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Laboratory and field investigations of the processes controlling gas exchange across the air-water interface

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Laboratory and field investigations of the processes controlling gas exchange across the air-water interface

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Content LABORATORY AND FIELD INVESTIGATIONS O F THE PROCESSES CONTROLLING G AS EXCHANGE ACROSS THE AIR-WATER INTERFACE by Blayne Alan Hartman A Dissertation Presented to the FACULTY O F THE GRADUATE SCHOOL UNIVERSITY O F SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR O F PHILOSOPHY (Geological Sciences) January, 1983 UMI Number: DP28564 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. U M I Dissertation Publishing UMI DP28564 Published by ProQuest LLC (2014). Copyright in the Dissertation held by the Author. Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code ProQuest ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106- 1346 UNIVERSITY OF SOUTHERN CALIFORNIA THE GRADUATE SCHOOL UNIVERSITY PARK LOS ANGELES. CALIFORNIA 9 0 0 0 7 This dissertation, written by B1 ay n e _ _ Alan „H a rtma. n........................................ under the direction of h\s.... Dissertation Com mittee, and approved by all its members, has been presented to and accepted by The Graduate Schoolj in partial fulfillment of requirements of the degree of D O C T O R O F P H I L O S O P H Y DISSERTATION COMMITTEE ^ Chairman TO BUD and ELEANOR who would have wished to see this day, and to JUDY, ELLIS, CARL, PAM, and W ENDY who made this day possible. CONTENTS ILLUSTRATIONS............................................................................................... .■ TABLES.............................................................................................................. X ABSTRACT.......................................................................................................... X I I ACKNOW LEDGEMENTS......................................................................................... xv NOTATION.......................................................................................................... x v i i i CHAPTER 1. INTRODUCTION TO G A S EXCHANGE...................................... 1 Motivation........................................................................................... 1 Principles of Gas Exchange......................................................... 3 Models of Gas Exchange................................................................. 5 Summary of Predictive Models..................................................... 12 CHAPTER 2. LABORATORY INVESTIGATIONS O F THE DEPENDENCIES O F G AS EXCHANGE O N MOLECULAR DIFFUSIVITY AND FLUID TURBULENCE............................................................... 14 INTRODUCTION................................................................................................. 14 METHODS............................................................................................................ 20 Generation and Measurement of Turbulence.............................. 20 Computation of the Turbulence Parameters.............................. 24 Determination of Gas Exchange Rate....................................... 28 RESULTS............................................................................................................ 33 Fluid Turbulence.............................................................................. 33 Gas Exchange Rates.......................................................................... 41 DISCUSSION..................................................................................................... 46 CHAPTER 3. PROCESSES CONTROLLING G AS EXCHANGE RATES IN SOUTH SAN FRANCISCO BAY........................................... 58 INTRODUCTION................................................................................................. 58 Review of Previous Work on Processes Controlling Gas Exchange in Natural Systems............................................... 58 Current Shear.............................................................................. 58 Wind Shear................ 61 Waves, Bubbles, Convection, and Surface films 65 Description of the Study Area................................................... 68 METHODS............................................................................................................ 70 RESULTS............................................................................................................ 74 DISCUSSION..................................................................................................... 90 Sediment-Water Exchange................................................................ 90 Air-Water Exchange.......................................................................... 94 Dependencies of Gas Exchange on Current Velocity and Wind Speed............................................................................ 94 Comparison of Gas Exchange Rates Determined by the Mass Balance and Floating Chamber Methods................... 100 Comparison with Previous Models of Gas Exchange.... 102 CHAPTER 4. MEASUREMENT A ND PREDICTION O F G AS EXCHANGE RATES IN WIND-DOMINATED SYSTEMS................................ 107 Estimation of Fluid Turbulence from Salt Dissolution.. 108 Laboratory Comparison of Exchange Rates Measured with Floating Chambers.................................................................. I l l Prediction of Gas Exchange Rates in Wind-Dominated Systems................................................................................................. 116 CONCLUSIONS................................................................................................... 123 REFERENCES..................................................................................................... 126 i v APPENDICES APPENDIX I. LABORATORY AND FIELD DATA.......................................... 134 Radon Activity in the Water Column of San Francisco Bay.......................................................................... 135 Radon and Radium Activities in the Sedimentary Column of South San Francisco Bay................................ 148 In-situ Fluxes of Radon Across the Sediment- Water Interface Measured with Benthic Chambers... 153 In-situ Fluxes of Radon Across the Air- Water Interface Measured with Floating Chambers.. 156 Gas Transfer Coefficients from the Laboratory Experiments.............................................................................. 158 Turbulence Data from the Laboratory Experiments............................................................................... 159 APPENDIX I I . COMPUTER PROGRAMS......................................................... 171 Gas Data Processing Programs...................................................... 172 GASRUN......................................................................................... 172 GASCAL......................................................................................... 172 GASPLOT....................................................................................... 175 Tubulence Data Processing Programs......................................... 175 DIGIT........................................................................................... 175 STREAK......................................................................................... 179 LENGTH......................................................................................... 179 Modeling Programs......................................................................... 189 B O X 13........................................................................................ 189 APPENDIX I I I . LABORATORY MANUAL....................................................... 194 Turbulence Tank Apparatus............................................................ 194 Turbulence Generation......................................................... 194 Tank....................................................................................... 194 Grid....................................................................................... 194 Oscillating Mechanism................................................... 196 v Illumination Assembly.......................................................... 205 Lamp....................................................................................... 205 Lenses and Chopping Wheel........................................... 207 Streak Photography.......................................................................... 209 Equipment and Operating Conditions.............................. 209 Camera and Tracer Particles...................................... 209 Image Distance and Zoom Setting.............................. 211 Film, F-stop, and Exposure time.............................. 214 Focusing.......................................................................... 215 Fiducial Lamps.................................................................. 215 Developing.......................................................................... 216 Digitizing Procedures................................................... 216 Computation of Streak Length..................................... 217 Gas Analysis....................................................................................... 221 Gas Chromatography................................................................ 221 Radon Measurements................................................................ 225 Procedures for an Experimental Run......................................... 227 Preparational Procedures................................................. 227 Adjustment of the Grid................................................. 227 Filling and Draining the Tank.................................. 230 Water Preparation............................................................ 230 Experimental Run Procedures............................................. 232 Streak Photography.......................................................... 232 Sampling of Tank Water................................................. 233 Salt Dissolution Experiments.................................... 234 ILLUSTRATIONS Figure Page 1-1. Representation of the two single-parameter gas exchange models.......................................................................... 6 2-1. Schematic of the turbulence tank apparatus.................. 21 2-2. Streak photograph from a typical experimental run.. 23 2-3. Typical plot of the turbulent velocity correlation function vs. streak separation distance......................................................................................... 27 2-4. Plot of the logarithmic change in tank water concentration of the five gases from one experimental run........................................................................ 32 2-5. Profiles of the 3-component turbulent velocity vs. distance from the interface from the turbulence experiments............................................................ 34 2-6. Profiles of the 3-component turbulent kinetic energy vs. distance from the grid from the turbulence experiments............................................................ 35 2-7. Profiles of the integral length scale vs. distance from the grid from the turbulence experiments................................................................................... 39 2-8. Ratio of the vertical to horizontal turbulent velocities vs. distance from the grid for five of the turbulence experiments.................................. 40 2-9. Profiles of the turbulent Reynolds number vs. distance from the grid from five of the turbulence experiments............................................................ 42 2-10. Profiles of the energy dissipation rate vs. distance from the grid from five of the turbulence experiments............................................................ 43 2-11. Log-log plot of the normalized gas transfer coefficient vs. normalized molecular d iffu s iv ity ................................................................................... 47 2-12. Relationship between the gas transfer coefficient and the 3-component turbulent velocity at the interface........................................................................ 50 vi i Page 2-13. Relationship between the gas transfer coefficient and the turbulent Reynolds number at the interface........................................................................ 52 2-14. Relationship between the gas transfer coefficient and the quotient of the 3- component turbulent velocity and the turbulent length scale at the interface........................ 53 2-15. Relationship between the gas transfer coefficient and the square root of the product of the molecular diffusivity and surface renewal rate................................................................ 55 2-16. Relationship between the gas transfer co efficient and the product of the square root of the molecular diffusivity and the fourth root of the energy dissipation rate................................ 57 3-1. Dependence of the reaeration rate coefficient with current shear observed in previous field and laboratory studies............................................................ 59 3-2. Dependence of the gas transfer coefficient with wind speed observed in wind tunnel experiments 62 3-3. Relationship between film thickness and wind velocity observed in natural systems.............................. 64 3-4. M ap of south San Francisco Bay showing station locations and bottom topography......................................... 69 3-5. Radon to radium activity ratios in composite sedimentary cores for each sampling season for the channel and shoal areas in a section of south San Francisco Bay...................................................................... 78 3-6. Representation of the 13-box model used to construct a radon mass balance and of the bottom topography across the center of the study section.. 