7 Inorganic Phosphorus

7.1 Contributors

Matthew R. Hipsey, Peisheng Huang, and Cayelan C. Carey

7.2 Overview

Phosphorus is a critically-important element in aquatic ecosystems. Many empirical studies have demonstrated that phosphorus can be the primary limiting nutrient for phytoplankton growth and thus is fundamental to determining water quality in freshwater, estuarine, and marine ecosystems. PO43- is the primary inorganic form of phosphorus that is taken up by microbes and aquatic plants (phytoplankton and macrophytes) to build biomass as organic phosphorus. Given that phosphorus is a core building block of an aquatic ecosystem, aed_phosphorus (\(\mathrm{PHS}\)) is designed as a low-level module for managing inorganic phosphorus cycling, and is able to be linked to by higher order modules associated with primary production (described in the Phytoplankton chapter in this book), and organic matter breakdown (described in the Organic Matter chapter in this book).

The general phosphorus processes specifically resolved in this module are sorption/desorption, atmospheric deposition, dissolved sediment flux, and sedimentation and resuspension.

7.3 Model Description

This module supports one state variable to capture the dissolved phosphate concentration, \(PO_4\) (also referred to as Filterable Reactive Phosphorus, \(FRP\)), and optionally users can account for sorbed phosphate, denoted \(PO_4^{ads}\). The module is a low-level module that supports the processes shaping inorganic phosphorus dynamics and is designed to be linked to by other modules that interact with phosphate. The dynamics of \(PO_4\) are summarised as:

\[\begin{eqnarray} \frac{D}{Dt}PO_4 = \color{darkgray}{ \mathbb{M} + \mathcal{S} } \quad &+& \overbrace{\check{f}_{wetdep}^{frp}+\hat{f}_{sed}^{frp} - f_{sorp}^{frp} }^\text{aed_phosphorus} \\ \tag{7.1} &+& \color{brown}{ f_{min}^{DOP} - f_{gpp}^{PHY}- f_{gpp}^{MAG} } \\ \nonumber \end{eqnarray}\]

where \(\mathbb{M}\) and \(\mathcal{S}\) refer to water mixing and boundary source terms, respectively, and the coloured \(\color{brown}{f}\) terms reflect the optionally configurable contributions from other modules; these include the breakdown of \(DOP\) by aerobic heterotrophic bacteria to \(PO_4\), and photosynthetic phosphate uptake by phytoplankton and macroalgae.

The sorbed \(PO_4\) pool is resolved as:

\[\begin{eqnarray} \frac{D}{Dt}PO_4^{ads} = \color{darkgray}{ \mathbb{M} + \mathcal{S} } \quad &+& \overbrace{\check{f}_{drydep}^{pip}+\hat{f}_{resus}^{pip} + f_{sorp}^{frp} - f_{set}^{pip} }^\text{aed_phosphorus} \\ \tag{7.2} \end{eqnarray}\]

7.3.1 Process Descriptions

In the basic phosphorus module configuration, \(FRP\) and \(FRP-ads\) are able to be modified by sorption/desorption, atmospheric deposition (wet and dry fall), dissolved sediment release and settling and resuspension of adsorbed phosphorus. The specific equations for these processes are summarised below.

7.3.1.1 Phosphate sorption - desorption

If the user optionally chooses to include an adsorbed PO4 pool, then the model allows for simulation of partitioning between the dissolved pool and a selected sorbent. The sorption processes is assumed to be at equilibrium within a modelled time-step and so is not included as a kinetic term in the model ODE solution (as suggested in Eq X), but rather is solved and applied at the end of the time-step integration.

The amount of PO4 that can sorb onto the chosen particle group can be computed based on one of several sorption equation options.

For reporting, the term \(f_{sorp}^{frp}\) is computed as …/dt.

7.3.1.2 Atmospheric deposition

Inorganic phosphorus can be added to the surface cells of an aquatic system through two kinds of atmospheric deposition: wet (as FRP) and dry (as sorbed FRP). These functions can be turned on by setting the parameters simDryDeposition and simWetDeposition to .TRUE. in the phosphorus AED module.

