10 Phytoplankton

10.1 Contributors

10.2 Overview

The approach to simulate algal biomass is to adopt several plankton functional types (“PFT’s”) that are typically defined based on specific groups such as diatoms, dinoflagellates and cyanobacteria. Whilst each group that is simulated is unique, they share a common mathematical approach and each simulate growth, death and sedimentation processes, and customisable internal nitrogen, phosphorus and/or silica stores if desired. Distinction between groups is made by adoption of groups specific parameters for environmental dependencies, and/or enabling options such as vertical migration or N fixation.

10.3 Model Description

The main balance equation for a single configured phytoplankton group, \(PHY_a\), is described as:

\[\begin{eqnarray} \frac{D}{Dt}PHY_{a} = \color{darkgray}{ \mathbb{M} + \mathcal{S} } \quad &+& \overbrace{ f_{gpp}^{PHY_{a}} - f_{rsp}^{PHY_{a}} - f_{mor}^{PHY_{a}} - f_{exc}^{PHY_{a}} + f_{set}^{PHY_{a}} + \hat{f}_{res}^{PHY_{a}} }^\text{aed_phytoplankton} \\ \tag{10.1} &-& \color{brown}{ f_{grz}^{ZOO} - \hat{f}_{grz}^{BIV} } \\ \nonumber \end{eqnarray}\]

where \(\mathbb{M}\) and \(\mathcal{S}\) refer to water mixing and boundary source terms, respectively. The main processes controlling the rate of phytoplanklton biomass accumulation are gross primary productivity, respiration, mortality, excretion and exudation, settling and vertical migration, and resuspension. In addition, the coloured \(\color{brown}{f}\) terms reflect phytoplankton related fluxes computed by other (optionally) linked modules such as the zooplankton (\(\mathrm{ZOO}\)) or bivalve (\(\mathrm{BIV}\)) modules, which compute grazing/filtration fluxes based on their rate of phytoplankton consumption.

The default method for simulating phytoplankton biomass assess a constant intracellular C:N:P ratio. In this case, only a single state variable for carbon biomass is simulated and subject to trasnport, with the N and P content computed based on the C concentration at any point in time or space. The module also supports the simulation of dynamic intracellular stoichiometry should this be required. Within this setting, state variables are also optionally created for phytoplankton biomass N and P content (termed \(IN\) and \(IP\), respectively):

\[\begin{eqnarray} \frac{D}{Dt}IN_{a} = \color{darkgray}{ \mathbb{M} + \mathcal{S} } \quad &+& \overbrace{ f_{upt}^{IN_{a}} - f_{rsp}^{IN_{a}} - f_{mor}^{IN_{a}} - f_{exc}^{IN_{a}} + f_{set}^{IN_{a}} + \hat{f}_{res}^{IN_{a}} }^\text{aed_phytoplankton} \\ \tag{10.2} &-& \color{brown}{ f_{grz}^{ZOO} - \hat{f}_{grz}^{BIV} } \\ \nonumber \end{eqnarray}\] and \[\begin{eqnarray} \frac{D}{Dt}IP_{a} = \color{darkgray}{ \mathbb{M} + \mathcal{S} } \quad &+& \overbrace{ f_{upt}^{IP_{a}} - f_{rsp}^{IP_{a}} - f_{mor}^{IP_{a}} - f_{exc}^{IP_{a}} + f_{set}^{IP_{a}} + \hat{f}_{res}^{IP_{a}} }^\text{aed_phytoplankton} \\ \tag{10.3} &-& \color{brown}{ f_{grz}^{ZOO} - \hat{f}_{grz}^{BIV} } \\ \nonumber \end{eqnarray}\]

A detailed overview of the above functions for C, N and P for each of the various process rates is provided next.

10.3.1 Process Descriptions

Photosynthesis & Nutrient Uptake

For each phytoplankton group, \(a\), the maximum potential growth rate at 20˚C is multiplied by the minimum value of expressions for limitation by light, phosphorus, nitrogen and silica (when configured). While there may be some interaction between limiting factors, a minimum expression is likely to provide a realistic representation of growth limitation (Rhee and Gotham, 1981). Therefore, photosynthesis is parameterized as the uptake of carbon, and depends on the temperature, light and nutrient dimensionless functions (adopted from Hipsey & Hamilton, 2008; Li et al., 2013):


\[\begin{equation} \text{Phytoplankton Growth Equation} \tag{10.4} \end{equation}\] \[\begin{align} {f_{gpp}^{PHY_{a}}} &= \: [PHY_{a}] \times \end{align}\] \[\begin{align} \underbrace{{R_{growth}^{PHY_{a}}}}_{\text{Max growth rate at 20˚C}} \times \underbrace{(1-{k_{pr}^{PHY_{a}}})}_{\text{Photorespiratory loss}} \times \underbrace{{\Phi_{tem}^{PHY_{a}}}(T)}_{\text{Temperature scaling}} \times \underbrace{{\Phi_{str}^{PHY_{a}}}(T)}_{\text{Metabolic stress}} \times \end{align}\] \[\begin{align} &{\text{min}}\begin{Bmatrix}\underbrace{\Phi_{light}^{PHY_{a}}(I)}_{\text{Light limitation}},\underbrace{\Phi_{N}^{PHY_{a}}(NO_{3},NH_{4},PHY_{N_{a}})}_{\text{N limitation}},\underbrace{\Phi_{P}^{PHY_{a}}(PO_{4},PHY_{P_{a}})}_{\text{P limitation}},\underbrace{\Phi_{Si}^{PHY_{a}}(RSi)}_{\text{Si limitation}}\end{Bmatrix} \times \end{align}\]


