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3.17.2 Equations Solved

The physical ocean model velocity and diffusivities are used to redistribute the 5 tracers within the ocean. Additional redistribution comes from chemical and biological sources and sinks. For any tracer $ A$ :

$\displaystyle \frac{\partial A}{\partial t}=-\nabla \cdot (\vec{u^{*}} A)+\nabla \cdot (\mathbf{K}\nabla A)+S_A$    

where $ \vec{u^{*}}$ is the transformed Eulerian mean circulation (which includes Eulerian and eddy-induced advection), $ \mathbf{K}$ is the mixing tensor, and $ S_A$ are the sources and sinks due to biological and chemical processes.

The sources and sinks are:

$\displaystyle S_{DIC}$ $\displaystyle =$ $\displaystyle F_{CO_2} + V_{CO_2} + r_{C:P} S_{PO_4} + J_{Ca}$ (3.88)
$\displaystyle S_{ALK}$ $\displaystyle =$ $\displaystyle V_{ALK}-r_{N:P} S_{PO_4} + 2 J_{Ca}$ (3.89)
$\displaystyle S_{PO_4}$ $\displaystyle =$ $\displaystyle -f_{DOP} J_{prod} - \frac{\partial F_P}{\partial z} + \kappa_{remin} [DOP]$ (3.90)
$\displaystyle S_{DOP}$ $\displaystyle =$ $\displaystyle f_{DOP} J_{prod} -\kappa_{remin} [DOP]$ (3.91)
$\displaystyle S_{O_2}$ $\displaystyle =$ $\displaystyle \left\{ \begin{array}{ll} -r_{O:P} S_{PO_4} & \mbox{if $O_2>O_{2crit}$} \\ 0 & \mbox{if $O_2<O_{2crit}$} \end{array} \right.$ (3.92)

where:
  • $ F_{CO_2}$ is the flux of CO$ _2$ from the ocean to the atmosphere
  • $ V_{CO_2}$ is ``virtual flux'' due to changes in $ DIC$ due to the surface freshwater fluxes
  • $ r_{C:P}$ is Redfield ratio of carbon to phosphorus
  • $ J_{Ca}$ includes carbon removed from surface due to calcium carbonate formation and subsequent cumulation of the downward flux of CaCO$ _3$
  • $ V_{ALK}$ is ``virtual flux'' due to changes in alkalinity due to the surface freshwater fluxes
  • $ r_{N:P}$ Redfield ratio is nitrogen to phosphorus
  • $ f_{DOP}$ is fraction of productivity that remains suspended in the water column as dissolved organic phosphorus
  • $ J_{prod}$ is the net community productivity
  • $ \frac{\partial F_P}{\partial z}$ is the accumulation of remineralized phosphorus with depth
  • $ \kappa_{remin}$ is rate with which $ DOP$ remineralizes back to $ PO_4$
  • $ F_{O_2}$ is air-sea flux of oxygen
  • $ r_{O:P}$ is Redfield ratio of oxygen to phosphorus
  • $ O_{2crit}$ is a critical level below which oxygen consumption if halted

These terms (for the first four tracers) are described more in Dutkiewicz et al. [2005] and by McKinley et al. [2004] for the terms relating to oxygen.

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Next: 3.17.3 Code configuration Up: 3.17 Biogeochemistry Tutorial Previous: 3.17.1 Overview   Contents
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