7.3.1.3 Dissolved sediment flux

PO43- can flux into the water column from the sediment, using the parameter \(F_{sed}^{frp}\), which sets the maximum flux rate. The maximum flux rate is limited by temperature, using the parameter theta_sed_frp, according to

\[\begin{equation} f_{sed}^{FRP}=F_{sed}^{frp} \theta_{sedfrp}^{T-20}\Phi_{O2}^{frp}\left[O_2\right] \tag{7.3} \end{equation}\]

This assumes that there is a higher flux at higher temperatures.

Oxygen mediation of the sediment phosphorus flux: The sediment flux can be changed by bottom water O2 concentration. If the aed_oxygen module is correctly linked to the phosphorus module then this setting will switch on automatically. The parameter K_sed_frp can be used to tune the PO43- flux dependence on bottom water O2. At high O2 concentrations, PO43- flux decreases, and at low O2 concentrations, the flux is close to the parameter F_{sed}^{frp}, as shown by the equation below.

\[\begin{equation} \Phi_{O2}^{frp}\left[O_2\right]=\frac{K_{sedfrp}}{K_{sedfrp}+O_2} \tag{7.4} \end{equation}\]

7.3.1.4 Sedimentation and resuspension

7.3.3 Feedbacks to the Host Model

The inorganic phosphorus module has no feedbacks to the host hydrodynamic model.

7.3.4 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 7.1. The diagnostic outputs able to be output are summarised in Table 7.2.

State variables

Table 7.1: Phosphorus - state variables
AED name Symbol Description Unit Type Typical Range Comments
aed_phosphorus
PHS_frp \[\mathbf{PO_4}\] dissolved phosphate concentration \[\small{mmol\:P/m^3}\] pelagic 0 - 10 .
PHS_frp_ads \[\mathbf{PO_4^{ads}}\] adsorped phosphate concentration \[\small{mmol\:P/m^3}\] pelagic 0 - 10 activated when simPO4Adsorption=T
Dependent variables
OXY_oxy \[\mathbf{O_2}\] dissolved oxygen concentration \[\small{mmol\: O_2/m^3}\] pelagic 0 - 500 optional for sediment release, via phosphorus_reactant_variable
SDF_Fsed_frp \[\mathbf{F}_{sed}^{frp}\] sediment \(PO_4\) flux \[\small{mmol \:P/m^2/s}\] benthic 0 - 10 spatial sediment flux set via Fsed_frp_variable; read and output as /day, but internally used as /s
NCS_ssX (or TSS) \[\mathbf{SS}\] suspended particulate matter concentration (linked variable or externally provided) \[\small{g/m^3}\] pelagic 0 - 200 required for sorption, set po4sorption_target_variable
NCS_ss1_vvel \[\mathbf{V_{ss1}}\] sedimentation velocity of particulate matter \[\small{m/s}\] pelagic -0.001 - 0.0001 automatically linked when w_po4ads = -999.9 .
CAR_pH \[pH\] pH of water \[\small{-}\] pelagic 2 - 12 optional for sorption, via pH_variable

Diagnostics

Table 7.2: Phosphorus - diagnostic variables
AED name Symbol Description Unit Type Typical Range Comments
diag_level = 0+
PHS_atm_dip_flux \[\mathbf{\mathcal{F}}_{atm}^{dip}\] \(DIP\) (\(PO_4 + PO_4^{ads}\)) atmospheric deposition flux \[\small{mmol\: P/m^2/d}\] surface 0 - 50 activated when simWetDeposition=T or simDryDeposition=T
diag_level = 2+
PHS_sed_frp \[\mathbf{\mathcal{F}}_{sed}^{frp}\] \(PO_4\) exchange across sediment-water interface \[\small{mmol\: P/m^2/d}\] benthic 0 - 50 .


