create_equations: Create a list of equations for recalculating gasanalyzer data.

Description

This function creates a list of equations that can be used to recalculate gas-exchange data by passing the resulting object to the recalculate() method. Various useflags can be defined to tune the equations. In addition, custom equations can be defined as arguments. Note that the calculations may fail if commons are missing in the gas-exchange data.

Usage

create_equations(useflags = "default", ...)

Value

A list of language objects with equations

Arguments

useflags: character vector with the type of equations to create (see Details). Leave empty to obtain the default set. An unknown flag returns an empty list, and a warning listing all valid flags.
...: custom equations. the arguments must tagged function expressions. Note that the function body must be wrapped in curly brackets. The tags will be matched against the names of a data frame when applying the return value with recalculate().

Details

The useflags argument currently supports several pre-defined sets of equations.

Gas-Exchange and fluorescence models

default: A set with the most commonly-used derived quantities in the gas-exchange (GasEx) and chlorophyll fluorescence (FLR) categories. The equations are described in detail by von Caemmerer and Farquhar (1981) and LI-COR Biosciences Inc (2022).

GoffGratch1946

Replaces or adds equations related to the calculation of the saturated water pressure of the leaf (GasEx.SVPleaf) and chamber air (GasEx.SVPcham). The calculation is based on that described by Goff and Gratch (1946) and only takes the temperature into account.

Buck1981

Replaces or adds equations for (GasEx.SVPleaf) and (GasEx.SVPcham). based on the description by Buck (1981). Takes temperature and pressure into account.

Buck1996

Replaces or adds equations for (GasEx.SVPleaf) and (GasEx.SVPcham) based on the description by Buck (1996). Takes temperature and pressure into account.

cuticular_conductance

Replaces the equations related to CO2 and H2O conductance and substomatal CO2 (GasEx.gtw; GasEx.gsw; GasEx.gtc; GasEx.Ci) with versions that take into account cuticular conductance (Márquez et al., 2021, 2023). Requires manually specifying the cuticular conductance to water (Const.gcw) and CO2 (Const.gcc).

boundary_conducance

Replaces or adds equations related to the boundary layer conductance (GasEx.gbw) and leaf temperature derived from the energy balance equations (GasEx.TleafEB) with a version that is valid for a sample with no stomata. This is typically used when estimating GasEx.gbw using filter paper (Parkinson, 1985). Note that the leaf thermocouple (Meas.Tleaf) is used to estimate air temperature (and should therefore not touch the sample). This can be overridden by a custom equation. The sample emissivity (Const.eps), the ratio between heat and water conductance for the chamber air (Const.ra_rv) and the fraction of the area exchanging radiative and sensible heat (Const.asH) can be adjusted. For solving the energy balance equations, the method described by Bristow (1987) is used.

gm_fluorescence

Adds derived variables for mesophyll conductance (FLR.gm) and chloroplast CO2 mole fractions (FLR.Cc) based on gas exchange and chlorophyll fluorescence (Harley et al., 1992). It is strongly recommended to first calibrate the electron transport rates reported in the FLR.ETR column. In addition, the equations require adding columns for the respiration rate in the light (Const.RL), and the CO2 photo-compensation point (Const.GammaStar).

Isotope models

d13C: Adds derived variables related to the stable carbon isotope discrimination model for C3 plants (Farquhar and Cernusak, 2012; Evans and von Caemmerer, 2013) aimed at estimating the mesophyll conductance d13C.gm and chloroplast CO2 mole fraction (d13C.Cc). Requires additional columns with data on the carbon isotope composition in sample and reference air (d13CMeas.delta13CO2s; d13CMeas.delta13CO2r) and in the air where the plants were grown (d13CConst.delta13CO2g), and values for respiration in the light (Const.RL) and the CO2 photo-compensation point (Const.GammaStar).

d13C_dis

Requires the d13C flag, but modifies the modeled carbon isotope discrimination d13C.Deltai and d13C.gm using the assumption that the carbon pools of respiration and assimilation are disconnected (as described by Busch et al., 2020).

d13C_e_Busch2020

Requires the d13C flag, but modifies the calculation of the effective respiratory fractionation (d13C.ep) to better take into account the effect of the growth conditions (Busch et al. 2020). Additionally requires a value for the observed discrimination against 13CO2 under growth conditions (d13CConst.Deltag).

These implement calculations as close as possible to those used in the instrument firmware and are typically related to the specific configurations or instrument design. In addition, some methods are provided for recalculating low-level instrument variables.

