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An O18/O16 study of water flow in natural snow 1975

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AN 0 » V o * 6 STUDY OF WATER FLOW I N N aro BAL SNOW by Timothy K. Ahern B . S c , Whitworth C o l l e g e , 1972 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the Department of Geophysics and Astronomy We accept t h i s t h e s i s as conforming t o the r e q u i r e d standard The U n i v e r s i t y Of B r i t i s h Columbia A p r i l , 1975 In presenting t h i s t h e s i s in p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I f u r t h e r agree that permission for extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s re p r e s e n t a t i v e s . It i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission. Department The U n i v e r s i t y of B r i t i s h Columbia 20 75 Wesbrook Place Vancouver, Canada V6T 1W5 Date 2V i Abstract One of the most successful applications of oxygen isotope variations i n nature has been t h e i r use i n glaciology. Yearly i s o t o p i c variations i n snowfall provide a means of determining past c l i m a t o l o g i c a l trends from deep i c e cores. The most notable example of t h i s type of application would be the Greenland Ice Core discussed by Dansgaard et a l . (1969). When u t i l i z i n g variations i n stable isotope r a t i o s as an i n d i c a t i o n of past climates two fundamental assumptions must be made. F i r s t , i t i s assumed that the isotopic r a t i o of p r e c i p i t a t i o n f a l l i n g i n the area varies i n some regular manner with a period of one year. The second assumption i s that the isotopic composition of the snow does not change after i t accumulates on the ground. This thesis project was an attempt to study the inter a c t i o n between the l i q u i d and s o l i d phases of water inside naturally occuring snow. One of the most reasonable methods of studying t h i s i n t e r a c t i o n i s by studying i s o t o p i c changes inside the snowpack when l i q u i d water with an 018/0** r a t i o much greater than the snowpack i s uniformly distributed on top of the snow. I t was found that water flow i n several d i f f e r e n t types of sub-zero snow could be described quite s a t i s f a c t o r i l y in terms of isotopic , density and temperature variations. I t was further concluded that accurate q u a l i t a t i v e descriptions of flow would be extremely d i f f i c u l t without the is o t o p i c i i information. The most unique r e s u l t of t h i s thesis project was the discovery that i s o t o p i c patterns i n cold snow seemed to be manifestations of e a r l i e r water movement. That i s to say, movement of the tracer through the snow tended to enhance the o r i g i n a l i s o t o p i c pattern of the snow. The positions of the i s o t o p i c maxima and minima could usually be explained i n terms of density variations. The above r e s u l t has d e f i n i t e implications f o r the use of oxygen isotope variations f o r the determination of past climates from i c e cores. I f l i q u i d water, eith e r from rain or surface melting, i s present i n the snowpack at any time we must conclude that i s o t o p i c variations may be introduced in t o the snowpack that are not related to c l i m a t o l o g i c a l factors. Isotopic dating of such cores would obviously be i n error. The conclusion reached by many researchers that l i q u i d water movement inside a snowpack w i l l tend to homogenize the snow i s o t o p i c a l l y does not seem to apply to sub-zero snowpacks. In addition to the f i e l d project discussed above, t h i s thesis presents a comprehensive description of the instrumentation and techniques used to measure the i s o t o p i c compositions of water samples with a precision of fourteen parts i n one hundred thousand 9 & complete analysis of the exchange of oxygen isotopes between water and carbon dioxide i s presented. A determination of factors that can introduce errors into the analysis of water samples i s also given. I t i i i i s somewhat su r p r i s i n g that the non-zero voltage c o e f f i c i e n t s of resistance for the Victoreen Hi-meg r e s i s t o r s can be a major source of error i n the analyses. i v TABIE OF C08TBHTS Abstract .............................................. i Table Of Contents i v L i s t Of Tables ........................................ v i i L i s t Of Figures ...................................... • v i i i Acknowledgments ................... .... ................ x I. Introduction And Background 1 1.1 A Review of Previous i s o t o p i c Bork On G l a c i e r s And Snow • 1 1.2 General Techniques o f Heasuring The o * « / 0 1 6 Ratio In A Hater Sample ......................... 5 1.3 Motivations Of This Study ...., 8 I I . The Dual Bean Mass Spectrometer .................. 10 2.1 General Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2 The Dual Collector Assembly ................... 13 2.3 The Heasuring System . . . . . . . . . . . . . . • . . . . . . . . . . . 16 2.4 The Sample Inlet System 26 I I I . Experimental Technique Of Determining Eel ....... 35 3.1 Laboratory Procedures 35 3.1.1 Sample Preparation ....................... 35 3.1.2 The E q u i l i b r a t i o n Of Hater And Carbon Dioxide .................. . . . . . . . , 39 3.1.3 The Bass Spectrometer Analysis Of A Carbon Dioxide Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.2 Correction Factors Applied To Hass Spectrometer Analyses ........................ . . . . . . . . . . . . . . . . 58 3.2.1 Switching correction 60 V 3.2.2 Tank Carbon Dioxide Correction ........ 63 3.2.3 Linear Correction To Force Agreement With world Standards .............................. 66 3.2.4 Corrections That Sere Hot Applied To These Data ..................... 73 IV. Sources Of Error In Determining o* 8/0 1 6 Batios ... 77 4.1 Multiple Begression Analysis Of Mass Spectrometer Parameters 77 4.2 Equality of Mass 46 Peak Heights 82 4.3 Sources Of Error In The E q u i l i b r a t i o n Of Hater With Carbon Dioxide ............................. 85 4.4 Isotopic Fractionation Of A Carbon Cioxide Sample During Sample Preparation 87 4.5 A n a l y t i c a l Precision Of Analyses .............. 90 V. An Isotopic Study Of Water Flow In Hatural Snow ... 95 5.1 Introduction • 9 5 5.2 The Type Of Snowpacks Studied ....98 5.3 Snowpack Parameters Measured 99 5.4 Experimental Procedure ........100 5.5 Uncertainties In Sampling Technique ........... 103 5.6 D i f f i c u l t i e s Encountered And Disadvantages In Stable Isotope Methods In Snow Hydrology 106 VI. The Isotopic Tracing Of Hater Movement In Snow ...109 6.1 Introduction 109 6.2 Tracing Experiment P1 .110 6.3 Isotopic Tracing Experiment—-T1 .......118 6.4 Isotopic Tracing Experiment---T2 123 v i 6.5 Isotopic Tracing Experiment- T3 ..............126 6.6 Isotopic Tracing Experiment-~PL2 ............. 130 6.7 Isotopic Tracing Experiment-—PL3 136 6.8 Isotopic And Hass Balance In The A r t i f i c i a l Tracing Experiments ...f......141 6.9 Conclusions ................................... 144 L i s t Of Horks Consulted ............................... 147 Appendix I-Property Of The DEL Function-Combination . . . 1 5 5 Appendix I I - Property Of The DEL Function-Inversion . . . 1 5 6 Appendix III-Isotopic Mixing of Two Hater Samples . . . . . 1 5 7 Appendix IV-Isotopic Fractionation And Rayleigh D i s t i l l a t i o n 159 Appendix V-Determination Of A "Best" Weighting Function 162 Appendix Vl-Property Of The DEL Function-Error Propagation 164 v i i LIST OF TABLES 3.1 Data Comparing Two Methods Of Sample Analysis ....58 3.2 The Precision of Two Methods Of Sample Analysis . . 5 9 3.3 Data Used To Check The Li n e a r i t y Of Analyses .....68 3.4 World Average Values Of Hater Standards . . . . . . . . . . 7 0 3.5 U.B.C. Measurements Of The Hater Standards 70 3.6 Machine Corrected Del Values Of Horld Standards ..72 4.1 Results Of Regression Analysis ...................81 4.2 Error In DEL Caused By A Difference In Mass 46 Peak Heights ......84 4.3 Gauge Reading VS Rayleigh Error In Del 90 4.4 Summary Of Errors Involved In Measuring Hater Samples .....................................•......9 3 5.1 Lateral Homogeneity In A Representative Snowpack . 1 0 5 6.1 Summary Of Data P1 • . . . 1 1 2 6.2 Summary Of Data T1 ............................. 120 6.3 Summary Of Data T2 .....124 6.4 Summary Of Data T3 .............................128 6.5 Summary Of Data PL2 ............................ 132 6.6 Summary Of Data PL3 138 6.7 Conservation Of Mass Considerations For Five Tracing Experiments ................................143 6.8 Isotopic Conservation In Tracing Experiments . . . . . 1 4 4 V l l l LIST OF FIGURES 2.1 Dual Collector System .14 2.2 Hass Spectrometer MeasuringSystem ............... 18 2.3 Block Diagram Showing E f f e c t Of Gain And Offsets .21 2.4 Determination Of C a l i b r a t i o n Constant K .,.,......23 2.5 The Sample Introduction System .......27 2.6 The Back Diffusion Problem 29 2.7 The Volume Bate Of Flow Into The Hass Spectrometer . , 31 2.8 The Operation Of The Magnetic Valves •••33 3.1 Sample Flasks And Sample Tubes Used In This Study 36 3.2 The Sample Preparation Line ...................... 37 3.3 The Proposed Hodel For Hater And Carbon Dioxide E g u i l i b r a t i o n 41 3.4 The E q u i l i b r a t i o n Of A Carbon Dioxide Sample .....46 3.5 Eq u i l i b r a t i o n Time For Samples Of Various Compositions ..........•.,......... 48 3.6 The Cubic Splines For A T y p i c a l Analysis .........56 3.7 The Observed Switching Transient 60 3.8 The L i n e a r i t y Of Isotopic Analyses Based On A Mixing Experiment ..................................69 3.9 E l e c t r i c a l Analogue Of Magnetic Valves Of I n l e t System 7 5 4.1 The Effect Of Peak Matching On The DEL Value Obtained . 84 6.1 Sample Positions And Stratigraphic Features In P i t i x 6.2 Isotopic Changes With Time Of Two Snow Layers ....113 6.3 Isotopic P r o f i l e Of P i t In Experiment P1 .........114 6.4 Variation Of Density With Depth T1 121 6.5 Isotopic Composition as A Function Of Depth T1 . . 1 2 1 6.6 The Correlation Between Isotopic And Density Changes T1 .,............ 122 6.7 Isotopic Composition As A Function Of Depth T2 .125 6.8 Density As A Function Of D e p t h — T 2 .............. 125 6.9 The Correlation Between Isotopic And tensity Changes T2 126 6.10 The Variation Of Density With Depth T3 ........ 129 6.11 Isotopic Variations With Depth—-T3 ............. 129 6.12 Positions Of Samples Taken In Tracing Experiment PL2 . , .... .... .... . . , 131 6.13 Temperature P r o f i l e For Experiment PL2 .......... 133 6.14 Density Variations With Depth—-PL2 ............. 133 6.15 Isotopic Variations With Depth—PL2 134 6.16 Correlation Between Isotopic Changes And Density Changes PL2 . 135 6.17 Snow Stratigraphy And Sample Location PL3 .....136 6.18 Isotopic Composition As A Function Of Depth——PL3 m t t \ 1 3 9 6.19 Density Variations As A Function Of Depth PL3 .139 6.20 The Correlation Between Isotopic And Density Changes—--PL3 140 6.21 The Physical Bodel Used In The Study Of Water Flow ........... ................... ................. 142 X Acknowledgments The study of water movement in snow using an i s o t o p i c a l l y enriched tracar was f i r s t suggested by Dr. K. E. Best. His i n t e r e s t and assistance i n the e a r l y stages of the project are greatly appreciated. I would l i k e to thank my supervisor. Dr. R.D. Russell, fo r his help i n several aspects of t h i s project. His advice i n areas of mass spectrometry and related instrumentation was extremely useful. Capable t e c h n i c a l assistance was provided by CM. T u n s t a l l , K.D. Schreiber, H. Verwoerd and R. E. Mel drum ( a l l of the Department of Geophysics and Astronomy) and by J . Lees and E. Williams (Physics department). I would l i k e to thank Dr. R.D. Russell and Dr. G.K.C. Clarke f o r reading t h i s thesis and for t h e i r comments and suggestions. During t h i s thesis project f i n a n c i a l assistance was received from two University of B r i t i s h Columbia post-graduate scholarships and from the Graduate Research Committee of the University of B r i t i s h Columbia. The cost of adapting the mass spectrometer instrumentation to oxygen research was provided by the Polar Continental Shelf Group of the Department of Energy Mines and Resources through a contract. The major parts of t h i s research were from NRC grant numbers A-0720 and A-0131. I. INTRODUCTION AND BACKGROUND 1.1 A Review Of Previous Isotopic Horfc On Glaciers And Snow During the past f i f t e e n years many researchers have studied the i s o t o p i c composition cf polar g l a c i e r s , temperate g l a c i e r s and snow. I n i t i a l investigations by Dansgaard (1961), Epstein and Sharp (1967), Epstein Sharp and Gow (1965) , and Herlivat et a l . (1967b) were r e s t r i c t e d to polar regions where the complicating e f f e c t s of percolating water and ablation were minimized. They were thus able to i d e n t i f y a periodic variation i n the ice cores preserved i n the ice as changes i n the i s o t o p i c composition. They were also able to f i n d a d i r e c t c o r r e l a t i o n between the deuterium/hydrogen r a t i o s (D/H) and oxygen-18/oxygen-16 ra t i o s (0 1 8/0 1 6)» In addition, some empirical evidence was found regarding the expected t h e o r e t i c a l v a r i a t i o n of is o t o p i c r a t i o s with a l t i t u d e . The work being done on temperate g l a c i e r s i s s t i l l i n a formative stage, Epstein and Sharp (1959), Sharp et a l . (1960), Hacpherson and Krouse (1967), Arnason (1969b), Ambach et a l . (1971) and Best (1972) are only a few who have studied the i c e and snow from temperate g l a c i e r s i n North America and Europe and, as expected, have found the iso t o p i c data much harder to interprete than s i m i l a r data from polar g l a c i e r s . According to these authors the great v a r i a t i o n in 2 the winter layers of snow caused by the varying is o t o p i c composition of the p r e c i p i t a t i o n tends to be reduced as melting proceeds. The conclusion cf these researchers was that as the melting process progressed, the gla c i e r tended to become homogenized by the capture of freezing rain and snow i n crevasses on the g l a c i e r surface. Sharp et a l . (1960) also speculated that some of the homogenization was due to the existence of water trapped in the snow layers. As expected there was noticeable enrichment of oxygen-18 i n the ice as the melting season progressed because the l i q u i d phase, and thus the e f f l u e n t , would be enriched i n the l i g h t e r isotope. In these studies i s o t o p i c exchange between the l i q u i d and s o l i d phases of the water was neglected. Arnason (1969b) and Buason (1972) have since shown that t h i s exchange should not be neglected i n the case of hydrogen isotopes i n temperate g l a c i e r s . Isotopic methods applied to snow present even more d i f f i c u l t i e s than studies on the i c e of temperate g l a c i e r s . Nevertheless, the importance of understanding the hydrological p r i n c i p l e s governing water storage and runoff has prompted several researchers to use iso t o p i c data f o r studies of natural snow. Gonfiantini and P i c c i o t t o (1959) were among the f i r s t to study oxygen isotope variations in the polar regions. Deutsch et a l . (1966) have used oxygen isotopes to determine net accumulation rates of sncw on an alpine g l a c i e r using the d i s t i n c t " i s o t o p i c seasons" encountered. They found poor c o r r e l a t i o n between analyses 3 of i s o t o p i c data of yearly accumulation rates when compared to s t r a t i g r a p h i c studies, which normally form the basis of such investigations. This i s i n agreement with Gonfiantini et a l . (1963) who concluded that snowpack metamorphism destroys yearly features in the s t r a t i g r a p h i c sense. For t h i s reason the yearly i s o t o n i c v a r i a t i o n described by Epstein and Sharp (1967) i s a more r e l i a b l e i ndicator of accumulation rates. Dincer et a l . (1970a) and Dincer et a l . (1970b) used t r i t i u m and oxygen-18 analyses to calculate the r a t i o of the subsurface runoff to the t o t a l runoff from a snowpack with the constraint of conservation of i s o t o p i c species. They also studied the maturation process of a " t y p i c a l " snowpack and have observed that percolation tends to homogenize the pack i s o t o p i c a l l y . The f i n a l conclusion reached above i s important. It implies that the most damaging e f f e c t that l i q u i d water movement can have on a snowpack i s the removal of the i s o t o p i c record. This i s not what was found i n the present study at a l l . This researcher has found that d i s t i n c t i s o t o p i c variations can actually be caused by water movement and at times the o r i g i n a l i s o t o p i c p r o f i l e can even be enhanced. This of course means that i s o t o p i c peaks that were introduced by the percolation of water might be i d e n t i f i e d as a yearly i s o t o p i c peak and introduce errors i n the interpretation of such data. The project that i s most clo s e l y associated with this study i s that of Krousa and Smith (1972). Working i n the snowpacks of the Sierra Hevadas they were able to trace the movement of water i n the snowpack with a p r o f i l i n g density gauge and isotopic analyses of representative samples. By introducing i s o t o p i c analyses into t h e i r study, Krouse and Smith were able to i d e n t i f y the source of water that existed at various l e v e l s i n the snowpack. The a b i l i t y to determine the o r i g i n of l i q u i d water inside the snowpack seemed so important that an intensive study of water-snow int e r a c t i o n within a snowpack seemed desirable. Krouse and Smith used natural i s o t o p i c variations in the r a i n as the primary source of l i q u i d water. In the present study a l l experiments were done with an a r t i f i c i a l tracer of d i s t i l l e d seawater. Many d i f f e r e n t types of snow were studied i n an e f f o r t to see i f conclusions about water movement in snow hold true for various types of snow. I t was found that the water flow within a s p e c i f i c snowpack was explainable using only density measurements, isotopic measurements and on some occasions temperature variations. Conclusions were f i n a l l y made about water flow in very cold snowpacks but i t i s believed that c a r e f u l measurements of many parameters are necessary to characterize the snow before conclusions can be stated with a high degree of confidence for isothermal snowpacks. 5 1.2 General Techniques Of Measuring The o 1 8 / ° 1 6 Batio In A Water Sample Water vapor i t s e l f i s unsuitable for introduction into a mass spectrometer because of the long time required to pump i t out on completion of the analysis. For t h i s reason carbon dioxide i s equilibrated with the water sample under inv e s t i g a t i o n , as described by Epstein and Hayeda ( 1 9 5 3 ) . Carbon dioxide i s r e a d i l y analyzed i n a mass spectrometer and from i t s i s o t o p i c composition the i s o t o p i c composition of the water sample can be determined. I t i s d i f f i c u l t to measure absolute i s o t o p i c abundances with great pr e c i s i o n . However, the difference i n composition between two samples can be determined with a precision of better than two parts i n ten thousand. For t h i s reason, results of is o t o p i c studies of oxygen are generally reported i n terms of a DEL scale as follows: DEL(X/S) = (R x/R g - 1) 10* 11 .1 ] where Rx and Rs ref e r to the r a t i o s of the i n t e n s i t i e s of the mass 46 and mass 44 ion beams for the carbon dioxide equilibrated with the unknown water sample and the standard carbon dioxide, respectively. The symbol 46/44 w i l l be used i n t h i s thesis to refer to the r a t i o of the ion beam currents at mass 46 and mass 44. As shown by Epstein (1959), the DEL value thus obtained i s the same as the DEL value obtained by d i r e c t measurement of the o * 8 / ° 1 6 r a t i o i n the water sample. The properties of the DEL function are subtle. For 6 instance, i f a DEL value was measured r e l a t i v e tc standard A and i t was required to know the DEL value r e l a t i v e to another standard, standard B, the following r e l a t i o n s h i p can be used: DEL(X/B) = DEL(X/A) + DEL(A/B) + DEL(X/A)DEL(A/B)/10 3 C 1- 2] As another example, i f one had the value of DEL (A/B) but needed the value of DEL (B/A) the following r e l a t i o n s h i p i s used: DEL(B/A) = -DEL(A/B) 10 3/[DEL(A/B) + 10 3] [1.3] Many other features of the DEL function e x i s t and those pertinent to t h i s study are derived i n Appendices I, II, III and VI. The standard normally used i n isotopic studies of oxygen i n water samples i s "Standard Mean Ocean Water" (SHOW) as defined by Craig (1961a). In f a c t no true samples of SMOW exi s t and so the International Atomic Energy Agency has di s t r i b u t e d a standard referred to as IAEA SMOW which has a DEL value quite close to SHOW. The reference standard used i n c a l c u l a t i n g a l l DEL values i n t h i s project was IAEA SMOW. By Craig's d e f i n i t i o n of SHOW i t has an o* 8/0»* r a t i o that i s 1.008 times the 0* 8/0 1 6 r a t i o of HBS1, another common laboratory standard. Many laboratories throughout the world have measured the value cf HBS1 r e l a t i v e to IAEA SMOW and on the basis of these measurements the average value obtained for DEL(NBS1/IAEA SMOW) i s -7.86. By using equations 1.2 and 1.3 and the average value of DEL (HBS1/IAEA SMOW) the following r e s u l t i s obtained. DEL(IAEA SM0W/SM0W) = -0.08 [1.4] 7 Measurements made r e l a t i v e to IftEA SHOW can easily be expressed r e l a t i v e to SHOW by using eguations 1.2 and 1.4. I t should be noted that the difference between these two standards i s smaller than the present a n a l y t i c a l precision of analyses made at most laboratories. I t i s d i f f i c u l t to maintain constant operating conditions for a mass spectrometer and so i f the unknown sample and the reference standard are measured at diff e r e n t times the r e s u l t i n g DEL w i l l be i n error. For t h i s reason carbon dioxide that has been eguilibrated with the unknown sample and carbon dioxide that serves as a working standard are admitted a l t e r n a t e l y into the mass spectrometer. The 46/44 r a t i o of the unknown i s measured f o r a given period of time, then magnetic valves are switched and the working standard i s analyzed for the same period of time. This process i s repeated several times and in so doing any changes i n the mass spectrometer w i l l have less e f f e c t in the calculated DEL value. Mass spectrometers used to measure oxygen isotope r a t i o s are usually based on the design of A.0. Nier (1947). Modifications to th i s basic design are usually those proposed by HcKinney et a l . (1950) and Nier et a l . (1947) which enable small differences i n the 46/44 r a t i o to be measured. The es s e n t i a l features of such mass spectrometers are: a sample i n l e t system capable of al t e r n a t e l y introducing small aliguots of unknown samples and working standard to the source region of the mass spectrometer; a 8 source capable of i o n i z i n g the carbon dioxide and accelerating the ions through several thousand v o l t s ; a magnetic analyzer, usually a 6 0 ° or 9 0 ° sector f i e l d electromagnet which separates the mass 46 and 44 i c n beams; and a dual c o l l e c t o r arrangement from which the ion currents can be used to determine the 46/44 r a t i o of the carbon dioxide. Sp e c i f i c features of the mass spectrometer used in t h i s project are described in Chapter I I . 1.3 Motivations Of This Study The conversion of a mass spectrometer from one capable of analyzing lead tetramethyl to one capable of measuring oxygen isotope r a t i o s in a sample cf cazbon dioxide was begun i n the summer of 1972 under the d i r e c t i o n of Dr. G.P. Erickson working on a temporary summer appointment. The system became operational i n the spring of 197 3. A great deal of, t e s t i n g and developing of procedures was required to reduce a n a l y t i c a l uncertainties to an acceptable l e v e l . Much of the work of t h i s project was tc develop and analyze these procedures. The more i n t e r e s t i n g portion of t h i s thesis project was the f i e l d project o r i g i n a l l y proposed by Dr. Ken West. The investigations of Krouse and Smith had demonstrated the usefulness of stable isotopes i n snow hydrology and Dr. West proposed an intensive study of the in t e r a c t i o n between the l i q u i d and s o l i d phases of water i n snowpacks. Surprisingly l i t t l e had already been done i n terms of an 9 a r t i f i c i a l tracing experiment and so i t was f e l t the information gained from such a project would be most useful to researchers u t i l i z i n g more conventional methods i n snow hydrology. Chapter II deals with the actual changes made i n the HcKinney-Nier mass spectrometer used i n t h i s study. The use of inexpensive parametric amplifiers tc replace conventional vibrating reed electrometers i n the measuring system i s described i n d e t a i l . Chapter III deals with the actual technique of measuring the i s o t o p i c r a t i o s of a water sample and would be useful to persons interested i n how the DEL values are ac t u a l l y obtained i n any study. The fourth chapter deals with possible sources of error ex i s t i n g i n the iso t o p i c analysis of water samples. Chapters V and VI deal with the re s u l t s of the f i e l d experiment and have d e f i n i t e implications for studies i n snow hydrology. Some en t i r e l y new concepts have been presented i n t h i s study and anyone using stable isotopes as a tool i n studying water-snow or water-ice systems may find them useful. 10 I I . THE DUftL BEAH MASS SPECTROHETER 2.1 General Features The mass spectrometer used i n t h i s study was designed and constructed by F. K o l l a r and R.D. Russell (Kollar, 1960) for the precise measurement of lead isotope r a t i o s . It i s e s s e n t i a l l y a McKinney-Hier mass spectrometer (Hier, 1947; McKinney et a l . 1950; Hier et a l . 1947) with some source modifications as described by K c l l a r and c o l l e c t o r modifications made by the author with assistance from R. D. Russell. The defl e c t i o n plates described by Kollar are normally grounded except when beam deflection i s required to zero amplifiers i n the measuring system. Elect r o n i c supplies are those described by Russell and B e l l i s (1971). A general discussion of the c o l l e c t o r region and the associated measuring system i s described by Russell and Ahern (1974) and i n greater d e t a i l i n t h i s thesis. Some of the s p e c i f i c d e t a i l s of the machine are: a 90 degree sector magnet; 12 inch radius of curvature; source e x i t s l i t of 0.004 inches; c o l l e c t o r s l i t widths of 0.070 inches and 0.140 inches for the beams of mass to charge r a t i o cf 46 and 44 respectively; tungsten ribbon filament; accelerating p o t e n t i a l variable from 1.5 kv to 5.0 kV; two Faraday cups that are "leakproof" from the point of view of the ion beams and secondary electrons; and a gas sample introduction system that i s capable of allowing alternate admission of standard and unknown carbon dioxide samples to the source 11 region of the mass spectrometer (Nier, Ney, Inghram, 1917). Since t h i s mass spectrometer was i n i t i a l l y used f o r measuring lead isotope r a t i o s i t has some properties that are superior to spectrometers with small r a d i i of curvature. This i s primarily i t s a b i l i t y to resolve peaks so completely i n the mass range 44 to 46. Using formulas derived i n Duckworth (1958) the resolution of the mass spectrometer was found to be 157 for the 46 c o l l e c t o r system and 82 f o r the 44 c o l l e c t o r system. This means that the 44 c o l l e c t o r i s just able to separate mass 82 from mass 83 on the spectrogram. Since we are interested in c o l l e c t i n g only the 46 and 44 ion beams t h i s means that the beams are separated a substantial distance and the 45 beam can be eliminated by c o l l i s i o n with the defining s l i t s . The actual dispersion per unit mass at mass 46 i s 0.261 inches and at mass 44 0.273 inches. With the elimination of the 45 beam the r a t i o we measure i s d i r e c t l y proportional to the o* 8/0 1 6 r a t i o of the water i f we make the f i r s t order approximation of neglecting ions of the form C 13C» 70>* and C»*0* 70» 7 flowing into the 46 cup and neglecting the loss of 0 1 8 atoms i n molecules of the form C»20» 8C* 8, C»20* 70» 8, C»30» 80* 8, Ci3oi7o» 8, c 1 3 0 l 8 0 1 8 a l l of which are of low r e l a t i v e abundance. The above approximations introduce errors of less than the a n a l y t i c a l uncertainty of the method and are j u s t i f i a b l e . Since the 45 beam i s not co l l e c t e d we do not make the corrections for C 1 3 or for the 45 ion beam i n the 44 c o l l e c t o r , common i n many laboratories. 