J.3 Nitrogen

Nitrogen offers two limitation functions, one for each of the basic and advanced phytoplankton constituent models. These are described separately following. If nitrogen fixing is implemented for a particular phytoplankton group, then the calculations following are not implemented and \(L_{nit}^{phy}\) is set to one.

J.3.1 Basic phytoplankton constituent model

If internal phytoplankton nutrients are not simulated dynamically, Equation (J.9) is used to compute \(L_{nit}^{phy}\).

\[\begin{equation} L_{nit}^{phy} = \frac{\left(\left[N\right]_{avail} - \left[N\right]_{min}^{phy}\right)}{\left(\left[N\right]_{avail} - \left[N\right]_{min}^{phy}\right) + K_{lim-N}^{phy}} \tag{J.9} \end{equation}\]

\(\left[N\right]_{avail}\) is the available ambient nitrogen pool on which phytoplankton can draw for primary productivity, and is the sum of inorganic (ammonium and nitrate) nitrogen. \(\left[N\right]_{min}^{phy}\) is the nitrogen concentration below which phytoplankton is no longer permitted to uptake nitrogen. \(K_{lim-N}^{phy}\) is the half saturation nitrogen concentration for phytoplankton uptake.

All these parameters are considered by the WQ Module to be combined quantities, i.e. they are not specific to any particular nitrogen species, but rather, to nitrogen-N concentrations across all species uptaken. In the case of the basic phytoplankton constituent model, this is simply the sum of ammonium-N and nitrate-N concentrations.

Equation (J.9) has that when \(K_{lim-N}^{phy}\) is equal to the difference between ambient nitrogen concentration and \(\left[N\right]_{min}^{phy}\), i.e. when

\[\begin{equation} K_{lim-N}^{phy} = \left[N\right]_{avail} - \left[N\right]_{min}^{phy} \tag{J.10} \end{equation}\]

then \(L_{nit}^{phy}\) = 0.5. The form of \(L_{nit}^{phy}\) with varying \(\left[N\right]_{min}^{phy}\) and \(K_{lim-N}^{phy}\) is provided in Figure J.3, for constant \(\left[N\right]_{avail}\) = 1.0 mg/L.

Figure J.3: Move the slider to see the effect of changing \(K_{lim-N}^{phy}\) on the computed nitrogen limitation function

The parameter \(K_{lim-N}^{phy}\) is the same as that specified in the computation of the the fraction of ammonium that is taken up with primary production (Appendix K.2.1) in the basic phytoplankton constituent model (Equation (K.3)). As such its setting should be considered in terms of its impacts on both nitrogen limitation and uptake processes.

J.3.2 Advanced phytoplankton constituent model

If internal phytoplankton nutrients are simulated dynamically, and phytoplankton concentrations are greater than the specified (or default) minimum, then Equation (J.11) is used to compute \(L_{nit}^{phy}\).

\[\begin{equation} L_{nit}^{phy} = \frac{X_{N-C-max}^{phy} \times \left(1.0 - \frac{X_{N-C-min}^{phy} \times \left[PHY\right] }{\left[IN\right]}\right)}{X_{N-C-max}^{phy} - X_{N-C-min}^{phy}} \tag{J.11} \end{equation}\]

\(X_{N-C-min}^{phy}\) and \(X_{N-C-max}^{phy}\) are the specified (or default) minimum and maximum internal nitrogen to Chl a (or carbon if using mmm units) ratios, respectively and \(\left[PHY\right]\) and \(\left[IN\right]\) are the current internal Chl a (or carbon) and nitrogen concentrations in the computational cell being considered, respectively. Substituting the definition for the minimum nitrogen to Chl a (or carbon) ratio \(X_{N-C-min}^{phy}=\left[IN\right]_{min}/\left[PHY\right]\) (where \(\left[PHY\right]\) is in either mgL or mmm units) into Equation (J.11) and rearranging, reveals the form of \(L_{nit}^{phy}\) as per Equation (J.12).

\[\begin{equation} L_{nit}^{phy} = \frac{X_{N-C-max}^{phy} \times \left(1.0 - \frac{\left[IN\right]_{min}} {\left[IN\right]}\right)}{X_{N-C-max}^{phy} - X_{N-C-min}^{phy}} \tag{J.12} \end{equation}\]

\(\left[IN\right]_{min}\) is the minimum internal nitrogen concentation corresponding to the current phytoplankton group \(\left[PHY\right]\). Equation (J.12) demonstrates that:

• If an internal nitrogen concentration is equal to \(\left[IN\right]_{min}\), then \(L_{nit}^{phy}\) is zero. This means that no internal nitrogen is available for primary production in the current timestep and that nitrogen is therefore completely preventing growth
• If an internal nitrogen concentration is equal to \(\left[IN\right]_{max}\), then \(L_{nit}^{phy}\) is one. This means that maximum internal nitrogen is available for primary production in the current timestep and that nitrogen is therefore placing no limit on growth

If internal phytoplankton nutrients are simulated dynamically, and phytoplankton concentration is less than the specified (or default) minimum, then phytoplankton will look to external (i.e. ambient water column) nitrogen pools to support primary productivity. The associated limitation function is therefore computed in the same manner as Equation (J.9) in Appendix J.3.1. If this is the case, then the parameters \(K_{lim-N}^{phy}\) and \(\left[N\right]_{min}^{phy}\) are used.

This same parameter is also used in the computation of the nitrogen that is taken up with primary production (Appendix K.2.2) in the advanced phytoplankton constituent model (Equation (K.4)). As such its setting should be considered in terms of its impacts on both nitrogen limitation and uptake processes in the advanced phytoplankton constituent model.