83 3-7. Relationships of the gas transfer coefficients computed from the chamber measurements with current velocity and with wind speed.............................. 96 3-8. Relationships of the gas transfer coefficients computed from the mass balance with current velocity and with wind speed.............................................. 98 v i i i Page 3-9. Comparison of gas transfer coefficients computed from a radon mass balance to values computed from floating chambers and to values predicted from the O'Connor and Dobbins (1958) gas exchange model 101 3-10. Dependencies of the gas transfer coefficients computed from a radon mass balance and predicted from gas exchange models with wind friction velocity......................................................................................... 105 4-1. Relationship between sodium sulfate dissolution rate and renewal rate observed in the laboratory experiments............................................................ 110 4-2. Relationship between the gas transfer co efficient and sodium sulfate dissolution rate observed in the field and laboratory experiments................................................................................... 112 4-3. Relationship between the surface renewal rate and wind speed observed in wind-dominated, natural systems........................................................................................... 120 APPENDIX FIGURES A III-1 . Schematic of the gear reduction assembly from the turbulence generating assembly.................................. 197 A III-2 . Torque required to oscillate the grid at various frequencies and stroke lengths and torque supplied by 3/4 H P and 1 H P motors..................................................... 201 A III-3 . Schematic of the drive train and grid support assembly from the turbulence generating assembly... 203 A111-4. Schematic of the turbulence tank apparatus showing the orientation and spacing of the collimating lenses used in the laboratory experiments.................... 208 A III-5 . Schematic of the gas chromatograph and stripping system used for the dissolved gas analyses................. 222 A III-6 . Schematic of the radon stripping system used for the dissolved radon analyses......................................... 228 Table 2- 1. 2 - 2 . 2-3. 2-4# 3-1. 3-2. 3-3. 3-4. 3-5. 3-6. 4-1. 4-2. 4-3. TABLES Measured dependencies of the gas transfer coefficient with molecular d iffu s iv ity........................ Operating conditions and results from experiments of diffusing turbulence from oscillating g rid s .... Experimental conditions, turbulent parameters at the interface, and selected power law dependencies from the laboratory experiments....................................... Gas transfer coefficients from the laboratory experiments................................................................................. Radon and radium concentrations for a section of south San Francisco Bay....................................................... Radon to radium activity ratios, radon activities, and integrated deficiencies of radon in the sedimentary column for a section of south San Francisco Bay............................................................................ In-situ fluxes of radon across the sediment-water inteTTace measured with stirred and unstirred chambers....................................................................................... Gas transfer coefficients computed from the i n-situ radon flux across the air-water interface measured with floating chambers....................................... Gas transfer coefficients and horizontal diffusivities for a section of south San Francisco Bay computed from a radon mass balance........................ Summary of measured radon fluxes across the sediment-water interface and flux expected by molecular diffusion................................................................ Dissolution rate of sodium sulfate tablets from the laboratory experiments................................................. Comparison of gas transfer coefficients measured in floating chambers and computed from the change in tank water concentration in laboratory experi ments.............................................................................................. Measurements of gas exchange rates and wind speed in wind dominated systems................................................... Page I 15 18 i 29 44 75 ! 76 80 81 87 i 92 | i 109 | j 115 ! APPENDIX TABLES AI-1. Radon activity in the water column of San Francisco Bay........................................................................... 135 AI-2. Radon and radium activities in the sedimentary column for a section of south San Francisco Bay.................................................................................................... 148 AI-3. In-situ fluxes of radon across the sediment- water interface measured with benthic chambers 153 AI-4. In-situ radon fluxes across the air-water Tnterface measured with floating chambers.................... 156 AI-5. Gas transfer coefficients computed from the laboratory experiments............................................................ 158 AI-6. Turbulence data from the laboratory experiments.... 159 A111-1. Calibration of the grid oscillation frequency with motor controller dial setting.................................. 198 A111-2. Calibration of the exposure time with voltage applied to the chopping wheel motor................................ 210 A111-3. Lengths of selected target board squares measured with the photo-digitizer.................................... 213 All 1-4. Distance between fiducial points measured from slides from different picture runs.................................. 220 A111-5. Operating conditions used during gas analyses on the Carle gas chromatograph........................................... 223 All 1-6. Precision of transfer coefficients determined by digitization of peak areas............................................. 226 A111-7. Efficiency and precision test data for the ! radon stripping system 229 j | ABSTRACT I | The processes controlling gas exchange across the air-water i interface have been investigated in laboratory and field experiments j I with the primary goal of developing a predictive model for gas i I exchange rates in natural systems. A model capable of predicting gas I exchange rates in natural systems is necessary for rational decisions i regarding air and water quality management. j i j The dependencies of gas exchange on molecular diffusivity and on i I i | parameters characteristic of the fluid turbulence near the interface I i were investigated in laboratory experiments. The exchange rates of j : five gases (02 , N 2 , CHi*, C O 2 , Rn), the turbulent fluctuating j I j ! velocities, and the turbulent integral length scales were measured | 1 j 1 concurrently under controlled laboratory conditions. Turbulence was | generated by oscillating a grid in a tank and the turbulent I parameters determined by streak photography. Gas transfer j coefficients were computed from the temporal change in concentration i | of each gas, assuming the rate of exchange is proportional to the | deviation from saturation. Experiments were conducted at three | different grid positions and two oscillation frequencies. The ; turbulent velocity decreased nearly exponentially with distance from | the grid. Turbulent integral length scales increased linearly with i 1 i 1 I distance from the grid, except near the interface where boundary j ! ; effects became important. The turbulent flow field was isotropic | ! except for regions close to the interface. Gas exchange rates j appeared to depend upon the square root of the molecular diffusivity | 1 1 1 and upon the ratio of the turbulent velocity to the integral length j x ii | scale. These results support a surface renewal model of gas exchange. In the fie ld , naturally-occurring radon-222 was used as a tracer for gas exchange. Radon-222 concentrations in the water and sedimentary columns and radon exchange rates across the sediment-water and air-water interfaces have been measured in a section of south San Francisco Bay. Sediment-water exchange rates, determined by two independent methods, agree reasonably well on a yearly basis. The benthic fluxes from shoal areas are nearly a factor of two greater than fluxes from the channel areas based on a yearly average. Fluxes from the shoal and channel areas are greater by factors of 4 and 2, respectively, over fluxes expected by simple molecular diffusion. Values of the gas transfer coefficient for radon exchange across the air-water interface were determined by direct measurement using floating chambers and by constructing a radon mass balance for the water column. The results from both methods indicate a linear dependence between gas exchange and wind speed, but no dependence on current velocity. Rates measured with the floating chambers are , i ! higher than rates given by the mass balance approach for the same j wind speed. Best estimates for the transfer coefficient are given by the mass balance approach and range from 0.5 m/day to 1.8 m/day, with j a mean value of 1.0 m/day for six sampling periods over a six-year j i j period. j XI 11 Gas exchange coefficients predicted for this system from the 1 stagnant film model, using an empirical relationship between film ] : thickness and wind speed observed in lakes and the oceans, are withinj 15% of the coefficients determined from the mass balance and are j | considerably more accurate than coefficients predicted from other gas! 1 i exchange models. Exchange rates predicted from the laboratory relationship are a factor of 3 lower than the measured rates and do j not show the same trend with wind speed. This discrepancy probably | stems from an inability to measure the fundamental turbulance : j ! | parameters in the fie ld . Application of surface renewal models for | the prediction of exchange rates in natural systems will require the ; development of methods to measure fluid turbulence in the fie ld. | Until such time, empirical relationships must suffice. | Attempts to derive an empirical relationship between exchange i rate and fluid turbulence intensity based upon salt dissolution were j ! j unsuccessful in both laboratory and field experiments. Compilation i j | | of all existing measurements of gas exchange rates in wind-dominated,! natural systems indicates that estimates of average exchange rates j can be made to within 15% from measurements of wind speed alone. ACKNOW LEDGEMENTS I always look forward to writing the acknowledgements section to any report because i t gives m e the opportunity to reflect back upon the people I've interacted with and the pleasant memories that always seen to go along. Writing this section is a special treat, because not only can I reflect upon the events during the past two and one-half years of this dissertation, but also upon a seven and one-half year graduate tenure at USC. I hope that m y readers are in a patient mood. Initial thanks go to the entire staff of the Geology Department at USC for their support, patience, and for being "normal people". It's hard for m e to make an accurate comparison between this department and others, however, I feel that other departments would have to go a long way to beat the staff at USC for combined intelligence and personality. I ' l l always look back warmly to m y days (all seven and one-half years) in Science and Stauffer Halls (and even on the Velero). A special thanks to Richard Stone (posthumously) and Teh-Lung (Richard) Ku for in itia lly "opening the door" for m e to come to California. Thanks to all m y fellow graduate students for the intellectual, but mostly social, times we shared. The "56" crew of Mike Korosec, Jim Buika, Dean Malouta, and captained by Tom O'Neil. To Pat Shanks for his faculty locker. To Tom Hartnett, Sam Limerick, and Vic Lamanuzzi for the first-year struggles and laughs. To the San Francisco Bay group (BAGS: Boys After Gases xv and Sediments) of Larry Miller (bag winner), Chris Fuller, Joe _F. Donoghue, Becky (and, of course Susan) Rea, Steve Warren, and Will Berelson. Last, but not least, to Tom (should have) Nardin for taking m e off on fanatical adventures through the world of Wall Street. There were a number of Doctors (besides those on the geology faculty at USC) whom were instrumental to the success of this dissertation. Jim Morrisey, the Doctor of Hosology (Masters in V-belts), supplied countless consultations on a variety of technical matters ranging from the dynamics of hose to fine cuisines; and, in all seriousness made m e realize how important it is to have a close friend. Dave Morris, the Doctor of Machinology, was instrumental in the design and construction of the laboratory apparatus and, despite our early "battles", did one hell of a job. Carroll Waite, the Doctor of Gasology, constantly dazzled m e with his extensive knowledge on compressed gases and always provided a friendly voice and warming chuckle upon every "service call". Carl (St^ch, Stretch, Scratch) Audi a, the Doctor of Woodology; Chuck Markley, the Doctor of Scubaology; Steve Smoral, the Doctor of Truckology, and Wayne Lutz, the Doctor of Flightology, all provided "cures" for a number of pressing problems in and out of the 1aboratory. Thanks to the people who worked with m e and for m e in the laboratory. (Fast) Eddy Hurst, Ray (how many more slides?) Skelly, and Steve (outta here) Isenogle all provided invaluable support xvi in the laboratory work and data reduction. Janet Dodds and Alana Blake somehow managed not to "clock" m e during my frequent revisions of their (already perfect) drafted figures. Sue Turnbow did an excellent job of typing this verbose document and calming m e down during those frantic Saturdays just before the deadline. Thanks to Dr. Teh-Lung Ku, Dr. Jim Kremer and Dr. Robert Sweeney for their advisement throughout m y graduate