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Toward catchment hydro‐biogeochemical theories

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Abstract Headwater catchments are the fundamental units that connect the land to the ocean. Hydrological flow and biogeochemical processes are intricately coupled, yet their respective sciences have progressed without much integration. Reaction kinetic theories that prescribe rate dependence on environmental variables (e.g., temperature and water content) have advanced substantially, mostly in well‐mixed reactors, columns, and warming experiments without considering the characteristics of hydrological flow at the catchment scale. These theories have shown significant divergence from observations in natural systems. On the other hand, hydrological theories, including transit time theory, have progressed substantially yet have not been incorporated into understanding reactions at the catchment scale. Here we advocate for the development of integrated hydro‐biogeochemical theories across gradients of climate, vegetation, and geology conditions. The lack of such theories presents barriers for understanding mechanisms and forecasting the future of the Critical Zone under human‐ and climate‐induced perturbations. Although integration has started and co‐located measurements are well under way, tremendous challenges remain. In particular, even in this era of “big data,” we are still limited by data and will need to (1) intensify measurements beyond river channels and characterize the vertical connectivity and broadly the shallow and deep subsurface; (2) expand to older water dating beyond the time scales reflected in stable water isotopes; (3) combine the use of reactive solutes, nonreactive tracers, and isotopes; and (4) augment measurements in environments that are undergoing rapid changes. To develop integrated theories, it is essential to (1) engage models at all stages to develop model‐informed data collection strategies and to maximize data usage; (2) adopt a “simple but not simplistic,” or fit‐for‐purpose approach to include essential processes in process‐based models; (3) blend the use of process‐based and data‐driven models in the framework of “theory‐guided data science.” Within the framework of hypothesis testing, model‐data fusion can advance integrated theories that mechanistically link catchments' internal structures and external drivers to their functioning. It can not only advance the field of hydro‐biogeochemistry, but also enable hind‐ and fore‐casting and serve the society at large. Broadly, future education will need to cultivate thinkers at the intersections of traditional disciplines with hollistic approaches for understanding interacting processes in complex earth systems. This article is categorized under: Engineering Water > Methods
A conceptual diagram of a headwater catchment as a natural integrator of hydrological flow paths and biogeochemical processes. The flow paths depend on external hydroclimatic forcings and internal catchment structures above ground (e.g., vegetation, topography) and below ground (e.g., distribution of porosity, permeability). Reactive materials are illustrated here using organic carbon (OC, red) that decreases in abundance with depth and dissolving minerals that increase with depth. These physical and chemical structures also dictate the contact time of water with reactive materials, regulating both rates of biogeochemical transformations and concentrations of reaction products (e.g., DOC, Ca, Si) that enter the stream
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Spatial and temporal scales represented by different tracers. While surface hydrologists have routinely used stable water isotopes (2H and18O) and nonreactive tracers (Cl, Br) for transit time quantification, groundwater age tracers can be used to date water older than months to years to constrain the long tail of transit time distributions (in the black box). The figure is reprinted with permission from Sprenger et al. (2019)
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Mixing lines in water isotopes and reactive solutes. (a) dual‐isotope plot with data from Brooks et al. (2010) contrasting the isotopic compositions of groundwater and xylem water. Groundwater follows the meteoric line while xylem water reflects soil water that has been fractionated by evaporation and therefore deviates from the meteoric water line. (b) Mixing diagrams using Na‐normalized molar ratios in the 60 largest rivers on earth (Gaillardet et al., 1999). Open and filled circles are for rivers with TDS (total dissolved solids) >500 mg/L and TDS <500 mg/L, respectively. River chemistry indicates the lithology of the river's source lithology. The patterned inserts represent chemical compositions of silicates, carbonates, and evaporites as end member lithologies (reprinted with permission from Elsevier)
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A road map toward integrated hydro‐biogeochemical theories. Transit time theory and biogeochemical reaction theory have been developed in their respective disciplines. Developing hydro‐biogeochemical theories will require integration of these existing theories; it will also require expanding measurements beyond stream channels and into the subsurface, and cleverly using process‐based and data‐driven model tools, all within the framework of hypothesis testing
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(a) Relationships between water table depth and discharge; (b) depth profiles of concentrations of Ca and Total Organic Carbon (TOC) (b) during spring melt in the Svartberget catchment in northern Sweden (figure based on data reprinted with permission from Bishop et al. (2004)); (c) Concentration‐discharge relationship in Coal Creek, Colorado, a snow‐melt dominated high elevation mountain catchment (Zhi et al., 2019). DOC concentrations increase with discharge as the water table rises into the organic carbon‐enriched shallow soil. The opposite behavior is seen for Ca
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Deepening and shallowing of roots and flow paths may develop under changing climate and human domination in the Anthropocene. (a) Deepening flow paths may develop during droughts and woody encroachments. They can enhance the deeper penetration of water and reactive solutes (e.g., O2, CO2, NO3), accelerate rock weathering at depth, and produce cations and dissolved inorganic carbon (DIC). (b) Shallowing flow paths can expand as a result of impervious surfaces and pipes in urban areas and shallow‐rooted crops and engineered drainage in agriculture lands. These structures can short‐circuit water fluxes from soils to streams, minimizing interactions with reactive minerals at depth. These changes may alter water cycles, gas fluxes (CO2, N2) and solutes, ultimately modulating climate‐water‐human interactions and feedbacks
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(a) Simulation output illustrating the relevance of spatial heterogeneity to physical flow and carbonate dissolution. Water flows through a cross‐section of a heterogeneous rock with unevenly distributed, low‐permeability carbonate (magnesite) within a high‐permeability sandstone quartz domain. The average cluster length of carbonate here is 2 cm. The simulation is at an average flow velocity of 2.7 m/day. The subpanels in (a) illustrate (from left to right) spatial distributions of permeability (κ), magnesite volume percentage, steady‐state flow velocity (v), Mg as a product of magnesite dissolution, and local dissolution rates in individual grid blocks (rMgCO3). (b) the probability distribution of local residence time in individual grids:τa,nr,ifor nonreactive sandstone grids (blue),τa,r,ifor reactive carbonate grids (red), and combined overall distributionτa,i.Reprinted with permission from Wen & Li, 2017
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