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functional_dependencies.Rmd
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functional_dependencies.Rmd
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---
title: "Summary of functional dependencies"
author: "Beni Stocker"
output:
rmarkdown::html_vignette:
md_extensions: ["-autolink_bare_uris"]
vignette: >
%\VignetteEngine{knitr::knitr}
%\usepackage[utf8]{inputenc}
%\VignetteIndexEntry{Summary of functional dependencies}
---
```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE, warning = FALSE, message = FALSE)
library(dplyr)
library(ggplot2)
library(rpmodel)
```
Functional dependencies in the model exposed and visualized!
## C3 Photosynthesis
### Temperature
At constant conditions (VPD = 300 Pa, CO2 = 400 ppm, fAPAR = 1, PPFD = 30 mol m-2 d-1, elevation = 0 m a.s.l.)
```{r}
out_ts <- rpmodel::rpmodel(
tc = seq(10, 30, by = 1),
vpd = 300,
co2 = 400,
fapar = 1,
ppfd = 30,
elv = 0,
c4 = FALSE,
do_ftemp_kphio = FALSE,
do_soilmstress = FALSE
) %>%
as_tibble() %>%
mutate(setup = "ORG",
tc = seq(10, 30, by = 1)) %>%
bind_rows(
rpmodel::rpmodel(
tc = seq(10, 30, by = 1),
vpd = 300,
co2 = 400,
fapar = 1,
ppfd = 30,
elv = 0,
c4 = FALSE,
do_ftemp_kphio = TRUE,
do_soilmstress = FALSE
) %>%
as_tibble() %>%
mutate(setup = "BRC",
tc = seq(10, 30, by = 1))
)
out_ts %>%
ggplot(aes(x = tc, y = gpp, color = setup)) +
geom_line() +
labs(x = "Temperature (deg C)", y = "GPP (g m-2 d-1)")
out_ts %>%
ggplot(aes(x = tc, y = chi, color = setup)) +
geom_line() +
labs(x = "Temperature (deg C)", y = "chi")
out_ts %>%
ggplot(aes(x = tc, y = vcmax, color = setup)) +
geom_line() +
labs(x = "Temperature (deg C)", y = "Vcmax (g m-2 d-1)")
```
### VPD
At constant conditions (T = 20 deg C, CO2 = 400 ppm, fAPAR = 1, PPFD = 30 mol m-2 d-1, elevation = 0 m a.s.l.)
```{r}
out_ts <- rpmodel::rpmodel(
tc = 20,
vpd = seq(0, 4000, by = 50),
co2 = 400,
fapar = 1,
ppfd = 30,
elv = 0,
c4 = FALSE,
do_ftemp_kphio = FALSE,
do_soilmstress = FALSE
) %>%
as_tibble() %>%
mutate(setup = "ORG",
vpd = seq(0, 4000, by = 50)) %>%
bind_rows(
rpmodel::rpmodel(
tc = 20,
vpd = seq(0, 4000, by = 50),
co2 = 400,
fapar = 1,
ppfd = 30,
elv = 0,
c4 = FALSE,
do_ftemp_kphio = TRUE,
do_soilmstress = FALSE
) %>%
as_tibble() %>%
mutate(setup = "BRC",
vpd = seq(0, 4000, by = 50))
)
out_ts %>%
ggplot(aes(x = vpd, y = gpp, color = setup)) +
geom_line() +
labs(x = "VPD (Pa)", y = "GPP (g m-2 d-1)")
out_ts %>%
ggplot(aes(x = vpd, y = chi, color = setup)) +
geom_line() +
labs(x = "VPD (Pa)", y = "chi")
out_ts %>%
ggplot(aes(x = vpd, y = vcmax, color = setup)) +
geom_line() +
labs(x = "VPD (Pa)", y = "Vcmax (g m-2 d-1)")
```
### PPFD
At constant conditions (T = 20 deg C, VPD = 300 Pa, CO2 = 400 ppm, fAPAR = 1, elevation = 0 m a.s.l.)
