I.4 Settling

The settling rate \(V_{settle}^{phy}\) (also referred to as motility) of a phytoplankton group is applied within the WQ Module for each phytoplankton group, prior to the corresponding primary production, respiration and exudation rate calculations. There are several phytoplankton settling models available within the WQ Module. These are described following, and once the settling rate has been computed, the flux (loss) of phytoplankton carbon to the sediments (i.e. from the bottom cell of each computational water column only) is computed for each phytoplankton group via Equation (I.13).

\[\begin{equation} \href{AppDiags.html#WQDiagPhySedmtn}{F_{sedmtn\langle computed\rangle}^{phy}} = \frac{V_{settle}^{phy}}{dz} \times \left[PHY\right] \tag{I.13} \end{equation}\] \(dz\) is the relevant cell thickness, and divides the flux to produce a per volume result for consistency with other corresponding diagnostics (such as mortality). These fluxes are summed over all simulated phytoplankton groups to compute the community sedimentation rate, \(F_{sedmtn\langle computed\rangle}^{comm}\). The latter is in per area units.

The corresponding sedimentation flux of phytoplanktonic nitrogen is computed via either Equation (I.14) (basic model) or (I.15) (advanced model). The same diagnostic variable name is used to report these fluxes, regardless of the phytoplankton model used.

\[\begin{equation} \href{AppDiags.html#WQDiagPhySedmtnN}{F_{sedmtn-N\langle computed\rangle}^{phy}} = \frac{V_{settle}^{phy}}{dz} \times \left[PHY\right] \times X_{N-C-con}^{phy} \tag{I.14} \end{equation}\] \(X_{N-C-con}^{phy}\) is the specified (or default) constant ratio of internal nitrogen to carbon in the phytoplankton group being considered.

\[\begin{equation} \href{AppDiags.html#WQDiagPhySedmtnN}{F_{sedmtn-N\langle computed\rangle}^{phy}} = \frac{V_{settle}^{phy}}{dz} \times \left[IN\right] \tag{I.15} \end{equation}\] \(\left[IN\right]\) is the internal phytoplankton nitrogen concentration.

The corresponding sedimentation flux of phytoplanktonic phosphorus is computed via either Equation (I.16) (basic model) or (I.17) (advanced model). The same diagnostic variable name is used to report these fluxes, regardless of the phytoplankton model used.

\[\begin{equation} \href{AppDiags.html#WQDiagPhySedmtnP}{F_{sedmtn-P\langle computed\rangle}^{phy}} = \frac{V_{settle}^{phy}}{dz} \times \left[PHY\right] \times X_{P-C-con}^{phy} \tag{I.16} \end{equation}\] \(X_{P-C-con}^{phy}\) is the specified (or default) constant ratio of internal phosphorus to carbon in the phytoplankton group being considered.

\[\begin{equation} \href{AppDiags.html#WQDiagPhySedmtnP}{F_{sedmtn-P\langle computed\rangle}^{phy}} = \frac{V_{settle}^{phy}}{dz} \times \left[IP\right] \tag{I.17} \end{equation}\] \(\left[IP\right]\) is the internal phytoplankton phosphorus concentration.

I.4.1 None

In this model, phytoplankton settling \(V_{settle}^{phy}\) is set to zero and phytoplankton are simply advected by the hydrodynamic flow field.

I.4.2 Constant

In this model, phytoplankton settling \(V_{settle}^{phy}\) is set to a constant value, and phytoplankton are settled at this velocity. A negative specification of this quantity corresponds to a downwards settling velocity.

I.4.3 Constant with density correction

In this model, phytoplankton settling \(V_{settle}^{phy}\) is set to a constant value, and phytoplankton are settled at this velocity, but corrected for ambient water density effects, as per Equation (I.18).

\[\begin{equation} V_{sett\langle computed\rangle}^{phy} = V_{settle}^{phy} \times \frac{\mu_{20}\times\rho_w}{\mu\times\rho_{w20}} \tag{I.18} \end{equation}\]

\(V_{settle}^{phy}\) is the specified settling rate (velocity) at 20\(^o\)C, \(\mu\) and \(\rho_w\) are the ambient water dynamic viscosity (in Ns/m\(^2\)) and density (in kg/m\(^3\)), respectively, and \(\mu_{20}\) and \(\rho_{w20}\) are the dynamic viscosity and density of freshwater at 20\(^o\)C, respectively. A negative specification of \(V_{settle}^{phy}\) corresponds to a downwards settling velocity.

I.4.4 Stokes

In this model, phytoplankton settling is computed using the Stokes equation and cell diameter and density, as per Equation (I.19).

\[\begin{equation} V_{sett\langle computed\rangle}^{phy} = -g \times d_{phy}^2 \times \frac{\left(\rho_{phy}-\rho_w\right)}{18\mu} \tag{I.19} \end{equation}\] \(g\) is acceleration due to gravity, \(d_{phy}\) and \(\rho_{phy}\) are phytoplankton cell diameter and density, respectively, and \(\rho_w\) and \(\mu\) are the ambient water density and dynamic viscosity, respectively. This model is only available if phytoplankton cell density is dynamically simulated. Cell density is therefore required to be simulated as a computed variable in both cases, with supporting initial and boundary condition specifications. Cell diameter is fixed at 1 \(\times\) 10 \(^{-5}\) m.

Even though a half saturation light intensity \(I_K\) is not required to compute the settling velocity directly, it is required to compute the cell density term in Equation (I.19). Cell density is computed as described in Appendix M.2. \(I_K\) can therefore be specified in the command to set stokes settling (referred to as \(I_{K-sto}\)), if it is not already specified in a phytoplankton constituent model light limitation function.

I.4.5 Motile

The motility settling model can only be used if internal nutrients are simulated, via deployment of the advanced phytoplankton constituent model.

In this model, phytoplankton are permitted to be motile, with the motility velocity being either a user specified value (and either upwards or downwards), or zero. This motility behaviour is governed by phytoplankton internal nutrient status and ambient environmental conditions, as follows:

If \(Q \lt 0.675 \times X_{N-C-max}^{phy}\) then phytoplankton is starved of nutrients and swims downwards at a rate \(V_{mot}^{phy}\)
If \(Q \gt 0.750 \times X_{N-C-max}^{phy}\) then phytoplankton is replete of nutrients and:
- If local photosynthetically available radiation is greater than \(I_{K-mot}\) then phytoplankton swim up at \(V_{mot}^{phy}\)
- If local photosynthetically available radiation is less than \(I_{K-mot}\) then phytoplankton are not motile
If \(0.675 \times X_{N-C-max}^{phy} \lt Q \lt 0.750 \times X_{N-C-max}^{phy}\) then phytoplankton are not motile

\(V_{mot}^{phy}\) is the user specified motility velocity where a negative value is treated as a downwards motility, \(Q\) is the instantaneous ratio of phytoplankton internal nitrogen to carbon computed by the WQ Module (N/C, not \(R_{IN-IP}^{phy}\)), \(X_{N-C-max}^{phy}\) is the maximum internal nitrogen to carbon concentration ratio either user specified (or default) in the advanced constituent model and \(I_{K-mot}\) is the half saturation constant for light limitation of growth. A value of \(I_{K-mot}\) specified in the settling model will be ignored if it has been specified in the light limitation model.

Overriding all of the above is the condition that if local photosynthetically available radiation is greater than 95% of the water surface value, motility is set to zero as phytoplankton are considered to already be at the surface of the model domain.