The temporal dynamics of water ages provide crucial insights into hydrological processes and transport mechanisms, yet there remains a significant gap in quantifying water age variability across different temporal scales. This study utilizes a comprehensive dataset spanning 70 years of hydrological observations and tritium records (1953–2022) with a semi-distributed hydrological model with integrated tracer routing routine based on StorageAge Selection functions SAS, to explore the temporal evolution of water ages in the 4000 km2 Upper Neckar River basin, Germany. Our findings indicate a systematic convergence of the variability of young water fractions and other metrics of water age in riverflow and evaporation towards stable values when averaging over increasing time scales. While at daily scales exhibiting considerable variability with young water fractions in riverflow Fwy,Q ∼ 0.01–0.91 and in evaporation Fwy,E ∼ 0.02–0.75, the variability of Fwy,Q and Fwy,E gradually reduces with increasing averaging time scales and converge to 0.45–0.47 and 0.96–0.97, respectively, between individual decades. Liquid water input (PL), comprising rainfall and snow melt, emerges as the dominant driver of Fwy,Q across all time scales. In contrast, Fwy,E shows varying controls with time scale: soil moisture content governs daily fluctuations, whereas PL dominates at the decadal scale. Overall, water ages demonstrate remarkable stability with only minor deviations in response to climatic variability: a 20% fluctuation in average decadal PL results in only ∼4% variation in Fwy,Q and ∼1% in Fwy,E over the study period. These findings suggest a lack of major long-term dynamics in water ages. Consequently, the results suggest that the physical transport dynamics in the Upper Neckar River basin, and potentially in comparable river basins with similar water age characteristics, can be considered near-stationary over multiple decades.@en

Fe(II) minerals can mediate the abiotic reduction of trichloroethylene (TCE), a widespread groundwater contaminant. If reaction rates are sufficiently fast for natural attenuation, the process holds potential for mitigating TCE pollution in groundwater. To assess the variability of abiotic TCE reduction rate constants, we collected pseudo-first-order rate constants for natural sediments and rocks from the literature, as well as intrinsic (surface-area-normalized) rate constants of individual minerals. Using a Bayesian hierarchical modeling approach, we were able to differentiate the contributions of natural variability and experimental error to the total variance. Applying the model, we also predicted rate constants at new sites, revealing a considerable uncertainty of several orders of magnitude. We investigated whether incorporating additional information about sediment composition could reduce this uncertainty. We tested two sets of predictors: reactive mineral content (measured by X-ray diffraction) combined with surface areas and intrinsic rate constants, or the extractable Fe(II) content. Knowledge of the mineral composition only marginally reduced the uncertainty of predicted rate constants. We attribute the low information gain to the inability to measure the (reactive) surface areas of individual minerals in sediments or rocks, which are subject to environmental factors like aqueous geochemistry and redox potential. In contrast, knowing the Fe(II) content reduced the uncertainty about the first-order rate constant by nearly two orders of magnitude, because the relationship between Fe(II) content and rate constants is approximately log–log-linear. We demonstrate how our approach provides estimates for the range of cleanup times for a simple example of diffusion-controlled transport in a contaminated aquitard.@en

Stochastic modeling of contaminant reactions requires the definition of prior distributions for the respective rate constants. We use data from several experiments reported in the literature to better understand the distribution of pseudo-first-order rate constants of abiotic TCE reduction in different sediments. These distributions can be used to choose informed priors for these parameters in reactive-transport models.

Groundwater contamination with trichloroethylene (TCE) persists at many hazardous waste sites due to back diffusion from low-permeability zones such as clay lenses. In recent years, the abiotic reduction of TCE by reduced iron minerals has gained attention as a natural attenuation process, but there is uncertainty as to whether the process is fast enough to be effective. Pseudo-first-order rate constants have been determined in laboratory experiments and are reported in the literature for various sediments and rocks, as well as for individual reactive minerals. However, rate constants can vary between sites and aquifer materials. Reported values range over several orders of magnitude.