12 The operation of the mass spectrometer during the data a c q u i s i t i o n period i s controlled by an Inderdata Model 4 computer (Blenkinsop, 1972; Russell et a l . 1971). Analog signals proportional to the i n t e n s i t i e s of the ion beams i n question are fed into a ratiometric d i g i t a l voltmeter (RDVM). The Interdata computer reads several r a t i o estimates, performs d i g i t a l f i l t e r i n g and passes back f i l t e r e d data points to a teletype. After a specified period of time the computer snitches two magnetic valves and analysis of the sample in the other side of the sample introduction system begins. This process i s repeated u n t i l f i v e data points exist for both the unknown sample and the working standard. F i n a l data reduction was done by a Fortran IV program on the IBM 370 computer at the University of B r i t i s h Columbia. Since most of the s p e c i f i c d e t a i l s of the mass spectrometer are found i n the references above, i t i s s u f f i c i e n t to l i m i t discussion to those modifications of the mass spectrometer made f o r the conversion from lead tetramethyl to stable isotope applications. The primary differences are i n the c o l l e c t o r assembly, the measuring system and the sample i n l e t system. Each of these w i l l now be discussed i n some d e t a i l . 13 2.2 The Dual Collector Assembly The s p e c i f i c d e t a i l s of the c o l l e c t o r assembly introduce two new practices to the mass spectrometry laboratory at UBC. These are: 1. The defining s l i t s consist of two separate plates, one plate defining the y dimension of the ion beam and one plate defining the z dimension. The two plates forming the defining s l i t s are physically separated in the c o l l e c t o r assembly by a distance of 0.630 inches and t h i s has caused no apparent complications i n the operation of the mass spectrometer. The construction of the s l i t s was found to be r e l a t i v e l y simple when compared to previous methods of s l i t construction. Again the abundant resolution allowed this technique to be implemented. 2. The use of two parametric amplifiers (Philbrick Model 1702) for the f i r s t stage amplification of the ion beams enabled us to place the amplifiers inside the vacuum system thus eliminating the need to pass a high impedance lead into the vacuum system. Thus the signals are less susceptible to noise contamination than would otherwise be the case. The s p e c i f i c construction of the c o l l e c t o r region i s shown in Figure 2.1. A l l c o l l e c t o r s l i t s are made of Nichrom V metal sheeting and milled to the s p e c i f i c dimensions by D. Schreiber of the Department cf Geophysics and Astronomy. The y defining s l i t i s held at a p o t e n t i a l of +300 volts D.C. which prevents secondary electrons 14 SIDE VIEW OF COLLECTOR ASSEMBLY Y DEFINING SLIT Z> PARAMETRIC AMPLIFIER .1UO" .070" SUPPRESSORS O O O CZZZD o o o O O O ( ) ( ) O O O .186" .169" SUPPRESSOR & Z SLIT SUPPRESSOR Y SLIT M i l l 0 t A- MASS hk FARADAY -90v CUP . Qy B- VERTICAL SUPPRESSOR 300v Z DEFINING SLIT ft- MASS U6 FARADAY CUP U6 ION BEAMS o o o o 0 o . 5 0 0 " Figure 2.1 Dual C o l l e c t o r System created by the c o l l i s i o n of an ion beam with a s l i t edge from reaching the Faraday cups. The f i r s t suppressor i s held at ground potential and serves as a mask that prevents the f i e l d on the y defining s l i t from influencing ion t r a j e c t o r i e s near the cups. The next combination of s l i t s includes the z defining s l i t and a second suppressor. This combination i s held at a potential of -90 volts D.C. and performs the task of preventing any secondary electrons created at the Faraday cups from escaping, and thus giving non-linear contributions to the ion beam currents. The two Faraday cups are situated approximately 0.05 inches immediately above the second suppressor and are separated by a v e r t i c a l suppressor physically and e l e c t r i c a l l y connected to the second suppressor. It was found that t h i s suppressor 15 made i t physically impossible for a scattered ion to enter the wrong c o l l e c t o r . Since t h i s suppressor was added i t i s f e l t that no serious problems can be attributed to secondary electrons. The Faraday cups are constructed from a single piece of Nichrome and the seams have been s i l v e r soldered to make them impermeable to ions. The two parametric amplifiers s i t on a f i b e r g l a s s c i r c u i t board through which a l l e l e c t r i c a l connections are made. The mass 44 Faraday cup i s attached by f i r s t spot welding a small piece of copper to the closed end and then soldering the combination to a copper plate on the bottom of the c i r c u i t board. Due to the larger feedback resistance i n the 46 c i r c u i t more care was taken i n t h i s connection. A small hole was d r i l l e d through the center of the c i r c u i t board and a Teflon i n s u l a t o r placed i n the hole. The 46 Faraday cup was then r i g i d l y suspended from a 12 gauge Hichrome wire connected through the Teflon plug to the negative input of the 46 parametric amplifier. Leads to the c i r c u i t board and c o l l e c t o r plates were insulated by putting Teflon tubing around the bare leads where possible. Connections were made with a wire wrapping t o o l . Use of solder was kept to a minimum. The Victoreen Whi-Heg w r e s i s t o r s were supported by a metal spring assembly attached to the tops of the parametric amplifiers using A r a l d i t e epoxy. At the present time neither the 44 or 46 ion teams are focussed on the defining s l i t s . Plans have been made to correct t h i s i n the near future. The apparatus has proven 16 to be s a t i s f a c t o r y and no serious d i f f i c u l t i e s can be attributed to f o c a l problems within the c o l l e c t o r . 2.3 The Measuring System When measuring oxygen isotopic r a t i o s , one i s confronted with the problem of converting ion beam currents i n the neighborhood of one picoampere into manageable signal s . This i s usually accomplished by passing the current through a very high resistance i n the feedback loop of an electrometer c i r c u i t . Such electrometers have t y p i c a l l y been of the vibrating reed or vibrating capacitor type analyzed i n d e t a i l by Palevsky et a l . (1947). A vibrating capacitor electrometer has three favorable c h a r a c t e r i s t i c s : i t s h i f t s the information to a more convenient frequency range; i t can have an output impedance very much lower than the input impedance; and i t has s i g n i f i c a n t power gain. Excellence of such electrometers has prompted their application i n many mass spectrometers throughout the world. Signal amplification and noise c h a r a c t e r i s t i c s of such electrometers s t i l l set the standard i n measuring systems for mass spectrometers. An a l t e r n a t i v e approach to ion current measurement i s that of the D.C. electrometer tubes described by Russell et a l . (1964) and Stacey et a l . (1965). They are characterized by a very high input impedance, a s u f f i c i e n t l y short rise time to record the mass spectrum on a chart recorder, and r e l a t i v e l y low noise. The main disadvantage of electrometer tubes i s t h e i r poor d r i f t c h a r a c t e r i s t i c s . Nevertheless the mass spectrometry laboratory at the University of B r i t i s h Columbia has used these amplifiers i n mass spectrometers designed for measuring strontium isotope r a t i o s and lead isotope r a t i o s for f i f t e e n years. Within the past two years Several manufacturers (including Teledyne-Philbrick and Analogic) have started producing parametric operational a m p l i f i e r s . These amplifiers are small i n size and are e s s e n t i a l l y the s o l i d state equivalent of the v i b r a t i n g reed electrometer. The e f f e c t of the mechanical vibrating reed i s obtained by a varying pot e n t i a l d i s t r i b u t i o n i n a varactor diode. Thus the charge d i s t r i b u t i o n can be modulated to ef f e c t a varying capacitance. If a constant or slowly varying charge e x i s t s on the modulated capacitance, a time-varying voltage r e s u l t s which can be amplified by a low noise A.C. amplifier. The output of t h i s amplifier i s then phase-sensitively demodulated to restore correct p o l a r i t y and i s then boosted by a conventional D.C. output stage. A more comprehensive description of a varactor bridge operational amplifier can be found in Analogic Devices S p e c i f i c a t i o n Sheet C016-50-1/69. For our purposes i t i s not necessary to understand the operation of the parametric amplifier tut i t i s only necessary to take note of the important c h a r a c t e r i s t i c s of such amplifiers. Two Teledyne-Philbrick parametric amplifiers model 1702 were used i n the measuring system shown i n Figure 2.2. The important c h a r a c t e r i s t i c s 18 ' 44 RI : R2 T / W V W I yvVVVVT RDVM 46 R S : V 46 .47 _L UF" R6 -WWV^ H i 22K IOK IM IUF IM 7 2 > R 8 . I j RI 2 x IO -j | R2 IK | R3 IM | R4 220 K I R5 IxlO" I R6 IK | R7 IM LfH__î °_K_J F i g u r e 2.2 Mass Spectrometer Measuring System of the T e l e d y n e - P h i l b r i c k o p e r a t i o n a l a m p l i f i e r s are found i n T e l e d y n e - P h i l b r i c k S p e c i f i c a t i o n Sheet 12m 12-71 •Parametric O p e r a t i o n a l A m p l i f i e r 1702/170 201». Some of the most important c h a r a c t e r i s t i c s are: 1. A minimum open loop v o l t a g e gain of 10s.- 2. Maximum v o l t a g e o f f s e t without e x t e r n a l t r i m 5 mV. 3. Maximum i n p u t b i a s c u r r e n t 5 fA. 4. A common mode in p u t impedance of 1 0 1 4 ohms. Tue low i n p u t b i a s c u r r e n t and high i n p u t impedance/ land themselves q u i t e w e l l to picoampere c u r r e n t measurement. The b a s i c f e a t u r e s of the measuring system o f Figure 2.2 are found i n R u s s e l l and Ahern (1974). The treatment g i v e n there n e g l e c t s zero o f f s e t s and t h i s p o i n t warrants a more 1 9 complete a n a l y s i s i n t h i s t h e s i s as i t i s b e l i e v e d t h a t o f f s e t s can be a s i g n i f i c a n t source cf e r r o r . The D . C . c i r c u i t a n a l y s i s given here w i l l make the usual approximations t h a t a l l the c u r r e n t f l o w i n g i n t o the Faraday cup w i l l flow through the feedback r e s i s t o r , the in p u t to each p a r a m e t r i c a m p l i f i e r i s held a t a v i r t u a l ground, and th a t the e f f e c t of a l l o f f s e t s can te repre s e n t e d by a constant v o l t a g e added to the output. By using K i r c h o f f ' s laws and assuming a l l the ion c u r r e n t passes through the feedback r e s i s t o r s i t i s a s t r a i g h t f o r w a r d c a l c u l a t i o n to show: V,, = - V l ( l + R , / R j - i ^ (R 3+R 1R 3/R 1 (+R 2R 3/R l t+R 1+R 2) [ 2 . 1 ] and s i m i l a r l y Vi,!* = -V2 (l+R 7/Re)-in 6 (R 7+R5R7/Re+R 6R7/Rs+Rs+Re) / [2.2] where r e s i s t a n c e s and vo l t a g e s are as shown i n Figure 2.2. In the a c t u a l c i r c u i t i t has been found t h a t a m p l i f i e r o f f s e t s can be a s i g n i f i c a n t source of e r r o r i n the measured DSL value. For t h i s reason i t i s important t c understand how a m p l i f i e r o f f s e t s a f f e c t the EEL value to be c a l c u l a t e d . To a f i r s t approximation each a m p l i f i e r can be represented by a black box t h a t m u l t i p l i e s an in p u t v o l t a g e t y . a gain (Gi) and adds to th a t v o l t a g e seme o f f s e t v c l t a g e ( A i ) . By using the numbering convention given on Figure 2.2 the b u f f e r a m p l i f i e r f o l l o w i n g the p r e c i s i o n d i v i d e r w i l l have gai n G5 and o f f s e t A5. With t h i s n o t a t i o n the c i r c u i t a n a l y s i s can be c a r r i e d t o the po i n t where the r e l a t i o n s h i p between the " t r u e " DEL, assuming no measuring system 20 o f f s e t s , a n d the m e a s u r e d DEL c a n be o b t a i n e d . Once t h i s a n a l y s i s i s c o m p l e t e d i t b e c o m e s e v i d e n t t h a t a c e r t a i n z e r o i n g p r o c e d u r e w i l l e l i m i n a t e a n y e r r o r s due t o a m p l i f i e r o f f s e t s . I f we d e f i n e P and Q a s f o l l o w s : P = / ( R 3 R i , + R i R 3 + ' R 2 R 3 + R1R4 + R2R4) [ 2 . 3 ] Q = R 8 / ( R 7 R 8 + R 5 R 8+R6R7+R5R8+R6R8) [ 2 . 4 ] a n d i f we a s s u m e t h e a m p l i f i e r t e s t v o l t a g e s V1 and V2 a r e z e r o , as i s n o r m a l l y t h e c a s e , t h e n i t i s c l e a r f r o m F i g u r e 2 . 3 t h e v o l t a g e s g i v e n a t t h e R. D. V . M. W i l l b e : EHk = - G 3 i i » ' i t / P + G3A1 + A 3 / [ 2 . 5 ] a n d E 4 6 = - G ^ G e i i f e V Q + G ^ G e A a + G e A u - G s G e e i ^ / P [ 2 . 6 ] + G 5 G 6 e A 1 + G G A 5 + A 6 where THETA i s t h e r e a d i n g o f t h e p r e c i s i o n d i v i d e r . We c a n now s o l v e e q u a t i o n s 2.5 a n d 2 . 6 f o r t h e 44 a n d 46 i o n beam c u r r e n t s : i u u = ( - E l t l t + G 3 A i + A 3 ) P / G 3 [ 2 . 7 } - (-E„6 - G s G s Q i ^ / P + G e A i i + G ^ G s A z + G s G e e A t + G s A s + A ^ Q r „ „ , 1 1 + 4 Gi+Ge L2.8-\ s u b s t i t u t i n g e q u a t i o n 2 . 7 i n t o 2 . 8 g i v e s : i 4 6 = [ - E 4 6 - G 5 G 6 0 (-E 4 4 / G 3 + A 1 + A 3 / G 3 ) + G l t G 5 A z + G 6 A l t + G 5 G 6 e A i + G 6 A 5 + A 6 ] Q / G l t G e [ 2 . 9 ] I t i s now c l e a r t h a t we c a n w r i t e a n e x p r e s s i o n f o r t h e VP VQ A. G, 9 21 34 RDVM %6 Figure 2.3 Block Diagram Shewing E f f e c t of Gain and Offsets r a t i o of the; 46 to 44 ion beam currents. Bj making the following d e f i n i t i o n s : S = ^ G 5 G 6 9 A 3 / G 3+G 4 G 6 A 2 + G 6 A 4+G 6 A 5+A 6 [2.10] T = G 3A!+ A 3 we f i n d that: [2.11] R = i i , 6 / i * n = Q G 3 / ( P G 4 G 6 ) [E^e-GsGeOE^/Ga + S J / t E ^ + T ] [2.12] The RDVM produces a reading that i s proportional tc the true r a t i o of i t s inputs. That i s : $ = UE„e/E*„ [2.13] where cj> i s the reading of the RDVM and U i s a meter c a l i b r a t i o n constant. The v a l i d i t y of eguation 2.13 was checked empirically by using a s i x d i g i t precision divider and was shown to be v a l i d to the most s i g n i f i c a n t d i g i t of the RDVM. 2 2 By using equations 1 . 1 and 2 . 1 2 we can now determine what the true DEL value i s in terms of parameters we can measure. I f we adopt the notation that parameters unigue to the r a t i o appearing i n the denominator of 1 . 1 w i l l have a superscript "s" then the true DEL becomes: D E L / 1 0 3 = K<l>-G5G K9U/G 3+SU/E,^)/(l+T/E 1 ( l t) ] ^ W I U [ ( ( f r S - G s G e e u / G g + S U / E S O / U + T / E ? , ) ] - 1 ,, 1 2 • 1 4 J At f i r s t t h i s equation seems quite cumbersome tc use tut i f we note equations 2 . 1 0 and 2 . 1 2 we f i n d that a c a l i b r a t i o n constant K can be e a s i l y measured for the entire measuring system by just noting how PHI changes with a change i n THETA for any fixed r a t i o . d<j>/d6 = K = G 5 GeU[l / G 3 - A 3 / ( G 3 E 4 4 ) ] [ 2 . 1 5 ] since A3 can e a s i l y be set to zero before determination of K , equation 2 . 1 5 becomes: K = G 5 G 6 U / G 3 A 3 = 0 [ 2 . 1 6 ] One such determination of K i s given i n Figure 2 . 4 . This and s i m i l a r plots t e s t i f y to the l i n e a r i t y of the measuring system. Rewriting equation 2 . 1 4 we obtain: DEL / I f ) 3 - [(^-KQ + S U / E . ^ / d + T / E , , ) ! / 1 0 " [ (cj^-Ke + S U / E f O / d + T / E ? , ) ] " [ 2 . 1 7 ] which involves only the approximation that A3=0.0 when K was determined. In t h i s form i t now becomes evident how we may zsro amplifiers before an analysis to make off s e t errors 23 1 1——•- 1 1 1 1 — - i 1 — 4.45 4.525 4.6 4.675 4.75 .4.B2S 4.9 4.975 5.05 THETfl (XIO"1 ) 5.125 Figure 2.4 Determination of Calibration Constant K i n s i g n i f i c a n t i n the ca l c u l a t i o n of DEL. Ey applying a s u f f i c i e n t l y high voltage to the deflector plates i n the source, ion beams can ba deflected so that no current i s flowing into the Faraday cups. By so doing the voltage at the 44 input to the BDVM given by equation 2.5 becomes: EkH = G 3 A i + A 3 the voltage at the output of the two parametric amplifiers becomes: Vi* k = A i V \ 6 = A z From equation 2.6 the 46 input to the HDVH becomes: E 4 6 = G 6 ( G 1 + A 2 + A 1 ( + 0 G 5 A i + A 5 ) + A 6 The voltages at these four points (V**,V**,E**,E» 6) are e a s i l y accessable and may be measured and nulled. If we f i r s t zero V** then by d e f i n i t i o n A1 eguals zero and E 4 * 24 becomes equal to A3. I f we now zero E 4  both A1 and A3 are equal t o zero and by equation 2.11 T i s equal t o ze r o . The next step i s to zero the 46 parametric a m p l i f i e r which makes A2 equal to zero. I f next we zero E 4 6 then we knew from the above equation t h a t : E u = G&A^ + G 6A 5 + A 6 = 0 ' I n s e r t i n g t h i s i n f o r m a t i o n i n t o equation 2.10, remembering th a t A1, A2, and A3 are a l r e a d y zero, shows t h a t S i s now equal to zero. H i t h both S and T equal to zero aquation 2.14 reduces t o : DEL = [((j)-c|) S)/(<j> S-Ke)]10 3 [2.18] which i s a simple formula e a s i l y a p p l i e d s i n c e cf> i s the RDVH reading when the unknown i s being analyzed, <J>S i s the RDVM r e a d i n g when the standard i s being a n a l y z e d , 6 i s the s e t t i n g of the p r e c i s i o n d i v i d e r and K i s found from equation 2.16. In p r a c t i c e onlv A1 and A2 were s e t to zero before an a n a l y s i s . Other o f f s e t s were p e r i o d i c a l l y checked and were always l e s s than 3 mV and thus i n t r o d u c e d very s m a l l e r r o r s . N e v e rtheless, the s i m p l i c i t y of the zer o i n g procedure g i v e n above warrants i t s i n c l u s i o n i n f u t u r e i s o t o p i c analyses. The measuring system d e s c r i b e d has been used f o r the a n a l y s i s of approximately seven hundred samples and only one severe drawback has been d i s c o v e r e d . I t i s not uncommon f o r the parametric a m p l i f i e r s used to have b a s e l i n e 25 / / d i s c o n t i n u i t i e s of up to 15 mv i n the 46 parametric amplifier and when t h i s happens the resultant DIL can be in error by up to 0.3 DEL units. Such d i s c o n t i n u i t i e s are quite noticeable i n the PHI values and such analyses are rerun immediately u n t i l an analysis free of gross d i s c o n t i n u i t i e s i s obtained. This involves a great deal of time and so plans have been made to i n s t a l l a baseline compensation c i r c u i t i n at l e a s t the 46 c o l l e c t o r system. This has not yet been implemented. The noise c h a r a c t e r i s t i c s of t h i s measuring system are controlled through analog f i l t e r i n g provided by amplifiers number three and number four. Further d i g i t a l f i l t e r i n g i s done by the Interdata Model 4 computer. The ncise c h a r a c t e r i s t i c s at the output of the parametric amplifiers i s controlled primarily by the capacitors in p a r a l l e l with r e s i s t o r s R3 and B7. The f i l t e r i n g thus provided is s u f f i c i e n t and no problems associated with noise i n the measuring system are believed to e x i s t . The noise c h a r a c t e r i s t i c s of the parametric amplifiers have been compared d i r e c t l y to a Carey Model No. 31 vibrating reed electrometer and a measuring system using the Analogic varactor bridge diode i n a mass spectrometer used by Dr. P.H. Reynolds at Dalhousie University. I t was found that the vibrating reed electrometer had an equivalent ncise current of 1.31 femtoamperes. The Analogic varactcr bridge diode had a noise current of 1.9 femtoamperes after much f i l t e r i n g . The Teledyne-Philbrick parametric amplifier had 26 a n o i s e c u r r e n t of 3.6 femtoamperes. A l l c f these ware c a l c u l a t e d with a 1 0 1 1 ohm feedback r e s i s t o r and a time constant of 0.47 seconds. Such r e s u l t s seem q u i t e s a t i s f a c t o r y e s p e c i a l l y when r e l a t i v e c o s t s are c o n s i d e r e d . The c o s t of a v i b r a t i n g reed e l e c t r o m e t e r i s approximately $1500 f o r a t o t a l investment of about $3000 f o r a complete measuring system. The measuring system of F i g u r e 2.2 has a t o t a l c ost of l e s s than $150 e x c l u d i n g the RDVM and l a b o r c o s t s . 2.4 The Sample I n l e t System The sample i n t r o d u c t i o n system i n a gas source mass spectrometer must be capable of i n t r o d u c i n g r e p r e s e n t a t i v e a l i q u o t s of an unknown sample to the source r e g i o n of the mass spectrometer. In a mass spectrometer designed to measure oxygen i s o t o p e r a t i o s of a carbon d i o x i d e sample i t i s a l s o necessary t h a t the sample i n t r o d u c t i o n system be capable of a l t e r n a t e l y d e l i v e r i n g samples of unknown and standard carbon d i o x i d e . The system shown i n F i g u r e 2.5 i s a r e p r e s e n t a t i o n of the i n t r o d u c t i o n system on the mass spectrometer used i n t h i s study. I t c o n s i s t s of two complete i n l e t systems each f e a t u r i n g : 1. A 2 - l i t e r sample r e s e r v o i r bulb. 2. Approximately 60 cm of 0.4 mm diameter c a p i l l a r y t u b i n g . 27 HASS SPECTROMETER Figure 2.5 The Sample Introduction System 3. A set of magnetic valves which allow alternate analysis of standard and unknown carbon dioxide. In addition the i n l e t system has an independent vacuum system allowing rapid removal and replacement of a new sample. The 2 - l i t e r reservoir serves as a large volume containing the sample during the analysis. I t should be of s u f f i c i e n t size so that the pressure on the high pressure side of the c a p i l l a r y does not change appreciably during the course of an analysis and thus a l t e r the volume flow into the mass spectrometer. In a d d i t i i c n t c t h i s i t should be large enough to prevent s i g n i f i c a n t changes i n i s o t o p i c composition due to any f r a c t i o n a t i o n of the sample. The c a p i l l a r y tubing serves a very important function. 28 It prevents any compositional discontinuity at the leak i t s e l f from migrating as f a r as the sample reservoir. The importance of th i s feature cannot be over emphasized since i t ensures that the i s o t o p i c r a t i o i n the reservoir w i l l not be altered by back d i f f u s i o n . If flow through the i n l e t system toward the leak i s viscous a l l molecular species of carbon dioxide (e.g. c»zo»*0» 8 and c 1 2 C » « 0 1 6 ) w i l l t r a v e l at the same v e l o c i t y and therefore the isotopic composition w i l l be uniform and constant i n time. It i s not uncommon to have molecular flow at the leak of a mass spectrometer. In t h i s case the iso t o p i c composition of the carton dioxide passing through the molecular leak w i l l be enriched i n the l i g h t e r isotope. The result of this i s that the region immediately before the leak w i l l be enriched i n the heavier isotope. I t i s i n t u i t i v e l y obvious that i f there i s to te a steady state the i s o t o p i c r a t i o of the carbon dioxide leaving the molecular leak w i l l equal the i s o t o p i c composition of the carbon dioxide in the r e s e r v c i r . Since the 46/44 ra t i o of the carbon dioxide immediately behind the molecular leak i s greater than the gas flowing into that region, a d i f f u s i o n front w i l l begin moving toward the reservoir. At some distance the d i f f u s i o n front w i l l become stationary due to the net mass flow towards the leak. A steady state c a l c u l a t i o n , suggested by R.D. Russell, can be made for the location of the stationary d i f f u s i o n front. By inserting measured values cf the parameters, the length of the c a p i l l a r y tubing can be chosen so the 29 d i f f u s i o n f r o n t o c c u r s w e l l w i t h i n t h e l e n g t h o f t h e c a p i l l a r y a n d t h e r e f o r e n e v e r a f f e c t s t h e i s o t o p i c r a t i o i n t h e r e s e r v o i r . The p r o b l e m i s d e s c r i b e d i n F i g u r e 2 . 6 . P.APTT.T.AT1Y T U B I N G NEEDLE VALVE GAS FLOW STATIONARY ' r TO MASS FROM < = > Q DIFFUSION * — ' c = > RESERVOIR FRONT _ J - — • " I SPEC. <- X F i g u r e 2 . 6 T h e Back D i f f u s i o n P r o b l e m I t was s h o w n by E i n s t e i n ( s e e f o r e x a m p l e D a n i e l s a n d A l b e r t y ) t h a t f o r a B r o w n i a n p r o c e s s t h e mean o f t h e s q u a r e o f t h e d i s p l a c e m e n t s i n a p a r t i c u l a r d i r e c t i o n x i s r e l a t e d t o t h e d i f f u s i o n c o e f f i c i e n t D b y : D = x 2 / ( 2 t ) [ 2 . 2 0 ] where t i s t h e t i m e t a k e n t o a d v a n c e a d i s t a n c e x . From 2 . 2 0 i t i s c l e a r t h a t t h e v e l o c i t y o f t h e d i f f u s i o n f r o n t i s g i v e n b y : v = d x / d t = [ D / 2 t ) } h [ 2 . 2 1] S u b s t i t u t i n g 2 . 2 0 i n t o 2 . 2 1 g i v e s : v = D / x [ 2 . 2 2 ] w h i c h i s t o s a y t h a t t h e d i f f u s i o n f r o n t moves t o w a r d t h e r e s e r v o i r a t a m o n o t o n i c a l l y d e c r e a s i n g v e l o c i t y . T h e r e i s a n e t g a s f l o w t o w a r d t h e l e a k w h i c h w i l l e x a c t l y c o u n t e r a c t t h e v e l o c i t y o f t h e d i f f u s i o n f r o n t a t some p o i n t . I t i s c l e a r t h e v e l o c i t y o f t h e g a s f l o w , c , i s g i v e n b y : c = Q/A [ 2 . 2 3 ] where Q i s t h e v o l u m e o f g a s f l o w p a s t a n y g i v e n p o i n t p e r 30 s e c o n d a n d a i s t h e c r o s s - s e c t i o n a l a r e a o f t h e c a p i l l a r y . To f i n d t h e p o s i t i o n o f t h e s t a t i o n a r y d i f f u s i o n f r o n t t h e v e l o c i t i e s g i v e n i n 2 . 2 2 a n d 2 . 2 3 o u s t be e x a c t l y e q u a l a n d o p p o s i t e i n d i r e c t i o n . D/x = Q/A [ 2 . 2 4 ] x = DA/Q [ 2 . 2 5 ] S i n c e t h e v a l u e o f t h e d i f f u s i o n c o e f f i c i e n t i s u s u a l l y g i v e n a t S T P i t i s n e c e s s a r y t o e x a o i n e t h e d e p e n d e n c e c f D on p r e s s u r e and t e m p e r a t u r e . I t i s c o m m o n l y known (see P a g e , p . 351) t h a t f o r s e l f - d i f f u s i o n o f i d e a l g a s e s : D = u y s / 8 [ 2 . 2 6 ] where y i s t h e mean f r e e p a t h a n d " s i s t h e a v e r a g e v e l o c i t y o f t h e m o l e c u l e . I t i s a l s o c o m m o n l y known t h a t : y = kT/ [ /2 T r a 2 p ] [ 2. 2 7 ] s = [(8V.T)/(um)]* [ 2 . 2 8 ] where k i s t h e B o l t z m a n n c o n s t a n t , T i s t h e a b s o l u t e t e m p e r a t u r e , TTU2 i s t h e e f f e c t i v e c r o s s - s e c t i c n a l a r e a o f t h e m o l e c u l e , P i s t h e p r e s s u r e o f t h e g a s i n t h e s y s t e m and m i s t h e mass o f t h e m o l e c u l e . F r o m e q u a t i o n s 2 . 2 6 , 2 . 2 7 a n d 2 . 2 8 i t i s c l e a r t h a t : D = D ° ( P ° / P ) ( T / T ° ) 3 / 2 [ 2 . 2 9 ] w h e r e t h e s u p e r s c r i p t 0 r e p r e s e n t s v a l u e s a t S T P . From t h e i d e a l g a s l a w i t i s c l e a r t h a t : Q = Q°(T/T°) (P°/P) [ 2 . 3 0 ] S u b s t i t u t i o n o f 2 . 2 9 a n d 2 . 3 0 i n e q u a t i o n 2 . 