Introduction to Post Analysis Spreadsheets · 2014-08-01 · Introduction to CFIRMS Post Analysis Spreadsheets (Defense against the dark arts 100) By Paul Brooks, University of California,

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 Corvallis, Oregon. • Andrew Thompson, formerly Dept. ESPM,

UC Berkeley. • Willi Brand and the Iso lab group, Max

Planck Institute, Jena Germany.

• And all the countless others who have made suggestions over the years.

What are the Dark Arts?

• Memory effects • Drift of the isotope ratio with time. • Outliers in replicate injections (filtering). • Non-linearity with sample size. • Normalizing (scaling) of data with two

standards, even if they drift with time at different rates.

Defense against the dark arts 4th year.

“(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.

Snape’s introduction to the Dark Arts, 6th year.

“The Dark Arts,” said Snape, “are many and varied, ever-changing, and eternal. Fighting them is like fighting a many-headed monster, which, each time a neck is severed sprouts a head even fiercer and cleverer then before. You are fighting that which is unfixed, mutating, indestructible.”

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.

Good analytical chemistry

Never assume an analysis doesn’t drift, is linear, is not noisy or doesn’t need normalizing.

Assume you are wrong and prove you are right!

What is a post analysis spreadsheet?

• A post analysis spreadsheet is used to do additional calculations on data after an analysis is completed.

• The calculations are usually ones that are not possible with the instruments software.

• These calculations include drift correction with time, and adjustments for non-linearity with sample size, memory correction, filtering of data etc.

Presenting the theory • Attempts to share spreadsheets between

analysts has not been very successful, as each analysts needs are very different.

• Therefore, the rest of this lecture will be on the theory of how the corrections used at the isotope facility at UC Berkeley.

• This should allow other analysts to construct their own spread sheet using these mathematical techniques.

• The author would appreciate any suggestions on improvements to this technique.

This course objectives. • Describe a simple method for memory correction • Describe a method for filtering out outlier in multiple

sample analysis (multiple replicates of water injections). • Describe the mathematical theory of drift correction with

time including both a smooth curve correction and a peak to peak correction.

• Show that a similar mathematical method can adjust for non-linearity of standard delta value with size.

• Show a dual mixing model for non-linearity with size. • Describe how corrections can be made even when two

different isotope ratio standards drifting at different rates. • Describe checking the final corrections with a quality

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: [email protected] Web: http://www.iaea.org/water

This Spreadsheet was developed by B. Newnman, T. Kurttas, A. Tanweer, and P. Aggarwal

of the IAEA water Resources Programme

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 -0.05 0.00 12.27

14 12.6 -0.28 -0.03 12.60 -0.03 0.00 12.60

15 -217.3 229.88 22.99 -240.30 229.61 2.98 -243.28

16 -236.5 19.17 1.92 -238.40 249.05 3.24 -241.64

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 -217.3 =E14-E15 =F15*G$1*0.01 =E15+G15 =E13-E15 =I15*J$1*0.01 =H15-J15

16 -236.5 =E15-E16 =F16*G$1*0.01 =E16+G16 =E14-E16 =I16*J$1*0.01 =H16-J16

Filter for size of sample

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

outliers 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

outliers 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)





19 =IF(AC19="","",ABS(AC19-AD19)) =IF(AF19>AG$2*AE19,"",AC19) =AVERAGE(AG14:AG19)

AF AG

2 outlier= 1.2 Filter to remove outlier ratios

Why is drift correction necessary?

• Even when referenced to a reference gas, isotope ratios for calibration standards can drift with time.

• By adjusting all the results in an analysis for this drift, the quality control standard results can be improved.

The following is an example of how spreadsheets can used for analysis of 18O water, using a

Thermo Gas Bench.

Dummy: to warm up instrument BDW: calibration standard BSMOW: quality control BWW: quality control Numbers: unknowns

1 dummy - US standard2 dummy - US standard3 dummy - US standard4 dummy - US standard5 dummy - US standard6 BSMOW7 1 18 2 29 SPW3

10 3 311 4 412 BSMOW13 5 514 6 615 BWW16 7 717 8 818 BSMOW19 9 920 10 1021 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.

The instrument takes 5 samples (dummies) before the results start to become consistent.

