Type:	Package
Title:	P-Model
Description:	Implements the P-model (Stocker et al., 2020 <doi:10.5194/gmd-13-1545-2020>), predicting acclimated parameters of the enzyme kinetics of C3 photosynthesis, assimilation, and dark respiration rates as a function of the environment (temperature, CO2, vapour pressure deficit, light, atmospheric pressure).
Version:	1.2.3
License:	GPL-3
Encoding:	UTF-8
RoxygenNote:	7.3.1
Depends:	R (≥ 3.6)
Suggests:	ggplot2, dplyr, purrr, tidyr, knitr, rmarkdown, testthat, covr
VignetteBuilder:	knitr
URL:	https://github.com/geco-bern/rpmodel
BugReports:	https://github.com/geco-bern/rpmodel/issues
NeedsCompilation:	no
Packaged:	2024-06-27 20:27:42 UTC; benjaminstocker
Author:	Benjamin Stocker [aut, cre], Koen Hufkens [ctb]
Maintainer:	Benjamin Stocker <benjamin.stocker@gmail.com>
Repository:	CRAN
Date/Publication:	2024-06-27 20:40:02 UTC

Calculates the CO2 compensation point

Description

Calculates the photorespiratory CO2 compensation point in absence of dark respiration, \Gamma* (Farquhar, 1980).

Usage

calc_gammastar(tc, patm)

Arguments

Details

The temperature and pressure-dependent photorespiratory compensation point in absence of dark respiration \Gamma* (T,p) is calculated from its value at standard temperature (T0 = 25 deg C) and atmospheric pressure (p0 = 101325 Pa), referred to as \Gamma*0, quantified by Bernacchi et al. (2001) to 4.332 Pa (their value in molar concentration units is multiplied here with 101325 Pa to yield 4.332 Pa). \Gamma*0 is modified by temperature following an Arrhenius-type temperature response function f(T, \Delta Ha) (implemented by ftemp_arrh) with activation energy \Delta Ha = 37830 J mol-1 and is corrected for atmospheric pressure p(z) (see calc_patm) at elevation z.

\Gamma* = \Gamma*0 f(T, \Delta Ha) p(z) / p_0

p(z) is given by argument patm.

Value

A numeric value for \Gamma* (in Pa)

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

Examples

print("CO2 compensation point at 20 degrees Celsius and standard atmosphere (in Pa):")
print(calc_gammastar(20, 101325))

Calculates the Michaelis Menten coefficient for Rubisco-limited photosynthesis

Description

Calculates the Michaelis Menten coefficient of Rubisco-limited assimilation as a function of temperature and atmospheric pressure.

Usage

calc_kmm(tc, patm)

Arguments

Details

The Michaelis-Menten coefficient K of Rubisco-limited photosynthesis is determined by the Michalis-Menten constants for O2 and CO2 (Farquhar, 1980) according to:

K = Kc ( 1 + pO2 / Ko)

where Kc is the Michaelis-Menten constant for CO2 (Pa), Ko is the Michaelis-Menten constant for O2 (Pa), and pO2 is the partial pressure of oxygen (Pa), calculated as 0.209476 p, where p is given by argument patm. Kc and Ko follow a temperature dependence, given by the Arrhenius Equation f (implemented by ftemp_arrh):

Kc = Kc25 f(T, \Delta Hkc)

Ko = Ko25 f(T, \Delta Hko)

Values \Delta Hkc (79430 J mol-1), \Delta Hko (36380 J mol-1), Kc25 (39.97 Pa), and 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). T is given by the argument tc.