2 5 g i v e s : 31 x = (D°/Q°) (T/T°)'5A [2.31] where a l l parameters are now e v a l u a t e d at STP. The volume flow r a t e , Q, can be measured by noting the change i n the pressure i n the mass spectrometer as a f u n c t i o n of time. Such a d e t e r m i n a t i o n i s shown g r a p h i c a l l y i n F i g u r e 2.7. From t h i s f i g u r e we a s c e r t a i n t h a t 18.7? of « 1 37.0 F i g u r e 2.7 The Volume Bate of Flow i n t o the Hass Spectrometer the sample i s consumed i n 22 hours. S i n c e the volume of the r e s e r v o i r i s 2.4 l i t e r s t h i s corresponds to a volume flow equal t o : Q=5.67 x 10-3 c m 3 / s with t h i s i n f o r m a t i o n and n o t i n g t h a t the sample l i n e p r e s s u r e equals 5 t o r r and T equals 295°K we can c a l c u l a t e Q° from equation 2.30. Q° = 4.03 x 10-s cmVs 32 the diameter of the c a p i l l a r y tubing i s 0.043 cm sc A= 1.45 x 10-3 cm*. The value of the d i f f u s i o n c o e f f i c i e n t of carbon d iox ide d i f f u s i n g in to a i r was found in tables to be: D= 0.139 cm*/s The c o e f f i c i e n t for s e l f d i f f u s i o n of carbon dioxide w i l l be l ess than 0.139 c m 2 / s and so the x ca lcu la ted w i l l be larger than the true x. Insert ing the above values in to 2.31 g ives : x= 5.4 cm It i s not known whether the leak used was viscous or molecular. The actual c a p i l l a r y tubing i s approximately 60 cm long and so even i f the leak i s molecular the s ta t ionary d i f f u s i o n front would occur wel l within the c a p i l l a r y . It has been observed empi r i ca l l y that the composition of the reservo i r does not change with time (see Chapter IV) . Of course the d i f f u s i o n f ront i s not r e a l l y a step funct ion as assumed in the above c a l c u l a t i o n but instead a broader d i f f u s i o n boundary. Ca lcu la t ions made by fi.D. Russe l l from a numerical so lu t ion of the d i f f u s i o n equation with net flow opposing the motion of the front give comparable r e s u l t s . More importantly such c a l c u l a t i o n s show the v a l i d i t y of the assumption of s t a t i o n a r i t y of the f ront . The magnetic valves (Figure 2.8) used i n th is i n l e t system are e s s e n t i a l l y the same as those proposed by McKinney et a l . (1950) and Epste in (1953). The ac tua l magnetic valves are ava i lab le through Glass Instruments 33 A MASS SPECTROMETER \ I A MAGNET COIL C02 FROM LHS IRON CORE VALVE SHOWN Uf POSITION TO ADMIT C02 TO MASS SPEC. CQ2 FROM RHS WASTE I I VACUUM Figure 2.8 The Operation of the Magnetic Valves Inc. Pasadena, C a l i f o r n i a and have been found to be quite s a t i s f a c t o r y . The small glass piston has an iron red i n i t s center so that i t can be raised to divert gas flow into a waste vacuum system or lowered to allow gas flow into the mass spectrometer. The current flowing i n the magnetic c o i l s i s such that when gas from one side of the sample i n l e t system i s flowing into the mass.spectrometer, gas from the other side i s being pumped away. The performance of similar magnetic valves has often been questioned as t e s t i f i e d to by the presence cf a valve mixing correction at many laboratories as indicated by Begbie et a l . (1972). The adjustment i s one that corrects for a "leaky" valve that allows a f i n i t e amount of gas to 34 pass when i t i s "closed". If t h i s happens i t i s clear that a mixture of the two sides of the i n l e t system i s being analyzed instead of only one side. Such corrections have not been found necessary with the magnetic valve system employed i n t h i s study. The v a l i d i t y of ever making such corrections w i l l be examined i n Chapter III. 35 I I I , EXPERIMENTAL TECHNIQUE OF DETERMINING EEL 3.1 Laboratory Procedures Techniques f o r measuring oxygen i s o t o p e r a t i o s vary c o n s i d e r a b l y i n l a b o r a t o r i e s around the world. Techniques must be developed at each l a b o r a t o r y f o r t a k i n g a water sample and determining i t s i s o t o p i c composition. The f i n a l t e s t of the o v e r a l l process i s the r e p r o d u c i b i l i t y i t y i e l d s . The procedure developed a t the U n i v e r s i t y of B r i t i s h Columbia has been shown to s u c c e s s f u l l y reproduce measurements to 0.14 DEL u n i t s which i s q u i t e adequate f o r g l a c i o l o g i c a l r e s e a r c h . The a n a l y s i s of a water sample i n v o l v e s two s t a g e s . The water sample must be e q u i l i b r a t e d with carbon d i o x i d e and the e q u i l i b r a t e d carbon d i o x i d e must be analyzed i n the mass spectrometer. 3.1.1 Sample P r e p a r a t i o n The sample p r e p a r a t i o n i n v o l v e s the e q u i l i b r a t i o n of carbon d i o x i d e with the water sample as d e s c r i b e d by E p s t e i n and Mayeda (1953). Some major a l t e r a t i o n s have been made to t h e i r b a s i c procedure and so a d e t a i l e d d e s c r i p t i o n of the p r e p a r a t i o n i s given here. Ten m i l l i l i t e r s o f water i s loaded i n t o a 60 ml Pyrex sample f l a s k (see F i g u r e 3.1a) through the sidearm. The a c i d i t y of the sample i s checked at t h i s time and i f the pH of the sample i s g r e a t e r than 8 a 36 A V , J SAMPLE FLASK SAMPLE TUBE B SIDEVTEW HIGH VACUUM STOPCOCK Figure 3.1 Sample F l a s k s and Sample Tubes Used i n T h i s Study drop of n i t r i c a c i d should be added t o ensure r a p i d e q u i l i b r a t i o n o f the water and carbon d i o x i d e as f i r s t noted by F a u r h o l t (1924). In the water samples analyzed i n t h i s study the a d d i t i o n of n i t r i c a c i d was never necessary. A f t e r being loaded, the sample f l a s k i s connected t c the sample p r e p a r a t i o n l i n e shown i n F i g u r e 3.2 using a Vi t o n " O - r i n g " and a s p r i n g clamp. The i n t e r i o r o f the high vacuum stopcock i s then evacuated by the pumping system of the p r e p a r a t i o n l i n e . To save time, seven t o ten f l a s k s are placed on the sample p r e p a r a t i o n l i n e a t the same time. L i q u i d n i t r o g e n i s then placed around each sample f l a s k u n t i l the water samples are f r o z e n , the stopcocks are opened and the a i r i n the f l a s k s i s pumped away. A f t e r the stopcocks are c l o s e d the water samples are thawed with warm 37 F i g u r e 3.2 The Sample P r e p a r a t i o n L i n e water to remove any d i s s o l v e d gases, p r i m a r i l y n i t r o g e n and oxygen. The samples are then r e f r o z e n with l i q u i d n i t r o g e n and any remaining a i r i s removed. The next s t e p i n the sample p r e p a r a t i o n i s to allow the i c e to melt and then to immerse the f l a s k s i n a mixture of dry i c e and methanol, h e n c e f o r t h r e f e r r e d to as " s l u r r y " . The temperature of t h i s mixture i s 201°K which i s s u f f i c i e n t to f r e e z e water i n the vacuum system but not carbon d i o x i d e . A f t e r the water, i s completely f r o z e n a l l stopcocks are opened and any carbon d i o x i d e t h a t was d i s s o l v e d i n the water samples i s pumped away. A dewar of s l u r r y i s p l a c e d on the water t r a p and the mercury manometer i s made ready f o r use by c l o s i n g one stopcock. The connection to the vacuum system i s then c l o s e d and carbon d i o x i d e from the r e s e r v o i r i s t r a n s f e r r e d from the gas-pipet i n t o the sample f l a s k s to a pressure of 3 8 t w e n t y c e n t i m e t e r s m e r c u r y . T h e f l a s k s t o p c o c k s a r e c l o s e d a n d t h e s a m p l e s a r e p l a c e d i n a c o n s t a n t t e m p e r a t u r e b a t h a t 2 5 . 3 + .1 o c . T h e e q u i l i b r a t i o n o f t h e c a r b o n d i o x i d e w i t h t h e w a t e r i s a p r o c e s s t h a t h a s b e e n s t u d i e d i n some d e t a i l . The r e a c t i o n r a t e i s n o t d e t e r m i n e d by t h e c h e m i c a l r e a c t i o n b u t i s g o v e r n e d by t h e p h y s i c a l p r o c e s s o f w a t e r t r a n s p o r t f r o m t h e b o t t o m o f t h e s a m p l e f l a s k t o t h e g a s - l i q u i d i n t e r f a c e . T h i s p r o c e s s w i l l be d i s c u s s e d i n d e t a i l i n t h e n e x t s e c t i o n . I t i s s u f f i c i e n t t o s a y t h a t a f t e r some p e r i o d o f t i m e t h e i s o t o p i c c o m p o s i t i o n o f t h e c a r b o n d i o x i d e w i l l r e f l e c t t h e c o m p o s i t i o n o f t h e w a t e r s a m p l e . A f t e r t h e s a m p l e h a s b e e n e q u i l i b r a t e d , t h e s a m p l e f l a s k s a r e t a k e n f r o m t h e b a t h a n d i m m e d i a t e l y p l a c e d i n t h e s l u r r y on t h e s a m p l e , p r e p a r a t i o n l i n e . A f t e r f r e e z i n g no f u r t h e r e q u i l i b r a t i o n t a k e s p l a c e . T h e o n l y s t e p l e f t i n t h e s a m p l e p r e p a r a t i o n i s t h e r e m o v a l o f t h e c a r b o n d i o x i d e f r o m t h e s a m p l e f l a s k a n d i t s t r a n s f e r t o a s a m p l e t u b e s u c h a s t h e o n e s h o w n i n F i g u r e 3 .1b. T h i s i s a c c o m p l i s h e d a s f o l l o w s . A d e w a r o f s l u r r y i s p l a c e d on t h e w a t e r t r a p t o e n s u r e t h a t o n l y d r y c a r b o n d i o x i d e i s t r a n s f e r r e d t o t h e s a m p l e t u b e . T h i s s t e p i s i m p o r t a n t f o r two r e a s o n s ; f i r s t , i f any w a t e r v a p o r i s i n t h e s a m p l e t u b e t h e c a r b o n d i o x i d e w i l l r e - e q u i l i b r a t e w i t h t h a t v a p o r t h u s a l t e r i n g i t s c o m p o s i t i o n o v e r a p e r i o d o f t i m e . S e c o n d l y , i f w a t e r v a p o r i s i n t r o d u c e d i n t o t h e mass s p e c t r o m e t e r i t w i l l a d s o r b on t h e g l a s s and m e t a l s u r f a c e s . C a r b o n d i o x i d e t e n d s t o 39 adsorb on the water molecules and thus the mass spectrometer a c q u i r e s a memory s i n c e any new carbon d i o x i d e samples w i l l be contaminated by the pr e v i o u s sample. T h i s memory was very n o t i c e a b l e u n t i l the step of d r y i n g the carbon d i o x i d e was i n c l u d e d i n the sample p r e p a r a t i o n . A f t e r c o o l i n g the water t r a p with s l u r r y and evac u a t i n g a sample tube, l i q u i d n i t r o g e n i s p l a c e d around the sample tube. The stcpcock to the pumps i s c l o s e d , the stopcock on the sample f l a s k i s opened and the sample s t a r t s t r a n s f e r r i n g . The pressure i s monitored i n the sample p r e p a r a t i o n l i n e u n t i l i t i s l e s s than 1.2 x 1 0 - 3 t o r r . T h i s ensures t h a t any f r a c t i o n a t i o n of the sample due to s e l e c t i v e f r e e z i n g o f the carbon d i o x i d e w i l l cause an e r r o r i n DEL of l e s s than 0.1 DEL u n i t s . A d i s c u s s i o n of the above c a l c u l a t i o n i s given i n the next chapter. A f t e r t r a n s f e r the stopcock of the sample tube i s c l o s e d and the sample i s ready f o r mass spectrometer a n a l y s i s . t 3.1.2 The E q u i l i b r a t i o n Of Hater And Carbon Dioxide Unless the amount of time i t takes to e q u i l i b r a t e the carbon d i o x i d e with the water sample i s known, e r r o r s may r e s u l t from i n s u f f i c i e n t r e a c t i o n time. The chemi c a l r e a c t i o n of carbon d i o x i d e with water was s t u d i e d i n d e t a i l by M i l l s and Drey (1939,1940). They p o i n t out t h a t i t was F a u r h o l t (1921,1924) t h a t f i r s t r e c o g n i z e d t h a t the r e a c t i o n 40 process was determined by the pH of the s o l u t i o n . When the pH i s l e s s than 8 the r e a c t i o n i s one c f simple h y d r a t i o n : C 0 2 + H 2 0 ^ H 2 C 0 3 pH < 8 [ 3 . 1 ] I f the pH of the s o l u t i o n r i s e s above 10 then a much slower b i - m o l e c u l a r r e a c t i o n predominates: C 0 2 + 0 H " ^ H C 0 7 pH > 10 [3.2] The h a l f - l i f e of r e a c t i o n 3 .1 i s approximately 17 minutes at 2S°C but when the carbonate ion of 3.2 i s present the time of h a l f exchange was about 28 hours. For t h i s reason i t i s c l e a r t h a t i t i s necessary to f o r c e r e a c t i o n 3 .1 to occur by having a pH l e s s than 8. I f the i s o t o p i c e q u i l i b r a t i o n between the water and carbon d i o x i d e were the r a t e c o n t r o l l i n g step i t i s c l e a r t h a t the e q u i l i b r a t i o n would be n i n e t y - n i n e percent complete i n l e s s than two hours. The r a t e of e q u i l i b r a t i o n was s t u d i e d as p a r t o f t h i s r e s e a r c h and such was not the case. I t appeared that the h a l f r e a c t i o n took approximately two hours i n s t e a d o f seventeen minutes and so some process other than the chemical r e a c t i o n i s the r a t e c o n t r o l l i n g s t e p . I t seems reasonable t h a t the i n c r e a s e d time of e q u i l i b r a t i o n i s a r e s u l t of inadequate mixing o f water i n the sample f l a s k . I t i s probably true t h a t the r e a c t i o n between the carbon d i o x i d e and the water at the s u r f a c e takes p l a c e i n the time suggested by H i l l s and Orey. However the water i n the bottom of the f l a s k c i r c u l a t e s s l o w l y and t h i s c i r c u l a t i o n c o n t r o l s the o v e r a l l r e a c t i o n r a t e . Since no d i s c u s s i o n of the e q u i l i b r a t i o n mechanism « 1 c o u l d be f o u n d t h e f o l l o w i n g m o d e l i s p r o p o s e d . SYSTEM 1 BOTTOM WATER 018=N1(18) INITIALLY HAS ISOTOPIC COMPOSITION OP WATER SYSTEM 2 SURFACE WATER OR VAPOR 0 1 8«N 2(18) 016=N2(16) INITIALLY EQUILIBRATED WITH C02 K 3 SYSTEM 3 co 2 o l 8=N 3(l8) 0l6=N3(l6) INITIALLY EQUILIBRATED WITH SYSTEM 2 WATER h > v. F i g u r e 3 . 3 T h e P r o p o s e d M o d e l f o r H a t e r a n d C a r b o n D i o x i d e E q u i l i b r a t i o n T h e p h y s i c a l d e s c r i p t i o n o f t h e e q u i l i b r a t i o n p r o c e s s i n v o l v e s t h r e e a s s u m p t i o n s : 1. T h e e q u i l i b r a t i o n t i m e i s c o n t r o l l e d b y t h e p h y s i c a l t r a n s p o r t c o n s t a n t s k x a n d k 2 and i s e s s e n t i a l l y i n d e p e n d e n t c f t h e c h e m i c a l r a t e c o n s t a n t s k 3 a n d k 4 . 2 . T h e number o f O 1 * a t o m s i n a l l t h r e e s y s t e m s r e m a i n s a p p r o x i m a t e l y c o n s t a n t and o n l y c h a n g e s i n i s o t o p i c r a t i o s due t o v a r i a t i o n s i n t h e 0 1 8 c o n t e n t n e e d be c o n s i d e r e d . 3 . T h e number o f 0 1 8 a t o m s b e i n g t r a n s p o r t e d f r o m s y s t e m i t o s y s t e m j i s p r o p o r t i o n a l t o t h e number o f o 1 8 a t o m s i n s y s t e m i . ( i . e . we a s s u m e a f i r s t o r d e r p r o c e s s a s s u g g e s t e d by M c K a y , 1938) / «2 I f we l e t Ni(18) stand f o r the number cf oxygen-18 atoms i n system 1 and s i m i l a r e x p r e s s i o n s f o r systems 2 and , 3 we can w r i t e : d [ N i ( 1 8 ) ] / d t = k!N 2(18) - k 2N!(18) [ 3 . 3 ] d [ N 2 ( 1 8 ) ] / d t = k 2 N i ( 1 8 ) - k i N 2 ( 1 8 ) [3-4] from equation 3.4 N!(18) = [ l / k 2 ] [ d ( N 2 ( 1 8 ) ) / d t ] + [k!/k 2]N 2(18) [3.5] d i f f e r e n t i a t i n g 3.5 g i v e s d [Ni (18) ] / d t = [ l / k 2 ] d 2 ( N 2 ( 1 8 ) ) / d t + [ k 1 / k 2 ] d ( N 2 ( 1 8 ) ) / d t [3.6] s u b s t i t u t i o n of 3.5 and 3.6 i n t o 3.3 g i v e s d 2 [ N 2 ( 1 8 ) ] / d t 2 + ( k ! + k 2 ) d [ N 2 ( 1 8 ) ] / d t = 0 [3.7] The s o l u t i o n of 3.7 i s given as f o l l o w s : N*<18> = irhr e ' ( k l + k 2 ) t + [3.8] ki+k 2 ki+k 2 t l / i s i n a d d i t i o n to equation 3.5 y i e l d s : / Nj(18) = A [ l / k 2 - l / ( k ! + k 2 ) ] - B / [ k 1 + k 2 ] e " ( k l + k 2 ) t [3.9] I f the i n i t i a l v alues of N x(18) and N 2(18) are s u b s t i t u t e d i n t o equations 3.8 and 3.9 we o b t a i n : N 2(18) = kjN§(18)-k 2N?(18) ki+ k 2 + [N?(18)+N§(18)] e - ( k j + k 2 ) t [3.10 ] where the s u p e r s c r i p t ° i n d i c a t e s i n i t i a l v a l u e s . I f we d e f i n e P12 = Ni(16)/N 2(16) p 2 3 = N 2(16)/N 3(16) [3.11] 43 and d e f i n e the o 1 8 / 0 1 6 r a t i o s as f e l l o w s : Rj = Ni (18)/Ni(16) R 2 = N 2(18)/N 2(16) [3.12] then i t f o l l o w s t h a t N?(18)/N 2(16) = R ? P i 2 [3.13] d i v i d i n g both s i d e s of equation 3.10 by N 2(16) w i l l then g i v e : R 2 .= kiR§-k 2Pi 2R? ki+k 2 r ( k 1 + k 2 ) t + J c ^ _ t r O + R 0 ] K. i +K 2 [3.14] S i n c e we assume that the chemical e q u i l i b r a t i o n between the carbon d i o x i d e and the water i n system 2 i s r a p i d we can w r i t e : R, = aR 2 = ki+k 2 r ( k i + k 2 ) t + J c ^ _ j o + R § ] [ 3 > 1 5 ] k i + k 2 where a i s the s e p a r a t i o n f a c t o r as given by Compston and E p s t e i n (1958) to be equal to 1.0407 at 25°C. As shown i n s e c t i o n 3.2.2 there i s a r e l a t i o n s h i p between R? and R°. I t i s worthwhile t c t r a n s l a t e R§ i n t o terms of R? s i n c e i t i s p o s s i b l e to estimate R° but R°3 would depend upon the value of p 2 3 . From the tank carbon d i o x i d e c o r r e c t i o n given i n s e c t i o n 3.2.2 i t i s t r u e t h a t : aR? = R3(l+a/p23)' -ap 2 3R n [3.16] where the f o l l o w i n g assumptions have bean made: 1. The is o t o p i c r a t i o of system 2 i s the same as system 1 before chemical e q u i l i b r a t i o n begins, i . e . the water i s well mixed. 2. R° i s the r a t i o of the carbon dioxide a f t e r the eq u i l i b r a t i o n with the water i n system 2 which corresponds to the f i n a l carbon dioxide r a t i o calculated i n section 3.2.2 3. R T i s the r a t i o of the tank carbon dioxide. Substitution of 3.16 into 3.15 gives: k l p 2 3 a+p 2 3 a CaRS+ -f-R ) - a k 2 p 1 2 R ? P 2 3 i ,--(ki+k 2) t k i + k 2 [3.17] I t i s clear that R3 i s given by a function of the form c 2 t R 3 = c,e + c by equation 1.1 the DEL w i l l be DEL(R 3/SMOW) .= l O O O c i £ C 2 t + ( _ c j _ SMOW RSMOW which i s also of the form: DEL(R 3/SMOW) = p ! e P 2 t + p 3 - 1 )1000 [3.18] The f i n a l dependance of DEL upon the parameters deserves some attention. I t i s clear from equation 3. 17 that pi i s dependent upon the i n i t i a l i s o topic r a t i o of the water and upon the r e l a t i v e amounts of water and carbon dioxide ( P 1 2 and p 1 3 ). The h a l f - l i f e of the reaction i s determined only by the transport constants k x and k 2 which are constant given any f i x e d conditions. The P3 term i s also a function of R ° , p i 2 , and P 2 3 . The conclusion i s that the values of P I and p 3 vary between samples but that p 2 i s constant. He therefore deduce that i f we study the reaction time on any water sample we should be able to calculate the time necessary for the reaction of any other water samples. The e q u i l i b r a t i o n process was studied empirically ty e q u i l i b r a t i n g a 10 ml water sample that was i s c t o p i c a l l y very d i f f e r e n t from the tank carbon dioxide i n i t i a l l y placed over i t . Representative aliquots cf carbon dioxide were withdrawn at i n t e r v a l s of approximately one hour and t h e i r i s o t o p i c composition measured r e l a t i v e to IAEA SMOH. The r e s u l t s of t h i s experiment are given i n Figure 3 . 4 . Figure 3 . 4 i s a least squares f i t to an exponential function of the form given by equation 3 . 1 8 . Data points were weighted in proportion to the r e c i p r o c a l of the a n a l y t i c a l variance i n determining zhe DEI value. Error bars on the graph are taken at the one-sigma l e v e l . The re s u l t of the f i t i s excellent and confidence i n the estimate of the parameters i s high. The value of p 2 was found to be: p 2 = (-0.52 ± .01)hr" 1 [ 3 . 1 9 ] In general water samples whose equilibrated carbon dioxide i s very d i f f e r e n t i s o t o p i c a l l y from the tank carbon dioxide w i l l take longer tc be within a specified range of the steady state value than samples that have nearly the same i s o t o p i c composition i n their equilibrated carbon 46 o o Figure 3.4 The E q u i l i b r a t i o n of a Carbon Dioxide Sample dioxide. In fact i t i s clear that i f the i s o t o p i c r a t i o of the carbon dioxide i n f i n a l equilibrium with the water sample was i d e n t i c a l to tank carbon dicxide i t would take no time at a l l to e q u i l i b r a t e . Therefore i f one wishes to know how long i t takes a water sample to reach equilibrium with the carbon dioxide above i t i n the sample flask the equilibrium DEL value must be s p e c i f i e d . Using the value of p 2 i n equation 3.19, i t i s possible to determine the time necessary for the carbon dioxide to be within a given number of DEL units of the steady state value. The c a l c u l a t i o n i s straightforward. Remembering the reaction proceeds according to equation 3.18 we write: y = P l e x p ( p 2 t ) + p 3 [ 3 . 2 0 ] where p 3 i s the f i n a l equilibrium EEL value of the carbon dioxide (t i n f i n i t e ) , pj plus p 3 i s the DEL value of the 47 t a n k c a r b o n d i o x i d e (t e q u a l t o z e r o ) a n d P 2 i s a c o n s t a n t a s g i v e n i n e q u a t i o n 3 . 1 9 . I f Q i s t h e m a g n i t u d e o f t h e d i f f e r e n c e b e t w e e n t h e s t e a d y s t a t e v a l u e and t h e v a l u e a t some t i m e t i s i s c l e a r t h a t : Q = I P 3-y| = | - P 1 e x p ( p 2 t ) | [ 3 . 2 1 ] Q = |p 3-DEL(TANK/SMOW)exp(p 2 t)| The v a l u e o f DEL (TANK/SMOW) i s known v e r y w e l l where SMOW i s t h e i s o t o p i c r a t i o o f c a r b o n d i o x i d e i n e q u i l i b r i u m w i t h SHOW a n d i s : DEL(TANK/SMOW) = -18.75 [ 3 . 2 2 ] a s m e n t i o n e d p r e v i o u s l y : DEL(.X/SMOW) = . p 3 [ 3 . 2 3 ] w i t h t h i s i n f o r m a t i o n e q u a t i o n 3 . 2 1 b e c o m e s : Q = |DEL(X/SM0W)+18.75 | e x p ( - . 5 2 t ) [ 3 . 2 4 ] s o l v i n g f o r t t = 0 |Q| < DEL(X/SM0W)+18.75 [ 3 . 2 5 ] t = (-1 / .52)An|Q/[DEL(X/SM0W)+18.75]| elsewhere F i g u r e 3.5 i s a p l o t o f e q u a t i o n 3 . 2 1 f c r t h e t h r e e v a l u e s o f Q s p e c i f i e d . F o r t h e s a m p l e s a n a l y z e d i n t h i s p r o j e c t t h e e r r o r due t o i n s u f f i c i e n t e q u i l i b r a t i o n t i m e must be l e s s t h a n . 0 1 DEL u n i t s s i n c e t h e minimum e q u i l i b r a t i o n t i m e was f i f t e e n h o u r s . O t h e r l a b o r a t o r i e s h a v e s t u d i e d t h e e q u i l i b r a t i o n o f c a r b o n d i o x i d e a n d w a t e r . S e v e r a l i n t e r e s t i n g and p e r t i n e n t o b s e r v a t i o n s w e r e made by t h e I n s t i t u t e f o r T h e r m a l S p r i n g ' . I ' U 8 DEL(X/SMOW) Figure 3 . 5 E q u i l i b r a t i o n time f o r samples of various compositions Research of Okayama University. Hatsubaya (1972) studied the e f f e c t of the pH of the water sample on the equilibrium DEL value. The re s u l t of t h i s study was that pH values between 2 and 10 did not a f f e c t the DEL value obtained after overnight e q u i l i b r a t i o n . There i s no reason to suspect a di f f e r e n t conclusion at U.B.C. although the equilibrium time i s longer than was Matsubaya's. A more in t e r e s t i n g r e s u l t occurred when Matsubaya studied the ef f e c t of water sample size on the time necessary for e q u i l i b r a t i o n . One would expect that e q u i l i b r a t i o n time would increase with sample size because of increased mixing problems. Matsubaya found the converse was true and the time for e q u i l i b r a t i o n increased for any given water sample i f the volume of the water was decreased. A plausible explanation of t h i s observation can be obtained "9 by re-examining equation 3.17. It i s clear that only the parameter p 2 affects the e q u i l i b r a t i o n rate for any given water sample. Clearly the chemical environment does not change and so the increase i n e q u i l i b r a t i o n time must be attributed to the transport constants k r and k 2 . These transport constants are a measure of the e f f i c i e n c y of the mixing process. Matsubaya used round bottom e g u i l i b r a t i o n f l a s k s such that the angle of inter s e c t i o n between the water surface and the f l a s k became more severe by adding more water. I t i s reasonable to assume mixing would therefore improve i f sample size were increased, causing a decrease i n reaction time. This e f f e c t i s counteracted somewhat by increased sample s i z e and i t i s hard to see i n t u i t i v e l y which e f f e c t dominates. This provides a possible explanation of the empirical observation of Matsubaya. The separation factor a i s a constant that has teen prec i s e l y determined by O'Neil and Epstein (1966) and i s 1.04073 • .00005 at 25°C. This i s i n close agreement with the much used value of 1.039 quoted by Craig (1957). Staschewski (1964) presents an extremely good analysis of the variation of a with temperature and the effect of temperature variations i n the water cn the DEL value w i l l be analyzed in Chapter IV. There remains a f i n a l point cf i n t e r e s t i n the re l a t i o n s h i p given by equations 3.17 and 3.18. If one examines equations 3.3 and 3.4 at steady state he deduces that: k 2 / k i = N 2 ( 1 8 ) / N i ( 1 8 ) 50 but at steady state the water i s well nixed and R2 = Ri t h i s leads to the fact that k 2/k x = N 2(16)/Nj(16)•= I / P 1 2 By examining equations 3.17 and 3.18 we see that since p ; i s known from the experimental e q u i l i b r a t i o n and since R? and RT and p 1 3 plus p 2 3 can be estimated by knowing the amount of carbon dioxide and water inserted i n the reaction vessel, an estimate of the value of p 1 2 can be made. S i m i l a r l y a second estimate can be obtained using the expression for p 3. The ca l c u l a t i o n s are tedious and w i l l not be presented here since i t i s a minor point. The analysis was c a r r i e d out and the value of p 1 2 was estimated to be approximately 3500, which i s probably better than an order cf magnitude c a l c u l a t i o n . Therefore the system which we have defined to be system two corresponds to a layer of water about 2 microns deep on the surface of the water in the sample f l a s k . At t h i s point the question arises i f the reaction between the carbon dioxide and water might actually occur in the gas phase. Knowing the vapor pressure of water and the volume of the vacuum above the water sample indicates that the r a t i o of water to water vapor i n the e q u i l i b r a t i o n f l a s k i s approximately 12,000. The difference between t h i s number and the previous estimate of 3500 can not be shewn with a high degree of confidence. He therefore conclude that i t i s quite possible that the reaction between carbon dioxide and water takes place e n t i r e l y i n the gas phase. 