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Quantifying and upscaling chemical turnover in the hyporheic zone (HZ) is difficult due to limited reaction rate data, unknown carbon quality, and few methods for upscaling local measurements to river networks. Here we develop a method for quantifying reaction kinetics in situ in the HZ and upscaling biogeochemical turnover to catchment scales. Radon-222 was used to quantify water residence times in the HZ of the Roter Main River (RM), Germany. Residence times were then combined with O2, NO3−, CO2, DOC, and carbon quality (EEMs, SUVA) data to estimate Monod and first-order reaction rates. Monod parameters µmax and ksat for NO3− reduction were 11 µmol l−1 h−1 and 52 µmol l−1, respectively, while the first-order rate was 0.04 h−1. Carbon quality was highly bioavailable in the HZ and is unlikely to be limiting. Reaction kinetics was incorporated into the FINIFLUX model to upscale NO3− mass loss over a 32 km reach of the RM. The aims were to (1) to estimate hyporheic efficiency using Damkohler numbers (Da), and (2) calculate NO3− mass loss in the HZ over the reach. The Da analysis suggests that the hyporheic zone is inefficient for NO3− processing, however, this is somewhat misleading as the largest NO3− mass loss occurs at the shortest residence times where Da ≪ 1. This is due to the largest water flux occurring in the uppermost part of the sediment profile. Nitrate processing in the HZ accounted for 24 kg NO3− h−1 over the reach, which was 20% of the NO3− flux from the catchment.

A quantitative understanding of groundwater-surface water interactions is vital for sustainable management of water quantity and quality. The noble gas radon-222 (Rn) is becoming increasingly used as a sensitive tracer to quantify groundwater discharge to wetlands, lakes, and rivers: a development driven by technical and methodological advances in Rn measurement. However, quantitative interpretation of these data is not trivial, and the methods used to date are based on the simplest solutions to the mass balance equation (e.g., first-order finite difference and inversion). Here we present a new implicit numerical model (FINIFLUX) based on finite elements for quantifying groundwater discharge to streams and rivers using Rn surveys at the reach scale (1–50 km). The model is coupled to a state-of-the-art parameter optimization code Parallel-PEST to iteratively solve the mass balance equation for groundwater discharge and hyporheic exchange. The major benefit of this model is that it is programed to be very simple to use, reduces nonuniqueness, and provides numerically stable estimates of groundwater fluxes and hyporheic residence times from field data. FINIFLUX was tested against an analytical solution and then implemented on two German rivers of differing magnitude, the Salzach (∼112 m3 s−1) and the Rote Main (∼4 m3 s−1). We show that using previous inversion techniques numerical instability can lead to physically impossible negative values, whereas the new model provides stable positive values for all scenarios. We hope that by making FINIFLUX freely available to the community that Rn might find wider application in quantifying groundwater discharge to streams and rivers and thus assist in a combined management of surface and groundwater systems.