career. To Carol McClenning for putting up with my requests and keeping m y paycheck straight for seven years. To Dorothy Bjur, Patrick Hartney, and the rest of the Sea Grant crew who continued to support m e for five years , despite a three-year maximum. To Dr. Dave Peterson, Dr. John Conomos, and the rest of the USGS group for their boats and support during the field expeditions. To Dr. Tom m y Dickey for extraordinary intellectual : and personal support throughout the doctoral program. W hen I wrote my Masters Thesis, I saved the two most special people for last. I t ’ s comforting to know that four and one-half years later, those same two people hold even a greater share of m y heart. Wendy and Doug, words can't express m y affection and gratitude for the influence you've had on m e over the past seven and one-half years. I can only say that whenever I think of the time I've spent with each of you, I consider myself a very lucky man. xvi i NOTATION The following is a lis t of the notation used throughout this dissertation. Units are given except for parameters for which the units are obvious. Parameters are defined in the text after their fir s t occurrence. a acceleration A area Ae amplitude of sinusoidal eddy velocity as defined in the eddy cell model by Lamont and Scott (1970) Asam Peak area samPle Astan Peak area standard ATTsam attenuation for sample (unitless) ATTstan attenuation for standard (unitless) Cd gas concentration in overlying gas phase (mass/volume) C -j in itia l (time=0) gas concentration in water (mass/volume) C0 gas concentration in water at saturation with the overlying gas phase (mass/volume) Cw gas concentration in water (mass/volume) Dm molecular diffusivity (length2/time) horizontal eddy diffusivity (length2/time) turbulent diffusivity (length2/time) f ( r ) two point parallel velocity correlation function (unitless) g acceleration due to gravity h water depth or chamber height H dimension!ess Henry's Law constant J mass flux per unit area (mass/area-time) k von Karman coefficient (unitless) k 2 reaeration coefficient (tim e*1) K gas transfer coefficient (length/time) kG,KI,KL gas transfer coefficient (length/time) for the gas boundary layer, interface, and liquid Boundary layer L three-component, turbulent integral length scale (length) Ls length scale of small eddies as defined in the eddy cell model of Lamont and Scott (1970) Lk Kolmogorov length scale (length) m mass n»N,Np number of data points, streaks, and streak pairs, respectively Pi partial pressure of gas i (atm) q three-component turbulent velocity r separation distance between two streaks Rt total resistance to gas exchange (time/length) R ej_ turbulent Reynolds number (dimensionless) renewal rate (time X) stroke length of grid oscillation (length) Sc Schmidt number (dimensionless) j t time !T temperature TKF 3 component turbulent kinetic energy (length/time2) !u' x-component, horizontal fluctuating velocity Z x-component, horizontal instantaneous velocity up> Up" parallel, turbulent velocity vectors j ut x-component, root-mean-square turbulent velocity as defined in the large eddy model of Fortesque and Pearson (1967) U mean x-component velocity ;U* gas phase friction velocity jv' y-component, horizontal fluctuating velocity V current velocity or grid velocity Vi standard loop volume on the gas chromatograph Vsam volume of water sample injected into stripper |Vstan volume of gas standard injected into the gas chromatograph j w1 vertical (z-component) fluctuating velocity W wind speed jw* liquid phase friction velocity x power law exponent (unitless) xx,xz,xt power law exponents relating the x-component, horizontal fluctuating velocity, z-component fluctuating velocity, and 3-component turbulent velocity, respectively to I distance from the grid xx horizontal distance grid displacement, equal to 1/2 the stroke length digitized streak lengths from streak photographs digitized distance between fiducial points digitized distance between target board squares power law exponent (unitless) true distance between target board squares distance from grid correction factor for chemical reaction (unitless) coefficient relating turbulent length scale to distance from grid (unitless) stagnant film thickness (length) turbulent energy dissiptation rate (1 ength3/time) characteristic eddy length scale (length) as defined in the large eddy model of Fortesque and Pearson (1970) grid oscillation frequency (time-1 ) flux supplied by molecular diffusion (atoms/m 2-sec) kinematic viscosity (1ength 2/time) density of air and water, respectively torque (mass-1 ength 2/sec 2) replacement time CHAPTER 1 1 I INTRODUCTION TO G AS EXCHANGE Motivation Knowledge of gas exchange rates across the air-water interface is necessary for understanding a variety of problems and processes in aqueous systems, including the reaeration rates of rivers and estuaries, nutrient recycling in coastal systems, and the role of the oceans in controlling the atmospheric concentrations of potentially harmful gases [C02, N20, S02]. The direct measurement of these rates in natural systems is d iffic u lt, thus considerable research effort has been invested into the formulation of models which represent the exchange process and enable prediction of exchange rates from easily measured hydrodynamic or meterological parameters. The problem with this approach for the determination of exchange rates is that considerable doubt exists over the accuracy of exchange rates predicted from currently available relationships. The doubt stems from a lack of agreement between predicted rates and rates measured in laboratory and field studies. The result of this comparison suggests that values predicted from the available models are, at best, within a factor of 2 of the measured exchange rates. This level of agreement is not acceptable for water-quality and air-quality management decisions, where a factor of two can have serious economic and/or environmental ramifications. 1 Presumably, the discrepancy between observed and predicted j i ! exchange rates may be attributed to inadequacies in the predictive relationships and inaccuracies in the rates measured in the fie ld . Thus, improvement in gas exchange prediction requires a better understanding of the physics of gas transfer and of the environmental parameters which control the transport processes in i I natural systems# j This thesis presents the in itia l results from a research program designed to study these problems. The approach is to determine the relationships between gas transfer and characteriStic molecular and turbulent parameters through laboratory measurements and to relate the observed dependencies to the environmental parameters controlling these processes in natural systems through field measurements. Ultimately, the results from these efforts should prove useful in the formulation of gas exchange models. The material presented herein has been organized into four chapters and an appendix. Chapter 1 gives an introduction to the theory of gas exchange, discusses the models proposed to predict j exchange rates, and discusses the problems with applying these j models for the prediction of gas exchange rates in natural systems. | Chapter 2 presents the results from laboratory investigations on I the dependencies of gas exchange on molecular diffusivity and on I parameters characteristic of the fluid turbulence. Chapter 3 j presents measurements of gas exchange rates in a natural system, j i ! examines the processes controlling the exchange rate, and compares 2 | the observed rates to values given from previous models of gas ; exchange. Chapter 4 discusses methods to measure gas exchange in natural systems and relates the field data to the results from previous investigations on exchange rates in natural systems. Finally, the appendix contains complete listings of the laboratory and field data, descriptions of the computer programs used in data ! analysis, and detailed descriptions of the experimental apparatus i and procedures used in the laboratory. Principles of Gas Exchange i ! The transfer of gas between an agitated liquid and a gas phase has been shown experimentally to be described by the equation: where J is the mass flux per unit area ( mass time-area K is the gas transfer coefficient / Iength\ , also commonly time referred to as the transfer velocity or piston velocity, and AC is the concentration difference between the gas phase and bulk solution. The reciprocal of K can be thought of as the resistance to gas transfer. Near the air-water interface, resistance to gas transport occurs in the gas boundary layer, the interface, and the liquid boundary layer. The total resistance may be expressed as the sum of the individual resistances (Liss and Slater, 1974): J = K A C (l-D ( 1- 2) 3 where Kq, Kj, and K j_ are the transfer coefficients for the gas boundary layer, interface, and liquid boundary layer, respecti vely, H is the dimensionless Henry's Law constant, a is a correction factor for chemical reaction (cO>l). In most cases, one of the resistances in equation (1-2) tends to dominate. For surfaces devoid of films, T f is very large and Kj approaches zero. For gases of low solubility, H is large, diffusion through the gas film is rapid relative to the liquid film, and thus the resistance of the gas phase is small compared to the liquid phase. If chemical reaction is small or slow, a approaches unity and equation (1-2) reduces to: fconcentration in gas phase j and concentration in liquid phase 1 1 (1-3) Therefore, the flux expression becomes: J = KL (Cw - Co) (1-4) 1ength where K |_ is the liquid phase gas transfer coefficient ( time ), Cw is the gas concentration in the bulk flu id , and C0 is the gas concentration at the interface which is assumed to be in equilibrium with the gas phase. C0 is equal to Cd/H where Cd is the gas concentration in the overlying gas phase. 4 i The d iffic u lty with the direct application of equation (1-4) is that the gas transfer coefficient cannot be measured directly. Thus, considerable research effort has been invested into the formulation |of predictive relationships for Kl. Predictive equations may be formulated from theoretical principles of the gas transfer process, from empirically derived |relationships , or by semi-empirical methods in which a theoretically I derived equation is f i t to experimental data. Models based upon i [theoretical principles are preferable to purely empirical | relationships because, by nature, they are applicable to more than one gas and can be applied to a variety of systems under different j conditions. A variety of models have been proposed from theoretical Iprinciples to describe gas transfer, the difference between them being the manner in which the dynamics of gas transport are represented. ; jModels of Gas Exchange One of the earliest models of gas exchange is the stagnant film |nodel , firs t proposed by Whitman (1923). He postulated that the rate limiting step to transfer between air and water is molecular diffusion through a hypothetical "stagnant" water film. This model bssumes that the rest of the fluid has a uniform composition (perfectly mixed) while the concentration in the film falls linearly from the value measured in solution to a value which is in Equilibrium with the overlying atmosphere (Figure 1-la). At steady state, integration of Fick's second law of diffusion over the film i 5 Co LIQUID OR-* SURFACE FILM EXAGGERATED THICKNESS Figure 1-1. Representation of the two single-parameter gas exchange models. A. Stagnant film model. B. Surface renewal model. O'! thickness and combination with equation (1-4) gives: ! <L = °m/6 ( ! - 5) | length2 where D m is the molecular diffusivity ( time ) and 6 is the film thickness (length). I i i The film thickness is assumed to be a function of the fluid turbulence and the fluid physical properties. The primary objection to the stagnant film model is that i t is physically unrealistic to expect a stagnant film at the interface. i As an alternative to the film model, Higbie (1935) developed a model i of gas transfer which assumed that the controlling mechanism for gas exchange is replacement of the surface fluid by the bulk fluid ! (Figure 1-lb). While at the surface, the liquid exchanges gas by molecular diffusion. Higbie further assumed that every liquid ' element at the surface is exposed for the same amount of time before s replacement and that the liquid element exchanges gas as i f it were ! stagnant and in fin ite ly deep. The expression for the gas transfer coefficient was derived by integrating Fick's second law of diffusion; with certain boundary conditions and was given as: 1/2 K j_ = 2 [Dm /Troll (1~6) ; where 0 is the replacement time, which depends upon the fluid turbulence. Danckwerts (1951), criticizing Higbie's assumption of uniform exposure time, included a random distribution of surface ages for the fluid elements in Higbie's model. In this model, the 7 gas transfer coefficient takes the form: 1/2 KL = [Dms] (1-7) where s refers to the fraction of surface area which is replaced with fresh liquid per unit time, i . e . , a renewal rate (time"1). Again, the hydrodynamics of the fluid are incorporated into one parameter, s. An alternative approach to the stagnant film and surface renewal models has been proposed by Kishinevski (1955) and King (1966) and is based upon the concept that a continuous gradation probably exists from purely molecular transport at the interface to turbulent transport with increasing depth. These models have been referred to as s t i11-surface models (Danckwerts, 1951) and turbulent film models (Holley, 1978; Hasse and Liss, 1980). In these models, the transfer coefficient is assumed to be dependent upon both molecular and eddy diffusivity such that: 1 r z dz KL = Dm+Dt (1-8) o ' where z is the thickness of the film and ^t is the turbulent (eddy) diffusivity which is a function of z. The d iffic u lty with applying these models for predicting K j_ i s that each model contains at least one parameter (<5, 0 , s, Dt) which |cannot be measured directly. Application of these models to the prediction of gas exchange in the field requires that the unknown !parameters be related to measurable parameters which are thought to control gas exchange. This has been done through assumption based upon scaling arguments or through empirical methods. Modification of the stagnant film model has been done by relating the film thickness to wind speed based upon laboratory and ifield measurements of exchange rates (Emerson, 1975; Broecker et a l . , 1980). Film thicknesses are calculated from measured gas fluxes using equation (1-5). i Dobbins (1956) and O'Connor and Dobbins (1958) expressed the surface renewal model in terms of measurable stream parameters by assuming the turbulent velocity to be equal to 10% of the stream velocity and the turbulent length scale to be equal to 10% of the water depth. Their expression for K [_ was: n 1 / 2 r m V i K |_ = h (1-9) where V is the stream velocity and h is the water depth. Note that (V/h) is representative of a renewal rate. 9 Fortescue and Pearson (1967) developed an expression for the surface renewal model in terms of measurable parameters by assuming that large eddies in the liquid phase are responsible for gas transfer into a turbulent fluid (large eddy model). The eddy motion was modeled with a series of roll cells, whose dimensions were taken to be the integral scale of the turbulent flow fie ld . The expression for the mass transfer coefficient was given as: where u -^ -j s the root mean square of the horizontal (x-component) turbulent fluctuating velocity and A is the characteristic length scale of the roll cells. Brtko and Kabel (1978) modified this expression by assuming the eddy length scale to be equal to the water depth and by approximating ut through the liquid phase friction velocity (w*) and relating w * to the gas phase friction velocity (U*) by assuming equal shear stress at the interface. Their expression for K |_ was given as: where Pa and ?w are the densities of air and water, respectively. 