Paolo Benettin

Storage selection functions: A coherent framework for quantifying how catchments store and release water and solutes

We discuss a recent theoretical approach combining catchment-scale flow and transport processes into a unified framework. The approach is designed to characterize the hydrochemistry of hydrologic systems and to meet the challenges posed by empirical evidence. StorAge Selection functions (SAS) are defined to represent the way catchment storage supplies the outflows with water of different ages, thus regulating the chemical composition of out-fluxes. Biogeochemical processes are also reflected in the evolving residence time distribution and thus in age-selection. Here we make the case for the routine use of SAS functions and look forward to areas where further research is needed.

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.

Kinematics of age mixing in advection‐dispersion models

This paper investigates age mixing processes arising in advection-dispersion models, where large-scale travel and residence time distributions can be explicitly calculated based on the underlying velocity field. In particular, we analyze spatially integrated age mixing dynamics by comparing the age distributions of the storage and of the outflow(s). The relevance of the work lies in the impact of age mixing dynamics on the shape of travel time distributions (TTDs), which ultimately control the long-term memory of catchment transport processes. We set up a theoretical framework that bridges previous Lagrangian and Eulerian water age theories in heterogeneous media. The framework allows for the analysis of the dynamical connection between water age distributions in large-scale volume and flux samples. Theoretical advances are then illustrated through the application to a finite one-dimensional domain with constant advection and dispersion coefficient. Therein, we analyze the type of mixing emerging for different Peclet numbers and diverse spatiotemporal patterns of solute input. We find that in spite of the enhanced nonstationarity of TTDs, the type of mixing is markedly invariant. Moreover, for relatively low Peclet numbers the different ages available in the control volume are systematically removed from the domain at a rate nearly proportional to their relative abundance (random sampling). Emerging large-scale patterns of age mixing yield theoretical and practical implications for watershed hydrology, where TTDs can be used to infer general patterns of catchment response across scales.

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.

Transport of fluorobenzoate tracers in a vegetated hydrologic control volume: 2. Theoretical inferences and modeling

A theoretical analysis of transport in a controlled hydrologic volume, inclusive of two willow trees and forced by erratic water inputs, is carried out contrasting the experimental data described in a companion paper. The data refer to the hydrologic transport in a large lysimeter of different fluorobenzoic acids seen as tracers. Export of solute is modeled through a recently developed framework which accounts for nonstationary travel time distributions where we parameterize how output fluxes (namely, discharge and evapotranspiration) sample the available water ages in storage. The relevance of this work lies in the study of hydrologic drivers of the nonstationary character of residence and travel time distributions, whose definition and computation shape this theoretical transport study. Our results show that a large fraction of the different behaviors exhibited by the tracers may be charged to the variability of the hydrologic forcings experienced after the injection. Moreover, the results highlight the crucial, and often overlooked, role of evapotranspiration and plant uptake in determining the transport of water and solutes. This application also suggests that the ways evapotranspiration selects water with different ages in storage can be inferred through model calibration contrasting only tracer concentrations in the discharge. A view on upscaled transport volumes like hillslopes or catchments is maintained throughout the paper.

Young runoff fractions control streamwater age and solute concentration dynamics

Abstract We introduce a new representation of coupled solute and water age dynamics at the catchment scale, which shows how the contributions of young runoff waters can be directly referenced to observed water quality patterns. The methodology stems from recent trends in hydrologic transport that acknowledge the dynamic nature of streamflow age and explores the use of water age fractions as an alternative to the mean age. The approach uses a travel time‐based transport model to compute the fractions of streamflow that are younger than some thresholds (e.g., younger than a few weeks) and compares them to observed solute concentration patterns. The method is here validated with data from the Hubbard Brook Experimental Forest during spring 2008, where we show that the presence of water younger than roughly 2 weeks, tracked using a hydrologic transport model and deuterium measurements, mimics the variation in dissolved silicon concentrations. Our approach suggests that an age–discharge relationship can be coupled to classic concentration–discharge relationship, to identify the links between transport timescales and solute concentration. Our results highlight that the younger streamflow components can be crucial for determining water quality variations and for characterizing the dominant hydrologic transport dynamics.

Using SAS functions and high-resolution isotope data to unravel travel time distributions in headwater catchments: TRAVEL TIME DISTRIBUTIONS AND SOLUTE DYNAMICS

We use high-resolution tracer data from an experimental site to test theoretical approaches that integrate catchment-scale flow and transport processes in a unified framework centered on selective age sampling by streamflow and evapotranspiration fluxes. Transport processes operating at the catchment scale are reflected in the evolving residence time distribution of the catchment water storage and in the age selection operated by out-fluxes. Such processes are described here through StorAge Selection (SAS) functions parameterized as power laws of the normalized rank storage. Such functions are computed through appropriate solution of the master equation defining formally the evolution of residence and travel times. By representing the way in which catchment storage generates outflows composed by water of different ages, the main mechanism regulating the tracer composition of runoff is clearly identified and detailed comparison with empirical data sets are possible. Properly calibrated numerical tools provide simulations that convincingly reproduce complex measured signals of daily deuterium content in stream waters during wet and dry periods. Results for the catchment under consideration are consistent with other recent studies indicating a tendency for natural catchments to preferentially release younger available water. The study shows that power law SAS functions prove a powerful tool to explain catchment-scale transport processes that also has potential in less intensively monitored sites.

Reply to comment by Porporato and Calabrese on "Storage selection functions: A coherent framework for quantifying how catchments store and release water and solutes""

Reference EPFL-ARTICLE-219960doi:10.1002/2015Wr018045View record in Web of Science Record created on 2016-07-19, modified on 2016-08-09

Reply to comment by Porporato and Calabrese on “Storage selction functions: A coherent framework for quantifying how catchments store and release water and solutes”

Reference EPFL-ARTICLE-219960doi:10.1002/2015Wr018045View record in Web of Science Record created on 2016-07-19, modified on 2016-08-09

Reply to comment by Rinaldo et al. on “Storage selection functions: A coherent framework for quantifying how catchments store and release water and solutes”

Reference EPFL-ARTICLE-219960doi:10.1002/2015Wr018045View record in Web of Science Record created on 2016-07-19, modified on 2016-08-09