Introduction to CFIRMS Post Analysis Spreadsheets ( Defense against - - PowerPoint PPT Presentation
Introduction to CFIRMS Post Analysis Spreadsheets ( Defense against the dark arts 100 ) By Paul Brooks, University of California, Berkeley. 2014 ASITA UC Davis Acknowledgments Mark Rollog, formerly USGS Palo Alto. William Rugh, EPA
By Paul Brooks, University of California, Berkeley. 2014 ASITA UC Davis
“(The dark arts) can be fought, and I’ll be teaching you how, but it takes real strength of character, and not everyone’s got it. Better avoid it if you can. CONSTANT VIGILANCE!” he barked, and everyone jumped. “You’ve got to appreciate what the worst is. You don’t want to find yourself in a situation where you’re facing it. CONSTANT VIGILANCE!” he roared, and the whole class jumped again.”
Quote from Mad Eye Moody teaching the “Defense against the Dark Arts” class at Hogwarts school of witchcraft and wizardry. In “Harry Potter and the Goblet of Fire” by J. K. Rowling.
Quote from Severus Snape teaching the “Defense against the Dark Arts” class at Hogwarts school of witchcraft and wizardry. In “Harry Potter and the Half Blood Prince” by J. K. Rowling.
analysts has not been very successful, as each analysts needs are very different.
theory of how the corrections used at the isotope facility at UC Berkeley.
their own spread sheet using these mathematical techniques.
improvements to this technique.
sample analysis (multiple replicates of water injections).
time including both a smooth curve correction and a peak to peak correction.
non-linearity of standard delta value with size.
different isotope ratio standards drifting at different rates.
control standard.
Post-processing spreadsheet for the LGR DT-100 Liquid Water Stable Isotope Analyzer
For further information, please contact: Isotope Hydrology Section Division of Physical and Chemical Sciences Department of Nuclear Sciences and Applications International Atomic Energy Agency Wagramer Strasse 5 P.O. Box 100 A-1400 Vienna, Austria Phone:+43 1 2600 21736 Fax: +43 1 26007 E-mail: ihs@iaea.org Web: http://www.iaea.org/water This Spreadsheet was developed by B. Newnman, T. Kurttas, A. Tanweer, and P. Aggarwal
Memory correction (carryover) using examples from a heavily modified post analysis spreadsheet for an LGR laser system.
Output from LGR laser pasted into spreadsheet
Memory (carryover) correction page.
Simple memory correction for samples that are all the same size.
E F G H I J K 1) % carryover= 10 2) % carryover= 1.3 dH diff 1 to 2 corr corr value diff 1 to 3 corr 2 corr value 2 13 12.3 0.25 0.02 12.27
0.00 12.27 14 12.6
12.60
0.00 12.60 15
229.88 22.99
229.61 2.98
16
19.17 1.92
249.05 3.24
E F G H I J K 1 1) % carryover= 10 2) % carryover= 1.3 2 dH diff 1 to 2 corr corr value diff 1 to 3 corr 2 corr value 2 13 12.3 14 12.6 =E13-E14 =F14*G$1*0.01 =E14+G14 15
=E14-E15 =F15*G$1*0.01 =E15+G15 =E13-E15 =I15*J$1*0.01 =H15-J15 16
=E15-E16 =F16*G$1*0.01 =E16+G16 =E14-E16 =I16*J$1*0.01 =H16-J16
A filter system to return a blank cell when the size, column E, is greater or less than a % (cell N50) of column I.
N 50 3
E F G H I 13 1.07E+17 1.07E+17 1.07E+17 1.08E+17 14 1.04E+17 1.04E+17 1.08E+17 E F G H I 13 1.07E+17 =IF(E13>(I13+(N$50*0.01*I13)),"", E13) =IF(F13<(I13-(N$50*0.01*I13)),"", F13) 1.08E+17 14 1.04E+17 =IF(E14>(I14+(N$50*0.01*I14)),"", E14) =IF(F14<(I14-(N$50*0.01*I14)),"", F14) 1.08E+17
Command to remove isotope ratio if volume (mass) blank.
AC 13 =IF(checkplots!$G13="","",raw!L13) 14 =IF(checkplots!$G14="","",raw!L14) AC 13 0.0020144709 14 Formula to remove isotope ratio if volume (mass) blank. Where checkplots!G13 is the water volume, raw L13 is the isotope ratio.