51 3.1.3 The Mass Spectrometer Analysis Of A Carbon Dioxide Sample The f i n a l step i n obtaining a DEL value i s the mass spectrometer analysis of the equili b r a t e d carbon dioxide. Mass spectrometer techniques vary between laboratories and so a description of the exact technique used in t h i s study i s necessary. Details of the mass spectrometer were given i n Chapter II and so we are only concerned with the actual procedure employed. At the beginning of each day on which analyses were to be made a background spectrum was obtained. After a few days of routine analyses the background would remain unchanged unless d i f f i c u l t i e s in the vacuum system existed. P r i n c i p a l concern was the magnitude of the background peak at mass 46. It can be shown numerically that background peaks at mass 46 would not a f f e c t r e s u l t s s i g n i f i c a n t l y i f magnitudes were less than 10 mv. This was used as the primary c r i t e r i o n to determine whether analyses would be performed or not. Background was never higher than 10 mv at a case current of 300 microamps on days on which analyses were made. After running the background spectrum, an aliquot of dry tank carbon dioxide was inserted into the l e f t hand side (LHS) of the sample introduction system. Quantities were considered s u f f i c i e n t i f the source pressure rose tc between 2 x 10~ 6 and 4 x 1 0 - 6 t o r r as measured by an ion gauge 52 located several inches below the source. Experience showed that such pressures would give voltages of six to seven vol t s at mass 44 with a case current of 300 microamps and "optimum" source conditions. This tank carbon dioxide would then serve as a daily working standard and a l l measurements would be made r e l a t i v e to i t . After successful loading of the l e f t hand side of the sample introduction system and optimization of source conditions, a slow magnetic scan was made i n both d i r e c t i o n s over the mass 46 peak. Flatness of the mass 46 peak top was c r u c i a l unless no i n s t a b i l i t i e s existed i n the various power supplies. Peak shape could be altered by varying settings of the source parameters. Such parameters were manipulated u n t i l s a t i s f a c t o r y peak tops were obtained. With completion of t h i s step, analysis of the f i r s t unknown sample could begin. A sample tube containing carbon dioxide of unknown composition was attached to the ri g h t hand side (RES) of the sample introduction system with a "Vitcn" O-ring and spring clamp. The trapped a i r between the sample tube stopcock was removed using the sample l i n e pumping system a f t e r the stopcock to the magnetic valves had been closed to prevent a i r flowing into the mass spectrometer. The unknown carbon dioxide was then transferred into the large reservoir bulb on the right . hand side of the i n l e t system. This was accomplished by expanding the carbon dioxide i n the sample tube into the large bulbs in a series cf three to four small 53 a l i q u o t s . The amount of the sample i n the reservoir would be increased or decreased u n t i l the mass 46 peak height of the sample was equal to the mass 46 peak height of tank carbon dioxide i n the l e f t hand side of the i n l e t system. After accomplishing the peak matching, the magnetic valves would be cycled allowing the samples i n the two sides of the i n l e t system to alternately flow into the mass spectrometer. This process would continue f o r approximately ten minutes. After t h i s period of valve cycling the mass spectrometer high voltage supply would be adjusted such that the mass 46 ion beam was centered i n the Faraday cup. Source potentials would be adjusted to give maximum s e n s i t i v i t y and important machine parameters would be recorded for the future analysis of data discussed i n the following chapter. When the operator was convinced no p e c u l i a r i t i e s existed with the mass spectrometer, i t would be placed under the supervision of an Interdata Model 4 computer. The computer would i n i t i a l l y switch the magnetic valves into the configuration allowing the d a i l y working standard (tank carbon dioxide) to flow into the source of the mass spectrometer. It was found that a period of time was required a f t e r valve c y c l i n g for the i s o t o p i c r a t i o to reach steady state. For t h i s reason the f i r s t f i v e data points would be rejected and data analysis would begin with the sixt h point. The switching correction described i n the next section numerically compensates for non-steady state r a t i o s 54 i n both sides of the i n l e t system. After c o l l e c t i n g seven data points, the mean value and standard deviations of the PHI values are printed on a teletype, awaiting further data reduction. The magnetic valves were then cycled and the unknown sample was analyzed as described above. This process was repeated u n t i l f i v e PHI values were collected for both the unknown and the working standard. If the analysis was of acceptable precision the unknown sample was then pumped away by the mechanical pumps and ten minutes l a t e r a new sample was loaded into the mass spectrometer. I f major d i f f i c u l t i e s were encountered in the analysis of any carbon dioxide sample, they would r e f l e c t themselves i n the a n a l y t i c a l precision obtained. S p e c i f i c a l l y i f consecutive measures of PHI differences d i f f e r e d by more than 0.0010 i t was found, i n general, that the calculated uncertainty would exceed acceptable l i m i t s . Therefore i f t h i s occurred during an analysis the sample would be re-analyzed on the mass spectrometer. Thus with the same carbon dioxide i n the ri g h t hand side of the mass spectrometer source conditions would be reoptimized and ra-analysis would begin. This process would be repeated a maximum of four times or u n t i l an analysis with acceptable a n a l y t i c a l precision was obtained. No data were rejected but rather the weighting function derived i n Appendix V would be applied to a l l the CEI values obtained for the carbon dioxide sample i n question. In thi s manner only one 55 DEL value would be obtained f o r each e q u i l i b r a t i o n cf carbon d i o x i d e with water. Data r e d u c t i o n at the U n i v e r s i t y of B r i t i s h Columbia has been done i n two d i f f e r e n t ways. The data r e d u c t i o n e s s e n t i a l l y i n v o l v e s the t r a n s l a t i o n of the PHI v a l u e s i n t o a DEL value using equation 2.18 d e r i v e d i n Chapter I I . Samples analyzed f o r the P o l a r C o n t i n e n t a l S h e l f P r o j e c t ware reduced u s i n g a F o r t r a n IV program w r i t t e n by R.D. R u s s e l l . T h i s method does a l e a s t squares f i t of a Tchebychev polynomial t o the PHI v a l u e s of the unknown and standard samples. I t e s s e n t i a l l y c o n s t r u c t s two p a r a l l e l curves through the data p o i n t s where the d i f f e r e n c e between curves i s PHIDIF used i n the equation. The value of PHISTD i s taken t o be the average PHI value obtained when a n a l y z i n g the working standard i n the l e f t hand s i d e . The r e d u c t i o n program used i n t h i s study does not place the c o n s t r a i n t of p a r a l l e l curves on the data. Instead c u b i c s p l i n e curves are drawn through the data p o i n t s . I t can be shown t h a t the f u n c t i o n s thus determined are continuous through the f i r s t d e r i v a t i v e . These curves are piecewise s o l u t i o n s but t h i s seems adequate s i n c e t h e r e i s no reason to expect t h a t high order d e r i v a t i v e s are continuous when the method of sample measurements i s c o n s i d e r e d . F i g u r e 3.6 shows a t y p i c a l example of the curves used i n the d e t e r m i n a t i o n of CEL. A f t e r determining the form c f the c u b i c s p l i n e s the d i f f e r e n c e between the two curves i s e v a l u a t e d n u m e r i c a l l y 56 Figure 3.6 The Cubic Splines for a Typical Analysis five-hundred times. Therefore a good estimate of PHIDIF i s obtained in addition to determining i t s standard deviation. The same process i s used in determining PHISTD. The DEL value i s then calculated using the equation derived in Chapter II. The advantage of t h i s method i s that a more r e l i a b l e estimate of the a n a l y t i c a l error i s obtained. The DEL values obtained are of course r e l a t i v e to the working standard for that day. At lea s t twice a day samples of the DBC LTW standard ( d i s t i l l e d l o c a l tap water) are analyzed i n the mass spectrometer. By using equations derived i n Appendices I and II the DEL values can be altered such that the DEL values of a l l unknowns are made r e l a t i v e to UBC LTW. After applying several corrections discussed in the next section the values can then be made r e l a t i v e to IAEA SHOW. 57 A more straightforward method of analysis would be to place UBC LTW i n the l e f t hand side of the mass spectrometer and make measurements d i r e c t l y to i t . This method would assume perfect symmetry on both sides of the sample i n l e t system. As i t happens t h i s i s a bad assumption as indicated i n Table 3.1 below. The most l o g i c a l way of comparing the two methods of sample analysis i s to compare the standard deviation of the values obtained by each method. Table 3.2 provides a summary of the two methods. In seven out of ten cases the standard deviation of the measurements i s less when using a dummy working standard i n the l e f t hand side of the i n l e t system. It was primarily t h i s r e s u l t which led to the adoption cf t h i s procedure. The precision based on duplicate analyses i s much better i f sample l i n e symmetry i s net assumed. There e x i s t two drawbacks with the method used. F i r s t an extra analysis of UBC LTW i s required every day and second, each analysis of an unknown sample i s based upon two i n d i v i d u a l analyses. This fact means that the resultant error i n measurements i s increased by something l e s s than the square root of two. The method employed was copied from the I n s t i t u t e cf Thermal Spring Research, Hisasa, Japan. 58 SMOW -T- -+- NBS1 -7.87 -7.81 -8.04 (-8.07) (-7.70) NBS 1 NBS1A -24.45 -24.44 -24.52 (-24.54) (-24. 25) -16.60 -16.76 -16.62 (-16.88) (-16.50) NBS1 A TABLE 3. 1 SLAP -56.39 -56.17 -55,94 (-57.04) (-56.40) -49.37 -48.68 -48.29 (-49.07) (-48.97) -33.32 -32.74 -32.21 (-32.72) (-32.76) SLAP UBC LTW -17.58 -17.39 -17.51 (-18.09) (-17.52) -10.10 -9.59 -9.78 (-9.96) (-9.56) 6.61 7.04 7.10 (7.03) (7.18) 41.31 41. 13 41.09 (41.21) (40.70) DATA COMPARING TWO METHODS OF SAMPLE ANALYSIS The figures enclosed i n ( ) are values obtained assuming perfect sample l i n e symmetry. The unbracketed values were obtained by the method used i n t h i s study. The names of the standard i n the right hand side of the i n l e t system i s in the f i r s t row. The standard in the l e f t hand side i s found i n the l e f t hand box. 3.2 Correction Factors Applied To Mass Spectrometer Analyses Errors in measurements always e x i s t . Some errors are ndom in nature and can never be completely eliminated, 59 I "T • ~r~- ; • — T ' "" T — i | sample | DEL | DEL | sigma | sigma | j measured method 1 | method 2 | 1 I 2 | t— — — 1 |NBS1/SM0W J -7.91 | -7.88 | .12 1 .26 | | NBS1A/SM0W | -24.47 | -24.40 | .04 1 .20 | |SLAP/SHOW | -56.17 | -56.72 | .22 1 .45 | |LTW/SMOW | -17.U9 | -17.80 | .10 1 .40 | | NBS1A/NBS1 | -16.66 | -16.69 | .09 1 .27 | ISLAP/NBS1 | -48.78 | -49.02 I .55 1 .07 | |LTW/NBS1 -9.82 I -9.76 I .26 1 .28 | |SLAP/NBS1A | -32.76 1 -32.74 | .55 1 .03 | |LTW/NBS1A | -6.92 | 7.11 | .27 1 .11 I ILTW/SLAP | 41. 18 | 40.96 | .12 I .36 | I • i TABLE 3.2 THE PRECISION OF TWO METHODS OF SAMPLE ANALYSIS means and standard deviations of a l l boxe s i n Table are presented here. Method 1 refers to the method employed i n t h i s study while method 2 refers to the method assuming perfect sam pie l i n e symmetry. only reduced by multiple measurements and sound experimental design. Many systematic errors also e x i s t i n measurements and great e f f o r t should be taken to remove t h i s unwanted bias. In t h i s research project four corrections were applied to a l l data. The corrections (in the order applied) are; switching correction, tank carbon dioxide correction, a linear correction to force agreement with world averages, and a correction to make measurements r e l a t i v e to IAEA SMOW. Each of these corrections w i l l now be discussed. 60 3.2.1 Switching Correction k switching transient follows each cycling of the magnetic valves. It i s an empirical observation that the PHI values do not reach th e i r steady state value for a s i g n i f i c a n t period of time aft e r valve c y c l i n g . However, the behavior of the PHI values as they approach t h e i r steady state value i s so consistent that a correction can be made to compensate f o r the incorrect values obtained. If one plots the v a r i a t i o n of the PHI values with time the pattern observed approximates the exponential curves represented in Figure 3.7. TIME Figure 3.7 The Observed Switching Transient Data are only taken in the shaded area of each curve 61 a n d i t c a n be s e e n t h a t e a c h e s t i m a t e d PHI v a l u e w i l l be t o o l a r g e . T h i s means t h a t t h e e s t i m a t e d P H I D I F s h o u l d be m u l t i p l i e d by some c o r r e c t i o n f a c t o r a n d t h i s c o r r e c t i o n f a c t o r c a n be made a r b i t r a r i l y c l o s e t o one by w a i t i n g a s u f f i c i e n t l y l o n g p e r i o d o f t i m e b e f o r e c o l l e c t i n g d a t a . O b v i o u s l y a c o r r e c t i o n f a c t o r s h o u l d b e i n s e r t e d i n t o t h e e q u a t i o n t o d e t e r m i n e D E I . E a c h o f t h e c u r v e s i n F i g u r e 3 .7 c a n be a p p r o x i m a t e d by a n e x p o n e n t i a l f u n c t i o n . P H I x = P i e x p ( p 2 t ) + p 3 F H I S T D = P " e x P ( P s t ) + Pe I t i s c l e a r t h a t i n i t i a l l y ( t = 0 ) : P H I x = P l + p 3 P H I S T D = P 3 + P e a n d a t s t e a d y s t a t e ( t i n f i n i t e ) t h e P H I v a l u e s a r e : ?HE. X = P 3 P H I S T D = P 6 t h e r e f o r e t h e s t e a d y s t a t e e s t i m a t e o f P H I D I F i s : P H I D I F ( T ) = p 3 - P 6 h o w e v e r we make m e a s u r e m e n t s a t t i m e s t l a n d t 2 . T h e r e f o r e , i n g e n e r a l , the m e a s u r e d P H I D I F ; P H I E I F ( H ) w i l l n o t be e q u a l t o t h e t r u e P H I D I F ; P H I D I F ( T ) . I f t h e q u a n t i t i e s L1 a n d L2 a r e a s shown i n F i g u r e 3 . 7 , we c a n e s t i m a t e t h e a v e r a g e v a l u e s o f t h e m as f o l l o w s : 62 s i m i l a r l y ^ = ^ r ^ T ( e P 5 t 3 - a P 5 t 3 ) + P e P 5 t i j - t 3 With these s t i p u l a t i o n s the measured value of PBIDIF becomes: PHIDIF(m) = L I - L2 = E± 1 , P 2 t 2 P z t Pz t 2 - t i / + P 3 - 5 i r V ( e P s l * - e P 5 t 3 ) - p P5 t i j-t3 6 therefore PHIDIF should be multiplied by: P H I D I F ( T ) P H I D I F ( M ) From the preceding arguments i t should be clear that the value of PHIST used in equation 2.18 i s a l s o i n error and should be multiplied by: ^ 7 - V (IP5t^eP5t3)+pe P 5 t i t - t 3 The two corrections above were measured by doing a least squares f i t of empirical data to exponential curves. It was found that PHIDIF should be multiplied by 0.998 +.002 and PHIST should be multiplied by 0.999 + .001 to remove the systematic error observed when the magnetic valves are cycled. The corrected values of the two parameters are then placed i n the proper places i n equation 2.18 to determine the switching asymmetry corrected DEL value. 63 3.2.2 Tank Carbon Dioxide Correction If the mass of water placed i n the sample f l a s k i s ver; much greater than the mass of carbon dioxide placed over the water sample then the isotopic r a t i o of the water would remain unchanged during the e q u i l i b r a t i o n process. If one wishes to be r e a l i s t i c he must admit that for f i n i t e amounts of water a correction must be applied to the measured DEL value to compensate for the isotopic s h i f t of the water towards that of the carbon dioxide as e q u i l i b r a t i o n takes place. Craig (1957) was the f i r s t to present a formula that corrects for t h i s e f f e c t . This writer has derived Craig's r e l a t i o n s h i p independently and i t w i l l now be presented. At equilibrium the i s o t o p i c r a t i o s between the water and the carbon dioxide are related to each other by the separation f a c t o r : rC0 2.= a r H 2 0 [ 3 * 2 6 ] We now define " p M to be the r a t i o of the number of O1* atoms in the water to the number of 0 1 6 atoms in the carbon dioxide. If the superscript 0 denotes quantities before e q u i l i b r a t i o n and N(18) stands for the number of oxygen-18 atoms we can write: N 0 ( 1 8 ) H 2 O + N 0 ( 1 8 ) C O 2 = N ( 1 8 ) H 2 0 + N ( 1 8 ) C 0 2 [3.27] Dividing by N(16) , assumed to be constant during the co 2 e q u i l i b r a t i o n process, gives: !̂ i!liuo + ' l ^ c o i . !l±!Vo + !l±!W r 3 2 8. »<">co2 •1,<16>co2 " H<16>co2 N(16)co2 C 1 64 P r H 2 0 + r C 0 2 = p r H 2 0 + r C 0 2 C 3 - 2 9 ! substituting 3.26 into the above equation gives: p r o + r o = P + r = P±a n , 0 1 M H 2 0 C 0 2 a r C 0 2 C 0 2 a C 0 2 £ J . 3 U J a r o = £ ± a _ a o a r H 2 0 p r C 0 2 p r C 0 2 [ 3 . 3 1 ] d i v i d i n g by r s T and subtracting one from both sides c o 2 gives: ar° r r° H_2j0 £ + a ( C 0 2 . a . C 0 2 . r ^ sT 1 p ^ sT " 1 } " p ( _ ^ T 1 ) L * - ^ J r c o 2 r c o 2 r c o 2 s T assuming r C Q r e f e r s to a standard carbon dioxide sample we can substitute into the l e f t hand side of 3 . 3 2 t c have the equivalent water standard by using 3 . 2 6 . v sT 7 p V sT ; p k sT ; [ d « ^ J J H 2 0 C 0 2 C 0 2 Q + Q, fy D E L ( t r u e ) = D E L ( m e a s u r e d ) - - DEL(TANK C 0 2 ) [3.34] Since the carbon dioxide placed i n the l e f t hand side of the mass spectrometer was tank carbon dioxide the l a s t term w i l l be equal to zero. D E L ( t r u e ) = - P-^ DEL (measured) [3.35] 65 where DEL(measured) i s the value obtained from the mass spectrometer after applying the switching correction. The value of p i s easily obtained. Assuming 10 ml water samples with 50 cm 3 of carbon dioxide at 20 cm Hg pressure and a temperature of 201.15°C (dry-ice methanol) a value of 348 i s obtained f o r p. The separation factor a has been determined by many people including Ccmpston and Epstein (1958), Craig (1957), C«Neil and Epstein (1966) and Staschewski (1964). The value obtained by O'Neil and Epstein seems most r e l i a b l e . At 25°C the value cf a they obtained was 1.04073 + .00005. The tank carbon dioxide correction used i n t h i s study i s simply one of mu l t i p l i c a t i o n . From 3.35 i t i s c l e a r that: D E L ( t r u e ) = 1.0030 DEL(measured) [3.36] After applying the switching correction and the tank carbon dioxide correction we have the best estimate of the DEL value of the unknown r e l a t i v e to tank carbon dioxide. At least two times each day a sample cf carbon dioxide that has been equilibrated with UBC-LTW i s analyzed on the mass spectrometer. The only corrections applied to the UBC-LTW measurements are the switching correction and tank carbon dioxide corrections. By knowing the weighted average of the UBC-LTW values (see Appendix V) r e l a t i v e to the tank carbon dioxide and the value of each unknown r e l a t i v e to tank carbon dioxide we can use the equations derived in 66 Appendices I and II to calculate the DEL values of the unknowns r e l a t i v e to OBC-LTW. By using t h i s method of obtaining data we are assuming that the i s o t o p i c composition of the tank carbon dioxide remains constant during the course of a day. We make no assumptions about symmetry between the two sides of the sample i n l e t system since a l l samples of importance are placed i n the r i g h t hand side of the i n l e t system and therefore a l l asymmetries cancel out in the f i n a l data reduction. 3.2.3 Linear Correction To Force Agreement With World Standards The International Atomic Energy Agency (IAEA) and the National Bureau of Standards (NBS) d i s t r i b u t e four standard water samples which serve as the basis for intercomparisons between laboratories measuring i s o t c p i c r a t i c s i n water samples. Since these standards serve as the only intercomparison, the author adopted the philosophy that measurements of the world standards made at the University of B r i t i s h Columbia should be constrained to agree with the average world measurements of these standards. Other laboratories have adopted s i m i l a r methods and multiply a l l data by a li n e a r constant such that differences between laboratory measurements and world average values are minimized. I t was f e l t that j u s t i f i c a t i o n of a li n e a r 67 correction factor was necessary and for t h i s reason a mixing experiment was performed. If one mixes two l i q u i d s of d i f f e r e n t i s o t o p i c composition, the is o t o p i c r a t i o of the mixture w i l l l i e between the i s o t o p i c r a t i o s of the two l i q u i d s . Appendix III gives a complete derivation of the mixing problem. For our purposes we can use the small r a t i o approximation presented i n the appendix since o 1 8 / 0 1 6 r a t i o s are t y p i c a l l y of the order of 1:500. Therefore: D E L ( M I X ) = (x D E L ( A ) + y D E L ( B ) ) / ( x + y ) R<<1 [3.37] where x i s the number of m i l l i l i t e r s of l i q u i d A and y i s the number of m i l l i l i t e r s of l i q u i d B i n the mixture. For the case of oxygen isotopes the error i n treating the x and y values as masses instead of volumes i s le s s than six parts per mi l l i o n and t h i s introduces no measurable error. Two i s o t o p i c a l l y d i f f e r e n t water samples (approximately 25 DEL difference) were used i n t h i s experiment. Aliguots of each l i q u i d were accurately weighed and then mixed together. By a r b i t r a r i l y assigning the i s o t o p i c composition of one l i q u i d to 0 and the isotopic composition cf the other to 1 an experiment could be performed to test the l i n e a r i t y of oxygen analyses at U.B.C. Table 3.3 gives the results of the experiment. The errors presented in the fourth column of Table 3.3 are the a n a l y t i c a l errors i n mass spectrometer analysis and do not include errors in sample preparation, i f any. Figure 68 r T • — — r 1 i j Mass of | mass of | t h e o r e t i c a l l experimental | | l i q u i d A | l i q u i d B |composit ion| I i DEL | 54.8306 gj 0.0 g i - i 1 0.0 | -26.04 + .03 | | 49.8474 | 4.9721 | 0.09070 | -24.02 + .09 | | 44.8181 | 9.9735 | .18203 | -21.67 . 16 | j 39.9056 | 14.9266 | .27222 | -19.46 + . 10 | | 34.8734 | 19.8431 I .36265 | -12.23 . 10 | | 29.9101 | 24.8703 | .45400 | -15.00 + . 06 | | 24.9053 | 29.8912 | .54549 | -12.67 .08 | | 19.9559 | 34.7858 | .63545 | -10.49 + .11 | | 14.9422 | 39.8185 | .72714 | -8.30 .05 | | 9.9615 | 44.8328 | .81820 | - 6 . 19 + .09 | | 4.9854 | 49.8316 | .90905 | - 4 . 11 + .11 | I 0. | 54.7651 I 1.0 1 -1.58 + .05 | L _ L_ .A „. J j TABLE 3.3 DATA USED TO CHECK THE LINEARITY OF ANALYSES 3.8 i s a graphica l representat ion of the data in Table 3.3. The l i n e drawn i s the leas t squares l i n e as defined by York (1969). The slope of the given l ine i s 0.04095 + .00009. Therefore one can conclude that the data f i t a s t ra igh t l i n e as well as possib le given a n a l y t i c a l p rec is ions of 0.14 DEL. Therefore a l i n e a r co r r ec t io n fac tor i s j u s t i f i e d in fo rc ing agreement with the world averages. A t o t a l of 18 labora tor ies around the world have made measurements of the four water standards SHOW, NBS1, NBS1A and SLAP. The average values of the standards r e l a t i v e to SMOW are: i DEL (NBS1/SM0W)= -7.86 + .04 69 " M E A S U R E D ' D E U X / S N O W ) Figure 3.8 The Linearity of Isotopic Analyses Based on a Mixing Experiment DEL (NBS1A/SHOW)= -24.21 + .08 DEL (SLAP/SMOH)= -55.38 + .14 From the above values and the res u l t s found i n Appendices I and II the matrix i n Table 3.4 can be constructed: It should be pointed out that the world measurements of the above values do not appear to have normal d i s t r i b u t i o n s and for t h i s reason caution should be excercised i n using them. However, due to the large number of independent measurements, the average values must be known quite well as re f l e c t e d i n the quoted errors of the mean. The measurements in Table 3.5 were made at the University of B r i t i s h Columbia using the technique described i n t h i s manuscript. Direct comparison can be made between Tables 3.4 and 3.5. It should be noted that the data in Table 3.5 have been corrected tor the switching asymmetry 70 r - • T ~ - • T ~ r - I • SMOW | NBS1 | NBS1A t SLAP | 1 snow r 0.0 | -7.86 | -24.21 | -55.38 | | NBS1 1 7. 92 J 0.0 | -16.49 | -47.90 | | NBS1A 1 24.81 | 16.76 | 0.0 1-31.94 | | SLAP 1 58.62 | 50.31 | 32.99 I 0.0 | i x i, „. _x J TABLE 3.4 WORLD AVERAGE VALUES OF WATER STANDARDS The water standard i n the top row indicates the standard whose r a t i o appears i n the numerator of the d e f i n i t i o n of DEL, while the water standards in the f i r s t column represent the standard i n the denominator. and tank carbon dioxide. 1— T — - ~ T " '"" —i i | 0.0 1 -7.91 | -24.47 | -56.17 j -17.49 | | 7.97 | 0.0 | -16.66 | -48,78 | -9.82 | | 25.08 | 16.94 | 0.0 | -32,76 | 6.92 | 1 59.51 | 51.28 | 33.87 I o.o | 41.18 | | 17.81 | 9.92 I -6.87 | -39.55 I 0.0 | i , ,_ . J. ..j...... _ . j _ _j. J TABLE 3. 5 •• . U.B.C. MEASUREMENTS OF THE WATER STANDARDS The values i n t h i s table are the same type as i n Table 3.4. The f i f t h column and f i f t h row contain values for the UBC LTW Standard. The entries i n the two tables can be compared by the 71 use of equation 1.2. S p e c i f i c a l l y i t i s observed that DEL (i/j) = D E L ( i / k ) + DEL (k/j) + DEL (i/k) DEL (k/j)/1 000 where the s u b s c r i p t s r e p r e s e n t the s p e c i f i c rows and columns. For i n s t a n c e one can now c a l c u l a t e the value of DEL (HBS1/SMOW) i f he knows the value of DEL (HBS1/LTW) and EEL (LTW/SHOW). Ei g h t y comparisons of t h i s type can be made between T a b l e s 3.4 and 3.5. I f one t a k e s the d i f f e r e n c e between the entry i n Table 3.4 and the e q u i v a l e n t c a l c u l a t e d e n t r y i n Table 3.5 and sums the square of the d i f f e r e n c e s f o r a l l p o s s i b l e i n t e r c o m p a r i s o n s he has obtained a q u a n t i t y which i s a measure of the amount of agreement between the two t a b l e s . The o b j e c t i v e of t h i s e x e r c i s e i s to f i n d a c o n s t a n t m u l t i p l i c a t i o n f a c t o r by which one s h o u l d m u l t i p l y the e n t r i e s i n T a b l e 3.5 so t h a t the sum of the sguares of the d i f f e r e n c e s between the two t a b l e s i s minimized. Performing the necessary c a l c u l u s y i e l d s a c u b i c equation, the three r o o t s of which are the values of the d e s i r e d constant. In p r a c t i c e i t has been found t h a t f o r any data s e t the c a l c u l a t i o n g i v e s one r e a l r o o t very c l o s e to one and two conjugate complex r o o t s whose r e a l p a r t s and magnitudes are very much d i f f e r e n t from one. The c a l c u l a t i o n s were made usi n g the data of T a b l e s 3.4 and 3.5. The r e a l r o o t obtained was: W = 0.9827 [3.38] Using the i n i t i a l data i t was found t h a t the average d i f f e r e n c e squared between the e n t r i e s i n Tables 3.4 and 3.5 was 0.327. A f t e r a p p l y i n g the l i n e a r c o r r e c t i o n t o Table 72 3.5 i t was found that we had reduced the average difference squared to 0 . 0 3 , which i s an impressive improvement. The correction seems very useful and also very j u s t i f i a b l e i n li g h t of the above f a c t . A l l measurements in t h i s study were multiplied by th i s l i n e a r correction factor. Multiplying the data in Table 3.5 by the linear correction factor, W, gives the data in Table 3 . 6 . 0.0 7.83 24.65 58.48 17.50 I -7 .77 I 0.0 | 16.65 | 50.39 | 9.75 - 2 4 . 0 5 | -55.20 | -17.19 -16.37 | -47.94 | - 9 . 6 5 0.0 | -32. 19 I 6 .8 33.28 I o.o | 40.47 - 6 . 7 5 | -38.87 1 0 .0 TABLE 3.6 MACHINE CORRECTED DEL VALUES OF WORLD STANDARDS The table entries correspond exactly to the entries of Table 3 . 5 . After applying the li n e a r correction i t i s seen that we now have the necessary information;to change measurements r e l a t i v e to UBC-LTW to measurements r e l a t i v e to IAEA SMOW. S p e c i f i c a l l y we note: DEL (UBC-LTW./ IAEA SMOW) = - 1 7 . 1 9 [ 3 . 3 9 ] A l l DEL values l i s t e d in t h i s study have been treated i d e n t i c a l l y using the procedure presented in t h i s chapter. 73 3,2.4 Corrections That Were Hot Applied To These Data Several corrections which are made by many laboratories were not made to these data. A brief explanation cf why i t was not deemed necessary to make these corrections i s useful. Hany laboratories c o l l e c t both the mass 44 and 45 peaks i n the same Faraday cup. The main constituent i n the 45 beam i s c l 3 0 1 6 0 l * and therefore the r a t i o s must be corrected using the known C 1 3 / C 1 2 r a t i o of the sample. Since we c o l l e c t only the mass 44 beam i n one cup and mass 46 ion beam in the other i t was not necessary to make a correction fo r the mass 45 beam flowing i n t o the mass 44 c o l l e c t o r , A small f r a c t i o n of the mass 46 ion beam ccmes from ions of the form c » 3 0 » * 0 * 7 and C * 2 0 * 7 0 » 7 . S i m i l a r l y some small fra c t i o n of the oxygen-18 i s not measured i n molecules of the form C » 2 0 * * 0 » « , c » 2 0 * 8 C » » , c * 3 0 i « 0 » e and C i 3 0 » * 0 » 8 . Craig (1957) derived correction factors for such molecules and using any reasonable estimates of carbon and oxygen isotope r a t i o s i t can be shown that neglecting corrections of the above type contribute an error much les s than the a n a l y t i c a l precision. Another common correction applied to oxygen isotope measurements i s commonly referred to as a leak correction. Putting the same sample i n both sides of the mass spectrometer should produce a DEL value of zero. In general such i s not the case and t h i s i s attributed to 74 non-symmetrical leaks. A correction factor i s calculated to remove t h i s discrepancy. When using the method employed in t h i s study such corrections are not necessary since a l l c r i t i c a l carbon dioxide samples are placed i n the same side of the i n l e t system. Another common correction applied to analyses i s usually c a l l e d the "valve mixing correction". This attempts to correct for the fact that the magnetic valves may not be completely closed when they are intended to be. That i s the gas flowing into the mass spectrometer i s r e a l l y a mixture of the gas i n the two sides of the i n l e t system. The correction i s usually made by noticing any decrease i n the mass 44 peak height as the sample i n the side cf the i n l e t system not being analyzed i s pumped away. If a decrease in the peak height i s noticed, i t i s assumed that i t i s caused by the f a c t that there i s no more gas in the "closed" side of the i n l e t system to flow through the "leaky" valve. The author has searched for t h i s e f f e c t on many occasions and i t has never been detected. Furthermore i t i s f e l t that such corrections can never be made with confidence because the decreased peak height could be attributed to either the loss of flow from the "closed" side of the i n l e t system or more e f f i c i e n t removal of the gas i n the "open" side of the i n l e t system. An e l e c t r i c a l analogue i s h e l p f u l . The magnetic valves can be treated as a network of r e s i s t o r s as shown i n Figure 3.9. Points in the system where the pressure i s very low can 75 MASS - SPECTROMETER R. I(LHS) SEE FIG. 2.8 k R. w I(RHS) SAMPLE INTRODUCTION ~ SYSTEM VACUUM Figure 3.9 E l e c t r i c a l Analogue of Magnetic Valves of Inlet System be treated as v i r t u a l grounds. The resistances represent impedance to the gas flow, I (LHS) and I(RHS). If we wish to analyze the gas in the l e f t hand side the resistances R1 and R4 are made small while the resistances R2 and R3 are made larger. It i s clear that i f R2 and R3 are not many times greater than R1 and R4 respectively, then some of the gas in the r i g h t hand side w i l l flow into the mass spectrometer and some of the gas i n the l e f t hand side w i l l flow into the waste vacuum system. It should also be pointed out that the potential above R5 w i l l be approximately equal t o : V w = l(RHS)(R 3+R 6)R5/(R3+R6+Ri»'+R5) If the gas i n the r i g h t hand side i s now pumped away, 76 I (RHS) =0, the flow into the mass spectrometer w i l l decrease fo r one of two reasons: 1. The flow from the right hand side through R3 w i l l become zero. 2. The potential at Vw w i l l decrease and therefore the flow from the l e f t hand side through R2 and R5 into the waste vacuum system w i l l increase causing a decrease i n the flow through R1. Laboratories making the valve mixing correction assume the f i r s t case i s true and neglect the second case. Placing reasonable estimates as to the magnitudes of the various resistances shows t h e i r assumption to be i n v a l i d . I t should be noted that a mixing correction could be applied correctly i f the isotopic r a t i o of the gas flowing into the mass spectrometer i s monitored as the gas i n one side of the sample system i s pumped away. I f the gases were of s i g n i f i c a n t l y d i f f e r e n t i s o t o p i c composition one could make the correction with confidence since i t would be possible to determine which of the above two phenomena was occurring. Due to the good agreement between the O.E.C. data and the world standards there i s strong j u s t i f i c a t i o n for not making the three corrections mentioned above. Continual caution should be maintained to ensure that changes i n the sample i n l e t system with time do not make our assumptions i n v a l i d . 