Uncertainty assessment of quantifying spatially concentrated groundwater discharge to small streams by distributed temperature sensing

Authors

  • Florian Lauer,

    Corresponding author
    • Institute for Landscape Ecology and Resources and Management (ILR) and Research Centre for BioSystems, Land Use and Nutrition (IFZ), Justus-Liebig-University Gießen, Gießen, Germany
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  • Hans-Georg Frede,

    1. Institute for Landscape Ecology and Resources and Management (ILR) and Research Centre for BioSystems, Land Use and Nutrition (IFZ), Justus-Liebig-University Gießen, Gießen, Germany
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  • Lutz Breuer

    1. Institute for Landscape Ecology and Resources and Management (ILR) and Research Centre for BioSystems, Land Use and Nutrition (IFZ), Justus-Liebig-University Gießen, Gießen, Germany
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Corresponding author: F. Lauer, Institute for Landscape Ecology and Resources and Management (ILR) and Research Centre for BioSystems, Land Use and Nutrition (IFZ), Justus-Liebig-University Gießen, Heinrich-Buff Ring 26, D-35390 Gießen, Germany. (florian.lauer@umwelt.uni-giessen.de)

Abstract

[1] Groundwater discharge to streams can be distributed variably in space due to the heterogeneous composition of the subsurface. Fiber-optic distributed temperature sensing (DTS) has been applied to detect and quantify spatially concentrated groundwater discharge to streams. However, a systematic uncertainty assessment for this approach with respect to changing boundary conditions is missing, and limits of detection are unclear. In this study, artificial point sources with controlled inflow rates to a natural first-order stream were used to quantitatively test the approach for inflow rates in the range of <1% to approximately 19% of upstream discharge and varying temperature differences between stream water and inflowing water. Even small inflow fractions down to approximately 2% of upstream discharge could be detected with the DTS. Inflow fractions calculated from DTS-based stream temperature observations and independently measured inflow temperatures were comparable to measured inflow fractions. Average uncertainty estimation based on the error propagation calculations ranged between 9% and 22% for experiments well above the detection limits of the DTS but ranged up to 147% for experiments close to the lower end of the detectable range.

1. Introduction

[2] Diffuse groundwater discharge to streams is commonly considered to dominate along larger reaches, neglecting variability at smaller scales [e.g., Becker et al., 2004]. However, recent studies have demonstrated that spatially concentrated groundwater sources can play an important role in the water balance of small streams [Selker et al., 2006a; Krause et al., 2007; Lowry et al., 2007; Schuetz and Weiler, 2011; Westhoff et al., 2011b]. Such point sources of groundwater discharge can be related to open fissures in the bedrock [Selker et al., 2006a] or more generally to variability in subsurface structure and permeability [Kalbus et al., 2010; Krause et al., 2012]. In agricultural watersheds, tile trains can also function as groundwater point sources [Schuetz and Weiler, 2011]. Besides their importance for the gross water balance, identification and quantification of inflow from groundwater point sources are of potential importance for water quality issues. For example, in the case of nitrate, high fluxes to streams have been found to be associated with younger groundwater, whereas older groundwater was, to a large extent, denitrified [Kennedy et al., 2009]. Thus, fast preferential flow could be an important pathway for nitrate and other groundwater-related contaminants to streams.

[3] In recent years, a growing number of studies used distributed fiber-optic distributed temperature sensing (DTS) in order to delineate and also quantify spatially concentrated groundwater discharge to streams [Selker et al., 2006a; Lowry et al., 2007; Westhoff et al., 2007, 2011b; Mwakanyamale et al., 2012]. However, the use of temperature as a tracer in the context is not new [Anderson, 2005; Constantz, 2008], but many common approaches rely on a limited number of point measurements of temperature at different depths in the streambed. Vertical water fluxes are then calculated by fitting heat transport models to observed temperature profiles [Conant, 2004; Schmidt et al., 2006; Keery et al., 2007]. If groundwater point sources are related to structures like fissures in the bedrock or old tile trains, these methods are insufficient to identify such “hot spots” of groundwater discharge [Kalbus et al., 2006].