The instrument is calibrated with a -12.95 δ18O standard called BDW (Berkeley Distilled Water) every 6 samples.

Every 12 samples there are quality control standards, 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:

Gas Bench Output

[V] [Vs] 45/44 46/44 13/12 18/16-----------------------------------------------------------------------------------------------

37 031014082948 1 3.019 25.612 169.535 414.725 166.995 414.72537 031014083025 1 3.029 35.273 -39.012 -0.136 -39.015 -31.63237 031014083025 2 3.030 35.174 -38.943 -0.082 -38.943 -31.57937 031014083025 3 3.020 35.249 -38.900 0.000 -38.900 -31.50037 031014083025 4 6.390 27.117 -37.325 19.305 -37.909 -12.80337 031014083025 5 5.858 24.730 -37.284 19.429 -37.869 -12.68337 031014083025 6 5.333 22.548 -37.270 19.462 -37.855 -12.65137 031014083025 7 4.880 20.597 -37.158 19.552 -37.738 -12.56437 031014083025 8 4.437 18.800 -37.198 19.690 -37.786 -12.43037 031014083025 9 4.060 17.168 -37.165 19.767 -37.753 -12.35538 031014084030 1 3.022 25.437 169.147 414.812 166.577 370.24638 031014084107 1 3.032 35.142 -38.907 -0.050 -38.906 -31.54838 031014084107 2 3.031 34.957 -38.838 0.084 -38.836 -31.41938 031014084107 3 3.025 35.101 -38.900 0.000 -38.900 -31.50038 031014084107 4 6.986 29.442 -37.355 19.019 -37.931 -13.08038 031014084107 5 6.383 26.855 -37.320 19.061 -37.894 -13.03938 031014084107 6 5.817 24.541 -37.266 19.156 -37.840 -12.94738 031014084107 7 5.312 22.383 -37.259 19.070 -37.830 -13.03138 031014084107 8 4.849 20.459 -37.258 19.175 -37.832 -12.92938 031014084107 9 4.466 18.698 -37.218 19.262 -37.792 -12.84539 031014085149 1 3.026 34.943 -38.908 -0.002 -38.908 -31.50239 031014085149 2 3.017 35.059 -38.927 -0.054 -38.927 -31.552

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…

The data manipulations begun by pasting the output data into the worksheet titled: “*._1” This file condenses the data into a more usable form.

The lines of data are then copied to the next worksheet and condensed using another macro. The averages of either all 6 or the last 5 unknown peaks 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 13C42 2.98 0.00 2.71 2.18 0.34 -16.24 0.08 -16.25 0.08 -37.99 0.10 -38.01 0.0943 3.01 0.01 2.85 2.28 0.36 -42.49 0.18 -42.42 0.06 -37.69 0.18 -37.62 0.0744 3.04 0.01 2.86 2.30 0.36 -44.73 0.07 -44.70 0.05 -38.47 0.06 -38.45 0.0345 3.06 0.01 2.93 2.35 0.37 -29.29 0.08 -29.27 0.07 -35.72 0.10 -35.69 0.0746 3.07 0.00 2.69 2.16 0.34 -44.44 0.07 -44.44 0.07 -38.07 0.05 -38.07 0.0647 3.08 0.00 2.83 2.28 0.35 -44.69 0.08 -44.69 0.09 -38.23 0.06 -38.23 0.0648 3.10 0.01 2.87 2.31 0.36 -15.95 0.08 -15.92 0.07 -38.00 0.04 -38.01 0.0449 3.10 0.01 2.75 2.21 0.34 -41.70 0.05 -41.71 0.06 -38.78 0.06 -38.79 0.0650 3.10 0.01 6.12 4.92 0.77 -44.80 0.08 -44.81 0.09 -38.40 0.08 -38.40 0.0951 3.10 0.01 6.47 5.19 0.82 -53.87 0.03 -53.87 0.04 -37.86 0.05 -37.85 0.0552 3.10 0.00 6.33 5.08 0.80 0.61 0.02 0.61 0.02 -29.85 0.03 -29.85 0.0353 3.09 0.00 6.20 4.98 0.78 0.73 0.02 0.72 0.02 -29.99 0.02 -29.99 0.0254 3.09 0.00 6.18 4.95 0.79 -15.63 0.05 -15.63 0.05 -37.83 0.06 -37.84 0.0655 3.09 0.00 5.74 4.61 0.73 -42.61 0.07 -42.62 0.08 -38.38 0.03 -38.37 0.0356 3.09 0.00 6.46 5.18 0.82 -47.22 0.04 -47.23 0.04 -38.09 0.06 -38.09 0.0757 3.09 0.01 6.58 5.27 0.84 -28.88 0.07 -28.89 0.08 -35.83 0.04 -35.82 0.0458 3.08 0.00 6.24 5.02 0.79 -47.60 0.03 -47.60 0.03 -38.34 0.05 -38.35 0.0459 3.07 0.00 6.06 4.86 0.77 -42.30 0.03 -42.30 0.04 -38.46 0.08 -38.46 0.0960 3.07 0.00 6.35 5.11 0.80 -15.71 0.04 -15.71 0.04 -38.02 0.07 -38.02 0.0861 3.07 0.00 5.61 4.50 0.71 -42.12 0.05 -42.11 0.04 -38.69 0.03 -38.69 0.03

