Was That Assumption Necessary? Reconsidering Boundary Conditions for Analytical Solutions to Estimate Streambed Fluxes

Luce, Charles H.; Tonina, Daniele; Applebee, Ralph; DeWeese, Timothy

doi:10.1002/2017wr020618

Cited by 12 publications

(11 citation statements)

References 40 publications

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“…For completeness, we also report the equation to quantify the Darcian seepage flux, q :

q = γ \sqrt{ω {\overset{κ}{true}}_{e} true(η + \frac{1}{η} true)} \frac{1 - η^{2}}{1 + η^{2}} or q = γ ω \frac{Δ z}{Δ ϕ} \frac{1 - η^{2}}{1 + η^{2}}

where γ = ( ρ m c m )/( ρ w c w ), and ρ refers to density and c to specific heat capacity, while the subscripts w and m refer to the water and the sediment pore water matrix, respectively. In this work, we use γ = 0.957 as reported by Luce et al () for our set of laboratory experiments.…”

Section: Methodsmentioning

confidence: 99%

“…The seepage velocity estimate from the process will reflect the average velocity over the sampling window for temperature, so errors would be most pronounced during rapid changes. The temperature signal can be nonstationary, which is generally the case in the field, and this does not affect the analytical solution (Luce et al, 2017).…”

Section: Introductionmentioning

confidence: 99%

“…where c 5 (q m c m )/(q w c w ), and q refers to density and c to specific heat capacity, while the subscripts w and m refer to the water and the sediment pore water matrix, respectively. In this work, we use c 5 0.957 as reported byLuce et al (2017) for our set of laboratory experiments.…”

mentioning

confidence: 99%

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Monitoring Streambed Scour/Deposition Under Nonideal Temperature Signal and Flood Conditions

DeWeese

Tonina

Luce

2017

Water Resources Research

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Streambed erosion and deposition are fundamental geomorphic processes in riverbeds, and monitoring their evolution is important for ecological system management and in‐stream infrastructure stability. Previous research showed proof of concept that analysis of paired temperature signals of stream and pore waters can simultaneously provide monitoring scour and deposition, stream sediment thermal regime, and seepage velocity information. However, it did not address challenges often associated with natural systems, including nonideal temperature variations (low‐amplitude, nonsinusoidal signal, and vertical thermal gradients) and natural flooding conditions on monitoring scour and deposition processes over time. Here we addressed this knowledge gap by testing the proposed thermal scour‐deposition chain (TSDC) methodology, with laboratory experiments to test the impact of nonideal temperature signals under a range of seepage velocities and with a field application during a pulse flood. Both analyses showed excellent match between surveyed and temperature‐derived bed elevation changes even under very low temperature signal amplitudes (less than 1°C), nonideal signal shape (sawtooth shape), and strong and changing vertical thermal gradients (4°C/m). Root‐mean‐square errors on predicting the change in streambed elevations were comparable with the median grain size of the streambed sediment. Future research should focus on improved techniques for temperature signal phase and amplitude extractions, as well as TSDC applications over long periods spanning entire hydrographs.

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“…For completeness, we also report the equation to quantify the Darcian seepage flux, q :

q = γ \sqrt{ω {\overset{κ}{true}}_{e} true(η + \frac{1}{η} true)} \frac{1 - η^{2}}{1 + η^{2}} or q = γ ω \frac{Δ z}{Δ ϕ} \frac{1 - η^{2}}{1 + η^{2}}

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Monitoring Streambed Scour/Deposition Under Nonideal Temperature Signal and Flood Conditions

DeWeese

Tonina

Luce

2017

Water Resources Research

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“…The attributes of the diurnal temperature signal-based analytical solutions have been investigated broadly, including the influence of heterogeneity (Birkel et al, 2016;Irvine, Cranswick, Simmons, Shanafield, & Lautz, 2015), nonsinusoidal temperature signals (Luce, Tonina, Applebee, & DeWeese, 2017), nonconstant fluid fluxes Rau, Cuthbert, McCallum, Halloran, & Andersen, 2015), multidimensional flow (Cuthbert & Mackay, 2013;Lautz, 2010;Reeves & Hatch, 2016), and the uncertainty in flux estimates that results from uncertainties in thermal properties Shanafield, Hatch, & Pohll, 2011).…”

Section: Introductionmentioning

confidence: 99%

Quantitative guidance for efficient vertical flow measurements at the sediment–water interface using temperature–depth profiles