[4] The use of temperature as a tracer for groundwater discharge to streams is possible, because perennial groundwater temperatures are relatively stable, whereas stream temperatures undergo diurnal and annual cycles. Thus, groundwater discharge leads to damping of diurnal amplitudes of stream water and streambed temperatures [Constantz, 2008]. Furthermore, in small, well-mixed streams, a localized inflow of sufficient groundwater appears as a relatively abrupt step in longitudinal stream temperature profiles for times when groundwater and stream water temperatures are significantly different from each other [Selker et al., 2006a]. This shift in longitudinal stream temperature profiles detected with DTS has been used to quantify the contribution of groundwater point sources to stream discharge using simple mixing models, treating temperature as a conservative tracer [Selker et al., 2006a; Westhoff et al., 2010, 2007, 2011a]. The accuracy of the method is influenced by accuracy in temperature measurements, by the fraction of lateral inflow with respect to stream flow and the temperature difference between lateral inflow and stream water. Errors in the determination of temperature upstream and downstream of the point source potentially lead to large errors in calculated inflow fractions [Westhoff et al., 2007]. Briggs et al. [2012] applied the DTS-based approach to a concentrated groundwater source that contributed 5% to stream discharge. They found that results were comparable with the results obtained by geochemical tracers. However, so far no systematic uncertainty analysis for this DTS-based approach of spatially concentrated groundwater discharge quantification has been presented, and limits of detection and applicability are unclear.

[5] In a related method using ground-based infrared thermography for inferring stream temperatures, calculated groundwater inflow contributions in the range of 15%–75% could be detected, and results were in good agreement with the results obtained by other end-member-based approaches and discharge measurements [Schuetz and Weiler, 2011]. Since other error sources apply for the infrared thermography approach than for the DTS method regarding the temperature measurement and the way the temperature end-members are derived from measured data, results are not directly comparable. Furthermore, temperature resolutions potentially achieved by the DTS of up to 0.01°C [Selker et al., 2006b], which is higher than those of the thermographic system (0.08°C) [Schuetz and Weiler, 2011]. Thus, detection limits will differ.

[6] The aim of this study is to identify how accurate lateral inflows can be determined with DTS. To quantitatively test the method and identify the detection limits, we realized a set of controlled artificial point source experiments to a natural first-order stream. We determined the measurement errors related to the experimental setup and gave guidance to which temperature differences and inflow fractions are needed to obtain meaningful results.

2. Methods

2.1. Experimental Setup

[7] The field experiments presented in this study have been carried out in November and December 2011 at the Vollnkirchener Bach, a first-order low mountain range creek located in Hessen, Germany. The subsurface in the study area consists of Paleozoic schist covered by loess deposits. The stream section chosen for the experiment is characterized by turbulent flow conditions leading to rapid mixing of inflowing water and stream water. Lateral changes in water temperature are assumed to be negligible due to small width (approximately 0.2 m) of the Vollnkirchener Bach. Streambed consists of loamy deposits covered by some larger rock debris. Along the stream section chosen for the experiment, no evidence of significant concentrated natural groundwater discharge was evident in the stream temperature profiles (no steep changes where stream temperature was cooler than groundwater temperature).