AC AD AE AF AG AH 14 15 0.0019433775 16 0.0019444036 17 0.0019438525 18 0.0019434457 19 0.0019439051 =AVERAGE(AC14:AC19) =STDEV(AC14:AC19) H2O18/H2O average stdev abs diff from mean
removed average= AC AD AE AF AG AH 14 15 15.14 0.00 15.14 16 15.30 0.16 17 15.06 0.08 15.06 18 15.18 0.04 15.18 19 15.03 15.15 0.11 0.11 15.03 15.11
Filter to remove outlier ratios
H2O18/H2O average stdev abs diff from mean
removed average= AC AD AE AF AG AH 14 15 15.14 0.00 15.14 16 15.30 0.16 17 15.06 0.08 15.06 18 15.18 0.04 15.18 19 15.03 15.15 0.11 0.11 15.03 15.11 AF AG AH 14 =IF(AC14="","",ABS(AC14-AD19)) =IF(AF14>AG$2*AE19,"",AC14) 15 =IF(AC15="","",ABS(AC15-AD19)) =IF(AF15>AG$2*AE19,"",AC15) 16 =IF(AC16="","",ABS(AC16-AD19)) =IF(AF16>AG$2*AE19,"",AC16) 17 =IF(AC17="","",ABS(AC17-AD19)) =IF(AF17>AG$2*AE19,"",AC17) 18 =IF(AC18="","",ABS(AC18-AD19)) =IF(AF18>AG$2*AE19,"",AC18) 19 =IF(AC19="","",ABS(AC19-AD19)) =IF(AF19>AG$2*AE19,"",AC19) =AVERAGE(AG14:AG19) AF AG 2
1.2
Filter to remove outlier ratios
Dummy: to warm up instrument BDW: calibration standard BSMOW: quality control BWW: quality control Numbers: unknowns
1 dummy - US standard 2 dummy - US standard 3 dummy - US standard 4 dummy - US standard 5 dummy - US standard 6 BSMOW 7 1 1 8 2 2 9 SPW3 10 3 3 11 4 4 12 BSMOW 13 5 5 14 6 6 15 BWW 16 7 7 17 8 8 18 BSMOW 19 9 9 20 10 10
21 SPW3
18O analysis: running samples + standards
Sample input spreadsheet for 18O analysis:
Remember, water samples to be analyzed for 18O are equilibrated with CO2 and the CO2 is then analyzed on the gas bench.
results start to become consistent.
standard called BDW (Berkeley Distilled Water) every 6 samples.
either a 3.33 δ18O BSMOW (Berkeley Standard Mean Ocean Water), or a -6.47 BWW (Brooks Well Water). In between the standards are 4 unknowns.
18O analysis: running samples + standards
For water 18O analysis:
[V] [Vs] 45/44 46/44 13/12 18/16
031014082948 1 3.019 25.612 169.535 414.725 166.995 414.725 37 031014083025 1 3.029 35.273
37 031014083025 2 3.030 35.174
37 031014083025 3 3.020 35.249
0.000
37 031014083025 4 6.390 27.117
19.305
37 031014083025 5 5.858 24.730
19.429
37 031014083025 6 5.333 22.548
19.462
37 031014083025 7 4.880 20.597
19.552
37 031014083025 8 4.437 18.800
19.690
37 031014083025 9 4.060 17.168
19.767
38 031014084030 1 3.022 25.437 169.147 414.812 166.577 370.246 38 031014084107 1 3.032 35.142
38 031014084107 2 3.031 34.957
0.084
38 031014084107 3 3.025 35.101
0.000
38 031014084107 4 6.986 29.442
19.019
38 031014084107 5 6.383 26.855
19.061
38 031014084107 6 5.817 24.541
19.156
38 031014084107 7 5.312 22.383
19.070
38 031014084107 8 4.849 20.459
19.175
38 031014084107 9 4.466 18.698
19.262
39 031014085149 1 3.026 34.943
39 031014085149 2 3.017 35.059
Output from Finnigan MAT computer
reference sample This output of peaks converts to the following table of voltage signals and isotope ratios for both 13C and 18O:
From output to spreadsheet…
manipulations begun by pasting the output data into the worksheet titled: “*._1”
the data into a more usable form.
and condensed using another macro.
are now available.