li6400: Definitions for boundary layer conductance, temperature, and light related variables (GasEx.gbw; GasEx.Rabs; GasEx.TairCnd; LeafQ.alpha) specific to LI-6400 / LI-6400XT instruments (LI-COR Biosciences Inc, 2011).
li6800: Definitions for boundary layer conductance, light, leakage, temperature and light related variables (GasEx.gbw; GasEx.Rabs; GasEx.TairCnd; LeafQ.alpha; LeafQ.Qin; LeafQ.Conv; Leak.Fan; Leak.CorrFact; GasEx.Ca) specific to the LI-6800 instrument (LI-COR Biosciences Inc, 2022).
ciras4: Light absorptance (LeafQ.alpha) and the conversion between photon flux density and irradiance (LeafQ.Conv) is calculated by taking into account the effect of the different light sources that can be used with the CIRAS-4 instrument (PP Systems, 2024).
gfs3000: Boundary layer conductance (GasEx.gbw) and light sensor (LeafQ.Qin) calculations adjusted for the default chamber of the GFS-3000 instrument (Heinz Walz GmbH, 2019).
gfs3000_light_bot: Requires gfs3000, but modifies LeafQ.Qin to indicate that the bottom light sensor of the default chamber was used to quantify the light intensity incident on the leaf (Heinz Walz GmbH, 2019).
match: Takes a previously stored offset between sample and reference analyzers into account when recalculating water and CO2 mole fractions (Meas.H2Os; Meas.CO2s) as described by LI-COR Biosciences Inc (2022), Heinz Walz GmbH (2019) and PP Systems (2024). The corrected mole fractions are already stored in the data and therefore this calculation is usually not required. However, these equations are needed when recalculating mole fractions from lower level data (see the raw and O2_correction flags).
raw: Recalculates CO2 and H2O mole fractions from such low-level variables (Meas.CO2r; Meas.H2Or; Meas.CO2a; Meas.H2Oa) as described by LI-COR Biosciences Inc (2022). Currently only implemented for the LI-6800 because low-level instrument data are required. Requires storing raw data and the availability of factory calibration files. Requires and enables the match set.
O2_correction: Recalculates CO2 and H2O mole fractions (Meas.CO2r; Meas.H2Or; Meas.CO2a; Meas.H2Oa) at a potentially different oxygen concentration ( Const.Oxygen). Currently only implemented for the LI-6800 (LI-COR Biosciences Inc, 2022) and GFS-3000 (K. Siebke, Heinz Walz GmbH, personal communication). For the LI-6800, this requires loading of factory calibration files (import_factory_cals()). Requires and automatically enables the match flag.

References

Bristow KL. 1987. On solving the surface energy balance equation for surface temperature. Agricultural and Forest Meteorology 39:49–54.
Buck AL. 1981. New equations for computing vapor pressure and enhancement factor. Journal of Applied Meteorology 20:1527–1532.
Buck AL. 1996. Buck research CR-1A user’s manual. Boulder, CO: Buck Research Instruments.
Busch FA, Holloway-Phillips M, Stuart-Williams H, Farquhar GD. 2020. Revisiting carbon isotope discrimination in C3 plants shows respiration rules when photosynthesis is low. Nature Plants 6:245–258. https://www.hygrometers.com/wp-content/uploads/CR-1A-users-manual-2009-12.pdf
von Caemmerer S, Farquhar GD. 1981. Some relationships between the biochemistry of photosynthesis and the gas exchange of leaves. Planta 153:376–387.
Evans JR, von Caemmerer S. 2013. Temperature response of carbon isotope discrimination and mesophyll conductance in tobacco. Plant, Cell & Environment 36:745–756.
Farquhar GD, Cernusak LA. 2012. Ternary effects on the gas exchange of isotopologues of carbon dioxide. Plant, Cell & Environment 35:1221–1231.
Goff JA, Gratch S. 1946. Low-pressure properties of water from -160° F to 212° F. Transactions of the American Society of Heating and Ventilating Engineers 52:95–121.
Harley PC, Loreto F, Di Marco G, Sharkey TD. 1992. Theoretical considerations when estimating the mesophyll conductance to CO2 flux by analysis of the response of photosynthesis to CO2. Plant Physiology 98:1429–1436.
Heinz Walz GmbH. 2019. Portable gas exchange fluorescence system GFS-3000. Handbook of operation. 9th edition. https://www.walz.com/files/downloads/manuals/gfs-3000/GFS-3000_Manual_9.pdf
LI-COR Biosciences Inc. 2011. Using the LI-6400/LI-6400XT portable photosynthesis system. Version 6.2. https://www.licor.com/env/support/LI-6400/manuals.html
LI-COR Biosciences Inc. 2022. Using the LI-6800 portable photosynthesis system. Version 2.1. https://www.licor.com/env/support/LI-6800/manuals.html
Márquez DA, Stuart-Williams H, Farquhar GD. 2021. An improved theory for calculating leaf gas exchange more precisely accounting for small fluxes. Nature Plants 7:317–326.
Márquez DA, Stuart-Williams H, Cernusak LA, Farquhar GD. 2023. Assessing the CO2 concentration at the surface of photosynthetic mesophyll cells. New Phytologist 238:1446–1460.
Parkinson KJ. 1985. A simple method for determining the boundary layer resistance in leaf cuvettes. Plant, Cell & Environment 8: 223–226.
PP Systems. 2024. CIRAS-4 portable photosynthesis system. Operation manual. Amesbury, MA: PP Systems. Version 1.3.

Examples

Run this code

exampledir <- system.file("extdata", package = "gasanalyzer")

# import factory calibration for example data:
import_factory_cals(exampledir)

# read data from a txt file:
li6800 <- read_6800_txt(file.path(exampledir, "lowo2"))

# passing an invalid flags shows which flags are valid:
create_equations("help")

# create a default set of gas-exchange equations, for the 6800, but overwrite
# the default calculation of leaf light absorption with a custom value:
Eqs <- create_equations(c("default", "li6800"), LeafQ.alpha = \() {0.86})

#apply:
li6800_recalc <- recalculate(li6800, Eqs)

li6800$LeafQ.alpha
li6800_recalc$LeafQ.alpha

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