```{r}
out_ts <- rpmodel::rpmodel(
tc = 20,
vpd = 300,
co2 = 400,
fapar = 1,
ppfd = seq(1, 50, by = 1),
elv = 0,
c4 = FALSE,
do_ftemp_kphio = FALSE,
do_soilmstress = FALSE
) %>%
as_tibble() %>%
mutate(setup = "ORG",
ppfd = seq(1, 50, by = 1)) %>%
bind_rows(
rpmodel::rpmodel(
tc = 20,
vpd = 300,
co2 = 400,
fapar = 1,
ppfd = seq(1, 50, by = 1),
elv = 0,
c4 = FALSE,
do_ftemp_kphio = TRUE,
do_soilmstress = FALSE
) %>%
as_tibble() %>%
mutate(setup = "BRC",
ppfd = seq(1, 50, by = 1))
)
out_ts %>%
ggplot(aes(x = ppfd, y = gpp, color = setup)) +
geom_line() +
labs(x = "PPFD (mol m-2 d-1)", y = "GPP (g m-2 d-1)")
out_ts %>%
ggplot(aes(x = ppfd, y = chi, color = setup)) +
geom_line() +
labs(x = "PPFD (mol m-2 d-1)", y = "chi")
out_ts %>%
ggplot(aes(x = ppfd, y = vcmax, color = setup)) +
geom_line() +
labs(x = "PPFD (mol m-2 d-1)", y = "Vmax (g m-2 d-1)")
```
### Atmospheric pressure
At constant conditions (T = 20 deg C, VPD = 300 Pa, CO2 = 400 ppm, fAPAR = 1, PPFD = 30 mol m-2 d-1)
```{r}
calc_patm <- function( elv, patm0 = 101325 ){
# Define constants:
kTo <- 298.15 # base temperature, K (Prentice, unpublished)
kL <- 0.0065 # adiabiatic temperature lapse rate, K/m (Allen, 1973)
kG <- 9.80665 # gravitational acceleration, m/s^2 (Allen, 1973)
kR <- 8.3145 # universal gas constant, J/mol/K (Allen, 1973)
kMa <- 0.028963 # molecular weight of dry air, kg/mol (Tsilingiris, 2008)
# Convert elevation to pressure, Pa:
patm <- patm0*(1.0 - kL*elv/kTo)^(kG*kMa/(kR*kL))
return(patm)
}
out_ts <- rpmodel::rpmodel(
tc = 20,
vpd = 300,
co2 = 400,
fapar = 1,
ppfd = 30,
patm = calc_patm(seq(0, 4000, by = 40)),
c4 = FALSE,
do_ftemp_kphio = FALSE,
do_soilmstress = FALSE
) %>%
as_tibble() %>%
mutate(setup = "ORG",
patm = calc_patm(seq(0, 4000, by = 40))) %>%
bind_rows(
rpmodel::rpmodel(
tc = 20,
vpd = 300,
co2 = 400,
fapar = 1,
ppfd = 30,
patm = calc_patm(seq(0, 4000, by = 40)),
c4 = FALSE,
do_ftemp_kphio = TRUE,
do_soilmstress = FALSE
) %>%
as_tibble() %>%
mutate(setup = "BRC",
patm = calc_patm(seq(0, 4000, by = 40)))
)
out_ts %>%
ggplot(aes(x = patm, y = gpp, color = setup)) +
geom_line() +
labs(x = "P (Pa)", y = "GPP (g m-2 d-1)")
out_ts %>%
ggplot(aes(x = patm, y = chi, color = setup)) +
geom_line() +
labs(x = "P (Pa)", y = "chi")
out_ts %>%
ggplot(aes(x = patm, y = vcmax, color = setup)) +
geom_line() +
labs(x = "P (Pa)", y = "Vcmax (g m-2 d-1)")
```
## C4 Photosynthesis
### Temperature
At constant conditions (VPD = 300 Pa, CO2 = 400 ppm, fAPAR = 1, PPFD = 30 mol m-2 d-1, elevation = 0 m a.s.l.)