Temperature limitation: Temperature is a key environmental driver that shapes the responses of different phytoplankton groups. To allow for reduced growth at non-optimal temperatures, a temperature function is used where the maximum productivity occurs at a temperature \(T_{OPT}\); above this productivity decreases to zero at the maximum allowable temperature, \(T_{MAX}\). Below the standard temperature, \(T_{STD}\) the productivity follows a simple Arrenhius scaling formulation. In order to fit a function with these restrictions the following conditions are assumed: at \(T=T_{STD}\),\(\ {\ \Phi}_{tem}\left(T\right)=1\) and at \(T=T_{OPT},\ \ \frac{d\Phi_{tem}\left(T\right)}{dT}=0\), and at \(T=T_{MAX}\),\(\ \Phi_{tem}\left(T\right)=0\). This can be numerically solved using Newton’s iterative method and can be specific for each phytoplankton group. The temperature function is calculated according to (Griffin et al. 2001):

\[\begin{equation} \Phi_{tem}^{{PHY}_a}\left(T\right)=\vartheta_a^{T-20}-\vartheta_a^{k\left[T-{c1}_a\right]}+{c0}_a \tag{10.5} \end{equation}\]

where \({c1}_a\) and \({c0}_a\) are solved numerically given input values of: \(T_a^{std}\), \(T_a^{opt}\) and \(T_a^{max}\).

Light limitation: The level of light limitation on phytoplankton growth can be modelled as photoinhibition or non-photoinhibition. In the absence of significant photoinhibition, Webb et al. (1974) suggested a relationship for the fractional limitation of the maximum potential rate of carbon fixation for the case where light saturation behavior was absent (Talling, 1957), and the equations can be analytically integrated with respect to depth (Hipsey and Hamilton, 2008). For the case of photoinhibition, the light saturation value of maximum production (\(I_S\)) is used and the net level effect can be averaged over the cell by integrating over depth.

The aed_phytoplankton module contains several light functions, including those from a recent review by Baklouti et al. (2006). The user must select the sensitivity to light according to a photosynthesis-irradiance (P-I curve) formulation and each species must be set to be either non-photoinhibited or photoinhibited according to the options in Table 9.

Figure 10.1: Light limitation of pytoplankton via various model approaches.

Nutrient limitation: Limitation of the photosynthetic rate may be dampened according to nitrogen or phosphorus availability, and this is either approximated using a Monod expression of the static model is chosen, or based on the internal nutrient stoichiometry if the dynamic (Droop uptake) model is selected: For advanced users, an optional metabolic scaling factor can be included to reduce the photosynthetic capacity of the simulated organisms, for example due to metabolic stress due to undertaking N2 fixation:

\[\begin{equation} \Phi_{str}^{{PHY}_a}=\underbrace{f_{NF}^{{PHY}_a}+\left[{1-f}_{NF}^{{PHY}_a}\right]\Phi_N^{{PHY}_a}\left({NO}_3,{NH}_4,{PHY_N}_a\right)}_{N_{2}\text{ fixation growth scaling}} \tag{10.6} \end{equation}\]

The above discussion relates to photosynthesis and carbon uptake by the phytoplankton community. In addition users must choose one of two options to model the P, N uptake dynamics for each algal group: i) a constant nutrient to carbon ratio, or ii) simulation of dynamic intracellular stores. For the first model a simple Michaelis-Menten equation is used to model nutrient limitation with a half-saturation constant for the effect of external nutrient concentrations on the growth rate.

The internal phosphorus and nitrogen dynamics within the phytoplankton groups can be modelled using dynamic intracellular stores that are able to regulate growth based on the model of Droop (1974). This model allows for the phytoplankton to have dynamic nutrient uptake rates with variable internal nutrient concentrations bounded by user-defined minimum and maximum values (e.g., see Li et al., 2013).

The uptake of nitrogen must be partitioned into uptake of NO3, and NH4. The distinction between uptake of NO3 and NH4 is calculated automatically via a preference factor:

\[\begin{equation} {\ p}_{NH4}^{{PHY}_a}=\frac{{NO}_3\ {NH}_4}{\left({NH}_4+K_N^{{PHY}_a}\right)\left({NO}_3+K_N^{{PHY}_a}\right)}\frac{{NH}_4{\ K}_N^{{PHY}_a}}{\left({NH}_4+{NO}_3\right)\left({NO}_3+K_N^{{PHY}_a}\right)} \tag{10.7} \end{equation}\]
\[\begin{equation} p_{NO3}^{{PHY}_a}=1-{\ p}_{NH4}^{{PHY}_a} \tag{10.8} \end{equation}\]

For diatom groups, silica processes are simulated that include uptake of dissolved silica. The silica limitation function for diatoms is similar to the constant cases for nitrogen and phosphorus which assumes a fixed C:Si ratio.