One must choose to use either 5 or 6 peaks for all samples within a run – no picking and choosing!

Correcting Finnigan MAT data: 5 or 6 PEAKS?

stdevp stdevp stdevp stdevp6 peak 5 peak 6 peak 5 peakdelta 18O delta 18O delta 13C delta 13C

0.08 0.08 0.10 0.090.18 0.06 0.18 0.070.07 0.05 0.06 0.030.08 0.07 0.10 0.070.07 0.07 0.05 0.060.08 0.09 0.06 0.060.08 0.07 0.04 0.040.05 0.06 0.06 0.060.08 0.09 0.08 0.090.03 0.04 0.05 0.050.02 0.02 0.03 0.030.02 0.02 0.02 0.020.05 0.05 0.06 0.060.07 0.08 0.03 0.030.04 0.04 0.06 0.070.07 0.08 0.04 0.040.03 0.03 0.05 0.040.03 0.04 0.08 0.090.04 0.04 0.07 0.080.05 0.04 0.03 0.03

To decide whether to use 5 or 6 peaks, compare the standard deviations through your run (or the average for the entire run)

Most samples will have similar standard deviations with either 5 or 6 peaks.

However, occasionally including 6 peaks will greatly increase the standard deviation.

And sometimes using 6 peaks results in a lower error term.

Every BSMOW standard’s reported values is plotted against its position number in the run. Remember: BSMOW standards are included every 6th position The values drift over time with one “dark arts” spike. The “x” scale is the sample number or time, since the samples each take the same amount of time to run

Correcting Finnigan MAT data: DRIFT

# vs. BSMOW standard δ18O

-13.2

-13.0

-12.8

-12.6

-12.4

-12.2

0 50 100 150position # in run

δ18O reported

actual

# vs. BSMOW standard δ18O

-13.2

-13.0

-12.8

-12.6

-12.4

-12.2

0 50 100 150position # in run

δ18O

reportedfitcorrectedactual

1 2

A smooth curve is fit through all the reported BSMOW standards (and SPW3 standards on a separate graph). Then the difference between the fit curve and actual curve is added to the reported value. The corrected value is plotted. For example, 1 had –0.6 and 2 had –0.2 added.


standardsline # delta 18Ox x2 y fit corrected actual a b c

6 36 -12.29 -12.26 -12.98 -12.95 6.11711E-05 -0.012126704 -12.1936083812 144 -12.20 -12.33 -12.82 -12.95 2.16924E-05 0.00308276 0.09234752218 324 -12.40 -12.39 -12.96 -12.95 0.634638812 0.131455514 #N/A24 576 -12.40 -12.45 -12.90 -12.95 16.50166716 19 #N/A30 900 -12.57 -12.50 -13.01 -12.95 0.570315843 0.328330493 #N/A36 1296 -12.70 -12.55 -13.10 -12.9542 1764 -12.62 -12.60 -12.98 -12.9548 2304 -12.79 -12.63 -13.11 -12.9554 2916 -12.50 -12.67 -12.78 -12.9560 3600 -12.69 -12.70 -12.94 -12.9566 4356 -12.72 -12.73 -12.94 -12.9572 5184 -12.72 -12.75 -12.92 -12.9578 6084 -12.71 -12.77 -12.89 -12.9584 7056 -12.69 -12.78 -12.86 -12.9590 8100 -12.85 -12.79 -13.01 -12.95

