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data_processing [2010/05/05 11:27]
mdaeron
data_processing [2013/01/22 04:15] (current)
mdaeron [(2) Compute the composition of your sample gas]
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 ====== Data processing ====== ====== Data processing ======
  
-===== CO2 data processing ​=====+{{:​gas_corrections.zip|Python code for gas corrections in the "​imperial"​ reference frame}} 
 + 
 +===== CO2 data reduction ​=====
 ==== (1) Compute the isotopologue composition of your reference gas ==== ==== (1) Compute the isotopologue composition of your reference gas ====
  
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 ==== (2) Compute the composition of your sample gas ==== ==== (2) Compute the composition of your sample gas ====
  
-**(2.a) Measure the abundance ratios of your sample gas for masses 45 to 49**+**(2.a) Measure the abundance ratios of your sample gas for masses 45 to 49 (R<​sub>​45-Sample</​sub>,​ etc.)**
  
-...based on voltage ​measurements from your dual-inlet spectrometer:​+...based on peak height ​measurements from your dual-inlet spectrometer:​
   * V<​sub>​44-Ref</​sub>​ ... V<​sub>​49-Ref</​sub>​ for your reference gas   * V<​sub>​44-Ref</​sub>​ ... V<​sub>​49-Ref</​sub>​ for your reference gas
   * V<​sub>​44-Sample</​sub>​ ... V<​sub>​49-Sample</​sub>​ for your sample gas   * V<​sub>​44-Sample</​sub>​ ... V<​sub>​49-Sample</​sub>​ for your sample gas
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 **(2.b) Compute the bulk composition of your sample gas** **(2.b) Compute the bulk composition of your sample gas**
 +
 +One way to do that is to define:
 +
 +  * K = R<​sub>​17-VSMOW</​sub>​ × (R<​sub>​18-VSMOW</​sub>​)<​sup>​–λ</​sup>​
 +
 +You can then compute <fc red>​R<​sub>​18-Sample</​sub></​fc>​ by numerically solving the following equation: ​
 +
 +  * –3K<​sup>​2</​sup>​ × (<fc red>​R<​sub>​18-Sample</​sub></​fc>​)<​sup>​2λ</​sup>​ + 2K × R<​sub>​45-Sample</​sub>​ × (<fc red>​R<​sub>​18-Sample</​sub></​fc>​)<​sup>​λ</​sup>​ + 2<fc red>​R<​sub>​18-Sample</​sub></​fc>​ - R<​sub>​46-Sample</​sub>​ = 0
 +
 +({{http://​dx.doi.org/​10.1002/​rcm.1012|Assonov & Brenninkmeijer,​ 2003}})
 +
 +R<​sub>​17-Sample</​sub>​ and R<​sub>​13-Sample</​sub>​ may then be directly calculated:
 +
 +  * R<​sub>​17-Sample</​sub>​ = K × (R<​sub>​18-Sample</​sub>​)<​sup>​λ</​sup>​
 +  * R<​sub>​13-Sample</​sub>​ = R<​sub>​45-Sample</​sub>​ - 2R<​sub>​17-Sample</​sub>​
 +
 +==== (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:
 +
 +  * C<​sub>​12-Sample</​sub>​ = 1 / (1 + R<​sub>​13-Sample</​sub>​)
 +  * C<​sub>​13-Sample</​sub>​ = R<​sub>​13-Sample</​sub>​ / (1 + R<​sub>​13-Sample</​sub>​)
 +  * C<​sub>​16-Sample</​sub>​ = 1 / (1 + R<​sub>​17-Sample</​sub>​ + R<​sub>​18-Sample</​sub>​)
 +  * C<​sub>​17-Sample</​sub>​ = R<​sub>​17-Sample</​sub>​ / (1 + R<​sub>​17-Sample</​sub>​ + R<​sub>​18-Sample</​sub>​)
 +  * C<​sub>​18-Sample</​sub>​ = R<​sub>​18-Sample</​sub>​ / (1 + R<​sub>​17-Sample</​sub>​ + R<​sub>​18-Sample</​sub>​)
 +
 +Then (note the asterisk, here used to denote the stochastic state):
 +
 +  * Mass 44:
 +    * C*<​sub>​12-16-16-Sample</​sub>​ = C<​sub>​12-Sample</​sub>​ × C<​sub>​16-Sample</​sub>​ × C<​sub>​16-Sample</​sub>​
 +  * Mass 45:
 +    * C*<​sub>​13-16-16-Sample</​sub>​ = C<​sub>​13-Sample</​sub>​ × C<​sub>​16-Sample</​sub>​ × C<​sub>​16-Sample</​sub>​
 +    * C*<​sub>​12-17-16-Sample</​sub>​ = C<​sub>​12-Sample</​sub>​ × C<​sub>​17-Sample</​sub>​ × C<​sub>​16-Sample</​sub>​ × 2
 +  * Mass 46:
 +    * C*<​sub>​12-18-16-Sample</​sub>​ = C<​sub>​12-Sample</​sub>​ × C<​sub>​18-Sample</​sub>​ × C<​sub>​16-Sample</​sub>​ × 2
 +    * C*<​sub>​13-17-16-Sample</​sub>​ = C<​sub>​13-Sample</​sub>​ × C<​sub>​17-Sample</​sub>​ × C<​sub>​16-Sample</​sub>​ × 2
 +    * C*<​sub>​12-17-17-Sample</​sub>​ = C<​sub>​12-Sample</​sub>​ × C<​sub>​17-Sample</​sub>​ × C<​sub>​17-Sample</​sub>​
 +  * Mass 47:
 +    * C*<​sub>​13-18-16-Sample</​sub>​ = C<​sub>​13-Sample</​sub>​ × C<​sub>​18-Sample</​sub>​ × C<​sub>​16-Sample</​sub>​ × 2
 +    * C*<​sub>​13-17-17-Sample</​sub>​ = C<​sub>​13-Sample</​sub>​ × C<​sub>​17-Sample</​sub>​ × C<​sub>​17-Sample</​sub>​
 +    * C*<​sub>​12-18-17-Sample</​sub>​ = C<​sub>​12-Sample</​sub>​ × C<​sub>​18-Sample</​sub>​ × C<​sub>​17-Sample</​sub>​ × 2
 +  * Mass 48:
 +    * C*<​sub>​13-18-17-Sample</​sub>​ = C<​sub>​13-Sample</​sub>​ × C<​sub>​18-Sample</​sub>​ × C<​sub>​17-Sample</​sub>​ × 2
 +    * C*<​sub>​12-18-18-Sample</​sub>​ = C<​sub>​12-Sample</​sub>​ × C<​sub>​18-Sample</​sub>​ × C<​sub>​18-Sample</​sub>​
 +  * Mass 49:
 +    * C*<​sub>​13-18-18-Sample</​sub>​ = C<​sub>​13-Sample</​sub>​ × C<​sub>​18-Sample</​sub>​ × C<​sub>​18-Sample</​sub>​
 +
 +Then:
 +
 +  * C*<​sub>​44-Sample</​sub>​ = C*<​sub>​12-16-16-Sample</​sub>​
 +  * C*<​sub>​45-Sample</​sub>​ = C*<​sub>​13-16-16-Sample</​sub>​ + C*<​sub>​12-17-16-Sample</​sub>​
 +  * C*<​sub>​46-Sample</​sub>​ = C*<​sub>​12-18-16-Sample</​sub>​ + C*<​sub>​13-17-16-Sample</​sub>​ + C*<​sub>​12-17-17-Sample</​sub>​
 +  * C*<​sub>​47-Sample</​sub>​ = C*<​sub>​13-18-16-Sample</​sub>​ + C*<​sub>​13-17-17-Sample</​sub>​ + C*<​sub>​12-18-17-Sample</​sub>​
 +  * C*<​sub>​48-Sample</​sub>​ = C*<​sub>​13-18-17-Sample</​sub>​ + C*<​sub>​12-18-18-Sample</​sub>​
 +  * C*<​sub>​49-Sample</​sub>​ = C*<​sub>​13-18-18-Sample</​sub>​
 +
 +Ending up with the following "​stochastic abundance ratios":​
 +
 +  * R*<​sub>​45-Sample</​sub>​ = C*<​sub>​45-Sample</​sub>​ / C*<​sub>​44-Sample</​sub>​
 +  * R*<​sub>​46-Sample</​sub>​ = C*<​sub>​45-Sample</​sub>​ / C*<​sub>​44-Sample</​sub>​
 +  * R*<​sub>​47-Sample</​sub>​ = C*<​sub>​45-Sample</​sub>​ / C*<​sub>​44-Sample</​sub>​
 +  * R*<​sub>​48-Sample</​sub>​ = C*<​sub>​45-Sample</​sub>​ / C*<​sub>​44-Sample</​sub>​
 +  * R*<​sub>​49-Sample</​sub>​ = C*<​sub>​45-Sample</​sub>​ / C*<​sub>​44-Sample</​sub>​
 +
 +**(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 Δ<​sub>​47</​sub>​ values are typically underestimated by roughly the actual Δ<​sub>​47</​sub>​ value of your reference gas.
 +
 +  * rawΔ<​sub>​47</​sub>​ = 1000 × [ (R<​sub>​47-Sample</​sub>/​R*<​sub>​47-Sample</​sub>​ - 1) - (R<​sub>​46-Sample</​sub>/​R*<​sub>​46-Sample</​sub>​ - 1) - (R<​sub>​45-Sample</​sub>/​R*<​sub>​45-Sample</​sub>​ - 1) ]
 +  * rawΔ<​sub>​48</​sub>​ = 1000 × [ (R<​sub>​48-Sample</​sub>/​R*<​sub>​48-Sample</​sub>​ - 1) - 2 × (R<​sub>​46-Sample</​sub>/​R*<​sub>​46-Sample</​sub>​ - 1) ]
 +  * rawΔ<​sub>​49</​sub>​ = 1000 × [ (R<​sub>​49-Sample</​sub>/​R*<​sub>​49-Sample</​sub>​ - 1) - 2 × (R<​sub>​46-Sample</​sub>/​R*<​sub>​46-Sample</​sub>​ - 1) - (R<​sub>​45-Sample</​sub>/​R*<​sub>​45-Sample</​sub>​ - 1) ]
 +
 +({{http://​dx.doi.org/​10.1016/​j.gca.2005.08.021|Affek & Eiler, 2006}})
 +
 +==== (4) Correct for non-linearity,​ stretching, and other effects ====
 +
 +...using equilibrated CO<​sub>​2</​sub>​ standards prepared using various [[recipes]].
  
 //(to be continued soon)// //(to be continued soon)//
data_processing.1273073220.txt.gz · Last modified: 2012/04/04 09:08 (external edit)