Respiration, Excretion & Mortality

Metabolic loss of nutrients from mortality and excretion is proportional to the internal nitrogen to chla ratio multiplied by the loss rate and the fraction of excretion and mortality that returns to the detrital pool. Loss terms for respiration, natural mortality and excretion are modelled with a single ‘respiration’ rate coefficient. This loss rate is then divided into the pure respiratory fraction and losses due to mortality and excretion. The constant \(f_{DOM}\) is the fraction of mortality and excretion to the dissolved organic pool with the remainder into the particulate organic pool. Nutrient losses through mortality and excretion for the internal nutrient model are similar to the simple model described above, except that dynamically calculated internal nutrient concentrations are used.


\[\begin{align*} \hat{R}&=R_{resp}^{{PHY}_a}\ \ \Phi_{sal}^{{PHY}_a}\left(S\right)\ \ \left(\vartheta_{resp}^{{PHY}_a}\right)^{T-20} \tag{10.9}\\ f_{resp}^{{PHY_C}_a}&=k_{fres}^{{PHY}_a}\ \hat{R}\ \left[{PHY_C}_a\right] \tag{10.10}\\ f_{excr}^{{PHY_C}_a}&=\left(1-k_{fres}^{{PHY}_a}\right)\ k_{fdom}^{{PHY}_a}\ \hat{R}\ \ \left[{PHY_C}_a\right] \tag{10.11}\\ f_{mort}^{{PHY_C}_a}&=\left(1-k_{fres}^{{PHY}_a}\right)\ \left({1-k}_{fdom}^{{PHY}_a}\right)\ \hat{R}\ \left[{PHY_C}_a\right] \tag{10.12}\\ f_{excr}^{{PHY_N}_a}&=k_{fdom}^{{PHY}_a}\ \hat{R}\ \left[{PHY_N}_a\right] \tag{10.13}\\ f_{mort}^{{PHY_N}_a}&=\left(1-k_{fdom}^{{PHY}_a}\right)\ \hat{R}\ \left[{PHY_N}_a\right] \tag{10.14}\\ f_{excr}^{{PHY_P}_a}&=k_{fdom}^{{PHY}_a}\ \hat{R}\ \left[{PHY_P}_a\right] \tag{10.15}\\ f_{mort}^{{PHY_P}_a}&=\left(1-k_{fdom}^{{PHY}_a}\right)\ \hat{R}\ \ \left[{PHY_P}_a\right] \tag{10.16}\\ f_{excr}^{{PHY_{Si}}_a}&=\hat{R}\ \left[{PHY_{Si}}_a\right] \tag{10.17} \end{align*}\]

The salinity effect on mortality is given by various quadratic formulations, depending on the groups sensitivity to salinity (Griffin et al 2001; Robson and Hamilton, 2004). An example of the use of various salinity limitation options is shown in Figure 3.

Figure 10.1: Salinity growth suppression of pytoplankton via various model approaches.

Figure 10.1: Salinity respiration amplification of pytoplankton via various model approaches.

10.3.3 Feedbacks to the Host Model

The phytoplankton module can feedback conditions to the hydrodynamic model by modifying the light extinction coefficient. For each group simulated a specific attenuation coefficient, \(K_e\), is applied, and is specific for each group simulated.

This total light extinction computed by the PHY model is:

\[\begin{equation} K_{d}^{phy} = \sum_{a}K_{e_{PHY_a}} PHY_a \end{equation}\]

10.3.4 Variable Summary

The default variables created by this module, and the optionally required linked variables needed for full functionality of this module are summarised in Table 10.1. The diagnostic outputs able to be output are summarised in Table 10.2.

State Variables

Table 10.1: Phytoplankton - state variables
AED name Symbol Description Unit Type Typical Range Comments
aed_phytoplankton
PHY_{group} \[\mathbf{PHY}\] phytoplanton group water column concentration \[\small{mmol\: C/m^3}\] pelagic 0-1000 select group using index from aed_phyto_pars database
PHY_{group}_IN \[\mathbf{PHY_N}\] internal nitrogen concentration of phytoplakton group \[\small{mmol\: N/m^3}\] pelagic 0 - 200 activated when simINDynamics \(\gt 1\)
PHY_{group}_IP \[\mathbf{PHY_P}\] internal phosphorus concentration of phytoplakton group \[\small{mmol\: P/m^3}\] pelagic 0-20 activated when simIPDynamics \(\gt 1\)
PHY_{group}_rho \[\mathbf{PHY_{\rho}}\] phytoplankton group mean cell density \[\small{kg\: C/m^3}\] pelagic 900-1200 activated for a group when settling=3
PHY_mpb \[\mathbf{MPB}\] coarse particulate organic matter \[\small{mmol\: C/m^2}\] benthic 0-5000 activated when do_mpb \(\gt 0\)
Dependent variables
CAR_dic \[\mathbf{DIC}\] dissolved inorganic carbon concentration \[\small{mmol\: C/m^3}\] pelagic NA optionally linked
NIT_amm \[\mathbf{NH_4}\] dissolved ammonium concentration \[\small{mmol\: N/m^3}\] pelagic NA optionally linked
PHS_frp \[\mathbf{PO_4}\] dissolved phosphate concentration \[\small{mmol\: P/m^3}\] pelagic NA optionally linked
OXY_oxy \[\mathbf{O_2}\] dissolved oxygen concentration \[\small{mmol\: O_2/m^3}\] pelagic 0 - 500 optionally linked
NIT_nit \[\mathbf{NO_3}\] dissolved nitrate concentration \[\small{mmol\: N/m^3}\] pelagic NA optionally linked
OGM_doc \[\mathbf{DOC}\] dissolved organic carbon concentration \[\small{mmol\: C/m^3}\] pelagic 0 - 5000 optionally linked
OGM_poc \[\mathbf{POC}\] particulate organic carbon concentration \[\small{mmol\: C/m^3}\] pelagic NA optionally linked
OGM_don \[\mathbf{DON}\] dissolved organic nitrogen concentration \[\small{mmol\: N/m^3}\] pelagic NA optionally linked
OGM_pon \[\mathbf{PON}\] particulate organic nitrogen concentration \[\small{mmol\: N/m^3}\] pelagic NA optionally linked
OGM_dop \[\mathbf{DOP}\] dissolved organic phosphorus concentration \[\small{mmol\: P/m^3}\] pelagic NA optionally linked
OGM_pop \[\mathbf{POP}\] particulate organic phosphorus concentration \[\small{mmol\: P/m^3}\] pelagic NA optionally linked
SIL_rsi \[\mathbf{RSi}\] reactive silica concentration \[\small{mmol\: Si/m^3}\] pelagic NA optionally linked
NCS_resus \[\mathbf{\mathcal{F}}_{resus}\] sediment resuspension rate \[\small{g/m^2/s}\] benthic 0 - 10 required for PHY resuspension, set via resus_link