This is the spreadsheet that actually makes the drift correction. The fitted line shown before is a quadratic polynomial fit:

y = x2a+xb+c Where x is the line number and y is the delta value of BDW


Instead of the quadratic formula just discussed, drift can also be calculated using a peak to peak correction. For this correction, one assumes linear drift between each pair of two standards and uses the slope of the connecting line to make corrections. For instance, to achieve the correct BDW value of –12.95‰, -0.66 must be added to #6 and –0.75 to #12 and the appropriate intermediate values to each sample in-between.

sample name delta 18O1 dummy -16.252 dummy -16.06 corrected3 dummy -16.14 delta 18O4 dummy -16.115 dummy -16.27 +6 BDW -12.29 -0.66 -12.957 Shipley Valley 1 -6.38 1 -0.6732 -7.068 Shipley Valley 4 -2.62 2 -0.6887 -3.319 BSMOW 4.53 3 -0.7041 3.82

10 Shipley Valley 5 -5.20 4 -0.7196 -5.9211 Shipley Valley 9 -6.25 5 -0.7351 -6.9812 BDW -12.20 -0.75 -12.95


smooth p2p averagecorrected additive p2p and

# Name delta 18O delta 18O smooth1 dummy -16.992 dummy -16.793 dummy -16.864 dummy -16.825 dummy -16.976 BDW -12.987 Shipley Valley 1 -7.06 -7.06 -7.068 Shipley Valley 4 -3.29 -3.31 -3.309 BSMOW 3.87 3.82 3.85

10 Shipley Valley 5 -5.84 -5.92 -5.8811 Shipley Valley 9 -6.88 -6.98 -6.9312 BDW -12.82 -12.95 -12.8813 Shipley Valley 12 -4.71 -4.81 -4.7614 Shipley Valley 14 -6.84 -6.93 -6.8815 BWW -6.30 -6.36 -6.3316 Shipley Valley 16 -7.08 -7.11 -7.1017 Shipley Valley 19 -3.46 -3.47 -3.4718 BDW -12.96 -12.95 -12.96

There is no particular reason to use the smoothed fit versus peak to peak correction.


Whichever has the best results for quality control can be used or they can be averaged.

Constructing as spread sheet for the smooth curve correction.

• This is a simple example using a data set that drifts linearly with time.

• Standards every 5 samples drift from a value of -12.00 to -12.45, it is obvious that the values drifted with time.

• How can this be corrected?

line number reported delta value (RV)

x y

5 -12.00

10 -12.01

15 -12.15

20 -12.16

25 -12.30

30 -12.30

35 -12.44

40 -12.45

average= -12.23

stdev= 0.18

When graphed the drift looks linear.

example of linear drift

-12.60

-12.40

-12.20

-12.00

-11.800 10 20 30 40 50

line number

delta

val

ue

line number

reported delta value (RV)

fit curve (FC) linest function

linest function

x y y=xa+b a b

5 -12.00 -11.98 -0.012821429 -11.91129

10 -12.02 -12.04 0.000745181 0.018815

15 -12.12 -12.10 0.980135053 0.024147

20 -12.16 -12.17 296.039575 6

25 -12.20 -12.23

30 -12.30 -12.30 LINEST(known_y's,known_x's,const,stats)

35 -12.34 -12.36

40 -12.45 -12.42

average= -12.20 -12.20

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 of standard (AV) linest function

linest function

x y y=xa+b AV a b

5 -12.00 -11.98 -12.00 -0.012821429 -11.91129

10 -12.02 -12.04 -12.00 0.000745181 0.018815

15 -12.12 -12.10 -12.00 0.980135053 0.024147

20 -12.16 -12.17 -12.00 296.039575 6

25 -12.20 -12.23 -12.00

30 -12.30 -12.30 -12.00 LINEST(known_y's,known_x's,const,stats)

35 -12.34 -12.36 -12.00

40 -12.45 -12.42 -12.00

average= -12.20

stdev= 0.16

Assuming the correct value of the standard is -12.00, this can be put in the spread sheet.

