I.1 Primary productivity

The primary productivity rate is computed in a series of stages within the WQ Module, where the combination of these stages used for any given phytoplankton group depends on group configuration. These stages are described below. For clarity, supporting functions nested within primary productivity rate calculations (such as limitation functions) are initially presented in passing, but are cross referenced to detailed descriptions in subsequent Appendices.

The rate of primary productivity (often referred to as just productivity or growth rate) of a phytoplankton group is a /day rate. It is computed initially within the WQ Module as per Equation (I.2).

\[\begin{equation} R_{prod\langle computed\rangle}^{phy} = R_{prod}^{phy} \times L_T^{phy} \times \text{min}\left(L_{lght}^{phy},L_{nit}^{phy},L_{phs}^{phy},L_{sil}^{phy}\right) \tag{I.2} \end{equation}\]

For each phytoplankton group, \(R_{prod}^{phy}\) is the user specified (or default) phytoplankton productivity (growth) rate at 20\(^o\)C with no light, temperature, salinity, silicate or nutrient limitation, and \(L_T^{phy}\), \(L_{lght}^{phy}\), \(L_{nit}^{phy}\), \(L_{phs}^{phy}\), \(L_{sil}^{phy}\) are the computed limitation functions for water temperature, light, nitrogen, phosphorus and silicate, respectively. These functions, when appropriate, act to modify \(R_{prod}^{phy}\), noting that only \(L_T^{phy}\) always does so. The other limitation functions in Equation (I.2) act collectively, with only the most limiting (i.e. the smallest function value) of \(L_{lght}^{phy}\), \(L_{nit}^{phy}\), \(L_{phs}^{phy}\) and \(L_{sil}^{phy}\) being selected to also multiplicatively modify \(R_{prod}^{phy}\) with \(L_T^{phy}\).

If nitrogen fixing is implemented, then the productivity rate computed in Equation (I.2) is further modified as per Equation (I.3).

\[\begin{equation} R_{prod\langle computed\rangle}^{phy} = R_{prod\langle computed\rangle}^{phy} \times \left(f_{nfix}^{phy} + L_{nit}^{phy} \times \left(1.0 - f_{nfix}^{phy}\right)\right) \tag{I.3} \end{equation}\]

\(f_{nfix}^{phy}\) accounts for the metabolic cost of nitrogen fixing on primary productivity and is the user specified (or default) reductive factor applied to productivity under full nitrogen fixing conditions. Specifically:

Full nitrogen fixing occurs when \(L_{nit}^{phy}\) is zero (i.e. no water column nitrogen is available for uptake), and Equation (I.3) then has \(R_{prod\langle computed\rangle}^{phy}\) reduced by the factor \(f_{nfix}^{phy}\)
No nitrogen fixing occurs when \(L_{nit}^{phy}\) is one (i.e. excess water column nitrogen is available for uptake), and Equation (I.3) then has \(R_{prod\langle computed\rangle}^{phy}\) unchanged

Salinity limitation of primary productivity is not mandatory, and can be switched on and off by the user, or equally set to be an enhancer of respiration rather then reducer of productivity. If salinity limitation of productivity is implemented, then the \(R_{prod\langle computed\rangle}^{phy}\) computed above is further modified as per Equation (I.4).

\[\begin{equation} R_{prod\langle computed\rangle}^{phy} = R_{prod\langle computed\rangle}^{phy} \times L_{sal-pp}^{phy} \tag{I.4} \end{equation}\] \(L_{sal-pp}^{phy}\) is the limitation on primary productivity due to salinity and is between zero and one, as per the other limitation functions noted above.

Once the rate of primary productivity has been computed by applying Equation (I.2), and potentially Equations (I.3) and (I.4), the corresponding flux of carbon (i.e. phytoplankton growth) to a phytoplankton group is computed as per Equation (I.5).

\[\begin{equation} \href{AppDiags.html#WQDiagPhyPriProd}{F_{prod\langle computed\rangle}^{phy}} = R_{prod\langle computed\rangle}^{phy} \times \left[PHY\right] \tag{I.5} \end{equation}\] \(\left[PHY\right]\) is the ambient phytoplankton group concentration. These fluxes are summed over all simulated phytoplankton groups to compute the community primary productivity, \(F_{prod\langle computed\rangle}^{comm}\).

The corresponding fluxes of nitrogen due to this primary productivity are described by Equations (K.2) (basic model) and (K.4) (advanced model). Similarly, the corresponding fluxes of phosphorus are described by Equations (K.7) (basic model) and (K.8) (advanced model). The same diagnostic variable name is used to report these fluxes, regardless of the phytoplankton model used.

The WQ Module uses a minimum concentration \(\left[PHY\right]_{min}\) to maintain phytoplankton concentrations above zero. This is because if concentrations decrease to zero, then by Equation (I.5), phytoplankton fluxes (and therefore concentrations) will remain at zero regardless of computed primary productivity rates.