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 4 th 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, 6 th 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.

Memory correction (carryover) using examples from a heavily modified post analysis spreadsheet for an LGR laser system. 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 of the IAEA water Resources Programme

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. 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 N 50 3

Command to remove isotope ratio if volume (mass) blank.

Formula to remove isotope ratio if volume (mass) blank. Where checkplots!G13 is the water volume, raw L13 is the isotope ratio. AC 13 0.0020144709 14 AC 13 =IF(checkplots!$G13="","",raw!L13) 14 =IF(checkplots!$G14="","",raw!L14)

Filter to remove outlier ratios abs diff from outliers H2O18/H2O average stdev 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 AC AD AE AF AG AH 14 15 0.0019433775 16 0.0019444036 17 0.0019438525 18 0.0019434457 19 =AVERAGE(AC14:AC19) =STDEV(AC14:AC19) 0.0019439051

AF AG Filter to remove outlier ratios 2 1.2 outlier= abs diff from outliers H2O18/H2O average stdev 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) =IF(AC18="","",ABS(AC18-AD19)) =IF(AF18>AG$2*AE19,"",AC18) 18 19 =IF(AC19="","",ABS(AC19-AD19)) =IF(AF19>AG$2*AE19,"",AC19) =AVERAGE(AG14:AG19)

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 18 O water, using a Thermo Gas Bench.

18 O analysis: running samples + standards Sample input spreadsheet for 18 O analysis: Dummy: to warm up instrument 1 dummy - US standard BDW: calibration standard 2 dummy - US standard 3 dummy - US standard BSMOW: quality control 4 dummy - US standard BWW: quality control 5 dummy - US standard 6 BSMOW Numbers: unknowns 7 1 1 8 2 2 9 SPW3 10 3 3 11 4 4 12 BSMOW Remember, water samples 13 5 5 to be analyzed for 18 O are 14 6 6 15 BWW equilibrated with CO 2 and 16 7 7 the CO 2 is then analyzed on 17 8 8 18 BSMOW the gas bench. 19 9 9 20 10 10 21 SPW3

18 O analysis: running samples + standards For water 18 O analysis: The instrument takes 5 samples (dummies) before the results start to become consistent. The instrument is calibrated with a -12.95 δ 18 O standard called BDW (Berkeley Distilled Water) every 6 samples. Every 12 samples there are quality control standards, either a 3.33 δ 18 O BSMOW (Berkeley Standard Mean Ocean Water), or a -6.47 BWW (Brooks Well Water). In between the standards are 4 unknowns.

Gas Bench Output

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