# Coupled leaf gas exchange model

### Description

A coupled photosynthesis - stomatal conductance model, based on the Farquhar model of photosynthesis, and a Ball-Berry type model of stomatatal conductance. Includes options for temperature sensitivity of photosynthetic parameters, dark respiration (optionally calculated from leaf temperature), and mesophyll conductance.

### Usage

1 2 3 4 5 6 7 8 9 10 11 | ```
Photosyn(VPD = 1.5, Ca = 400, PPFD = 1500, Tleaf = 25, Patm = 100,
RH = NULL, gsmodel = c("BBOpti", "BBLeuning", "BallBerry"), g1 = 4,
g0 = 0, gk = 0.5, vpdmin = 0.5, D0 = 5, GS = NULL, alpha = 0.24,
theta = 0.85, Jmax = 100, Vcmax = 50, gmeso = NULL, TPU = 1000,
Rd0 = 0.92, Q10 = 1.92, Rd = NULL, TrefR = 25, Rdayfrac = 1,
EaV = 82620.87, EdVC = 0, delsC = 645.1013, EaJ = 39676.89,
EdVJ = 2e+05, delsJ = 641.3615, GammaStar = NULL, Km = NULL,
Ci = NULL, Tcorrect = TRUE, returnParsOnly = FALSE, whichA = c("Ah",
"Amin", "Ac", "Aj"))
Aci(Ci, ...)
``` |

### Arguments

`VPD` |
Vapour pressure deficit (kPa) (not needed when RH provided) |

`Ca` |
Atmospheric CO2 concentration (ppm) |

`PPFD` |
Photosynthetic photon flux density ('PAR') (mu mol m-2 s-1) |

`Tleaf` |
Leaf temperature (degrees C) |

`Patm` |
Atmospheric pressure (kPa) (but see warning below!) |

`RH` |
Relative humidity (in %) (not needed when VPD provided) |

`gsmodel` |
One of BBOpti (Medlyn et al. 2011), BBLeuning (Leuning 1995), or BallBerry (Ball et al. 1987) |

`g0, g1` |
Parameters of Ball-Berry type stomatal conductance models. |

`gk` |
Optional, exponent of VPD in gs model (Duursma et al. 2013) |

`vpdmin` |
Below vpdmin, VPD=vpdmin, to avoid very high gs. |

`D0` |
Parameter for the BBLeuning stomatal conductance model. |

`GS` |
Optionally, stomatal conductance (to H2O). If provided, |

`alpha` |
Quantum yield of electron transport (mol mol-1) |

`theta` |
Shape of light response curve. |

`Jmax` |
Maximum rate of electron transport at 25 degrees C (mu mol m-2 s-1) |

`Vcmax` |
Maximum carboxylation rate at 25 degrees C (mu mol m-2 s-1) |

`gmeso` |
Mesophyll conductance (mol m-2 s-1). If not NULL (the default), Vcmax and Jmax are chloroplastic rates. |

`TPU` |
Triose-phosphate utilization rate (mu mol m-2 s-1); optional. |

`Rd0` |
Dark respiration rata at reference temperature ( |

`Q10` |
Temperature sensitivity of Rd. |

`Rd` |
Dark respiration rate (mu mol m-2 s-1), optional (if not provided, calculated from Tleaf, Rd0, Q10 and TrefR) |

`TrefR` |
Reference temperature for Rd (Celcius). |

`Rdayfrac` |
Ratio of Rd in the light vs. in the dark. |

`EaV, EdVC, delsC` |
Vcmax temperature response parameters |

`EaJ, EdVJ, delsJ` |
Jmax temperature response parameters |

`Km, GammaStar` |
Optionally, provide Michaelis-Menten coefficient for Farquhar model, and Gammastar. If not provided, they are calculated with a built-in function of leaf temperature. |

`Ci` |
Optional, intercellular CO2 concentration (ppm). If not provided, calculated via gs model. |

`Tcorrect` |
If TRUE, corrects input Vcmax and Jmax for actual Tleaf (if FALSE, assumes the provided Vcmax and Jmax are at the Tleaf provided) |

`returnParsOnly` |
If TRUE, returns calculated Vcmax,Jmax,Km and GammaStar based on leaf temperature. |

`whichA` |
Which assimilation rate does gs respond to? |

`...` |
Further arguments passed to |

### Details

The coupled photosynthesis - stomatal conductance model finds the intersection between the supply of CO2 by diffusion, and the demand for CO2 by photosynthesis. See Farquhar and Sharkey (1982) for basic description of this type of model, Duursma (2015) for more details on the implementation in the `plantecophys`