Correcting Finnigan MAT data: AVERAGING
avrg. stdevp 1 std avrg stdevp avrg stdevp avrg stdevp avrg stdevp avrg stdevp # ref. ref. samp samp samp 6 peak 6 peak 5 peak 5 peak 6 peak 6 peak 5 peak 5 peak volts volts volts volts volts delta 18O delta 18O delta 18O delta 18O delta 13C delta 13C delta 13C delta 13C 42 2.98 0.00 2.71 2.18 0.34
0.08
0.08
0.10
0.09 43 3.01 0.01 2.85 2.28 0.36
0.18
0.06
0.18
0.07 44 3.04 0.01 2.86 2.30 0.36
0.07
0.05
0.06
0.03 45 3.06 0.01 2.93 2.35 0.37
0.08
0.07
0.10
0.07 46 3.07 0.00 2.69 2.16 0.34
0.07
0.07
0.05
0.06 47 3.08 0.00 2.83 2.28 0.35
0.08
0.09
0.06
0.06 48 3.10 0.01 2.87 2.31 0.36
0.08
0.07
0.04
0.04 49 3.10 0.01 2.75 2.21 0.34
0.05
0.06
0.06
0.06 50 3.10 0.01 6.12 4.92 0.77
0.08
0.09
0.08
0.09 51 3.10 0.01 6.47 5.19 0.82
0.03
0.04
0.05
0.05 52 3.10 0.00 6.33 5.08 0.80 0.61 0.02 0.61 0.02
0.03
0.03 53 3.09 0.00 6.20 4.98 0.78 0.73 0.02 0.72 0.02
0.02
0.02 54 3.09 0.00 6.18 4.95 0.79
0.05
0.05
0.06
0.06 55 3.09 0.00 5.74 4.61 0.73
0.07
0.08
0.03
0.03 56 3.09 0.00 6.46 5.18 0.82
0.04
0.04
0.06
0.07 57 3.09 0.01 6.58 5.27 0.84
0.07
0.08
0.04
0.04 58 3.08 0.00 6.24 5.02 0.79
0.03
0.03
0.05
0.04 59 3.07 0.00 6.06 4.86 0.77
0.03
0.04
0.08
0.09 60 3.07 0.00 6.35 5.11 0.80
0.04
0.04
0.07
0.08 61 3.07 0.00 5.61 4.50 0.71
0.05
0.04
0.03
0.03
samples within a run – no picking and choosing!
Correcting Finnigan MAT data: 5 or 6 PEAKS?
stdevp stdevp stdevp stdevp 6 peak 5 peak 6 peak 5 peak delta 18O delta 18O delta 13C delta 13C 0.08 0.08 0.10 0.09 0.18 0.06 0.18 0.07 0.07 0.05 0.06 0.03 0.08 0.07 0.10 0.07 0.07 0.07 0.05 0.06 0.08 0.09 0.06 0.06 0.08 0.07 0.04 0.04 0.05 0.06 0.06 0.06 0.08 0.09 0.08 0.09 0.03 0.04 0.05 0.05 0.02 0.02 0.03 0.03 0.02 0.02 0.02 0.02 0.05 0.05 0.06 0.06 0.07 0.08 0.03 0.03 0.04 0.04 0.06 0.07 0.07 0.08 0.04 0.04 0.03 0.03 0.05 0.04 0.03 0.04 0.08 0.09 0.04 0.04 0.07 0.08 0.05 0.04 0.03 0.03
peaks, compare the standard deviations through your run (or the average for the entire run)
standard deviations with either 5
peaks will greatly increase the standard deviation.
results in a lower error term.
position number in the run.
take the same amount of time to run
Correcting Finnigan MAT data: DRIFT
# vs. BSMOW standard δ18O
50 100 150 position # in run δ
18O
reported actual
# vs. BSMOW standard δ18O
50 100 150 position # in run δ
18O
reported fit corrected actual
1 2
standards (and SPW3 standards on a separate graph).
curve is added to the reported value. The corrected value is plotted.
Correcting Finnigan MAT data: DRIFT
standards line # delta 18O x x2 y fit corrected actual a b c 6 36
6.11711E-05 -0.012126704
12 144
2.16924E-05 0.00308276 0.092347522 18 324
0.634638812 0.131455514 #N/A 24 576
16.50166716 19 #N/A 30 900
0.570315843 0.328330493 #N/A 36 1296
42 1764
48 2304
54 2916
60 3600
66 4356
72 5184
78 6084
84 7056
90 8100
correction.
y = x2a+xb+c Where x is the line number and y is the delta value of BDW
Correcting Finnigan MAT data: DRIFT
also be calculated using a peak to peak correction.
pair of two standards and uses the slope of the connecting line to make corrections.
appropriate intermediate values to each sample in-between.