Diagnostics

Table 10.2: Phytoplankton - diagnostic variables
AED name Symbol Description Unit Type Typical Range Comments
diag_level = 0+
PHY_set \[\mathbf{f_{set}^{\mathbb{PHY}}}\] phytoplankton community sedimentation flux \[\small{mmol\: C/m^3/d}\] pelagic NA
PHY_res \[\mathbf{\hat{f}_{res}^{\mathbb{PHY}}}\] phytoplankton community resuspension flux \[\small{mmol\: C/m^2/d}\] pelagic NA
PHY_gpp \[\mathbf{f_{gpp}^{\mathbb{PHY}}}\] gross phytoplankton community primary production rate \[\small{mmol\: C/m^3/d}\] pelagic NA
PHY_ncp \[\mathbf{f_{gpp}^{\mathbb{PHY}}} - \mathbf{f_{rsp}^{\mathbb{PHY}}}\] net phytoplankton community production \[\small{mmol\: C/m^3/d}\] pelagic NA
diag_level = 1+
PHY_upt_no3 \[\mathbf{f_{upt_{NO3}}^{\mathbb{PHY}}}\] phytoplankton community \(NO_3\) uptake rate \[\small{mmol\: N/m^3/d}\] pelagic NA
PHY_upt_nh4 \[\mathbf{f_{upt_{NH4}}^{\mathbb{PHY}}}\] phytoplankton community \(NH_4\) uptake rate \[\small{mmol\: N/m^3/d}\] pelagic NA
PHY_upt_n2 \[\mathbf{f_{upt_{N2}}^{\mathbb{PHY}}}\] phytoplankton community \(N_2\) uptake rate \[\small{mmol\: N/m^3/d}\] pelagic NA
PHY_upt_po4 \[\mathbf{f_{upt_{PO4}}^{\mathbb{PHY}}}\] phytoplankton community \(PO_4\) uptake rate \[\small{mmol\: P/m^3/d}\] pelagic NA
PHY_upt_dic \[\mathbf{f_{upt_{DIC}}^{\mathbb{PHY}}}\] phytoplankton community \(CO_2\) uptake rate \[\small{mmol\: C/m^3/d}\] pelagic NA
PHY_tchla \[\mathbf{\mathbb{TCHLA}}\] total chlorophyll-a concentration \[\small{\mu g \, /L}\] pelagic NA
PHY_in \[\mathbf{\mathbb{IN}}\] total phytoplankton nitrogen concentration \[\small{mmol\: N/m^3}\] pelagic NA
PHY_ip \[\mathbf{\mathbb{IP}}\] total phytoplankton phosphorus concentration \[\small{mmol\: P/m^3}\] pelagic NA
PHY_mpb_ben \[\mathbf{MPB}\] microphytobenthos concentration \[\small{mmol\: C/m^2}\] benthic 0 - 10000 activated when do_mpb >0
PHY_mpb_gpp \[\hat{f}_{gpp}^{MPB}\] benthic phytoplankton primary production \[\small{mmol\: C/m^2/d}\] benthic NA activated when do_mpb >0
PHY_mpb_rsp \[\hat{f}_{rsp}^{MPB}\] benthic phytoplankton net production \[\small{mmol\: C/m^2/d}\] benthic NA activated when do_mpb >0
PHY_mpb_swi \[\hat{f}_{swi}^{MPB}\] microphytobenthos vertical exchange \[\small{mmol\: C/m^2/d}\] benthic NA activated when do_mpb >0
diag_level = 10+
PHY_{name}_NtoP \[\mathbf{\chi_{N:P}^{PHY}}\] phytoplankton internal N:P ratio for the \(a^{th}\) group, name \[\small{-}\] pelagic NA
PHY_{name}_vvel \[\mathbf{\omega_{p}^{PHY_a}}\] phytoplankton sedimentation velocity for the \(a^{th}\) group, name \[\small{m/d}\] pelagic NA
PHY_{name}_gpp_c \[\mathbf{f_{gpp}^{PHY_a}}\] phytoplankton gross primary production for the \(a^{th}\) group, name \[\small{mmol\: C/m^3/d}\] pelagic NA
PHY_{name}_rsp_c \[\mathbf{f_{rsp}^{PHY_a}}\] phytoplankton respiration rate for the \(a^{th}\) group, name \[\small{mmol\: C/m^3/d}\] pelagic NA
PHY_{name}_exc_c \[\mathbf{f_{exc}^{PHY_a}}\] phytoplankton excretion rate for the \(a^{th}\) group, name \[\small{mmol\: C/m^3/d}\] pelagic NA
PHY_{name}_mor_c \[\mathbf{f_{mor}^{PHY_a}}\] phytoplankton mortality rate for the \(a^{th}\) group, name \[\small{mmol\: C/m^3/d}\] pelagic NA
