K.2 Nitrogen

The WQ Module allows for phytoplankton to uptake nitrate and ammonium (i.e. inorganic nitrogen) to meet primary production nitrogen demands. The parallel uptake of organic nitrogen (i.e. simulation of mixotrophic phytoplankton) is not yet implemented within the WQ Module. Uptake is computed differently for the basic and advanced phytoplankton constituent models

K.2.1 Basic phytoplankton constituent model

If internal phytoplankton nutrients are not simulated dynamically, nitrogen uptake is calculated as per Equation (K.2).

\[\begin{equation} F_{N-uptake}^{phy} = R_{prod\langle computed\rangle}^{phy} \times \left[PHY\right] \times X_{N-C-con}^{phy} \tag{K.2} \end{equation}\]

\(F_{N-uptake}^{phy}\) is the uptake of water column inorganic nitrogen, \(R_{prod\langle computed\rangle}^{phy}\) is the computed primary productivity rate, \(\left[PHY\right]\) is a computational cell’s phytoplankton concentration and \(X_{N-C-con}^{phy}\) is the specified (or default) constant ratio of internal nitrogen to carbon in the phytoplankton group being considered.

This quantity \(F_{N-uptake}^{phy}\) is the total uptake of inorganic nitrogen. In order to disaggregate this uptake into that of ammonium and nitrate, the WQ Module applies Equation (K.3), for ammonium concentrations greater than zero.

\[\begin{equation} \left.\begin{aligned} f_{amm-uptake}^{phy} =& \frac{\left[NH_4\right]\times\left[NO_3\right]}{\left(\left[NH_4\right] + K_{lim-N}^{phy}\right)\times\left(\left[NO_3\right]+K_{lim-N}^{phy}\right)} + \frac{\left[NH_4\right]\times K_{lim-N}^{phy}}{\left(\left[NH_4\right] + \left[NO_3\right]\right)\times\left(\left[NO_3\right]+K_{lim-N}^{phy}\right)} \\ \\ F_{amm-uptake}^{phy} =& F_{N-uptake}^{phy} \times f_{amm-uptake}^{phy} \\ \\ F_{nit-uptake}^{phy} =& F_{N-uptake}^{phy} \times \left(1.0 - f_{amm-uptake}^{phy}\right) \end{aligned}\right\} \tag{K.3} \end{equation}\]

For a phytoplankton group, \(f_{amm-uptake}^{phy}\) is the fraction of nitrogen uptake that is ammonium, \(\left[NH_4\right]\) and \(\left[NO_3\right]\) are the ambient water column ammonium and nitrate concentrations, respectively, \(K_{lim-N}^{phy}\) is the half saturation nitrogen concentration for phytoplankton uptake and \(F_{amm-uptake}^{phy}\) and \(F_{nit-uptake}^{phy}\) are the uptake by phytoplankton of ammonium and nitrate, respectively. These fluxes (whether computed from Equation (K.3) or (K.4)) are summed over all simulated phytoplankton groups to compute the community ammonium and nitrate uptake, \(F_{amm-uptake\langle computed\rangle}^{comm}\) and \(F_{nit-uptake\langle computed\rangle}^{comm}\), respectively.

The form of \(f_{amm-uptake}^{phy}\) in Equation (K.3) with ammonium concentration is presented in Figure K.1. Use the “play” button or drag the slider to see how different half saturation concentrations \(K_{lim-N}^{phy}\) change the fraction of ammonium taken up by phytoplankton (ordinate), as a function of ambient ammonium concentration (abscissa). Nitrate concentration is set to a fixed 5 mg/L.

Figure K.1: Move the slider to see the effect of changing \(K_{lim-N}^{phy}\) on the fraction of ammonium taken up by phytoplankton. Nitrate concentration is set to 5 mg/L and is fixed

To complement Figure K.1, the form of \(f_{amm-uptake}^{phy}\) in Equation (K.3) with nitrate concentration is presented in Figure K.2, using the same ordinate axis limits. Use the “play” button or drag the slider to see how different half saturation concentrations \(K_{lim-N}^{phy}\) change the fraction of ammonium taken up by phytoplankton (ordinate), as a function of ambient nitrate concentration (abscissa). Ammonium concentration is set to a fixed 2 mg/L.

Figure K.2: Move the slider to see the effect of changing \(K_{lim-N}^{phy}\) on the fraction of ammonium taken up by phytoplankton. Ammonium concentration is set to 2 mg/L and is fixed

The parameter \(K_{lim-N}^{phy}\) is the same as that used for calculation of the nitrogen limitation function in the basic (and advanced if internal nitrogen stores are exhausted) phytoplankton constituent model, so its specification should be considered in terms of its influence on both uptake on limitation.