77 IV. SOURCES OF ERROR IS DETERMINING C 1 8/0* 6 RATIOS During the course of obtaining i s o t o p i c compositions of samples from the f i e l d project to be discussed i n the next two chapters, approximately three hundred mass spectrometer analyses were performed. of these analyses approximately one-hundred ten were r e p l i c a t e analyses of water samples whose isotopic composition had been previously determined. By recording various mass spectrometer parameters associated with an analysis i t i s possible to i d e n t i f y probable sources of error in an analysis. An alternative method i s to hold a l l but one of the parameters constant and study the effect i t has on the measured DEL value. This technique i s time consuming and d i f f i c u l t to accomplish at times. A t h i r d approach used.in i d e n t i f y i n g possible sources of error i s to make th e o r e t i c a l c a l c u l a t i o n s to ascertain i f various factors are important i n an analysis. A l l three of the above methods were used i n t h i s study and the r e s u l t s of each w i l l be presented here. 4 . 1 Multiple Regression Analysis Of Mass Spectrometer Parameters It i s d i f f i c u l t to determine whether a l t e r i n g mass spectrometer potentials, pressures, currents, etc. a f f e c t s the measured isotopic r a t i o s . Such a determination i s extremely useful because i t allows the operator to know which variable he can a l t e r without a f f e c t i n g the EEL value 78 he determines. For each mass spectrometer analysis of a water sample the values of seven d i f f e r e n t mass spectrometer variables were recorded. These variables were: 1. The number of analyses already made that day. 2. The time since the f i r s t analysis of the day was made. 3. The t o t a l filament emission current. 4. The , operating pressure i n the mass spectrometer when the unknown sample i s being analyzed. 5. The DEL value of the sample analyzed immediately before the present analysis. 6. The magnitude (in volts) of the mass 46 peak f o r the unknown sample. 7. The magnitude (in volts) of the mass 46 peak for the tank carbon dioxide working standard. By noting the DEL values and associated a n a l y t i c a l uncertainties i t i s possible to determine i f any of the seven variables above a f f e c t the measured DEL values by performing a multiple regression analysis. The data used for t h i s analysis were obtained over the course of f i v e months. The approach was to perform a multiple regression on the data with DEL values being the dependent variables. Normally a multiple regression i s performed when a l l values of the dependent variables are from the same d i s t r i b u t i o n . In our problem i t i s clear that we are sampling d i s t r i b u t i o n s with many d i f f e r e n t means 79 since the data are from the analysis of many d i f f e r e n t water samples. For t h i s reason we must construct as many ••dummy" variables as there are water samples with duplicate analyses. Say there are m samples that have been analyzed two or more times. The Kth dummy variable i s assigned the value 1 for the Kth sample and 0 otherwise. In t h i s manner the difference between water samples w i l l be manifest by the c o e f f i c i e n t s of the appropriate dummy variable and i n pr i n c i p l e the average value of the Kth dependent variable minus the c o e f f i c i e n t of the Kth dummy variable should be constant. The success of the regression analysis was confirmed by checking the above rela t i o n s h i p . In performing the multiple regression analysis i t i s necessary to make three assumptions: 1 . The e f f e c t of random error i s small compared to the eff e c t of variatio n s i n the seven independent variables. This assumption i s r e a l i z e d i f the number of duplicates i s much greater than the number of independent variables. The r a t i o in t h i s analysis was eight to one. 2. The relationships between the dependent variables and the independent variables i s the same except for an additive constant, the c o e f f i c i e n t of the appropriate dummy variable. 3. The e f f e c t of an error i n an independent variable 80 i s not a function of the magnitude of that variable. This i s to say that the dependent variable i s a l i n e a r combination of the independent variables. The regression analysis of data was performed using a multiple regression program supported by the University of B r i t i s h Columbia Computing Centre. In t h i s manner the c o e f f i c i e n t s i n the regression equation 4.1 are a l l determined: DEL = b 0 + bivj + ... + b V f 4. 11 n n *• J where the v's are the independent variables and the dummy variables. From 4.1 i t follows d i r e c t l y that: V = - ( b 0 + b i v i + ... + b v)/b. + DEL/b. C.2] i n n . I i *• To obtain estimates of allowable variations in the machine parameters in question we must in s e r t average values of the variables into 4.2. In addition i f we i n s i s t that the measured DEL value must be within some value "e" of the optimum value we rewrite 4.2 as follows: V. = -(b 0+ b1.v.I+ ... +b v )/b. + (DEL±e)/b. [4.3] i n n i ' i By allowing e to vary from 0.05 to 0.15 we obtain the l i m i t s of variations permissable i n the machine parameters. Comparing these values with the actual variations i n the parameters indicates which variables may a f f e c t the measured DEL value and are therefore possible sources of error. 81 Table 4.1 summarizes the r e s u l t s of the multiple regression analysis. r — —v | ACTUAL| | SIGHA | . , ALLOWED VARIATION BY | REGRESSION ANALYSIS | _ T r -— -i e=.05 | e=.10 | e=.15 | 1 • |Prior No. of Runs 1 3.62 | 4.02 | 8.02 | 11.70 | jNet Time (Hours) | 5.06 | 120.6 | 240.6 | 351.0 | |Emission Current | 85.68 | 132.5 | 264.4 | 385.8 | j Pressure 1 .4387 | .4513 | .9005 | 1.314 | jPrevious DEL 1 7.67 | 87.77 | 175.2 | 255.6 | ISample Peak Height | .0728 | .0145 | .0288 | .0421 | js t d . Peak Height | .0736 | .0165 | .0329 | .0481 | i . . J , . ! „ ... ... J j. i TABLE 4.1 RESULTS OF REGRESSION ANALYSIS The f i r s t column gives the actual standard deviation of the corresponding machine parameter. If any of the entries i n the la s t three columns are smaller than the actual standard deviation then an error i n DEL w i l l r e s u l t and the magnitude of the error w i l l be greater than or egual to e. It i s clear from the table that the f i r s t f i v e variables cause l i t t l e error i n the measured DEL values but the magnitudes of the mass 46 peaks of both the sample and standard seem to a f f e c t the outcome. Calculations based on the voltage c o e f f i c i e n t of resistance f o r the Victoreen r e s i s t o r s (Whittles, 1960) used i n the measuring system indicate that n o n - l i n e a r i t i e s i n the r e s i s t o r s can a c t u a l l y account for an error i n DEL of 0.14 when the magnitude of the mass 44 peak decreases from seven to f i v e v o l t s . Future analyses should attempt to hold peak heights constant since non-zero voltage c o e f f i c i e n t s of resistance may explain the unexpected r e s u l t obtained i n the regression analysis. 4.2 Equality Of Hass 46 Peak Heights Many arguments can be made for constraining either the mass 44 or mass 46 peak heights to be equal f o r the two sides of the mass spectrometer i n l e t system. If one believes he has a large background i n the mass spectrometer or i f he i s worried about non-zero baselines i t i s best to equalize the smaller of the two peaks, i . e . the mass 46 peaks. If these problems are n e g l i g i b l e then i t would be advantageous to match the mass 44 peaks to ensure a constant gas flow into the mass spectrometer which in turn would cause a constant pressure in the source region. The parametric amplifiers used i n the mass spectrometer measuring system can d r i f t s u f f i c i e n t l y to a l t e r the measured isotopic values obtained. During the course of an analysis the mass 46 baseline can d r i f t as much as 10 mv from the i n i t i a l zero. In addition to t h i s , d i s c o n t i n u i t i e s as large as 15 mv have been observed. To minimize such problems i t was decided that a l l analyses i n t h i s study would be carried out with equal mass 46 peak heights. I t i s necessary to know how the DEL value varies with the magnitude of the peak height difference so we know how cl o s e l y we should match the mass 46 peak heights. A 10 mv 83 baseline o f f s e t w i l l cause le s s than 0.1* error for samples d i f f e r i n g by 20 DEL units, i f i t s 46 peaks are matched within 20 mv. An experiment was performed where the i n i t i a l amount of carbon dioxide placed i n the unknown side of the mass spectrometer was s u f f i c i e n t to cause the mass 46 peak height of the unknown sample to exceed the corresponding peak height of the working standard by 100 mv. The DEL value was measured and the a n a l y t i c a l precision noted. The peak height of the sample side was then decreased, by removing a portion of the carbon dioxide through a viscous leak, and the DEL redetermined. This process was repeated several times. The r e s u l t s are displayed i n Figure 4.1. The slope of the least squares l i n e was determined to be 1.22 + .42. D i f f i c u l t i e s are believed to exist with the c i r c l e d point and so i t was discarded, even though the apparent precision was high, and the slope was redetermined as 2.31 + .39. With these values i t i s possible to estimate the allowable va r i a t i o n i n peak height difference for a given error i n the DEL value. I t i s clear that i f we use the second slope determined we w i l l obtain a more severe constraint than i s probably necessary. The r e s u l t s are given i n Table 4.2. It i s clear from the table that i f the peaks are matched to within 20 mv the r e s u l t i n g error i n DEL w i l l be less than 0.05. In practice peaks were normally matched within 10 mv and rarely d i f f e r e d by more than 20 mv. It can therefore be concluded that the error in measurements due to unequal peak 84 I | A l l Points Included I |One Point Excluded I —h Error i n DEL .05 ,041 volts ,022 + .004 I I .10 | .15 | .20 I I I I .082 |.123 |.164 I .043 |.065 |.087 I TABLE 4.2 EfiROB IN DEL CAUSED BY A DIFFEBENCE IN MASS 46 PEAK HEIGHTS heights i s acceptable 85 4.3 Sources Of Error In The E q u i l i b r a t i o n Of Hater With Carbon Dioxide In addition to errors that e x i s t i n the mass spectrometer analysis of unknown samples d i f f i c u l t i e s can exis t i n the e g u i l i b r a t i o n of water and carbon dioxide. I t i s clear from the discussion presented i n Chapter III that errors can r e s u l t from i n s u f f i c i e n t e q u i l i b r a t i o n time. For the is o t o p i c compositions of samples i n t h i s study i t was shown (Figure 3.5) that e q u i l i b r a t i o n times greater than twelve hours would ensure errors l e s s than 0.05 DEL units. A l l samples analyzed i n t h i s study met t h i s c r i t e r i a . An add i t i o n a l source of error i s re l a t e d to the constancy of the temperature i n the water bath. Errors a r i s e because the separation factor defined in equation 3.15 of the previous chapter, i s not independent of temperature. A complete investigation of the e f f e c t was made by Staschewski (1964). Staschewski empirically determined the following r e l a t i o n s h i p : l o g i o ( a ) = 8 .247/T - 0.00969 [<*.4] converting to Naperian logarithms y i e l d s : 5,n ( a ) = 18.989/T - 0.02231 , [4.5] a = . 9779 e 1 8 . 9 8 9 / T [4.6] We wish to determine what e f f e c t changing the bath temperature has on the measured DEL value. Let us assume that the i s o t o p i c e q u i l i b r a t i o n of the standard tcok place at the optimum temperature of 25.3°C but the unknown sample 86 was equ i l ib ra ted at some other temperature. If we define K as fo l lows: K = a t / a 2 5 . 3 [4.7] i t fo l lows from Appendix VI that: DEL(m) = K DEL(T) + ( K - l ) l O 3 C 4 •8 ] where DEL (m) i s the measured value and DEL (T) i s the true value of DEL obtained i f T i s equal to 25. 3°C. Combination of 4.6 and 4.7 gives: K = .9384 exp(18.989/T) £4.9] s u b s t i t u t i n g 4.9 in to 4.8 g ives: DEL(m) = .9384 exp(18.989/T) [DEL(T)+1000] - 1000 [4 .10] Since we are in terested in the v a r i a t i o n of DEL (m) with changes i i i temperature, we d i f f e r e n t i a t e 4.10 with respect to T. 18.989/T d [DEL(m) 1 = - 1 8 . 9 8 9 ( . 9 3 8 4 DEL(T)+938.4)e dT T For the DEL values measured in t h i s study we can assume that 0.9384 DEL (T) i s much smaller than 938.4 and we obtain the approximate express ion: ADEL = (-17819/T 2)e x p(18.989/T)AT [4 .12] where ADEL i s measured in DEL uni ts and T i s measured i n °K. We are normally very c lose to a temperature of 25 .3°C and in . t h i s region equation 4.12 reduces t o : ADEL = -0.21AT [ 4 . 1 3 ] 87 The water bath i n t h i s study was r e g u l a t e d t o + .13°C which t r a n s l a t e s i n t o a maximum e r r o r i n DEL of l e s s than 0.03 DEL u n i t s . We t h e r e f o r e conclude t h a t e r r o r c o n t r i b u t i o n s from v a r i a b l e e q u i l i b r a t i o n bath temperatures are n e g l i g i b l e . 4.4 I s o t o p i c F r a c t i o n a t i o n Of A Carbon Dioxide Sample During Sample P r e p a r a t i o n The process of e q u i l i b r a t i n g a water sample with carbon d i o x i d e was d e s c r i b e d i n Chapter I I I . The l a s t step i n t h a t process i n v o l v e d t r a n s f e r r i n g the e q u i l i b r a t e d carbon '» d i o x i d e from over the water sample i n t o a sample tube. During t h i s exchange the pressure i n the p r e p a r a t i o n l i n e i s monitored t o ensure adequate sample t r a n s f e r . I t i s most probable t h a t the gas flow i n the sample p r e p a r a t i o n l i n e obeys v i s c o u s flow laws d u r i n g most of the sample t r a n s f e r . However i t i s p o s s i b l e t h a t the l i g h t e r carbon d i o x i d e molecule { c l z O l 6 0 1 6 ) migrates a t a f a s t e r r a t e than the h e a v i e r i s o t o p i c s p e c i e s ( C 1 2 0 * 6 0 1 8 ) . Such a process would indeed be t r u e i f the carbon d i o x i d e had to d i f f u s e through a background of some gas t h a t d i d not f r e e z e i n a vacuum at l i q u i d n i t r o g e n temperatures (e.g. n i t r o g e n , oxygen). Other processes c o u l d a l s o i n t r o d u c e i s o t o p i c f r a c t i o n a t i o n . For i n s t a n c e the f a c t t h a t the h e a v i e r i s o t o p i c s p e c i e s may f r e e z e f a s t e r than the l i g h t e r molecule c o u l d a l t e r the i s o t o p i c c omposition of the carbon d i o x i d e 88 collected i n the sample tube. The problem before us i s , assuming that f r a c t i o n a t i o n does indeed take place, what f r a c t i o n of the sample must be transferred to guarantee acceptable errors in the i s o t o p i c r a t i o ? This problem can be solved using the r e s u l t s of the Rayleigh d i s t i l l a t i o n found i n Appendix IV. The only unknown quantity i s a , the f r a c t i o n a t i o n factor. I t seems reasonable that the greatest source of f r a c t i o n a t i o n would be from unequal d i f f u s i o n rates in the sample l i n e and so a w i l l be equal to the square root of the mass r a t i o of the two i s o t o p i c species of carbon dioxide i n question. We therefore write: a = (44/46)^ = 0.978 [4.14] From Appendix IV we write: q / r 0 = [ l - f 1 / a ] / ( l ~ f ) r«l [4.15] where q i s the i s o t o p i c r a t i o of the carbon dioxide molecules that have reached the sample tube, r i s the true i s o t o p i c r a t i o of the unfractionated carbon dioxide, and f i s the f r a c t i o n of the gas molecules that have not yet undergone f r a c t i o n a t i o n (i.e. the r a t i o of the current pressure to the o r i g i n a l pressure i n the sample l i n e ) . We again must use the r e s u l t derived i n Appendix VI to estimate the error r e s u l t i n g in the DEL value as a function of f. I t should be noted that i f f=0 (i.e. a l l the sample has transferred) then q/r0=1 and no error w i l l r e s u l t i n the measured DEL value. From the appendix: 89 DEL(measured) = q / r 0 D E L ( T R U E ) + ( q / r 0 - 1 ) 1 0 3 [4.1.6] Since the DEL values are much l e s s than 1000 we can write: DEL(ERROR) = DEL(m e a s u r e d ) - D E L ( T R U E ) = ( q / r o ~ l ) 1 0 3 [4.17] combining 4.15 and 4.17 gives: The transfer i s monitored using a thermocouple pressure gauge. The i n i t i a l pressure i n the system i s 16.46 t o r r . Using equation 4. 18 and the value of a i n equation 4.14 we obtain Table 4.3. Normally samples would transfer to gauge readings greater than 65, meaning errors would be less than .04 CEL. Samples that pulled over to gauge readings of less than 60 would be equilibrated and analyzed again. Such redeterminations seldom gave differences larger than the a n a l y t i c a l precision and so we conclude that, i f the sample i s being fractionated, the degree of fr a c t i o n a t i o n i s les s than that assumed i n t h i s analysis. It i s important to note that even assuming the worst case, contributions to the error of the analysis are extremely small. In many of the instances when the pressure would not decrease to a gauge reading of 60 i t would s t a b i l i z e in the 46 to 50 range. It i s possible that i n these cases we are seeing the e f f e c t of outgassing of stopcock grease or the DEL(ERROR) = [ ( 1-f 1/a ) / ( l - f ) - 1 ] 1 0 3 [4.18] 90 r ~ — r - T— "i T i j Gauge | pressure | f X 103 |Correction |DEL (error) | | Beading | t o r r | [ J 1 30 | .1 I 6.075 | 1.000662 | .662 | 1 40 | .06 | 3.645 | 1.000433 1 .433 | I 50 | .032 | 1.944 | 1.000255 | .255 | I 58 1 .017 | 1.033 | 1.000148 I .148 | 1 59 | .015 | .9113 | 1.000132 I .132 | 1 60 | .014 | .8505 J 1.000125 I .125 | 1 61 l .012 | .7290 | 1.000109 | . 109 | I 62 | .010 | .6075 | 1.000093 | .093 | I 63 | .0078 | .4739 | 1.000075 | .075 | I 64 | .0010 | .3645 | 1.000059 | .059 | I 65 | .0042 | .2552 | 1.000043 | .043 | I 66 | .0031 | .1883 | 1.000033 | .033 | I 67 | .0023 | .1397 | 1.000025 | .025 | I 68 | .0017 | . 1033 | 1.000019 | .019 | I 69 | .0012 | .0729 | 1.000014 I .014 | I 70 | .0010 | .0608 | 1.000012 | .012 | i • . -X_ -A - J. — 1 TABLE 4.3 GAUGE READING VS RAYLEIGH ERROR IN DEL p a r t i a l pressure of some contaminant. I t was observed that duplicate analyses of such samples always agreed within a n a l y t i c a l error. 4.5 A n a l y t i c a l Precision Of Analyses The f i n a l test of experimental technique l i e s i n how well isotopic r a t i o s can be reproduced. Ideally, many measurements would be made of a single water sample and the standard deviation of those analyses calculated in the normal way. Altern a t i v e l y many d i f f e r e n t samples can be analyzed two or more times and give an equivalent estimate of the precision. Confidence i n the estimate of precision 9 1 requires nearly twice as many measurements cf duplicate pairs compared to measurements of a sing l e sample. The method of determining the precision of analyses from r e p l i c a t e pairs i s found i n Youden (1951). B a s i c a l l y , one calculates the sum of squares difference f o r each d i f f e r e n t sample of water and evaluates the number of degrees of freedom for that sample by subtracting one from the number of r e p l i c a t e analyses. fie f i n a l l y obtain the variance estimate of the measurements by di v i d i n g the t o t a l sum of squares by the t o t a l number of degrees of freedom for the data set. The c a l c u l a t i o n of precision was c a r r i e d out and proved to be very informative. On the basis of 52 water samples that were analyzed twice, 4 water samples analyzed three times and one sample that was analyzed f i v e times, the a n a l y t i c a l precision taken at the one-sigma l e v e l i s 0.14. Many laboratories state t h e i r precision as 0.1 and so the measurements at the University of B r i t i s h Columbia are of comparable quality. As discussed i n Chapter I I I , each measured value of an unknown water sample was based on two mass spectrometer analyses, a measurement of the unknown sample r e l a t i v e to the tank carbon dioxide and a determination of the l o c a l working standard (OBC LTW) r e l a t i v e to the same tank carbon dioxide. For t h i s reason one would expect that our a n a l y t i c a l precision would not be as high as laboratories that make only a s i n g l e mass spectrometer measurement per 9 2 sample. The above proposition was checked by determining the a n a l y t i c a l precision based on the d a i l y determinations of UBC LTW to the tank carbon dioxide working standard. On the average two and one-quarter determinations cf a UBC-LTW standard were made d a i l y . From these duplicate analyses the precision of a single mass spectrometer measurement was found to be .125. Assuming that an average of 2.23 UBC LTW standards were analyzed daily we would deduce that the error i n the measurement of an unknown sample would be: ( e r r o r ) 2 = (..125) 2 + (. 125) 2 /2 . 23 [4.19] e r r o r = 0 . 1 5 This estimate of precision agrees extremely well with the actual a n a l y t i c a l precision of 0.14. We can therefore conclude that the method used i n t h i s study ( i . e . each DEL value based on two mass spectrometer analyses) increases the standard deviation very l i t t l e . I t s most serious disadvantage i s that i t requires one addit i o n a l analysis of a standard each day. The estimates of a n a l y t i c a l error above include both errors i n sample preparation and errors i n the mass spectrometer analysis of a sample. The data reduction method used i n t h i s study gives an estimate of the l a t t e r error f o r each sample analyzed. The average a n a l y t i c a l error of a mass spectrometer analysis i s 0.12. This implies that the error i n sample preparation must be approximately 93 sample p r e p a r a t i o n e r r o r of a s i n g l e sample 1.06* a n a l y t i c a l e r r o r i n mass spectrometer a n a l y s i s 1.10 t o t a l e r r o r i n measuring a s i n g l e sample 1.12 sample p r e p a r a t i o n e r r o r f o r method used I.07* a n a l y t i c a l e r r o r i n mass spectrometer a n a l y s i s I.12 t o t a l e r r o r f o r method used i n t h i s study 1.14 * these numbers are q u i t e u n c e r t a i n TABLE 4.4 SUMMARY OF ERRORS INVOLVED IN MEASURING HATER SAMPLES 0.07. He t h e r e f o r e conclude t h a t the l a r g e s t source of e r r o r i n t h i s study i s the a n a l y t i c a l e r r o r a s s o c i a t e d with the mass spectrometer and not with sample p r e p a r a t i o n . A n a l y t i c a l e r r o r s are o f t e n dependent upon the magnitude o f the q u a n t i t y being measured. That i s to say the f r a c t i o n a l e r r o r i s c o n s t a n t but not the a b s o l u t e e r r o r . The e r r o r s determined i n t h i s p r o j e c t seemed to be independent of » the magnitude of the DEL v a l u e . T h i s o b s e r v a t i o n was s u b s t a n t i a t e d by determining the c o r r e l a t i o n c o e f f i c i e n t between DEL values and t h e i r a s s o c i a t e d a n a l y t i c a l e r r o r . The c o r r e l a t i o n was found to be 0.16. This i m p l i e s near independence between DEL v a l u e s and a s s o c i a t e d e r r o r s . He thus conclude t h a t e r r o r s i n measurements are constant w i t h i n the range of i s o t o p i c compositions i n t h i s p r o j e c t . Table 4.4 summarizes what i s known about e r r o r s i n measurement i n t h i s study. 