Biogeochemistry

All Eulerian tracers are advected, diffused, and affected by sources and sinks:

\[\frac{\partial X}{\partial t} = - \nabla \cdot (\boldsymbol{u}X) + \nabla \cdot (\boldsymbol{K}\nabla X) + S_X\]

where $\boldsymbol{u}=(u,v,w)$ is the velocity field provided by a physical model (see Model Simulation), $\boldsymbol{K}$ is the mixing tensor also from the physical model, and $S_X$ is the source and sink term for tracer $X$.

The source and sinks term, $S_X$, can be different for each tracer and include biological transformations, chemical reactions, and external sources and sinks as detailed below.

The advection scheme used is Third Order Direct Space-Time with Flux Limiting.

Carbon Cycle

\[S_{DIC} = -\sum_j PS_j\cdot n_j + k_{DOC}\cdot DOC + F_C\]

\[\begin{align} S_{DOC} & = k_{POC} \cdot POC + f_{C,m} \cdot \sum_j ((Bm_j+Cq_j)\cdot n_{j,m}) \nonumber\\ & \quad + f_{C,g} \cdot \sum_j ((Bm_j+Cq_j)\cdot n_{j,g}) - k_{DOC} \cdot DOC \nonumber \end{align}\]

\[\begin{align} S_{POC} & = (1-f_{C,m}) \cdot \sum_j ((Bm_j+Cq_j)\cdot n_{j,m}) \nonumber\\ & \quad + (1-f_{C,g}) \cdot \sum_j ((Bm_j+Cq_j)\cdot n_{j,g}) - k_{POC} \cdot POC \nonumber \end{align}\]

where $n_j$ is the cell number of species $j$, $n_{j,m}$ is the dead cell number of species $j$, $n_{j,g}$ is the grazed cell number of species $j$.

Nitrogen Cycle

\[\begin{align} S_{HN4} &= -\sum_j VNH4_j\cdot n_j + k_{DON}\cdot DON - k_{nit}\cdot NH4 \nonumber\\ S_{NO3} &= -\sum_j VNO3_j\cdot n_j + k_{nit}\cdot NH4 \nonumber \end{align}\]

\[\begin{align} S_{DON} & = k_{PON} \cdot PON + f_{N,m} \cdot \sum_j ((Bm_j*R_{NC}+Nq_j)\cdot n_{j,m}) \nonumber\\ & \quad + f_{N,g} \cdot \sum_j ((Bm_j*R_{NC}+Nq_j)\cdot n_{j,g}) - k_{DON} \cdot DON \nonumber \end{align}\]

\[\begin{align} S_{PON} & = (1-f_{N,m}) \cdot \sum_j ((Bm_j*R_{NC}+Nq_j)\cdot n_{j,m}) \nonumber\\ & \quad + (1-f_{N,g}) \cdot \sum_j ((Bm_j*R_{NC}+Nq_j)\cdot n_{j,g}) - k_{PON} \cdot PON \nonumber \end{align}\]

Phosphorus Cycle

\[S_{PO4} = -\sum_j VPO4_j\cdot n_j + k_{DOP}\cdot DOP\]

\[\begin{align} S_{DOP} & = k_{POP} \cdot POP + f_{P,m} \cdot \sum_j ((Bm_j*R_{PC}+Pq_j)\cdot n_{j,m}) \nonumber \\ & \quad + f_{P,g} \cdot \sum_j ((Bm_j*R_{PC}+Nq_j)\cdot n_{j,g}) - k_{DOP} \cdot DOP \nonumber \end{align}\]

\[\begin{align} S_{POP} & = (1-f_{P,m}) \cdot \sum_j ((Bm_j*R_{PC}+Pq_j)\cdot n_{j,m}) \nonumber\\ & \quad + (1-f_{P,g}) \cdot \sum_j ((Bm_j*R_{PC}+Pq_j)\cdot n_{j,g}) - k_{POP} \cdot POP \nonumber \end{align}\]

Parameters