package, and Duursma et al. (2014) for an example application (that uses this implementation).

The model of Farquhar et al. (1980) is used to estimate the dependence of leaf net photosynthesis rate (ALEAF) on intercellular CO2 concentration (Ci). The temperature response of photosynthetic parameters, including Vcmax, Jmax, Gammastar, and Km follow Medlyn et al. (2002).

At the moment, two stomatal conductance models are implemented, both are Ball-Berry type models. The 'BBOpti' model is a slightly more general form of the model of Medlyn et al. 2011 (see Duursma et al. 2013). It is given by (in notation of the parameters and output variables of `Photosyn`

),

*GS = g0 + 1.6*(1 + g1/D^(1-gk))*ALEAF/CA*

where gk = 0.5 if stomata behave optimally (cf. Medlyn et al. 2011).

The 'BBLeuning' model is that of Leuning (1995). It is given by,

*GS = g0 + g1*ALEAF/(Ca * (1 + VPD/D0))*

Note that this model also uses the g1 parameter, but it needs to be set to a much higher value to be comparable in magnitude to the BBOpti model.

The 'BallBerry' model is that of Ball et al. (1987). It is given by,

*GS = g0 + g1*RH*ALEAF/Ca*

Where RH is relative humidity.

For the full numerical solution to the Cowan-Farquhar optimization, use the `FARAO`

function (which was used in Medlyn et al. 2011 for comparison to the approximation there presented).

If the mesophyll conductance `gmeso`

is provided, it is assumed that Vcmax and Jmax are the chloroplastic rates, and leaf photosynthesis is calculated following Ethier and Livingston (2004).

If Ci is provided as an input, this function calculates an A-Ci curve. Otherwise, Ci is calculated from the intersection between the 'supply' and 'demand', where 'demand' is given by the Farquhar model of photosynthesis (A=f(Ci)), and supply by the stomatal conductance. The latter is, by default, estimated using the stomatal conductance model of Medlyn et al. (2011), but two other models are provided as well (Ball-Berry and Leuning, see `gsmodel`

argument). Otherwise, stomatal conductance may be directly provided via the `GS`

argument.

Note that the function `Aci`

is provided as a shorthand for `Photosyn(Ci=x)`

.

By default, the `Photosyn`

function returns the hyperbolic minimum of Vcmax and Jmax-limited photosynthetic rates. This is to avoid the discontinuity at the transition between the two rates. Both Ac and Aj are also returned should they be needed. Note that those rates are output as gross photosynthetic rates (leaf respiration has to be subtracted to give net leaf photosynthesis).

### Value

Returns a dataframe.

### Atmospheric pressure

A correction for atmospheric pressure (Patm) is implemented in `fitaci`

, but **not in Photosyn**. In `fitaci`

, the necessary corrections are applied so that estimated Vcmax and Jmax are expressed at standard pressure (Patm=100kPa). In Photosyn, however, the corrections are much more complicated and tend to be very small, because effects of Patm on partial pressures are largely offset by increases in diffusivity (Terashima et al. 1995, Gale 1973).

Note that Patm is an argument to the Photosyn function, but it only affects calculations of Km and GammaStar (as used by fitaci), and transpiration rate. Setting only Patm **does not correct for atmospheric pressure effects on photosynthesis rates**.

### References

Duursma, R.A., Payton, P., Bange, M.P., Broughton, K.J., Smith, R.A., Medlyn, B.E., Tissue, D. T., 2013, Near-optimal response of instantaneous transpiration efficiency to vapour pressure deficit, temperature and [CO2] in cotton (Gossypium hirsutum L.). Agricultural and Forest Meteorology 168 : 168 - 176.