-12.50

-12.40

-12.30

-12.20

-12.10

-12.00

-11.900 10 20 30 40 50

yy=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

-12.50

-12.40

-12.30

-12.20

-12.10

-12.00

-11.90

-11.800 10 20 30 40 50

lines number

delta

val

ue y

y=xa+b

=AD-FC+RV

AV

line number

reported delta value (RV)

fit curve (FC)

corrected value (CV)

actual delta vaule of standard (AV) linest function

linest function

x y y=xa+b =AV-FC+RV AV a b

5 -12.00 -11.98 -12.02 -12.00 -0.014171429 -11.90714

10 -12.01 -12.05 -11.96 -12.00 0.001147609 0.028976

15 -12.15 -12.12 -12.03 -12.00 0.962142544 0.037187

20 -12.16 -12.19 -11.97 -12.00 152.4892562 6

25 -12.30 -12.26 -12.03 -12.00

30 -12.30 -12.33 -11.97 -12.00 LINEST(known_y's,known_x's,const,stats)

35 -12.44 -12.40 -12.04 -12.00

40 -12.45 -12.47 -11.98 -12.00

average= -12.23 -12.23 -12.00

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 -12.00 -12.30 -11.70 -12

31 -14.05 -12.31 -13.74 -12

32 -11.87 -12.32 -11.55 -12

33 -18.45 -12.33 -18.12 -12

34 -13.45 -12.35 -13.10 -12

35 -12.02 -12.36 -11.66 -12

36 -19.48 -12.37 -19.11 -12

37 -11.36 -12.39 -10.97 -12

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 -12.00 -11.98 -12.02 -12 -0.012821429 -11.91129

10 -12.02 -12.04 -11.98 -12 0.000745181 0.018815

15 -12.12 -12.10 -12.02 -12 0.980135053 0.024147

20 -12.16 -12.17 -11.99 -12 296.039575 6

25 -12.20 -12.23 -11.97 -12

30 -12.30 -12.30 -12.01 -12 LINEST(known_y's,known_x's,const,stats)

35 -12.34 -12.36 -11.98 -12

40 -12.45 -12.42 -12.03 -12

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 c6 36 -12.04 -12.06 -11.98 -12 0.000234586 -0.0021994 -12.05678

12 144 -12.03 -12.05 -11.98 -12 0.000137241 0.007591795 0.08934318 324 -12.06 -12.02 -12.04 -12 0.896533814 0.064038461 #N/A24 576 -12.04 -11.97 -12.07 -12 21.66248327 5 #N/A30 900 -11.90 -11.91 -11.99 -12 0.177672416 0.020504622 #N/A36 1296 -11.72 -11.83 -11.89 -12 LINEST(known_y's,known_x's,const,stats)42 1764 -11.76 -11.74 -12.02 -1248 2304 -11.65 -11.62 -12.03 -12

30 900 -12.00 -11.91 -12.09 -1231 961 -14.05 -11.90 -14.15 -1232 1024 -11.87 -11.89 -11.98 -1233 1089 -18.45 -11.87 -18.58 -1234 1156 -13.45 -11.86 -13.59 -1235 1225 -12.02 -11.85 -12.17 -1236 1296 -19.48 -11.83 -19.65 -1237 1369 -11.36 -11.82 -11.54 -12

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.

Adjust for effect of sample size.

• The x values in the previous equations can also be reported beam area for each sample, adjusting the data value for sample size.

• Simply superimpose sample beam area instead of line number in the spreadsheet.

• Linest can also be used in the form y=ax2+bx+c, and more complex forms.

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

26.0026.50

27.0027.50

28.00

0 100000 200000 300000

area

delta

val

ue reportedfitcorractual

Example of area vs. delta value non-linearity correction

What about situations when a peak to peak correction is

better than a smooth curve fit?

•This data has been corrected using a peak to peak (p2p) correction.

•Note BDW standards are every 6th line.

•The standards should be –12.00 but vary, for example #18 is –12.06, #24 –12.24.

