L.4 Silicate

Equation (L.7) describes the calculation of excretion losses, if silicate is included in phytoplanktonic calculations.

\[\begin{equation} F_{Si-excr}^{phy} = \left(\left(f_{excr-loss}^{phy} \times R_{resp\langle computed\rangle}^{phy}\right) + R_{exud\langle computed\rangle}^{phy}\right) \times X_{Si-C}^{phy} \times \left[PHY\right] \tag{L.7} \end{equation}\]

\(F_{Si-excr}^{phy}\) is the excretive loss of silicate, \(f_{excr-loss}^{phy}\) 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, \(X_{Si-C}^{phy}\) is the specified (or default) constant ratio of internal silicate to carbon in the phytoplankton group being considered and \(\left[PHY\right]\) is a computational cell’s phytoplankton concentration.

Equation (L.8) describes the calculation of mortality losses.

\[\begin{equation} F_{Si-mort}^{phy} = \left(\left(1.0 - f_{excr-loss}^{phy}\right) \times R_{resp\langle computed\rangle}^{phy}\right) \times X_{Si-C}^{phy} \times \left[PHY\right] \tag{L.8} \end{equation}\]

Some key features of the Equations (L.7) and (L.8) are as follows:

• As for nitrogen and phosphorus losses, the key feature of Equations (L.7) and (L.8) 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
• Despite not simulating particulate silicate, Equations (L.7) and (L.8) nonetheless ensure that the mass of silicate delivered to the dissolved pool (that is simulated by the WQ Module) is consistent with that of carbon, nitrogen and phosphorus.