[8] The experimental setup is shown in Figure 1. A DTS system (Oryx, Sensornet, UK) was installed along a 400 m reach of the Schwingbach and an 850 m reach of the Vollnkirchener Bach. The laser unit of the DTS system was placed inside a building with permanent power supply and additionally protected by an insulated wooden box. This provided a relatively stable temperature environment for the unit. Maximal temperature difference between two experiments inside the box was 1.38°C (measured with external Pt100 temperature sensor of the DTS unit), and no fast temperature changes were observed. The fiber-optic cable (DamSense, Sensornet, UK) was placed onto the streambed surface and was fixed using steal pegs that were loosely attached to the cable using wire straps to keep it submerged. The spatial resolution of the DTS was set to approximately 1 m. Scans of 300 s were collected from both sides of the fiber-optic cable (looped at cable end) to enable for double-ended loss correction. This resulted in a temporal resolution of 600 s with a temperature precision of approximately 0.04°C for the DTS (according to manufacture specifications). A comparison of the DTS data with independent temperature measurements (GTH 1170, Greisinger, Germany, accuracy 0.2°C) taken manually next to the fiber-optic cable (Figure 1, T2 and T3) during the experiments showed a root-mean-square error (RMSE) of 0.24°C, which is assumed to represent the absolute accuracy of the DTS. A pumping system connected to a 1 m3 water tank was used to generate an artificial point source in the Vollnkirchener Bach at approximately 426 m distance from the DTS laser unit. The pumping system consists of a submersible bilge pump that was placed close to the bottom of the water tank. Water was pumped directly into the stream through a polyvinyl chloride (20 m length, inner diameter 0.032 m), and flow rates were measured and logged at 1 s intervals using a magneto-inductive flowmeter (PROMAG 50W, Endress & Hauser, Germany, flowmeter accuracy 0.5%–2.0% depending on the flow rate). On both sides of the flowmeter, a straight pipe section (greater than five times the inner diameter of the pipe) allowed for calming of flow to ensure correct measurements. Flow rates were adjusted manually and kept constant during the experiments using an electronic actuator for the pump and a metal ball valve (approximately 0.15 m long, inner diameter 0.032 m) at the outlet of the hose. The valve is essential to ensure that the hose is completely filled with water especially during low pumping rates. It was positioned on top of a stone above the water level with the outlet pointing directly to the stream water surface (approximately 0.02 m distance). During two experiments with higher flow rates, it was covered with stream water. A direct contact to the fiber-optic cable was avoided to ensure that it did not influence the stream temperature measurements. Upstream of the lateral inflow stream discharge was manually measured using a RBC flume (Eijkelkamp, Netherlands).

Figure 1.

Experimental setup of the artificial point source experiment. Water volumes of known temperatures from the water tank are discharged into the stream controlled by a magnetoinductive flowmeter and a ball valve. Stream temperatures along a horizontal profile are determined by DTS, placed in a nearby building.

[9] The water temperature inside the tank was adjusted by adding different fractions of heated water (approximately 70°C–90°C) or crushed ice. Water was mixed manually until temperature did not change anymore inside the tank. During the experiments, water temperature inside the tank was measured at 5 s intervals using an independent temperature logger (Micro-Diver, Schlumberger Water Services, Delft, Netherlands, accuracy 0.2°C) located next to the inlet of the pump. Additionally, water temperatures inside the tank (Figure 1, T4) and directly in the outlet (Figure 1, T5) of the hose were measured manually during some experiments. An automated weather station (Campbell Scientific, UK) equipped with a CR1000 data logger located next to the discharge flume collected data on atmospheric boundary conditions (air temperature at 2 m height, wind speed and direction, relative humidity, solar radiation) at 300 s intervals.

[10] A total of 16 experiments (Table 1) were conducted with varying contributions of artificially created inflow to stream flow (ranging between approximately 1% and 19%) and varying temperature differences between stream water and lateral inflow (ΔT 1.2°C–4.2°C). Depending on the amount and stability of inflow rates, lateral inflow could be maintained to obtain 1–4 DTS scans during the evaluation period of each experiment (excluding the start-up time, cf. section 2.2).

Table 1. Temperatures, Flow Rates, and Related Uncertainties of Artificial Point Source Experiments
ID of ExperimentInflow Fraction Pumpinga (–)ΔTb (°C)Tup (°C) math formula (°C)Tdown (°C) math formula (°C)Tps (°C) math formula (°C) math formulac (°C)σdts (°C)Qup (L s−1)σup (L s−1)Qps (L s−1)σpsd (L s−1)
  1. a

    Inflow fraction of upstream discharge. Every line corresponds to one measurement interval of the DTS.

  2. b

    Defined as absolute difference between Tup and Tps.

  3. c

    Sum of math formula and a assumed uncertainty related to correction of inflow temperature (section 2.2) of 0.25°C if linear trend was used for correction and an assumed uncertainty of 0.1°C if corrected with manual measurements.

  4. d

    SD of inflow rate during the averaging interval plus an assumed maximum uncertainty of 4% of flow rate.