sample name delta 18O 1 dummy
2 dummy
corrected 3 dummy
delta 18O 4 dummy
5 dummy
+ 6 BDW
7 Shipley Valley 1
1
8 Shipley Valley 4
2
9 BSMOW 4.53 3
3.82 10 Shipley Valley 5
4
11 Shipley Valley 9
5
12 BDW
Correcting Finnigan MAT data: DRIFT
smooth p2p average corrected additive p2p and # Name delta 18O delta 18O smooth 1 dummy
2 dummy
3 dummy
4 dummy
5 dummy
6 BDW
7 Shipley Valley 1
8 Shipley Valley 4
9 BSMOW 3.87 3.82 3.85 10 Shipley Valley 5
11 Shipley Valley 9
12 BDW
13 Shipley Valley 12
14 Shipley Valley 14
15 BWW
16 Shipley Valley 16
17 Shipley Valley 19
18 BDW
peak to peak correction.
Correcting Finnigan MAT data: DRIFT
best results for quality control can be used or they can be averaged.
using a data set that drifts linearly with time.
samples drift from a value
drifted with time.
corrected?
line number reported delta value (RV) x y 5
10
15
20
25
30
35
40
average=
stdev= 0.18
example of linear drift
10 20 30 40 50 line number delta value
line number reported delta value (RV) fit curve (FC) linest function linest function x y y=xa+b a b 5
10
0.000745181 0.018815 15
0.980135053 0.024147 20
296.039575 6 25
30
LI NEST(known_y's,known_x's,const,stats) 35
40
average=
Using the Linest function, line number as x and delta value as y can be fitted to a linear y=xa+b function. Remember that to get the Linest function to work, it is necessary to hold down “shift+ctrl” while pushing “enter”.
line number reported delta value (RV) fit curve (FC) actual delta vaule
standar d (AV) linest function linest function x y y=xa+b AV a b 5
10
0.000745181 0.018815 15
0.980135053 0.024147 20
296.039575 6 25
30
LI NEST(known_y's,known_x's,const,stats) 35
40
average=
stdev= 0.16
Assuming the correct value of the standard is -12.00, this can be put in the spread sheet.
10 20 30 40 50 y y=xa+b AV
A graph of the spread sheet data so far. Note that the fit curve follows the standard values closely. How a the y points (reported values RV) adjusted to the actual values (AV)?
The difference between the actual values and the fit curve can be subtracted and added onto the reported values (RV). The arrows below show how the reported values have been corrected.
simple linear drift correction
10 20 30 40 50 lines number delta value y y=xa+b =AD-FC+RV AV
line number report ed delta value (RV) fit curve (FC) corrected value (CV) actual delta vaule
standa rd (AV) linest function linest function x y y=xa+b =AV-FC+RV AV a b 5
10
0.001147609 0.028976 15
0.962142544 0.037187 20
152.4892562 6 25
30
LI NEST(known_y's,known_x's,const,stats) 35
40
average=
stdev= 0.18 0.03
A column is added into the spread sheet that simply subtracts the Actual Value (AV) from the fit curve (FC) and then adding the reported value. This results in a much lower standard deviation for the data.
30
31
32
33
34
35
36
37
line number reported delta value (RV) (FC) (CV) (AV) linest function linest function x y y=xa+b =AV-FC+RV AV a b 5
10
0.000745181 0.018815 15
0.980135053 0.024147 20
296.039575 6 25
30
LI NEST(known_y's,known_x's,const,stats) 35
40
Using the line number the calculations can now be extended to all the reported values in-between the calibration standards, correcting all the values for drift over time.
line number reported delta value (RV) (FC) (CV) (AV) linest function linest function linest function x x2 y y=x2a+xb+c =AV-FC+RV AV a b c 6 36
0.000234586
12 144
0.000137241 0.007591795 0.089343 18 324
0.896533814 0.064038461 #N/A 24 576
21.66248327 5 #N/A 30 900
0.177672416 0.020504622 #N/A 36 1296
LINEST(known_y's,known_x's,const,stats) 42 1764
48 2304
30 900
31 961
32 1024
33 1089
34 1156
35 1225
36 1296
37 1369
By adding a column with the line number squared (x2) into the spreadsheet, and re-placing the linest function with one 3 columns wide and 5 high, a polynomial function of the form y=x2a+xb+c for the fitted curve (FC) can be calculated. This will generally fit a smooth drift.