1/2 KL = 1.46 [Dm ut/A] ( 1- 10) (1- 11) 10 Lamont and Scott (1970) developed another modification of the ! surface renewal model in which they suggest that large eddies are responsible for fluid transport from the bulk liquid to the surface, but that gas transfer is accomplished through smaller eddies at the surface. In this model, K j_ is given as: 1/2 KL = 0.445 [Dm Ae/Ls] (1-12) where Ae is the amplitude of a one-dimensional sinusoidal shearing motion at the mid plane of the small eddies and Ls is the dimension of the small eddy cells. Lamont and Scott (1970) related the dimension of the eddy cell and the amplitude of the shearing motion to the energy dissipation rate j and obtained: 1/2 1/4 KL = 0.4 D m (e/v) (1-13) 1ength3 where e is the energy dissipation rate ( time ) and 1ength2 v is the kinematic viscosity ( time ). Brtko and Kabel (1978) related the energy dissipation rate to the turbulent energy spectrum and expressed K |_ as: I 1/2 ru* pa 3/2 1 - 1 / 4 Kl = 0.4 Dm CvF ( pw) T T J (1-14) where k is the von Karman coefficient, and I i i ! h is the water depth. j 11 r Note that the bracketed term has units of sec”1 and can be considered | to be a renewal rate. , Deacon (1977) expressed the turbulent film model in terms of j wind friction velocity using a treatment based upon the velocity profile in turbulent air flow over a smooth, fla t plate (Reichart, i ! 1951). Deacon's expression for Kl was: ! -2/3 KL = .082 Sc U* (pa /pw) (1-15) I ! where Sc is the Schmidt number, defined as the kinematic viscosity ' j divided by the molecular diffusivity (dimensionless). j Summary of Predictive Models There are two major problems with the application of these models for the prediction of gas exchange rates in the fie ld . First, i t is yet to be determined which model gives the best representation of the exchange process. Considerable disagreement exists over the functional dependence of Kl with the molecular diffusivity and with n 1/2 n i the velocity term. Although the difference between um and um does not introduce much error for most gases, the difference between the functional dependence on the velocity term can lead to significant ! | differences in predicted exchange rates. Second, i t is not clear which environmental parameters are important for characterizing gas i exchange in the fie ld . Several processes may be important for gas transport depending upon the environmental conditions. Thus, these ! models may predict Kl values which are substantially lower than true values i f more than one process is important or i f the dominant ' process is other than the one upon which the model is based. 12 Clearly, these problems need to be resolved before accurate prediction of gas exchange is possible. This requires improved understanding of the molecular and turbulent processes of gas transfer and of the relationships between these processes and the meteorological and hydrodynamic parameters which generate turbulence in natural systems. 13 CHAPTER 2 ! i LABORATORY INVESTIGATIONS O F THE DEPENDENCIES O F G AS EXCHANGE O N MOLECULAR DIFFUSIVITY AND FLUID TURBULENCE j INTRODUCTION j ! Gas transfer across the air-water interface is presumed to be controlled by molecular and turbulent transport processes near the interface. Consequently, an understanding of the physics of gas transport, and thus the development of predictive models of gas exchange rates, requires knowledge of the functional relationships between gas exchange and the parameters characteristic of these processes. Molecular transport is dependent upon the molecular d iffus ivity. Although considerable research effort has been i invested into establishing the dependence of gas exchange on this parameter, the functional relationship has not been clearly I determined. This fact is illustrated in Table 2-1 which summarizes J the results from five recent studies. The variation in the j observed power law dependencies covers the entire range predicted j by the theoretical models of gas exchange (Chapter 1). Thus, it is | j not possible to choose between the models based upon these results. I i It is generally believed that the lack of agreement arises from the ! uncertainty in the values of the molecular diffusivities of the measured gases. Turbulent transport should be controlled by the fluid j 14 TABLE 2-1. Measured dependencies of the gas transfer coefficient with molecular diffusivity (K|_ a D m x). Source Lab/Field Gases Considered X Peng (1974) Lab C02, 02, R n 1.0 Hammond (1975)* Lab Kr, 02, C02, N2, Rn 0.74 Torgerson et a l . (1982) Field He, R n 1.2 Ledwell (1982) Lab N2, 0 2, C H , He 0.5 Holmen** (1982) Lab H2, He, Xe 1.3 * Used data of Peng (1974) and Tsivoglou (1972). **Unpublished results. 15. turbulence near the interface, although bubble and aerosol transport processes may be more important during rough surface conditions. Fluid turbulence is generally characterized as eddy motions, which transport parcels of fluid from one layer to another at various velocities. The eddys are erratic and non-predictable and are defined in a probability sense. This requires the principles of statistics to quantitatively define the parameters of turbulence. The two most commonly defined parameters are a turbulent (eddy) velocity and an eddy length scale. The velocity at any point in turbulent flow varies in magnitude and direction and can be represented by a mean and fluctuating component. The fluctuations vary in time and, by definition, the arithmetic mean of the fluctuations are zero. A quantitative measure of the turbulent velocity is computed as the root-mean-square of the fluctuating component. Although the velocity fluctuations define the intensity of turbulence, some measure is required to define the scale of turbulence. A turbulent length scale is considered to represent the distance that a parcel moves from its point of departure from the mean motion to its point of remixing with the main body of the flu id . Physically, this length can be thought of as the average size of the eddies responsible for mixing. Taylor (1920) proposed an approach for the estimation of this parameter based upon the correlation of the parallel velocities between all points in the turbulent flow (see methods section). 16 The measurement and characterization of fluid turbulence have I been performed previously in a number of studies concerned with ' turbulent mixing. Table 2-2 summarizes the experimental conditions j j and general results from these studies. Despite this ab ility to measure characteristic turbulence parameters, l i t t l e work has been concerned with establishing the dependencies of the gas transfer coefficient on these parameters. j O'Connor and Dobbins (1958) investigated the relationship between gas exchange and the oscillation rate of a turbulence generating grid and concluded that gas exchange is proportional to the square root of the turbulent velocity. Since no direct measurements of the fluid turbulence were made, it was assumed that the turbulent velocity was directly proportional to the oscillation rate of the grid. Fortesque and Pearson (1976) examined the dependence of the exchange rate of C02 with fluid turbulence in a water flume. Values for the turbulence parameters were not measured directly, but were assumed to be the same as those j determined in earlier wind-tunnel studies by Bachelor (1948). They j I concluded that gas exchange is proportional to the square root of a j surface renewal rate, defined as the turbulent velocity divided by j the turbulent integral length scale. However, the validity of this { i result is questionable due to complications introduced by the ! spatial variability in the turbulent parameters and presumably the | i gas exchange rate along the flume length. Further, they did not measure the turbulence parameters in their laboratory apparatus. j TABLE 2-2. Operating conditions and results from experiments of diffusing turbulence from oscilla tin g grids. Notation described in text. Values for x^, xz> x^. are absolute values. Tank Water Width Depth (cm) (cm) Grid Type S t r o k e Length (cm) Bouvard & Dumas (1967) Thompson & Turner (1975) Hopfinger & Toly (1976) Dickey (1977) McDougal 1 (1979) This work 67.5 38 25.4 12.7 Perforated 8.0 Square bar; Rod 67.5 40.5 Square bar; Rod 61.6 166.3 Perforated 25.4 12.7 Square bar 61.5 61.5 Rod 1.0 1.4 4.0 9.0 4.3 1.0 6.0 Osci11 Freq. (Hz) Grid Mesh (cm) 6.0 2. 0- 6.0 5.0 10.0 4.0 5.0 3.5 4.5 5.1 5.0 Grid Sol. Re 8.0 .60 ^6000 3.3-5.0 5.0 .32 ^ 50 32 -v 40 1.5 1 .0 - 1.5 32 -v 700-4800 1.0 34 % 700-1500 .5 1.5 5.1 .34 ^ 400-715 1.2-3.1 .8-2. .09-.11 .17-.34 1.0 .3 .2-.9 .15-.23 This chapter presents the results from laboratory experiments designed to investigate the dependencies of gas exchange on the molecular d iffu s iv ity , and parameters characteristic of the fluid turbulence. The exchange rates of five gases (02, N 2, C02, C H k, Rn), and the turbulent velocity and turbulent length scale were measured simultaneously under a variety of controlled turbulence conditions. The observed relationships are discussed and are compared to those suggested by currently available predictive model s. 19 METHODS This section gives a concise summary of the apparatus and procedures used in the laboratory experiments. Detailed descriptions of the apparatus components and design, procedures, and development of the procedures are given in Appendix I I I . Generation and Medsurement of Turbulence Turbulence was generated in a plexiglas tank (62 cm x 62 cm x 76 cm) with a vertically oscillating grid (Figure 2-1). The advantages of generating turbulence by this method are that isotropic turbulence can be generated in the horizontal plane and that previous studies on the characterization of fluid turbulence have employed similar arrangements, thereby enabling a comparison with earlier work. The grid was 61 cm square and consisted of two planes of stainless steel tubing (1.0 cm O.D.) with a mesh size of 5 cm. The position of the grid in the tank, grid oscillation frequency, and oscillation stroke length were all adjustable, which enabled the generation of different turbulence flow fields. Turbulent velocities and length scales were determined by streak photography, using an approach similar to one described by Dickey and Mel lor (1980). Inert, neutrally buoyant particles of P lio lite VT (Goodyear Chemical Co.) were added to the water and cp illuminated with a high intensity Hg-vapor lamp (40,000 cm) in a darkened room. Particles diameters of 0.35 ± . 07 m m yielded good TRACER BEADS I LIGHT BAFFLE ~ j x LENS Hg-VAPOR LAMP CAMERA (A) ECCENTRIC MOTOR HEARINGS GRID C K X c rc G rm n CHOPPING WHEEL PHOTODIODE in n: : n (B) Figure 2-1. Schematic of the turbulence tank apparatus. A. Top view. B. Side view. Grid not shown in top view, tracer beads not shown in side view. Diagram scale: 1:20. 