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data_processing

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Data processing

CO2 data reduction

(1) Compute the isotopologue composition of your reference gas

…using the following parameters:

• δ13CRef: the nominal carbon isotope composition of your reference gas vs VPDB
• δ18ORef: the nominal oxygen isotope composition of your reference gas vs VSMOW
• λ = 0.5164, the terrestrial mass-dependent fractionation parameter between 17O and 18O [missing reference]
• R13-VPDB = 0.0112372, the abundance ratio of 13C/12C for VPDB [missing reference]
• R17-VSMOW = 0.0003799, the abundance ratio of 17O/16O for VSMOW [missing reference]
• R18-VSMOW = 0.0020052, the abundance ratio of 18O/16O for VSMOW [missing reference]

(1.a) Compute abundance ratios of 13C/12C, 17O/16O and 18O/16O

• R13-Ref = R13-VPDB × (1 + δ13CRef/1000)
• R18-Ref = R18-VSMOW × (1 + δ18ORef/1000)
• R17-Ref = R17-VSMOW × (R18-Ref / R18-VSMOW)λ

(1.b) Compute abundances of 12C, 13C, 16O, 17O and 18O

• C12-Ref = 1 / (1 + R13-Ref)
• C13-Ref = R13-Ref / (1 + R13-Ref)
• C16-Ref = 1 / (1 + R17-Ref + R18-Ref)
• C17-Ref = R17-Ref / (1 + R17-Ref + R18-Ref)
• C18-Ref = R18-Ref / (1 + R17-Ref + R18-Ref)

(1.c) Compute abundances of isotopologues with masses 44 to 49

…by making the assumption that your reference gas is stochastic (this is usually not true, but we correct for that later in the process).

• Mass 44:
• C12-16-16-Ref = C12-Ref × C16-Ref × C16-Ref
• Mass 45:
• C13-16-16-Ref = C13-Ref × C16-Ref × C16-Ref
• C12-17-16-Ref = C12-Ref × C17-Ref × C16-Ref × 2
• Mass 46:
• C12-18-16-Ref = C12-Ref × C18-Ref × C16-Ref × 2
• C13-17-16-Ref = C13-Ref × C17-Ref × C16-Ref × 2
• C12-17-17-Ref = C12-Ref × C17-Ref × C17-Ref
• Mass 47:
• C13-18-16-Ref = C13-Ref × C18-Ref × C16-Ref × 2
• C13-17-17-Ref = C13-Ref × C17-Ref × C17-Ref
• C12-18-17-Ref = C12-Ref × C18-Ref × C17-Ref × 2
• Mass 48:
• C13-18-17-Ref = C13-Ref × C18-Ref × C17-Ref × 2
• C12-18-18-Ref = C12-Ref × C18-Ref × C18-Ref
• Mass 49:
• C13-18-18-Ref = C13-Ref × C18-Ref × C18-Ref

(1.d) Compute binned abundances of isotopologues grouped by mass

• C44-Ref = C12-16-16-Ref
• C45-Ref = C13-16-16-Ref + C12-17-16-Ref
• C46-Ref = C12-18-16-Ref + C13-17-16-Ref + C12-17-17-Ref
• C47-Ref = C13-18-16-Ref + C13-17-17-Ref + C12-18-17-Ref
• C48-Ref = C13-18-17-Ref + C12-18-18-Ref
• C49-Ref = C13-18-18-Ref

(2) Compute the composition of your sample gas

(2.a) Measure the abundance ratios of your sample gas for masses 45 to 49

…based on voltage measurements from your dual-inlet spectrometer:

• V44-Ref … V49-Ref for your reference gas
• V44-Sample … V49-Sample for your sample gas

Ideally, these voltages reflect abundance ratios, so that:

• R45-Sample = R45-Ref × V45-Sample / V44-Sample × V44-Ref / V45-Ref
• R46-Sample = R46-Ref × V46-Sample / V44-Sample × V44-Ref / V46-Ref
• R47-Sample = R47-Ref × V47-Sample / V44-Sample × V44-Ref / V47-Ref
• R48-Sample = R48-Ref × V48-Sample / V44-Sample × V44-Ref / V48-Ref
• R49-Sample = R49-Ref × V49-Sample / V44-Sample × V44-Ref / V49-Ref

And, using the conventional δ notation (relative to your reference gas):

• δ45 = 1000 × (1 - R45-Sample/R45-Ref) = 1000 × (1 - V45-Sample / V44-Sample × V44-Ref / V45-Ref)
• δ46 = 1000 × (1 - R46-Sample/R46-Ref) = 1000 × (1 - V46-Sample / V44-Sample × V44-Ref / V46-Ref)
• δ47 = 1000 × (1 - R47-Sample/R47-Ref) = 1000 × (1 - V47-Sample / V44-Sample × V44-Ref / V47-Ref)
• δ48 = 1000 × (1 - R48-Sample/R48-Ref) = 1000 × (1 - V48-Sample / V44-Sample × V44-Ref / V48-Ref)
• δ49 = 1000 × (1 - R49-Sample/R49-Ref) = 1000 × (1 - V49-Sample / V44-Sample × V44-Ref / V49-Ref)

