L.3 Phosphorus

Equation (L.5) describes the calculation of excretion losses.

\[\begin{equation} \href{AppDiags.html#WQDiagPhyExcrP}{F_{P-excr}^{phy}} = \left(\left(f_{excr-loss}^{phy} \times R_{resp\langle computed\rangle}^{phy}\right) + R_{exud\langle computed\rangle}^{phy}\right) \times X_{P-C}^{phy} \times \left[PHY\right] \tag{L.5} \end{equation}\]

\(F_{P-excr}^{phy}\) is the excretive loss of phosphorus, \(f_{excr-loss}^{phy}\) is the fraction of combined excretive and mortality losses that is excretive only, \(R_{resp\langle computed\rangle}^{phy}\) and and \(R_{exud\langle computed\rangle}^{phy}\) are the computed respiration and exudation rates, respectively, and \(\left[PHY\right]\) is a computational cell’s phytoplankton concentration. If the basic phytoplankton constituent model is used, then \(X_{P-C}^{phy}\) is the specified (or default) constant ratio of internal phosphorus to carbon. If the advanced phytoplankton constituent model is used, then \(X_{P-C}^{phy}\) is the dynamically computed ratio of internal phosphorus to carbon concentrations, where this ratio varies only between the specified (or default) minimum and maximum ratios \(X_{P-C-min}^{phy}\) and \(X_{P-C-max}^{phy}\), respectively.

Equation (L.6) describes the calculation of mortality losses.

\[\begin{equation} \href{AppDiags.html#WQDiagPhyMortP}{F_{P-mort}^{phy}} = \left(\left(1.0 - f_{excr-loss}^{phy}\right) \times R_{resp\langle computed\rangle}^{phy}\right) \times X_{P-C}^{phy} \times \left[PHY\right] \tag{L.6} \end{equation}\]

\(F_{P-mort}^{phy}\) is the mortality loss of phosphorus and the other terms in Equation (L.6) as the same as Equation (L.5), noting the inclusion of (1 - \(f_{excr-loss}^{phy}\)) in Equation (L.6) to isolate the fraction of the combined excretive and mortality loss that is mortality only.

As for nitrogen losses, the key feature of Equations (L.5) and (L.6) is that if \(f_{excr-loss}^{phy}\) is set to 1.0, then mortality losses are zero. This is consistent with interpreting this parameter as the proportion of combined excretive and mortality losses that are excretive. The converse applies for a \(f_{excr-loss}^{phy}\) of 0.0.