10.1932.403.870.0274.220.0136.260.0120.260.221.30.10.2500.011
0.1922.393.960.0174.300.0136.360.0230.270.221.30.10.2500.013
20.1851.654.450.0264.270.0132.800.0000.100.321.30.10.2400.012
0.1851.744.540.0174.340.0182.800.0470.150.321.30.10.2400.012
30.1172.414.530.0144.740.0176.940.0440.290.241.30.10.1530.007
40.1041.693.510.0213.350.0161.820.0420.290.191.30.10.1350.016
0.1041.693.590.0143.470.0121.900.0380.290.191.30.10.1350.012
50.0974.214.000.0244.300.0178.210.0280.130.151.30.10.1260.008
0.0974.133.990.0224.320.0168.120.0290.130.151.30.10.1260.006
0.0974.014.000.0234.330.0228.010.0340.130.151.30.10.1260.006
60.0961.653.420.0233.280.0121.760.0200.270.191.30.10.1250.013
70.0893.844.170.0214.380.0138.010.0200.120.31.30.10.1160.007
80.0832.674.460.0164.630.0227.130.0370.290.241.30.10.1080.006
0.0832.644.500.0144.650.0217.130.0090.260.241.30.10.1080.006
90.0632.745.270.0185.380.0178.020.0090.260.221.30.10.0830.005
0.0632.835.310.0165.420.0178.140.0320.280.221.30.10.0830.005
0.0633.075.330.0175.430.0178.400.0440.290.221.30.10.0830.005
100.0583.464.030.0414.180.0197.490.0270.130.31.30.10.0760.004
110.0522.904.340.0204.440.0167.240.0070.260.241.30.10.0680.005
120.0453.864.000.0274.130.0167.860.0220.120.151.30.10.0580.004
0.0453.754.020.0234.180.0167.770.0160.120.151.30.10.0580.004
0.0453.704.010.0284.140.0137.710.0300.130.151.30.10.0580.005
130.0402.555.140.0165.220.0157.690.0160.120.221.30.10.0530.004
0.0402.565.170.0105.250.0157.730.0100.110.221.30.10.0530.004
140.0194.135.580.0145.660.0209.710.0170.120.307.10.20.1360.006
0.0193.805.690.0195.810.0129.490.0030.100.307.10.20.1360.007
150.0161.355.340.0225.310.0163.990.0440.140.316.50.20.1040.005
0.0161.265.380.0265.360.0184.120.0290.130.316.50.20.1040.005
0.0161.245.440.0175.430.0214.200.0180.120.316.50.20.1040.005
0.0161.185.470.0205.460.0194.290.0250.130.316.50.20.1040.005
160.0083.035.760.0155.790.0198.790.0140.110.307.10.20.0540.003
0.0082.995.790.0155.860.0128.780.0110.110.307.10.20.0540.003
0.0082.935.810.0185.850.0148.740.0250.130.307.10.20.0540.003
0.0082.885.850.0155.880.0198.730.0200.120.307.10.20.0540.003

2.2. Analysis Methods

[11] Following the approach proposed by Selker et al. [2006a], relative contribution of lateral inflow from a point source to stream discharge can be quantified based on the stream temperatures upstream and downstream of the mixing zone, if the temperature of the lateral inflow is known and if this temperature is significantly different from the stream temperature (equation (1)).

display math(1)

where Qps is the lateral inflow rate from the point source, and Qup is the stream discharge both in L s−1. Tup, Tdown, and Tps are the upstream and downstream temperatures and the temperature of point source water in degree Celsius, respectively. The application of (1) is limited by the assumptions that all terms are constant over the measuring interval and no other energy losses or gains occur within the mixing zone.

[12] To determine Tps and the contribution of the point source to measured stream discharge (calculated based on the right-hand side of equation (1)), pumping rates and water temperatures in the tank were averaged over a time period of 600 s in accordance with the averaging period of the DTS. Further, the standard deviations (SDs) for both measured variables were calculated, and time periods with SD >0.02 L s−1 for the pumping rate and >0.05°C for water tank temperature were excluded from further analyses to eliminate time periods showing large fluctuations in inflow rates or temperatures.