```{r}
out_ts <- rpmodel::rpmodel(
tc = seq(10, 30, by = 1),
vpd = 300,
co2 = 400,
fapar = 1,
ppfd = 30,
elv = 0,
c4 = TRUE,
do_ftemp_kphio = FALSE,
do_soilmstress = FALSE
) %>%
as_tibble() %>%
mutate(setup = "ORG",
tc = seq(10, 30, by = 1)) %>%
bind_rows(
rpmodel::rpmodel(
tc = seq(10, 30, by = 1),
vpd = 300,
co2 = 400,
fapar = 1,
ppfd = 30,
elv = 0,
c4 = TRUE,
do_ftemp_kphio = TRUE,
do_soilmstress = FALSE
) %>%
as_tibble() %>%
mutate(setup = "BRC",
tc = seq(10, 30, by = 1))
)
out_ts %>%
ggplot(aes(x = tc, y = gpp, color = setup)) +
geom_line() +
labs(x = "Temperature (deg C)", y = "GPP (g m-2 d-1)")
out_ts %>%
ggplot(aes(x = tc, y = chi, color = setup)) +
geom_line() +
labs(x = "Temperature (deg C)", y = "chi")
out_ts %>%
ggplot(aes(x = tc, y = vcmax, color = setup)) +
geom_line() +
labs(x = "Temperature (deg C)", y = "Vcmax (g m-2 d-1)")
```
### VPD
At constant conditions (T = 20 deg C, CO2 = 400 ppm, fAPAR = 1, PPFD = 30 mol m-2 d-1, elevation = 0 m a.s.l.)
```{r}
out_ts <- rpmodel::rpmodel(
tc = 20,
vpd = seq(0, 4000, by = 50),
co2 = 400,
fapar = 1,
ppfd = 30,
elv = 0,
c4 = TRUE,
do_ftemp_kphio = FALSE,
do_soilmstress = FALSE
) %>%
as_tibble() %>%
mutate(setup = "ORG",
vpd = seq(0, 4000, by = 50)) %>%
bind_rows(
rpmodel::rpmodel(
tc = 20,
vpd = seq(0, 4000, by = 50),
co2 = 400,
fapar = 1,
ppfd = 30,
elv = 0,
c4 = TRUE,
do_ftemp_kphio = TRUE,
do_soilmstress = FALSE
) %>%
as_tibble() %>%
mutate(setup = "BRC",
vpd = seq(0, 4000, by = 50))
)
out_ts %>%
ggplot(aes(x = vpd, y = gpp, color = setup)) +
geom_line() +
labs(x = "VPD (Pa)", y = "GPP (g m-2 d-1)")
out_ts %>%
ggplot(aes(x = vpd, y = chi, color = setup)) +
geom_line() +
labs(x = "VPD (Pa)", y = "chi")
out_ts %>%
ggplot(aes(x = vpd, y = vcmax, color = setup)) +
geom_line() +
labs(x = "VPD (Pa)", y = "Vcmax (g m-2 d-1)")
```
### PPFD
At constant conditions (T = 20 deg C, VPD = 300 Pa, CO2 = 400 ppm, fAPAR = 1, elevation = 0 m a.s.l.)
Varying PPFD from 1 to 50 mol m-2 d-1.
