Elsevier

Journal of Hydrology

Volume 380, Issues 1–2, 15 January 2010, Pages 154-164
Journal of Hydrology

Estimation of seepage rates in a losing stream by means of fiber-optic high-resolution vertical temperature profiling

https://doi.org/10.1016/j.jhydrol.2009.10.033Get rights and content

Summary

Vertical temperature profiling in the river beds of losing streams has been shown to be useful in obtaining seepage rates. We present a method for high-resolution vertical temperature profiling in surface-water sediments for detailed quantification of seepage flux over depth and time. The method is based on fiber-optic distributed temperature sensing, in which temperature profiles along an optical fiber are obtained by making use of Raman scattering. An optical fiber was wrapped around a 2 in. PVC tube and installed vertically within the streambed sediment. The wrapping transfers the spatial resolution along the fiber of 1 m to a vertical resolution of about 5 mm. The high-resolution temperature profiler was tested at a losing reach of the Swiss prealpine River Thur resulting in a 20-day long temperature time series with a temporal resolution of 10 min. The time series are analyzed by means of dynamic harmonic regression to obtain the diurnal contributions of the measured time series at all depths and time points. The time for the diurnal temperature signal to reach the observation depth and the associated attenuation of the signal are calculated from the phase angles and amplitudes of the diurnal contributions. The time shift results in an apparent celerity of diurnal temperature propagation, which is converted into an apparent seepage rate by fitting the data to the analytical solution for convective–conductive heat transfer in a semi-infinite, uniform, one-dimensional domain with a sinusoidal surface temperature. The high spatial resolution allows the location of discontinuities in the river bed which would have remained undetected if temperature had been measured only at a few individual depths to be identified. This is a particular strength of the fiber-optic high-resolution temperature profiler. The time series also give evidence of sporadic high infiltration rates at times of high water tables.

Introduction

The transition zone between surface water bodies and groundwater is known as the hyporheic zone. In recent years, this zone has been identified as crucial for the ecological status of the open-water body and the quality of groundwater. The hyporheic zone acts as habitat for benthic organisms playing an important role in river ecology. Furthermore, transformations of nutrients (Brunke and Gonser, 1997, Triska et al., 1993) and pollutants (Bosma et al., 1996, Schwarzenbach and Westall, 1981) occur within the hyporheic zone. For the assessment of groundwater quality in the vicinity of losing rivers, it is of particular importance to know how fast river water infiltrates into the underlying aquifer.

The exchange processes between surface water and groundwater vary both in time and space (Brunke and Gonser, 1997, Huggenberger et al., 1996, Woessner, 2000). Temporal fluctuations may be caused by asynchronous water-table fluctuations in the river and the aquifer (Wroblicky et al., 1998), whereas the reasons for spatial variations lie in the heterogeneity of streambed sediments and associated hydraulic conductivity (Fleckenstein et al., 2006, Huggenberger et al., 1996, Kalbus et al., 2009), in river morphology and stream curvature (Cardenas et al., 2004, Gooseff et al., 2005, Harvey and Bencala, 1993), and in spatially varying hydraulic gradients (Storey et al., 2003). Clogging layers within the river bed may be formed during continuous low river water level periods, causing a reduction in bank filtration. During floods, the clogging layers may be eroded. Such changes in the hydraulic characteristics of the river bed contribute to the dynamics of hyporheic exchange.

Natural rivers exhibit stronger spatial and temporal dynamics of the river bed than regulated rivers. Current efforts of river restoration are designed to re-establish a more natural sediment regime. This increases the variability and potentially the magnitude of hyporheic-exchange processes, and also affects the associated alluvial aquifer systems. Groundwater management in such contexts requires methods for quantifying the exchange of water and solute mass between surface and subsurface water bodies.

A wide range of methods exist to estimate water flux between surface water and groundwater. Kalbus et al. (2006) have reviewed the most common methods, including direct measurement of water flux (seepage meter), estimates of specific discharge from piezometer data (hydraulic gradient, hydraulic tests), heat-tracer methods (based on vertical streambed temperature profiles), and mass balance approaches (differential discharge gauging, solute tracer methods).

