in smaller-diameter wells (a FO cable with a smaller bend radius may be required).
3 Field Application
 The GFC tool was applied at the Geohydrologic Experimental and Monitoring Site (GEMS) in northeast Kansas, United States (Figure S2 in the Supporting Information). Over the last two decades, GEMS has been the site of extensive research on flow and transport in heterogeneous formations [Butler, 2005]. The shallow subsurface consists of ~10.7 m of alluvial sand and gravel (the focus of this work) overlain and hydraulically confined by ~11.5 m of silt and clay and underlain by low-K bedrock.
 Despite the great amount of previous work at GEMS, information on groundwater velocity remains sparse and highly uncertain. Three primary factors are contributing to the large uncertainty in velocity estimates. First, there is significant spatial variability in K at this site; K in the sand and gravel interval ranges from ~1 × 10−4 to over 6 × 10−3 m/s with a vertically averaged value of ~1.4 × 10−3 m/s. Second, the hydraulic gradient is very small and difficult to measure accurately (regional gradient ~4.5 × 10−4 [Devlin and McElwee, 2007]). Third, the flow field is continuously changing with time in response to localized recharge, stage changes in the Kansas River and its tributaries, and two intermittently operating (typically 7–10 h/day) water supply wells that are 310 m and 530 m from the test well. Although these conditions are far from ideal, they are reflective of those commonly faced in field settings.
 The 10.2 cm ID PVC well used for flux characterization (Gems4S), which is screened over most of the sand and gravel interval (bottom 1.7 m not screened), was installed with a 28 cm OD hollow-stem auger. The formation collapsed back virtually instantaneously (natural filter pack) with the withdrawal of the auger flights. The well was then intensively developed using a straddle packer tool (pumping the interval between the packers) that was moved in 0.3 m increments. The collapse and subsequent development are assumed to have produced a relatively homogeneous mixture of sands and gravels in the immediate vicinity of the screen. Five test intervals were used to span the screened interval, with adjacent profiles overlapping by 0.5–1.0 m for quality control. All heating tests were conducted during the overnight hours when the nearby wells were typically not pumped. To reduce in-well vertical water movement produced by pumping of these wells, an inflatable packer was placed above the top of the screen. This was necessary because pumping-induced head changes in the confined aquifer are relatively large and water can flow from and to the cased portion of the well during the pumping and recovery periods, respectively. An ice bath was used to calibrate DTS temperature measurements at the surface (supplemented with measurements from two downhole temperature sensors for some profiles); the temperature calculation was based on a double-ended calibration procedure [van de Giesen et al., 2012].
4 Results and Discussion
 Figure 2 displays example GFC temperature data during heating. The high-frequency fluctuations on the temperature traces are primarily caused by measurement noise. This noise is greatly reduced by the averaging in equation ((1)). The rate of temperature increase varies with depth during a GFC heating test. For instance, the average temperature increase during the 5 h of heating is 1.18°C at depth 14.1 m, as compared to 1.05°C at 13.5 m and 1.03°C at 14.5 m; the higher temperature increase at depth 14.1 m can be explained by a relatively smaller rate of groundwater flux. The Peclet number (ratio of thermal advection to conduction) is about 0.1 (K 1.4 × 10−3 m/s, gradient 4.5 × 10−4, κ 2 W/m °C, and characteristic length (test well ID) 0.1 m), indicating the relatively large role of conduction in the overall heat transport. However, as emphasized earlier, the κ in the immediate vicinity of the well screen (within the filter pack) should vary little, so differences in ΔTave between depths can be primarily attributed to variability in groundwater flux. Additional numerical simulations (Figures S5–S10 in the Supporting Information) show that when the κ of the filter pack is 2 W/(m °C) (a typical value for saturated sands), a horizontal Darcy flux of 4 × 10−6 m/s can reduce ΔTave by ~0.2°C as compared to no flow (close to the maximum temperature difference observed in our field tests).