Value

A numeric value for K (in Pa)

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

Examples

print("Michaelis-Menten coefficient at 20 degrees Celsius and standard atmosphere (in Pa):")
print(calc_kmm(20, 101325))

Calculates atmospheric pressure

Description

Calculates atmospheric pressure as a function of elevation, by default assuming standard atmosphere (101325 Pa at sea level)

Usage

calc_patm(elv, patm0 = 101325)

Arguments

Details

The elevation-dependence of atmospheric pressure is computed by assuming a linear decrease in temperature with elevation and a mean adiabatic lapse rate (Berberan-Santos et al., 1997):

p(z) = p0 ( 1 - Lz / TK0) ^ ( g M / (RL) )

where z is the elevation above mean sea level (m, argument elv), g is the gravity constant (9.80665 m s-2), p0 is the atmospheric pressure at 0 m a.s.l. (argument patm0, defaults to 101325 Pa), L is the mean adiabatic lapse rate (0.0065 K m-2), M is the molecular weight for dry air (0.028963 kg mol-1), R is the universal gas constant (8.3145 J mol-1 K-1), and TK0 is the standard temperature (298.15 K, corresponds to 25 deg C).

Value

A numeric value for p

References

Allen, R. G., Pereira, L. S., Raes, D., Smith, M.: FAO Irrigation and Drainage Paper No. 56, Food and Agriculture Organization of the United Nations, 1998

Examples

print("Standard atmospheric pressure, in Pa, corrected for 1000 m.a.s.l.:")
print(calc_patm(1000))

Calculates an empirical soil moisture stress factor

Description

Calculates an empirical soil moisture stress factor as a function of relative soil moisture (fraction of field capacity).

Usage

calc_soilmstress(soilm, meanalpha = 1, apar_soilm = 0, bpar_soilm = 0.685)

Arguments

Details

The soil moisture stress factor is calculated using a quadratic function that is 1 above soilm = 0.6 and has a sensitivity, given by the y-axis cutoff, (zero soil moisture), determined by average aridity (argument meanalpha) as:

\beta = q(\theta - \theta*)^2 + 1

for \theta < \theta* and \beta = 1.0 otherwise. \theta* is fixed at 0.6. q is the sensitivity parameter and is calculated as a linear function of average aridity, quantified by the local annual mean ratio of actual over potential evapotranspiration, termed \alpha:

q=(\beta0-1)/(\theta*-\theta0)^2

\theta0 is 0.0, and

\beta0 = a + b \alpha

a is given by argument apar, b is given by argument bpar.

Value

A numeric value for \beta

References

Stocker, B. et al. Geoscientific Model Development Discussions (in prep.)

Examples

## Relative reduction (%) in GPP due to soil moisture stress at
## relative soil water content ('soilm') of 0.2:
print((calc_soilmstress(0.2)-1)*100 )

CO2 partial pressure

Description

Calculates CO2 partial pressure from concentration in ppm.

Usage

co2_to_ca(co2, patm)

Arguments

Value

CO2 partial pressure in Pa.

Dampen inputs of rpmodel

Description

Applies an exponential dampening input time series with specified time scale.

Usage

dampen_vec(vec, tau)

Arguments

Value

A numeric vector of equal length as x with damped variation. The dampening is calculated as:

S(t+1) - S(t) = (X(t+1) - S(t)) / \tau

Where X is the daily varying time series given by argument x, S is the dampened time returned by this function, and \tau is the decay time scale of a perturbation, given by argument tau.

Examples

## Not run: 
dampen_vec(
 vec = 20 * (sin(doy*pi/(365)))^2 + rnorm(365, mean = 0, sd = 5),
 tau = 40 
 )

## End(Not run)

Density of water

Description

Calculates the density of water as a function of temperature and atmospheric pressure, using the Tumlirz Equation.

Usage

density_h2o(tc, p)

Arguments

Value

numeric, density of water, kg/m^3

References

F.H. Fisher and O.E Dial, Jr. (1975) Equation of state of pure water and sea water, Tech. Rept., Marine Physical Laboratory, San Diego, CA.

Examples

 # Density of water at 20 degrees C and standard atmospheric pressure
 print(density_h2o(20, 101325))

Calculates the Arrhenius-type temperature response

Description

Given a kinetic rate at a reference temperature (argument tkref) this function calculates its temperature-scaling factor following Arrhenius kinetics.