To assess the uncertainty and variability of pseudo-first-order rate constants, we compiled data reported in several studies. We built a statistical model based on a hierarchical Bayesian approach to predict probability distributions of rate constants at new sites based on this data set. We then investigated whether additional information about the sediment composition at a site could reduce the uncertainty. We tested two sets of predictors: reactive mineral content or the extractable Fe(II) content. Knowing the reactive mineral content reduced the uncertainty only slightly. In contrast, knowing the Fe(II) content greatly reduced the uncertainty because the relationship between Fe(II) content and rate constants is approximately log-log-linear. Using a simple example of diffusion-controlled transport in a contaminated aquitard, we show how the uncertainty in the predicted rate constants affects the predicted remediation times.@en

The presence of anthropogenic organic micropollutants in rivers poses a long-term threat to surface water quality. To describe and quantify the in-stream fate of single micropollutants, the advection–dispersion–reaction (ADR) equation has been used previously. Understanding the dynamics of the mixture effects and cytotoxicity that are cumulatively caused by micropollutant mixtures along their flow path in rivers requires a new concept. Thus, we extended the ADR equation from single micropollutants to defined mixtures and then to the measured mixture effects of micropollutants extracted from the same river water samples. Effects (single and mixture) are expressed as effect units and toxic units, the inverse of effect concentrations and inhibitory concentrations, respectively, quantified using a panel of in vitro bioassays. We performed a Lagrangian sampling campaign under unsteady flow, collecting river water that was impacted by a wastewater treatment plant (WWTP) effluent. To reduce the computational time, the solution of the ADR equation was expressed by a convolution-based reactive transport approach, which was used to simulate the dynamics of the effects. The dissipation dynamics of the individual micropollutants were reproduced by the deterministic model following first-order kinetics. The dynamics of experimental mixture effects without known compositions were captured by the model ensemble obtained through Bayesian calibration. The highly fluctuating WWTP effluent discharge dominated the temporal patterns of the effect fluxes in the river. Minor inputs likely from surface runoff and pesticide diffusion might contribute to the general effect and cytotoxicity pattern but could not be confirmed by the model-based analysis of the available effect and chemical data.@en

Molecular-biological data and omics tools have increasingly been used to characterize microorganisms responsible for the turnover of reactive compounds in the environment, such as reactive-nitrogen species in groundwater. While transcripts of functional genes and enzymes are used as measures of microbial activity, it is not yet clear how they are quantitatively related to actual turnover rates under variable environmental conditions. As an example application, we consider the interface between rivers and groundwater which has been identified as a key driver for the turnover of reactive-nitrogen compounds, that cause eutrophication of rivers and endanger drinking water production from groundwater. In the absence of measured data, we developed a reactive-transport model for denitrification that simultaneously predicts the distributions of functional-gene transcripts, enzymes, and reaction rates. Applying the model, we evaluate the response of transcripts and enzymes at the river-groundwater interface to stable and dynamic hydrogeochemical regimes. While functional-gene transcripts respond to short-term (diurnal) fluctuations of substrate availability and oxygen concentrations, enzyme concentrations are stable over such time scales. The presence of functional-gene transcripts and enzymes globally coincides with the zones of active denitrification. However, transcript and enzyme concentrations do not directly translate into denitrification rates in a quantitative way because of nonlinear effects and hysteresis caused by variable substrate availability and oxygen inhibition. Based on our simulations, we suggest that molecular-biological data should be combined with aqueous geochemical data, which can typically be obtained at higher spatial and temporal resolution, to parameterize and calibrate reactive-transport models.@en

Environmental omics and molecular-biological data have been proposed to yield improved quantitative predictions of biogeochemical processes. The abundances of functional genes and transcripts relate to the number of cells and activity of microorganisms. However, whether molecular-biological data can be quantitatively linked to reaction rates remains an open question. We present an enzyme-based denitrification model that simulates concentrations of transcription factors, functional-gene transcripts, enzymes, and solutes. We calibrated the model using experimental data from a well-controlled batch experiment with the denitrifier Paracoccous denitrificans. The model accurately predicts denitrification rates and measured transcript dynamics. The relationship between simulated transcript concentrations and reaction rates exhibits strong non-linearity and hysteresis related to the faster dynamics of gene transcription and substrate consumption, relative to enzyme production and decay. Hence, assuming a unique relationship between transcript-to-gene ratios and reaction rates, as frequently suggested, may be an erroneous simplification. Comparing model results of our enzyme-based model to those of a classical Monod-type model reveals that both formulations perform equally well with respect to nitrogen species, indicating only a low benefit of integrating molecular-biological data for estimating denitrification rates. Nonetheless, the enzyme-based model is a valuable tool to improve our mechanistic understanding of the relationship between biomolecular quantities and reaction rates. Furthermore, our results highlight that both enzyme kinetics (i.e., substrate limitation and inhibition) and gene expression or enzyme dynamics are important controls on denitrification rates.

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