(2.b) Compute the bulk composition of your sample gas

One way to do that is to define:

• K = R17-VSMOW × (R18-VSMOW)–λ

You can then compute <fc red>R18-Sample</fc> by numerically solving the following equation:

• –3K2 × (<fc red>R18-Sample</fc>) + 2K × R45-Sample × (<fc red>R18-Sample</fc>)λ + 2<fc red>R18-Sample</fc> - R46-Sample = 0

R17-Sample and R13-Sample may then be directly calculated:

• R17-Sample = K × (R18-Sample)λ
• R13-Sample = R45-Sample - 2R17-Sample

(3) Compute "raw" Δ values of your sample gas

(3.a) “Scramble” your sample gas

This means computing the abundance of each isotopologue of a gas with the same bulk composition as your sample, but in a stochastic state. This is done by following the steps (1.b) to (1.d) above:

• C12-Sample = 1 / (1 + R13-Sample)
• C13-Sample = R13-Sample / (1 + R13-Sample)
• C16-Sample = 1 / (1 + R17-Sample + R18-Sample)
• C17-Sample = R17-Sample / (1 + R17-Sample + R18-Sample)
• C18-Sample = R18-Sample / (1 + R17-Sample + R18-Sample)

Then (note the asterisk, here used to denote the stochastic state):

• Mass 44:
• C*12-16-16-Sample = C12-Sample × C16-Sample × C16-Sample
• Mass 45:
• C*13-16-16-Sample = C13-Sample × C16-Sample × C16-Sample
• C*12-17-16-Sample = C12-Sample × C17-Sample × C16-Sample × 2
• Mass 46:
• C*12-18-16-Sample = C12-Sample × C18-Sample × C16-Sample × 2
• C*13-17-16-Sample = C13-Sample × C17-Sample × C16-Sample × 2
• C*12-17-17-Sample = C12-Sample × C17-Sample × C17-Sample
• Mass 47:
• C*13-18-16-Sample = C13-Sample × C18-Sample × C16-Sample × 2
• C*13-17-17-Sample = C13-Sample × C17-Sample × C17-Sample
• C*12-18-17-Sample = C12-Sample × C18-Sample × C17-Sample × 2
• Mass 48:
• C*13-18-17-Sample = C13-Sample × C18-Sample × C17-Sample × 2
• C*12-18-18-Sample = C12-Sample × C18-Sample × C18-Sample
• Mass 49:
• C*13-18-18-Sample = C13-Sample × C18-Sample × C18-Sample

Then:

• C*44-Sample = C*12-16-16-Sample
• C*45-Sample = C*13-16-16-Sample + C*12-17-16-Sample
• C*46-Sample = C*12-18-16-Sample + C*13-17-16-Sample + C*12-17-17-Sample
• C*47-Sample = C*13-18-16-Sample + C*13-17-17-Sample + C*12-18-17-Sample
• C*48-Sample = C*13-18-17-Sample + C*12-18-18-Sample
• C*49-Sample = C*13-18-18-Sample

Ending up with the following “stochastic abundance ratios”:

• R*45-Sample = C*45-Sample / C*44-Sample
• R*46-Sample = C*45-Sample / C*44-Sample
• R*47-Sample = C*45-Sample / C*44-Sample
• R*48-Sample = C*45-Sample / C*44-Sample
• R*49-Sample = C*45-Sample / C*44-Sample

(3.b) Compute raw Δ values

These Δ values are called “raw” because they have not yet been corrected for a number of analytical artifacts. Most importantly, we have assumed that your reference gas is in a stochastic state, which is unlikely. This is why raw Δ47 values are typically underestimated by roughly the actual Δ47 value of your reference gas.

• rawΔ47 = 1000 × [ (R47-Sample/R*47-Sample - 1) - (R46-Sample/R*46-Sample - 1) - (R45-Sample/R*45-Sample - 1) ]
• rawΔ48 = 1000 × [ (R48-Sample/R*48-Sample - 1) - 2 × (R46-Sample/R*46-Sample - 1) ]
• rawΔ49 = 1000 × [ (R49-Sample/R*49-Sample - 1) - 2 × (R46-Sample/R*46-Sample - 1) - (R45-Sample/R*45-Sample - 1) ]

(4) Correct for non-linearity, stretching, and other effects

…using equilibrated CO2 standards prepared using various recipes.

(to be continued soon)

data_processing.1273240656.txt.gz · Last modified: 2012/04/04 09:08 (external edit)

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