Description Usage Arguments Value References Examples
R implementation of the Pmodel and its corollary predictions (Prentice et al., 2014; Han et al., 2017).
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22  rpmodel(
tc,
vpd,
co2,
fapar,
ppfd,
patm = NA,
elv = NA,
kphio = ifelse(do_ftemp_kphio, ifelse(do_soilmstress, 0.087182, 0.081785), 0.049977),
beta = 146,
soilm = stopifnot(!do_soilmstress),
meanalpha = 1,
apar_soilm = 0,
bpar_soilm = 0.733,
c4 = FALSE,
method_optci = "prentice14",
method_jmaxlim = "wang17",
do_ftemp_kphio = TRUE,
do_soilmstress = FALSE,
returnvar = NULL,
verbose = FALSE
)

tc 
Temperature, relevant for photosynthesis (deg C) 
vpd 
Vapour pressure deficit (Pa) 
co2 
Atmospheric CO2 concentration (ppm) 
fapar 
(Optional) Fraction of absorbed photosynthetically active
radiation (unitless, defaults to 
ppfd 
Incident photosynthetic photon flux density
(mol m2 d1, defaults to 
patm 
Atmospheric pressure (Pa). When provided, overrides

elv 
Elevation above sealevel (m.a.s.l.). Is used only for
calculating atmospheric pressure (using standard atmosphere (101325 Pa),
corrected for elevation (argument 
kphio 
Apparent quantum yield efficiency (unitless). Defaults to
0.081785 for 
beta 
Unit cost ratio. Defaults to 146.0 (see Stocker et al., 2019). 
soilm 
(Optional, used only if 
meanalpha 
(Optional, used only if 
apar_soilm 
(Optional, used only if 
bpar_soilm 
(Optional, used only if 
c4 
(Optional) A logical value specifying whether the C3 or C4
photosynthetic pathway is followed.Defaults to 
method_optci 
(Optional) A character string specifying which method is
to be used for calculating optimal ci:ca. Defaults to 
method_jmaxlim 
(Optional) A character string specifying which method
is to be used for factoring in Jmax limitation. Defaults to 
do_ftemp_kphio 
(Optional) A logical specifying whether
temperaturedependence of quantum yield efficiency after Bernacchi et al.,
2003 is to be accounted for. Defaults to 
do_soilmstress 
(Optional) A logical specifying whether an empirical
soil moisture stress factor is to be applied to downscale light use
efficiency (and only light use efficiency). Defaults to 
returnvar 
(Optional) A character string of vector of character strings specifying which variables are to be returned (see return below). 
verbose 
Logical, defines whether verbose messages are printed.
Defaults to 
A named list of numeric values (including temperature and pressure dependent parameters of the photosynthesis model, Pmodel predictions, including all its corollary). This includes :
ca
: Ambient CO2 expressed as partial pressure (Pa)
gammastar
: Photorespiratory compensation point Γ*,
(Pa), see gammastar.
kmm
: MichaelisMenten coefficient K for photosynthesis
(Pa), see kmm.
ns_star
: Change in the viscosity of water, relative to its
value at 25 deg C (unitless).
η* = η(T) / η(25 deg C)
This is used to scale the unit cost of transpiration. Calculated following Huber et al. (2009).
chi
: Optimal ratio of leaf internal to ambient CO2 (unitless).
Derived following Prentice et al.(2014) as:
χ = Γ* / ca + (1 Γ* / ca) ξ / (ξ + √ D )
with
ξ = √ (β (K+ Γ*) / (1.6 η*))
β is given by argument beta
, K is
kmm
(see kmm), Γ* is
gammastar
(see gammastar). η* is ns_star
.
D is the vapour pressure deficit (argument vpd
), ca is
the ambient CO2 partial pressure in Pa (ca
).
ci
: Leafinternal CO2 partial pressure (Pa), calculated as (χ ca).
lue
: Light use efficiency (g C / mol photons), calculated as
LUE = φ(T) φ0 m' Mc
where φ(T) is the temperaturedependent quantum yield efficiency modifier
(ftemp_kphio) if do_ftemp_kphio==TRUE
, and 1 otherwise. φ 0
is given by argument kphio
.
m'=m if method_jmaxlim=="none"
, otherwise
m' = m √( 1  (c/m)^(2/3) )
with c=0.41 (Wang et al., 2017) if method_jmaxlim=="wang17"
. Mc is
the molecular mass of C (12.0107 g mol1). m is given returned variable mj
.
