Generate an error function for C4 A-Ci curve fitting — error_function_c4

Creates a function that returns an error value (the negative of the natural logarithm of the likelihood) representing the amount of agreement between modeled and measured An values.

Usage

error_function_c4_aci(
    replicate_exdf,
    fit_options = list(),
    sd_A = 1,
    absorptance = 0.85,
    f_spectral = 0.15,
    rho = 0.5,
    theta = 0.7,
    x_etr = 0.4,
    ao_column_name = 'ao',
    a_column_name = 'A',
    gamma_star_column_name = 'gamma_star',
    jmax_norm_column_name = 'Jmax_norm',
    kc_column_name = 'Kc',
    ko_column_name = 'Ko',
    kp_column_name = 'Kp',
    oxygen_column_name = 'oxygen',
    pcm_column_name = 'PCm',
    qin_column_name = 'Qin',
    rl_norm_column_name = 'RL_norm',
    total_pressure_column_name = 'total_pressure',
    vcmax_norm_column_name = 'Vcmax_norm',
    vpmax_norm_column_name = 'Vpmax_norm',
    hard_constraints = 0
  )

Arguments

replicate_exdf: An exdf object representing one CO2 response curve.
fit_options: A list of named elements representing fit options to use for each parameter. Values supplied here override the default values (see details below). Each element must be 'fit', 'column', or a numeric value. A value of 'fit' means that the parameter will be fit; a value of 'column' means that the value of the parameter will be taken from a column in replicate_exdf of the same name; and a numeric value means that the parameter will be set to that value. For example, fit_options = list(RL_at_25 = 0, Vcmax_at_25 = 'fit', Vpmax_at_25 = 'column') means that RL_at_25 will be set to 0, Vcmax_at_25 will be fit, and Vpmax_at_25 will be set to the values in the Vpmax_at_25 column of replicate_exdf.
sd_A: The standard deviation of the measured values of the net CO2 assimilation rate, expressed in units of micromol m^(-2) s^(-1). If sd_A is not a number, then there must be a column in exdf_obj called sd_A with appropriate units. A numeric value supplied here will overwrite the values in the sd_A column of exdf_obj if it exists.
absorptance: The leaf absorptance (dimensionless). See Equation 35 from S. von Caemmerer (2021).
f_spectral: The spectral quality adjustment factor (dimensionless). See Equation 35 from S. von Caemmerer (2021).
rho: The fraction of light absorbed by photosystem II rather than photosystem I (dimensionless). See Equation 35 from S. von Caemmerer (2021).
theta: An empirical curvature factor (dimensionless). See Equation 34 from S. von Caemmerer (2021).
x_etr: The fraction of whole-chain electron transport occurring in the mesophyll (dimensionless). See Equation 29 from S. von Caemmerer (2021).
ao_column_name: The name of the column in replicate_exdf that contains the dimensionless ratio of solubility and diffusivity of O2 to CO2.
a_column_name: The name of the column in replicate_exdf that contains the net assimilation in micromol m^(-2) s^(-1).
gamma_star_column_name: The name of the column in replicate_exdf that contains the dimensionless gamma_star values.
jmax_norm_column_name: The name of the column in exdf_obj that contains the normalized Jmax values (with units of normalized to Jmax at its optimal temperature).
kc_column_name: The name of the column in replicate_exdf that contains the Michaelis-Menten constant for rubisco carboxylation in microbar.
ko_column_name: The name of the column in replicate_exdf that contains the Michaelis-Menten constant for rubisco oxygenation in mbar.
kp_column_name: The name of the column in replicate_exdf that contains the Michaelis-Menten constant for PEP carboxylase carboxylation in microbar.
oxygen_column_name: The name of the column in exdf_obj that contains the concentration of O2 in the ambient air, expressed as a percentage (commonly 21% or 2%); the units must be percent.
pcm_column_name: The name of the column in replicate_exdf that contains the partial pressure of CO2 in the mesophyll, expressed in microbar.
qin_column_name: The name of the column in exdf_obj that contains values of the incident photosynthetically active flux density in micromol m^(-2) s^(-1).
rl_norm_column_name: The name of the column in replicate_exdf that contains the normalized RL values (with units of normalized to RL at 25 degrees C).
total_pressure_column_name: The name of the column in exdf_obj that contains the total pressure in bar.
vcmax_norm_column_name: The name of the column in replicate_exdf that contains the normalized Vcmax values (with units of normalized to Vcmax at 25 degrees C).
vpmax_norm_column_name: The name of the column in replicate_exdf that contains the normalized Vpmax values (with units of normalized to Vpmax at 25 degrees C).
hard_constraints: To be passed to calculate_c4_assimilation; see that function for more details.