x x2 y y=x2a+xb +c # type area area2 reported fit corr actual a b c 2 varcell 112,517 1.E+10 26.30 26.09 26.65 26.44 1.40667E-11 8.32037E-06 24.97282 1 sigma 133,039 2.E+10 26.42 26.33 26.53 26.44 1.22543E-11 4.03837E-06 0.318101 13 sigma 150,192 2.E+10 26.49 26.54 26.39 26.44 0.961457685 0.098858253 #N/A 14 varcell 158,898 3.E+10 26.61 26.65 26.40 26.44 162.145811 13 #N/A 25 sigma 150,634 2.E+10 26.56 26.55 26.46 26.44 3.169287196 0.127048406 #N/A 26 varcell 107,320 1.E+10 26.04 26.03 26.45 26.44 37 sigma 142,919 2.E+10 26.32 26.45 26.31 26.44 38 varcell 104,366 1.E+10 25.98 25.99 26.42 26.44 49 sigma 134,528 2.E+10 26.34 26.35 26.43 26.44 50 varcell 168,432 3.E+10 26.66 26.77 26.33 26.44 61 sigma 141,052 2.E+10 26.43 26.43 26.44 26.44 62 varcell 242,670 6.E+10 27.85 27.82 26.47 26.44 73 sigma 147,533 2.E+10 26.61 26.51 26.54 26.44 74 varcell 111,833 1.E+10 25.96 26.08 26.32 26.44 85 sigma 133,013 2.E+10 26.43 26.33 26.54 26.44 86 varcell 84,935 7.E+09 25.70 25.78 26.36 26.44 average= 26.42 26.42 26.44 stdevp= 0.45 0.45 0.09
Example of area vs. delta value non-linearity correction
area vs.delta value
25.50 26.00 26.50 27.00 27.50 28.00 100000 200000 300000 area delta value reported fit corr actual
Example of area vs. delta value non-linearity correction
corrected using a peak to peak (p2p) correction.
standards are every 6th line.
should be –12.00 but vary, for example #18 is –12.06, #24 –12.24.
that has to be added to each standard to make it –12.00
line number name reported value delta 18O number
between standards amount to add to reported value corrected value RV NL AD CV 6 BDW
0.04
7 1
1 0.0413
8 2 3.49 2 0.0391 3.53 9 BSMOW 4.30 3 0.0369 4.34 10 3
4 0.0347
11 4 0.70 5 0.0326 0.74 12 BDW
0.03
13 5
1 0.0355
14 6
2 0.0406
15 BWW
3 0.0458
16 7
4 0.0509
17 8
5 0.0560
18 BDW
0.06
19 9
1 0.0912
20 10
2 0.1213
21 BSMOW 3.44 3 0.1514 3.60 22 11
4 0.1815
23 12
5 0.2115
24 BDW
0.24
25 13
1 0.2036
26 14
2 0.1656
27 BWW
3 0.1276
28 15
4 0.0895
29 16
5 0.0515
30 BDW
0.01
reported value for each line should have an amount added (AD) added that is adjusted depending on the position of the sample between the standards.
(CV) is the reported value (RV) plus the amount to add (AD).
line number name reported value delta 18O number
between standards amount to add to reported value corrected value RV NL AD CV=RV+AD 6 BDW
0.04
7 1
1 0.0413
8 2 3.49 2 0.0391 3.53 9 BSMOW 4.30 3 0.0369 4.34 10 3
4 0.0347
11 4 0.70 5 0.0326 0.74 12 BDW
0.03
13 5
1 0.0355
14 6
2 0.0406
15 BWW
3 0.0458
16 7
4 0.0509
17 8
5 0.0560
18 BDW
0.06
19 9
1 0.0912
20 10
2 0.1213
21 BSMOW 3.44 3 0.1514 3.60 22 11
4 0.1815
23 12
5 0.2115
24 BDW
0.24
25 13
1 0.2036
26 14
2 0.1656
27 BWW
3 0.1276
28 15
4 0.0895
29 16
5 0.0515
30 BDW
0.01
The amount to add (AD) is assumed to drift completely linearly between standards. Below is a graph showing AD
line (standard) #18, #24 and #30.
line number vs. amount to add (AD)
0.00 0.05 0.10 0.15 0.20 0.25 0.30 5 10 15 20 25 30 35 line number amount to add (AD)
# name reported value delta 18O number
between standards amount to add to reported value corrected value RV NL AD CV=RV+AD 18 BDW
0.06
19 9
1 0.0912
20 10
2 0.1213
21 BSMOW 3.44 3 0.1514 3.60 22 11
4 0.1815
23 12
5 0.2115
24 BDW
0.24
The amount to add (AD) is calculated by subtracting the reported value from the actual value. For example, for #18 std below the amount to add (AD) is equal to the value of the standard, -12, minus the reported value RV of –12.06, so For #18 AD= -12.00 – (-12.06) = 0.06. For the #18 standard: AD= -12.24-(-12.24) The AD is then adjusted proportionately between #18 and #24.
