Fit a Light Response Curve (LRC) by an index to get a parameter file

This function uses the equation: $$\text{NEE} \sim \frac{a_1 \cdot \text{PAR} \cdot a_x}{a_1 \cdot \text{PAR} + a_x} - r$$

Where \(r\) is ecosystem respiration (\(\mu\)mol CO2 m-2 s-1), \(a_1\) is the apparent quantum efficiency of CO2 uptake (CO2), and \(a_x\) is the maximum CO2 uptake rate on the ecosystem scale.

The equation requires photosynthetically active radiation, PAR, in \(\mu\)mol m-2 s-1 and net ecosystem exchange, NEE, in \(\mu\)mol m-2 s-1.

Usage

LRC_PARMS_01(
  data.frame = NULL,
  iterations = NULL,
  priors.lrc = brms::prior("normal(-0.01, 0.1)", nlpar = "a1", lb = -0.2, ub = 0) +
    brms::prior("normal(-7.65, 0.33)", nlpar = "ax", lb = -30, ub = -0.01) +
    brms::prior("normal(2.10, 0.11)", nlpar = "r", lb = 1.9, ub = 2.2),
  idx.colname = NULL,
  NEE.colname = NULL,
  PAR.colname = NULL
)

Arguments

data.frame

(dataframe) A dataframe that contains net ecosystem exchange (NEE), an index, and photosynthetically active radiation (PAR).

iterations

(numeric) The number of iterations to run brms::brm().

priors.lrc

(brmsprior dataframe) The priors for brms::brm() to use. Default priors are as follows:

brms::prior("normal(-0.01, 0.1)", nlpar = "a1", lb = -0.2, ub = 0) +
brms::prior("normal(-7.65, 0.33)", nlpar = "ax", lb = -30, ub = -0.01) +
brms::prior("normal(2.10, 0.11)", nlpar = "r", lb = 1.9, ub = 2.2)

idx.colname

(character) The name of the column containing the index.

NEE.colname

(character) The name of the column containing NEE.

PAR.colname

(character) The name of the column containing PAR.

Value

(dataframe) Dataframe of parameter values by the index used to fit them.

Details

Model parameters are fit using the R package brms.

Rhat (Potential Scale Reduction Factor): Indicates how well the different Markov chains in your analysis have converged to the same posterior distribution. Ideally, Rhat should be close to 1 for all parameters. A high Rhat value suggests potential convergence issues and the need to run the chains longer.

Bulk ESS (Effective Sample Size - Bulk): Estimates the effective number of independent samples from the central part of the posterior distribution.

Tail ESS (Effective Sample Size - Tail): Estimates the effective number of independent samples from the tails of the posterior distribution. Important for assessing the reliability of quantile estimates (e.g., 95% confidence intervals).

Key points to remember: Aim for Rhat close to 1 and high values for both Bulk ESS and Tail ESS.

Examples

if (FALSE) { # !is.null(cmdstanr::cmdstan_version(error_on_NA = FALSE))
# Import flux tower data
tower.data <- read.csv(system.file("extdata", "AMF_US-Skr_BASE_HH_2-5_Formatted.csv",
                                   package = "CarbonExchangeParameters"))

# Fit curve parameters for each YearMon:
Example_LRC_PARMS_01 <- LRC_PARMS_01(data.frame = tower.data,
                                     iterations = 1000,
                                     priors.lrc = brms::prior("normal(-0.01, 0.1)",
                                                    nlpar = "a1", lb = -0.2, ub = 0) +
                                                  brms::prior("normal(-7.65, 0.33)",
                                                    nlpar = "ax", lb = -30, ub = -0.01) +
                                                  brms::prior("normal(2.10, 0.11)",
                                                    nlpar = "r", lb = 1.9, ub = 2.2),
                                     idx.colname = 'YearMon',
                                     NEE.colname = 'NEE_PI',
                                     PAR.colname = 'SW_IN')

}