21 streak images and were small enough to follow the pertinent scales of motion. Streak photographs were taken with a 35 m m camera equipped with a variable focal length (zoom) lens. The zoom lens enabled the camera to be located at long distances from the plane of illumination to reduce distortion due to refraction. A zoom setting of 105 m m and an image distance of approximately 2 m was used for all experiments. Exposure times were controlled by an opaque rotating wheel with a cutout window, which chopped the light beam at a pre-set rate, and were measured with a photodiode and counter-timer. A piece of mylar was placed asymetrically within the chopping wheel window to create photographic streak images consisting of short and long bright sections, separated by a dim section. A typical streak photograph is shown in Figure 2-2. Particle velocity vectors (magnitude and direction) were determined from the length of the resulting streak images and the orientation of the short and long sections. Measurements of streak lengths were performed by projecting 35 m m negatives onto a photodigitizing table (^60 cm x 40 cm) and digitizing the streaks. The precision of the instrument was 0.1% for lengths of 1 cm or greater (Appendix I I I ) . Conversion of the streak images to true distance was accomplished by measuring all streak lengths relative to a set of fiducial points. The photographic distance between 22 Figure 2-2. Typical streak photograph from an experimental run. Note position of grid and fiducial points. Head and tail sections of streak images are visible for some streaks. fiducial points was calibrated to true distance by photographing a target board of known dimensions which was suspended in the plane of illumination prior to each experimental run. Approximately j 20,000 streak images (requiring 100 to 150 exposures) were digitized for each experimental run. Computation of the Turbulent Parameters The three-dimensional turbulent flow field was deduced from the two-dimensional photographs assuming isotropic turbulence in the horizontal plane. Earlier studies by Dickey (1977) and Dickey and Mellor (1980) with a steroscopic system support this assumption. The photographic section was divided into a computational matrix consisting of 5 horizontal and 18 vertical elements of ^ 9 cm by ^ 2 cm and the streak images falling in each element were used to compute the turbulence parameters for that element. This procedure was motivated by results presented by McDougall (1979), which showed that mean velocities should be | computed on a local rather than a cross-sectional basis because of j inherent lateral heterogeneity. The velocity vectors for each element were ensemble averaged ! and the mean horizontal component computed as: j i N ^ ! ^ik N £ (uik)n (2-1) ! n=l where U-j^ is the mean x-component, horizontal velocity in element u-jk is the instantaneous horizontal component of velocity in the x-directi on, and 24 N is the number of streaks ( ~ 200) in each matrix element (i,k). The fluctuating component of the velocity was determined as: (ui k ) n = (ui k ) n “ ^ik (2-2) and the turbulent fluctuating velocity was found by taking the root-mean-square of the ensemble average of the fluctuating components: — 1/2 1 N , 1/2 [ui|<] = £ N E (ui|<) ] n=l n (2-3) — 1/2 The vertical component, [w-jk ] , was computed similarly, the y- — 1/2 — 1/2 component, [ v - j k ] , was assumed equal to [u-j^D > and the 3-component turbulent velocity was computed as: , 2 ,2 1/2 lik = (2uik + w-j|<) (2-4) The turbulent velocity for an entire vertical element ( q k ) was found by averaging q-jk for each of the 5 horizontal bins and the 3-component turbulent kinetic energy computed as: TKE = 1/2 qk (2-5) The depth to the midpoint of each vertical element was used to locate the computed parameters relative to the interface and grid (i .e ., qk -*q(z)). 25 Turbulent integral length scales were determined from the normalized area under the turbulence velocity correlation curve as fir s t proposed by Taylor (1920). Two point parallel turbulence velocity correlations were computed by the method described by Dickey and Mellor (1980). Briefly, the turbulence velocity vectors for a pair of streaks are resolved onto a line connecting the midpoint positions of each, yielding the parallel velocity components. The product of these two components is computed as a function of the separation distance between the pair. This procedure is repeated for all possible pairs and a normalized correlation function computed as: N 1 P u u" (r) z Pi Pi u i." ( r ) 1-1 (2-6) f(r) = P P _ " UP UP2 where Up & Up" are the parallel components of the turbulent t velocity vectors, Np is the total number of pairs within a specified interval (of r ± r /2 ), and r is the mean separation distance. The turbulent integral length scale is computed as: r L = J f ( r) dr (2-7) r=o A typical correlation plot is shown in Figure 2-3. Errors in the reported turbulence parameters are introduced primarily by the number of streaks digitized (i.e., sample size) and are estimated to be ±15% (see Dickey, 1977 for error analysis technique). 26 0.6 AREA = 2.05 0.4 0.2 8 1 0 1 2 1 4 2 4 6 r (cm) Figure 2-3. Plot of the turbulent velocity function vs. streak separation distance for one vertical element from turbulence run #4. Area refers to the digitized area under the correlation curve (hashed) and is equivalent to the inteqral length scale for this element (decth). Values of a turbulent Reynolds number (Re^J and energy dissipation rate (e) were computed from the turbulence parameters j as: ! i ReL = qL/v (2-8) and e = q3/l5L (2-9) The latter expression is taken from Mellor (1973). Determination of Gas Exchange Rate Prior to an experimental run, tank water concentrations of oxygen and nitrogen were reduced to approximately 50% of saturation by stripping with helium. Concentrations of C02, CH^, and Rn were elevated above saturation by bubbling C02 and CH^ gas through the water and by the addition of water high in Rn ac tivity. The water was adjusted to a pH of 3.5 to 4.0 to eliminate the effect of chemical reaction on C02 transport. Tank water was stirred after these procedures to insure homogenization. Grid oscillation was then in itiated. A typical experimental run lasted 4 to 6 hours. Water samples were drawn every 20 minutes for 02, N2, C02, and CH^ and every hour ; for Rn. Water salinities and temperatures were nearly constant for j all runs, ranging from 33°/oo to 36°/oo and 18°C to 21°C, ! respectively (Table 2-3). Samples were drawn from several depths in the tank during early runs and the dissolved gas concentrations ! i were found to be homogeneous throughout the tank. j 28 TABLE 2-3. Experimental conditions, turbulent parameters at the interface, and selected power law dependencies from the laboratory experiments. Values in parentheses are questionable (see text). Grid Oscillation Depth Speed Temp Sal q L r Run § (cm) (Hz) (°C) (°/oo) (cm/set) (cm) K L (cm2/sec3 x_ z t_ B 1 9 3.5 18 32 1.8 (2.3) (360-540) 1 [.19-.13) Ia - 1. 20bC I a -1.42bc Ia. -. 77 ! h . 16 2 31.5 3.5 19 30 (1.3) (4.0) (338) 1 (.056) 2 .37?c ■ N -2.76ac ■ - . 86ac. N Nb 3 13.0 3.5 20 32 1.2 3.3 397 .035 - 2-55h - 1 .83 - . 86? -1.71 -.40? - .54 .36? .20 4 16.8 3.5 20 35 1.0 5.0 500 .013 -3.08? -1.25 -1.17? -1 .45 - • 17h -. 70 .41? . 23 5 16.8 4.5 21 35 1.5 4.8 715 .047 - 1-36k -1.23d - 1. 21? -.82 - . 22? -. 51 . 20? . 15 6 13.0 4.5 20 36 1.8 3.2 572 .121 -2.48a -1.41 -.78? -1 .78 -. 21a -. 64b .50a .16^ I - in s u ffic ie n t data a - values for data above grid N - no data b - values c - values for data for z < below grid 20 cm only Dissolved 02 , N 2 , CO 2 , and C H f+ were measured by injecting 1 m l water samples into a Swinnerton stripper, connected in series with a dual-column, dual detector gas chromatograph (Carle Inst. Co. Model A G C 311). Oxygen, N2, and CH4 were measured immediately after sampling using a 3/16" x 8' molecular sieve 5A column at 48°C. Carbon dioxide analyses were run on a 1/4" x 6‘ chromosorb 101 column at 55°C. Water samples for C02 analyses were drawn separately and stored in glass syringes for 5 to 24 hours prior to analysis. To prevent exchange during storage, syringe tips were stuck into rubber stoppers immersed in water, and the assemblies stored in a refrigerator. Chromatographic peaks were recorded on a two-pen chart recorder (Houston Inst. Co.) equipped with a disk integrator. For some runs, peak areas were measured on a photodigitizer. Gas concentrations were computed from the area under the chromatographic peaks using Equation A III-12. Analytical precision of the gas analyses was^3%. Dissolved radon concentrations were determined by stripping 25 m l water samples with helium, passing the gases through a drying column (CaSO^) into an evacuated c e ll, and alpha counting in scintillation chambers. Water samples were generally stripped within minutes of sampling. Analytical precison for these analysis is^ 5% (Appendix I I I ) . I i Gas transfer coefficients were determined by measuring the j 3 change in tank water concentration through time. The time rate of ! change of gas concentration in the tank water can be written as: 30 dCw k l W = T (Cw-C0 ) (2-10) where h is the depth of water in the tank. I f the gas concentration in the gas phase does not change, the solution of equation (2-10) with the boundary condition, at t=0, C w=C-j is: The gas transfer coefficient can be computed from the slope of the best f i t line on a semi-log plot of (Cw-C0)/C-j-C0) vs. time. A typical plot from one experimental run is shown in Figure 2-4. Computed slopes for radon had to be corrected for decay. Values of C0 for 02 and N2 were taken from the solubility tables of Weiss (1970). Values of C 0 for C02, CH^, and Rn were negligible compared to the water concentration (Cw). ( 2- 11) 31 L O G [ (CW-CAIR) / (C I-C A IR )] RUN NUM BER* GAS OXYGEN (o) NITROGEN (o) C02<*) METHANE (+) RADO N (x) 16 KLiMZDAYl 2.01+ 0.16 2.10+ 0.30 a 09+0.06 2.00+0.01 1.75+0.22 30. 90. 150. OSCILLATION TIME (MINUTES) 210. Figure 2-4. Plot of the logarithmic change in tank water saturation for the five gases with time for gas run #16. Tabulated Kl values are the slopes (1 lse) of the b e s t-fit lines. Radon value corrected for decay. Plotted points for the evading gases (CO;?, CH4, Rn) are absolute values, thus the slopes are positive. Dark square at (0,0) represents the i n it ia l value for each gas. CAIR is analagous to C0 in equation 2-11. 270. I RESULTS Fluid Turbulence Streak photographs were taken and the fluid turbulence was characterized at six different grid settings. The experimental conditions are listed in Table 2-3. These conditions were chosen to fa ll within the range of measured values of gas exchange in natural systems and to insure minimal disturbance of the surface. | Profiles of the turbulent velocity and turbulent kinetic energy in | the water column for all experiments are shown in Figures 2-5 and | 2-6 (Table Al-6 lists the computed values for each run). The observed values for these parameters ranged from 1.0 cm/sec to 3.0 cm/sec for the turbulent velocity and from 0.5 cm /sec to 4.5 cm /sec for the turbulent kinetic energy. As expected, both parameters decrease with increasing distance from the grid in all i experiments, except for run #2 in which a minimum at ^ 20 cm from the grid is apparent. The reason for this anomalous pattern is unclear, but may be due to the large depth of the grid during this run. This idea is supported by run #1 in which the profiles of q and TKE at large distances below the grid (> 20 cm) begin to ! deviate from the trends closer to the grid.* ! i *As this document goes to press, the data from a second experiment at the same conditions as run #2 are being processed and in it ia lly show the same patterns as these observed for run #2 in Figures 2-5 and 2-6. DISTANCE F R O M INTERFACE (cm) TURBULENT VELOCITY (cm/sec) 0 -i 5 - 10- 15- 2 0 - 2 5 - 3 0 - 3 5 - 40-1 1.0 2.0 3.0 ____ I___I £ 1_0_Q __Q RUN No.I (3.5 Hz) 1.0 l_ 2.0 30 _) 1 O O Q Q RUN No.2 (3.5Hz) 1.0 2 0 3.0 I ---------1 ___I o o o a RUN No.3 (3.5 H z) 10 2.0 3.0 1.0 2.0 3.0 10 2.0 3.0 I ________ i i I ________ I ____ I I -------- 1 ---- 1 Q Q 0 Q RUN No.4 (3.5 Hz) Q Q O Q RUN No.5 (4.5H z) Q Q 0_0 RUN No.6 (4.5 Hz) Figure 2-5. Profiles of the 3-component turbulent velocity vs. distance from the interface for the turbulence experiments. Location of grid shown by horizontal line with circles, DISTANCE F R O M G R ID (cm) TURBULENT KINETIC ENERGY (cm/sec)2 35 - 30 - 2 5 - 20 - 1 5 - 10 - 5 - 0- -5 - -10 - -15 - -2 0 - -2 5 - - 3 0 - ,7 .91.0 2.0 .5 7 1.0 2.0 .6 .8 1.0 2.0 .3 .4 .6 .8 1.0 2.0 .6 .8 10 2.0 .4 .6 .8 1 .0 2.0 3.0 I I i i i I___i i i i i I 1 1 I i J -------------------- 1 I----------1 — i— i i i J- J 1 I I I i I--------------------J I— I— l i I ‘ *--------------------- 1 ------------* RUN No.I (3.5Hz) RUN N o. 2 (3.5 Hz) S m ' RUN N o. 3 (3.5Hz) RUN No.4 (3.5 Hz ) RUN No.5 (4.5 Hz) \ A RUN N o. 6 (4.5 Hz) Figure 2-6. Profiles of the 3-component turbulent kinetic energy vs. distance from the grid from the turbulence experiments. Location of interface shown by the wavy line. Dashed lines give the best semi-log f i t to the computed values for distances less than 20 cm from the grid. One reason for this pattern may be due to the formation of j large-scale cells in the tank. The d iffic u ltie s encountered with generating horizontally isotropic turbulence without the formation of large-scale cells were fir s t noted by Hopfinger and Toly (1976). This problem appears to become relevant for large aspect ratios (defined as the ratio of the distance from grid to surface vs. the horizontal dimensions of the tank). W hen larger scale, non-turbulent motions are set-up in the tank, the sampling of mean versus turbulent motions becomes more d iffic u lt. For example, the large eddy, non-turbulent motion may change in time and hence be included as fluctuating, turbulent motion because of the ensemble averaging procedure. This results in over-estimation of turbulence and may explain the peculiar increase of q with distance away from the grid seen in run #2. Presumably, this situation does not arise in the other runs because of the lower aspect ratios, and hence relatively small proportion of energy in large scale, non-turbulent j The profiles in Figures 2-5 and 2-6 can be reasonably f i t by simple exponential relationships for distances < 20 cm from the grid, except for run #2. However, results from previous oscillating grid experiments have usually been expressed as power law dependencies in the form: eddi es. [u‘2] !/2 a z"XX ( 2- 12) (2-13) (2-14) [ w . 