K.3 Phosphorus

The WQ Module allows for phytoplankton to uptake filterable reactive phosphorus (i.e. inorganic phosphorus, FRP) to meet primary production phosphorus demands. The parallel uptake of organic phosphorus (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.3.1 Basic phytoplankton constituent model

If internal phytoplankton nutrients are not simulated dynamically, phosphorus uptake is calculated as per Equation (K.7).

\[\begin{equation} F_{P-uptake}^{phy} = R_{prod\langle computed\rangle}^{phy} \times \left[PHY\right] \times X_{P-C-con}^{phy} \tag{K.7} \end{equation}\]

\(F_{P-uptake}^{phy}\) is the uptake of inorganic phosphorus, \(R_{prod\langle computed\rangle}^{phy}\) is the computed primary productivity rate, \(\left[PHY\right]\) is a computational cell’s phytoplankton concentration and \(X_{P-C-con}^{phy}\) is the specified (or default) constant ratio of internal phosphorus to carbon in the phytoplankton group being considered. This flux (whether computed from Equation (K.7) or (K.8)) is summed over all simulated phytoplankton groups to compute the community FRP uptake, \(F_{P-uptake\langle computed\rangle}^{comm}\).

K.3.2 Advanced phytoplankton constituent model

If internal phytoplankton nutrients are simulated dynamically, phosphorus uptake is calculated as per Equation (K.8).

\[\begin{equation} F_{P-uptake}^{phy} = R_{P-uptake}^{phy} \times L_{T}^{phy} \times \left[PHY\right] \times \frac{\left(X_{P-C-max}^{phy} - \frac{\left[IP\right]}{\left[PHY\right]}\right)}{\left(X_{P-C-max}^{phy} - X_{P-C-min}^{phy}\right)} \times \frac{\left(\left[P\right]_{avail} - \left[P\right]_{min}^{phy}\right)}{\left(\left[P\right]_{avail} - \left[P\right]_{min}^{phy}\right) + K_{lim-P}^{phy}} \tag{K.8} \end{equation}\]

\(F_{P-uptake}^{phy}\) is the uptake of water column FRP, \(R_{P-uptake}^{phy}\) is the specified (or default) rate of uptake of FRP, \(L_{T}^{phy}\) is the temperature limitation function, \(\left[PHY\right]\) and \(\left[IP\right]\) are a computational cell’s phytoplankton and internal phosphorus concentrations respectively, \(X_{P-C-min}^{phy}\) and \(X_{P-C-max}^{phy}\) are the specified (or default) minimum and maximum ratios of internal phosphorus to carbon in the phytoplankton group being considered, respectively, \(\left[P\right]_{avail}\) is the available (i.e. ambient water column) FRP pool on which phytoplankton can draw for primary productivity, \(\left[P\right]_{min}^{phy}\) is the FRP concentration below which phytoplankton is no longer permitted to uptake phosphorus and \(K_{lim-P}^{phy}\) is the half saturation FRP concentration for phytoplankton uptake. These last three parameters (and the last term in Equation (K.8)) are the same as that applied to the basic phytoplankton constituent model as per Equation (K.7), via calculation of the limitation function applied to \(R_{prod\langle computed\rangle}^{phy}\) (as per Equation (J.13)).

Equation (K.8) reveals the following:

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

If for example the internal phosphorus concentration \(\left[IP\right]\) at a particular timestep and computational cell is equal to \(X_{P-C-max}^{phy}\times \left[PHY\right]\), then Equation (K.8) has that internal phosphorus stores are full and that uptake is therefore zero. Conversely, if \(\left[IP\right]\) at a particular timestep and computational cell is equal to \(X_{P-C-min}^{phy} \times \left[PHY\right]\), then internal phosphorus stores are at their lowest and therefore (in themselves) do not limit uptake of water column FRP. Finally, if the available water column FRP \(\left[P\right]_{avail}\) is equal to the specified (or default) minimum allowable FRP concentration for uptake \(\left[P\right]_{min}^{phy}\), then uptake to internal nutrient stores is zero.

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