R/calc_kmm.R

In dsval/rpmodel-grid-dev: P-Model

#' Calculates the Michaelis Menten coefficient for Rubisco-limited photosynthesis
#'
#' Calculates the Michaelis Menten coefficient of Rubisco-limited assimilation
#' as a function of temperature and atmospheric pressure.
#'
#' @param tc Temperature, relevant for photosynthesis (deg C)
#' @param patm Atmospheric pressure (Pa)
#'
#' @details The Michaelis-Menten coefficient \eqn{K} of Rubisco-limited
#' photosynthesis is determined by the Michalis-Menten constants for
#' O2 and CO2 (Farquhar, 1980) according to:
#' \deqn{
#'   K = Kc ( 1 + pO2 / Ko)
#' }
#' where \eqn{Kc} is the Michaelis-Menten constant for CO2 (Pa), \eqn{Ko} is
#' the Michaelis-Menten constant for O2 (Pa), and \eqn{pO2} is the partial
#' pressure of oxygen (Pa), calculated as \eqn{0.209476 p}, where \eqn{p} is
#' given by argument \code{patm}.  \eqn{Kc} and \eqn{Ko} follow a temperature
#' dependence, given by the Arrhenius Equation \eqn{f} (implemented by
#' \link{calc_ftemp_arrh}):
#' \deqn{
#'    Kc = Kc25 f(T, \Delta Hkc)
#' }
#' \deqn{
#'    Ko = Ko25 f(T, \Delta Hko)
#' }
#' Values \eqn{\Delta Hkc} (79430 J mol-1), \eqn{\Delta Hko} (36380 J mol-1),
#' \eqn{Kc25} (39.97 Pa), and \eqn{Ko25} (27480 Pa) are taken from Bernacchi
#' et al. (2001) and have been converted from values given therein to units of Pa
#' by multiplication with the standard atmosphere (101325 Pa). \eqn{T} is given
#' by the argument \code{tc}.
#'
#' @references Farquhar,  G.  D.,  von  Caemmerer,  S.,  and  Berry,  J.  A.:
#'             A  biochemical  model  of photosynthetic CO2 assimilation in leaves of
#'             C 3 species, Planta, 149, 78–90, 1980.
#'
#'             Bernacchi,  C.  J.,  Singsaas,  E.  L.,  Pimentel,  C.,  Portis,  A.
#'             R.  J.,  and  Long,  S.  P.:Improved temperature response functions
#'             for models of Rubisco-limited photosyn-thesis, Plant, Cell and
#'             Environment, 24, 253–259, 2001
#'
#' @return A numeric value for \eqn{K} (in Pa)
#'
#' @examples print("Michaelis-Menten coefficient at 20 degrees Celsius and standard atmosphere (in Pa):")
#' print(calc_kmm(20, 101325))
#'
#' @export
#'
calc_kmm <- function( tc, patm ) {

  dhac   <- 79430      # (J/mol) Activation energy, Bernacchi et al. (2001)
  dhao   <- 36380      # (J/mol) Activation energy, Bernacchi et al. (2001)
  kco    <- 2.09476e5  # (ppm) O2 partial pressure, Standard Atmosphere

  ## k25 parameters are not dependent on atmospheric pressure
  kc25 <- 39.97   # Pa, value based on Bernacchi et al. (2001), converted to Pa by T. Davis assuming elevation of 227.076 m.a.s.l.
  ko25 <- 27480   # Pa, value based on Bernacchi et al. (2001), converted to Pa by T. Davis assuming elevation of 227.076 m.a.s.l.

  ## conversion to Kelvin
  tk <- tc + 273.15

  kc <- kc25 * calc_ftemp_arrh( tk, dha=dhac )
  ko <- ko25 * calc_ftemp_arrh( tk, dha=dhao )

  po  <- kco * (1e-6) * patm         # O2 partial pressure
  kmm <- kc * (1.0 + po/ko)

  return(kmm)
}