Usage

ftemp_arrh(tk, dha, tkref = 298.15)

Arguments

Details

To correct for effects by temperature following Arrhenius kinetics, and given a reference temperature T_0, f calculates the temperature scaling. Arrhenius kinetics are described by an equation of form x(T)= exp(c - \Delta H_a / (T R)). The temperature-correction function f(T, \Delta H_a) is thus given by f=x(T)/x(T_0) which is:

f = exp( \Delta H_a (T - T_0) / (T_0 R T_K) )

\Delta H_a is given by argument dha. T is given by argument tk and has to be provided in Kelvin. R is the universal gas constant and is 8.3145 J mol-1 K-1. Note that this is equivalent to

f = exp( (\Delta H_a/R) (1/T_0 - 1/T) )

Value

A numeric value for f

Examples

# Relative rate change from 25 to 10 degrees Celsius (percent change)
print( (1.0-ftemp_arrh( 283.15, 100000, tkref = 298.15))*100 )

Calculates the instantaneous temperature response of Jmax

Description

Given Jmax at a reference temperature (argument tcref) this function calculates its temperature-scaling factor following modified Arrhenius kinetics based on Kattge & Knorr (2007). Calculates f for the conversion

V = f Vref

Usage

ftemp_inst_jmax(tcleaf, tcgrowth = tcleaf, tcref = 25)

Arguments

Details

The function is given by Kattge & Knorr (2007) as

fv = f(T, \Delta Hv) A/B

where f(T, \Delta Hv) is a regular Arrhenius-type temperature response function (see ftemp_arrh) with Hv=49884 J mol-1,

A = 1 + exp( (T0 \Delta S - Hd) / (T0 R) )

and

B = 1 + exp( (T \Delta S - Hd) / (TK R) )

Here, T is in Kelvin, T0=293.15 K, Hd = 200000 J mol-1 is the deactivation energy and R is the universal gas constant and is 8.3145 J mol-1 K-1, and

\Delta S = aS - bS T

with aS = 659.70 J mol-1 K-1, and bS = 0.75 J mol-1 K-2, and T given in degrees Celsius (!)

Value

A numeric value for fv

References

Kattge, J. and Knorr, W.: Temperature acclimation in a biochemical model of photosynthesis: a reanalysis of data from 36 species, Plant, Cell and Environment, 30,1176–1190, 2007.

Examples

# Relative change in Jmax going (instantaneously, i.e.
# not acclimatedly) from 10 to 25 degrees (percent change):
print((ftemp_inst_jmax(25)/ftemp_inst_jmax(10)-1)*100 )

Calculates the temperature response of dark respiration

Description

Given the dark respiration at the reference temperature 25 degress Celsius, this function calculates its temperature-scaling factor following Heskel et al. 2016.

Usage

ftemp_inst_rd(tc)

Arguments

Details

To correct for effects by temperature Heskel et al. 2016, and given the reference temperature T0 = 25 deg C, this calculates the temperature scaling factor to calculate dark respiration at temperature T (argument tc) as:

fr = exp( 0.1012 (T0-T) - 0.0005(T0^2 - T^2) )

where T is given in degrees Celsius.

Value

A numeric value for fr

References

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., Martinez-De 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.

Examples

## Relative change in Rd going (instantaneously, i.e. not 
## acclimatedly) from 10 to 25 degrees (percent change):
print( (ftemp_inst_rd(25)/ftemp_inst_rd(10)-1)*100 )

Calculates the instantaneous temperature response of Vcmax

Description

Given Vcmax at a reference temperature (argument tcref) this function calculates its temperature-scaling factor following modified Arrhenius kinetics based on Kattge & Knorr (2007). Calculates f for the conversion

V = f Vref

Usage

ftemp_inst_vcmax(tcleaf, tcgrowth = tcleaf, tcref = 25)