2 ] 1 / 2 a z " Xz - xt and q a z 36 where xx, xz , and xt are the respective powers obtained from fits of the data plotted in log-1og form and z is the distance from the grid (cm). Hence, power law dependencies were computed from the data from each experiment, except for run #2 (Table 2-3). The range of values are compared to values from previous experiments in Table 2-2. The agreement is relatively good considering the differences in the experimental arrangements. The decay of turbulence above the grid is not as rapid as below the grid, as illustrated by the computed power laws for q (*t) ln 2-3. Additionally, the absolute values of these parameters for a given distance away from the grid are larger below the grid. The reason for these effects are not clear, but may be due to the influence of the interface on the turbulent flow above the grid. One possibility is that small scale oscillation of the interface may increase the energy transfer through the water column above the grid. The effect of this process would be to homogenize the energy through the water column, and thus the observed energy and velocity profiles above the grid are more uniform than below. Further, some of the induced energy from the grid may be stored as potential energy in the distortion of the interface, and thus less kinetic energy is available for turbulent motion. Assuming that the total amount of induced energy from the grid is the same for regions above and below the grid, this could explain the lower absolute values observed above the grid. Additional experiments are required to test this hypothesis. 37 Profiles of the integral length scale in the water column for j all runs are presented in Figure 2-7. The observed length scales j for the five experiments range from 1.0 cm to 5.0 cm. Below the grid, the length scale increases linearly with distance. The slope of the best-fit line is relatively constant for all runs (Table 2-3), ranging from .15 to .23 with a mean (± lse*) of 0.18*.02. These slopes are close to slopes observed by Thompson and Turner i (1975) and Hopfinger and Toly (1976) (Table 2-2). Above the grid, the dependence appears to deviate from a linear relationship in runs #2, #3, #4, and #5. However, the results from run #2 are questionable as discussed previously. For the other 3 runs, a i linear dependence gives as good a statistical f i t as exponential and power law relationships due to the small data base. However, a less rapid increase near the surface is consistent with the concept of the flattening of eddies near a boundary (e.g. Hunt and Graham, 1978; Thomas and Hancock, 1977). This idea is further supported by Figure 2-8 which illustrates the departure from isotropy near the interface. The vertical fluctuating velocity is approximately one- half the horizontal fluctuating velocity within a distance of the i order of the integral length scale away from the surface. This is j in general agreement with the theory of Hunt and Graham (1978) and | the experiments of McDougall (1979). *se refers to the standard error of the mean, defined as (a/ / n ) , where n is the number of measurements. 38 DISTANCE FROM GRID (cm) INTEGRAL LENGTH SCALE (cm) 10 2 0 3 0 4 0 10 2 0 3 0 4 0 5 0 10 2i 3 0 4 0 5 0 10 2 0 3 0 4 0 5 0 10 2 0 3 0 4 0 5 0 1.0 2 0 3 0 4 0 I I_I I L _J I I __I I__I 1 _1 _1 _1 —I I —I 1 —I ------- 1 —I 1 --1 —I--I —I--1 —I_I I _I I I I 1 __I l I i i i i i i i i i i i i I 30 20 - - 10- 's • X \ • \ \ • \ • \ \ • \ \ \ \ \ • \ \ RUN #1 RUN # 2 RUN # 3 RUN # 4 RUN # 5 RUN # 6 (3.5 Hz) (3.5 Hz) <3.5 Hz) (3.5 Hz) (4.5 Hz) (4.5 Hz) Figure 2-7. Profiles of the integral length scale vs. distance from the grid from the turbulence experiments. Location of interface shown by wavy line. Dashed lines are the least squares c o f i t to the computed values below the grid. Dashed curves are a visual f i t to the values above the grid. C D DISTANCE FROM GRID (cm) W,c U' / 2 4 .6 .8 1.0 1.2 1.4 1.6 4 .6 .8 10 1.2 14 1.6 I__ I__I_I I I I 20 - 10- 0- - 10- - 2 0 - RUN #1 4 6 8 10 I 2 1 .4 I 6 I I I__I I I I 4 6 8 I.O 1 .2 1 .4 16 4 6 8 10 I.2 14 16 I I I I I I I I I I I I I 1 (3.5 Hz) RUN #3 (3.5 Hz) RUN * 4 (3.5 Hz) RUN * 5 (4.5 Hz) RUN * 6 (4.5 Hz) O Figure 2-8. Ratio of the vertical to horizontal turbulent velocities vs. distance from the grid. Location of interface shown by wavy line. Run #2 not shown. Turbulent length scale appears to depend only upon distance from the grid, as illustrated by the similar values and profiles for experiments conducted at the same grid position (runs #3 and #6; runs #4 and #5). Stroke length is probably also important, however this dependence was not investigated. Profiles of the turbulent Reynolds number and energy dissipation rate are shown in Figures 2-9 and 2-10. The implications of these figures have yet to be understood, and thus they are presented here for reference only. Gas Exchange Rates Exchange rates were determined for each of the turbulence runs listed in Table 2-3. Exchange rates at the conditions given for runs #1, #2, and #4 were determined in a number of separate experiments to test the precision of the apparatus. The mean values (± lse) of the observed transfer coefficients are summarized by run number in Table 2-4. The precision of the transfer coefficients for all gases ranges from approximately 2% to 20% for all runs with multiple analyses, indicating that the turbulence I conditions in the tank remained relatively uniform for constant j I grid settings. The best precision in the computed transfer co efficients was obtained with the C02 and the CH^ analyses. This i result is not surprising since oxygen and nitrogen were susceptible j i to contamination errors during injection and the number of radon j i samples drawn for each run were so few (4 to 6) that a small amount j ! I 41 DISTANCE FROM G RID (cm) Re, 4 0 0 5 0 0 6 0 0 3 0 0 4 0 0 5 0 0 6 0 0 ■ i ■ I I I i I i I i I 20 - 1 0 - 0 - -10 - -2 0 - - 3 0 J RUN #1 (3.5 Hz) RUN # 3 (3.5 Hz) I00 2 0 0 3 0 0 4 0 0 5 0 0 I i I i I i I » I i RUN # 4 (3.5 Hz) 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 I i l ■ I i I i I I I i-J l I i I i I i I i J RUN # 5 (4.5 Hz) RUN # 6 (4.5 Hz) Figure 2-9. Profiles of the turbulent Reynolds number vs. distance from the grid from five of the turbulence experiments. Location of interface shown by wavy line. € (cm2 /sec3) 0 0 01 0.2 0.3 0 4 0 0 01 0 2 0 3 0 4 0 5 0 0 01 0 2 0 3 0 4 0 5 0 0 01 0 2 0 3 0 4 0 5 0 6 0 7 0 0 01 0 2 0 3 0 4 0 5 0 6 0 7 OR 0 9 — I I —I —I —I —1 —I L. 1 I I —I —1 —I — 1_ 1 I L_J I L I ~L .J — I—1-_J 1—L L _J I —L. J I l_i. _l._l l 1 L . I 1 I 1 1 I 1 1 I I I I 20 - 1 0 - 10- CO - 2 0 - - 3 0 RUN * 1 (3 .5 Hz) RUN * 3 (3 .5 Hz) RUN * 4 (3 5 Hz) RUN * 5 (4 5 H z) RUN * 6 (4 5 Hz) Figure 2-10. Profiles of the turbulent energy dissipation rate vs. distance from five of the turbulence experiments. Location of the interface shown by wavy line. CO TABLE 2 - 4 . Gas t r a n s f e r c o e f f i c i e n t s i n m / d a y ( ± 1 s e ) f r o m t h e l a b o r a t o r y e x p e r i m e n t s . N u m b e rs 1n p a r e n t h e s e s r e p r e s e n t t h e n u m b e r o f s e p a r a t e e x p e r i m e n t s f r o m w h i c h t h e v a l u e s w e r e d e r i v e d . The l a s t c o l u m n g i v e s t h e p o w e r l a w d e p e n d e n c e b e t w e e n t h e t r a n s f e r c o e f f i c i e n t a n d m o l e c u l a r d i f f u s i v i t y . N u m b e rs i n b r a c k e t s a r e t h e m o l e c u l a r d i f f u s i v i t i e s ( c m V s e c ) f o r e a c h g a s a t t h e e x p e r i m e n t a l c o n d i t i o n s . Run 0 „ N_ CO. CH Rn x # [ 2 . 0 6 x 1 0 - 5T [ 1 . 7 1 x 1 0 - 5T Cl . 6 4 x 1 0 - ST [ 1 . 7 5 x l 0 - 5] [ 1 . 2 x l 0 - 5] ___ 1 1 . 2 6 * . 0 7 ( 2 ) 1 . 2 6 * . 0 8 ( 2 ) 1 . 3 4 * . 0 4 ( 2 ) 1 . 2 6 ^ . 0 4 ( 3 ) 1 . 1 5 * . 1 8 ( 2 ) . 1 8 2 0 . 5 0 - . 0 4 ( 3 ) 0 . 5 5 ± . 0 2 ( 3 ) 0 . 5 1 ± . 0 2 ( 3 ) 0 . 4 9 * . 0 2 ( 3 ) 0 . 4 3 * . 0 2 ( 2 ) . 3 2 3 0 . R R * . 0 6 ( l ) 0 . 8 5 ± . 0 9 ( l ) 0 . 8 6 * . 0 3 ( 1 ) 0 . 9 4 ± . 0 3 ( l ) . 0 8 4 0 . 6 6 - . 0 4 ( 3 ) 0 . R 7 ± . 0 5 ( 4 ) 0 . 5 9 * . 0 2 ( 3 ) 0 . 6 2 ± . 0 2 ( 3 ) 0 . 5 8 * . 0 9 ( 2 ) . 3 0 5 0 . 9 7 ± . 1 2 ( 1 ) 1 . 0 7 ± . 1 3 ( 1 ) 0 . 7 3 ± . 0 7 ( 1 ) 0 . 7 2 ± . 0 1 ( 1 ) 0 . 7 4 ± . 0 7 ( 1 ) . 4 6 fi ------ ------ 1 . 2 2 ± . 0 4 ( 1 ) 0 . 9 9 ± . 0 5 ( 1 ) 0 . 9 1 ± . 1 4 ( 1 ) . 4 4 44 of scatter led to a large uncertainty in the computed coefficients for this gas. The mean transfer coefficients range from 0.43 m/day to 1.34 m/day for all runs, which falls within the range of values measured in natural systems (Broecker et_ aj_., 1980). Systematic trends in the coefficients between gases are d iffic u lt to identify. Generally, the coefficients for Rn are lower than those for the other gases. Although small variations are apparent between gases, generally these differences for a set of conditions are less than ±lse. It is likely that the lack of systematic trends is because the variations in the computed transfer coefficients are small relative to the analytical precision ( ±lse). The solution to this problem is to increase the precision of the transfer coefficients and/or to select gases which show a larger variation in exchange rate. 45 DISCUSSION The functional dependence of gas exchange rate on molecular diffusivity can be determined by comparing the exchange rates of gases with different diffusivities under the same experimental conditions. Molecular diffusivities were taken from Broecker and Peng (1974) and were assumed to be the same for all runs (Table 2-4). This assumption should be valid since the water salinity and temperature were nearly constant for all experiments (Table 2-3). j i W hen computed separately for each run, the power dependencies x ( K |_ a D m ) range from x=0.08 to 0.46 with a mean (± lse) of 0 .3 ± .l. If only the values for C02, CH^ and R n are considered, the computed mean is 0.4±.2. Alternatively, the data from all 6 runs can be considered simultaneously, by normalizing the values of the calculated transfer coefficients and the molecular diffusivity for each gas to the values for one gas. Methane was chosen as the reference gas since the precision in the computed transfer coefficients was the highest. The relationship between the normalized parameters is shown in Figure 2-11. The plotted points are the mean values j (±lse) of the normalized values computed from the data in Table j i i 2-4. The results from run #2 were used in this analysis since the j relative exchange rates of the gases should not depend upon the j > l turbulent flow field (in the absence of bubbles and aerosols). j The slope of the best f i t line to the 1og-transformed normalized | i values is ^ 0.3. Although the small data base and large error in 46 K c h -20- .20 -20 0 - 4 0 ( is fj O C02 • c h 4 A R n A 0 2 □ No F i g u r e 2 - 1 1 . L o g - l o g p l o t o f t h e n o r m a l i z e d g a s t r a n s f e r c o e f f i c i e n t v s . n o r m a l i z e d m o l e c u l a r d i f f u s i v i t y . P l o t t e d p o i n t s a r e mean v a l u e s (+ I s e ) o f t h e i n d i v i d u a l r a t i o s f o r e a c h e x p e r i m e n t . The s o l i d l i n e g i v e s t h e b e s t f i t t o t h e d a t a p o i n t s . E r r o r s i n t h e d i f f u s i v i t y v a l u e s n o t shown and n o t c o n s i d e r e d in t h e b e s t f i t l i n e . -p » the transfer coefficients relative to variations preclude statistical confirmation of this dependence, these data suggest that a square root dependence between exchange rate and molecular diffusivity is more likely than a linear relationship. Additional measurements are required to improve the confidence in this exponent, preferably with a suite of gases covering a wider diffusivity range. Characterization of the gas exchange rate in terms of the fluid turbulence requires selection of the relevant turbulence parameters. In turn, this requires assumptions concerning the eddies which control gas transfer across the interface. In the analysis which follows, i t is assumed that the controlling eddies for gas exchange are those closest to the interface. Furthermore, i t is assumed that these eddies are best characterized by the 3-component turbulent velocity (q) and the integral length scale (L). Estimates of the values of these parameters at the interface were obtained by extrapolating the observed depth profiles to the interface. This procedure was straightforward for q, since the functional dependence of this parameter with distance from the grid ; I (z) was clear. However, estimation of L was more subjective, | because of the uncertainty in the dependence of L with z above the ! grid. Thus, estimates for L were obtained by drawing a curve I through the data based upon a best visual f i t (Figure 2-7). The I values obtained by this approach were within 10% of values obtained j 48 from a simple linear f i t to the data. Extrapolated values for q and L for all runs are summarized in Table 2-3. A single value of the length scale for run #1 could not be determined due to a lack of data. However, a range of probable L values for this run was obtained by assuming that the minimum value could be no less than the sole measured value 2) and that the maximum value could be no greater than the value observed in runs #3 and #6 ( ~ 3 ) . The latter assumption is reasonable since L increases with distance from the grid and the grid is closer to the interface in run #1. Note that the estimated values for run #2 are not consistent with the other runs as shown by the high value of q and the low value of L despite the deep depth of the grid. Clearly, these turbulence parameters do not adequately describe the flow field for this run, and thus the results from this run shall be neglected in the determination of the dependencies of gas exchange with the turbulence parameters. The dependencies of the transfer coefficient with q and with L can be determined by observing the change in the dependent variable (Kl_) with variations in one of the independent variables (q or L), while the other independent variable remains constant. The dependence between K |_ and q is shown in Figure 2-12 for two experimental conditions of nearly constant L. Also shown are the b est-fit curves to the data given by linear and square-root dependencies, with the constraint that Kj_=o at q=0. It is not 49 Ki_(m/day) Lx 3.3 0.8 0.6 0.4 0.2 0.8 12 2 0 0 4 1.6 4.9 cm '— d— ' 0 8 0 4 1 6 2 0 1.2 TURBULENT VELOCITY (cm /sec) Figure 2-12. Relationship between the gas tra n s fe r c o e ffic ie n t and turb u le n t v e lo c ity at the interface. Solid lin e s show the expected