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13-phosphorous.Rmd
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13-phosphorous.Rmd
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# Inorganic Phosphorus
## Contributors
Matthew R. Hipsey, Peisheng Huang, and Cayelan C. Carey
## 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. PO~4~^3-^ 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.
## 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} \\ (\#eq:phs1)
&+& \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} \\ (\#eq:phs2)
\end{eqnarray}
### 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.
#### 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.
#### 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.
#### Dissolved sediment flux
PO~4~^3-^ 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]
(\#eq:phs3)
\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 O~2~ concentration. If the [aed_oxygen module](#DO_1) 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 PO~4~^3-^ flux dependence on bottom water O~2~. At high O~2~ concentrations, PO~4~^3-^ flux decreases, and at low O~2~ concentrations, the flux is close to the parameter `F_{sed}^{frp}`, as shown by the equation below.
```{=tex}
\begin{equation}
\Phi_{O2}^{frp}\left[O_2\right]=\frac{K_{sedfrp}}{K_{sedfrp}+O_2}
(\#eq:phs4)
\end{equation}
```
#### Sedimentation and resuspension
### Optional Module Links
Other phosphate sources/sinks are indicated in Eq \@ref(eq:phs1) for $PO_4$. These include:
- aed_oxygen: Oxygen is used to control the rate of sediment release of phosphate.
- aed_carbon: pH can used to influence the sorption dynamics of phosphate.
- aed_organic_matter: organic matter minerization replenishes $PO_4$.
- aed_phytoplankton: phytoplankton photosynthesis consumes $PO_4$.
- aed_geochemistry: optional link to simulate the phosphate precipitation.
- aed_sedflux: modules to update the sediment-water exchange rate of $PO_4$.
### Feedbacks to the Host Model
The inorganic phosphorus module has no feedbacks to the host hydrodynamic model.
### 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 \@ref(tab:13-statetable). The diagnostic outputs able to be output are summarised in Table \@ref(tab:13-diagtable).
#### State variables {-}
```{r 13-statetable, echo=FALSE, message=FALSE, warning=FALSE}
library(knitr)
library(kableExtra)
library(readxl)
library(rmarkdown)
theSheet <- read_excel('tables/aed_variable_tables.xlsx', sheet = 8)
theSheet <- theSheet[theSheet$Table == "State variable",]
theSheetGroups <- unique(theSheet$Group)
theSheet$`AED name` <- paste0("`",theSheet$`AED name`,"`")
for(i in seq_along(theSheet$Symbol)){
if(!is.na(theSheet$Symbol[i])==TRUE){
theSheet$Symbol[i] <- paste0("$$",theSheet$Symbol[i],"$$")
} else {
theSheet$Symbol[i] <- NA
}
}
for(i in seq_along(theSheet$Unit)){
if(!is.na(theSheet$Unit[i])==TRUE){
theSheet$Unit[i] <- paste0("$$\\small{",theSheet$Unit[i],"}$$")
} else {
theSheet$Unit[i] <- NA
}
}
for(i in seq_along(theSheet$Comments)){
if(!is.na(theSheet$Comments[i])==TRUE){
theSheet$Comments[i] <- paste0("",theSheet$Comments[i],"")
} else {
theSheet$Comments[i] <- " "
}
}
kbl(theSheet[,3:NCOL(theSheet)], caption = "Phosphorus - *state* variables", align = "l",) %>%
pack_rows(theSheetGroups[1],
min(which(theSheet$Group == theSheetGroups[1])),
max(which(theSheet$Group == theSheetGroups[1])),
background = '#ebebeb') %>%
pack_rows(theSheetGroups[2],
min(which(theSheet$Group == theSheetGroups[2])),
max(which(theSheet$Group == theSheetGroups[2])),
background = '#ebebeb') %>%
row_spec(0, background = "#14759e", bold = TRUE, color = "white") %>%
kable_styling(full_width = F,font_size = 11) %>%
column_spec(2, width_min = "7em") %>%
column_spec(3, width_max = "18em") %>%
column_spec(4, width_min = "10em") %>%
column_spec(5, width_min = "5em") %>%
column_spec(7, width_min = "10em") %>%
column_spec(7, width_max = "20em") %>%
scroll_box(width = "770px", height = "465px",
fixed_thead = FALSE)
```
#### Diagnostics{-}
```{r 13-diagtable, echo=FALSE, message=FALSE, warning=FALSE}
library(knitr)
library(kableExtra)
library(readxl)
library(rmarkdown)
theSheet <- read_excel('tables/aed_variable_tables.xlsx', sheet = 8)
theSheet <- theSheet[theSheet$Table == "Diagnostics",]
theSheetGroups <- unique(theSheet$Group)
theSheet$`AED name` <- paste0("`",theSheet$`AED name`,"`")
for(i in seq_along(theSheet$Symbol)){
if(!is.na(theSheet$Symbol[i])==TRUE){
theSheet$Symbol[i] <- paste0("$$",theSheet$Symbol[i],"$$")
} else {
theSheet$Symbol[i] <- NA
}
}
for(i in seq_along(theSheet$Unit)){
if(!is.na(theSheet$Unit[i])==TRUE){
theSheet$Unit[i] <- paste0("$$\\small{",theSheet$Unit[i],"}$$")
} else {
theSheet$Unit[i] <- NA
}
}
for(i in seq_along(theSheet$Comments)){
if(!is.na(theSheet$Comments[i])==TRUE){
theSheet$Comments[i] <- paste0("",theSheet$Comments[i],"")
} else {
theSheet$Comments[i] <- " "
}
}
kbl(theSheet[,3:NCOL(theSheet)], caption = "Phosphorus - *diagnostic* variables", align = "l",) %>%
pack_rows(theSheetGroups[1],
min(which(theSheet$Group == theSheetGroups[1])),
max(which(theSheet$Group == theSheetGroups[1])),
background = '#ebebeb') %>%
pack_rows(theSheetGroups[2],
min(which(theSheet$Group == theSheetGroups[2])),
max(which(theSheet$Group == theSheetGroups[2])),
background = '#ebebeb') %>%
row_spec(0, background = "#14759e", bold = TRUE, color = "white") %>%
kable_styling(full_width = F,font_size = 11) %>%
column_spec(2, width_min = "7em") %>%
column_spec(3, width_max = "18em") %>%
column_spec(4, width_min = "10em") %>%
column_spec(5, width_min = "6em") %>%
column_spec(7, width_min = "10em") %>%
scroll_box(width = "770px", height = "245px",
fixed_thead = FALSE)
```
<br>
### Parameter Summary
The parameters and settings used by this module are summarised in Table \@ref(tab:13-parstable).