Duursma, R.A., Barton, C.V.M., Lin, Y.-S., Medlyn, B.E., Eamus, D., Tissue, D.T., Ellsworth, D.S., McMurtrie, R.E., 2014. The peaked response of transpiration rate to vapour pressure deficit in field conditions can be explained by the temperature optimum of photosynthesis. Agricultural and Forest Meteorology 189 - 190, 2-10. doi:10.1016/j.agrformet.2013.12.007

Duursma, R.A., 2015. Plantecophys - An R Package for Analysing and Modelling Leaf Gas Exchange Data. PLoS ONE 10, e0143346. doi:10.1371/journal.pone.0143346

Ethier, G. and N. Livingston. 2004. On the need to incorporate sensitivity to CO2 transfer conductance into the Farquhar von Caemmerer Berry leaf photosynthesis model. Plant, Cell & Environment. 27:137-153.

Farquhar, G.D., S. Caemmerer and J.A. Berry. 1980. A biochemical model of photosynthetic CO2 assimilation in leaves of C3 species. Planta. 149:78-90.

Farquhar, G. D., & Sharkey, T. D. (1982). Stomatal conductance and photosynthesis. Annual review of plant physiology, 33(1), 317-345.

Gale, J., 1972. Availability of Carbon Dioxide for Photosynthesis at High Altitudes: Theoretical Considerations. Ecology 53, 494-497. doi:10.2307/1934239

Leuning, R. 1995. A critical-appraisal of a combined stomatal-photosynthesis model for C-3 plants. Plant Cell and Environment. 18:339-355.

Medlyn, B.E., E. Dreyer, D. Ellsworth, M. Forstreuter, P.C. Harley, M.U.F. Kirschbaum, X. Le Roux, P. Montpied, J. Strassemeyer, A. Walcroft, K. Wang and D. Loustau. 2002. Temperature response of parameters of a biochemically based model of photosynthesis. II. A review of experimental data. Plant Cell and Environment. 25:1167-1179.

Medlyn, B.E., R.A. Duursma, D. Eamus, D.S. Ellsworth, I.C. Prentice, C.V.M. Barton, K.Y. Crous, P. De Angelis, M. Freeman and L. Wingate. 2011. Reconciling the optimal and empirical approaches to modelling stomatal conductance. Global Change Biology. 17:2134-2144.

Terashima, I., Masuzawa, T., Ohba, H., Yokoi, Y., 1995. Is Photosynthesis Suppressed at Higher Elevations Due to Low CO2 Pressure? Ecology 76, 2663-2668. doi:10.2307/2265838

### See Also

`FARAO`

, `fitaci`

, `AciC4`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 | ```
# Run the coupled leaf gas exchange model, set only a couple of parameters
Photosyn(VPD=2, g1=4, Ca=500)
# It is easy to set multiple values for inputs (and these can be mixed with single inputs);
r <- Photosyn(VPD=seq(0.5, 4, length=25), Vcmax=50, Jmax=100)
with(r, plot(VPD, ALEAF, type='l'))
# Set the mesophyll conductance
run1 <- Photosyn(PPFD=seq(50,1000,length=25), gmeso=0.15, Vcmax=40, Jmax=85)
with(run1, plot(PPFD, GS, type='l'))
# Run A-Ci curve only (provide Ci instead of calculating it).
arun1 <- Aci(Ci=seq(50, 1200, length=101), Vcmax=40, Jmax=85)
arun2 <- Aci(Ci=seq(50, 1200, length=101), Vcmax=30, Jmax=70)
with(arun1, plot(Ci, ALEAF, type='l'))
with(arun2, points(Ci, ALEAF, type='l', lty=5))
# Find the intersection between supply of CO2 and demand for CO2 (cf. Farquhar and Sharkey 1982).
# Set some parameters
gs <- 0.2 # stomatal conductance to H2O
Ca <- 400 # ambient CO2
gctogw <- 1.57 # conversion
gc <- gs / gctogw # stomatal conductance to CO2
# Demand curve (Farquhar model)
p <- Aci(seq(60,500,length=101), Ca=400)
# Provide stomatal conductance as input, gives intersection point.
g <- Photosyn(GS=gs, Ca=Ca)
# Intersection point visualized
par(yaxs="i")
with(p, plot(Ci, ALEAF, type='l', ylim=c(0,max(ALEAF))))
with(g, points(Ci, ALEAF, pch=19, col="red"))
abline(gc * Ca, -gc, lty=5)
legend("topleft", c(expression("Demand:"~~A==f(C[i])),
expression("Supply:"~~A==g[c]*(C[a]-C[i])),
"Operating point"),
lty=c(1,5,-1),pch=c(-1,-1,19),
col=c("black","black","red"),
bty='n', cex=0.9)
``` |

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