•AD is the amount that has to be added to each standard to make it –12.00

line number name

reported value delta 18O

number of lines between standards

amount to add to reported value

corrected value

RV NL AD CV6 BDW -12.04 0.04 -12.007 1 -2.29 1 0.0413 -2.258 2 3.49 2 0.0391 3.539 BSMOW 4.30 3 0.0369 4.34

10 3 -7.87 4 0.0347 -7.8411 4 0.70 5 0.0326 0.7412 BDW -12.03 0.03 -12.0013 5 -0.11 1 0.0355 -0.0814 6 -6.56 2 0.0406 -6.5215 BWW -5.65 3 0.0458 -5.6016 7 -3.11 4 0.0509 -3.0617 8 -0.97 5 0.0560 -0.9118 BDW -12.06 0.06 -12.0019 9 -4.74 1 0.0912 -4.6520 10 -1.66 2 0.1213 -1.5421 BSMOW 3.44 3 0.1514 3.6022 11 -7.66 4 0.1815 -7.4723 12 -4.58 5 0.2115 -4.3724 BDW -12.24 0.24 -12.0025 13 -2.83 1 0.2036 -2.6326 14 -3.13 2 0.1656 -2.9627 BWW -5.61 3 0.1276 -5.4828 15 -7.61 4 0.0895 -7.5229 16 -2.94 5 0.0515 -2.8930 BDW -12.01 0.01 -12.00

•It is assumed that the 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.

•The corrected value (CV) is the reported value (RV) plus the amount to add (AD).

line number name




corrected value

RV NL AD CV=RV+AD6 BDW -12.04 0.04 -12.007 1 -2.29 1 0.0413 -2.258 2 3.49 2 0.0391 3.539 BSMOW 4.30 3 0.0369 4.34


The amount to add (AD) is assumed to drift completely linearly between standards. Below is a graph showing AD vs. the samples line. Note the very sudden change from 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

0 5 10 15 20 25 30 35

line number

amou

nt to

add

(AD

)

# name




corrected value

RV NL AD CV=RV+AD18 BDW -12.06 0.06 -12.0019 9 -4.74 1 0.0912 -4.6520 10 -1.66 2 0.1213 -1.5421 BSMOW 3.44 3 0.1514 3.6022 11 -7.66 4 0.1815 -7.4723 12 -4.58 5 0.2115 -4.3724 BDW -12.24 0.24 -12.00

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 B1 0.062 1 0.09123 2 0.12134 3 0.15145 4 0.18156 5 0.21157 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




corrected value

RV NL AD CV=RV+AD6 BDW -12.04 0.04 -12.007 1 -2.29 1 0.0413 -2.258 2 3.49 2 0.0391 3.539 BSMOW 4.30 3 0.0369 4.34


•A similar formula is copied into each sample (not standard line) of the AD column.

•The AD value for each line is added to the RV value to calculated the corrected value (CV).

Should a smooth curve or p2p correction be used?

• It depends on what works best for a particular analysis, depending on the quality control results.

• There is no one answer that fits all analysis! • Since every lab has different requirements, it

probably makes most sense for the analysts to create their own post analysis spread sheets, hence this course.

Dual Mixing Model Linearity Correction (Fry 1992)

Elemental analysis for N of small sample is frequently corrected using a dual mixing model as described by Fry et al. 1992. Anal. Chem. 64:288-291

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

Theory of Dual Mixing Model Correction

• Assumes that there is a blank value for N which is present in every sample.

• This blank has a fixed value for size and isotope ratio.

• The size is that for the measured blank. • The isotope ratio of the blank is calculated

by analyzing a standard over a range of sizes that span the unknown size range.

Mathematics

corrected delta = ((delta samp)x(samp area))+((delta blank)x(blank area))

(samp area + blank area)

Calculation of blank delta δ 15N N beam

# y x 1/x

51 0.20 0.21 4.81

39 -0.01 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

-0.50

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

repo

rted

del

ta N

y=xa + b calculated using linest function.

blank 0.02 49.30 -15.03 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

What happens if two standards drift at different rates?

• It is now recognized as being highly desirable to 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.

• For example, when calibrating for HD using VSMOW at 0.0 delta D, some systems report SLAP, for example, -402.0 instead of –428.0.

• These mass spectrometers must be “normalized” using a standard curve.

• Unfortunately these standards do not always drift at the same rate over time.