```{r 13-parstable, echo=FALSE, message=FALSE, warning=FALSE}
library(knitr)
library(kableExtra)
library(readxl)
library(rmarkdown)
theSheet <- read_excel('tables/aed_variable_tables.xlsx', sheet = 8)
theSheet <- theSheet[theSheet$Table == "Parameter",]
theSheetGroups <- unique(theSheet$Group)
theSheet$`AED name` <- paste0("`",theSheet$`AED name`,"`")
for(i in seq_along(theSheet$Symbol)){
if(!is.na(theSheet$Symbol[i])==TRUE){
theSheet$Symbol[i] <- paste0("$$",theSheet$Symbol[i],"$$")
} else {
theSheet$Symbol[i] <- " "
}
}
for(i in seq_along(theSheet$Unit)){
if(!is.na(theSheet$Unit[i])==TRUE){
theSheet$Unit[i] <- paste0("$$\\small{",theSheet$Unit[i],"}$$")
} else {
theSheet$Unit[i] <- NA
}
}
for(i in seq_along(theSheet$Comments)){
if(!is.na(theSheet$Comments[i])==TRUE){
theSheet$Comments[i] <- paste0("",theSheet$Comments[i],"")
} else {
theSheet$Comments[i] <- "-"
}
}
kbl(theSheet[,3:NCOL(theSheet)], caption = "Phosphorus module parameters and configuration options", align = "l",) %>%
pack_rows(theSheetGroups[1],
min(which(theSheet$Group == theSheetGroups[1])),
max(which(theSheet$Group == theSheetGroups[1])),
background = '#ebebeb') %>%
pack_rows(theSheetGroups[2],
min(which(theSheet$Group == theSheetGroups[2])),
max(which(theSheet$Group == theSheetGroups[2])),
background = '#ebebeb') %>%
pack_rows(theSheetGroups[3],
min(which(theSheet$Group == theSheetGroups[3])),
max(which(theSheet$Group == theSheetGroups[3])),
background = '#ebebeb') %>%
pack_rows(theSheetGroups[4],
min(which(theSheet$Group == theSheetGroups[4])),
max(which(theSheet$Group == theSheetGroups[4])),
background = '#ebebeb') %>%
row_spec(0, background = "#14759e", bold = TRUE, color = "white") %>%
kable_styling(full_width = F,font_size = 11) %>%
column_spec(2, width_min = "7em") %>%
column_spec(3, width_max = "19em") %>%
column_spec(4, width_min = "10em") %>%
column_spec(5, width_min = "5em") %>%
column_spec(7, width_min = "10em") %>%
scroll_box(width = "770px", height = "1300px",
fixed_thead = FALSE)
```
<br>
## 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:
```{fortran, eval = FALSE}
&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
/
```
<br>
An example `aed.nml` parameter specification block for the `aed_phosphorus` module that includes all options is shown below:
```{fortran, eval = FALSE}
&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
/
```
## Case Studies & Examples
### 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.
<center>
{width=90%}
</center>
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.
### Publications
```{r echo=FALSE, message=FALSE, warning=FALSE}
library(gt)
library(tidyverse)
library(kableExtra)
library(rmarkdown)
aed <- read.csv("tables/13-phosphorus/phosphorus_pubs.csv", check.names=FALSE)
aed %>%
gt() %>%
tab_options(container.height = px(500),
container.width = pct(100),
table.width = pct(100),
container.overflow.y = TRUE,
container.overflow.x = TRUE,
table.font.size = 12,
column_labels.background.color = "#14759e",
row_group.background.color = "lightgrey",
column_labels.font.weight = "bold",
column_labels.font.size = 14) %>%
fmt_markdown(columns = everything())
```