95 V. AS ISOTOPIC STUDY OF WATER FLOW IN NATURAL SNOW 5.1 Introduction j Understanding of the physics of waterflow i n snowpacks has increased considerably i n the past f i v e to ten years. Much of the work has been done by S. Colbeck of the U.S. Army Corp of Engineers Cold Regions Research and Engineering Laboratory (CRREL). Colbeck has presented a physical model that describes the bulk water flow through both homogeneous and s t r a t i f i e d snow. Experimental data support the simple gravity flow model proposed f o r homogeneous snow (Colbeck and Davidson, 1972) but at present the e f f e c t of impermeable layers i n the snow remains a t h e o r e t i c a l supposition. (Colbeck, 1973) I t i s unfortunate that the studies of Colbeck reveal nothing about the actual processes an "average" water molecule undergoes. Quantitative studies only reveal net flow at any given depth and cannot unambiguously determine the source of the water. Therefore i f one i s interested in studying the inter a c t i o n between the l i q u i d and s o l i d phases of water, which was the purpose of the present study, d i f f e r e n t techniques must be brought tc bear on the problem. Gerdel (1948,1954) was among the f i r s t to study water movement in natural snowpacks for which attempts to study the i n t e r a c t i o n between the l i q u i d and s o l i d phases were made. The experiments he conducted were done u t i l i z i n g dyes i n varying concentration. Two d i f f i c u l t i e s exist i n dye 96 tracing experiments. F i r s t , the introduction of the dye al t e r s the physical c h a r a c t e r i s t i c s cf the snowpack and therefore an unnatural s i t u a t i o n i s studied. Second, i t i s quite conceivable that dye suspended i n l i q u i d water does not behave the same as water. An example of t h i s would be the case in which a water wave encounters a layer of high density snow. The dye may come out of solution and freeze i n the dense layer but water formed by melting i n the layer may continue to flow. It would be much better to study the actual water molecules. The f i r s t d i f f i c u l t y has been addressed by Langham (1973). He has devised a method of introducing the dye into the snowpack so that i t s introduction does not a l t e r the properties of the snowpack. However, i t i s probable that the migration of dye throughout the lower part of the snowpack a c t u a l l y a l t e r s physical properties of the snow. Even neglecting t h i s argument i t i s s t i l l true that data from dye tracing experiments express facts about the d i s t r i b u t i o n of the dye i n the snowpack and net the water i t s e l f . Therefore from a purely philosophical point of view, dye tracing experiments have inherent d i f f i c u l t i e s . Stable isotopes provide an i n t e r n a l l a b e l for water that cannot a l t e r the physical properties of the snowpack to any s i g n i f i c a n t degree. Therefore, the most l o g i c a l method of studying water percolation i n snewpacks would be through changes i n the stable isotope d i s t r i b u t i o n . In fact several researchers have pursued studies related to stable isotope 97 d i s t r i b u t i o n s i n natural snowpacks. These include Judy et a l . (1970), Friedman and Smith (1972) and Meiman et a l . (1972) who studied the natural v a r i a t i o n , both i n time and space, of hydrogen isotopes i n seasonal snowpacks. Krouse and Smith (1972) conducted a study i n the Sierra Nevada Hountain Range i n which water movement was actually monitored with a density p r o f i l i n g gauge as well as oxygen isotope variations. They used natural i s o t o p i c variations i n the p r e c i p i t a t i o n as the tracer and so were apparently looking at i s o t o p i c changes smaller than the present study. Arnason et a l . (1972) and Buason (1972) have conducted si m i l a r investigations i n both natural and a r t i f i c i a l snowpacks and have been able to gain empirical support f o r a numerical model proposed by Buason. Agreement between the theory and experiments i s exceptionally gcod but unfortunately the theory i s over-parameterized and d i f f i c u l t to apply to natural snowpacks. Krouse and Smith point out that the study of water flow i n snowpacks would lend i t s e l f quite well tc a r t i f i c i a l tracing using d i s t i l l e d sea water to simulate r a i n f a l l . To the knowledge of t h i s writer the present study i s the f i r s t attempt to apply t h i s idea to natural snow and therefore the observations are unique. An obvious advantage i s the high degree of c o n t r o l i n parameters allowing access to information that i s often extremely d i f f i c u l t to obtain. The purpose of t h i s f i e l d project i s to investigate the i n t e r a c t i o n between the l i q u i d and s o l i d phases cf water i n 98 the snowpack. The method to be used i s an a r t i f i c i a l tracer enriched i n the isotope oxygen-18 introduced on the top of the snowpack. Temporal changes i n the i s o t o p i c and density p r o f i l e s of the pack w i l l give i n s i g h t into the exchange of tracer and snow. 5.2 The Type Cf Snowpacks Studied It i s often d i f f i c u l t to make generalizations about physical properties of snowpacks because of the i n t e r r e l a t i o n s h i p s that e x i s t between c h a r a c t e r i s t i c parameters. One must c l e a r l y state the physical properties of the snowpack. being studied and conclusions reached must be q u a l i f i e d as applying to that s p e c i f i c type of snow. In addition to t h i s West (personal communication) points out that the geographical . l o c ation seems to a l t e r snow properties and so even the study area maj a f f e c t conclusions. Recognizing the above d i f f i c u l t i e s , experiments were designed such that snow c h a r a c t e r i s t i c s varied a great deal between successive t r a c i n g experiments. Therefore some generalizations can be made i f the same phenomenon i s observed i n d i f f e r e n t types of snow. However i t i s important to note that a l l tracing experiments were conducted on Ht. Seymour, B r i t i s h Columbia and therefore l i t t l e can be said about the v a l i d i t y of the conclusions reached i n t h i s experiment i n other locations. I t i s the a u t h o r s subjective opinion that the snowpacks studied were 99 s u f f i c i e n t l y d i f f e r e n t that r e s u l t s are most l i k e l y applicable to many other l o c a l i t i e s . It i s f e l t that the conclusions reached for cold, sub-zero snowpacks are va l i d i n general but the study of the one isothermal s i t u a t i o n y i e l d s l i t t l e infomation. 5.3 Snowpack Parameters Heasured The l i s t of physical parameters that must be specified t o characterize a snowpack i s extremely long (Colbeck, 1974b). It was recognized from the beginning that measurement of a l l these parameters would require so much e f f o r t that the number of i n d i v i d u a l tracing experiments would be limited to one or two. It was judged more important to l i m i t the parameters studied and increase the number of tracing experiments to s i x . For t h i s reason the parameters recorded, both before and a f t e r the tracer was applied, were: 1. temperature 2. density 3. i s o t o p i c composition 4. positions and c h a r a c t e r i s t i c s of s t r a t i g r a p h i c layers and a general description of snow texture It would have been b e n e f i c i a l to measure the r a t i o of l i q u i d water to snow at various times and depths, and indeed the information i s useful, but the calorimetry used would have 100 been extremely time consuming and so was neglected. 5.4 Experimental Procedure When studying water movement in snow, horizontal layers that are impermeable to water can d r a s t i c a l l y a l t e r flow patterns (Colbeck, 1973). For t h i s reason experimental technique was varied s u f f i c i e n t l y to detect the r e l a t i v e amounts of d i r e c t i o n a l flow. The d i f f e r e n t methods of monitoring the water flow were: 1. Onconstrained flow i n natural snow with layering. 2. Flow i n non - s t r a t i f i e d snow constrained to remove any horizontal flow component. 3. Flow i n layered snow constrained to the v e r t i c a l d i r e c t i o n . The most e f f e c t i v e method of studying the i s o t o p i c d i s t r i b u t i o n i n the snow was found to be through the use of snow pi t s as described by wast (1972). S l i g h t modifications were made to West 1s procedure. The sampling tubes consisted of a s t a i n l e s s s t e e l tube approximately 36" long and one-half inch i n diameter. These sampling tubes were inserted perpendicularly into the working face of the snow p i t with a twisting motion to prevent freezing and compaction. The unusual dimensions of the tubes allowed us to obtain an extremely long snow sample and thus short period variations were f i l t e r e d out i n the actual sampling. The diameter was chosen so that; the required amount of 1 0 1 sample was obtained with a si n g l e tube i n s e r t i o n . I t was not unusual to observe compaction i n the sampling tube but t h i s did not seem to cause complications, as w i l l be shown by the mass balance studies. The p i t was normally dug less than one hour before the time the tracer was applied and so the edge e f f e c t of the open p i t was assumed minimal. A perpendicular l i n e was marked on the p i t wall and samples taken at four to s i x inch i n t e r v a l s . Densities and i s o t o p i c compositions of these samples were l a t e r determined in the laboratory. Temperatures were taken and a general description of snow structure and stratigraphy was made. The i s o t o p i c a l l y enriched tracer was then sprinkled on the surface of the snow above the working face. After two to f i v e hours, and at intermediate times, the snowpit was resampled and the same information recorded. In two of the three p i t sampling experiments a forty-four inch square lysimeter was placed approximately f i v e feet below the surface of the snow and i n the working face of the p i t . The tracer never reached the lysimeter in the case of the sub-zero snowpack and so we conclude that i t either had a strong horizontal v e l o c i t y component or i t froze before reaching the lysimeter. Another d i f f i c u l t y e x i s t s i n the method of lysimeter i n s e r t i o n used in t h i s study. When the s l o t was cut into the working face the normal flow that existed i n the snow was interrupted. in f a c t , what probably happens i s that any water flow that was 102 taking place before the introduction of the opening stops and the water begins accumulating above the s l o t u n t i l the po t e n t i a l energy of the water column can overcome the potential b a r r i e r . During t h i s time the water probably flows around the lysimeter. I t may require a day to reach a steady state (Hanciewizk, personal communication) and therefore i t i s not surprising that no e f f l u e n t was co l l e c t e d i n the lysimeter. Hass balance considerations indicate that the tracer probably did not reach the l e v e l of the lysimeter anyway. The importance of horizontal flow i n natural snow was studied by comparing r e s u l t s from snowpits and snow tubes. The snow tubes were square, white a c r y l i c tubes, seven feet long with a cross-sectional area of one square foot. Access ports d r i l l e d every six inches allowed i n s e r t i o n of a s t a i n l e s s s t e e l sample tube and removal of a snow sample. The tubes were inserted into the snow by force from the top. In t h i s manner water flow was constrained to the v e r t i c a l . The conclusions reached i n t h i s portion of the f i e l d project were e s s e n t i a l l y the same as the unconstrained r e s u l t s obtained from the p i t s . Therefore we conclude that flow i n cold snow, with limit e d * l a y e r i n g , i s e s s e n t i a l l y v e r t i c a l . This supposition w i l l be investigated i n the next chapter. In two cases water flow through homogeneous snow without layering was studied. In these instances the seven foot long tubes were f i l l e d from the top with fresh snow that had f a l l e n within the l a s t t w o d a y s . T h e s n o w was 1 ° 3 ' thoroughly mixed before being introduced into the tube. The i s o t o p i c a l l y enriched tracer was sprinkled on the top of the column of snow and was sampled a f t e r two or three hours. O r i g i n a l i s o t o p i c composition was assumed to be constant (measured by taking four aliguots of the snow as i t was inserted in the tube). I n i t i a l densities were calculated by assuming a constant density gradient and by assuming conservation of mass. Results from these experiments show the interaction between the l i g u i d and s o l i d phases of water extremely well. Unfortunately, i t was not p r a c t i c a l to measure temperature variations i n these cases. In a l l , s i x independent tracing experiments were conducted i n the snow on Mt. Seymour during the months of January through Harch, 1974. The variety of snow encountered enables one to make general statements about the inte r a c t i o n of snow and percolating water i n sub-zero snowpacks. The i n d i v i d u a l experiments are discussed i n the next chapter. 5 . 5 Uncertainties In Sampling Technique * The method of sampling the snowpack was destructive; that i s , the snow co l l e c t e d before applying the tracer was removed from the system. When the snowpack was sampled at a l a t e r time i t was necessary to take a sample of snow one to two inches away from the o r i g i n a l sampling point. Therefore the l a t e r a l v a r i a t i o n s i n density and is o t o p i c compositions would necessarily have to be smaller than the variations we wished to measure. For t h i s reason a short sampling experiment was conducted. A layer of apparently homogeneous snow s i x inches thick was selected for the experiment. A sample was c o l l e c t e d every three inches along a horizontal l i n e i n t h i s layer. If v a r i a t i o n s existed i n any given horizontal layer we would expect to see them manifest i n the data obtained as long as the scale of the variations was l e s s than a few feet. Since we are interested i n variations i n the order of inches, the experiment should y i e l d the required information. Both the density and the isotopic composition were measured i n the laboratory for each of the ten samples co l l e c t e d . The r e s u l t s are given i n Table 5.1. The experimental uncertainty i n sampling the i s o t o p i c composition of the horizontal snow layer was found to be 0.17. This i s not s i g n i f i c a n t l y d i f f e r e n t than the a n a l y t i c a l precision of the mass spectrometer analyses of 0.14. We can therefore conclude that the sampling technique does not introduce errors into the i s o t o p i c measurements greater than 0.1 DEL. This i s l e s s than the magnitude, of the i s o t o p i c changes we wish to study. The experimental uncertainty i n measuring the density of the horizontal layer was found to be 0.017 for densities i n the neighborhood of .245 gm/cm3. Due to the consistency of the i s o t o p i c r e s u l t s the variation i n the density measurements i s probably not a r e a l feature of the snow but instead i s caused by our method of taking snow samples. As 105 I I I i ISample |Density (gm/cm3)| EEL(x/SHOH) | I I I I I _+ - + - —i I I I I | HI | .265 | -14.70 | I I I I | H2 | .270 | -14.82 | I I I I | H3 | .225 | -14.76 | I I I I | H4 | .223 | -14.94 | I I I I | H5 | .234 | -14.84 | I I I I | H6 | .246 | -14.71 | I I I I | H7 | .233 | -14.95 | I I I I | H8 | .251 | -15.13 | I I I I | H9 | .260 | -14.98 | I I I I | H10 | .242 | -14.53 | I I I I i 1 _ 1 — J |~Hean |"~ .245 I -14.84 | . i ; L 1 J i ; 1— - - , 1 | Sigma | .017 I 0.17 | TABLE 5.1 LATERAL HOMOGENEITY IH A REPRESENTATIVE SNOBPACK previously stated, i t was not uncommon to observe compaction of the snow insid e the s t a i n l e s s s t e e l sampling tubes. I t seems reasonable to assume that the amount of compaction i s l i n e a r l y r e l a t e d to the mass of snow in the sample tube which i n turn i s d i r e c t l y related to the density of the snow. If compaction of the snow i s the source of variation i n density measurements as i s suspected, then i t follows 106 that uncertainties i n density measurements can be represented as having a constant percentage error rather than constant absolute error. From the figures i n Table 5.1 we note that d e n s i t i e s are i n error by seven percent. This i s i n agreement with uncertainties obtained by other workers (Church, personal communication). 5.6 D i f f i c u l t i e s Encountered And Disadvantages In Stable Isotope Methods In Snow Hydrology As i t turns out, snow i s an extremely d i f f i c u l t substance i n which to make measurements. Insertion of any apparatus into the snowpack a l t e r s flow patterns, physical c h a r a c t e r i s t i c s of the snow and even stratigraphy. Digging snow p i t s exposes the working face to abnormal temperatures and edge ef f e c t s can be sensed up to one foot away from the wall. Cross country skiers e a s i l y a l t e r surface densities of snowpacks. Even i f one could study water-snow i n t e r a c t i o n without a l t e r i n g i t s natural state he would find i t an extremely complicated system. Horizontal layering can disturb v e r t i c a l flow to such an extent that a r t i f i c i a l tracing experiments become impossible. Insertion of lysimeters suffers from the d i f f i c u l t y discussed i n section 5.4. Short days and harsh weather also hamper f i e l d measurements. In addition to the above problems the researcher using stable isotopes encounters unique d i f f i c u l t i e s . Compared to dye tracing experiments, the laboratory time and cost of 107 analyzing a water sample are extremely high. It was estimated that every sample obtained for t h i s project took an average of three to four hours f i e l d and laboratory time compared to much less than an hour for dye tracing samples. The cost of an oxygen analysis i s normally about twenty-five d o l l a r s i f done commercially. A more serious drawback to stable isotope techniques in snow hydrology i s that one has no i n d i c a t i o n of what his r e s u l t s w i l l be u n t i l a f t e r he has l e f t the sampling s i t e . For t h i s reason he can not adjust his sampling technique to compensate for unexpected phenomena. He must b l i n d l y proceed, c o l l e c t i n g samples assuming nothing i s going wrong. Therefore errors i n sampling that become evident after mass spectrometer analysis cannot be corrected by a d d i t i o n a l sampling. This i s probably i t s most serious drawback. A f i n a l d i f f i c u l t y one encounters i n f i e l d sampling i s that the amount of tracer one must apply to the surface of the snow must be s u f f i c i e n t to cause appreciable i s o t o p i c changes. T y p i c a l l y the large mass of snow within a few feet of the surface required s i x t y pounds of tracer to cause i s o t o p i c s h i f t s of f i v e DEL units. This i s a serious drawback when the sampling area must be reached cn foot, as i t was i n t h i s experiment. Even considering the disadvantages inherent to stable isotope tracking of water percolation i n snow, i t i s f e l t that the additional information one can gain from i t warrants i t s use. Certainly many of the conclusions of the 108 next chapter could not have been reached by any other method. Careful introduction of a tracer on the surface of the snowpack i s unlikely to introduce changes int o the snowpack that normal rain or meltwater would not have introduced anyway. It s t i l l remains the most natural method that can be used i n snow hydrology and for t h i s reason alone i t s use i s j u s t i f i e d . 109 VI. THE ISOTOPIC TRACING OF HATER HOVEHENT IN SNOW 6.1 Introduction A t o t a l of s i x isotopic tracing experiments were made near Brockton K n o l l on Ht. Seymour, B r i t i s h Columbia during the months of January, February and Hatch in 1974. The s i t e was selected due to the proximity of a remote weather st a t i o n operated by Dr. H. Church of the University of B r i t i s h Columbia and Dr. B. Sagar of Simon Fraser University. The data from t h i s meteorological s t a t i o n were made re a d i l y available. The s p e c i f i c s i t e of the tracing experiments was on the southern side of Brockton Knoll in a r e l a t i v e l y f l a t meadow. Extremely high winds were often encountered at t h i s s i t e and the amount of d r i f t i n g and snow depths were much greater than those at the weather st a t i o n . In spite of the d r i f t i n g at the project s i t e , s t r a t i g r a p h i c layers were nearly always horizontal (an exception to t h i s i s i n experiment P L 3 ) . A l l samples were taken using the s t a i n l e s s s t e e l tubes described i n the previous chapter. These tubes were sharpened on the leading edge i n such a manner as tc prevent loss of snow or c o l l e c t i o n of unwanted snow. Holes i n the snowpack were always checked to ensure complete removal of the snow sample. Snow densities were calculated by weighing the mass of snow i n each sample and dividing by the volume of the s p e c i f i c sampling tube used. The i s o t o p i c composition was- determined from the saime sample for which 110 the density was measured. Temperatures of the snowpack were taken with a mercury-in-glass thermometer, ca l i b r a t e d at the i c e point and the b o i l i n g point. & general description of the position and c h a r a c t e r i s t i c s of s t r a t i g r a p h i c layers was recorded f o r l a t e r reference. Snow texture was categorized i n broad categories; l i g h t powder, medium packed, compact, and i c e . The data obtained f o r each tracing experiment w i l l be presented in the following sections. 6.2 Tracing Experiment P1 On January 19, 1974, an i n i t i a l tracing experiment was c a r r i e d out at the Bt. Seymour s i t e . The main purpose of t h i s experiment was t c study the magnitude of i s o t o p i c changes that would be encountered. For t h i s reason no density data were obtained but the densities were probably within the range of 0.2 to 0.3 gm/cm3. This experiment gave some very i n t e r e s t i n g r e s u l t s showing the possible e f f e c t s which could be monitored i s o t o p i c a l l y . To perform the experiment a p i t s i x and one-half feet deep, eight feet long and four feet wide was dug. Samples representing the i n i t i a l i s o t o p i c composition of the snow were taken immediately. The positions of the sample holes are shown by the closed c i r c l e s on Figure 6.1. The relationships between th e i r location and the s t r a t i g r a p h i c layers i s c l e a r l y shown. D i s t i l l e d seawater with an i s o t o p i c composition of -1.02 DEL r e l a t i v e to IAEA SHOW was placed on top of the 111 • LOW DENSITY SNOW MEDIUM PACKED SNOW COMPACT SNOW ICE LAYERS 70 105- lUo •ja-r-: z<-z-z-î fc<-z-z-z-z: " 5 loO 213 BEFORE TRACER 107 POSITION(CM) • 1 HR AFTER yl.5* HR AFTER % 2.5 HR AFTER TRACER TRACER TRACER Figure 6.1 Sample positions and Stratigraphic Features i n P i t P1 pack. Approximately 15140 ml was dispersed uniformly over an eight foot by three foot area. In addition to t h i s , 1890 ml of the tracer was sprinkled on a one foot diameter c i r c l e one-half foot back from the p i t wall and over each of the four sampling columns shown i n Figure 6.1. It i s a straightforward c a l c u l a t i o n to show that, assuming v e r t i c a l flow, the application of the tracer i n t h i s manner i s equivalent to d i s t r i b u t i n g 34400 ml cf tracer uniformly over the eight foot by three foot area. Snow samples were taken approximately one hour, one and one-half hours, and two and one-half hours after the tracer application. The re s u l t s of the isotopic analyses are given i n Table 6.1. 112 r - T | Depth | T " Time | DEL Before T — r —i | DEL | | After | | 0. | - J -13.81 I -13.12 | | 17.78 | 2.24 | -13.53 | -12.95 I | 35.56 | 2.30 | -13.38 j -13.08 | I 44.1*5 | 0.94 | -13.91 1-13.42 | | 44.45 | 1.44 | -13.91 I -13.39 | | 44.45 | 2.33 | -13.91 | -13.90 | 1 53.34 j 2.36 | -14.26 | -14.49 J | 71.12 | 2.41 | -13.34 I -13.47 | | 80.01 | 1.04 | -13.18 | -12.89 | | 80.01 | 1.54 | -13.18 1-12.93 | | 80.01 | 2.44 | -13.18 I -13.02 | | 88.90 | 2.47 | -13.29 | -12.96 | | 106,68| 2.53 J -13.53 | -13.64 | 1 X . . , . . . X . -X- — J TABLE 6.1 SUMMARY OF DATA P1 There are b a s i c a l l y two things that can be studied from these data; the temporal change i n i s o t o p i c composition at depths of 45 cm and 80 cm and the variation of the iso t o p i c composition with depth due to the tracer application. Both ef f e c t s were e a s i l y seen in t h i s experiment. Figure 6.2 shows how the i s o t o p i c composition of two layers of snow responded to passage of l i q u i d water. The lower curve represents the i s o t o p i c composition of the snow at a depth of 45 cm while the upper curve represents the 113 i s o t o p i c composition at 80 cm. The d e f i n i t e peaks show the retention of l i g u i d water for some time i n the two layers before i t percolated to lower layers. Normally one would in v- i DEPTH 80 cm 7*j 1 1 1 — i 1— T ' —r 1 -1.0 -0.5 0.0 0.5 1.0 t.S 2.0 2.5 3.0 T I M E S I N C E T R A C E R ( H R S ) Figure 6.2 Isotopic Changes with Time of Two Snow Layers expect the peak at 80 cm to lag the peak closer to the surface. In fact, with the broadness of the peak i t i s d i f f i c u l t to either prove or disprove t h i s f a c t . Referring to the s t r a t i g r a p h i c p r o f i l e one sees that the average flow rate between the surface and 45 cm was probably less than the flow rate between 45 cm and 80 cm. Therefore i t would not be at a l l surprising to f i n d that the peak flow at 80 cm lags the peak flow at 44.45 cm by less than 0.5 hours. The main conclusion to be reached from Figure 6,2 i s that oxygen isotopes can c l e a r l y demonstrate the presence cf l i g u i d water i n the snowpack and indeed can be used to determine 114 when water content reaches a maximum at any given layer. The three curves in Figure 6.3 show the o r i g i n a l i s o t o p i c composition of the snowpack ( c i r c l e s ) , the i s o t o p i c composition of the snow two and one-half hours a f t e r tracer application ( t r i a n g l e s ) , and the net change i n i s o t o p i c composition (plus signs). I n i t i a l l y the DEL values ranged DEPTH(CM) Figure 6.3 Iso€opic P r o f i l e of P i t i n Experiment P1 between -14.26 and -13.18. This difference could e a s i l y be attributed to i s o t o p i c variations within the sncw as i t accumulated on Ht. Seymour. After the tracer has percolated through the snowpack the isotopic variation l i e s between -14.49 and -12.89 DEL. What i s even more in t e r e s t i n g i s that the change i n isotopic composition with depth follows the same general pattern as the o r i g i n a l 115 i s o t o p i c v a r i a t i o n . It should be noted that the curve representing the change i n is o t o p i c composition i s independent of both the o r i g i n a l composition and f i n a l composition of the snowpack. What t h i s feature i s e s s e n t i a l l y t e l l i n g us i s that the passage of l i q u i d water through the snowpack has enhanced the i s o t o p i c variations i n the snowpack. This i s an exact contradiction to the observations of the researchers referred to i n Chapter I which indicated that meltwater tends to decrease isotopic variations i n the pack. The solution to t h i s dilemma may be that meltwater tends to create isothermal snowpacks at 0°C, whereas t h i s project was conducted i n sub-zero snow. I t i s believed the i s o t o p i c enhancement observed i n t h i s tracing experiment was the f i r s t such case ever found. Due to the high c o r r e l a t i o n between the i n i t i a l i s o t o p i c p r o f i l e and the change i n is o t o p i c composition af t e r application of the tracer, i t seems reasonable that the o r i g i n a l i s o t o p i c v a r i a t i o n was a r e s u l t of water flow i n the snowpack and not of i s o t o p i c variations i n the snow as i t was deposited. During the week preceding t h i s tracing experiment heavy p r e c i p i t a t i o n was recorded at the meteorological station and was most l i k e l y i n the form of r a i n based on temperature readings. Therefore, i t i s reasonable to assume that a great deal of water had passed through the snowpack since the snow had f a l l e n . The o r i g i n a l i s o t o p i c pattern found i n 1 16 the snow could well have been caused by water passage. One can speculate as to what i s causing the i s o t o p i c v a r i a t i o n with passage of water. The best example of the high c o r r e l a t i o n between i n i t i a l and net change in i s o t o p i c compositions i s near the i s o t o p i c minimum at 55 cm depth. The question then a r i s e s : Is there some underlying physical feature of the snowpack that could cause the observed is o t o p i c patterns. Beferring to Figure 6.1 shows that a three inch layer of medium packed snow does indeed separate the samples taken at 53 cm and 71 cm. Therefore we conclude that either s t r a t i g r a p h i c horizons or snow compaction seem to have an e f f e c t on i s o t o p i c d i s t r i b u t i o n s in cold snow. The curve representing the change i n i s o t o p i c composition has several features which can be explained. The i n i t i a l portion of the curve does not have high c o r r e l a t i o n with the i n i t i a l i s o t o p i c p r o f i l e . This could very well be a r e s u l t of disturbing the i n i t i a l s t r a t i g r a p h i c features of the snowpack when applying the tracer. The disturbance could well reach to the 15 cm depth. Another possible explanation i s that since the point at 0 cm depth i s an extrapolation cf measured data, our extrapolation may have been i n error. The portion of the difference curve above 60 cm i s decreasing monotonically with depth. Since the i s o t o p i c composition of the tracer was -1.02 DEL we would expect the snow to be shifted towards more positive DEL values. As the l i q u i d percolates through the snow two things happen; one, a 117 substantial portion of the o r i g i n a l tracer freezes and cannot a f f e c t snow at lower depths and two, the l i q u i d phase becomes contaminated with the o r i g i n a l snow and becomes i s o t o p i c a l l y l i g h t e r . Both of these e f f e c t s help explain the i n i t i a l monotonically decreasing c h a r a c t e r i s t i c encountered i u many of the tracing experiments. The portion of the difference curve between 45 cm and 75 cm i s negative. A natural guestion to ask i s how can the snow become i s o t o p i c a l l y l i g h t e r when the tracer applied was enriched i n the heavy isotope? The solution to t h i s dilemma l i e s i n the fr a c t i o n a t i o n of i s o t o p i c species as water freezes or conversely as snow melts. The heavier i s o t o p i c species (H 0 1 8) tends to freeze before the l i g h t e r species. Conversely the l i g h t e r i s o t o p i c species (H 0 1 6) w i l l melt at a higher rate than the heavy species. Suzuoki and Kimura (1973) show that the fr a c t i o n a t i o n can be as large as 3 DEL units for an equilibrium system. Since the heavy isotope i s p r e f e r e n t i a l l y removed from the l i q u i d phase i t follows that the l i q u i d phase gets progressively l i g h t e r with increasing depth. Therefore isotopic changes i n the negative d i r e c t i o n are r e a l i z a b l e . The i s o t o p i c minimum at 55 cm probably occurs because of the medium packed snow layer. The amount of l i q u i d that i s frozen per centimeter of snow increases i n compact snow layers. Therefore a substantial portion of the remaining i s o t o p i c a l l y l i g h t l i g u i d phase i s removed i n the packed snow causing the iso t o p i c minimum. 