PHY_{name}_set_c \[\mathbf{f_{set}^{PHY_a}}\] phytoplankton sedimentation rate for the \(a^{th}\) group, name \[\small{mmol\: C/m^3/d}\] pelagic NA
PHY_{name}_gpp_n \[\mathbf{f_{gpp}^{IN_a}}\] phytoplankton gross primary production for the \(a^{th}\) group, name \[\small{mmol\: N/m^3}\] pelagic NA
PHY_{name}_rsp_n \[\mathbf{f_{rsp}^{IN_a}}\] phytoplankton respiration rate for the \(a^{th}\) group, name \[\small{mmol\: N/m^3}\] pelagic NA
PHY_{name}_exc_n \[\mathbf{f_{exc}^{IN_a}}\] phytoplankton excretion rate for the \(a^{th}\) group, name \[\small{mmol\: N/m^3}\] pelagic NA
PHY_{name}_mor_n \[\mathbf{f_{mor}^{IN_a}}\] phytoplankton mortality rate for the \(a^{th}\) group, name \[\small{mmol\: N/m^3}\] pelagic NA
PHY_{name}_set_n \[\mathbf{f_{set}^{IN_a}}\] phytoplankton sedimentation rate for the \(a^{th}\) group, name \[\small{mmol\: N/m^3}\] pelagic NA
PHY_{name}_gpp_p \[\mathbf{f_{gpp}^{IP_a}}\] phytoplankton gross primary production for the \(a^{th}\) group, name \[\small{mmol\: P/m^3/d}\] pelagic NA
PHY_{name}_rsp_p \[\mathbf{f_{rsp}^{IP_a}}\] phytoplankton respiration rate for the \(a^{th}\) group, name \[\small{mmol\: P/m^3/d}\] pelagic NA
PHY_{name}_exc_p \[\mathbf{f_{exc}^{IP_a}}\] phytoplankton excretion rate for the \(a^{th}\) group, name \[\small{mmol\: P/m^3/d}\] pelagic NA
PHY_{name}_mor_p \[\mathbf{f_{mor}^{IP_a}}\] phytoplankton mortality rate for the \(a^{th}\) group, name \[\small{mmol\: P/m^3/d}\] pelagic NA
PHY_{name}_set_p \[\mathbf{f_{set}^{IP_a}}\] phytoplankton sedimentation rate for the \(a^{th}\) group, name \[\small{mmol\: P/m^3/d}\] pelagic NA
PHY_{name}_fI \[\mathbf{\Phi_{light}^{PHY_{a}}}\] phytoplankton growth limitation function for the \(a^{th}\) group, name \[\small{-}\] pelagic 0 - 1
PHY_{name}_fNit \[\mathbf{\Phi_{N}^{PHY_{a}}}\] phytoplankton growth limitation function for the \(a^{th}\) group, name \[\small{-}\] pelagic 0 - 1
PHY_{name}_fPho \[\mathbf{\Phi_{P}^{PHY_{a}}}\] phytoplankton growth limitation function for the \(a^{th}\) group, name \[\small{-}\] pelagic 0 - 1
PHY_{name}_fSil \[\mathbf{\Phi_{Si}^{PHY_{a}}}\] phytoplankton growth limitation function for the \(a^{th}\) group, name \[\small{-}\] pelagic 0 - 1
PHY_{name}_fT \[\mathbf{\Phi_{tem}^{PHY_{a}}}\] phytoplankton growth limitation function for the \(a^{th}\) group, name \[\small{-}\] pelagic 0 - 1.5
PHY_{name}_fSal \[\mathbf{\Phi_{sal}^{PHY_{a}}}\] phytoplankton growth limitation function for the \(a^{th}\) group, name \[\small{-}\] pelagic 0 - 5
PHY_tphy \[\mathbf{TPHY}\] total phytoplankton community, \(\mathbb{PHY}\) concentration \[\small{mmol\: C/m^3/d}\] pelagic NA
PHY_ppr \[\mathbf{f_{gpp}^{\mathbb{PHY}}} / \mathbf{f_{rsp}^{\mathbb{PHY}}}\] gross phytoplankton \(P:R\) ratio \[\small{-}\] pelagic NA
PHY_npr \[\mathbf{f_{ncp}^{\mathbb{PHY}}} / \mathbf{f_{rsp}^{\mathbb{PHY}}}\] net phytoplankton P:R ratio \[\small{-}\] pelagic NA
PHY_par \[\mathbf{I_{PAR}}\] photosynthetically active radiation \[\small{W/m^2}\] pelagic 0-1200


10.3.5 Parameter and Option Summary

The module requires users to set both module level confiuration options and parameters, and group-specific parameters.

The group-specific parameters and settings are read in through the aed_phyto_pars, summarised in Table 10.3.

