Calculate temperature-dependent values using Arrhenius equations

Calculate leaf-temperature-dependent values of various parameters using Arrhenius equations. It is rare for users to call this function directly; instead, it is used internally by calculate_temperature_response.

Usage

calculate_temperature_response_arrhenius(
    exdf_obj,
    arrhenius_parameters,
    tleaf_column_name = 'TleafCnd'
  )

Arguments

exdf_obj

An exdf object representing data from a Licor gas exchange measurement system.

arrhenius_parameters

A list of named lists. Each list element should describe the Arrhenius scaling factor (c), activation energy in kJ / mol (Ea), and units (units) for a variable that follows an Arrhenius temperature dependence. The name of each list element should be the corresponding name of the variable.

tleaf_column_name

The name of the column in exdf_obj that contains the leaf temperature in units of degrees C.

Details

The Arrhenius equation is often used to calculate the temperature dependence of the rate of a chemical reaction. It is often stated as follows:

(1) rate = A * exp(-Ea / (R * T))

where A is the "pre-exponential factor" that sets the overall scaling, Ea is the activation energy, R is the ideal gas constant, and T is the temperature in Kelvin. See, for example, the Wikipedia page for the equation.

In photosynthesis research, it is common to use an alternative form of the equation, where the pre-exponential factor A is rewritten as an exponent A = exp(c), where c is a "scaling factor" whose value can be calculated from A according to c = ln(A)). In this formulation, the equation becomes:

(2) rate = exp(c) * exp(-Ea / (R * T)) = exp(c - Ea / (R * T))

The advantage of this version is that the natural logarithm of the rate is equal to c - Ea / (R * T). This means that the Arrhenius paramerer values can be easily determined from a linear fit of log(rate) against 1 / (R * T); c is the y-intercept and -Ea is the slope.

In calculate_temperature_response_arrhenius, the scaling factor (c), activation energy (Ea), and units (units) for a variable must be specified as elements of a list, which itself is a named element of arrhenius_parameters. For example, if a variable called Kc has c = 38.05, Ea = 79.43, and units of micromol mol^(-1), the arrhenius_parameters argument could be specified as follows: list(Kc = list(c = 38.05, Ea = 79.43, units = 'micromol mol^(-1)')).

It is rare to directly specify the Arrhenius parameters; instead, it is more typical to use one of the pre-set values such as those included in c3_temperature_param_sharkey.

Sometimes a publication will specify the value of a variable at 25 degrees C instead of the Arrhenius scaling factor c. In this case, there is a "trick" for determining the value of c. For example, if the Arrhenius exponent should be X at 25 degrees C, then we have the following: X = exp(c - Ea / (R * (25 + 273.15))), which we can solve algebraically for c as follows: c = ln(X) + Ea / f, where f = R * (25 + 273.15). As a special case, for parameters normalized to 1 at 25 degrees C, we have c = Ea / f. The value of f can be accessed as PhotoGEA:::f.

Another common scenario is that we may wish to convert the units of a variable defined by Arrhenius exponents. For example, let's say Y is determined by an Arrhenius exponent, i.e., that Y = exp(c - Ea / (R * T)), and we want to convert Y to different units via a multiplicative conversion factor cf. Then, in the new units, Y becomes Y_new = cf * Y = cf * exp(c - (R * T)). Through algebra, it is possible to combine cf with the original value of c as c_new = c + ln(cf). Then we can continue calculating Y_new using an Arrhenius factor as Y_new = exp(c_new - Ea / (R * T)).

Value

An exdf object based on exdf_obj that includes one new column for each element of arrhenius_parameters, where the temperature-dependent values of these new columns are determined using the temperature values specified by the tleaf_column_name column. The category of each of these new columns is calculate_temperature_response_arrhenius to indicate that they were created using this function.

Examples

# Read an example Licor file included in the PhotoGEA package
licor_file <- read_gasex_file(
  PhotoGEA_example_file_path('ball_berry_1.xlsx')
)

licor_file <- calculate_temperature_response_arrhenius(
  licor_file,
  list(Kc_norm = c3_temperature_param_sharkey$Kc_norm)
)

licor_file$units$Kc_norm      # View the units of the new `Kc_norm` column
#> [1] "normalized to Kc at 25 degrees C"
licor_file$categories$Kc_norm # View the category of the new `Kc_norm` column
#> [1] "calculate_temperature_response_arrhenius"
licor_file[,'Kc_norm']        # View the values of the new `Kc_norm` column
#>  [1] 1.910018 1.769200 1.676876 1.646016 1.645876 1.628370 1.586497 2.240778
#>  [9] 2.068778 2.071206 2.019640 2.071358 2.069276 2.076637 2.432435 2.291906
#> [17] 2.212798 2.201974 2.194358 2.086708 2.166221 2.525028 2.344517 2.225575
#> [25] 2.173927 2.194267 2.085659 2.078922