If do_soilmstress==TRUE
, LUE is multiplied with a soil moisture stress factor,
calculated with soilmstress.
mj
: Factor in the lightlimited assimilation rate function, given by
m = (ci  Γ*) / (ci + 2 Γ*)
where Γ* is given by gammastar
.
mc
: Factor in the Rubiscolimited assimilation rate function, given by
mc = (ci  Γ*) / (ci + K)
where K is given by kmm
.
gpp
: Gross primary production (g C m2), calculated as
GPP = Iabs LUE
where Iabs is given by fapar*ppfd
(arguments), and is
NA
if fapar==NA
or ppfd==NA
. Note that gpp
scales with
absorbed light. Thus, its units depend on the units in which ppfd
is given.
iwue
: Intrinsic water use efficiency (iWUE, Pa), calculated as
iWUE = ca (1χ)/(1.6)
gs
: Stomatal conductance (gs, in mol C m2 Pa1), calculated as
gs = A / (ca (1χ))
where A is gpp
/Mc.
vcmax
: Maximum carboxylation capacity Vcmax (mol C m2) at growth temperature (argument
tc
), calculated as
Vcmax = φ(T) φ0 Iabs n
where n is given by n=m'/mc.
vcmax25
: Maximum carboxylation capacity Vcmax (mol C m2) normalised to 25 deg C
following a modified Arrhenius equation, calculated as Vcmax25 = Vcmax / fv,
where fv is the instantaneous temperature response by Vcmax and is implemented
by function ftemp_inst_vcmax.
jmax
: The maximum rate of RuBP regeneration () at growth temperature (argument
tc
), calculated using
A_J = A_C
rd
: Dark respiration Rd (mol C m2), calculated as
Rd = b0 Vcmax (fr / fv)
where b0 is a constant and set to 0.015 (Atkin et al., 2015), fv is the instantaneous temperature response by Vcmax and is implemented by function ftemp_inst_vcmax, and fr is the instantaneous temperature response of dark respiration following Heskel et al. (2016) and is implemented by function ftemp_inst_rd.
Additional variables are contained in the returned list if argument method_jmaxlim=="smith19"
omega
: Term corresponding to ω, defined by Eq. 16 in
Smith et al. (2019), and Eq. E19 in Stocker et al. (2019).
omega_star
: Term corresponding to ω^\ast, defined by
Eq. 18 in Smith et al. (2019), and Eq. E21 in Stocker et al. (2019).
Bernacchi, C. J., Pimentel, C., and Long, S. P.: In vivo temperature response functions of parameters required to model RuBPlimited photosynthesis, Plant Cell Environ., 26, 1419–1430, 2003
Heskel, M., O’Sullivan, O., Reich, P., Tjoelker, M., Weerasinghe, L., Penillard, A.,Egerton, J., Creek, D., Bloomfield, K., Xiang, J., Sinca, F., Stangl, Z., MartinezDe La Torre, A., Griffin, K., Huntingford, C., Hurry, V., Meir, P., Turnbull, M.,and Atkin, O.: Convergence in the temperature response of leaf respiration across biomes and plant functional types, Proceedings of the National Academy of Sciences, 113, 3832–3837, doi:10.1073/pnas.1520282113,2016.
Huber, M. L., Perkins, R. A., Laesecke, A., Friend, D. G., Sengers, J. V., Assael,M. J., Metaxa, I. N., Vogel, E., Mares, R., and Miyagawa, K.: New international formulation for the viscosity of H2O, Journal of Physical and Chemical ReferenceData, 38, 101–125, 2009
Prentice, I. C., Dong, N., Gleason, S. M., Maire, V., and Wright, I. J.: Balancing the costs of carbon gain and water transport: testing a new theoretical frameworkfor plant functional ecology, Ecology Letters, 17, 82–91, 10.1111/ele.12211,http://dx.doi.org/10.1111/ele.12211, 2014.
Wang, H., Prentice, I. C., Keenan, T. F., Davis, T. W., Wright, I. J., Cornwell, W. K.,Evans, B. J., and Peng, C.: Towards a universal model for carbon dioxide uptake by plants, Nat Plants, 3, 734–741, 2017. Atkin, O. K., et al.: Global variability in leaf respiration in relation to climate, plant functional types and leaf traits, New Phytologist, 206, 614–636, doi:10.1111/nph.13253, https://nph.onlinelibrary.wiley.com/doi/abs/10.1111/nph.13253.
Smith, N. G., Keenan, T. F., Colin Prentice, I. , Wang, H. , Wright, I. J., Niinemets, U. , Crous, K. Y., Domingues, T. F., Guerrieri, R. , Yoko Ishida, F. , Kattge, J. , Kruger, E. L., Maire, V. , Rogers, A. , Serbin, S. P., Tarvainen, L. , Togashi, H. F., Townsend, P. A., Wang, M. , Weerasinghe, L. K. and Zhou, S. (2019), Global photosynthetic capacity is optimized to the environment. Ecol Lett, 22: 506517. doi:10.1111/ele.13210
Stocker, B. et al. Geoscientific Model Development Discussions (in prep.)
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