Table 10.3: Phytoplankton group-specific parameters and configuration options
AED name Symbol Description Unit Type Typical Range Comments
General
p_name \[a\] name of phytoplankton group \[\small{-}\] string
user specified name of chosen phytoplankton group, \(a\)
p_initial \[PHY |_{t=0}\] initial concentration of phytoplankton \[\small{mmol\: C/m^3}\] float 0-1000 can be overwritten by initial condition files
p0 \[PHY_0\] minimum concentration of phytoplankton \[\small{mmol\: C/m^3}\] float 1-20
Xcc \[\chi_{C:chla}^{PHY}\] carbon to chlorophyll ratio \[\small{mg\: C/mg\: chla}\] float 10 - 1000
Growth
R_growth \[R_{growth}^{PHY}\] phytoplankton group maximum growth rate at \(20^{\circ}C\) \[\small{/d}\] float 0.1 - 5.0
fT_Method \[\Theta_{tem}^{phy}\] specifies temperature limitation function of growth \[\small{-}\] integer 0-1 0 = no temperature limitation 1= CAEDYM style
theta_growth \[\theta_{growth}^{phy}\] Arrenhius temperature scaling for growth function \[\small{-}\] float 1 - 1.2
T_std \[T_{std}\] standard temperature \[\small{^{\circ}C}\] float 20
T_opt \[T_{opt}\] optimum temperature \[\small{^{\circ}C}\] float NA
T_max \[T_{max}\] maximum temperature \[\small{^{\circ}C}\] float NA
Light
lightModel \[\Theta_{lgt}^{phy}\] switch to assign the type of light response function \[\small{-}\] integer 0-1
I_K \[I_K\] half saturation constant for light limitation of growth \[\small{W/m^2}\] float NA used if \(\Theta_{lgt}^{phy}\) is 0
I_S \[I_S\] saturating light intensity for optimum photosynthesis \[\small{W/m^2}\] float NA used if \(\Theta_{lgt}^{phy}\) is 1
KePHY \[K_e\] specific attenuation coefficient \[\small{/m/(mmol\:C/m^3)}\] float NA
Respiration
f_pr \[f_{pr}\] fraction of primary production lost to exudation \[\small{-}\] float NA
R_resp \[R_{resp}^{PHY}\] phytoplankton respiration/metabolic loss rate at \(20^{\circ}C\) \[\small{/d}\] float 0.01 - 0.3
theta_resp \[\theta_{resp}^{phy}\] Arrhenius temperature scaling factor for respiration \[\small{-}\] float 1 - 1.2
k_fres \[k_{fres}\] fraction of metabolic loss that is true respiration \[\small{-}\] float 0 - 1
k_fdom \[k_{fdom}\] fraction of metabolic loss that is released as DOM \[\small{-}\] float 0 - 1
Salinity
salTol \[\Theta_{sal}^{phy}\] type of salinity limitation function \[\small{-}\] integer 0, 1, 2, 3, 4
S_bep \[S_{bep}\] salinity limitation value at maximum salinity (\(S_{maxsp}\)) \[\small{-}\] float NA
S_maxsp \[S_{maxsp}\] maximum salinity where growth is possible \[\small{g/kg}\] float NA
S_opt \[S_{opt}\] optimal salinity for growth \[\small{g/kg}\] float NA
Nitrogen
simDINUptake \[\Theta_{din}^{phy}\] switch for the selected group to simulate \(DIN\) uptake \[\small{-}\] integer 0, 1
simDONUptake \[\Theta_{don}^{phy}\] switch for the selected group to simulate \(DON\) uptake \[\small{-}\] integer 0
simNFixation \[\Theta_{n2}^{phy}\] switch for the selected group to simulate \(N_2\) fixation \[\small{-}\] integer 0, 1
simINDynamics \[\Theta_{in}^{phy}\] switch for the selected group to simulate dynamic intracellular \(N\) store \[\small{-}\] integer 0, 1, 2
N_o \[N_o\] external \(DIN\) concentration below which uptake is 0 \[\small{mmol\: N/m^3}\] float NA
K_N \[K_N\] half-saturation concentration of nitrogen \[\small{mmol\: N/m^3}\] float NA
X_ncon \[\chi_{ncon}^{PHY}\] constant internal nitrogen concentration \[\small{mmol\: N/m^3}\] float NA used if simINDynamics = 0 or 1
X_nmin \[\chi_{nmin}^{PHY}\] minimum internal nitrogen concentration \[\small{mmol\: N/m^3}\] float NA used if simINDynamics = 2
X_nmax \[\chi_{nmax}^{PHY}\] maximum internal nitrogen concentration \[\small{mmol\: N/m^3}\] float NA used if simINDynamics = 2
R_nuptake \[R_{nuptake}^{PHY}\] maximum nitrogen uptake rate \[\small{mmol\: N/m^3/d\: /(mmol\: C/m^3)}\] float NA used if simINDynamics = 2
k_nfix \[k_{nfix}\] growth rate reduction under maximum nitrogen fixation \[\small{-}\] float NA used if simINDynamics \(\gt 0\)
R_nfix \[R_{nfix}^{PHY}\] nitrogen fixation rate \[\small{/d}\] float NA used if simINDynamics \(\gt 0\)
Phosphorus
simDIPUptake \[\Theta_{dip}^{phy}\] switch for the selected group to simulate \(DIP\) uptake \[\small{-}\] integer NA
simIPDynamics \[\Theta_{ip}^{phy}\] switch for the selected group to simulate dynamic intracellular \(P\) store \[\small{-}\] integer NA
P_0 \[P_o\] external \(DIP\) concentration below which uptake is 0 \[\small{mmol\: P/m^3}\] float NA
K_P \[K_P\] half-saturation concentration of phosphorus \[\small{mmol\: P/m^3}\] float NA
X_pcon \[\chi_{pcon}^{PHY}\] constant internal phosphorus concentration \[\small{mmol\: P/m^3}\] float NA
X_pmin \[\chi_{pmin}^{PHY}\] minimum internal phosphorus concentration \[\small{mmol\: P/m^3}\] float NA
X_pmax \[\chi_{pmax}^{PHY}\] maximum internal phosphorus concentration \[\small{mmol\: P/m^3}\] float NA
R_puptake \[R_{puptake}^{PHY}\] maximum phosphorus uptake rate \[\small{mmol\: P/m^3/d\: /(mmol\: C/m^3)}\] float NA
Silica
simSiUptake \[\Theta_{si}^{phy}\] switch for the selected group to simulate \(Si\) uptake \[\small{-}\] integer NA
Si_0 \[Si_o\] external \(SiO2\) concentration below which uptake is 0 \[\small{mmol\: Si/m^3}\] float NA
K_Si \[K_{Si}\] half-saturation concentration of silica uptake \[\small{mmol\: Si/m^3}\] float NA
X_sicon \[\chi_{sicon}^{PHY}\] constant internal silica concentration \[\small{mmol\: Si/m^3}\] float NA
Settling
w_p \[\omega_{phy}\] sedimentation rate \[\small{m/d}\] float -1 - 1 used if \(\Theta_{set}^{phy}\) is 1 or 2
d_phy \[d_{phy}\] phytoplankton group mean cell diameter \[\small{m}\] float NA used if \(\Theta_{set}^{phy}\) is 3
c1 \[c_1\] rate coefficient for density increase \[\small{kg/m^3/s}\] float NA used if \(\Theta_{set}^{phy}\) is 3
c3 \[c_3\] minimum rate of density decrease with time \[\small{kg/m^3/s}\] float NA used if \(\Theta_{set}^{phy}\) is 3
f1 \[f_1\] fraction of maximum intracellular nitrogen where motility tends down towards nutrients \[\small{-}\] float NA used if \(\Theta_{set}^{phy}\) is 4
f2 \[f_2\] fraction of maximum intracellular nitrogen where motility tends up towards light \[\small{-}\] float NA used if \(\Theta_{set}^{phy}\) is 4