In this paper, we present a new method for measuring highly resolved vertical temperature profiles in surface-water sediments. We wrap an optical fiber around a piezometer tube and measure the temperature distribution along the fiber by means of distributed temperature sensing (DTS) based on Raman scattering. From the travel time and attenuation of the diurnal temperature signal, we can estimate the apparent velocity and diffusivity of temperature propagation, which can then be used to approximate infiltration rates. A particular strength of the new measurement technique lies in the high spatial and temporal resolution, enabling us to detect non-uniformity and temporal changes in vertical water flux. We demonstrate the applicability of the method at a restored river section of the River Thur in Switzerland, which is currently under intensive investigation with respect to hyporheic-exchange processes.

Heat is an easy to measure natural physical parameter. The vertical and lateral temperature distribution is a function of boundary conditions, heat conduction and convection (Anderson, 2005, Bredehoeft and Papadopulos, 1965, Lapham, 1989, Stallman, 1965, Suzuki, 1960). Streambed temperature profiles have been used to identify losing and gaining reaches of rivers (Constantz, 2008, Constantz and Stonestrom, 2003, Silliman and Booth, 1993). Conant (2004) as well as Schmidt et al. (2007) obtained spatial patterns of groundwater exfiltration using temperature and piezometer data from a dense monitoring network. They analyzed snapshots of vertical temperature profiles with a model assuming steady-state heat transfer. The applicability of this model is questionable because river temperatures typically exhibit a diurnal cycle so that the streambed temperature is transient.

Under infiltrating conditions, the steady-state contribution to temperature profiles cannot be used for the quantification of seepage rates. However, time series obtained at several depths contain information on both effective convection and conduction in the sediment. Because diurnal temperature variations are periodic and more or less sinusoidal, Stallman’s (1965) analytical expression of the convection–conduction equation for sinusoidal boundary conditions is a good starting point for the analysis of temperature data. Hatch et al. (2006) applied a band-pass filter to pairs of temperature time series obtained at different depths within the sediment. Mean flow rates were estimated from the amplitude and phase angle determined for each day using a semi-automated computer program. Kerry et al. (2007) extracted sinusoidal components with periods of one day from temperature time series at various depths using DHR (Young et al., 1999). In this approach, the amplitude and phase angle were estimated as continuous, auto-correlated time variables. Following the analysis of amplitude and phase-angle information of Stallman (1965), Kerry et al. (2007) obtained the seepage rate as a continuous time variable rather than as a set of daily values.

Traditional temperature sensors, such as thermocouples and platinum resistance thermometers, measure temperatures only at individual points. In order to obtain spatial profiles one may either install a large number of individual sensors, or a single sensor is moved along the profile, leading to an asynchronous measurement. An alternative to traditional thermometry is fiber-optic distributed temperature sensing (DTS), which has recently been applied in hydrological studies (Selker et al., 2006a, Tyler et al., 2009). In DTS, temperature is measured along an optical fiber of up to several km in length with a spatial resolution of about 1 m. Thus, thousands of traditional thermometers are replaced by a single fiber. Depending on the required accuracy, the temporal resolution is in the order of several minutes. Thus DTS is an attractive method to obtain long profiles of temperatures that vary on time scales of hours and longer.

DTS is based on the temperature dependence of Raman scattering (Dakin et al., 1985, Kurashima et al., 1990). Light from a laser pulse is scattered along the optical fiber. In addition to standard Rayleigh scattering, in which the frequencies of the original and scattered light are identical, secondary maxima with shifted wavelengths exist. Raman scattering describes a particular pair of secondary maxima. The scattered light with longer wavelength (Stokes) is not affected by temperature, whereas the amplitude of the scattered light with shorter wavelength (anti-Stokes) depends exponentially on temperature of the fiber at the scattering point. The back-scattered light is detected in the DTS control unit with high temporal resolution. The distance to the point where the scattering occurred is the time since the pulse was released times the speed of light, whereas the ratio of the Stokes to Anti-Stokes signals is informative about the temperature at the scattering point. By sampling the responses to multiple pulses with a high temporal resolution, the temperature along the fiber can be measured with high accuracy and high spatial resolution. A more detailed overview of the technique is given by Selker et al. (2006a). Tyler et al. (2009) summarized calibration, operation, limitations, and system accuracies of DTS for hydrological purposes.