Details

When fitting A-Ci curves, it is necessary to define a function that calculates the likelihood of a given set of alpha_psii, gbs, Jmax_at_opt, RL_at_25, Rm_frac, Vcmax_at_25, Vpmax_at_25, and Vpr values by comparing a model prediction to a measured curve. This function will be passed to an optimization algorithm which will determine the values that produce the smallest error.

The error_function_c4_aci returns such a function, which is based on a particular A-Ci curve and a set of fitting options. It is possible to just fit a subset of the available fitting parameters; by default, the fitting parameters are RL_at_25, Vcmax_at_25, and Vpmax_at_25. This behavior can be changed via the fit_options argument.

For practical reasons, the function actually returns values of -ln(L), where L is the likelihood. The logarithm of L is simpler to calculate than L itself, and the minus sign converts the problem from a maximization to a minimization, which is important because most optimizers are designed to minimize a value.

A penalty is added to the error value for any parameter combination where An is not a number, or where calculate_c4_assimilation produces an error.

Value

A function with one input argument guess, which should be a numeric vector representing values of the parameters to be fitted (which are specified by the fit_options input argument.) Each element of guess is the value of one parameter (arranged in alphabetical order.) For example, with the default settings, guess should contain values of RL_at_25, Vcmax_at_25, and Vpmax_at_25 (in that order).

Examples

# Read an example Licor file included in the PhotoGEA package
licor_file <- read_gasex_file(
  PhotoGEA_example_file_path('c4_aci_1.xlsx')
)

# Define a new column that uniquely identifies each curve
licor_file[, 'species_plot'] <-
  paste(licor_file[, 'species'], '-', licor_file[, 'plot'] )

# Organize the data
licor_file <- organize_response_curve_data(
    licor_file,
    'species_plot',
    c(9, 10, 16),
    'CO2_r_sp'
)

# Calculate temperature-dependent values of C4 photosynthetic parameters
licor_file <- calculate_arrhenius(licor_file, c4_arrhenius_von_caemmerer)

licor_file <- calculate_peaked_gaussian(licor_file, c4_peaked_gaussian_von_caemmerer)

# Calculate the total pressure in the Licor chamber
licor_file <- calculate_total_pressure(licor_file)

# Calculate PCm
licor_file <- apply_gm(licor_file, 'C4')

# Define an error function for one curve from the set
error_fcn <- error_function_c4_aci(
  licor_file[licor_file[, 'species_plot'] == 'maize - 5', , TRUE]
)

# Evaluate the error for RL_at_25 = 0, Vcmax_at_25 = 35, Vpmax_at_25 = 180
error_fcn(c(0, 35, 180))
#> [1] 140.3377

# Make a plot of error vs. Vcmax_at_25 when the other parameters are fixed to
# the values above.
vcmax_error_fcn <- function(Vcmax_at_25) {error_fcn(c(0, Vcmax_at_25, 180))}
vcmax_seq <- seq(20, 50)

lattice::xyplot(
  sapply(vcmax_seq, vcmax_error_fcn) ~ vcmax_seq,
  type = 'b',
  xlab = 'Vcmax at 25 degrees C (micromol / m^2 / s)',
  ylab = 'Negative log likelihood (dimensionless)'
)