K.2.2 Advanced phytoplankton constituent model

If internal phytoplankton nutrients are simulated dynamically, nitrogen uptake is calculated as per Equation (K.4).

\[\begin{equation} F_{N-uptake}^{phy} = R_{N-uptake}^{phy} \times L_{T}^{phy} \times \left[PHY\right] \times \frac{\left(X_{N-C-max}^{phy} - \frac{\left[IN\right]}{\left[PHY\right]}\right)}{\left(X_{N-C-max}^{phy} - X_{N-C-min}^{phy}\right)} \times \frac{\left(\left[N\right]_{avail} - \left[N\right]_{min}\right)}{\left(\left[N\right]_{avail} - \left[N\right]_{min}\right) + K_{lim-N}^{phy}} \tag{K.4} \end{equation}\]

\(F_{N-uptake}^{phy}\) is the uptake of water column inorganic nitrogen, \(R_{N-uptake}^{phy}\) is the specified (or default) rate of uptake of inorganic nitrogen, \(L_{T}^{phy}\) is the temperature limitation function, \(\left[PHY\right]\) and \(\left[IN\right]\) are a computational cell’s phytoplankton and internal nitrogen concentrations respectively, \(X_{N-C-min}^{phy}\) and \(X_{N-C-max}^{phy}\) are the specified (or default) minimum and maximum ratios of internal nitrogen to carbon in the phytoplankton group being considered, respectively, \(\left[N\right]_{avail}\) is the available (water column) 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 and \(K_{lim-N}^{phy}\) is the half saturation nitrogen concentration for phytoplankton uptake. These last three parameters (and the last term in Equation (K.4)) are the same as that applied to the basic phytoplankton constituent model as per Equation (K.2), via calculation of the limitation function applied to \(R_{prod\langle computed\rangle}^{phy}\) (as per Equation (J.9)).

Equation (K.4) reveals the following:

• The uptake of water column nitrogen to internal phytoplankton stores is governed by the specified (or default) nitrogen uptake rate
• This rate is modified by
  • Temperature, using the specified (or default) temperature limitation model for uptake (Section J.2)
  • The current internal nitrogen concentrations, relative to the specified (or default) minima and maxima
  • Ambient water column inorganic nitrogen concentrations, and
  • The half saturation nitrogen concentration for uptake, which is the same parameter as used in the basic phytoplankton constituent model

If for example the internal nitrogen concentration \(\left[IN\right]\) at a particular timestep and computational cell is equal to \(X_{N-C-max}^{phy} \times \left[PHY\right]\), then Equation (K.4) has that internal nitrogen stores are full and that uptake is therefore zero. Conversely, if \(\left[IN\right]\) at a particular timestep and computational cell is equal to \(X_{N-C-min}^{phy} \times \left[PHY\right]\), then internal nitrogen stores are at their lowest and therefore (in themselves) do not limit uptake of water column nitrogen. Finally, if the available water column nitrogen \(\left[N\right]_{avail}\) is equal to the specified (or default) minimum allowable nitrogen concentration for uptake \(\left[N\right]_{min}^{phy}\), then uptake to internal nutrient stores is zero.

If uptake from the water column to internal stores occurs, then the split between ammonium and nitrate uptake is computed as per Equation (K.3).

The parameter \(K_{lim-N}^{phy}\) is the same as that used for calculation of the nitrogen limitation function in the advanced phytoplankton constituent model if internal nitrogen stores are exhausted, so its specification should be considered in terms of its influence on both uptake on limitation.

K.2.3 Nitrogen fixing

If nitrogen fixing by phytoplankton is simulated, then a modification to the above computed nitrogen uptakes (for both the basic and advanced phytoplankton constituent models) is applied. The flux of atmospheric nitrogen is computed as per Equation (K.5).

\[\begin{equation} F_{N-fix}^{phy} = R_{N-fix}^{phy} \times \left(1.0 - L_{nit}^{phy}\right) \times \left[PHY\right] \tag{K.5} \end{equation}\]

\(F_{N-fix}^{phy}\) is the fixing of atmospheric nitrogen, \(R_{N-fix}^{phy}\) is the specified (or default) rate of nitrogen fixing, \(L_{nit}^{phy}\) is the nitrogen limitation function computed via either Equation (J.9) or (J.11) for the basic and advanced phytoplankton constituent models, respectively, before \(L_{nit}^{phy}\) is set to one. Once computed, \(F_{N-uptake}^{phy}\) is modified as follows:

• If \(|F_{N-fix}^{phy}| \ge |F_{N-uptake}^{phy}|\) then all uptake is assigned to \(F_{N-fix}^{phy}\), and \(F_{N-uptake}^{phy}\) is set to zero.
• If If \(|F_{N-fix}^{phy}| \le |F_{N-uptake}^{phy}|\) then nitrogen water column uptake is reduced as per Equation (K.6).

\[\begin{equation} F_{N-uptake\langle computed \rangle}^{phy} = F_{N-uptake}^{phy} \times \frac{\left(|F_{N-uptake}^{phy}| - F_{N-fix}^{phy}\right)}{|F_{N-uptake}^{phy}|} \tag{K.6} \end{equation}\]

Equation (K.6) is a simple linearisation that maps \(F_{N-uptake\langle computed \rangle}^{phy}\) to a value between 0.0 (where \(F_{N-fix}^{phy} = F_{N-uptake}^{phy}\)) and \(F_{N-uptake\langle computed \rangle}^{phy}\) (where \(F_{N-fix}^{phy}\) is zero).