Irvine

Kurylyk

Briggs

2019

Hydrological Processes

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Upward discharge to surface water bodies can be quantified using analytical models based on temperature-depth (T-z) profiles. The use of sediment T-z profiles is attractive as discharge estimates can be obtained using point-in-time data that are collected inexpensively and rapidly. Previous studies have identified that T-z methods can only be applied at times of the year when there is significant difference between the streambed-water interface and deeper sediment temperatures (e.g., winter and summer). However, surface water temperatures also vary diurnally, and the influence of these variations on discharge estimates from T-z methods is poorly understood.For this study, synthetic T-z profiles were generated numerically using measured streambed interface temperature data to assess the influence of diurnal temperature variations on discharge estimation and provide insight into the suitable application of T-z methods. Results show that the time of day of data collection can have a substantial influence on vertical flux estimates using T-z methods. For low groundwater discharge fluxes (e.g., 0.1 m d −1 ), daily transience in streambed temperatures led to relatively large errors in estimated flow magnitude and direction. For higher discharge fluxes (1.5 m d −1 ), the influence of transient streambed temperatures on discharge estimates was strongly reduced. Discharge estimates from point-in-time T-z profiles were most accurate when the uppermost point in the T-z profile was near the bed interface daily mean (two time periods daily). Where temperature time series data are available, daily averaged T-z profiles can produce accurate discharge estimates across a wide range of discharge rates. Seasonality in shallow groundwater temperature generally had a negligible influence on vertical flow estimates. These findings can be used to plan field campaigns and provide guidance on the optimal applicationof T-z methods to quantify vertical groundwater discharge to surface water bodies. K E Y W O R D Sanalytical solutions, gaining stream, groundwater discharge, groundwater, surface water exchange, heat as a groundwater tracer, hyporheic flow, river-aquifer interactions, streambed mapping

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“…These methods are not without their limitations, and numerous studies have been performed to analyze the conditions where the use of periodic heat signals to quantify Darcy fluxes break down as well as to help provide appropriate guidance when transitioning to a field setting. These studies include the investigation of nonideal field conditions that violate the assumptions established by Stallman () such as nonuniform flow fields (Cuthbert & Mackay, ; Reeves & Hatch, ), nonsinusoidal temperature signals (Lautz, ; Luce et al, ), transient fluid fluxes (Rau et al, ), heterogeneity (Birkel et al, ; Irvine, Cranswick, et al, ), and thermal property uncertainty (Irvine, Lautz, et al, ; Shanafield et al, ). Results from studies that are based on the violation of fundamental assumptions, while useful for exploring what errors are introduced when these assumptions are violated, do not provide a field‐based metric for determining if a Darcy flux estimate is accurate or not, nor do they provide a means for determining if a field‐derived Darcy flux is the result of an assumption violation.…”

Section: Introductionmentioning

confidence: 99%

Limits on Groundwater‐Surface Water Fluxes Derived from Temperature Time Series: Defining Resolution‐Based Thresholds

Glose

Lowry

Hausner

2019

Water Resources Research

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Heat as a tracer is frequently used to quantify Darcy fluxes across the groundwater-surface water interface. Often quantified through the analysis of diurnal or annual periodic temperature signals, these temperature time series methods rely on the advective transport of heat by flowing water perturbing the periodic conducted heat signal. Multiple methodologies have been developed that rely on temperature time series data collected from at least two unique depths a set distance apart. However, the lower limits at which these methods can no longer reliably quantify a Darcy flux are not well established. To examine these lower limits, synthetic temperature time series data were generated using a numerical model for various combinations of head gradients, sensor spacing, and thermal properties of the sediment. Darcy fluxes were subsequently quantified using the combined method and directly compared to prescribed Darcy fluxes. The dimensionless Péclet number, representing the ratio of advective to conductive heat flux, was used to establish threshold values at which the combined amplitude ratio and phase shift method was no longer able to reliably quantify a Darcy flux. The lowest recharge Darcy flux that can be quantified ranges from 0.07 to 0.2 m/day, dependent on the resolution of the sensor used to collect data, a narrower range than previously reported. When transitioning to a field setting, where the accuracy of Darcy fluxes is not known, a newly developed relationship between the true and inferred Péclet numbers can be used to evaluate quantified Darcy fluxes for accuracy.

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Was That Assumption Necessary? Reconsidering Boundary Conditions for Analytical Solutions to Estimate Streambed Fluxes

Cited by 12 publications

References 40 publications

Monitoring Streambed Scour/Deposition Under Nonideal Temperature Signal and Flood Conditions

Monitoring Streambed Scour/Deposition Under Nonideal Temperature Signal and Flood Conditions

Quantitative guidance for efficient vertical flow measurements at the sediment–water interface using temperature–depth profiles

Limits on Groundwater‐Surface Water Fluxes Derived from Temperature Time Series: Defining Resolution‐Based Thresholds

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