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

U. Schneidewind, M. van Berkel, C. Anibas, G. Vandersteen, C. Schmidt, I. Joris, P. Seuntjens, O. Batelaan, H. J. Zwart

Research output: Contribution to journalArticleAcademicpeer-review

23 Citations (Scopus)
15 Downloads (Pure)


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.

Original languageEnglish
Pages (from-to)6596-6610
Number of pages15
JournalWater Resources Research
Issue number8
Publication statusPublished - 1 Aug 2016


  • frequency domain
  • groundwater-surface water interaction
  • heat tracer
  • hyporheic zone
  • maximum-likelihood estimator


Dive into the research topics of 'LPMLE3: A novel 1-D approach to study water flow in streambeds using heat as a tracer'. Together they form a unique fingerprint.

Cite this