[13] Manual temperature measurements inside the water tank (T4, Figure 1) and at the outlet of the hose (T5, Figure 1) showed that significant cooling or heating of water occurred on the way through the pumping system resulting in maximum offsets of 1.5°C. These offsets were found to be linearly dependent (r2 = 0.82) on the gradient between water temperatures in the tank and air temperatures. Because manual measurements at the outlet of the hose have not been conducted during all experiments, this linear relationship was used to dynamically correct the measured tank temperatures (slope = 0.1523), where no direct observations were available. This is assumed to be acceptable because weather conditions during the field experiment were comparable. The linear model has an estimated error of approximately 0.25°C, which is considered to represent the uncertainty in adjusted inflow temperatures. Other meteorological variables such as solar radiation did not show any significant impact on the observed temperature offsets. Upstream (Tup) and downstream temperatures (Tdown) were derived from the DTS temperature measurements by fitting linear trends to the stream temperature observations outside the mixing reach to obtain a mean and a SD. For the downstream side, we extrapolated this trend to the upstream end of the mixing reach (Figure 2). The fitting distance was adapted to the local conditions to most accurately represent the observed temperature gradients. During some of the experiments with the lowest inflow fraction, a fitting distance of up to 20 m instead of 10 m as proposed originally by Selker et al. [2006a] was found to deliver more stable results, because otherwise noise in the temperature observations leads to erroneous representations of the temperature gradients. To ensure that thermal equilibrium with respect to lateral inflow was established along the approximately 20 m section downstream of the point source, we used a start-up time of 10–30 min with constant pumping rates, ahead of every evaluation period. This was verified by visual inspection of the temperature profiles.

Figure 2.

Determination of Tup and Tdown for a stream temperature profile corresponding to inflow fraction of 19% and ΔT 2.4°C (Id1 in Figure 3 and Table 1) between lateral inflow and stream water. Dotted blue lines mark the assumed borders of the mixing zone. On the upstream side, a linear trend is fitted from approximately 436 to 426 m to determine Tup and math formula. On the downstream side, a linear trend is fitted from approximately 410 to 420 m, and this trend is extrapolated to the upstream end of the mixing zone at approximately 426 m to determine Tdown and math formula.

[14] Following Genereux [1998], the uncertainty of the DTS-derived inflow fractions that results from error propagation can be estimated using equation (2).

display math(2)

where math formula is the SD of the temperature-derived inflow fractions, and math formula and math formula are the standard errors of estimates of the fitted linear trends used to derive Tup and Tdown in degree Celsius, respectively (Figure 2). math formula is the SD of the inflow temperatures, and σdts is the RMSE of the DTS in degree Celsius. The uncertainty in inflow fractions calculated directly based on measured inflow rates from the pumping system and discharge at the RBC flume can be estimated according to equation (3).

display math(3)

where math formula is the SD of the calculated inflow fractions, σup is the SD of stream discharge, and σps is the SD of the measured inflow rate.

[15] The relative error (Er) used in the analysis is calculated according to equation (4). Here, Qps.flow is the inflow fractions calculated from direct flow measurements from the tank (right-hand side of (1)), and Qps.flow is the temperature-based inflow fraction (left-hand side of (1)).

display math(4)

[16] The relative uncertainty (Ur) is calculated according to equation (5).

display math(5)

3. Results and Discussion

[17] A set of artificial point source experiments were carried out using the experimental setup described above, with proportions of lateral inflow to stream flow in the range of <1%–19% and temperature differences between inflowing and stream water (ΔT) in the range of 1.2°C–4.2°C. Absolute lateral inflow rates ranged between 0.05 and 0.25 L s−1, showing variations of 0.2%–7.5% (average of 1.4%) in mean simulated inflow rates. Stream discharge showed only little variation during the experiments. Most experiments were carried out during a low-flow period where measured stream discharge was 1.3 ± 0.1 L s−1. Two experiments were carried out on the falling limb of a flood wave, where discharge ranged between 6.5 ± 0.2 and 7.1 ± 0.2 L s−1, respectively. SDs of inflow temperatures over the averaging periods of the DTS ranged between approximately 0.01°C and 0.05°C. Figure 2 shows an example of the observed stream temperature profile around the artificial point source. The temperature depression on the upstream side of the point source was caused by the cable being exposed to air due to a small cascade in the stream.