USGSPR

-10-8-6-4-20

0 100 200 300

injection number

del

ta D delta H

curv fit

corraverage

USGSA

-400

-398

-396

-394

-392

-3900 100 200 300

injection number

delta

D delta HCurv fitcorraverage

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.

-68

-66

-64-62

-60

-580 100 200 300

injection number (#)

delta

D

no drift correction

2 standard drfitcorrection

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 -9.8 -393.4 -9.2 -115.1 -399.2 -1.3 -110.7 -1.8 1.036073 8.380562264 69696 USGSPR -9.1 -393.4 -9.2 -115.1 -399.2 -1.3 -110.7 -1.1 1.036106 8.38777265 70225 USGSPR -9.4 -393.4 -9.2 -115.1 -399.2 -1.3 -110.7 -1.3 1.036139 8.394825266 70756 WQEV -76.9 -393.3 -9.2 -115.1 -399.2 -1.3 -110.7 -71.2 1.036171 8.401725267 71289 WQEV -79.4 -393.3 -9.2 -115.2 -399.2 -1.3 -110.7 -73.9 1.036203 8.408472268 71824 WQEV -79.3 -393.3 -9.2 -115.2 -399.2 -1.3 -110.7 -73.8 1.036235 8.415064269 72361 WQEV -79.6 -393.3 -9.2 -115.2 -399.2 -1.3 -110.7 -74.0 1.036267 8.421502270 72900 WQEV -79.7 -393.3 -9.2 -115.2 -399.2 -1.3 -110.7 -74.2 1.036298 8.427786

inject. y=xa+binject. number x USGSA USGSPR WQEsker actual actual actual correctednumber squared sample delta H curv fit curve fit curve fit USGSA USGSPR WQEsker delta H a b

1 1 USGSA -380.2 -393.3 -2.2 -110.5 -399.2 -1.3 -110.7 -385.8 1.018097 1.2969192 4 USGSA -393.1 -393.3 -2.2 -110.5 -399.2 -1.3 -110.7 -398.9 1.0182 1.3430543 9 USGSA -392.9 -393.3 -2.3 -110.6 -399.2 -1.3 -110.7 -398.7 1.018302 1.3890484 16 USGSA -393.6 -393.3 -2.3 -110.6 -399.2 -1.3 -110.7 -399.4 1.018404 1.4349015 25 USGSA -393.1 -393.3 -2.4 -110.6 -399.2 -1.3 -110.7 -398.9 1.018506 1.4806146 36 WQEsker -112.0 -393.3 -2.4 -110.7 -399.2 -1.3 -110.7 -112.6 1.018608 1.5261857 49 WQEsker -109.9 -393.3 -2.5 -110.7 -399.2 -1.3 -110.7 -110.4 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

