Nutrient cycling at the land-ocean interface

Water samples collected by the Joye lab are regularly analyzed for a number of chemical species. These measurements reflect the combined effect of both transport processes and reactions taking place in the subsurface. Because of the tight coupling between many processes, an intuitive interpretation of the data is difficult.

Mathematical models are tools that help in the interpretation of the data, allowing for the integration of knowledge gained on individual processes. In groundwater settings, they typically represent mass conservation for all chemical species considered:

The left hand side measures the change of mass per total volume and time, the first term on the right is the transport due to dispersion and advection, and the last term the reaction rates: C is the concentration of a solute, porosity, D the dispersion/diffusion coefficient, v the fluid flow velocity, and sum(R) the netreaction rate at which C is either produced or consumed. These represent rate expressions for all the processes shown above (see processes).

Because of the reactions, the governing equations are coupled. We are solving them using a finite element approach. Because we are interested in these processes at the land-ocean interface, the effect of salt on fluid density and hence flow patterns are considered. In each timestep, we first solve for the pressure field, considering density driven flow:

Then we obtain flow velocity via a Darcy approximation:

These velocities are then used in the above mass conservation equation. To solve for the reaction rates, the rates are computed at the beginning of each timestep. This requires small timesteps when rates are fast. As an alternative, we use operator splitting (Steefel & MacQuarrie 1996), where within each timestep, first the transport problem is solved. Subsequently, the effect of reactions is solved for each finite element. The advantage of this sequential approach is that this allows for the use of stiff ordinary differential solvers that are tailored to the problem at hand.

These concepts are combined with data from the study sites.

Well field layout at the Moses Hammock site, established by C. Ruppel as part of previous Sea Grant project. The lower 3 panels show rainfall data and freshwater heads and head differences between three of the wells (Data Joye Lab).