Arguments

Details

The function is given by Kattge & Knorr (2007) as

fv = f(T, \Delta Hv) A/B

where f(T, \Delta Hv) is a regular Arrhenius-type temperature response function (see ftemp_arrh) with Hv=71513 J mol-1,

A = 1 + exp( (T0 \Delta S - Hd) / (T0 R) )

and

B = 1 + exp( (T \Delta S - Hd) / (TK R) )

Here, T is in Kelvin, T0=293.15 K, Hd = 200000 J mol-1 is the deactivation energy and R is the universal gas constant and is 8.3145 J mol-1 K-1, and

\Delta S = aS - bS T

with aS = 668.39 J mol-1 K-1, and bS = 1.07 J mol-1 K-2, and T given in degrees Celsius (!)

Value

A numeric value for fv

References

Kattge, J. and Knorr, W.: Temperature acclimation in a biochemical model of photosynthesis: a reanalysis of data from 36 species, Plant, Cell and Environment, 30,1176–1190, 2007.

Examples

## Relative change in Vcmax going (instantaneously, i.e. 
## not acclimatedly) from 10 to 25 degrees (percent change):
print((ftemp_inst_vcmax(25)/ftemp_inst_vcmax(10)-1)*100 )

Calculates the temperature dependence of the quantum yield efficiency

Description

Calculates the temperature dependence of the quantum yield efficiency following the temperature dependence of the maximum quantum yield of photosystem II in light-adapted tobacco leaves, determined by Bernacchi et al. (2003)

Usage

ftemp_kphio(tc, c4 = FALSE)

Arguments

Details

The temperature factor for C3 photosynthesis (argument c4 = FALSE) is calculated based on Bernacchi et al. (2003) as

\phi(T) = 0.352 + 0.022 T - 0.00034 T^2

The temperature factor for C4 (argument c4 = TRUE) photosynthesis is calculated based on pers. comm. by David Orme, correcting values provided in Cai & Prentice (2020). Corrected parametrisation is:

\phi(T) = -0.064 + 0.03 T - 0.000464 T^2

The factor \phi(T) is to be multiplied with leaf absorptance and the fraction of absorbed light that reaches photosystem II. In the P-model these additional factors are lumped into a single apparent quantum yield efficiency parameter (argument kphio to function rpmodel).

Value

A numeric value for \phi(T)

References

Bernacchi, C. J., Pimentel, C., and Long, S. P.: In vivo temperature response func-tions of parameters required to model RuBP-limited photosynthesis, Plant Cell Environ., 26, 1419–1430, 2003 Cai, W., and Prentice, I. C.: Recent trends in gross primary production and their drivers: analysis and modelling at flux-site and global scales, Environ. Res. Lett. 15 124050 https://doi.org/10.1088/1748-9326/abc64e, 2020

Examples

## Relative change in the quantum yield efficiency
## between 5 and 25 degrees celsius (percent change):
print(paste((ftemp_kphio(25.0)/ftemp_kphio(5.0)-1)*100 ))

Invokes a P-model function call

Description

R implementation of the P-model and its corollary predictions (Prentice et al., 2014; Han et al., 2017).

Usage

rpmodel(
  tc,
  vpd,
  co2,
  fapar,
  ppfd,
  patm = NA,
  elv = NA,
  kphio = ifelse(c4, 1, ifelse(do_ftemp_kphio, ifelse(do_soilmstress, 0.087182,
    0.081785), 0.049977)),
  beta = ifelse(c4, 146/9, 146),
  soilm = stopifnot(!do_soilmstress),
  meanalpha = 1,
  apar_soilm = 0,
  bpar_soilm = 0.733,
  c4 = FALSE,
  method_jmaxlim = "wang17",
  do_ftemp_kphio = TRUE,
  do_soilmstress = FALSE,
  returnvar = NULL,
  verbose = FALSE
)

Arguments

Value

A named list of numeric values (including temperature and pressure dependent parameters of the photosynthesis model, P-model predictions, including all its corollary). This includes :

• ca: Ambient CO2 expressed as partial pressure (Pa)

• gammastar: Photorespiratory compensation point \Gamma*, (Pa), see calc_gammastar.