[18] Based on equations (1)-(3), lateral inflow fractions and related uncertainties were calculated from temperatures and direct flow measurements. Results are shown in Figure 3. The values were averaged over the evaluation period of each experiment if more than one data set was available. The individual data sets involved are shown in Table 1. In most of the cases, uncertainty bounds of the temperature-based inflow fractions overlap with the uncertainty bounds of the inflow fractions calculated from flow measurements. Nevertheless, uncertainty in temperature-based inflow fractions is large in some cases. This applies in particular if the uncertainty in Tps that results from the correction of water temperatures in the tank to compensate for temperature changes on the way through the pumping system is considered (gray area in Figure 3). The uncertainties that result from errors in DTS measurements and variability of water temperatures in the tank ( math formula) alone are lower. Uncertainty in inflow fractions calculated from the flow measurements is usually smaller than for temperature, except for the very low inflow fractions.

Figure 3.

Average inflow fractions based on the direct flow measurements (black) and temperature-dependent calculations using DTS readings (red). The red error bars include all uncertainties listed in Table 1 but neglect the uncertainty related to correction of inflow temperatures (section 2.2). Shaded area shows the uncertainty in temperature-based inflow fractions including the uncertainty related to inflow temperature correction using math formula (Table 1) instead of math formula. Values are averaged (n = 1 – 4) for each experiment.

[19] Figure 4a shows the average relative error of the temperature-based inflow fractions plotted against the signal-to-noise ratio. Larger relative errors are in most cases associated with low signal-to-noise ratios. For experiments 15 and 16, the signal-to-noise ratio is close to or below one. For these experiments, no clear temperature change distinguishable from the background noise was apparent. Determined temperature changes caused by lateral inflow for these experiments are lower than or in the order of observed measurement noise that showed average values of approximately 0.04°C ± 0.013(1 SD) (precision of DTS is approximately 0.04°C). Lateral inflows of all other experiments could be detected with the DTS. Except experiments 2 and 7, all experiments with average relative errors above 22% are associated with signal-to-noise ratios below 4. This feature is more pronounced in the estimated relative uncertainties shown in Figure 4b, where all uncertainties above 30% are associated with signal-to-noise ratios below 4.

Figure 4.

(a) Average relative error according to equation (4) and (b) average relative uncertainty according to equation (5) (excluding the error related to correction of Tps) against the signal-to-noise ratio, defined as the ratio of the absolute difference between Tup and Tdown caused by lateral inflow (signal) and the sum of the standard errors of estimates math formula and math formula used in the determination of Tup and Tdown (noise; Figure 2). Numbers indicate related ID of experiments in Table 1 and Figure 3. Colors correspond to the product of inflow fraction from artificial point source times ΔT (defined as |TupTin|). The vertical red lines mark the detection limit for lateral inflow (signal-to-noise ratio = 1).

[20] As one would expect, observed stream temperature changes caused by lateral inflow showed a strong linear relationship (r2 = 0.92) to the product of the artificially created inflow fraction and ΔT used here as proxy for the total heat flux, whereas measurement noise was relatively stable. Thus, low signal-to-noise ratios are mostly associated with lower values of this product. Corresponding values of ΔT and measured inflow fraction are listed in Table 1.

[21] Results suggest that inflow fractions calculated based on the directly measured inflow rates and discharge are comparable with the inflow fractions calculated using the temperature-based approach, which is in agreement with results of Schuetz and Weiler [2011] and Briggs et al. [2012]. Inflow fractions down to approximately 2% could be detected with the DTS. However, from a quantitative point of view, total change in stream temperature caused by lateral inflow should be several times larger than the measurement noise to reduce uncertainty. These results are in agreement with the findings of Westhoff et al. [2007], who reported that estimated errors based on error propagation calculations were large if changes in temperatures due to lateral inflow were small.

[22] Concerning this point it is important to note that temperature resolution and measurement noise depend on the specification of a particular DTS installation and among other factors on the integration time and the calibration method [Selker et al., 2006b; Tyler et al., 2009]. In this study, we used the onboard algorithm supplied by the manufacturer for double-ended loss correction and applied a static offset calibration (recalibrated ones) with manual temperature measurements while monitoring the temperature at two turbulent locations in the stream (Figure 1). A static offset was assumed to be acceptable due to the short-time duration of the experiments and the stable temperatures of the house where the DTS unit was located. As shown in Table 1, this setup resulted in errors in absolute temperature readings of the DTS. This part of the uncertainty could be reduced in future applications by applying improved calibration procedures as was shown by Suárez et al. [2011] and van de Giesen et al. [2012].