To adjust the AD proportionately between the standards a simple formula is created in Excel as shown below. This calculates the difference between the amount to add in B1 and B7, divides this by the number of samples between the standards, and then multiplies the result by the position of the sample between the standards. Each formula for each cell is shown below.
A B 1 0.06 2 1 0.0912 3 2 0.1213 4 3 0.1514 5 4 0.1815 6 5 0.2115 7 0.24
=B$1-(((B$1-B$7)/6)*A2 =B$1-(((B$1-B$7)/6)*A3 =B$1-(((B$1-B$7)/6)*A4 =B$1-(((B$1-B$7)/6)*A5 =B$1-(((B$1-B$7)/6)*A6
line number name reported value delta 18O number
between standards amount to add to reported value corrected value RV NL AD CV=RV+AD 6 BDW
0.04
7 1
1 0.0413
8 2 3.49 2 0.0391 3.53 9 BSMOW 4.30 3 0.0369 4.34 10 3
4 0.0347
11 4 0.70 5 0.0326 0.74 12 BDW
0.03
13 5
1 0.0355
14 6
2 0.0406
15 BWW
3 0.0458
16 7
4 0.0509
17 8
5 0.0560
18 BDW
0.06
19 9
1 0.0912
20 10
2 0.1213
21 BSMOW 3.44 3 0.1514 3.60 22 11
4 0.1815
23 12
5 0.2115
24 BDW
0.24
25 13
1 0.2036
26 14
2 0.1656
27 BWW
3 0.1276
28 15
4 0.0895
29 16
5 0.0515
30 BDW
0.01
is copied into each sample (not standard line) of the AD column.
each line is added to the RV value to calculated the corrected value (CV).
particular analysis, depending on the quality control results.
probably makes most sense for the analysts to create their own post analysis spread sheets, hence this course.
peach ugN in tin vs. delta 15N
0.00 0.50 1.00 1.50 2.00 2.50 3.00 0.0 100.0 200.0 300.0 400.0 ug N in tin delta 15N
measured d 15N actual Fry corr actual -0.2 ‰ actual +0.2 ‰ Linear (actual -0.2
Example of dual mixing model (Fry) used to correct EA analysis
corrected delta =
((delta samp)x(samp area))+((delta blank)x(blank area)) (samp area + blank area)
δ 15N N beam # y x 1/x 51 0.20 0.21 4.81 39
0.22 4.55 63 0.30 0.23 4.40 27 0.38 0.26 3.92 15 1.27 0.29 3.39 59 1.53 0.80 1.26 23 1.56 0.95 1.06 47 1.99 0.96 1.04 35 1.43 1.09 0.92 11 1.66 1.78 0.56 41 1.51 2.34 0.43 65 1.67 2.63 0.38 17 1.68 2.87 0.35 29 1.84 3.45 0.29 53 1.74 3.52 0.28 25 1.71 3.62 0.28
0.00 0.50 1.00 1.50 2.00 2.50 0.00 1.00 2.00 3.00 4.00 5.00 6.00 1/beam area reported delta N
y=xa + b calculated using linest function.
blank 0.02 49.30
Calculated from above curve
The blank value can now be substitute in the equation and all the corrected delta values calculated. corrected delta =
((delta samp)x(samp area))+((delta blank)x(blank area)) (samp area + blank area)
corrected delta =
((delta samp)x(samp area))+(( -15.03 )x( 0.02 )) (samp area + 0.02)
This corrects for linearity with size, additional normalization (scaling) may still be required. Normally only 10 variable weight standards would be used per analysis.
peach ugN in tin vs. delta 15N
0.00 0.50 1.00 1.50 2.00 2.50 3.00 0.0 100.0 200.0 300.0 400.0 ug N in tin delta 15N
measured d 15N actual Fry corr actual -0.2 ‰ actual +0.2 ‰ Linear (actual -0.2
Example of dual mixing model (Fry) used to correct EA analysis
An example of a spreadsheet with the final calculations
calibrate with two different isotope ratio standards in any analysis to check that the mass spectrometer is correctly linear from one isotope standard to another.
VSMOW at 0.0 delta D, some systems report SLAP, for example, -402.0 instead of –428.0.
“normalized” using a standard curve.
drift at the same rate over time.
