R/Temperature_Response_Functions.R

In TEST-BNL/R-Canopy_Photosynthesis: Canopy photosynthesis testbed

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# Functions for applying temperature response functions to photosynthesis
# parameters
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##'
##' @description Bernacchi temperature response function for photosynthesis parameters
##' @details Bernacchi temperature response function for photosynthesis parameters
##' 
##' @title Func_Temperature_Bernacchi
##' 
##' @param delta_H Activation energy
##' @param c Scaling constant
##' @param Tleaf leaf temperature in degrees C
##'
##' @return temperature scale factor
##'
##' @references Bernacchi et al., 2002
##' 
##' @export
##' @author Jin Wu
##' @author Shawn Serbin
##'
Func_Temperature_Bernacchi <- function(delta_H, c, Tleaf) {
  Tk <- Tleaf + 273.15
  R <- 8.3144598  # J/K/mol, universal gas constant
  delta_H <- delta_H * 1000  # unit conversion from kJ/mol to J/mol
  scale <- exp(c - delta_H/(R * Tk))  #scale factor
  return(scale)
}
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##'
##' @description Medlyn Arrhenius function
##' @details Medlyn Arrhenius temperature response function for photosynthesis parameters, based
##' on Bernacchi et al. 2002.  Used for Vcmax, Jmax, Rd, Kc, Ko, Gamma*
##' 
##' @title Func_Temperature_Medlyn
##' 
##' @param Tleaf.1 Original leaf temperature (degrees C)
##' @param Tleaf.2 Leaf temperature to scale parameter to (degrees C)
##' @param Param Parameter (e.g. Vcmax, Kc, Gamma*) value at Tleaf.1
##' @param Ea Activation energy for Arrehnius function.  Dependent on parameter of interest
##'
##' @return Parameter scaled to Tleaf.2 following the Arrhenius function in Medlyn et al., 2002
##' 
##' @references Bernacchi et al., 2002; 2003; Medlyn et al., 2002
##'
##' @export
##' @author Jin Wu
##' @author Shawn Serbin
##'
Func_Temperature_Medlyn <- function(Tleaf.1, Tleaf.2, Param, Ea) {
  # R <- 0.008314472 # J/K/mol, universal gas constant
  R <- 8.3144598  # J/K/mol, universal gas constant
  Ea <- Ea * 1000  # unit conversion from kJ/mol to J/mol
  Param.T2 <- Param * exp((Ea * ((Tleaf.2 + 273.15) - (Tleaf.1 + 273.15)))/((Tleaf.1 + 
    273.15) * R * (Tleaf.2 + 273.15)))
  return(Param.T2)
}
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##'
##' @title Func_Temperature_June
##' @description June temperature response function for photosynthesis parameters
##' @details June temperature response function for photosynthesis parameters
##' 
##' @param P25 Vcmax/Jmax at 25 degrees C
##' @param Topt Temperature optimum of Vcmax/Jmax
##' @param Tleaf leaf temperature in degrees C
##'
##' @references Bernacchi et al. 2013 and June et al. 2004
##'
##' @export
##' @author Jin Wu
##' @author Shawn Serbin
##'
Func_Temperature_June <- function(P25, Topt, Tleaf) {
  # Omega--parameters controlling the temperature sensitivity of Jmax
  Omega <- 11.6 + 0.18 * Topt  # empirical relationship from June et al. 2004; Fig. 4
  scale <- ((Tleaf - Topt)/Omega)^2
  Jmax <- P25 * exp(-scale)
  return(Jmax)
}
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##'
##' @description Temperature response functions for scaling leaf-level photosynthesis parameters
##' @details Temperature response functions for scaling leaf-level photosynthesis parameters
##' 
##' @title Func_Temperature_Response
##'
##' @param VC25 Vcmax at 25 degrees C
##' @param J25 Jmax at 25 degrees C
##' @param Tleaf leaf temperature in degrees C
##' @param Topt Temperature optimum of Vcmax/Jmax
##' @param Press Atmospheric pressure in Pa
##'
##' @references Bernacchi et al., 2002, 2003, 2013
##'
##' @return List containing: Vcmax - Vcmax at leaf temperature, Jmax - Jmax at leaf temperature,
##' Gamma_star - Gamma* at leaf temperature, Kc - Kc MM constant at leaf temperature, Ko - Ko MM constant at leaf temperature,
##' PSII - PSII at leaf temperature, Phi - Phi at leaf temperature, Rd - leaf respiration at leaf temperature,
##' Vomax - Vomax (max oxygen evolution) at leaf temperature
##'
##' @export
##' @author Jin Wu
##' @author Shawn Serbin
##'
Func_Temperature_Response <- function(V25, J25, Tleaf, Topt, Press) {
  