re lationships fo r lin e a r and square-root dependencies, w ith the constraint that the curves pass through the o rig in . Numbers in parentheses give the run number fo r each set of points. O CO 2 • CH4 A Rn A 0 2 □ N 2 cn o possible to select between these two dependencies due to the limited data base. In addition, the dependence of K |_ on the I I integral length scale could not be examined, because of a lack of data at constant turbulent velocity for a range of length scales. A multiple stepwise regression analysis eliminates the constraint that one of the independent variables remain constant, and thus the data from all experiments can be considered i I simultaneously. This analysis indicates that K |_ is directly i proportional to the turbulent velocity raised to some power and inversely proportional to the length scale raised to some power, although the small data base and large scatter in the gas transfer coefficients precludes the quantification of these dependencies with any certainty. This functional form is confirmed by Figures 2-13 and 2-14 which show the relationships between K [_ and the product of q and L (proportional to the Reynolds number), and of K |_ i with the quotient of q and L ( i . e . , a surface renewal rate). ! Clearly, no relationship exists between Kj_ and the Reynolds number over the range of Reynolds numbers generated in four experiments. This is not surprising in light of the results from the regression I I analysis and indicates that gas exchange cannot be characterized by ; ! a Reynolds number. However, there is a strong correlation between | i K |_ and q/L. Determination of the exact functional dependence between these parameters is d iffic u lt without additional points at lower and higher values of q/L. The goodness of f i t to the data given by linear and square root dependencies are s tatis tica lly j identical ( r 2 = .79 and .79, respectively). However, i f it is j 51 1.4 _ (3) (1) (4 ) (6) (5) 0 1.2 '------------------1 --------------' O A □ 1.0 • # A 1 D A o tj 0.8 A 0 C02 \ £ 4 * • CH4 _i V/ 0.6 5 A Rn J c A O 2 0.4 □ n 2 0.2 1 1 l 1 1 1 I 1 400 500 600 700 Re Figure 2-13 . Relationship between the gas transfer coefficient and turbulent Reynolds number at the interface. Num bers in parentheses give the run number for each set of points. Error bars on data for run # 1 show possible range of Reynolds number for this run. cn ro KL ( m / d a y ) (4) (5) (3) (6) (I) 0.8 0.6 0.4 0.2 0.2 0.4 0.6 0.8 0 C 0 2 • c h 4 A Rn ▲ 0 2 □ n 2 cn co Figure 2-14. Relationship between the gas transfer coefficient and the quotient of the turbulent velocity and the integral length scale at the interface. Error bars on data for run #1 show possible range of values for this run. Solid lines show the best fits to the data given by linear and square-root dependencies. assumed that during conditions of negligible turbulence gas i transfer occurs solely by molecular diffusion, then the boundary condition, K j_ ^ 0 at q/L=0 can be added. Clearly, the intercept given by the square root dependence is much closer to (0,0) than that given by the linear dependence (Figure 2-14) suggesting that the functionality is closer to a square root dependence. Combination of the observed molecular and turbulent i dependencies indicates that the transfer coefficient should be j 1/2 dependent upon [Dm(q/L)] . This is identical in form to the relationship given by the surface renewal models of gas transfer proposed by Higbie (1935), with 0 = L/q, and later by Danckwerts (1970), with s=q/L. Figure 2-15 shows this relationship for the measured transfer coefficients. A linear dependence provides a good f i t to the data, which supports the validity of this functional form. The b est-fit line is: 1/2 Kl = .4 (Dm s) (2-15) The uncertainty in the computed coefficient (the slope of the line) is approximately a factor of 2 when all the error is assumed to be derived from uncertainty in K |_ only. This coefficient is two ! ! to three times lower than coefficients of 1.0 and 1.1 given in the | theoretical surface renewal models of Danckwerts (1970) and Higbie j (1935). Fortesque and Pearson (1967) predicted a coefficient of j ^1.5 (equation 1-10) and observed a coefficient of M . 2 in their i laboratory work based upon the x-component root-mean-square j 1 I turbulent velocity. This equates to ^1.0 when expressed in terms j 54 I >» o ■ o E 08 O# 0.6 0.4 0 2 .0 5‘ 3 0 2.5 0.5 0 15 .20 [Dm s] /2 (m/day) O CO 2 • ch4 A Rn A 0 2 □ No Figure 2-15. Relationship between the gas transfer coefficient and the square root of the product of the molecular diffusivity and surface renewal rate. The solid line show s the best least-squares f i t to the data. Error bars show n for the data from run # 1 only. on < n of q. However, they did not measure the values of the turbulence parameters directly, which makes i t d iffic u lt to interpret the significance of this coefficient. Lamont and Scott (1970) predict a coefficient of 0.44 (equation 1-12), however, i t is d iffic u lt to correlate their turbulence parameters (Ae, Ls) to q and L. The energy dissipation formulation by these same authors (equation 1-13) gives a good description of the laboratory data as shown in Figure 2-16, however the coefficient given by the slope of the b e s t-fit line (MD.6) is nearly a factor of 2 lower than the coefficient given by Lamont and Scott ( vL.2). It is not definitively clear why the proportionality coefficient observed in the laboratory experiments are different from the values given by the previous models, although i t is likely that the reason is due to differences in the definition of the relevant turbulent parameters. Additional work is required before the best parameters for characterizing gas exchange are defined. Thus, the conclusions to be drawn from this work are that the surface renewal model appears to give an adequate description of the physics of gas transport across an undeformed air-water interface, however predicted rates are sensitive to the selection and determination of the required turbulence parameters. W hen the renewal rate is expressed in terms of the 3-component turbulent velocity and integral length scale at the interface, as determined by extrapolating the depth profiles of these parameters to the surface, the proportionality coefficient in the surface renewal 56 model is ^0 .4. ( m /day) 1.2 - 1.0 - 0.8 - 0.6 - 0.4- 0.2 - 0.04 0.2 0.4 I 0.6 n— 1.2 0.8 1.0 1.2 1.4 Djf2 (m/day) I 1 .6 1.8 2.0 “T~ 2.2 2.4 o C02 • ch4 A Rn A O J o a n 2 "1 2.6 cn •^ j Figure 2-16. Relationship between the gas transfer coefficient and the functional form of the energy dissipation model of Lamont and Scott (1970). Error bars on values from run #1 show possible range of values for this run. Solid line shows the best-fit to the transformed data. CHAPTER 3 ! PROCESSING CONTROLLING G AS EXCHANGE RATES IN SOUTH SAN FRANCISCO INTRODUCTION j Review of Previous Work on Processes Controlling Gas Exchange in ! Natural Systems j i At present, the measurement and characterization of fluid turbulence in natural systems is not possible. However, since gas exchange across the air-water interface depends upon the fluid turbulence near the interface, relationships should exist between the gas transfer coefficient and the parameters which generate turbulence within the water column. In coastal systems, turbulence is induced into the water column primarily by wind and current shear, waves, bubbles, and convective overturn. One or more of these processes may control the exchange rate depending upon the system and the environmental conditions. Current Shear Exchange in rivers appears to be primarily controlled by j current shear, which in turn is a function of current velocity, shape of the channel, stra tific atio n , and bottom roughness. Most of the research on the relationship between current shear and gas j exchange has been performed by engineers interested in stream I reaeration (see Bennett and Rathbun, 1972 for a good review). The | results of many of these studies are shown in Figure 3-1, which j i shows the relationship between the reaeration coefficient (K2) and water depth.* Generally, i t has been found that gas exchange j % is equivalent to KL/h, where h is water depth. 58 Reaeration Rate Coefficient, days IOOO 100 10 I 0.1 II C V J o.ot 0.001 ___ 0.01 0.1 I 10 100 h = Water Depth, ft. Figure 3-1. Dependence of the reaeration rate coefficient with current shear observed in previous fie ld and laboratory studies (after Holley, 1977). 59 Curves Calculated For Mean Velocity of I fps And Slope of 0.0 0 0 1 Rectangular Envelope of Observed Values A Dobbins 1964 B Krenkel I9 6 0 Thackston 1966 D Neguleacu 8 Rojanski 1969 E Thackston 8 Krenkel 1969 (Eq 17) Fortescue & Pearson 1967 O'Connor & Dobbins 1958 O'Connor 8 Dobbins 1958 ----- Isaocs 8 Gaudy 1968 Owens et. al 1964 Isaacs 8 Gaudy 1968 L ChurchiI I et. al 1962 (Eq 16) M Owens et. a I. 1964 Bennett 8 Rothbun 1972 (Eq 18) 0 Tsivaglou 8 Wallace 1972 is proportional to the current velocity raised to some power and to some parameter(s) describing the hydraulic character!'sties of the channel (such as depth, slope, roughness) raised to some other power(s). The values of the exponents in the power relationships vary with the particular study, ranging primarily from 0.4 to 1.0 for the dependence with current velocity and from 0.0 to -0.85 for the dependence with depth. Bennett and Rathbun (1972) and Rathbun (1977) performed critic al reviews of the laboratory and field studies and concluded that no one relationship can be applied to all systems. Additionally, they found that the predicted exchange coefficients were generally greater than the measured values. Figure 3-1 illustrates that large differences between predicted K ^ _ values are possible from the various equations. Bennett and Rathbun (1972) f i t the data from all of the fie ld studies and obtained an expression for K |_ as .607 V KL = B U.'6"89 (3-1) i h j where B is a constant (equal to 8.76), | V is the current speed (ft/s e c ), and h the water depth ( f t . ) j i The functional dependencies between K |_ with V and h in this | I equation are remarkably close to the dependences predicted by j O'Connor and Dobbins' (1958) model (equation 1-9). | I | 60 ! I Wind Shear For systems in which current shear is low, such as lakes and ocean environments, wind shear probably controls the exchange rate. Research efforts on the relationship between K [_ and wind speed have been extensive, yet the functional dependence is s t ill not clear. The majority of measurements on the effects of wind speed have been performed in wind tunnels. The results from many of these studies are shown in Figure 3-2. These data clearly illu strate a strong dependence between gas exchange rate and wind speed, however, there is some disagreement over the functionality. Early work (Hoover and Berkshire, 1955; Kanwisher, 1963; Liss, 1973) suggested that K [_ was a function of the square of the wind speed. Recent work (Broecker et_ aj_., 1978; Jahne et al . , 1979; Merlivat, 1980; Liss et al . , 1981) suggests that K [_ is linearly related to the wind speed, with abrupt changes in the slope of the dependence for higher wind speeds. Over the entire range of experimental wind speeds, the two linear regions can be approximated with a square dependence, in accordance with the earlier studies. However, as can be seen from Figure 3-2, the slopes of the linear relationships and the wind speed at which the dependence changes slope d iffer substantially between studies. The reason for this effect is not clear, but is probably related to differences in the scales and fetches of the systems. Thus, for a given wind speed the fluid turbulence was probably considerably different between tunnels. This idea is strongly supported by the relatively high values observed by 61 v Downing and Truesdale (1955) 140- o Kanwisher (1963) □ Hoover and Berkshire (1969) ▲ Liss (1973) 0 Mattingly (1977) • Broecker et al. (1978) 120 - ■ Jahne et al. (1979) ▼ Merlivat (1960) a Liss et al. (1981) 100 - . t ‘ 20 H • V o 4 40-| ■ y I ▼ A c > 9 2------'------J------'------1------'------ 1------'----- T o ' « WIND SPEED (m/sec) Figure 3-2. Relationship between the gas transfer coefficient and wind soeed observed in wind tunnel experiments. 62 Jahne et a l . (1979) since they conducted their experiments in a circular wind tunnel of unlimited fetch as opposed to the limited fetch in the other studies. The relationship between gas exchange rate and wind speed observed in field studies is also unclear. The most extensive set of measurements were made during the Antarctic Geosecs cruises (Peng et a l . , 1979), but no dependence between exchange rate and wind speed was observed. D ifficulties in the correlation between the measured rates and wind speeds could be the reason for this result. Deacon (1981) reexamined these data and suggested that a s ta tis tic a lly significant dependence existed between these parameters, but that the functionality was not clear. Tsunogai and Tanaka (1980) computed exchange rates from oxygen budgets in Funka Bay and observed that the computed rates were dependent upon the square or cube of the wind speed. Broecker et a l . (1980) took average values of exchange rates measured in a variety of systems and observed an exponential relationship between exchange rate (expressed as a film thickness) and wind speed (Figure 3-3). I Clearly, the dependence between wind speed and exchange rate j j has yet to be resolved. Comparison of the laboratory and field j data is d iffic u lt, because of the different scales of the systems. While laboratory measurements may provide useful information on the j functional relationship between exchange rate and wind speed, i t is j i doubtful that the absolute values of K |_ and the wind speed range i over which these relationships hold can be applied to natural j systems. 