• kmm: Michaelis-Menten coefficient K for photosynthesis (Pa), see calc_kmm.

• ns_star: Change in the viscosity of water, relative to its value at 25 deg C (unitless).

  \eta* = \eta(T) / \eta(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:

  \chi = \Gamma* / ca + (1- \Gamma* / ca) \xi / (\xi + \sqrt D )

  with

  \xi = \sqrt (\beta (K+ \Gamma*) / (1.6 \eta*))

  \beta is given by argument beta, K is kmm (see calc_kmm), \Gamma* is gammastar (see calc_gammastar). \eta* is ns_star. D is the vapour pressure deficit (argument vpd), ca is the ambient CO2 partial pressure in Pa (ca).

• ci: Leaf-internal CO2 partial pressure (Pa), calculated as (\chi ca).

• lue: Light use efficiency (g C / mol photons), calculated as

  LUE = \phi(T) \phi0 m' Mc

  where \phi(T) is the temperature-dependent quantum yield efficiency modifier (ftemp_kphio) if do_ftemp_kphio==TRUE, and 1 otherwise. \phi 0 is given by argument kphio. m'=m if method_jmaxlim=="none", otherwise

  m' = m \sqrt( 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 mol-1). m is given returned variable mj. If do_soilmstress==TRUE, LUE is multiplied with a soil moisture stress factor, calculated with calc_soilmstress.

• mj: Factor in the light-limited assimilation rate function, given by

  m = (ci - \Gamma*) / (ci + 2 \Gamma*)

  where \Gamma* is given by calc_gammastar.

• mc: Factor in the Rubisco-limited assimilation rate function, given by

  mc = (ci - \Gamma*) / (ci + K)

  where K is given by calc_kmm.

• gpp: Gross primary production (g C m-2), 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 (1-\chi)/(1.6)

• gs: Stomatal conductance (gs, in mol C m-2 Pa-1), calculated as

  gs = A / (ca (1-\chi))

  where A is gpp/Mc.

• vcmax: Maximum carboxylation capacity Vcmax (mol C m-2) at growth temperature (argument tc), calculated as

  Vcmax = \phi(T) \phi0 Iabs n

  where n is given by n=m'/mc.

• vcmax25: Maximum carboxylation capacity Vcmax (mol C m-2) 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 m-2), 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 \omega, defined by Eq. 16 in Smith et al. (2019), and Eq. E19 in Stocker et al. (2019).

• omega_star: Term corresponding to \omega^\ast, defined by Eq. 18 in Smith et al. (2019), and Eq. E21 in Stocker et al. (2019).

patm

References

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

and their drivers: analysis and modelling at flux-site and global scales, Environ. Res. Lett. 15 124050 https://doi.org/10.1088/1748-9326/abc64e, 2020 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., Martinez-De 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 func-tional 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: 506-517. doi:10.1111/ele.13210

Stocker, B. et al. Geoscientific Model Development Discussions (in prep.)

Examples

## Not run: 
 rpmodel(
  tc = 20,
  vpd = 1000,
  co2 = 400,
  ppfd = 30,
  elv = 0)

## End(Not run)

Viscosity of water

Description

Calculates the viscosity of water as a function of temperature and atmospheric pressure.

Usage

viscosity_h2o(tc, p)

Arguments

Value

numeric, viscosity of water (mu), Pa s

References

Huber, M. L., R. A. Perkins, A. Laesecke, D. G. Friend, J. V. Sengers, M. J. Assael, ..., K. Miyagawa (2009) New international formulation for the viscosity of H2O, J. Phys. Chem. Ref. Data, Vol. 38(2), pp. 101-125.

Examples

print("Density of water at 20 degrees C and standard atmospheric pressure:")
print(density_h2o(20, 101325))