118 The enrichment of the snow i n the heavy isotope between 75 cm and 90 cm i s d i f f i c u l t to explain. One can speculate that the downward continuation of the heat wave encountering the low density snow causes substantial melting to occur depleting the snow i n the l i g h t isotope. This could also explain the i n f l e c t i o n point at 90 cm as the point where the released l i q u i d phase begins refreezing. Isotopic conservation does e x i s t i n the snow between 70 cm and 105 cm depth which supports the above speculation. Density measurements would have added more weight to t h i s argument. The following tracing experiments w i l l more c l e a r l y demonstrate the features of the curve discussed. In fact, the arguments presented here include information from the other tracing experiments. The feature most c h a r a c t e r i s t i c of experiment P1 i s the high c o r r e l a t i o n between the i n i t i a l i s o t o p i c p r o f i l e and the change i n i s o t o p i c composition. The implications of t h i s w i l l be discussed l a t e r . 6.3 Isotopic Tracing Experiment T1 Two tracing experiments were performed i n unnatural conditions. The white a c r y l i c tubes described i n the previous chapter were f i l l e d with snow that had f a l l e n within the l a s t day. The snow was thoroughly mixed before being placed in the tube. An interesting observation was made concerning the i s o t o p i c uniformity within the snow from a single storm. The snow that went into the tubes was sampled four times 11* before mixing. I t i s most probable that a l l the snow came from a s i n g l e storm since only the upper six inches of snow was used and i t had been snowing heavily immediately before the experiment. Normally one would expect that the snow over the f i f t y square foot area from which the snow was co l l e c t e d would have uniform i s o t o p i c composition. Such was not the case. The is o t o p i c composition of the four snow samples col l e c t e d varied from -14.95 to -17.88 DEL• The most reasonable explanation of t h i s observation i s that the i s o t o p i c composition of the p r e c i p i t a t i o n changes due to the depletion of the reservoir and f r a c t i o n a t i o n between the system and the p r e c i p i t a t i o n . Such observations have been made by other researchers who were studying the problem more cl o s e l y (Judy et a l . # 1970). The amount of tracer used was 7070 ml. Its DEL value was -1.47 and i t s temperature at the time of application was +4.0 °C. The r e s u l t s of t h i s a r t i f i c i a l tracing experiment are given i n Table 6.2. As expected the unnatural s i t u a t i o n gives r e s u l t s that are more straightforward than the natural s i t u a t i o n discussed i n the previous section. The i n i t i a l densities were calculated by assuming conservation of mass and a constant density gradient that p a r a l l e l e d the deep portion of the density curve (after t r a c e r ) . Both the density measured after the tracer was applied and the calculated i n i t i a l density curves are shown i n Figure 6.4. The + curve represents the change i n density. The 120 f |Depth | cm I Time |Hrs. " 1 T" | Density | | Before | Density j After | — T- DEL | Before | — — • T DEL | After | I 0. ! . 1 -137 | .325 | -16.25 | -12.99 | |15.24 I 1.85 I .153 | .295 | -16.25 | -13.18 | |45.72 | 2.01 I .184 | .211 | -16.25 | -13.70 | |76.20 | 2.10 I .215 | .225 | -16.25 | -14.65 | |106.68 | 2.16 | .247 | .245 | -16.25 | -15.89 | |137.16 1 2.23 | .278 | .312 | -16.25 | -15.99 | |167.64 1 2.30 I .309 | .331 | -16.25 | -16.68 | 1213.36 1 " | .356 j .37 | -16.25 | -16. 25 | I _ . . j . . j J _ — i . ,A. i TABLE 6.2 SOHBAfiY OF DATA— T1 large density increase i n the f i r s t 45 cm implies that the tracer did not penetrate past that point i n the snow. However, the i s o t o p i c data t e l l guite a d i f f e r e n t story. Figure 6.5 i s a graphical presentation of the i s o t o p i c measurements. It i s quite clear that the tracer affected the snow column to a depth of over one meter. Therefore i t seems evident that a portion of the snow i n the upper part of the column melted as the tracer percolated through i t . At the same time some of the i s o t o p i c a l l y heavy tracer froze. As i t turns out the amount of o r i g i n a l tracer freezing and snow melting between 45 and 95 cm was nearly equal r e s u l t i n g in only a small density increase but a sizable i s o t o p i c 121 UJ a. to 2 (X I <_)° 0.0 90.0 120.0 DEPTH(CM) 210.0 240.0 Figure 6.4 Variation of Density with Depth T1 UJ o CO •z. cr x <_> 0.0 T 30.0 O Before Tracer A After Tracer + Net Change 1 r 60.0 90.0 120.0 DEPTH(CM) 150.0 180.0 210.0 240.0 Figure 6 . 5 Isotopic Composition as a Function of Depth T 1 enrichment. E s s e n t i a l l y a l l the o r i g i n a l tracer had mixed with thesnow i n the f i r s t meter. The water that was 122 o r i g i n a l l y in the snowpack s t i l l existed a t a depth of one meter and cbntinued to percolate through the lower portion of the tube accounting for the small increase i n density. Figure 6.6 presents two of the curves i n the previous two graphs i n a manner that i s more suitable f o r comparing density and i s o t o p i c changes. It i s evident that some of the change i n density i s due to the tracer freezing. The O Density Variations A Isotopic Variations ~l 1 1 T — 1 1 90.0 . 120.0 150.0 160.0 210.0 240.0 DEPTH[CM) Figure 6.6 The Correlation Between Isotopic and Density changes T1 c o r r e l a t i o n c o e f f i c i e n t between the two curves i s 0.76 which i s f a i r l y high, meaning that over half the change i n density can be attributed to a simple freezing of the tracer. It does indicate a more complicated process i s also occurring since otherwise a higher c o r r e l a t i o n would have been obtained. This tends to support the arguments presented above. 123 6.4 Isotopic Tracing Experiment T2 An experiment very s i m i l a r tc experiment T1 was conducted a week l a t e r on February 1, 1974. The sampling i n t e r v a l was decreased to s i x inches from twelve. Snow temperatures of -2.5°C were su b s t a n t i a l l y colder than the -1.0°C temperatures of experiment T l . This should lead to higher correlations between iso t o p i c and density changes. The tracer employed had a DEL value of -1.31 and a temperature of 4.5°C when applied. Again 7070 ml cf tracer was used. I n i t i a l densities were calculated as in the previous section. Large i s o t o p i c variations between -14.36 and -18.65 again existed i n the four samples of snow co l l e c t e d as the tube was f i l l e d . The r e s u l t s of the experiment are found i n Table 6.3. The i s o t o p i c pattern obtained i s i n Figure 6.7. I t appears that the tracer only reached a depth of 45 cm which i s considerably less than obtained for the previous experiment. The colder snow temperatures probably account for t h i s observation. The large discontinuity i n i s o t o p i c composition below 90 cm i s cause for concern. It seems t e a l since the trend continues for three sampling i n t e r v a l s . I t probably i s a manifestation of inadequate mixing of the snow before i n s e r t i o n i n the sampling column. I t i s most l i k e l y not a r e s u l t of water flow. The density information, found i n Figure 6.8, indicates sizable density changes e x i s t up to 30 and 60 cm from the top of the snow column. This agtees reasonably well with 124 r" - 1 — - r - •T - r •— " x — : |Depth | cm |Time | |Hrs. | Density Before | Density | After | DEL j Before | DEL | After |0. i - 1 . 140 | .351 | -16.61 | -11.84 | 15.24 1 2.03 | . 152 | .312 I -16.61 | -12.70 I30.48 1 2.15 | . 163 I • 178 | -16.61 | -14.81 I45.72 I 2.20 | . 175 | .176 | -16.61 | -15.89 I60.96 j 2.25 | .187 | .241 | -16.61 | -15.52 |76.20 | 2.27 | . 198 I .218 | -16.61 | -15.99 191.44 I 2.32 | .210 | .222 | -16.61 | -15.61 | 106.68 I 2.33 | .222 i .211 j -16.61 | -17.80 | 121.92 I 2.43 | .233 | .220 | -16.61 | -17.68 |137. 16 I 2.47 | .245 | .231 | -16.61 | -17.17 |167.64 I 2.52 | .268 | .324 I -16.61 | -16.16 |213.36 I - I . 303 | .295 | -16.61 | -16.61 i - j . x. . j . . _ . ..x . j TABLE 6.3 SUMMARY OF DATA T2 our estimate from the i s o t o p i c p r o f i l e . It would seem that the colder snow s i m p l i f i e s the int e r a c t i o n between so l i d and l i q u i d phases i n the snow. Simple freezing of the tracer predominates and l i t t l e snow seems to be raised enough i n temperature to bring about melting. Figure 6.9 shows the relationship between is o t o p i c changes and density changes. The co r r e l a t i o n c o e f f i c i e n t between the two sets of data i s 0.92, implying that e s s e n t i a l l y a l l the int e r a c t i o n that occurred between the 125 8 IN "'CO O Before Tracer A After Tracer + Net Change \ f 1 f 1 I 1 J V S : i i 1 'v / i 1 1 1 1 0.0 30.0 60.0 90.0 120.0 150.0 160.0 210.0 240.0 DEPTH(CM) Figure 6.7 Isotopic Composition as a Function of Depth T2 to LJ UJ 60.0 90.0 120.0 DEPTH(CM) 150.0 160.0 210.0 240.0 Figure 6.8 Density as a Function of Depth T2 s o l i d and l i g u i d phase was the freezing of the tracer. 126 d X c_> O Density Variations A.Isotopic Variations 90.0 ,1 120.0 DEPTHICM) ' T i 210.0 240.0 Figure 6.9 The Correlation Between Isotopic and Density Changes T2 We conclude from the two tracing experiments i n homogeneous, unlayered snow that, neglecting complicating e f f e c t s of rapid density changes or s t r a t i g r a p h i c features, the tracer simply freezes into the snowpack with l i t t l e of the o r i g i n a l pack melting. The colder the snowpack the more dominant i s the e f f e c t . As snow approaches warmer temperatures the i n t e r a c t i o n between l i q u i d and s o l i d phases increases and displacement of material o r i g i n a l l y in the snowpack begins. 6.5 Isotopic Tracing Experiment T3 The i n s e r t i o n of the a c r y l i c snow tubes into the natural snow proved most d i f f i c u l t . Ey welding the s t a i n l e s s s t e e l knife edges on the leading edge of the tubes, enough strength was obtained to allow the i n s e r t i o n 127 of the snow tube into natural snow. It should be noted that the a c r y l i c tubes used i n t h i s portion of the experiment become quite b r i t t l e at sub-zero temperatures and therefore are probably not the best material to use in studies of t h i s kind. The o r i g i n a l i sotopic composition and densities were sampled by taking four aliguots of snow immediately outside the a c r y l i c column at the depths corresponding to the locations of the access ports i n the snow tubes. The r e t r i e v a l of the snow samples from the s t a i n l e s s s t e e l tubes normally required the use of a plunger to force the snow out i n t o the c o l l e c t i o n b o t t l e . This did not seem to affect the snow densities measured. I t i s possible that some systematic error was made i n c a l c u l a t i n g the densities but t h i s i s only a supposition. I t i s important to note that the i n i t i a l densities in experiment T3 are questionable. It i s f e l t that the trend shown i n the i n i t i a l d e n sities i s correct but that the magnitudes are i n error by some constant factor. The data from t h i s experiment are presented i n Table 6.4. Since the i n i t i a l densities were unrealizably small and d i f f i c u l t i e s existed i n their determination, a l l i n i t i a l d ensities were multiplied by 6.56 to force conservation of mass. These are probably the most r e a l i s t i c densities that can be obtained from the data. The density and iso t o p i c p r o f i l e s are given in Figures 6.10 and 6.11 respectively. The i n i t i a l density p r o f i l e i s 128 r - i — i ~ T— - i ~ i |Depth |Time | Density | Density | DEL | DEL | cn |Hrs. | Before | After | Before | After i • • . , i i J i i l r J J | i i I 1 12.7 1 1 .190 I • 195 | -18.00 | -16.62 |27.94 1 2.60 | .210 | .229 | -15.40 I -13.08 I 43.18 1 2.63 | .249 | .355 I -14.84 | -11.92 |58.42 1 2.67 | .236 | .260 I -20.72 | -21 . 12 |73.66 1 2.70 | .262 1 .345 I -11.47 | -11.39 |88.90 1 2.73 | .295 1 .363 1 -12.14 | -11.66 1104.14 1 2.77 | .295 1 .272 I -11.39 | -11.08 |119.38 1 I .308 1 .240 | -10.Q0 | -9.62 i __„ - J L J L . .j _ .j i. . j TABLE 6.4 SUHHARi OF DATA—T 3 that obtained a f t e r multiplying by the scaling factor of 6.56. The i n i t i a l density p r o f i l e shows a nearly l i n e a r density increase with depth. The density inversion near 60 cm may not be r e a l i f one considers magnitudes of the err o r s . The density p r o f i l e after the tracer was applied c l e a r l y accentuates both the density increase at 45 cm and the density minimum at 60 cm. The i s o t o p i c p r o f i l e indicates that e s s e n t i a l l y a l l the tracer froze out before reaching 60 cm depth, i n very good agreement with the density data. The density decrease near 105 cm depth has no clear explanation and may be an error i n sampling. Two points need to be made concerning the r e s u l t s of DEPTH(CM) Figure 6.10 The Variation of Density with Depth— r T 3 DEPTH(CM) Figure 6.11 Isotopic Variations with Depth—-T3 t h i s experiment. F i r s t , i t i s evident that again density variations are causing enhancement of i n i t i a l i s o t o p i c 130 features of the snow. The second point i s that the i s o t o p i c r e s u l t s i n cold snow consistently give very believable r e s u l t s , whereas i t i s much more d i f f i c u l t to obtain good density measurements using density tubes. I t would seem easier to obtain i s o t o p i c a l l y good snow samples than samples with correct density information. This would support the use of stable isotopes i n snow hydrology. 6.6 Isotopic Tracing Experiment PL2 A most informative experiment was conducted on March 3, 1974. By t h i s time procedures had been developed and tested to such an extent that samples could be r e l i a b l y c o l l e c t e d . ' The snow being studied had f a l l e n during the preceding week. I t was apparently uniform i n texture and no v i s i b l e layering was found. By t h i s time i t had become obvious that water flow i n t h i s type of snow was predominately v e r t i c a l and so sampling was done only i n a single v e r t i c a l column. The samples were coll e c t e d at the positions shown in Figure 6. 12. As i s shown up to four aliguots were taken i n some instances. The p i t f o r t h i s experiment had teen dug the previous day to enable a longer i n t e r v a l cf time to pass between ap p l i c a t i o n of the tracer and f i n a l sample c o l l e c t i o n . March 3, 1974 was an extremely harsh day with temperatures of -8°C, extremely high winds and heavy snows. For t h i s reason the tracing experiment had to be cut short as conditions became unbearable for the researchers. 131 SNOW SURFACE 12" SCALING i- 1 L • BEFORE TRACER A 2 HOURS AFTER TRACER Figure 6.12 Positions of Samples Taken i n Tracing Experiment PL2 nevertheless r e s u l t s obtained from t h i s experiment were extremely good. The data col l e c t e d i n t h i s experiment are presented in Table 6.5. For the f i r s t time, temperatures were recorded before and aft e r the tracer was applied. They proved to be a very useful i n d i c a t i o n of the progress of the l i q u i d i n the snowpack. The temperature p r o f i l e from t h i s experiment i s given i n Figure 6.13 and would seem to imply that a great deal of the tracer has accumulated i n the top 40 cm of the snow. The density information i s displayed i n Figure 6.14. As can be seen the i n i t i a l density p r o f i l e c l e a r l y manifests the homogeneity of the snowpack. The c o r r e l a t i o n A A A A A A ' A • A A • A • A • A NO VISIBLE LAYERING LYSIMETER 132 r T — — • r - T " T — r- |Depth | cm |Time | IHrs. | Density | Before | Density After | DEL | j Before | DEL After |0. I - '. .038 | 0. | -15.98 ( -17.18 115.24 I 1.65 | .051 | .034 | -14.82 | -15.04 |30.48 I 1.72 | .085 | . 153 | -12.84 | -9.07 |45.72 I 1.82 | .141 | .119 | -13.60 | -10.89 | 60.96 1 1.92 | .174 | .247 | -14.78 | -14.78 I 76.20 I 2.04 | .156 | .196 | -12.37 | -11.73 191.44 I 2. 14 | . 166 I .233 | -10.85 | -11.03 | 106.68 1 2.25 | .262 | .340 | -14.63 | -15.49 |124.46 1 - 1 . 350 I .423 | -16.52 | -17.72 • .a_ — L . i , J . X . TABLE 6.5 SDHHABY OP DATA—PL2 c o e f f i c i e n t between i n i t i a l density and depth i s 0.95, which implies simple compression and few inhomogeneities. The most notable feature i n the density p r o f i l e after the tracer was applied i s the abnormality at 45 cm depth. This i s c e r t a i n l y unexpected since the composition of the snow was o r i g i n a l l y so uniform. Above 45 cm the c o r r e l a t i o n between i n i t i a l and f i n a l densities i s 0. Below 45 cm the cor r e l a t i o n i s quite high and the corves p a r a l l e l each other extremely well. This high c o r r e l a t i o n implies errors in density measurements are much less than the accepted 7 percent. 133 T 160.0 DEPTH(CM) Figure 6.13 Temperature P r o f i l e for Experiment P L 2 160.0 DEPTH(CM) Figure 6.14 Density Variations with Depth PL2 The i s o t o p i c r e s u l t s of t h i s experiment are displayed 134 in Figure 6.15. Relatively large i s o t o p i c changes are O Before Trader A After Tracer + Net Change T 40.0 60.0 80.0 DEPTH(CM) Figure 6.15 Isotopic Variations with Depth PL2 evident in the f i r s t 50 cm of the snow column. Below 60 cm i s o t o p i c changes are smaller and, i n general, negative. I t would seem that the discontinuity i n the density p r o f i l e at 4 5 cm i s indeed aff e c t i n g the d i s t r i b u t i o n of the isotopes. As i n the other experiments i s o t o p i c peaks were enhanced when water passed through the snowpack. I t i s in t e r e s t i n g that the i s o t o p i c maximum at 30 cm i s enhanced much more than the maximum at 90 cm even though the l a t t e r peak was i n i t i a l l y twice as large as the upper peak. This seems to indicate that some parameter must have been d i f f e r e n t during the tracing experiment than during the percolation that caused the o r i g i n a l p r o f i l e . The temperatures encountered on t h i s day were much lower than most temperatures of the 135 previous week and therefore reduced penetration of the pack i s to be expected. Figure 6.16 allows easy comparison of i s o t o p i c changes and density changes. Again something peculiar happens at 15 DEPTH(CM) Figure 6.16 Correlation Between Isotopic Changes and Density Changes PI2 cm depth. Above 45 cm the co r r e l a t i o n between the two curves i s 0.79 implying that most of the increase in density i s a r e s u l t of the o r i g i n a l tracer freezing. Belcw 45 cm depth the c o r r e l a t i o n i s -0.80. This means that i s o t o p i c a l l y l i g h t water generated i n the upper 45 cm of snow i s refreezing at the lower depths causing increased density but a smaller o 1 8 / 0 1 6 r a t i o . The temperature p r o f i l e tends to support t h i s observaation since heat was transported below the 45 cm depth. The source of the heat could e a s i l y be that given off as the l i q u i d freezes. 136 6.7 Isotopic Tracing Experiment—-PL3 The f i n a l tracing experiment was conducted cn Harch 23, 1974. Relatively warm weather occurred just before t h i s date and as a re s u l t a great deal of meltwater had penetrated into the snowpack. The meltwater created several s t r a t i g r a p h i c layers of substantial s i z e as shown in Figure 6.17. The l i q u i d content of the snowpack was high enough to • MEDIUM PACKED SNOW COMPACT SNOW ICE THIN ICE LAYERS BEFORE TRACER 3.U HOURS 1.5* HOURS • AFTER • AFTER TRACER TRACER Figure 6. 17 Snow Stratigraphy and Sample Location PL 3 create an isothermal snowpack at 0°C. The st r a t i g r a p h i c horizons were not horizontal but were oriented i n such a way as to cause water to move away from the p i t wall and to the l e f t of the fi g u r e . For t h i s reason the samples were taken 137 at an angle to the v e r t i c a l . The densities encountered i n t h i s f i n a l experiment f a r exceeded any of the previous experimental values. The densities were t y p i c a l l y .45 gm/cm3 and t h i s introduced a problem with the amount of tracer applied.. Approximately 150 kilograms of snow existed i n the portion of the snowpack studied. The amount of tracer applied was only 14 kilograms. This r a t i o of nearly eleven times more snow than tracer should be compared with experiment PL2 where the r a t i o was a more reasonable f i v e and one-half. The r e s u l t s of t h i s experiment are nearly uninterpretable. The data are presented i n Table 6.6. The i s o t o p i c and density variations with depth are shown i n Figures 6.18 and 6.19 respectively. I n i t i a l l y the i s o t o p i c composition tends to decrease with depth which i s what one would expect i f meltwater ( i s o t o p i c a l l y l i g h t ) formed i n the upper part of the snow column, percolated to lower depths and refroze. At depths greater than 50 cm the net i s o t o p i c change i s near zero implying that l i t t l e of the o r i g i n a l tracer percolated past that depth. The i n i t i a l density p r o f i l e shows a gradual increase i n density with depth. The density p r o f i l e after application of the tracer o s c i l l a t e s e r r a t i c a l l y and displays nc obvious c h a r a c t e r i s t i c s . Possibly some ins i g h t into the water flow pattern i s found by di r e c t comparison of the density and is o t o p i c variations shown in Figure 6.20. The co r r e l a t i o n between the two curves above 45 cm i s -0.83. Below that 138 r |Depth | cm i , . , "1 T ~ |Time | |Hrs. | ~ T~ Density | Before | Density After ~l T | DEL | j Before | DEL After I i i i i 1 0 . 1 - 1 . 4 6 9 | . 5 2 8 | - 1 0 . 9 2 | - 1 0 . 7 9 |10.16 1 3 . 1 0 | . 4 1 6 | .411 I - 1 1 . 5 9 | - 1 1 . 2 0 | 2 0 . 3 2 I 3 . 1 6 | . 3 3 4 | . 2 3 9 I - 1 2 . 5 7 | - 1 1 . 5 9 | 3 0 . 4 8 I 1. 4 6 | . 3 5 2 | . 4 2 7 | - 1 2 . 1 0 | - 1 2 . 4 8 | 3 0 . 4 8 | 3.21 . | . 3 5 2 | . 3 4 5 I - 1 2 . 1 0 | - 1 1 . 1 3 | 4 0 . 6 4 | 3 . 2 6 | . 4 0 2 | . 5 5 7 1 - 1 3 . 1 7 | - 1 5 . 4 0 | 5 0 . 8 0 I 3 . 3 3 | . 4 1 7 | . 4 9 4 1 - 1 3 . 3 9 j - 1 2 . 9 8 I 6 0 . 9 6 I 1. 5 6 I . 4 3 1 | . 4 7 2 | - 1 4 . 0 6 | - 1 4 . 6 2 I 6 0 . 9 6 I 3. 41 | . 4 3 1 j . 3 9 7 | - 1 4 . 0 6 | - 1 4 . 2 6 1 7 1 . 1 2 I 3 . 4 8 | . 3 3 3 | . 3 8 4 I - 1 3 . 0 1 | - 1 3 . 0 8 1 8 1 . 2 8 I 3 . 5 3 | . 3 7 8 | .448 | - 1 2 . 6 7 | - 1 2 . 2 6 | 9 1 . 4 4 I 1.61 | .444 | . 5 5 2 | - 1 4 . 0 5 | - 1 4 . 1 3 1 9 1 . 4 4 i 3 . 58 | .444 | . 2 6 9 | - 1 4 . 0 5 | - 1 3 . 9 7 | 1 0 1 . 6 0 1 3 . 6 3 | . 4 3 7 | . 3 6 7 | - 1 4 . 0 4 | - 1 4 . 1 4 L . — i _ _. ± . i,, .x . J _ TABLE 6.6 SOHHABX OF DATA PL3 depth the c o r r e l a t i o n reduces to •0.3. The s t r a t i g r a p h i c p r o f i l e shows the presence of many cl o s e l y packed ice layers just above 45 cm depth which can possibly explain the abrupt change i n c o r r e l a t i o n . Since the c o r r e l a t i o n c o e f f i c i e n t i n the upper 45 cm i s negative i t means that the i s o t o p i c tracer never penetrated into the pack. The quarter inch 139 in tn a 120.0 DEPTH(CM) Figure 6.18 Isotopic Composition as a Function of Depth PL 3 DEPTH(CM) Figure 6.19 Density Variations as a Function of Depth—-PL3 thick i c e layer four inches below the surface of the snow 140 0.0 15.0 30.0 45.0 60.0 75.0 SO'.O 105.0 120.0 DEPTH(CM) Figure 6.20 The Correlation Between Isotopic and Density Changes PL3 most probably caused the tracer to flow h o r i z o n t a l l y and therefore the tracer did not penetrate into the sampled snow. The observed i s o t o p i c differences i n the upper 45 cm of snow must s t i l l be explained. The temperature of the applied tracer was *4oc. higher than usual. Since the snowpack was already at 0°C the heat from t h i s tracer most l i k e l y melted a portion of the o r i g i n a l snow. This would r e s u l t i n 700 grams cf l i g u i d that could be as much as 3 DEL units l i g h t e r than the o r i g i n a l snow. The large minimum near 40 cm may be a r e s u l t of t h i s water refreezing. The conclusions reached i n t h i s experiment are highly speculative but do seem to indicate that very l i t t l e tracer penetrated the snowpack. The presence of horizontal layers 141 would seem to make a r t i f i c i a l tracing experiments inappropriate. 6.8 Isotopic And Bass Balance In The A r t i f i c i a l Tracing Experiments An important consideration i n any tra c i n g experiment i s to see i f the tracer can be accounted f o r . In an i s o t o p i c tracing experiment one should be able to account for both the mass and the is o t o p i c species i f he has chosen the correct physical model. The model used i n t h i s experiment was as simple as possible. The tracer was assumed to flow downward, diverging i n a l l directions at an angle, theta. Since the tracer was dis t r i b u t e d over a rectangular area the snow affected by the tracer occupies the lower portion of a rectangular pyramid. The cross-sectional view of the model i s shown i n Figure 6.21. When the diverging tracer i n t e r s e c t s the p i t wall, i t i s assumed that the tracer stays within the snowpack and i s not l o s t . I t i s cle a r that the sample tubes c o l l e c t some snow that has not been altered by the tracer. For t h i s reason a mixing correction was applied to data where applicable. in t h i s manner the isotopic composition and densities a c t u a l l y correspond to the snow within the pyramid. To test for conservation of mass i t i s only necessary to compute the mass of snow within the pyramid both before 142 AREA OF Figure 6.21 The Physical Bedel Used i n the Study of Hater Flow and after the tracer was applied. The computation was done using a cubic s p l i n e integration of the density data. Since the i n i t i a l d e nsities i n the three experiments u t i l i z i n g the a c r y l i c sample columns were either not measured or questionable, conservation of mass was forced. The r e s u l t s of the mass balance cal c u l a t i o n s are presented i n Table 6.7. As can be seen, the mass i n experiment PL2 i s within 5% of the expected value. Since i t was a more complicated system than any of the a c r y l i c tube experiments <T), i t seems reasonable to make the assumption of conservation of mass i n those cases to obtain i n i t i a l densities. As can also be seen, only 2.6$ of the tracer stayed within the closed system i n experiment PL3. The above calculations are 143 r —r- 1 1 T l — i — r- 1 T2 | T3 ~ T | PL 2 _ T — - -| PL3 — i 1 . t | i n i t i a l mass | 48.9 I 43.9 j 25.5 | 113.0 | 148.4 8 | f i n a l mass I 55.9 1 51.1 | 28.9 | 140.7 | 148.8 j tracer mass | 7.07 1 7.07 | 3.43 I 20.37 | 14.00 |% mass y i e l d | 100 | 100 | 100 I 105 | 92 t . i. , J, X . - i . . .x _ i * a l l masses are i n kilograms TABLE 6.7 CONSERVATION OF NASS COBSIDERATIONS FOR FIVE TRACING EXPERIMENTS those obtained assuming no divergence of the tracer, ( i . e . v e r t i c a l flow). The demonstration of conservation of i s o t o p i c species i s s l i g h t l y more complicated. Using the re s u l t of Appendix III we see that i f i s o t o p i c species are conserved: MASS(TRACER)DEL(TRACER)+MASS(SNOW)DEL(SNOW^^ DEL(AFTER) = MASS (TRACER) + MASS (SNOW) 1 ] The mass and DEL value of the tracer were measured d i r e c t l y . The mass of snow was determined by integrating the i n i t i a l d e n sities. The i n i t i a l DEL of the snow i s calculated by integrating the product of i n i t i a l density, cross-sectional area and DEL over a l l depths. The i n t e g r a l i s normalized by dividing by the i n i t i a l mass. The average DEL value after the tracer was applied was calculated in a simi l a r manner. The r e s u l t s of the above calculations are presented in Table 6.8. The r e s u l t s indicate that the proposed model i s too simple. Neglecting PL 3, an average cf one-third of the 144 1 T l r | T3 T2 | PL2 PL 3 tracer mass |7.07 DEL tracer J-1.47 i n i t i a l mass |48.9 i n i t i a l DEL j-16.25 f i n a l DEL j-15.36 DEL egn. 6.1 |-14.38 0*8 y i e l d |47.3% 7.07 -1.31 43.9 -16.61 -15.80 -14.49 38.2% 3.43 -1.30 25.5 -13.93 -13.06 - 12.43 58. 