Field measurements and modeling of groundwater flow and biogeochemistry at Moses Hammock, a backbarrier island on the Georgia coast

Abstract

A combination of field measurements, laboratory experiments and model simulations were used to characterize the groundwater biogeochemical dynamics along a shallow monitoring well transect on a coastal hammock. A switch in the redox status of the dissolved inorganic nitrogen (DIN) pool in the well at the upland/saltmarsh interface occurred over the spring-neap tidal transition: the DIN pool was dominated by nitrate during spring tide and by ammonium during neap tide. A density-dependent reaction-transport model was used to investigate the relative importance of individual processes to the observed N redox-switch. The observed N redox-switch was evaluated with regard to the roles of nitrification, denitrification, dissimilatory nitrate reduction to ammonium (DNRA), ammonium adsorption, and variations in inflowing water geochemistry between spring and neap tides. Transport was driven by measured pressure heads and process parameterizations were derived from field observations, targeted laboratory experiments, and the literature. Modeling results suggest that the variation in inflow water chemistry was the dominant driver of DIN dynamics and highlight the importance of spring-neap tide variations in the high marsh, which influences groundwater biogeochemistry at the marsh-upland transition.

Appendices

Appendix 1: Governing equations and implementation

Governing equations

The governing equation is based on conservation of fluid mass, expressed as:

$$ {\frac{{\partial \left( {\rho \phi } \right)}}{\partial t}} = - \nabla \cdot \left( {\rho \phi v} \right) $$

(11)

where $\phi$ is porosity, t is time, v is fluid velocity, $\nabla$ is the gradient operator, and ρ is fluid density, dependent on temperature (T), salinity (S) and pressure (p). Here, ρ [kg m⁻³] is expressed as a linear function of salinity at a given temperature T*[°C]:

$$ \rho (S) = 1000.0821 - 0.0324(T^{*} - 4) - 0.0052(T^{*} - 4)^{2} + \left( {0.7925 - 0.0021\left( {T^{*} - 4} \right)} \right)S $$

(12)

which is based on a polynomial fit to the UNESCO equation of state ρ (S,T,p), with an error <0.3 kg m⁻³ for 0 < S < 35, 4 < T < 35°C at p = 1 bar. Assuming constant temperature and porosity, the left hand side of Eq. 11 is approximated by $\gamma \phi {\frac{\partial S}{\partial t}} + \beta \phi {\frac{\partial p}{\partial t}},$ where the salinity and pressure coefficients $\gamma = \left. {{\frac{\partial \rho }{\partial S}}} \right|_{p*,T*} ,$ $\beta = \left. {{\frac{\partial \rho }{\partial p}}} \right|_{S*,T*}$ are set to 0.7665 kg m⁻³ ppt⁻¹ and 4.55 × 10⁻⁷ kg m⁻³ Pa⁻¹, respectively. Using Darcy’s law to describe the flow (e.g., Bear 1972), the fluid velocity v can be expressed as a function of material properties and the pressure field:

$$ \phi v = - {\frac{\kappa }{\mu }}\left( {\nabla p - \rho \overrightarrow {g} } \right) $$

(13)

where κ is permeability [L²], μ is dynamic viscosity, set to 0.001 kg m⁻¹ s⁻¹, and g is gravitational acceleration. Combining Eqs. 11 and 13, the governing equation for the evolution of the pressure field becomes:

$$ \phi \beta {\frac{\partial p}{\partial t}} = \nabla \cdot \left( {{\frac{\kappa \rho }{\mu }}\left( {\nabla p - \rho \overrightarrow {g} } \right)} \right) - \phi \gamma {\frac{\partial S}{\partial t}} $$

(14)

Solid phase chemical constituents are considered immobile, and mass conservation is expressed as:

$$ {\frac{{d\left( {1 - \phi } \right)C_{i} }}{dt}} = \left( {1 - \phi } \right)R_{i} $$

(15)

where C _i is the solid mass of species i per volume solid phase and R _i the net rate of production or consumption per volume solid phase. For solutes, one can write:

$$ {\frac{{\partial \phi C_{i} }}{\partial t}} = \nabla \cdot \left( {D^{*} \nabla C_{i} } \right) - \nabla \cdot \left( {\phi vC_{i} } \right) + \phi R_{i} $$

(16)

where C _i is the solute concentration of species i in the fluid and the reaction rate R is expressed per volume pore fluid. The diffusion–dispersion tensor, D* [L² T⁻¹] is defined as (Scheidegger 1961):

$$ D_{ij}^{*} = \phi D^{m} \delta_{ij} + \left( {\alpha_{\text{L}} - \alpha_{\text{T}} } \right){\frac{{v_{i} v_{j} }}{|v|}} + \alpha_{T} |v|\delta_{ij} $$

(17)

where $D^{m}$ is the tortuosity corrected in situ molecular diffusion coefficient, $\delta_{ij}$ is the Kronecker symbol, and α _L and α _T are longitudinal and transverse dispersivities [L], respectively.

Implementation

In each time step, the pressure field is solved (14) from which the velocity field is calculated (13). Subsequently, the evolution of the chemical species is computed (15, 16). For solutes, this is accomplished using sequential non-iterative operator splitting (Steefel and MacQuarrie 1996). In this approach, concentrations of all species are first calculated subject to advective and dispersive transport only. Without coupling between species through the reaction term, the temporal evolution for each chemical compound due to transport can be solved individually. The governing equations are discretized using a Galerkin finite element formulation and forward Euler time stepping. The resulting algebraic set of equations is solved using a diagonally preconditioned conjugate gradient solver (Reddy 1993; Meile and Tuncay 2006). The impact of the reactions is then computed by solving a set of coupled, typically stiff, ordinary differential equations for each spatial node, using the public domain solver VODE (Brown et al. 1989) with backward differentiation and the generation of full Jacobian matrix settings. Equilibrium reactions are implemented via operator splitting through mass conserving distribution functions at the end of each time step (e.g., Tadanier and Eick 2002).

The implementation of the reaction network solver has been tested by comparison to simulations with explicit rate formulations and implementations using a fully implicit Newton–Raphson approach (Regnier et al. 1997; Meile 2003). Simulations are performed at grid Peclet numbers <4, and the time step is adapted depending on Courant numbers (<1), and adjusted to resolve large temporal changes in concentrations. The finite element mesh has been produced using the open source software emc2 (Saltel and Hecht 1995), and post-processing is done with the open-source software OpenDX and within the proprietary MATLAB environment.

Appendix 2

See Table 3.

Table 3 Reaction network

Appendix 3

See Table 4.

Table 4 Model parameters