7.3.5 Parameter Summary

The parameters and settings used by this module are summarised in Table 7.3.

Table 7.3: Phosphorus module parameters and configuration options
AED name Symbol Description Unit Type Typical Range Comments
Initialisation
frp_initial \[PO_4|_{t=0}\] initial \(PO_4\) concentration \[\small{mmol\: P/m^3}\] float 0 - 100 can be overwritten by initial condition files
frp_min \[PO_4\rfloor_{min}\] minimum \(PO_4\) concentration \[\small{mmol\: P/m^3}\] float 0 optional limitier
frp_max \[PO_4\rceil^{max}\] maximum \(PO_4\) concentration \[\small{mmol\: P/m^3}\] float 100 optional limitier
Sediment exchange
Fsed_frp \[F_{sed}^{frp}\] sediment \(PO_4\) flux at \(20^{\circ}C\) \[\small{mmol\: P/m^2/d}\] float -30 - 30 .
Ksed_frp \[K_{frp}^{oxy}\] half-saturation oxygen conc. controlling \(O_2\) flux \[\small{mmol\: O_2/m^3}\] float 20 - 100 .
theta_sed_frp \[\theta_{sed}^{frp}\] Arrhenius temperature multiplier for sediment \(O_2\) flux \[\small{-}\] float 1.0 - 1.2 .
phosphorus_reactant_variable \[O_2\] state variable used to control \(PO_4\) sediment release \[\small{-}\] string OXY_oxy optional link for oxygen control on sediment \(PO_4\) release
Fsed_frp_variable variable name to link to for spatially resolved sediment zones \[\small{-}\] string SDF_Fsed_frp optional link to enable spatially resolved fluxes
Sorption
simPO4Adsorption \[\Theta_{frp}^{sorption}\] option to allow include absorption \[\small{-}\] boolean T or F .
ads_use_external_tss option to use externally simulated \(TSS\) concentration as sorbent \[\small{-}\] boolean T or F if an external TSS variable is linked, this can be used for sorption
po4sorption_target_variable variable name to link to for \(PO_4\) sorbent \[\small{-}\] string NCS_ss1 or GEO_FeOH3 select variable of choice
PO4AdsorptionModel \[\Theta_{frp}^{sorption}\] selection of \(PO_4\) sorption method \[\small{-}\] integer 1 , 2 1: Ji (2008); 2: Chao et al. (2010)
Kpo4p \[K_{p}^{po4}\] sorption partitioning coefficient \[\small{m^3/g}\] float 0.01 - 0.1 .
Kadsratio \[K\] ratio of adsorption and desorp-tion rate coefficients (for \(\Theta_{frp}^{sorption}=2\)) \[\small{l/mg}\] float 0.7 see Chao et al. (2010)
Qmax \[Q_{max}\] maximum adsorption capacity (for \(\Theta_{frp}^{sorption}=2\)) \[\small{mg\:/mg\:SS}\] float 0.004 - 0.006 see Chao et al. (2010)
w_po4ads \[\omega_{po4-ads}\] sedimentation velocity of \(PO_4^{ads}\) \[\small{m/d}\] float -0.01 .
ads_use_pH option to include pH control on sorption coefficient \[\small{-}\] boolean T or F function based on pH sorption control on Fe minerals
pH_variable \[pH\] variable name to link to for pH to influence sorption \[\small{-}\] string CAR_pH .
Atmospheric exchange
simDryDeposition \[\Theta_{frp-ads}^{drydep}\] option to include dry (particulate) deposition of P \[\small{-}\] boolean T or F .
atm_pip_dd \[F_{pip}^{atm}\] \(PO_4^{ads}\) deposition rate \[\small{mmol\: P/m^2/d}\] float 0 - 10 .
simWetDeposition \[\Theta_{frp}^{wetdep}\] option to include wet deposition of P through rainfall \[\small{m}\] boolean T or F .
atm_frp_conc \[PO_4^{atm}\] \(PO_4\) concentration in rainfall \[\small{mmol\: P/m^3}\] float 0 - 2 .


