D17Oscaling

Perform two-point normalization of triple oxygen isotope measurements based on two or more reference materials with sufficiently different δ18O values.

The normalization applies two affine transformations:

• δ¹⁸O_new = a₁₈ ∙ δ¹⁸O_old + b₁₈
• δ¹⁷O_new = a₁₇ ∙ δ¹⁷O_old + b₁₇

Provided with (1) a set of measurements of one or more unknown samples, with uncertainties; (2) a set of measurement of two or more known reference materials, with uncertaines; (3) nominal (δ¹⁸O, Δ¹⁷O) values for the reference materials, D17Oscaling computes the normalized (δ¹⁸O, Δ¹⁷O) values for all unknown samples and the variance-covariance matrix describing the (correlated) uncertainties of these normalized values.

D17Oscaling is also capable of processing a list of “raw” individual (δ¹⁸O, Δ¹⁷O) analyses, compute the average composition of each sample and assign uncertainties to these average compositions based on the pooled variances of all δ¹⁸O and all Δ¹⁷O measurements, respectively.

Usage

First import D17Oscaling and define some reference materials:

from D17Oscaling import DataSet

RM = {
	'VSMOW': {'d18O': 0., 'D17O': 0.},
	'SLAP': {'d18O': -55.5, 'D17O': 0.},
}

Then create a DataSet() object, import some analytical data and print out what the DataSet looks like now:

# create DataSet() instance
data = DataSet()

# import some analytical data;
data.import_analyses(
	'examples/data.csv',
	columns = {
		'd18O': 'd18O_raw',
		'D17O': 'D17O_raw'
	},
)
# `columns` renames columns to 'd18O_raw' and 'D17O_raw',
# meaning that these values are not yet normalized.

# take a look
print(data)

This should look like this.

• The raw data we just imported is stored as a pandas.DataFrame in data.analyses.
• The pooled standard deviantion of d18O_raw and D17O_raw for this dataset is stored as data.SD_d18O_raw and data.SD_D17O_raw.
• The mean raw values for each analyte were automatically computed, with uncertainties derived from SD_d18O_raw, SD_D17O_raw, and the number of replicate analyses for each analyte. These mean values are saved as uncertainties.UFloat values in a pandas.DataFrame stored as data.analytes.

DataSet(
  [analyses] =
        UID Analyte   d18O_raw  D17O_raw
    0   X01     FOO -12.532655 -0.098675
    1   X02     BAR  -7.879440  0.097711
    2   X03     BAZ -50.274837 -0.126091
    3   X04   VSMOW  -0.085304  0.004308
    4   X05    SLAP -55.412060  0.021416
    5   X06     FOO -12.467660 -0.108063
    6   X07     BAR  -7.841212  0.088934
    7   X08     BAZ -50.160433 -0.138356
    8   X09   VSMOW   0.046751  0.006160
    9   X10    SLAP -55.585929  0.011290
    10  X11     FOO -12.508564 -0.105138
    11  X12     BAR  -7.943704  0.085655
    12  X13     BAZ -50.185312 -0.138463
    13  X14   VSMOW  -0.004993  0.006506
    14  X15    SLAP -55.518486  0.007433
    15  X16     FOO -12.613532 -0.098567
    16  X17     BAR  -7.725561  0.087401
    17  X18     BAZ -50.288610 -0.127896
    18  X19   VSMOW  -0.042833  0.001167
    19  X20    SLAP -55.535213  0.002187
  [SD_d18O_raw] = 0.07035790333040727
  [SD_D17O_raw] = 0.005786843071251322
  [analytes] =
             N         d18O_raw          D17O_raw
    Analyte
    BAR      4   -7.847+/-0.035   0.0899+/-0.0029
    BAZ      4  -50.227+/-0.035  -0.1327+/-0.0029
    FOO      4  -12.531+/-0.035  -0.1026+/-0.0029
    SLAP     4  -55.513+/-0.035   0.0106+/-0.0029
    VSMOW    4   -0.022+/-0.035   0.0045+/-0.0029
)

We can then normalize data.analytes based on the nominal compositions of the reference materials.

data.normalize(RM)
print(data)

As seen below, this adds two columns named d18O and D17O to data.analytes, corresponding to the normalized compositions of each analyte. These values are all uncertainties.UFloat values, so that their correlated uncertainties are all explictly computed and accessible using the methods described in the uncertainties documentation. The parameters a₁₈, b₁₈, a₁₇, and b₁₇ (see equations above) are also stored as uncertainties.UFloat values in data.a18, data.b18, data.a17, and data.b17.