  # Jmax temperature scaling
  Jmax_25 <- Func_Temperature_June(P25 = J25, Topt, 25)
  Jmax <- Func_Temperature_June(P25 = J25, Topt, Tleaf)  # reference: June et al. 2004; Bernacchi et al. 2013
  Jmax <- Jmax/Jmax_25 * J25
  
  # Temperature functions for Vcmax, Gamma_star, Ko, Kc, Rd delta_H <- 65.33 c <-
  # 26.35 s1 <- Func_Temperature_Bernacchi(delta_H, c, Tleaf) # Reference:
  # Bernacchi et al. 2001; Bernacchi et al. 2013 sl_25 <-
  # Func_Temperature_Bernacchi(delta_H, c, 25) # Reference: Bernacchi et al. 2001;
  # Bernacchi et al. 2013 Vcmax <- V25*s1/sl_25 rm(delta_H, c, s1, sl_25)
  
  # Alternative Vcmax scaling with Medlyn et al., 2002, using Bernacchi Ea TODO:
  # Modify this bit to allow for different Ea's in Vcmax scaling
  Vcmax <- Func_Temperature_Medlyn(25, Tleaf, V25, 65.33)
  
  # !!! should remove these hardcoded values here for delta_H and c
  delta_H <- 37.83
  c <- 19.02
  s1 <- Func_Temperature_Bernacchi(delta_H, c, Tleaf)  # reference: Bernacchi et al. 2001; Bernacchi et al. 2013
  sl_25 <- Func_Temperature_Bernacchi(delta_H, c, 25)  # reference: Bernacchi et al. 2001; Bernacchi et al. 2013
  Gamma_star <- 42.75 * s1/sl_25  # umol/mol
  rm(delta_H, c, s1, sl_25)
  
  delta_H <- 79.43
  c <- 38.05
  s1 <- Func_Temperature_Bernacchi(delta_H, c, Tleaf)  # reference: Bernacchi et al. 2001; Bernacchi et al. 2013
  sl_25 <- Func_Temperature_Bernacchi(delta_H, c, 25)  # reference: Bernacchi et al. 2001; Bernacchi et al. 2013
  Kc <- 404.9 * s1/sl_25  # umol/mol
  rm(delta_H, c, s1, sl_25)
  
  delta_H <- 36.38
  c <- 20.3
  s1 <- Func_Temperature_Bernacchi(delta_H, c, Tleaf)  # reference: Bernacchi et al. 2001; Bernacchi et al. 2013
  sl_25 <- Func_Temperature_Bernacchi(delta_H, c, 25)  # reference: Bernacchi et al. 2001; Bernacchi et al. 2013
  Ko <- 278.4 * s1/sl_25  # mmol/mol
  rm(delta_H, c, s1, sl_25)
  
  Phi <- 0.76 + 0.018 * Tleaf - 3.7 * (1e-04) * Tleaf^2  # growth temperature=25 from Bernacchi et al. 2003 % Curvature factor between An-PAR
  PSII <- 0.352 + 0.022 * Tleaf - 3.4 * (1e-04) * Tleaf^2  # maximum quantumn yield; using light adapted version from Bernacchi et al. 2003
  
  delta_H <- 46.39
  c <- 18.72
  s1 <- Func_Temperature_Bernacchi(delta_H, c, Tleaf)  # reference: Bernacchi et al. 2001; Bernacchi et al. 2013
  sl_25 <- Func_Temperature_Bernacchi(delta_H, c, 25)  # reference: Bernacchi et al. 2001; Bernacchi et al. 2013
  Rd <- 0.015 * V25 * s1/sl_25  # umol/mol
  rm(delta_H, c, s1, sl_25)
  
  # Oxygen
  Oxygen <- 210 * Press/(101325)  # mmol/mol
  
  # !!!!  not very sure for Vomax modeling !!! DO WE NEED THIS??  TODO: Remove this
  # from the code
  Vomax <- Vcmax * Ko * Gamma_star/(0.5 * Kc * Oxygen)  # according to equation 7 in Bernacchi et al. 2001
  Vomax25 <- V25 * 278.4 * 42.75/(0.5 * 404.9 * Oxygen)
  
  delta_H <- 60.11
  c <- 22.98
  s1 <- Func_Temperature_Bernacchi(delta_H, c, Tleaf)  # reference: Bernacchi et al. 2001; Bernacchi et al. 2013
  sl_25 <- Func_Temperature_Bernacchi(delta_H, c, 25)  # reference: Bernacchi et al. 2001; Bernacchi et al. 2013
  Vomax <- Vomax25 * s1/sl_25  # umol/mol
  rm(delta_H, c, s1, sl_25)
  # !!! !!!!
  
  output <- list(Vcmax = Vcmax, Jmax = Jmax, Gamma_star = Gamma_star, Kc = Kc, 
    Ko = Ko, PSII = PSII, Phi = Phi, Rd = Rd, Vomax = Vomax)
  return(output)
  
  
}  ## End of function
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### EOF