3% 20 .37 -0.73 113.0 -13.95 -13. 63 -11.93 16.2* 14.00 -1.02 148.4 -12.94 -12.93 -11.91 1.0* * a l l masses i n kilograms ** a l l DEL values r e l a t i v e to IAEA SHOW TABLE 6.8 ISOTOPIC CONSERVATION IN TRACING EXPERIMENTS tracer can be accounted f o r . This implies that a large f r a c t i o n of the tracer must run down the edge of the a c r y l i c sampling tubes and flow horizontally i n the case of PL2. I t i s i n t e r e s t i n g that the r e s u l t s of PL3 indicate nearly complete loss of the tracer as was inferred i n the previous section. I t i s important to note that the low y i e l d does not change any of the conclusions reached but only means the model chosen was too simple. Use of the correct model would not change the q u a l i t a t i v e description of water flow i n snow. 6.9 Conclusions Several d i f f e r e n t types, of snow were studied i n t h i s project. The r e s u l t s of f i v e tracing experiments i n sub-zero snowpacks gave consistent r e s u l t s and several conclusions can be reached. In the three situations where natural snow with layering was studied, the i s o t o p i c peaks 115 were enhanced, which implies, the o r i g i n a l i s o t o p i c p r o f i l e was a manifestation of e a r l i e r water movement in the pack. The locations of these i s o t o p i c peaks can be explained i n terms of density v a r i a t i o n s and/or locations of s t r a t i g r a p h i c layers. The above point i s very important. / Seasonal variat i o n s i n the i s o t o p i c composition of p r e c i p i t a t i o n have been used to study yearly accumulation of snow and c l i m a t o l o g i c a l changes over many centuries (Horner, 1972 Dansgaard et a l . , 1969). However t h i s project indicates that either r a i n or meltwater on a sub-zero snowpack can produce i s o t o p i c maxima and minima that could be f a l s e l y i d e n t i f i e d as yearly snowfall. The power of tracing water movement with stable isotopes was c l e a r l y demonstrated. In conjunction with density changes and temperature changes, the stable isotopes provide insight into what a c t u a l l y happened i n the snowpack. Density measurements alone could not have distinguished what ef f e c t s were due to the o r i g i n a l tracer and what e f f e c t s were caused by l i q u i d released by the heat in the tracer. I t i s also clear that dye experiments are incapable of c l e a r l y i d e n t i f y i n g e f f e c t s caused by melted snow from the snowpack. I t can be speculated that the horizontal component of water flow cannot be neglected even i n uniform snow. The loss of a portion of the tracer in a l l the experiments indicates substantial horizontal flow. 1«6 Although i s o t o p i c measurements require much more time and e f f o r t than density measurements, they seem to be much more r e l i a b l e . It i s r e l a t i v e l y easy to obtain a good is o t o p i c sample but i t was found d i f f i c u l t to acguire r e l i a b l e densities. Further investigations into the problem of water flow i n snow would be well advised to monitor densities with a p r o f i l i n g density gauge rather than with density tubes. Much remains to be done i n the study of water flow i n natural snow. This project has demonstrated the importance of using stable isotopes i f complete understanding i s desired. 147 LIST OF WORKS CONSULTED Ambach, W., Eisner, H., Hoser, H . , Rauert, W. and S t i c h l e r , W. (1971) Results of isotope measurements i n the outflow from the Kesselwandferner glacier i n Oetztal Alps. Annalen der Meteorologie. Neve Foloje, No. 5, 209-212. Arnason, B. (1969a) Equilibrium constant f o r the fr a c t i o n a t i o n of deuterium between i c e and water. Journal of Physical Chemistry. 73, 3491-3494. Arnason, B. (1969b) The exchange of hydrogen isotopes between ice and water i n temperate g l a c i e r s . Earth and Planetary Science L e t t e r s . 6, No. 6, 423-430. Arnason, B., Buason, Th., Martinec, J. and Theodorsson, P. (1972) The r o l e of snow and ice i n hydrology. Proceedings of the Banff symposia, September 1972. Beauregard Press Limited, i , 299-312. Begbie, P.J., Beckinsale, R.D., Freeman, N.J. and Rowell, R.E. (1972) A bakeable changeover valve for high precision mass spectrometric comparison of the isotope composition of gases. Review of S c i e n t i f i c Instruments. 43, No. 10, 1454-1455. Blenkinsop, j . (1972) Computer assisted mass spectrometry and i t s application to rubidium-strontium geochronology. Ph.D. Thesis, University of B r i t i s h Columbia, 109 p. Buason, Th. (1972) Equation cf isotope f r a c t i o n a t i o n between ice and water i n a melting snow column with continuous r a i n and percolation. Journal of Glaciology. 11, No. 63, 387-405. Cary Model 31, Vibrating Reed Electrometer, Instruction manual, Applied Physics Corporation, Monrovia, C a l i f o r n i a . Colbeck, S.C. (1972) A theory of water percolation i n snow. Journal of Glaciology 11, No. 63, 369-385. Colbeck, S.C. and Davidson, G. (1972) Water flow through homogeneous snow. The role of snow and ice in hydrology. Proceedings of the Banff symposia, September 1972. Beauregard Press Limited. 1, 242-257. Colbeck, S.C. (1973) Effects of St r a t i g r a p h i c layers on water flow through snow, U.S. Army Corp of Engineers- CRREL Research Report 311. 148 Colbeck, S.C. (1971a) The c a p i l l a r y e f f e cts on water percolation in homogeneous snow. Journal of Glaciology. 13, No. 67, 85-97. Colbeck, S.C. (1974b) Water flow through snow overlying an impermeable boundary. Water Resources Research. 1 0 , No. 1, 119-123. Coleman, H.L. and Gray, J. (1972) An adjustable gas source i n l e t system for an isotope mass spectrometer. Review of S c i e n t i f i c Instruments. 43, No. 10, 1501-1503. Compston, W. and Epstein, S. (1958) A method for the preparation of carbon dioxide from water vapor for oxygen isotope analysis. Transactions of the American Geophysical Onion. 39, 511-512. Craig, H. (1957) Isotopic standards for carbon and oxygen and correction f a c t o r s f o r mass-spectrometric analysis of carbon dioxide. Geochimica et Cosmochimica Acta. 1 2 , 133-149. Craig, H. (1961a) Standard f o r reporting concentration of deuterium and oxygen-18 i n natural waters. Science. 133, 1833-1834. Craig, H. (1961b) Isotopic variations i n meteoric waters. Science. 1 3 3 , No. 3465, 1702-1703. Daniels, F. and Alberty, R.A. (1967) Physical chemistry. John Wiley and Sons. 3rd e d i t i o n , 767 p. Dansgaard, W. (1953) The abundance of 0*» i n atmospheric water and water vapor. Te l l u s 5, No. 4, 461-469. Dansgaard, W. (1954) The oxygen-18 abundance in fresh water. Geochimica et Cosmochimica Acta. 6, 241-260. Dansgaard, W, (1961) The is o t o p i c composition cf natural waters. Hedd. om Groenland. 1 6 5, 1-120. Dansgaard, W. ' (1965) Stable isotopes in p r e c i p i t a t i o n . T e l l u s . 1 6 , No. 4, 436-468. Dansgaard, W., Johnsen, S.J. , Huller, J. and Langway, C C . (1969) One thousand centuries of c l i m a t i c record from Camp Century on the Greenland i c e sheet. Science J66, 378-381. Deutsch, S., Ambach, W. and Eisner, H. (1966) Oxygen isotope study of snow and f i r n on an alpine g l a c i e r . Earth and Planetary Science Letters. 1 , 197-201. 149 Dincer, T., Hartinec, J . , Payne, E. B. , ana Yen, C.K. (1970a) Variation of the trit i u m and O 1 8 content i n p r e c i p i t a t i o n and snowpack i n a representative basin in Czechoslovakia. Proceedings of the symposium on isotope hydrology, 1970. International atomic eneregy agency, Vienna, 23-42. Dincer, T., Payne, B.R. and Florkowski, T. (1970b) Snowmelt runoff from measurements of tr i t i u m and oxygen-18. Water Resources Research. 6, Bo. 1, 110-124. Duckworth, H.E. (1958) Hass Spectroscopy. Cambridge University Press, London, 206 p. Epstein, S. (1953) A mass spectrometer for the measurement of small differences i n isotope abundance r a t i o s . Hass spectroscopy i n Physics Research. National Bureau of Standards C i r c u l a r 522, 133. Epstein, S. and Mayeda, T. (1953) Variations of the 0* 8 content of waters from natural sources. Geochimica et Cosmochimica Acta. 4, 213-224. Epstein, S. (1959) Researches i n Geochemistry (editor Abelson) Wiley, New York, 217-240. Epstein, S, and Sharp, R.P. (1959) Oxygen isotope variations i n the Halaspina and Saskatchewan g l a c i e r s . Journal of Geology. 67, 88-102. Epstein, S., Sharp, R.P. and Gow, A. (1965) Six-year record of oxygen and hydrogen variations i n the south pole f i r n . Journal of Geophysical Research. 70, 1809-1814. Epstein, S. and Sharp, R.P. (1967) Oxygen and hydrogen isotope variations i n a f i r n core, l i g h t s Station, Western Antarctica. Journal of Geophysical Research. 72, No. 22, 5595-5598. Faurholt, V.C. (1921) Ober die prozesse NB2C00NH* + H*0 ^ (NH*)*C03 und CO* + H*0 ; * H 2CC 3. Z e i t s c h r i f t fur Anorganische Chemie. 120, 85-102. Faurholt, V.C. (1924) Etudes sur l e s solutions agueuses d'anhydride carbonigue et d'acide carbonigue. Journal de Chimie Physique. 21, 400-455. Friedman, I., Hachta, L. and S o l l e r , B. (1962) Water vapor exchange between a water droplet and i t s environment. Journal of Geophysical Research. 67, 2761-70. 150 Friedman, I. and Smith, G.I. (1972) Deuterium content of snow as an index to winter climate in the Sierre Nevada area. Science. 1 7 6 , 790-793. Gerdel, R.H. (1948) The storage and transmission of l i g u i d water i n the snowpack as indicated by dyes. Proceedings of the Western Snow Conference. 81-91. Gerdel, R.B. (1954) The transmission of water through snow. Transactions of the American Geophysical Onion. 35, No. 3, 475-485. v. • • • G o n f i a n t i n i , R. and P i c c i o t t o , E. (1959) Oxygen isotope variations in Antarctic snow samples. Nature. 184, 1557-1558. Gonfiantini, R., T o g l i a t t i , V . , Tongiorgi, E., De Breuck, W. and P i c c i o t t o , E. (1963) Snow stratigraphy and oxygen isotope variations i n the glaciologica1 p i t of King Baudouin Station, Queen Hand Land, Antarctica. Journal of Geophysical Research. 68, 3791-3798. Halsted, R.E. and Nier, A.O. (1950) Gas flow through the mass spectrometer viscous leak. Review of S c i e n t i f i c Instruments. 21, No. 12, 1019-1021. Hoefs, J. (1973) Stable Isotope Geochemistry. Springer-Verlag, New York, 140 p. Hogg, R.V. and Craig, A.T. (1970) Introduction to mathematical s t a t i s t i c s . The Hacmillan Company, New York. 3rd edition, 415 p. Honig, R.E. (1945) Gas flow i n the mass spectrometer. Journal of Applied Physics. .16, 646-654. Itagaki, K. (1967) S e l f - d i f f u s i o n i n s i n g l e - c r y s t a l ice. Journal of the Physical Society cf Japan. 22, No. 2, 427-431. Jackson, H.G., Libby, L.H. and Lukens, B. R. (1973) Heasuremnt of » 80/*«0 r a t i o using a f a s t neutron reactor. Journal of Geophysical Research 3. 78, No. 30, 7145-7148. Judy, C , Heiman, R.H. and Friedman, I. (1970) Deuterium variations i n an annual snowpack. Water Resources Research. 6, No. 1, 125-129. 151 Kistemaker, J. (1953) The influence of f r a c t i o n i z i n g and v i s c o s i t y e f f e c t s i n mass spectrometer gas handling systems. Hass spectroscopy in physics research. U.S. National Bureau of Standards Circular 522. 243-247. Koerner, R.M., Paterson, H.S.B. and Krouse, H.R. (1973) * 80 p r o f i l e i n ice formed between, the equilibrium and f i r n l i n e s . Nature Physical Science. 245, 137-140. K o l l a r , F. (1960) The precise intercomparison of lead isotope r a t i o s . Ph.D. Thesis, University of B r i t i s h Columbia. 107 p. Krouse, H.R. and Smith, J.L. (1972) 0 l 8/0»* abundance variations i n Sierra Nevada snowpacks and t h e i r use in hydrological research. The role of snow and i c e i n hydrology. Proceedings of the Banff symposia, September 1972. Beauregard Press Limited. 1, 24-38. Krouse, H.R. (1973) Stable isotopes i n the study of snow and ice resources. Symposium on advanced concepts and techniques i n the study of snow and i c e resources. U.S. International Hydrological Decade, Monterey. Langham, E.J. (1971) A new mthod of using dye to study meltwater movement within a snowpack. Runoff from snow and i c e , Symposium No. 8, Quebec. 2, 74-81. Langham, E.J. (1973) The occurrence and movement of l i g u i d water i n the snowpack. Symposium on advanced concepts and techniques i n the study of snow and ice resources. U.S.-International hydrological decade, Monterey 1973. Langham, E.J. (1974a) Network geometry of veins i n p o l y c r y s t a l l i n e i c e . Canadian Journal of Earth Sciences. 11, No. 9, 1274-1279. Langham, E.J. (1974b) Phase e q u i l i b r i a of veins in p o l y c r y s t a l l i n e i c e . Canadian Journal of Earth Sciences. 11, No. 9, 1280-1287. Macpherson, D. and Krouse, H.R. (1967) 0 1 8/0** r a t i o s in snow and i c e of the Hubbard and Kaskawulsh g l a c i e r s . Isotope techniques i n the hydrologic cycle- Geophysical Monographs 1, American Geophysical Union, Washington D.C., 180-194. Matsubaya, 0. (1971) Papers from the I n s t i t u t e for Thermal Spring Research, Ckayama University. No 40, 33-40. Matsubaya, 0. (1972) Papers from the I n s t i t u t e of Thermal Spring Research, Okayama University. No. 41, 1-7. 1 5 2 McKay, H.A.C. (1938) Kinetics of exchange reactions. Nature. 1 4 2 , 997-998. McKinney, CR.., McCrea, J.M., Epstein, S., A l l e n , H.A. and Drey, H.C. (1950) Improvements i n mass spectrometers for the measurement of small differences i n isotope abundance r a t i o s . Review of S c i e n t i f i c Instruments. 2 1 , 724-730. Meiman, J.R., Friedman, I. and Hardcastle, K. (1972) Deuterium as a tracer i n snow hydrology. The r o l e of snow and i c e i n hydrology. Proceedings of the Banff symposia, September 1972. Beauregard Press Limited. 1, 39-50. Merlivat, L. and Nief, G. (1967a) Fractionnement isotopigue lous des changements d'etat solide-vapeur et liguide-vapeur de l*eau a des temperatures i n f e r i e u r e s a 0°c. T e l l u s 1 9 , No. 1, 122-126. Merlivat, L., Lorius, C., Hajzqub, M., Nief, G. and Roth, E. (1967b) Etudes isotopiques en profcndeur d»un g l a c i e r en Antarctigue. Proceedings of the symposium on isotope hydrology, 1970. International atomic eneregy agency, Vienna, 671-681. M i l l s , G.A. and urey, B.C. (1939) Oxygen exchange between carbon dioxide, bicarbonate ion, carbonate ion and water. Journal of the American Chemical Society. 61, 534. M i l l s , G.A. and Orey, B.C. (1940) The ki n e t i c s of i s o t o p i c exchange between carbon dioxide, bicarbonate ion, carbonate ion and water. Journal of the American Chemical Society. 62, 1019-1026. Morner, N.A. (1972) Time scale and i c e accumulation during the l a s t 125,000 years as indicated by the Greenland 0>« curve. Geological Magazine. 1 0 9 , No. 1, 17-24. Nier, A.O. (1947) A mass spectrometer for isotope and gas analysis. . Review of S c i e n t i f i c Instruments. J 8 , No. 6, 398-419. Nier, A.O., Ney, E.P. and Inghram, M. G. (1947) A n u l l method for the comparison of two 'ion currents i n a mass spectrometer. Review of S c i e n t i f i c Instruments. 1 8 , No. 5, 294-297. 153 0*Neil, J.R. and Epstein, S. (1966) A method f o r oxygen isotope analysis of milligram quantities of water and some of i t s applications. Journal of Geophysical Research. 71, 4955-1961. 0»Neil, J. (1968) Hydrogen and oxygen isotope f r a c t i o n a t i o n between i c e and water. Journal of Physical Chemistry. 72, 3683-3684. Palevsky, H. , Swank, R.K. and Grenchik, R. (1947) Design of dynamic condenser electrometers. Review cf S c i e n t i f i c Instruments. J8 , Ho. 5, 298-314. Payne, B.R. (1967) Contributions of isotope techniques to the study of some hydrological problems. Isotope techniques i n the hydrological c y c l e , American Geophysical Onion Geophysical Monograph. JJ[, 62-68. Posey, J. and Smith, H. (1957) The equilibrium d i s t r i b u t i o n of l i g h t and heavy waters i n a freezing mixture. Journal of the American Chemical Society. , 79, 555-557. Roether, H. (1970) Water-C0 2 exchange set-up f o r the routine * 86xygen assay of natural waters. International Journal of Applied Radiation and Isotopes. 2 J , 379-387. Russell, R. D., Ostic, R.G. and Stacey, J.S. (1964) A hybrid electrometer preamplifier. Journal of S c i e n t i f i c Instruments. 41, 487. Russell, R.D. and B e l l i s , E.J. (1971) Mass spectrometer power supplies using a s i l i c o n c ontrolled a.c. switch. Mass spectroscopy. 19,, No. 1, 37-47. Russell, R.D., Blenkinsop, J . , Heldrum, R.D. and M i t c h e l l , D. L. (1971) On-line computer assisted mass spectrometry for geological research. Hass Spectroscopy. 19, No. 1, 19-36. Russell, R.D. and Ahem, T. K. (1974) Economical mass spectrometer ion current measurement with a commercial parametric amplifier. Review of S c i e n t i f i c Instruments. 45, No. 11, 1467-1469. Sharp, R.P., Epstein, S. and Vidziunas, I. (1960) Oxygen isotope r a t i o s i n the Blue G l a c i e r , Olympic Mountains, Hashington. Journal of Geophysical Research. 65, No. 12, 4043-4059. Staschewski, D. (1964) Experimentelle bestimmung der Oi e/o»* trennf aktoren i n den systemen C 0 2 / H 2 ° u n < 3 C0 2/D 20. Bunsen Gesellschaft fur Physikalische Chemie. 68, 454-457. 154 Stacey, J.S., Russell, R.D. and K o l l a r , F. (1965) Servo-amplifiers for ion current measurement i n mass spectrometry. Journal of S c i e n t i f i c Instruments. 4 2 , 390-394. Suzuoki, T. and Kimura, T. (1973) D/H and i a 0 / i 6 o f r a c t i o n a t i o n i n ice-water system. Hass Spectroscopy-Original Papers. 2 J , No. 3 , 229-233. Orey, H.C. and G r e i f f , L.J. (1935) Isotopic exchange e q u i l i b r i a . Journal of the American Chemical Society. 57, 321-327. Weichert, D.H., Russell, R.D. and Blenkinsop, J. (1967) A method for d i g i t a l recording for mass spectra. Canadian Journal of Physics. 4 5 , 2609-2619. Heichert, D. H., Russell, R.D. and Blenkinsop, J. (1968) The d i g i t a l recording of mass spectra. Journal of Physics of the Earth. 1.6, s p e c i a l issue, 155-161. West, K. E. (1972) H 2 0 l 8 / B 2 0 1 6 variations i n i c e and snow of mountainous regions of Canada. , Ph.D. Thesis, University of Alberta 123 p. Weston, R. (1955) Hydrogen isotope f r a c t i o n a t i o n between ic e and water. Geochimica et Cosmochimica Acta. 8, 281-284. Whittles, B.L. (1960) Voltage c o e f f i c i e n t of Victoreen high-meg r e s i s t o r s . Review of S c i e n t i f i c Instruments. 31 , No. 2 , 208-209. Whittles, B.L. (1964) Trace lead isotope studies with gas source mass spectrometry. Ph.D. Thesis, University cf B r i t i s h Columbia, 204 p. York, D. (19 69) Least squares f i t t i n g of a str a i g h t l i n e with correlated errors. Earth and Planetary Science Letters. 5 , 320-324. Youden, W.J. (1951) S t a t i s t i c a l methods for chemists. John Wiley and Sons, Inc., New York. 126 p. A 1 . 1 APPENDIX I Property of the DEL Function-Combination Given DEL (A/B) and DEL (B/C) f i n d DEL (A/C) where A,B and C represent d i f f e r e n t water standards with Ote/o** r a t i o s of Ra, Rb and Rc respectively. DEL (A/B) = (Ra/Rb-1)103 DEL (B/C) = (Rb/Rc-1)l0 3 [A 1.2] from A 1.1 and A 1.2 i t i s clear that: Ra= Rb[ DEL (A/B)+103 ]/10 3 [A1.3] Rb- Rc[DEL(B/C)+103 ]/10 3 [M.U] from A L U we obtain the following: Rc=103 Rb/[ DEL (B/C) + 10 3 ] [A1.5] from A1.3 and A1.5 we obtain: Ra/Rc= [ DEL (A/B) + 10 3 ][ DEL (B/C)+103 ]/10* £A1,6] DEL (A/C) = (Ra/Rc-1) 10 3 [A1«7] DEL(A/C)=[ (DEL (A/B) +103) (DEL (B/C+103)/10*-1 ]10 3 [A1.8] DEL (A/C) = DEL (A/B) • DEL (B/C) +DEL (A/B) DEL (B/C)/10 3 [A1.9] A2.1 156 APPENDIX II Property of the DEL Function-Inversion Given DEL (A/B) f i n d DEL (B/A) DEL (&/B)~ (Ra/Bb-1 ) 10 3 [A2. 1] Ra/Rb=[DEL (A/B) + 10 3 ]/10 3 [A2.2] Rb/Ra= 10 3/[ DEL (A/B)+103] [A2.3] (Rb/Ra-1)103= { £-DEL (A/B) ]/[ DEL (A/B) +10 3] } 10 3 [A2.4] DEL (B/A) = -1 0 3DEL (A/B) /£ DEL (A/B) + 10 3 ] £A2.5] A3.1 157 APPENDIX III Isotopic Mixing of Two Hater Samples I f one combines two i s o t o p i c a l l y d i f f e r e n t water samples, the i s o t o p i c composition of the mixture w i l l l i e between the is o t o p i c compositions of the o r i g i n a l l i q u i d s . The question before us then i s to determine the i s o t o p i c r a t i o of the mixture, given the r e l a t i v e amounts of the o r i g i n a l l i q u i d s and t h e i r i s o t o p i c compositions. Define the following q u a n t i t i e s : x = number of m i l l i l i t e r s of l i q u i d A i n mixture y = number of m i l l i l i t e r s of l i q u i d B i n mixture p = number of o » 8 atoms per m i l l i l i t e r i n l i q u i d A q = number of C»* atoms per m i l l i l i t e r i n l i q u i d A r = number of o 1 8 atoms per m i l l i l i t e r i n l i q u i d B s = number of 0»* atoms per m i l l i l i t e r i n l i q u i d B The o l 8/0»* r a t i o s of l i q u i d s A and B are then: R(A)=p/q [A3.1 ] R(B)=r/s [A3.2] Now assume that the number of water molecules i s constant in any given volume of water: p+g=r+s [A3.3] The i s o t o p i c r a t i o of the mixture i s : R (M) = (xp+yr)/(xq+ys) di v i d i n g numerator and denominator by g gives: R (M) = (xa+yb) / (x+yc) [A3. 4] wh ere a=p/q, b=r/q and c=s/q. From equations A3 .1 , A3.2 and A3.2 158 A 3 . 3 i t follows that: B(A)=a, R(B)=b/c ana a=b+c-1 [ A 3 . 5 ] Equations A 3 . 5 can be solved f o r a, b and c giving a=R (A) b=R (B)[R(A )+1 ]/[R ( B ) + 1 ] [ A 3 . 6 ] C = [ R ( A ) + 1 ] / [ R ( B ) + 1 ] i n s e r t i n g equations A 3 . 6 i n t o A 3 . 4 gives: R (H) = {XR (A) [ fi (B) + 1 ]+yB (B) [R (A) + 1 ] } { x [ R { B ) * 1 ] + y [ R { A ) + 1 ] } [ A 3 . 7 ] which i s the desired r e s u l t . A useful approximation f o r R(H) can be made i f the ra t i o s are small as i n the case of o 1 8 / 0 1 6 ( i . e . R<1/450). Making t h i s approximation we obtain: R(M)=[xB(A)+yR(B) ]/[x+y] [ A 3 . 8 ] since we normally determine DEL values r e l a t i v e to a standard having i s o t o p i c r a t i o R (S) we can rewrite A 3 . 8 i n terms of DEL (A) , DEL (B) and DEL (H) where: DEL (A) =[ R (A) /R (S) - 1 ] 1 0 3 with s i m i l a r expressions for DEL(B) and DEL (M). From A 3 . 8 R(M)/R(S)-1=[x[R (A)/R ( S ) - 1 ]*y[R (B)/B(S ) -1 ]}/[X*y] multiplying both sides by 1 0 3 gives: DEL (M) =[ xDEL (A) +y DEL (B) ]/[ x + y ] R « 1 [ A 3 . 9 ] A4.1 1 5 9 APPENDIX IV Isotopic Fractionation and Bayleigh D i s t i l l a t i o n In many cases where molecules are being transported from one system to another, i t i s possible for the molecular species to be transferred at d i f f e r e n t rates. This often r e s u l t s i n changes i n is o t o p i c r a t i o s between systems. I f we l e t x represent the number of one species of molecule and y represent the number of another type of molecule i n the o r i g i n a l sample we can make the following d e f i n i t i o n s : s=x+y [A4.1] where s i s the number of molecules i n the system at any time and: r=y/x [A4.2] where r i s the i s o t o p i c r a t i o i n the system. If we assume one molecular species leaves at a di f f e r e n t rate than the other species i t i s c l e a r that the is o t o p i c r a t i o of the molecules leaving the system at any instant w i l l not be equal to the iso t o p i c r a t i o i n the system. Hathematically t h i s can be written as: y/x=f dy/dx [A4. 3] where dy/dx i s the i s o t o p i c r a t i o of the molecules leaving the system and f i s the separation constant. I t should be clea r that due to fr a c t i o n a t i o n the is o t o p i c composition of the o r i g i n a l system w i l l change as AU.2 160 molecules are removed from the system. Using eguations A4 .1 , At,2 and A4.3 i t i s a straightforward c a l c u l a t i o n to solve for the i s o t o p i c r a t i o of the molecules i n the system as a function of the f r a c t i o n of the o r i g i n a l number of molecules remaining i n the system: ln[s/s<>]=f l n [ r / r O ] / [ 1-f] • ln[ (r+1)/(ro+1) ] [A4.4] where the superscript 0 indicates i n i t i a l values. The above equation can be solved for r numerically using the Newtcn-Raphson method. If the r a t i o s i n equation At.4 are much less than unity then AU.U reduces to: ( r / r o)a/(l-a) = s / s 0 r « i [AU.5J For oxygen isotopes t h i s approximation i s v a l i d and equation A4.5 t e l l s us what r i s as a function of s/s°, the f r a c t i o n of molecules remaining i n the system. This c a l c u l a t i o n was f i r s t suggested by s . D . Russell. Often we are interested i n determining the i s o t o p i c r a t i o of the molecules that have l e f t the o r i g i n a l system instead of the r a t i o of those that have remained. I f we l e t g represent the i s o t o p i c r a t i o of a l l molecules that have l e f t the o r i g i n a l system we can use the r e s u l t of Appendix I I I ( A 3 .8) to write: [sr+(so-s) q ] / s O=r o r « 1 [A4.6] which i s merely a statement of conservation of i s o t o p i c species. From A4.6 we write: q/r°=[ 1-sr/(s<>r0) ]/[1-s/s° ] r « 1 [AU.7] A U . 3 161 substituting AH.5 into A4.7 gives: g / r O = [ i - ( s / s O ) 1 / a ] / [ 1-s / s 0 ] r « 1 which i s the f i n a l r e s u l t . Equations A4.5 and A1.8 can be used i n many di f f e r e n t s i t u a t i o n s one of which would be a Bayleigh D i s t i l l a t i o n process where the i s o t o p i c r a t i o of water vapor may be calculated as a function of the amount of the o r i g i n a l reservoir that has evaporated. A5.1 162 APPENDIX V Determination of a "Best" Weighting F u n c t i o n In many s t u d i e s s e v e r a l experimental e s t i m a t e s o f a s i n g l e value are o b t a i n e d . O f t e n i t i s f e l t t h a t some of these e s t i m a t e s are more r e l i a b l e than o t h e r s and f o r t h i s reason more importance should be given t o them. The l o g i c a l t h i n g to do i s to apply some weighting f u n c t i o n to the data t h a t i s r e l a t e d t o the a n a l y t i c a l p r e c i s i o n of the v a r i o u s e s t i m a t e s . In t h i s study we wanted to maximize the p r e c i s i o n of the DEL v a l u e s o b t a i n e d , which i s the same t h i n g as minimizing the v a r i a n c e of the e s t i m a t e s . The weighting f u n c t i o n to be a p p l i e d was determined as f o l l o w s . I t i s commonly known (p. 168 Hogg and C r a i g ) t h a t i f we d e f i n e the weighted mean Y as f o l l o w s : Y= Iw.X. [A5.1] where the W»s are the weights and the X*s the i n d i v i d u a l e s t i m a t e s , then the v a r i a n c e o f Y i s : ° 2 = I(W.cr.)z [A5.2] i f the c o r r e l a t i o n c o e f f i c i e n t between the X estimates i s z e r o ( i . e . random sampling) Baking the usual c o n s t r a i n t t h a t the sum o f the weights i s equal t o u n i t y we w r i t e : H (W.,A) = I ( W . a . ) 2 - A (£W.-1)=0 [A5.3] where A i s a Lagrangian m u l t i p l i e r . M i n i m i z i n g 5.3 with A5.2 163 respect to the weights and the m u l t i p l i e r w i l l give an expression for H that minimizes the variance of the weighted DEL value determined by equation A 5 . 1 . Performing the necessary ca lcu lus g ives : W = [ 1 / ( a v ) z l / i l ( V a . ) 2 3 [ A 5 . U ] which i s the weighting funct ion that maximizes the prec is ion of the weighted DEL value. In the case were a l l a»s are equal we see that: W±=1/n [ A 5 . 5 ] where n i s the number of est imates. Likewise the variance of the weighted DEL value w i l l be: a 2 (Y)= (a.) V n [A5.6 ] i which i s just the standard er ror of the mean. The weighting funct ion of eguaticn A5.4 was used f o r a l l estimates of DEL i n t h i s p ro jec t . The a±'s were taken to be the a n a l y t i c a l standard dev ia t ions of the mass spectrometer analyses. A6.1 1 6 4 APPENDIX VI Property of the DEL Function-Error Propagation Due to Errors E x i s t i n g i n the Apparent Ratios At times i t i s possible for some factor to a f f e c t only one of the r a t i o s i n the determination of DEL, r e s u l t i n g in an error. That i s to say that the measured DEL i s given by: DEL (H) =[ kRx/Rs-1 ]103 [A6. 1] when the true DEL value should have been: DEL (T) =[ Rx/Rs-1 31 0 3 [A6.2] from A6.2 we see that: Rx/Rs=DEL (T)/103+1 [A6.3] kRx/Rs=kDEL (T)/10 3 + k C A6. U ] DEL (M) =[ kDEL (T) /10 3* (k-1) ]10 3 [A6.5] DEL (M) =kDEL (T) + (k-1 )10 3 [A6.6] DEL (T)=DEL (M)/k-(k-1) 103/k [A6.7] Eguations A6.6 and A6.7 can often be used to determine the error that r e s u l t s i n measuring i s o t o p i c r a t i o s i n c o r r e c t l y . These r e s u l t s are most useful in determining the effect that various errors i n analyses have on t h e re s u l t i n g DEL values.

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