The module level parameters and settings are read in as normal through the aed.nml, summarised in Table 10.4.

Table 10.4: Phytoplankton group-specific parameters and configuration options
AED name Symbol Description Unit Type Typical Range Comments
Groups
num_phy \[N_{a}^{phy}\] number of phytoplankton groups/species \[\small{-}\] integer 1 - 64
the_phy \[\mathbb{PHY}\] set of chosen group ID’s within the database file, where \(a \in \mathbb{PHY}\) \[\small{-}\] integer 1, 2, 3, …
settling \[\Theta_{set}^{phy}\] option to set the method of settling for \(PHY\) group \(a\) \[\small{-}\] integer 0 - 4
Microphytobenthos
do_mpb \[\Theta_{mpb}^{phy}\] option to include \(MPB\) as a simulated benthic variable \[\small{-}\] float 0 , 1, 2
R_mpbg \[R_{mpb-g}\] maximum growth rate of \(MPB\) \[\small{/d}\] float 0 - 3
R_mpbr \[R_{mpb-r}\] dark respiration rate of \(MPB\) \[\small{/d}\] float 0 - 1
I_Kmpb \[I_{K_{mpb}}\] half saturation constant for light limitation of growth \[\small{W/m^2}\] float 0 - 100
mpb_max \[MPB_{max}\] maximum biomass density of \(MPB\) \[\small{mmol\: C/m^2}\] float 10000
resuspension \[\Theta_{resus}^{phy}\] fraction to set the amount of resuspension for \(PHY\) group \(a\) \[\small{-}\] float 0 , 1
n_zones \[N_{sz}^{mpb}\] number of benthic zones where \(MPB\) is active \[\small{-}\] integer 0 - 64
active_zones \[\mathbb{Z}_{sz}^{mpb}\] set of benthic zones with \(MPB\) active, where \(sz \in \mathbb{Z}\) \[\small{-}\] integer 1, 2, 3, …
resus_link \[-\] variable simulating resuspension rate to link to \[\small{-}\] string NCS_resus
Links
p_excretion_target_variable \[DOP\] state variable to add DOP excretion \[\small{mmol\: P/m^3}\] string OGM_dop
n_excretion_target_variable \[DON\] state variable to add DON excretion \[\small{mmol\: N/m^3}\] string OGM_don
c_excretion_target_variable \[DOC\] state variable to add DOC excretion \[\small{mmol\: C/m^3}\] string OGM_doc
si_excretion_target_variable \[Si\] state variable to add Si excretion \[\small{mmol\: Si/m^3}\] string SIL_rsi
p_mortality_target_variable \[POP\] state variable to add POP mortality \[\small{mmol\: P/m^3}\] string OGM_pop
n_mortality_target_variable \[PON\] state variable to add PON mortality \[\small{mmol\: N/m^3}\] string OGM_pon
c_mortality_target_variable \[POC\] state variable to add POC mortality \[\small{mmol\: C/m^3}\] string OGM_poc
si_mortality_target_variable \[Si\] state variable to add Si mortality \[\small{mmol\: Si/m^3}\] string SIL_rsi
p1_uptake_target_variable \[FRP\] state variable to provide FRP for growth \[\small{mmol\: P/m^3}\] string PHS_frp
n1_uptake_target_variable \[NO_3\] state variable to provide \(NO_3\) for growth \[\small{mmol\: N/m^3}\] string NIT_nit
n2_uptake_target_variable \[NH_4\] state variable to provide \(NH_4\) for growth \[\small{mmol\: N/m^3}\] string NIT_amm
si_uptake_target_variable \[Si\] state variable to provide \(Si\) for growth \[\small{mmol\: Si/m^3}\] string SIL_rsi
do_uptake_target_variable \[DO\] state variable to increment \(O_2\) during growth \[\small{mmol\: O_2/m^3}\] string OXY_oxy
c_uptake_target_variable \[DIC\] state variable to provide \(DIC\) during growth \[\small{mmol\: C/m^3}\] string CAR_dic
Advanced
dbase \[-\] phytoplankton parameter database file \[\small{-}\] string aed_phyto_pars.csv aed_dbase link
min_rho \[\rho_{min}^{phy}\] minimum cellular density \[\small{kg/m^3}\] float 900 used if \(\Theta_{set}^{phy}\) is 3
max_rho \[\rho_{max}^{phy}\] maximum cellular density \[\small{kg/m^3}\] float 1200 used if \(\Theta_{set}^{phy}\) is 3
diag_level \[-\] extent of diagnostic output \[\small{-}\] integer 0 - 10 see Table X.X

