As recognized in the European Water Framework Directive, groundwater-dependent wetlands and their diverse ecosystems have important functions which need to be protected. The vegetation in such habitats is often dependent on quality, quantity and patterns of river discharge and groundwater-surface water interaction on a local or reach scale. Since groundwater-surface water exchange studies on natural rivers and wetlands with organic soils are scarce, more functional analysis is needed. To this end we combined different field methods including piezometer nests, temperature as tracer and seepage meter measurements. Some of these measurements were used as inputs and/or as validation for the numerical 1-D heat transport model STRIVE. In transient mode the model was used to calculate spatially distributed vertical exchange fluxes from temperature profiles measured at the upper Biebrza River in Poland over a period of nine months. Time series of estimated fluxes and hydraulic head gradients in the hyporheic zone were used to estimate the temporal variability of groundwater-surface water exchange. This paper presents a hierarchical approach for quantifying and interpreting groundwater-surface water interaction in space and time. The results for the upper Biebrza show predominantly upward water fluxes, sections of recharge, however, exist along the reach. The fluxes depend more on hydraulic gradients than on riverbed conductivity. This indicates that the fluvio-plain scale is required for interpreting the exchange fluxes, which are estimated on a local scale. The paper shows that a conceptual framework is necessary for understanding the groundwater-surface water interaction processes, where the exchange fluxes are influenced by local factors like the composition of the riverbed and the position of the measurement on a local scale, and by regional factors like the hydrogeology and topography on a fluvio-plain scale. The hierarchical methodology increases the confidence in the estimated exchange fluxes and improves the process understanding. The accuracy of the measurements and related uncertainties, however, remain challenges for wetland environments. Gaining quantitative information on groundwater-surface water interaction can improve modeling confidence and as a consequence helps to develop effective procedures for management and conservation of valuable groundwater dependent wetlands.

The use of temperature‐time series measured in streambed sediments as input to coupled water flow and heat transport models has become standard when quantifying vertical groundwater‐surface water exchange fluxes. We develop a novel methodology, called LPML, to estimate the parameters for 1‐D water flow and heat transport by combining a local polynomial (LP) signal processing technique with a maximum likelihood (ML) estimator. The LP method is used to estimate the frequency response functions (FRFs) and their uncertainties between the streambed top and several locations within the streambed from measured temperature‐time series data. Additionally, we obtain the analytical expression of the FRFs assuming a pure sinusoidal input. The estimated and analytical FRFs are used in an ML estimator to deduce vertical groundwater‐surface water exchange flux and its uncertainty as well as information regarding model quality. The LPML method is tested and verified with the heat transport models STRIVE and VFLUX. We demonstrate that the LPML method can correctly reproduce a priori known fluxes and thermal conductivities and also show that the LPML method can estimate averaged and time‐variable fluxes from periodic and nonperiodic temperature records. The LPML method allows for a fast computation of exchange fluxes as well as model and parameter uncertainties from many temperature sensors. Moreover, it can utilize a broad frequency spectrum beyond the diel signal commonly used for flux calculations.

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.