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Transit times—the link between hydrology and water quality at the catchment scale

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In spite of trying to understand processes in the same spatial domain, the catchment hydrology and water quality scientific communities are relatively disconnected and so are their respective models. This is emphasized by an inadequate representation of transport processes, in both catchment‐scale hydrological and water quality models. While many hydrological models at the catchment scale only account for pressure propagation and not for mass transfer, catchment scale water quality models are typically limited by overly simplistic representations of flow processes. With the objective of raising awareness for this issue and outlining potential ways forward we provide a nontechnical overview of (1) the importance of hydrology‐controlled transport through catchment systems as the link between hydrology and water quality; (2) the limitations of current generation catchment‐scale hydrological and water quality models; (3) the concept of transit times as tools to quantify transport; and (4) the benefits of transit time based formulations of solute transport for catchment‐scale hydrological and water quality models. There is emerging evidence that an explicit formulation of transport processes, based on the concept of transit times has the potential to improve the understanding of the integrated system dynamics of catchments and to provide a stronger link between catchment‐scale hydrological and water quality models. WIREs Water 2016, 3:629–657. doi: 10.1002/wat2.1155 This article is categorized under: Science of Water > Hydrological Processes Science of Water > Water Quality
(a) Examples for SAS functions with no age preference (uniform distribution), as well as with preferences for young and old water, respectively. (b) Comparison of cumulative SAS functions (CDF) with the functionality of using the concept of mixing coefficients. Mixing coefficients C = 0.2, 0.6, and 1 indicate examples for 20, 60, and 100% of an incoming signal, respectively, are stored and mix with the resident water, while 80, 40, and 0% of the incoming water, respectively, bypass the storage and are directly released again without further interaction with resident water.
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Illustrations of different conceptualized and simplified sampling (or mixing) processes. (a) A system characterized by a uniform storage age selection (SAS) function, sampling water with different ages from storage with equal probabilities (equivalent to the concept of a well‐ or completely mixed reservoir). (b) A system that releases water with preference for younger ages in storage (after Ref ). The symbol S indicates age‐ranked storage, P represents the input into the storage (e.g., precipitation), and Q a flux released from storage (e.g., stream flow). Green shades indicate water in storage, blue shades indicate water in fluxes, i.e., released from storage component.
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Conceptual and simplified illustration of the difference between residence time (pS), backward (pT,B), and forward (pT,F) transit time distributions. A precipitation signal enters the system at ti and is transiently stored. The volumes of all water parcels from the past still stored in the system at tj define pS. Water is released from storage according to specific mixing or storage age selection (SAS) mechanisms, which sample the runoff water from the distribution of water ages in storage at tj, resulting in the pT,B and pT,F (after Ref ).
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(a) Conceptualization of the difference between celerity‐driven hydrological response and velocity‐driven transport processes using the analogy of a game of billiards. A new input at t1 (red ball) causes a disturbance of the system that propagates with a celerity and that generates a response (blue ball) at t2. The red ball itself, however, is released from the system only at t5 as it travels at a velocity that is much smaller than the celerity. (b) For a groundwater‐dominated system, the propagation of the pressure wave to the stream is controlled by the wave celerity and the active storage Sa (i.e., the pressure head ha) while the movement of the actual particles is controlled by the flow velocity and the length of the flow trajectory through a hydrologically passive storage volume Sp (after Ref ), which (c) can be conceptualized in a model with a mixing volume below a given storage threshold. SU represents the unsaturated zone whose nonlinear behavior is indicated by the curved line.
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The upper three panels show the time series of (a) observed daily precipitation as well as of (b) observed (black) and modeled flow (blue), and (c) modeled storage in the Kerrien catchment in France. The fourth panel (d) shows the flow weighted average (bold, dark blue lines) and the daily (thin lines, shades from light to dark indicate increasing flow) age distributions pT,B of three selected modeled fluxes. The fifth panel (e) shows the volume weighted average (bold, dark green lines) and the daily (thin lines, shades from light to dark indicate increasing storage) age distributions pS of three selected modeled storage components. The sixth panel (f) shows the modeled relative contribution of fast (i.e., preferential) flows QF and groundwater flows QS. The two bottom panels show the time dynamic development of (g) pT,B and (h) pS, as indicated by their 5/25/50/75/95th percentiles. Note that more detailed information about the catchment and the model are available in Ref .
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Daily precipitation (light blue), runoff (dark blue), observed fertilizer‐derived Cl (orange circles), and precipitation‐derived Cl input concentrations (red circles), as well as Cl concentrations in runoff (dark red circles) for the small, agriculturally managed Kerrien catchment in France (see Ref ). Note that the circles sizes indicate the Cl mass flux relative to the largest mass flux during the observation period. The bars on the sides indicate the 5/95th interquantile range for Cl input concentrations (red), Cl concentrations in runoff (dark red), precipitation (light blue), and runoff (blue). The inset shows the runoff–Cl concentration relationship, with the black line indicating the log‐log slope of −1 that would be expected from the theoretical case of pure dilution (i.e., c α 1/Q), which would be the case if a catchment was a completely mixed, homogeneous entity.
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(a) Representation of a catchment as a lumped, completely mixed system, where P is precipitation and solute input, Sa is the hydrologically active storage that is controlled by the pressure head, Sp is a hydrologically passive mixing storage with constant water content. Evaporation is omitted here as it is rarely accounted for in convolution integral models for which this structure is an analogy. (b) Example of a possible semi‐distributed, topography and vegetation guided model set‐up in a catchment that is characterized by forest and grassland hillslopes as well as wetlands/riparian zones. The three different landscape classes are represented by three models that run in parallel. The hillslope classes are here distinguished by different parameter sets, while the wetland class reflects the distinct hydrological function of wetlands by a different model architecture. For each storage component suitable mixing/sampling mechanisms can be assumed that together with the different timescales of the storages result in different transport dynamics and thus different residence time distributions (pS) for water stored in and transit time distributions (pT) for water released from these components. This allows an improved resolution of the temporal dynamics in the system caused by changing contributions from the individual source areas and flow paths. S denotes storage components, R are recharge fluxes between storage components, Q are liquid fluxes release from the system, and E are evaporative fluxes released from the system. The subscripts I indicate interception storages, subscripts U represent unsaturated root zones, subscripts T denote hydrologically passive, unsaturated transition zones, subscripts F are fast responding components (e.g., preferential flow and overland flow), subscripts S denote slow responding components (e.g., deep groundwater), subscript L represents deep infiltration losses, subscripts H,F and H,G indicate hillslopes that are forest and grass covered, respectively, while subscript R represents riparian zones/wetlands. Light blue shades are hydrologically active storage components and dark blue shades indicate hydrologically passive storage components.
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Schematic of changing mixing processes in the soil profile under different wetness conditions with likely shapes of SAS functions associated with these conditions. (a) At the end of dry periods, the moisture content in the soil matrix is depleted. Incoming precipitation is, due to the elevated suction forces relatively quickly adsorbed and stored in the matrix and flow is mainly sustained by relatively old groundwater. (b) As the system wets up, the soil moisture deficits are reduced and less precipitation water enters the matrix, bypassing it, and interacting less with the water stored, through preferential flow paths (e.g., root canals, cracks, animal burrows, etc.). Flows are now mainly generated relatively young water reaching the stream for example as preferential flow. (c) At the beginning of a dry period, water stored in the matrix continues to recharge groundwater, further mixing with resident water. Flow is now mainly generated by groundwater, which however, has a higher proportion of younger water than at the end of the dry period.
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