 Figure 3 presents the average temperature increase ΔTave, along with K estimates obtained using multiple hydraulic test approaches (borehole flowmeter, multilevel slug tests, and dipole flow tests [Butler, 2005]) at the same well. The thin dashed lines are ΔTave profiles from 27 heating tests conducted between 12 December 2011 and 22 February 2012, with the thick solid line representing the average. The spread of the individual ΔTave profiles around the average is likely a result of the variability of the ambient flow field and, to a lesser degree, unresolved DTS calibration drifts and power input variations. Despite the spread, all profiles across a given depth interval show essentially identical hydrostratigraphic features (for the aquifer at this site, smaller velocities→silts and finer sands—and; higher velocities→coarser sands and gravels). The thermal profiles for the same depth range can be made to nearly coincide by applying a constant temperature shift (Figure 4; see Figures S3a–S3c in the Supporting Information for additional examples).
 The average of the thermal profiles from the heating tests displays many of the general features seen in K profiles from the same well (Figure 3). Most importantly, due to the unprecedented level of detail obtained with the GFC tool, valuable new insights can be gleaned into the fundamental controls on subsurface flow. For example, between 13.5 and 14.5 m, the hydraulic test profiles indicate the presence of a low-K zone that is generally consistent with grain size data (indicating a zone of fine sediments); however, further information about that zone is not available due to the relatively coarse resolution of those profiles [Butler, 2005]. In contrast, the thermal profiles provide a clear picture of the low-velocity zone, indicating a thin layer at 14.1 m that has a velocity much lower than that of the rest of the zone. In addition, there is a zone of relatively higher velocity (possibly the top of a coarsening upward sequence between 14.5 and 16 m) immediately below 14.5 m that was not detected by hydraulic tests. Between 16.5 and 18.0 m, the hydraulic test profiles show a decline of K. Based on the high-resolution thermal profiles, however, the decline in K in this depth range is primarily a result of another thin low-velocity layer at 17.3 m; between 16.5 and 17.3 m, the rate of groundwater flux appears to be increasing, and there is a thin zone of relatively high velocity immediately below the low-velocity layer. Obviously, for risk assessment and remediation activities, identification of such features will enable a more efficient allocation of resources. The detection of these thin zones of relatively high or low velocity, some of which are generally consistent with the K profiles, can also be considered strong evidence that vertical flow is of little significance at this site.
 The vertical distribution of K is commonly used as a convenient surrogate for the vertical distribution in horizontal groundwater flux. However, our results demonstrate that caution must be used when employing the vertical distribution in K for this purpose. For example, GFC profiles indicate that groundwater velocity at ~16 m depth is lower than that at ~12 m depth (Figure 3), despite the K estimate being considerably higher at ~16 m depth. This is likely due to variability in the local hydraulic gradient produced by hydrostratigraphic discontinuities. Although the vertical distribution in K can be a valid surrogate for the flux distribution in an aquifer with laterally continuous stratification, our results indicate that it may be far from that in more discontinuous systems.
 The current GFC tool has two major limitations. First, it only provides a qualitative indication of groundwater flux; further work is needed to establish the quantitative relationship between the average temperature increase and groundwater flux. This can be achieved through numerical modeling of the heating tests and lab experiments under controlled settings. Second, the current tool does not provide information about vertical flow; as discussed earlier, zoned heating can be used to address this limitation.
 We obtained near-continuous, high-resolution information about relative variations in horizontal groundwater flux using the novel coupling of the proven concept of a heat tracer for tracking groundwater movement with fiber-optic distributed temperature sensing (DTS) technology (high-resolution wrapped cable configuration). The thermal profiles display many of the same general features as hydraulic conductivity (K) profiles from the same well. The high resolution possible with DTS enables us to gain important insights into groundwater flow under commonly faced field conditions. Thin layers of relatively high or low velocity, which have been poorly characterized by other methods, are clearly identified from the thermal profiles. Identification of such features will improve our understanding of subsurface transport and lead to more efficient allocation of resources for site characterization and remediation. Finally, our results demonstrate that the vertical distribution in K may not be an accurate indicator of vertical variability in horizontal groundwater flux in highly heterogeneous settings.
 The authors thank Scott Tyler, Christine Hatch, and John Selker for generously sharing their DTS experience. Assistance on data processing from the Center for Transformative Environmental Monitoring Programs is appreciated. We also thank three anonymous reviewers and the Editor for their helpful comments.