USGSPR
100 200 300 injection number delta D delta H curv fit corr average
USGSA
100 200 300 injection number delta D delta H Curv fit corr average
These –6 delta D and –394 standards drift at different rates. The drift in each standard was predictable enough to fit a polynomial curve to each standard, shown in pink .
Effect of drift correction on quality control results for CF-IRMS.
100 200 300 injection number (#) delta D no drift correction 2 standard drfit correction l
No drift correction results in a drifting result for the quality control standard.
A standard curve correcting the reported δ D of the standards against the actual value for the standards showed that it is necessary to calculate a new standard curve for every sample injection of the analysis to account for different drift in the different standards.
263 69169 USGSPR
264 69696 USGSPR
8.38777 265 70225 USGSPR
266 70756 WQEV
267 71289 WQEV
268 71824 WQEV
269 72361 WQEV
270 72900 WQEV
inject. y=xa+b inject. number x USGSA USGSPR WQEsker actual actual actual corrected number squared sample delta H curv fit curve fit curve fit USGSA USGSPR WQEsker delta H a b 1 1 USGSA
2 4 USGSA
1.0182 1.343054 3 9 USGSA
4 16 USGSA
5 25 USGSA
6 36 WQEsker
7 49 WQEsker
1.01871 1.571615
Reported δ D (x) Curve fitted to drift for each standard Actual value of each standard Corrected sample value (y) using y = xa+b The a and b values for a least squares fit through the curve fit and actual values for the standards
An example of the spreadsheet used to calculate drift curves for each standard so that every injection number has a drift corrected value for each standard. Then the values a and b for a linear fit (y = xa+b) using the curve fit and actual value of the standard, is calculated for each injection. A corrected δ D for each injection can then be calculated from the actual reported δ D, taking into account the different drift in 3 different standards in the course of an analysis.
USGSPR
50 100 150 200 250 300 line number delta D delta H curv fit corr average
WQEsker
50 100 150 200 250 300 line number delta D delta H Curv fit corr average
USGSA
50 100 150 200 250 300 line # delta D delta H Curv fit corr average
A polynomial function can be fit to line (sample) # vs. dD for each standard. It is apparent that at each line # a value for each standard can be calculated from the polynomial fit. Example line #58 #225 USGSPR fit = -4.7 , -8.9 WQEsker fit= -112.1,-114.9 USGSA fit= -393.6,-393.6 #58 #225
line x x2 reporte d USGSP R WQEsk er USGS A number sample delta H curve fit curve fit curv fit 1 1 USGSA
2 4 USGSA
3 9 USGSA
4 16 USGSA
5 25 USGSA
6 36 WQEsker
7 49 WQEsker
8 64 WQEsker
9 81 WQEsker
10 100 WQEsker
11 121 USGSPR
12 144 USGSPR
13 169 USGSPR
14 196 USGSPR
15 225 USGSPR
16 256 WQEV
17 289 WQEV
18 324 WQEV
19 361 WQEV
20 400 WQEV
21 441 C106899-0021
22 484 C106899-0021
The value for each standard at each line number can now be calculated using drift correction describe earlier using a function in the form y=x2a+xb+c where x is line number and y is the value for the standard.
For line #58
X1 USGSPR curve fit
Y1 USGSPR actual
X2 WQEsker curve fit
Y2 WQEsker actual
X3 USGSA curv fit
Y3 USGSA actual
for line #225
X1 USGSPR curve fit
Y1 USGSPR actual
X2 WQEsker curve fit
Y2 WQEsker actual
X3 USGSA curv fit
Y3 USGSA actual
For any line number the X and Y values can be used to calculate a scaling curve in the form Y=X2A+B. X1 X2 X3 Y1 Y2 Y3 Line #58 scaling curve
Note: Every line must have its own normalization curve!!!
X1 X2 X3 Y1 Y2 Y3 Y=AX+B line reported USGSPR WQEsker USGSA actual actual actual corrected number sample delta H curve fit curve fit curv fit USGSPR WQEsker USGSA delta H A B 1 1 USGSA
1.02 1.30 2 4 USGSA
1.02 1.34 3 9 USGSA
1.02 1.39 4 16 USGSA
1.02 1.43 5 25 USGSA
1.02 1.48 6 36 WQEsker
1.02 1.53 7 49 WQEsker
1.02 1.57 8 64 WQEsker
1.02 1.62 9 81 WQEsker
1.02 1.66 10 100 WQEsker
1.02 1.71 11 121 USGSPR
1.02 1.75 12 144 USGSPR
1.02 1.80 13 169 USGSPR
1.02 1.84
A linest function can be created for every line of data, where X1, X2 and X3 are X values, and Y1,Y2 and Y3 are Y values. The corrected delta H (Y) is then calculated from the reported delta H (X)
Final proof of calculations, put the corrected quality control results into a long term external precision graph.
correction when two different standards drift at different rates.
this conference to discuss spreadsheet construction with anyone interested in hands on experience.
corrections, if so please let me know so I can learn them!
