Watersheds are the fundamental Earth surface units that receive and process water, mass, and energy (Li, 2019; Li et al., 2021; Hubbard et al., 2018). Watershed processes include land-surface interactions that regulate evapotranspiration and discharge as well as water partitioning between shallow soil lateral flow going into streams vs. downward flow and recharge into the deeper subsurface (Fig. 1). Complex biogeochemical interactions occur among soil, water, roots, and microbes along water's flow paths, regulating gas effluxes (e.g., CO2) and solute export (Fatichi et al., 2019; van der Velde et al., 2010; Benettin et al., 2020; Adler et al., 2021).

These hydrological and biogeochemical processes determine how Earth surface systems respond to hydroclimatic forcing and human perturbations. Understanding these processes remains challenging due to the complex process interactions. An example is the concentration–discharge (C–Q) relationships of solutes at stream and river outlets. Similar C–Q relationships have been observed for some solutes across watersheds under distinct geological and climatic conditions (Godsey et al., 2009; Basu et al., 2010; Moatar et al., 2017; Zarnetske et al., 2018; Godsey et al., 2019), whereas different solutes have shown contrasting patterns in the same watershed (Miller et al., 2017; Herndon et al., 2015; Musolff et al., 2015; Stewart et al., 2021; Zhi et al., 2020b). A general theory that can explain contrasting C–Q observations (e.g., flushing vs. dilution behaviors) under diverse watershed characteristics and external conditions remains elusive. The lack of mechanistic understanding presents major roadblocks to forecasting water quality and Earth system dynamics in the future.

One of the outstanding challenges is the lack of modeling tools that mechanistically link hydrological and biogeochemical processes at the watershed scale. Model development has advanced mostly within the disciplinary boundaries of hydrology and biogeochemistry (Li, 2019). Watershed hydrologic models focus on solving for water storage and fluxes (Fatichi et al., 2016). Reactive transport models (RTMs) have traditionally focused on transport and multi-component biogeochemical reactions mostly in groundwater systems with limited interactions with climate and other surficial conditions (Steefel et al., 2015; Li et al., 2017b). Some integration crossing disciplinary boundaries did occur in recent years. For example, SWAT (Soil and Water Assessment Tool) has a version that couples with the groundwater model MODFLOW and the surface water and groundwater quality model in RT3D (Bailey et al., 2017; Ochoa et al., 2020). CATHY (Catchment Hydrology) includes processes of pesticide decay (Gatel et al., 2019; Scudeler et al., 2016). Hydrologiska Byråns Vattenbalansavdelning (HBV) and the Hydrological Predictions for the Environment (HYPE) have modules that simulate processes relevant to nutrients and contaminants (Lindström et al., 2005, 2010). While these models can simulate processes such as leaching of nutrients from agriculture lands (Lindström et al., 2005, 2010; Bailey et al., 2017), they do not explicitly solve the multi-component reactive transport equations. In other words, reactions are often represented rudimentarily without honoring kinetics and thermodynamics theories in soil biogeochemistry and geochemistry. For example, nutrient leaching is calculated based on empirical equations without explicitly solving reactive transport equations. Reaction rates are represented using first-order decay (Gatel et al., 2019), assuming constant reaction rates that do not change with environmental conditions. Biogeochemical processes however are highly variable with seasonal dynamics and depend on local environments such as substrate availability, soil temperature, and soil moisture (Li et al., 2017a; Davidson and Janssens, 2006). These models therefore cannot capture the temporal variations in environmental factors that regulate soil biogeochemical reactions and stream and water chemistry.

To fill this model capability need, we augmented the watershed model RT-Flux-PIHM (Bao et al., 2017) into BioRT-Flux-PIHM (BioRT hereafter). Compared to RT-Flux-PIHM, BioRT has two additions. One is the capability of simulating biotic processes including plant uptake of nutrients, soil respiration, and other microbe-mediated redox reactions. Examples include soil respiration that produces CO2 and dissolved organic carbon (DOC) and nutrient transformation reactions such as nitrification and denitrification. The other is the addition of an optional deeper layer below shallow soil to enable the simulation of interacting deep-water and shallow soil water flow (Fig. 1). Here the deep water is loosely defined as the water below the soil zone, typically in less weathered, fractured subsurface that harbors relatively old and slow-moving groundwater contributing to streams. It is a fundamental component of the hydrologic cycle and water budget. The groundwater–surface-water interactions also modulate land–atmospheric energy exchanges and soil moisture dynamics (Keune et al., 2016). Evidence has been mounting in recent years that deeper water below the shallow soil interacts with streams, introduces water with distinct chemistry, sustains base flow in dry times, and buffers climate variability (Gurdak, 2017; Green, 2016; Taylor et al., 2013). Stream chemistry often reflects distinct chemistry from shallow soil water and deeper groundwater at different times, i.e., the so-called Shallow and Deep Hypothesis (Zhi et al., 2019; Zhi and Li, 2020; Botter et al., 2020). Including the deep-water component thus is essential for understanding mechanisms and predicting dynamics of water quality under changing climate and human conditions.