DataSet(
  [analyses] =
        UID Analyte   d18O_raw  D17O_raw
    0   X01     FOO -12.532655 -0.098675
    1   X02     BAR  -7.879440  0.097711
    2   X03     BAZ -50.274837 -0.126091
    3   X04   VSMOW  -0.085304  0.004308
    4   X05    SLAP -55.412060  0.021416
    5   X06     FOO -12.467660 -0.108063
    6   X07     BAR  -7.841212  0.088934
    7   X08     BAZ -50.160433 -0.138356
    8   X09   VSMOW   0.046751  0.006160
    9   X10    SLAP -55.585929  0.011290
    10  X11     FOO -12.508564 -0.105138
    11  X12     BAR  -7.943704  0.085655
    12  X13     BAZ -50.185312 -0.138463
    13  X14   VSMOW  -0.004993  0.006506
    14  X15    SLAP -55.518486  0.007433
    15  X16     FOO -12.613532 -0.098567
    16  X17     BAR  -7.725561  0.087401
    17  X18     BAZ -50.288610 -0.127896
    18  X19   VSMOW  -0.042833  0.001167
    19  X20    SLAP -55.535213  0.002187
  [SD_d18O_raw] = 0.07035790333040727
  [SD_D17O_raw] = 0.005786843071251322
  [analytes] =
             N         d18O_raw          D17O_raw         d17O_raw           d18O             d17O            D17O
    Analyte
    BAR      4   -7.847+/-0.035   0.0899+/-0.0029   -4.062+/-0.019   -7.83+/-0.05   -4.056+/-0.025   0.085+/-0.023
    BAZ      4  -50.227+/-0.035  -0.1327+/-0.0029  -26.971+/-0.019  -50.21+/-0.05  -26.974+/-0.026  -0.143+/-0.026
    FOO      4  -12.531+/-0.035  -0.1026+/-0.0029   -6.738+/-0.019  -12.51+/-0.05   -6.733+/-0.024  -0.109+/-0.022
    SLAP     4  -55.513+/-0.035   0.0106+/-0.0029  -29.695+/-0.019  -55.50+/-0.05  -29.699+/-0.027   0.000+/-0.028
    VSMOW    4   -0.022+/-0.035   0.0045+/-0.0029   -0.007+/-0.019    0.00+/-0.05    0.000+/-0.027   0.000+/-0.027
  [refmaterials] = {'VSMOW': {'d18O': 0.0, 'D17O': 0.0, 'd17O': 0.0}, 'SLAP': {'d18O': -55.5, 'D17O': 0.0, 'd17O': -29.69864899849639}}
  [a18] = 1.0002+/-0.0009
  [b18] = 0.022+/-0.035
  [a17] = 1.0003+/-0.0009
  [b17] = 0.007+/-0.019
)

Alternatively, one may perform the same normalization steps based directly on the analytes table, skipping the computation of d18O_raw and D17O_raw uncertainties (assigning these uncertainties is then solely the user's responsibility).

data = DataSet()
data.import_analytes('examples/analytes.csv')

print(data)

DataSet(
  [analytes] =
             N         d18O_raw          D17O_raw
    Analyte
    BAR      4   -7.847+/-0.035   0.0899+/-0.0029
    BAZ      4  -50.227+/-0.035  -0.1327+/-0.0029
    FOO      4  -12.531+/-0.035  -0.1026+/-0.0029
    SLAP     4  -55.513+/-0.035   0.0106+/-0.0029
    VSMOW    4   -0.022+/-0.035   0.0045+/-0.0029
)

And the normalized results are identical to those in the first example:

data.normalize(RM)
print(data)

DataSet(
  [analytes] =
             N         d18O_raw          D17O_raw         d17O_raw           d18O             d17O            D17O
    Analyte
    BAR      4   -7.847+/-0.035   0.0899+/-0.0029   -4.061+/-0.019   -7.83+/-0.05   -4.056+/-0.025   0.085+/-0.023
    BAZ      4  -50.227+/-0.035  -0.1327+/-0.0029  -26.971+/-0.019  -50.21+/-0.05  -26.974+/-0.026  -0.143+/-0.025
    FOO      4  -12.531+/-0.035  -0.1026+/-0.0029   -6.738+/-0.019  -12.51+/-0.04   -6.733+/-0.024  -0.108+/-0.022
    SLAP     4  -55.513+/-0.035   0.0106+/-0.0029  -29.695+/-0.019  -55.50+/-0.05  -29.699+/-0.027   0.000+/-0.028
    VSMOW    4   -0.022+/-0.035   0.0045+/-0.0029   -0.007+/-0.019    0.00+/-0.05    0.000+/-0.026   0.000+/-0.026
  [refmaterials] = {'VSMOW': {'d18O': 0.0, 'D17O': 0.0, 'd17O': 0.0}, 'SLAP': {'d18O': -55.5, 'D17O': 0.0, 'd17O': -29.69864899849639}}
  [a18] = 1.0002+/-0.0009
  [b18] = 0.022+/-0.035
  [a17] = 1.0003+/-0.0009
  [b17] = 0.007+/-0.019
)