Isotope Ratio – Discharge Relationships of Solutes Derived From Weathering Reactions

To date, the vast majority of studies seeking to link discharge to solute concentrations have been based on representations of fluid age distributions in watersheds that are time-invariant. As increasingly detailed spatial and temporal datasets become available for weathering-derived riverine solute concentrations, the capacity to link this mass flux to transient routing of reactive fluids through Critical Zone environments is vital to quantitative interpretation. Relationships between fluid age distributions and the stable isotope ratios of these geogenic solutes are even less developed, yet these signatures are vital to parsing the suite of water-rock-life interactions that create concentration-discharge relationships. Here we offer the first merging of a hydrological model featuring time-variant fluid age distributions with a geochemical model for isotopically fractionating weathering reactions. Using SiO2(aq) and the corresponding silicon isotope ratio δ30Si as an example, we show that the stable isotope signatures of riverine solutes produced by weathering reactions reflect a component of the fluid age distribution that is unique to the corresponding solute concentrations. This distinct sensitivity is the result of a stronger link between isotope ratios and the age distribution parameters describing a given watershed. This novel modeling framework is used to provide a quantitative basis for the interpretation of SiO2(aq) and δ30Si in six low-order streams spread across a diversity of climates, geologies, and ecosystems. To our knowledge, this is the first forward and process-based model to describe the isotopic signatures of solutes derived from weathering reactions in watersheds subject to time-varying discharge

Catchment transport and travel time distributions: theoretical developments and applications

The fate of water and solutes introduced into a watershed and sampled at the catchment outlet depends on a number of factors that include the underlying climatic forcing and the heterogeneity of subsurface environments. After a storm event, the hydrologic response of a watershed is known to rapidly displace large amounts of water that had been contained in the system storage prior to the arrival of the storm. The actual time spent by non-event water particles within the catchment spans a large range of timescales and typically exceeds the characteristic times of the hydrologic response by at least two orders of magnitude. Inferring water age is crucial for our understanding of streamflow generation and catchment-scale dispersion processes. Water travel time distributions can be used to address a number of environmental challenges, such as modeling the dynamics of river water quality, quantifying the interactions between shallow and deep flow systems and understanding nutrient loading persistence. The need for robust yet simple mathematical tools to describe water age dynamics is here addressed using a catchment-scale approach. In this context, water particles can be seen as a dynamic population whose evolution can be described through suitable partial differential equations. Novel theoretical solutions are here proposed, with extensive applications to real-world case studies that include the transport of chloride, isotopic content and silica. Coupling transport models to high-quality hydrochemical datasets allows for inferences on water age distributions and proves able to explain different features of measured water quality dynamics. The applications allowed an improved understanding of the underlying transport processes and many further developments can be foreseen along the path here pursued, inching towards a watershed theory

Using SAS functions and high resolution isotope data to unravel travel time distributions in headwater catchments

Acknowledgments. We are grateful to the European Research Council (ERC) VeWa project (GA335910) and NERC/JIP SIWA project (NE/MO19896/1) for funding. A.R. acknowledges the financial support from the ENAC school at EPFL. C.B. acknowledges support from the University of Costa Rica (project 217-B4-239 and the Isotope Network for Tropical Ecosystem Studies (ISONet)). Data to support this study are provided by the Northern Rivers Institute, University of Aberdeen and are available by the authors. The authors wish to thank Ype van der Velde, Arash Massoudieh, Jean-Raynald de Dreuzy and an anonymous referee for the useful review comments.Peer reviewedPublisher PD

Using water age to explore hydrological processes in contrasting environments

Peer reviewedPublisher PD

Re-designing the urban water cycle: Towards Water-Age-Neutral Habitats

peer reviewedKnowledge of how to articulate the “urban transition” is today urgently needed. Urbanization is on a steadily growing trend that impacts the water cycle as a whole. However, while the effects of urbanised/urbanising areas on water quantity (how much water) have been well studied for flood prevention, other effects –as those related to water quality (which water)– are less known. Taking hold from the most recent developments on the “water age” concept, i.e. the time that water resides in the landscape before exiting as runoff or evaporation, we propose a proof-of-concept study on the notion of “water-age-neutral” design. This concept envisions the possibility of lowering –through design– net impacts on the City-Territory’s “natural” water age balance. To do this, we selected 4 representative areas of 250x250 meters within the Panke watershed, in the metropolitan area of Berlin (DE), which are characterized by specific land-use/urban form patterns (industry, single family housing, residential slabs and residential open block housing). For these 4 areas, we used an ecohydrological model to analyse a set of water/land use interaction patterns and their outputs in terms of water flow partitioning and water age. We use such outputs to evaluate the broader impacts of land-use/urban form on the urban water cycle. These results are considered as a first step towards a larger evaluation of the multiple relationships between land-use/urban form and the water cycle as a whole.Water Age Neutral Habitat