The use of DTS in hydrological systems has been mainly focused on lateral measurements at the surface water–groundwater interface. Optical fibers have been laid out laterally to detect submarine groundwater discharge (Henderson et al., 2008), to identify groundwater discharge zones in streams (Lowry et al., 2007, Selker et al., 2006b) and to calibrate an energy-based stream temperature model with DTS data (Westhoff et al., 2007). A limitation of lateral DTS data is that groundwater discharge or recharge rates cannot directly be quantified. If groundwater temperatures differ from river temperatures, local exfiltration of groundwater leads to a local change of the temperature at the river bottom. However, the quantitative relationship between specific discharge and observed temperature is strongly affected by river velocities and vertical mixing within the river. Also, infiltration of river water has essentially no effect on the temperature at the river bottom.

Vertical temperature profiles in boreholes were obtained by DTS for the first time in the 1990s (Hurtig et al., 1994). The application in deep boreholes is simple because the optic fiber only has to be lowered down the borehole. For investigation of near-surface processes, we require a high spatial resolution of temperature. Because the spatial resolution of DTS along the fiber is in the range of 1 m, a straight cable in a shallow borehole will not give the required resolution. A second potential shortcoming of such a set-up lies in the danger of vertical convection in the open or fully screened borehole. To overcome these deficiencies, we adopted the technique of wrapping the optical fiber around a pole or tube, developed by Selker et al. (2006a) in the application of temperature monitoring in lakes and snow fields. Rather than inserting this profiler into an existing piezometer, we wrapped the fiber directly around a new piezometer tube which we install in the subsurface by a dual-tube direct-push technique. The temperature profile along the fiber is converted into a depth profile. The set of time series is analyzed by means of dynamic harmonic regression (Keery et al., 2007, Young et al., 1999).

Section snippets

Convection–conduction equation with sinusoidal boundary condition

We assume that horizontal variability of the seepage process and the related heat transport can be neglected, so that only the vertical component of flow and heat transfer need to be considered. We also consider local thermal equilibrium between groundwater and sediment matrix. Then, the heat transfer from the river into the aquifer can be described by the one-dimensional convection–conduction equation (modified after Anderson, 2005, Stallman, 1965):(ρsCs(1-n)+ρwCwn)Tt+ρwCwqTz-(λs(1-n)+(λw+ρ

Fiber-optic vertical temperature profiler

The fiber-optic vertical temperature profiler consists of a solid 2 in. PVC piezometer tube (OD = 50.8 mm) of 2 m length and an optical fiber (Fig. 1). We wrap 380 m of the optical fiber (OD = 0.9 mm) around the tube (OD = 60 mm) using a lathe. This converts the spatial resolution of the DTS from 1 m along the optical fiber to a vertical resolution of 4.9 mm along the 1.86 m long wrapped tube section. The optical fiber is protected against mechanical damage by covering it with a self-adhesive plastic film.

Distribution of temperature in time and depth

Fig. 4 shows the spatiotemporal distribution of temperature along the fiber-optic vertical temperature profiler. The part of the temperature profiler above the river bed measured the temperatures of river water and air. Fig. 4A shows the time series of these data as lines. The data of the river temperature logger agree well with the DTS measurements over the monitored period. Deviations occur due to calibration and signal noise of the DTS as well as solar radiation that maybe heats up the

Discussion and conclusions

All techniques for the estimation of seepage fluxes are prone to errors, uncertainties and limitations (Kalbus et al., 2006). Field investigations are often limited by instrumentation and insufficient resolution. But for detailed assessment of spatial heterogeneity and temporal variability of river–groundwater interaction, high-resolution measurements are necessary. The present work builds upon previous studies in which infiltration rates were determined from temperature time series (Constantz

Acknowledgements

This study was financed by the Competence Center Environment and Sustainability (CCES) of the ETH domain in the framework of the RECORD project (Assessment and Modeling of Coupled Ecological and Hydrological Dynamics in the Restored Corridor of a River (Restored Corridor Dynamics)). We thank Andreas Raffainer and Peter Gäumann of the Eawag workshop as well as Erwin Pieper of the Swiss Federal Institute of Material Research and Testing (Empa) for their help in wrapping the fiber-optic

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