[23] One possible limitation of the results in this study is related to the way the temperature changes in lateral inflow on the way through the pumping system were determined, in those cases where the temperatures were not directly measured. The linear relationship described in section 2.2 used for the correction of inflow temperature was based on the manual observations during experiments 2, 5, 7, 10, and 12–16. The majority of observations were conducted during experiments with intermediate and lower pumping rates (approximately 0.1 L s−1, on average). We cannot exclude that this leads to wrong estimates of the true inflow temperature especially for higher flows. Overestimation of temperature changes in case of very high pumping rates due to the reduced residence time of water in the hose seems likely. This could apply to experiment 1 (Figures 3 and 4 and Table 1), which would result in a decrease in temperature-based inflow rate. Given the relatively poor performance of experiment 2, this could point to general problem in simulation of high inflow rates, which could be a consequence of the shorter duration of these experiments resulting in lesser time of the downstream section to achieve thermal equilibrium with lateral inflow.

[24] For experiments 7 and 9, the uncertainty bounds of directly measured and temperature-based inflow fractions do not overlap. We were not able to find a clear reason for this. One potential error source that is difficult to determine and thus not included in the analysis is the systematic error in measured pumping rates caused by air bubbles in the flowmeter, which would cause an overestimation of actual inflow rate, since it is assumed that the pipe is entirely filled with water. We tried to avoid this by flushing the hose until no air bubbles were apparent in a transparent section of the hose prior to every experiment and by adjusting the valve at the outlet to make sure the hose is entirely filled with water. Still we cannot fully exclude this type of error.

[25] The way the temperature of lateral inflow is determined is generally a critical point of the applied method. A direct measurement of lateral inflow temperature is only possible if the point source can be identified visually and directly monitored with an independent temperature sensor. In the case of mixing within stream water, this approach may fail as was reported by Westhoff et al. [2011a]. Another approach is to wait until Tstream equals Tps during the day [Westhoff et al., 2007] or to monitor groundwater temperature in piezometers directly. Selker et al. [2006a] proposed a different alternative using only stream temperature observation, by eliminating the temperature of lateral inflow in equation (1) using a second stream temperature profile recorded at a different time with different stream temperatures assuming constant flow conditions. This approach was not tested in this study, because pumping experiments could not be sustained long enough for the stream temperature to significantly change between two recorded stream temperature profiles.

[26] This study was conducted in winter during conditions with low-heat input by solar radiation. Results may not be representative for other times of the year or for other climate conditions. For example, in summer when longitudinal stream temperature changes faster due to larger heat input by solar radiation, the impact of this heat source on Tdown may not be negligible, compared with the change caused by lateral inflow, especially if lateral inflow fraction is low. Moreover, at low water depth and slow flow velocities, direct heating of the fiber-optic cable could occur if solar radiation is strong [Neilson et al., 2010].

4. Conclusions

[27] In this study, an artificial point source experiment was carried out at a first-order natural stream to quantitatively test existing DTS-based quantification approaches for lateral inflow from groundwater point sources. Lateral inflow fractions in the range of <1%–19% of stream discharge were artificially created. Calculated inflow fractions were comparable with directly calculated inflow fractions, and even small inflow fractions could be detected if temperature difference between stream water and inflowing water was large enough. For the quantification of lateral inflow, the related step change in stream temperature should be several times larger than the noise associated with the stream temperature measurements to reduce the uncertainty in determination of Tup and Tdown. Nevertheless, we conclude that DTS measurements can be used to derive a robust estimate of the quantity of groundwater point source inflow rates. This could be of potential interest for studies attempting to quantify fluxes of contaminants to streams that are related to concentrated groundwater sources. Findings of this study may also be important for other studies that plan to use DTS in the context of identification and quantification of groundwater discharge. However, our results may not be generalized to all conditions and DTS installations. For example, in summer, direct sunlight might have a significant impact on the temperature readings of a fiber-optic cable positioned at very low water depths [Neilson et al., 2010]. Still, it has been shown that small, concentrated groundwater inflows can principally be detected and quantified if the difference between the stream water and groundwater temperature is large enough.

Ancillary