7.4 Setup & Configuration

An example aed.nml parameter specification block for the aed_phosphorus module that is modelling dissolved and particulare (sorbed) \(PO_4\) is shown below:

  &aed_phosphorus
    !-- Initial value
     frp_initial          = 0.25
    !-- Sediment flux
     Fsed_frp             = 0.08
     Ksed_frp             = 30.0
     theta_sed_frp        = 1.08
     phosphorus_reactant_variable ='OXY_oxy'
    !-- PO4 adsorption
     simPO4Adsorption     = .true.
     ads_use_external_tss = .true.
     PO4AdsorptionModel   = 1
     Kpo4p                = 0.01
     w_po4ads             = -0.01
  /


An example aed.nml parameter specification block for the aed_phosphorus module that includes all options is shown below:

  &aed_phosphorus
    !-- Initial value
     frp_initial = 0.25
    !-- Sediment flux
     Fsed_frp = 0.08
     Ksed_frp = 30.0
     theta_sed_frp = 1.08
     phosphorus_reactant_variable ='OXY_oxy'
     Fsed_frp_variable ='SDF_Fsed_frp'
    !-- PO4 adsorption
     simPO4Adsorption = .true.
     ads_use_external_tss = .false.
     po4sorption_target_variable ='NCS_ss1'
     PO4AdsorptionModel = 2
     Kpo4p = 0.01
     Kadsratio= 1.0
     Qmax = 1.0
     w_po4ads = -9999     ! Note: -9999 links PO4-ad settling to target_variable
     ads_use_pH = .false.
     pH_variable = 'CAR_pH'
    !-- Atmospheric deposition
     simDryDeposition = .false.
     atm_pip_dd = 0.00
     simWetDeposition = .true.
     atm_frp_conc = 0.01
  /

7.5 Case Studies & Examples

7.5.1 Case Study: Falling Creek Reservoir

Falling Creek Reservoir (FCR) is a eutrophic, drinking water supply reservoir located outside of Roanoke, Virginia, USA. In the summer months, FCR will quickly exhibit hypolimnetic anoxia after the onset of thermal stratification. To manage anoxia, managers deployed a hypolimnetic oxygenation system in FCR in which water is extracted from ~1 m above the sediment onshore, where super-saturated oxygen is injected into the water before it is returned to the hypolimnion at the same depth and temperature. Consequently, the hypolimnion of FCR experiences a wide range of oxygen conditions throughout the year, which have dramatic effects on phosphorus fluxes from the sediment.

Carey et al. (2022) analyzed the effect of oxygenation on phosphorus cycling in FCR over seven years, and used the aed_phosphorus model with the GLM hydrodynamic model to simulate the large temporal variability in phosphorus concentrations experienced under contrasting oxygenation conditions.

Figure 1: Modeled (black line) vs. observed (red points) total phosphorus (TP, left panel) and dissolved reactive phosphorus (DRP) in the hypolimnion of Falling Creek Reservoir, USA.

As evident from Figure 1, the model was generally able to recreate dissolved and total phosphorus dynamics in FCR (Carey et al. 2022). Carey et al. (2022) also used the validated model to explore the effects of anoxia on coupled biogeochemical cycling in the reservoir based on different oxygenation scenarios.

7.5.2 Publications

Author/Year Paper Title Description

Ladwig et al. (2021)

Lake thermal structure drives interannual variability in summer anoxia dynamics in a eutrophic lake over 37 years.

 NA

Carey et al. (2022)

Anoxia decreases the magnitude of the carbon, nitrogen, and phosphorus sink in freshwaters

 NA

Farrell et al. (2020)

Ecosystem-scale nutrient cycling responses to increasing air temperatures vary with lake trophic state

 NA

Ward et al. (2020)

Differential responses of maximum and median chlorophyll-a to air temperature and nutrient load in a 31-year oligotrophic lake simulation

 NA