Forensics, San Luis Obispo, Ca 93401 USA, and Peter Dillon, ERS Department, Trent University, Peterborough, ON, Canada K9J 7B8 for letting me use their HD data.
http://ib.berkeley.edu/groups/biogeochemistry/downloads.php
Some examples of spreadsheets with detailed descriptions for their use can be found at:
Pages in Berkeley 1.01 generic spreadsheet.
how to use
paste in names and weights paste in area and delta values from mass spectometer convert delta values to international scale calculate drift corrected % smooth correct 1 std p2p 1 std correct for non-linearity with size correct for non-linearity with size correct with 2nd std correct with 2nd std smooth 1 std total smooth 2 std total p2p 1 std total p2p 2 std total correct for carryover
1 2 3 4 5 6 7 8 9 10 11 12 A ID sigma var cell IC3 V9 empty tin sigma A3M69 A3M68 A3M67 A3M66 A3M65 A3M64 weight 1.066 0.714 0.981 0.779 1.024 1.064 0.85 0.969 0.981 1 1.022 B sigma var cell V9 A3M63 A3M62 A3M61 A3M60 A3L03 A3L02 A3L01 A3L00 A3L99 0.985 0.592 1.098 1.008 0.939 0.994 1.088 1.097 0.941 1.052 1.095 0.973 C sigma var cell IC3 A3L98 A3L97 A3L96 A3L95 A3L94 A3L93 A3L92 A3L91 A3L90 0.908 1.429 0.854 0.969 0.992 1.057 1.092 0.998 1.002 0.961 1.065 1.01 D sigma var cell V9 A3L89 A3L88 A3L87 A3L86 A3L85 A3L84 A3L83 A3L82 A3L81 0.909 0.742 1.045 1.068 0.995 1.03 1.031 1.002 0.91 0.988 1.011 0.989 E sigma var cell IC3 A3M63 A3M62 A3M61 A3M60 A3L03 A3L02 A3L01 A3L00 A3L99 0.927 0.53 1.486 0.961 1.002 1.083 0.919 1.026 1.015 1.023 1.058 0.921 F sigma var cell V9 A3L98 A3L97 A3L96 A3L95 A3L94 A3L93 A3L92 A3L91 A3L90 1.066 0.793 1.244 0.93 0.944 1.095 1.029 1.023 0.938 0.988 1.072 1.042 G sigma var cell IC3 A3L89 A3L88 A3L87 A3L86 A3L85 A3L84 A3L83 A3L82 A3L81 1.008 1.555 0.935 0.965 0.973 1.027 1.01 1.002 1.019 1.067 1.051 0.979 H sigma var cell V9 A3M69 A3M68 A3M67 A3M66 A3M65 A3M64 22P7L77 IC3 sigma 1.074 1.2 1.425 1.067 1.087 1.028 0.919 0.934 0.949 0.927 0.594 1.018
numbe r cell ID content weight 1 A1 sigma 1.066 sigma = sigma cellulose standard ; 0.9 - 1.1 mg 2 A2 var cell 0.714 var cell = sigma cellulose standard weighed around 3 A3 IC3 0.981 .6 to 1.6 mg 4 A4 V9 0.779 IC3 = standard; two weighed between 0.9 - 1.1 mg and 5 A5 empty tin three weighed the same as var cell 6 A6 sigma 1.024 V9 = standard; two weighed between 0.9 - 1.1 mg and 7 A7 A3M69 1.064 three weighed the same as var cell 8 A8 A3M68 0.85 9 A9 A3M67 0.969 samples should weigh between 0.9 - 1.1 mg 10 A10 A3M66 0.981 11 A11 A3M65 1 empty tin for blank
Example of weighing tray for samples continued
delta # sample
area 18O 1 Dummy 0.00 2 Dummy 137049 29.12 3 Dummy 142343 28.95 1 sigma 1.066 142872 28.93 2 var cell 0.714 105587 27.62 3 IC3 0.981 136064 33.72 4 V9 0.779 116661 29.68 5 empty tin 0.00 6 sigma 1.024 144230 28.14 7 A3M69 1.064 138207 28.09