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

We introduce LPMLE3, a new 1D 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 1D 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 sub-domains bound at the top and bottom by a temperature-time series. Information from a third temperature sensor within each sub-domain 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 sub-domain 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 sub-domain 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, non-vertical flow components could be identified and by making certain assumptions they could be quantified for each sub-domain. LPMLE3 performed well on both simulated and field data and can be considered a valuable addition to the existing 1D methods. This article is protected by copyright. All rights reserved.

Publication year:2016

Keywords:Groundwater-surface water interaction, hyporheic zone, heat tracer, frequency domain, maximum-likelihood estimator

CSS-citation score:2

Accessibility:Closed