10.4 Setup & Configuration

10.4.1 Setup Example

An example aed.nml configuration block for the aed_phytoplankton module that includes a single simulated group plus microphytobenthos (MPB) and resuspension effects, and doesn’t consider Si limitation, is shown below:

&aed_phytoplankton
!-- Configure phytoplankton groups to simulate
  num_phytos   =    1
  the_phytos   =    1
  settling     =    1
!-- Benthic phytoplankton group (microphytobenthos)
  do_mpb       =    1
  R_mpbg       =    0.5
  R_mpbr       =    0.05
  I_Kmpb       =  100.
  mpb_max      = 2000.
  resuspension =    0.45
  n_zones      =    4
  active_zones =    2,3,4,5
  resus_link   = 'NCS_resus'
!-- Set link variables to other modules
  p_excretion_target_variable  ='OGM_dop'
  n_excretion_target_variable  ='OGM_don'
  c_excretion_target_variable  ='OGM_doc'
  si_excretion_target_variable =''
  p_mortality_target_variable  ='OGM_pop'
  n_mortality_target_variable  ='OGM_pon'
  c_mortality_target_variable  ='OGM_poc'
  si_mortality_target_variable =''
  p1_uptake_target_variable    ='PHS_frp'
  n1_uptake_target_variable    ='NIT_nit'
  n2_uptake_target_variable    ='NIT_amm'
  si_uptake_target_variable    =''
  do_uptake_target_variable    ='OXY_oxy'
  c_uptake_target_variable     =''
!-- General options
  dbase = '../External/AED/aed_phyto_pars.nml'
  diag_level = 1
/


Note that when simulating benthic phytoplankton, the bottom zones in the model to be active must be selected.

Another example aed.nml block for the phytoplankton module that includes no benthic (bottom) phytoplankton, and three different groups is shown below:


&aed_phytoplankton
 !-- Configure phytoplankton groups to simulate
   num_phytos = 3       
   the_phytos = 1,2,3          ! cyanos,greens,diatoms
   settling   = 3,1,1          ! approach to settling/migration
 !-- Benthic phytoplankton group (microphytobenthos)
   do_mpb     = 0
 !-- Set link variables to other modules
   p_excretion_target_variable ='OGM_dop'
   n_excretion_target_variable ='OGM_don'
   c_excretion_target_variable ='OGM_doc'
   si_excretion_target_variable=''
   p_mortality_target_variable ='OGM_pop'
   n_mortality_target_variable ='OGM_pon'
   c_mortality_target_variable ='OGM_poc'
   si_mortality_target_variable=''
   p1_uptake_target_variable   ='PHS_frp'
   n1_uptake_target_variable   ='NIT_amm'
   n2_uptake_target_variable   ='NIT_nit'
   si_uptake_target_variable   ='SIL_rsi'
   do_uptake_target_variable   ='OXY_oxy'
   c_uptake_target_variable    ='CAR_dic'
 !-- General options
   dbase      = 'aed/aed_phyto_pars.csv' 
   diag_level =   10
   min_rho    =  900.0
   max_rho    = 1200.0
/


The numbers reported here are for example purposes and should be reviewed before use based on the users chosen site context.


In addition to adding the above code block to aed.nml, users must also supply a valid AED phytoplankton parameter database file (aed_phyto_pars). The database file can be supplied in either NML or CSV format, though after AED 2.0 it is reccomended users use the CSV option.

Users can create a standard file in the correct format from the online AED parameter database by selecting from the available groups of interest, downloading via the “Make CSV” button, and then tailoring to the simulation being undertaken as required. Carefully check the parameter units and values!


10.5 Case Studies & Examples

10.5.1 Case Study : Falling Creek Reservoir

Falling Creek Reservoir (FCR) is a water supply reservoir in Virginia.

Figure X: Example outputs from the FCR GLM-AED model, showing a) the total chl-a concentration depth profiles, and b) the change in biomass of the indivdual simulated groups.
Figure X: Example outputs from the FCR GLM-AED model, showing a) the total chl-a concentration depth profiles, and b) the change in biomass of the indivdual simulated groups.


An example GLM-AED simulation for FCR is available in the GLM example simulations provided on GitHub.