photosynthetic.capacity {bigleaf}R Documentation

Bulk Canopy Photosynthetic Capacity (Vcmax and Jmax)


Bulk canopy maximum carboxylation rate (Vcmax25), and maximum electron transport rate (Jmax25) at 25 degrees Celsius from bulk intercellular CO2 concentration using the Farquhar et al. 1980 model for C3 photosynthesis.


  C3 = TRUE,
  GPP = "GPP",
  PPFD = "PPFD",
  PPFD_j = c(200, 500),
  PPFD_c = 1000,
  Rleaf = NULL,
  Oi = 0.21,
  Kc25 = 404.9,
  Ko25 = 278.4,
  Gam25 = 42.75,
  Kc_Ha = 79.43,
  Ko_Ha = 36.38,
  Gam_Ha = 37.83,
  Vcmax_Ha = 65.33,
  Vcmax_Hd = 200,
  Vcmax_dS = 0.635,
  Jmax_Ha = 43.9,
  Jmax_Hd = 200,
  Jmax_dS = 0.64,
  Theta = 0.7,
  alpha_canopy = 0.8, = FALSE,
  Ci_C4 = 100,
  constants = bigleaf.constants()



Data.Frame or matrix with all required columns


C3 vegetation (TRUE, the default) or C4 vegetation (FALSE)?


Surface (or air) temperature (degC)


Gross primary productivity (umol m-2 s-1)


Bulk canopy intercellular CO2 concentration (umol mol-1)


Photosynthetic photon flux density (umol m-2 s-1)


PPFD threshold, below which the canopy is considered to be RuBP regeneration limited. Defaults to 500 umol m-2 s-1.


PPFD threshold, above which the canopy is considered to be Rubisco limited. Defaults to 1000 umol m-2 s-1.


Ecosystem respiration stemming from leaves (umol CO2 m-2 s-1); defaults to 0


Intercellular O2 concentration (mol mol-1)


Michaelis-Menten constant for CO2 at 25 degC (umol mol-1)


Michaelis-Menten constant for O2 at 25 degC (mmol mol-1)


Photorespiratory CO2 compensation point ('Gamma star') at 25 degC (umol mol-1)


Activation energy for Kc (kJ mol-1)


Activation energy for Ko (kJ mol-1)


Activation energy for Gam (kJ mol-1)


Activation energy for Vcmax (kJ mol-1)


Deactivation energy for Vcmax (kJ mol-1)


Entropy term for Vcmax (kJ mol-1 K-1)


Activation energy for Jmax (kJ mol-1)


Deactivation energy for Jmax (kJ mol-1)


Entropy term for Jmax (kJ mol-1 K-1)


Curvature term in the light response function of J (-)


Canopy absorptance (-)

if Rleaf is provided, should missing values be treated as NA (TRUE) or set to 0 (FALSE, the default)?


intercellular CO2 concentration below which photosynthesis is considered to be CO2-limited (umol mol-1), ignored if C3 = TRUE.


Kelvin - conversion degree Celsius to Kelvin
Rgas - universal gas constant (J mol-1 K-1)
kJ2J - conversion kilojoule (kJ) to joule (J)
J2kJ - conversion joule (J) to kilojoule (kJ)
se_median - conversion standard error (SE) of the mean to SE of the median


The maximum carboxylation rate at 25degC (Vcmax25) and the maximum electron transport rate at 25degC (Jmax25), which characterize photosynthetic capacity, are calculated as at leaf level. The required variables Gs and Ci can be calculated from surface.conductance and intercellular.CO2, respectively.

Gas exchange parameters are taken from Bernacchi et al. 2001 (apparent values, which assume an infinite mesophyll conductance). Negative and very low Ci values (the threshold is set to Ci < 80umol mol-1 at the moment) are filtered out.

Vcmax is calculated from the photosynthesis model by Farquhar et al. 1980. If net photosynthesis is Rubisco-limited (RuBP-saturated carboxylation rate, i.e. light has to be (near-)saturating):

Vcmax = (GPP * (Ci + Kc*(1.0 + Oi/Ko))) / (Ci - Gam)

where Kc and Ko are the Michaelis-Menten constants for CO2 and O2 (mmol mol-1), respectively, Oi is the O2 concentration, and Gam is the photorespiratory CO2 compensation point (umol mol-1). Under low-light conditions, the electron transport rate J is calculated from the RuBP regeneration-limited photosynthesis rate:

J = (GPP * (4.0 * Ci + 8.0 * Gam) / (Ci - Gam)

In this function, bulk canopy photosynthesis is assumed to be Rubisco/RuBP-regeneration limited, if incoming PPFD is above/below a specified threshold or range. These ranges are determined by the parameters PPFD_j and PPFD_c. If, for example, PPFD_j = c(100,400), all conditions with a PPFD between 100 and 400 are assumed to be in the RuBP-regeneration (i.e. light-limited) photosynthesis domain. The electron transport rate J is then only calculated for periods that meet this criterion.