This paper introduces the new developments in BioRT. The paper starts with a brief overview of water- and energy-related processes. It then introduces governing equations and reaction kinetics used in BioRT, followed by three examples that illustrate the new capabilities. The examples include the surface water and groundwater interactions, nitrate transformation and transport, and the production and export of DOC. The model can be set up in both spatially lumped or spatially explicit modes. The source code and the examples here are archived on the Zenodo website (10.5281/zenodo.3936073) and the GitHub website (https://github.com/Li-Reactive-Water-Group/BioRT-Flux-PIHM, last access: 23 September 2021).

BioRT-Flux-PIHM integrates three modules (Fig. 1). The Flux module is for land-surface processes including surface energy balance, solar radiation, and evapotranspiration (ET) (Shi et al., 2013). The hydrology module PIHM simulates water processes including precipitation, interception, infiltration, recharge, surface runoff, subsurface lateral flow, and deep-water flow (Qu and Duffy, 2007). The BioRT module simulates solute transport and reactions. The abiotic reactions included in RT-Flux-PIHM (Bao et al., 2017) are mineral dissolution and precipitation, aqueous and surface complexation, and ion exchange reactions. The newly added reactions include plant uptake of nutrients, soil respiration, and microbe-mediated redox reactions (e.g., carbon decomposition and nutrient transformation).

The land-surface and hydrology modules solve for soil temperature and water storage, from which water fluxes are calculated for surface runoff and shallow- and deep-water fluxes. The BioRT module uses the calculated soil temperature, water storage, and water fluxes to simulate solute transport (advective and diffusive–dispersive) and biogeochemical reactions in both shallow and deep zones (see governing equations in later sections). The reactions include kinetically controlled (e.g., microbe-mediated redox reaction, mineral dissolution, and precipitation) or equilibrium-controlled ones (e.g., ion exchange, surface complexation (sorption), and aqueous complexation). Users can define the types of reactions to be included and the form of reaction kinetics in input files. The output of BioRT includes the spatial distribution and time series of aqueous and solid concentrations, from which we can infer reaction rates.

The model can be set up running in either spatially lumped or spatially explicit modes. When running in spatially explicit mode, the simulation domain can be structured as prismatic grids based on topography. Each grid is partitioned into surface and shallow and deep subsurface layers. The surface layer calculates water flow above ground (surface runoff). The shallow zone is loosely defined as the highly permeable subsurface that contrasts the deep zone that is broadly defined as the lower permeability zone beyond the shallow zone. In many places, the shallow zone is the soil zone that is most conductive to water flow (e.g., lateral flow) and is responsive to hydroclimatic forcing. The deep subsurface zone is the less weathered layer that harbors the old groundwater that contributes to stream flow. Note that these definitions differ from those in the hydrology community, which often refers to the shallow soil lateral flow as groundwater, in a way that distinguishes it from the surface runoff (Dingman, 2015). These source waters from different depths of the subsurface often have distinct solid and water chemistry and are dominant at different hydrological conditions at different times of the year, as has been observed in many catchments and watersheds (Brantley et al., 2018; Zhi et al., 2019; Zhi and Li, 2020; Sullivan et al., 2016). The model is flexible for taking inputs from online data portals or local measurements, and it can accommodate low data availability (see the following Sect. 5 for data need and domain setup).

The system of differential equations for water storage (e.g., Eqs. 1 and 2, and S1 and S2) is assembled into a global system of ordinary differential equations (ODEs). It is solved in CVODE (short for C-language Variable-coefficients ODE solver, https://computing.llnl.gov/projects/sundials/cvode, last access: 10 January 2021), a numerical ODE solver in the SUite of Nonlinear and Differential/ALgebraic equation Solvers (SUNDIALS) (Hindmarsh et al., 2005). In BioRT, the transport step is first solved with water by the preconditioned Krylov (iterative) method and the generalized minimal residual method (Saad and Schultz, 1986). All primary species in element i are then assembled in a local matrix and solved iteratively using the Crank–Nicolson and Newton–Raphson methods in CVODE (Bao et al., 2017).