```{r}
out_ts <- rpmodel::rpmodel(
tc = 20,
vpd = 300,
co2 = 400,
fapar = 1,
ppfd = seq(1, 50, by = 1),
elv = 0,
c4 = TRUE,
do_ftemp_kphio = FALSE,
do_soilmstress = FALSE
) %>%
as_tibble() %>%
mutate(setup = "ORG",
ppfd = seq(1, 50, by = 1)) %>%
bind_rows(
rpmodel::rpmodel(
tc = 20,
vpd = 300,
co2 = 400,
fapar = 1,
ppfd = seq(1, 50, by = 1),
elv = 0,
c4 = TRUE,
do_ftemp_kphio = TRUE,
do_soilmstress = FALSE
) %>%
as_tibble() %>%
mutate(setup = "BRC",
ppfd = seq(1, 50, by = 1))
)
out_ts %>%
ggplot(aes(x = ppfd, y = gpp, color = setup)) +
geom_line() +
labs(x = "PPFD (mol m-2 d-1)", y = "GPP (g m-2 d-1)")
out_ts %>%
ggplot(aes(x = ppfd, y = chi, color = setup)) +
geom_line() +
labs(x = "PPFD (mol m-2 d-1)", y = "chi")
out_ts %>%
ggplot(aes(x = ppfd, y = vcmax, color = setup)) +
geom_line() +
labs(x = "PPFD (mol m-2 d-1)", y = "Vmax (g m-2 d-1)")
```
### Atmospheric pressure
At constant conditions (T = 20 deg C, VPD = 300 Pa, CO2 = 400 ppm, fAPAR = 1, PPFD = 30 mol m-2 d-1)
```{r}
calc_patm <- function( elv, patm0 = 101325 ){
# Define constants:
kTo <- 298.15 # base temperature, K (Prentice, unpublished)
kL <- 0.0065 # adiabiatic temperature lapse rate, K/m (Allen, 1973)
kG <- 9.80665 # gravitational acceleration, m/s^2 (Allen, 1973)
kR <- 8.3145 # universal gas constant, J/mol/K (Allen, 1973)
kMa <- 0.028963 # molecular weight of dry air, kg/mol (Tsilingiris, 2008)
# Convert elevation to pressure, Pa:
patm <- patm0*(1.0 - kL*elv/kTo)^(kG*kMa/(kR*kL))
return(patm)
}
out_ts <- rpmodel::rpmodel(
tc = 20,
vpd = 300,
co2 = 400,
fapar = 1,
ppfd = 30,
patm = calc_patm(seq(0, 4000, by = 40)),
c4 = TRUE,
do_ftemp_kphio = FALSE,
do_soilmstress = FALSE
) %>%
as_tibble() %>%
mutate(setup = "ORG",
patm = calc_patm(seq(0, 4000, by = 40))) %>%
bind_rows(
rpmodel::rpmodel(
tc = 20,
vpd = 300,
co2 = 400,
fapar = 1,
ppfd = 30,
patm = calc_patm(seq(0, 4000, by = 40)),
c4 = TRUE,
do_ftemp_kphio = TRUE,
do_soilmstress = FALSE
) %>%
as_tibble() %>%
mutate(setup = "BRC",
patm = calc_patm(seq(0, 4000, by = 40)))
)
out_ts %>%
ggplot(aes(x = patm, y = gpp, color = setup)) +
geom_line() +
labs(x = "P (Pa)", y = "GPP (g m-2 d-1)")
out_ts %>%
ggplot(aes(x = patm, y = chi, color = setup)) +
geom_line() +
labs(x = "P (Pa)", y = "chi")
out_ts %>%
ggplot(aes(x = patm, y = vcmax, color = setup)) +
geom_line() +
labs(x = "P (Pa)", y = "Vcmax (g m-2 d-1)")
```
### Temperature-dependence of quantum yield
```{r}
ftemp_c3_stocker <- function(...){0.081785 * ftemp_kphio(...)}
ftemp_c3_caiprentice <- function(tc){0.044 + 0.00275 * tc - 0.425e-4 * tc^2}
ggplot() +
geom_function(fun = ftemp_c3_stocker, args = list(c4 = FALSE)) +
geom_function(fun = ftemp_c3_caiprentice, color = "royalblue") +
xlim(0, 30) +
ylim(0, 0.1) +
labs(x = expression(paste("Temperature (", degree, "C)")), y = expression(varphi),
title = "Temperature dependence of quantum yield of C3 photosynthesis (BRC setup)",
subtitle = "Black: Stocker et al., 2020 | Blue: Cai & Prentice, 2020")
ftemp_c4_stocker <- function(...){1.0 * ftemp_kphio(...)}
ftemp_c4_caiprentice <- function(tc){-0.064 + 0.03 * tc - 0.000464 * tc^2 }
ggplot() +
geom_function(fun = ftemp_c4_stocker, args = list(c4 = TRUE), size = 2) +
geom_function(fun = ftemp_c4_caiprentice, color = "royalblue") +
xlim(0, 30) +
labs(x = expression(paste("Temperature (", degree, "C)")), y = expression(varphi),
title = "Temperature dependence of quantum yield of C4 photosynthesis (BRC setup)",
subtitle = "Black: Stocker et al., 2020 | Blue: Cai & Prentice, 2020")
```