-10

-5

00 50 100 150 200 250 300

line number

delta

D

delta H

curv fit

corr

average

WQEsker

-118.0

-116.0

-114.0

-112.0

-110.0

-108.00 50 100 150 200 250 300

line number

delta

D

delta H

Curv f it

corr

average

USGSA

-400

-395

-3900 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 USGSPR

WQEsker

USGSA

number sample delta H curve fit curve fit curv fit

1 1 USGSA -380.2 -2.2 -110.5 -393.3

2 4 USGSA -393.1 -2.2 -110.5 -393.3

3 9 USGSA -392.9 -2.3 -110.6 -393.3

4 16 USGSA -393.6 -2.3 -110.6 -393.3

5 25 USGSA -393.1 -2.4 -110.6 -393.3

6 36 WQEsker -112.0 -2.4 -110.7 -393.3

7 49 WQEsker -109.9 -2.5 -110.7 -393.3

8 64 WQEsker -110.4 -2.5 -110.7 -393.3

9 81 WQEsker -110.8 -2.6 -110.8 -393.3

10 100 WQEsker -110.7 -2.6 -110.8 -393.3

11 121 USGSPR -1.9 -2.7 -110.8 -393.3

12 144 USGSPR -2.4 -2.7 -110.8 -393.3

13 169 USGSPR -2.8 -2.8 -110.9 -393.3

14 196 USGSPR -2.8 -2.8 -110.9 -393.4

15 225 USGSPR -2.8 -2.8 -110.9 -393.4

16 256 WQEV -76.0 -2.9 -111.0 -393.4

17 289 WQEV -75.5 -2.9 -111.0 -393.4

18 324 WQEV -74.9 -3.0 -111.0 -393.4

19 361 WQEV -75.0 -3.0 -111.0 -393.4

20 400 WQEV -75.2 -3.1 -111.1 -393.4

21 441 C106899-0021 -48.3 -3.1 -111.1 -393.4

22 484 C106899-0021 -48.5 -3.2 -111.1 -393.4

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 -4.7 Y1 USGSPR actual -1.3

X2 WQEsker curve fit -112.1 Y2 WQEsker actual -110.71

X3 USGSA curv fit -393.6 Y3 USGSA actual -399.23

for line #225

X1 USGSPR curve fit -8.9 Y1 USGSPR actual -1.3

X2 WQEsker curve fit -114.9 Y2 WQEsker actual -110.71

X3 USGSA curv fit -393.6 Y3 USGSA actual -399.23

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

-68.1

-60.5

Note: Every line must have its own normalization curve!!!

------------------------------ X 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 -380.2 -2.2 -110.5 -393.3 -1.3 -110.71 -399.23 -385.8 1.02 1.30

2 4 USGSA -393.1 -2.2 -110.5 -393.3 -1.3 -110.71 -399.23 -398.9 1.02 1.34

3 9 USGSA -392.9 -2.3 -110.6 -393.3 -1.3 -110.71 -399.23 -398.7 1.02 1.39

4 16 USGSA -393.6 -2.3 -110.6 -393.3 -1.3 -110.71 -399.23 -399.4 1.02 1.43

5 25 USGSA -393.1 -2.4 -110.6 -393.3 -1.3 -110.71 -399.23 -398.9 1.02 1.48

6 36 WQEsker -112.0 -2.4 -110.7 -393.3 -1.3 -110.71 -399.23 -112.6 1.02 1.53

7 49 WQEsker -109.9 -2.5 -110.7 -393.3 -1.3 -110.71 -399.23 -110.4 1.02 1.57

8 64 WQEsker -110.4 -2.5 -110.7 -393.3 -1.3 -110.71 -399.23 -110.9 1.02 1.62

9 81 WQEsker -110.8 -2.6 -110.8 -393.3 -1.3 -110.71 -399.23 -111.2 1.02 1.66

10 100 WQEsker -110.7 -2.6 -110.8 -393.3 -1.3 -110.71 -399.23 -111.1 1.02 1.71

11 121 USGSPR -1.9 -2.7 -110.8 -393.3 -1.3 -110.71 -399.23 -0.2 1.02 1.75

12 144 USGSPR -2.4 -2.7 -110.8 -393.3 -1.3 -110.71 -399.23 -0.7 1.02 1.80

13 169 USGSPR -2.8 -2.8 -110.9 -393.3 -1.3 -110.71 -399.23 -1.0 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)

LINEST function for #58

Normalization for #58 and #225

Final proof of calculations, put the corrected quality control results into a long term external precision graph.

•It has proven very difficult to describe the concept of drift correction when two different standards drift at different rates.

•The author will be available at free times during the rest of this conference to discuss spreadsheet construction with anyone interested in hands on experience.

•Many of you probably have better ways of doing these corrections, if so please let me know so I can learn them!

•The author would like to thank Shaoneng He, Zymax 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:

•Thanks for coming, and looking interested!!!

Example post analysis spreadsheet for 18O cellulose samples.

Pages in Berkeley 1.01 generic spreadsheet.

how to use

output from mass spectometerpaste in namesand weights

paste in area and delta values from mass spectometer

convert delta values to international scalecalculate 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 with2nd std

smooth 1 std total

smooth 2std total

p2p 1std total

p2p 2std 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 0 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

Example of weighing tray for samples

number 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

Input data to final spreadsheet delta # sample wt. mg area 18O

1 Dummy 0 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 0.00 6 sigma 1.024 144230 28.14 7 A3M69 1.064 138207 28.09

Documents

Introduction to Post Analysis Spreadsheets · 2014-08-01 · Introduction to CFIRMS Post Analysis Spreadsheets (Defense against the dark arts 100) By Paul Brooks, University of California,