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LPMLE3: a novel 1-D approach to study water flow in streambeds using heat as a tracer

(2016) WATER RESOURCES RESEARCH. 52(8). p.6596-6610
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Abstract
We introduce LPMLE3, a new 1-D approach to quantify vertical water flow components at streambeds using temperature data collected in different depths. LPMLE3 solves the partial differential equation for coupled water flow and heat transport in the frequency domain. Unlike other 1-D approaches it does not assume a semi-infinite halfspace with the location of the lower boundary condition approaching infinity. Instead, it uses local upper and lower boundary conditions. As such, the streambed can be divided into finite subdomains bound at the top and bottom by a temperature-time series. Information from a third temperature sensor within each subdomain is then used for parameter estimation. LPMLE3 applies a low order local polynomial to separate periodic and transient parts (including the noise contributions) of a temperature-time series and calculates the frequency response of each subdomain to a known temperature input at the streambed top. A maximum-likelihood estimator is used to estimate the vertical component of water flow, thermal diffusivity, and their uncertainties for each streambed subdomain and provides information regarding model quality. We tested the method on synthetic temperature data generated with the numerical model STRIVE and demonstrate how the vertical flow component can be quantified for field data collected in a Belgian stream. We show that by using the results in additional analyses, nonvertical flow components could be identified and by making certain assumptions they could be quantified for each subdomain. LPMLE3 performed well on both simulated and field data and can be considered a valuable addition to the existing 1-D methods.
Keywords
THERMAL-DIFFUSIVITY, hyporheic zone, FLUID-FLOW, SURFACE-WATER, SPATIAL VARIABILITY, maximum-likelihood estimator, FLUXES, RIVER, TRANSIENT, heat tracer, frequency domain, TEMPERATURE TIME-SERIES, INDUCED HYPORHEIC EXCHANGE, HETEROGENEITY, groundwater-surface water interaction

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Chicago
Schneidewind, Uwe, M van Berkel, C Anibas, G Vandersteen, C Schmidt, I Joris, Piet Seuntjens, O Batelaan, and HJ Zwart. 2016. “LPMLE3: a Novel 1-D Approach to Study Water Flow in Streambeds Using Heat as a Tracer.” Water Resources Research 52 (8): 6596–6610.
APA
Schneidewind, U., van Berkel, M., Anibas, C., Vandersteen, G., Schmidt, C., Joris, I., Seuntjens, P., et al. (2016). LPMLE3: a novel 1-D approach to study water flow in streambeds using heat as a tracer. WATER RESOURCES RESEARCH, 52(8), 6596–6610.
Vancouver
1.
Schneidewind U, van Berkel M, Anibas C, Vandersteen G, Schmidt C, Joris I, et al. LPMLE3: a novel 1-D approach to study water flow in streambeds using heat as a tracer. WATER RESOURCES RESEARCH. 2016;52(8):6596–610.
MLA
Schneidewind, Uwe, M van Berkel, C Anibas, et al. “LPMLE3: a Novel 1-D Approach to Study Water Flow in Streambeds Using Heat as a Tracer.” WATER RESOURCES RESEARCH 52.8 (2016): 6596–6610. Print.
@article{8158698,
  abstract     = {We introduce LPMLE3, a new 1-D approach to quantify vertical water flow components at streambeds using temperature data collected in different depths. LPMLE3 solves the partial differential equation for coupled water flow and heat transport in the frequency domain. Unlike other 1-D approaches it does not assume a semi-infinite halfspace with the location of the lower boundary condition approaching infinity. Instead, it uses local upper and lower boundary conditions. As such, the streambed can be divided into finite subdomains bound at the top and bottom by a temperature-time series. Information from a third temperature sensor within each subdomain is then used for parameter estimation. LPMLE3 applies a low order local polynomial to separate periodic and transient parts (including the noise contributions) of a temperature-time series and calculates the frequency response of each subdomain to a known temperature input at the streambed top. A maximum-likelihood estimator is used to estimate the vertical component of water flow, thermal diffusivity, and their uncertainties for each streambed subdomain and provides information regarding model quality. We tested the method on synthetic temperature data generated with the numerical model STRIVE and demonstrate how the vertical flow component can be quantified for field data collected in a Belgian stream. We show that by using the results in additional analyses, nonvertical flow components could be identified and by making certain assumptions they could be quantified for each subdomain. LPMLE3 performed well on both simulated and field data and can be considered a valuable addition to the existing 1-D methods.},
  author       = {Schneidewind, Uwe and van Berkel, M and Anibas, C and Vandersteen, G and Schmidt, C and Joris, I and Seuntjens, Piet and Batelaan, O and Zwart, HJ},
  issn         = {0043-1397},
  journal      = {WATER RESOURCES RESEARCH},
  keyword      = {THERMAL-DIFFUSIVITY,hyporheic zone,FLUID-FLOW,SURFACE-WATER,SPATIAL VARIABILITY,maximum-likelihood estimator,FLUXES,RIVER,TRANSIENT,heat tracer,frequency domain,TEMPERATURE TIME-SERIES,INDUCED HYPORHEIC EXCHANGE,HETEROGENEITY,groundwater-surface water interaction},
  language     = {eng},
  number       = {8},
  pages        = {6596--6610},
  title        = {LPMLE3: a novel 1-D approach to study water flow in streambeds using heat as a tracer},
  url          = {http://dx.doi.org/10.1002/2015WR017453},
  volume       = {52},
  year         = {2016},
}

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