Modeling chloride transport using travel time distributions at Plynlimon, Wales

Here we present a theoretical interpretation of high-frequency, high-quality tracer time series from the Hafren catchment at Plynlimon in mid-Wales. We make use of the formulation of transport by travel time distributions to model chloride transport originating from atmospheric deposition and compute catchment-scale travel time distributions. The relevance of the approach lies in the explanatory power of the chosen tools, particularly to highlight hydrologic processes otherwise clouded by the integrated nature of the measured outflux signal. The analysis reveals the key role of residual storages that are poorly visible in the hydrological response, but are shown to strongly affect water quality dynamics. A significant accuracy in reproducing data is shown by our calibrated model. A detailed representation of catchment-scale travel time distributions has been derived, including the time evolution of the overall dispersion processes (which can be expressed in terms of time-varying storage sampling functions). Mean computed travel times span a broad range of values (from 80 to 800 days) depending on the catchment state. Results also suggest that, in the average, discharge waters are younger than storage water. The model proves able to capture high-frequency fluctuations in the measured chloride concentrations, which are broadly explained by the sharp transition between groundwaters and faster flows originating from topsoil layers

Nitrate and Water Isotopes as Tools to Resolve Nitrate Travel Times in a Mixed Land Use Catchment

For the sake of food production, nutrients like nitrogen (N) are applied on agricultural land to supply crops. However, due to common agricultural practice, the amount of N provided very often significantly exceeds the uptake potential of the plants resulting in a N surplus that accumulates in the soil. Organic soil nitrogen is slowly transformed to nitrate, which is then mobilized by water and moves through the subsurface, with the risk of contaminating receiving water bodies. High nitrate loads cause poor chemical states for 27% of all groundwater bodies in Germany and foster eutrophication in lakes and rivers and by this a loss of biodiversity. The main problem are legacy issues of nitrate pollution, because there is a time lag between N input and nitrate mobilization and transport. Research on nitrate travel times is highly relevant for a reliable prediction of the capability of catchments to store, buffer and release nitrate. However, it is not clear how long nitrate is stored and transported in catchment’s storage. For this study, a 11 km2 headwater catchment with mixed land use within the Northern lowlands of the Harz mountains in Germany was investigated from spring 2017 until the end of 2020. A monitoring program was set up, starting with biweekly samples for the first two years and daily samples for the remainder, with sub-daily samples during precipitation events. Samples were taken from stream water and when available from precipitation water. Nitrate concentrations as well as isotopic signatures of water (δ18O and δ2H) and nitrate (δ18O and δ15N) were analysed. To investigate nitrate travel times, the numerical model tran-SAS (Benettin and Bertuzzo, 2018) was set up und modified for this catchment. Here, a time-variant power law function was used as rank StorAge Selection (SAS) function to select the composition of fluxes considering their age. Nitrate with a distinct δ18O from water, formed during microbial activities in the upper soil zone is transported with leaching water into the subsurface storage where denitrification with the corresponding isotope fractionation occurs. The combination of stable isotopes of water and biogeochemical equations to describe the forming of nitrate isotopes and the fractionation of nitrate isotopes during denitrification, which depends on transit times is a novel tool to investigate nitrate age and nitrate transport. Together with the usage of a SAS-based transit time model to simulate nitrate transport and denitrification in the subsurface, tran-SAS is transformed into a simplified reactive transport model (RTM). A decoupling between nitrate age and water age as well as between nitrate travel times and water travel times is expected. Especially during precipitation events catchment’s processes and travel times are changing due to altering hydrological conditions. The model allows to investigate the age of water and nitrate during different hydrological conditions. This will become more and more important considering more frequent hydrological extremes (droughts and floods) and associated N mobilization in agricultural catchments

Linking water age and solute dynamics in streamflow at the Hubbard Brook Experimental Forest, NH, USA

We combine experimental and modeling results from a headwater catchment at the Hubbard Brook Experimental Forest (HBEF), New Hampshire, USA, to explore the link between stream solute dynamics and water age. A theoretical framework based on water age dynamics, which represents a general basis for characterizing solute transport at the catchment scale, is here applied to conservative and weathering-derived solutes. Based on the available information about the hydrology of the site, an integrated transport model was developed and used to compute hydrochemical fluxes. The model was designed to reproduce the deuterium content of streamflow and allowed for the estimate of catchment water storage and dynamic travel time distributions (TTDs). The innovative contribution of this paper is the simulation of dissolved silicon and sodium concentration in streamflow, achieved by implementing first-order chemical kinetics based explicitly on dynamic TTD, thus upscaling local geochemical processes to catchment scale. Our results highlight the key role of water stored within the subsoil glacial material in both the short-term and long-term solute circulation. The travel time analysis provided an estimate of streamflow age distributions and their evolution in time related to catchment wetness conditions. The use of age information to reproduce a 14 year data set of silicon and sodium stream concentration shows that, at catchment scales, the dynamics of such geogenic solutes are mostly controlled by hydrologic drivers, which determine the contact times between the water and mineral interfaces. Justifications and limitations toward a general theory of reactive solute circulation at catchment scales are discussed

Steady state fluctuation relation and time-reversibility for non-smooth chaotic maps

Steady state fluctuation relations for dynamical systems are commonly derived under the assumption of some form of time-reversibility and of chaos. There are, however, cases in which they are observed to hold even if the usual notion of time reversal invariance is violated, e.g. for local fluctuations of Navier-Stokes systems. Here we construct and study analytically a simple non-smooth map in which the standard steady state fluctuation relation is valid, although the model violates the Anosov property of chaotic dynamical systems. Particularly, the time reversal operation is performed by a discontinuous involution, and the invariant measure is also discontinuous along the unstable manifolds. This further indicates that the validity of fluctuation relations for dynamical systems does not rely on particularly elaborate conditions, usually violated by systems of interest in physics. Indeed, even an irreversible map is proved to verify the steady state fluctuation relation.Comment: 23 pages,8 figure