The original RT-Flux-PIHM has been applied to understand processes related to the geogenic solutes of Cl and Mg at the Shale Hills watershed and for Na in a watershed on Chimborazo in the Ecuadorian Andes (Table 1). The new BioRT-Flux-PIHM has been demonstrated for understanding the dynamics of DOC and nitrate at Shale Hills and Coal Creek. This section will present one hydrology and two biogeochemical examples in the Susquehanna Shale Hills Critical Zone Observatory (SSHCZO), a small headwater watershed in central Pennsylvania, USA. The mean annual precipitation is approximately 1070 mm and the mean annual temperature is 10 ∘C (Brantley et al., 2018). Soil carbon storage and respiration and nitrogen budget and fluxes have been studied in detail (Andrews et al., 2011; Hasenmueller et al., 2015; Weitzman and Kaye, 2018). Modeling work has been conducted to understand hydrological dynamics (Shi et al., 2013; Xiao et al., 2019), transport of the non-reactive tracer Cl, and the weathering-derived solute Mg (Bao et al., 2017; Li et al., 2017a).

BioRT-Flux-PIHM brings the reactive transport modeling capabilities to the watershed scale, enabling the simulation of subsurface shallow and deep flow paths and biogeochemical reactions influenced by hydroclimatic conditions and land-surface interactions. The expanded model capability of simulating bio-mediated processes such as plant uptake, soil respiration, and microbe-mediated redox reactions enables the simulation of carbon and nutrient cycling in the shallow subsurface. The inclusion of the deep-groundwater zone allows the exploration of the effects of subsurface structure on hydrological partitioning between shallow soil lateral flow and deep groundwater and their relationships with stream discharge. Although not shown here, the model can also simulate deeper groundwater coming from regional aquifers across the outer boundary. This can be particularly useful for watersheds of higher stream orders, where a large proportion of deep water may come from nearby regional aquifers.

The advantage and disadvantages of simple vs. complex models have long been debated in the modeling community (Fatichi et al., 2016; Li et al., 2021; Wen et al., 2021). The computational cost of solving a spatially distributed, nonlinear, multi-component reactive transport model is high, posing challenges for the application of ensemble-based analysis. With additional reactions and transport processes, the model includes more functions (such as reaction kinetic rate laws) and parameters (e.g., reaction rate constants, surface area) than hydrological models. The complexity brings in issues of equifinality, uncertainty, and data demands (Beven, 2006; Kirchner et al., 1996). These issues will persist even though reactive transport models will be constrained by additional chemical data.

It is in this spirit of balancing the cost and gain that we present both spatially distributed and lumped modes for the BioRT model (Li et al., 2021). Compared to the distributed version, the spatially implicit model requires less spatial data and is computationally inexpensive. It can assess the average dynamics of water and solute dynamics and focus on the interacting processes without resolving spatial details. The lumped approach can accommodate basins with low data availability, and it can be easier for students to learn. In contrast, spatially explicit representations enable the exploration of the hot spots (e.g., swales and riparian zones with high soil water DOC concentrations in Fig. 10e) and their contribution to stream chemistry at different times. Spatial heterogeneities in watershed properties (e.g., soil types and depth, lithology, vegetation, biomass, and mineralogy) are ubiquitous in natural systems and are challenging to resolve. A general understanding of the linkage between local catchment features and catchment-scale dynamics (e.g., stream concentration dynamics and solute export pattern) is often lacking. The spatially distributed model provides a tool to explore these questions. Ultimately, the choice of the model complexity level depends on research questions that the model is set to answer and the available data. At the end, we all need to balance cost and gain when deciding to use a simple or complex model, striving to be “simple but not simplistic” (Beven and Lane, 2019).

This paper introduces the watershed-scale biogeochemical reactive transport code BioRT (short for BioRT-Flux-PIHM). The code integrates processes of land-surface interactions, surface hydrology, and multi-component biogeochemical reactive transport. The new development enables the simulation of (1) biotic reactions including plant uptake, soil respiration, and microbe-mediated redox reactions and (2) surface water interactions with groundwater from a deeper subsurface that still interacts with streams. BioRT has been verified against the widely used reactive transport code CrunchTope for soil carbon, nitrogen, and phosphorus processes. It has been applied to understand carbon, nitrogen, and weathering processes at Shale Hills in Pennsylvania, Coal Creek in Colorado, and the Chimborazo watershed in the Andes in Ecuador. Here we showcase the modeling capability of surface–groundwater interactions and reactive transport processes relevant to nitrate and DOC in Shale Hills in two simulation modes. One is in a spatially lumped mode using averaged properties and another is in a spatially distributed mode with a consideration of spatial heterogeneity. Results show that the deep-groundwater flow that interacts with the stream is primarily controlled by the hydraulic conductivity contrast between the shallow and the deep zones. Biogeochemical reactions in shallow soil primarily determine the stream water chemistry under high-flow conditions. The spatially lumped method with two lumped grids can capture the temporal dynamics of average behavior and mass balance; the spatially distributed running mode can be used to understand the spatial dynamics and to identify hot spots of reactions. The code can be used for biogeochemical reactive transport simulations in watersheds under diverse climate, land cover, and geology conditions.