Jmax is calculated from J and absorbed irradiance:

J = (APPFD_PSII + Jmax - sqrt((APPFD_PSII + Jmax)^2 - 4.0 * Theta * APPFD_PSII * Jmax)) / (2.0 * Theta)

where APPFD_PSII is the absorbed PPFD by photosystem II (PS II), and Theta is a curvature parameter. APPFD_PSII is calculated as

PPFD * alpha_canopy * 0.85 * beta

where alpha_canopy is canopy-scale absorptance, 0.85 is a correction factor, and beta is the fraction of photons absorbed by PS II (assumed 0.5). alpha_canopy accounts for non-absorbing components of the ecosystem such as stems or soil, and is very likely ecosystem-specific. This parameter is relatively sensitive for the determination of Jmax25 at some sites.

Vcmax and Jmax at canopy level are assumed to follow the same temperature response as at leaf level. Hence, the respective parameter k at 25degC (k25) is calculated as (see e.g. Kattge & Knorr 2007):

k25 = k / ( exp(Ha * (Temp - Tref) / (Tref * Rgas * Temp)) * (1 + exp((Tref * dS - Hd) / (Tref * Rgas))) / (1 + exp((Temp * dS - Hd) / (Temp * Rgas))) )

where Ha is the activation energy (kJ mol-1), Hd is the deactivation energy (kJ mol-1), and dS is the entropy term (kJ mol-1 K-1) of the respective parameter. Tref is set to 298.15 K.

For C4 photosynthesis, the simplified model by von Caemmerer 2000 is used. For light-saturated photosynthesis, Vcmax is given by:

Vcmax = GPP

Note that in addition to the range PPFD_c, the range Ci_C4 discards all periods with low Ci, in which photosynthesis is likely to be CO2-limited (see von Caemmerer 2000 for details).

In the light-limited case, J is calculated as:

J = 3 * GPPj / (1 - 0.5)

The calculation of Jmax25 and Vcmax25 is identical to C3 photosynthesis as described above.


a data.frame with the following columns:


maximum bulk canopy carboxylation rate at 25degC (umol m-2 (ground) s-1)


maximum bulk canopy electron transport rate at 25degC (umol m-2 (ground) s-1)


The critical assumption is that bulk canopy photosynthesis is limited by one of the two limitation states. Incoming PPFD is assumed to determine the limitation states. Note however that the ranges (PPFD_j and PPFD_c) are likely ecosystem-specific. E.g. dense canopies presumably require higher PPFD_c thresholds than open canopies. A threshold of 500 umol m-2 s-1 PPFD for Rubisco-limited photosynthesis was assumed a reasonable working assumption (see Kosugi et al. 2013). Here, PPFD_c defaults to 1000 umol m-2 s-1. Note that even under very high/low irradiances, not all photosynthetically active plant material of an ecosystem will be in the same limitation state. Note that parameters describing bulk canopy photosynthetic capacity are not directly comparable to their leaf-level counterparts, as the former integrate over the entire canopy depth (i.e. are given per ground area, and not per leaf area). In general, the function should be used with care!


Lloyd J. et al., 1995: A simple calibrated model of Amazon rainforest productivity based on leaf biochemical properties. Plant, Cell and Environment 18, 1129-1145.

Rayment M.B., Loustau D., Jarvis P.G., 2002: Photosynthesis and respiration of black spruce at three organizational scales: shoot, branch and canopy. Tree Physiology 22, 219-229.

Kosugi Y. et al., 2013: Determination of the gas exchange phenology in an evergreen coniferous forest from 7 years of eddy covariance flux data using an extended big-leaf analysis. Ecol Res 28, 373-385.

Ueyama M. et al, 2016: Optimization of a biochemical model with eddy covariance measurements in black spruce forests of Alaska for estimating CO2 fertilization effects. Agricultural and Forest Meteorology 222, 98-111.

Bernacchi C.J., Singsaas E.L., Pimentel C., Portis JR A.R., Long S.P., 2001: Improved temperature response functions for models of Rubisco-limited photosynthesis. Plant, Cell and Environment 24, 253-259.

Bernacchi C.J., Pimentel C., Long S.P., 2003: In vivo temperature response functions of parameters required to model RuBP-limited photosynthesis. Plant, Cell and Environment 26, 1419-1430.

von Caemmerer, 2000: Biochemical models of leaf photosynthesis. Techniques in plant sciences No. 2. CSIRO Publishing, Collingwood VIC, Australia.

See Also

intercellular.CO2, Arrhenius.temp.response


DE_Tha_Jun_2014_2 <-,quality.control=FALSE,

# calculate Ga
Ga <- aerodynamic.conductance(DE_Tha_Jun_2014_2,Rb_model="Thom_1972")[,"Ga_h"]

# calculate Gs from the the inverted PM equation
Gs_PM <- surface.conductance(DE_Tha_Jun_2014_2,Tair="Tair",pressure="pressure",

# calculate Ci 
Ci <- intercellular.CO2(DE_Tha_Jun_2014_2,Ca="Ca",GPP="GPP",Gs=Gs_PM) 

# calculate Vcmax25 and Jmax25

[Package bigleaf version 0.8.2 Index]