63 STAGNANT FILM THICKNESS (microns) 1000 700 500 - 4 0 0 - 3 0 0 - 200 P Y R A M ID E L A 00 70 # B O M E X 50 40 30 GEOSECS W A LK E R GEOSECS ^ A N T A R C T IC • PAPA 20 ■ MONO WIND SPEED (m/s) Figure 3-3. Relationship between film thickness and wind velocity observed in natural systems. The solid line is the curve obtained in a wind tunnel by Broecker et a l . (1978). Solid circles represent values computed from radon measurements and the squares values from radiocarbon measurements (after Broecker et a l . 1980). --------- 64 I Waves, Bubbles, Convection, and Surface Films Research effort on the effects of waves, bubbles, convection, | and surface films on gas exchange rates has not been nearly as extensive as the effort applied to the effects of wind and current shear. Waves can influence gas exchange by causing an increase in the interfacial surface area, by changing the turbulent flow fie ld | | near the interface, by modifying the depth of the interfacial I boundary layer, and by increasing the roughness of the surface. The i | importance of these effects has yet to be determined. Kanwisher (1963), Broecker et a l . (1978), and Jahne et_ a]_. (1979) observed a rapid increase in the gas exchange rate with the onset of wind-generated waves in wind-tunnels. However, i t is not clear whether the waves were the cause for the increased exchange rate, or an effect of some other controlling process. Because the effects of locally generated waves are not understood, gas exchange is simply related to the wind speed under the assumption that the wave fie ld for a given wind speed is constant for all systems. The importance of non-locally generated waves (gravity or internal waves) on gas exchange is believed to be small for most j systems. Downing and Truesdale (1955) and Kanwisher (1963) ! generated waves mechanically in a wind tunnel and observed a ! decrease in the exchange rate. Merlivat (1981) performed a similar study and observed no significant changes in the exchange rates. Exchange by bubbles may be the dominant process during rough sea conditions in which wave-breaking is common. Quantitative assessment of this process is extremely d iffic u lt since i t requires knowledge of the number and size distribution of bubbles as a function of depth and also of the physics of gas transport between I bubbles and the flu id. These processes have yet to be defined, although research activity on this problem is intensive (see Thorpe, 1982). Since bubble production is ultimately a result of ' wind shear, the effect of bubbles is incorporated in the empirical relationships between gas exchange and wind speed. The problem ! with this approach is that i t is doubtful that bubble production is i solely a function of wind speed. Until our understanding of | bubbles improves, this simplified approach must be employed. ; The importance of convective overturn on gas exchange rates i has not been quantified, since i t is believed to be small relative to the other controlling processes. Convection could be important on small time scales during extremely quiescent conditons or on j longer time scales in sheltered lakes. i ! Although surface films do not generate turbulence in the water column, films are thought to influence gas exchange by increasing the resistance of the interface to gas transport and by changing ! the turbulence in the surface layer. The effects of surface films i on gas exchange have been studied in detail (for example, Liss, 1975; Hunter and Liss, 1981). These studies have shown that the increase in interfacial resistance requires a nearly continuous layer at the interface. This condition is unlikely to be fu lfille d in environments where wind and waves are present. The influence of films on the turbulent field is mostly due to the damping of capillary waves and this effect has been observed in natural systems, especially in areas where biological production or anthropogenic input of organic material is high. Thus, i t is conceivable that surface films could have a significant effect on gas transfer during low turbulence conditions. The conclusion to be drawn from the results of the previous work is that our knowledge of the dependencies of gas exchange on turbulent generating processes is fragmentary. Clearly, elucidation of the controlling processes, and thus the development of reliable predictive relationships requires additional measurements of exchange rates in the fie ld . One useful tool for deducing these rates is radon-222. The advantages of using radon as a tracer for exchange rates are: (1) i t is inert, thus its reaction kinetics are known, and (2) errors due to contamination are easy to avoid. This chapter presents radon data for the water and sedimentary columns for a section of south San Francisco Bay. Exchange rates of radon across the sediment-water and air-water interfaces are computed from these data and are compared to rates measured across both interfaces by in-situ methods. The measured 67 air-water exchange rates are used to investigate the processes controlling exchange across this interface and to test the accuracy of transfer coefficients given by four predictive relationships. Description of the Study Area A map of south San Francisco Bay (hereafter referred to as South Bay), including station locations and bottom topography, is shown in Figure 3-4. The majority of measurements were confined to the section of South Bay extending southward from USGS station 26 to the San Mateo Bridge. Inputs of radon from groundwater and run-off are low, and gradients in salinity and radon along the north-south axis are small throughout the middle reaches of South Bay. These characteristies allow the study section to be treated as a closed system with respect to radon exchange. Shoal areas (water depths < 4 m) constitute approximately 90% of the area of the study section, but only 50% of the water volume. Vertical gradients are absent except in the channel areas (4m - 10m depth), where small gradients exist. Circulation is tid a lly dominated and relatively constant throughout the year (Conomos, 1979). 68 CENTRAL BAY Bay Bridge OAKLAND '20 Golden Gate J ^ SAN FRANCISCO 22 23 24 SOUTH BAY 2 8 A 28B 26, San Mateo Bridge SAN FRANCISCO i n t ’l a ir p o r t 29 . 321 Dumbarton Bridge > .3 6 . KILOMETERS Figure 3-4. Map of south San Francisco Bay showing station locations and bottom topography. Isobaths in meters. The study section extends southward from station 26 to the San Mateo bridge. Note locations of stations 27, 28, 28A, 28B, 28C, 28D and the S.F. airport. 69 METHODS Radon concentrations in the water column were determined by the techniques of Broecker (1965) and Mathieu (1979). These consist of the extraction of radon from 20 lit e r samples onto activated charcoal at dry-ice temperature, followed by alpha counting in scintillation chambers. Radium concentrations were determined by the identical procedure after storage of the radon-free sample for at least two weeks to allow ingrowth of the daughter. Precision of the reported data is ±3% for both radon and radium concentrations. Exchange rates of radon across the sediment-water interface were determined by two methods: (1) by integrating the depth deficiency of radon versus radium in the sedimentary column as described by Key et a l . (1979) and Hammond and Fuller (1979), and (2) by direct measurement using in-situ chambers. Sedimentary radon and radium activities were obtained from gravity and diver-collected cores (5cm ID) by placing 2 to 5 cm sections into glass jars, adding 100 m l of water to form a slurry, sonicating in a water bath for 60 minutes, and extracting the radon for counting j as described by Hammond and Fuller (1979). Analytical precision is j | ±5% for the sediment samples. j In-si tu fluxes of radon from the sediments were measured using j plexiglas chambers (40cm X 40cm X 28cm) deployed by SCUBA divers, j typically for a 24 hour period. Chambers were inserted approximately 8 cm into the sediments, enclosing a column of water 70 20 cm high. Water samples were drawn into an evacuated bottle either through a nylaflow tube (1/4" 0D) extending from the chamber to the surface or directly from the chamber by a diver, depending upon surface roughness (in rough weather, there was an annoying tendency to pull the chambers off the bottom when drawing through the nylaflow). A volume of water equal to that drawn for analysis entered the chamber through a check valve during sampling. Some of the chambers were equipped with battery operated stirrers (2-6 RPM) to insure homogenization of the chamber water. Further details of the chamber design and sampling and computational procedures are given by Hammond and Fuller (1983). In-situ fluxes of radon across the air-water interface were determined using the same plexiglas chambers, but modified to insure floatation and gas-tight conditions. Using a method similar to that described by Copeland and Duffer (1964), chambers were covered with aluminum foil to reflect sunlight, fille d with helium, and allowed to d rift with the current. After approximately 60 minutes, the chamber gas was drawn into an evacuated bottle, and analyzed for radon. Gas transfer coefficients were calculated from the change in chamber gas concentration over the float period, using equation (1-4) in the form: J = h d^d = K i (^w-Cd/H) (3-2) “ arr where: h is the height of the chamber gas phase ( ^20 cm for most ments, and Cj is the radon concentration in the chamber gas. 71 The general solution to equation (3-2) is: h K |_ = - Ht In (Cw_Cd/H)t j n ^ 7 F t 0_ (3-3) where t is the deployment time and the subscript o represents the chamber gas concentration at t=0. For short deployment times, Cd/H<<Cw and equation (3-3) reduces to: h(Cdt - Cdo) KL = (3-4) During the chamber deployment procedures, some gas exchange occurred due to stripping by helium bubbles as the helium was added and due to turbulence induced beneath the chamber by the passing current. Thus, ^d0 was not equal to zero. Measurements of ^d0 were made on two chambers during November 1981 by sampling the chamber gases immediately after deployment and measuring the radon ac tiv ity . These values are presented in Table AI-4- (Appendix I) . The two measurements were remarkably consistent and represented approximately 20% of the observed flux in the chambers after float times of approximately 60 minutes. The magnitude of should depend upon the turbulence created o during deployment and the radon concentration in the water. In turn, the turbulence should depend primarily upon current velocity and surface roughness. Assuming the turbulence conditions to be constant for all sampling periods, estimates of for the other sampling periods were obtained from the product of the 72 ratio of the radon concentration at deployment time to the radon concentration on 11/3/81 (1.0 dpm/j) and the measured in itia l concentration on 11/3. These values are probably minima since the current velocity during the 11/3 "blank" measurements was the slowest recorded for all sampling periods and the water surface was nearly undisturbed. Thus, the computed transfer coefficients for these periods are probably upper lim its. ! RESULTS Radon and radium concentrations in the water column for the study section are presented in Table 3-1 and for the entire San Francisco Bay estuary in Table Al— 1• The tabulated concentrations are mean values ±1 se of all measurements made in the shoal and channel areas for each sampling period. The last row in Table 3-1 gives the average values for all sampling periods (weighing each i sampling date equally). Shoal areas generally have higher radon j concentrations than channel areas. The western shoal concentration is always higher than the eastern shoal, by an average factor of 1.5 for all sampling periods. Radon to radium activity ratios in the sediment column and the computed integrated deficiencies from these profiles are listed in Table 3-2 and illustrated in Figure 3-5. These data are averages of the values from all cores collected from 1976 to 1981, grouped by location and time of year. Data for the individual cores is given in Table AI-2. By averaging the data in this manner, scatter due to annual and spatial variations is minimized. Integrated deficiencies were calculated using a (Rn/Ra) equilibrium ratio equal to unity for all composite cores. This was reasonable since ; this ratio fe ll within 3% of unity for all but one composite core (28C, Winter), in which a lack of data at deeper intervals (>30 cm) may have precluded the attainment of equilibrium. This result is of particular interest because of the recent concern regarding the validity of the slurry method for measuring 74 TABLE 3-1. Radon and radium concentrations (in dpm/t) in the water column for a section of south San Francisco Bay extending from USGS station 26 to San Mateo Bridge, n represents the number of samples for the mean values in the preceding column. [Ra] [Rn] [Rn] [Rn] West Shoal & Date East Shoal n West Shoal n Channel n & Channel n 1/76 - - - - 1 . 70±0.05 1 - - 8/76 1.10+0.20 2 2.00±0.30 2 1 .18±0.14 4 - - 3/77 1.66±0.24 5 2 .05±0.25 7 1 .10±0.06 6 0 .20±.01 1 7/77 - - - - 1 . 17±0.02 30 - - 10/77 - - - - 1.62+0.06 20 - - 7/78 - - - - 1 .24±0.06 2 - - 6/79 - - 1 . 70±0.25 6 1 .15±0.06 4 - - 2/80 2.21±0.17 2 3.53±0.11 1 1.48±0.12 16 0 . 13±.01 4 3/80 - - - - 0.85±0.05 6 - - 6/80 0 .93±0.10 3 1.60±0.18 3 1.01±0.03 11 - - 10/80 2.44±0.28 4 3 .93±0.55 4 1.66±0.07 10 0 . 15±.01 2 2/81 - - 2 .38±0.16 4 1.10±0.11 11 - - 11/81 1.46±0.04 1 1.82±0.05 1 1.05±0.02 4 - - X " 1.63±0.24 6 2 .30±0.34 8 1.25±0.07 13 0 . 15±.01 3 I 75 i TABLE 3-2. Stati on 27 & 28 Radon to radium a c tiv ity ratio s, radium a c tiv itie s , and integrated deficiencies of radon in the sedimentary column for a section of south San Francisco Bay. n represents the number of samples analyzed. Deficiency Season interval (cm) Rn/Ra+'lse n _ Ra^ r > * ±lse /■Atoms \ W - s e c ' Winter 0-3 0.57±.06 6 3.66±.26 40±3 Feb.-Mar. 3-6 0.79+.04 6 4.08±.25 21+3 (7 cores) 6-9 0.84±.02 4 4.22±.34 17+4 9-20 0.90±.05 6 4 . 02±.22 37+11 20-30 0 . 93±.03 2 4.06±.28 24±12 30-35 0 . 98±.02 3 4 .35±.54 4±11 35-40 1.00±.02 0 - 40-50 1.03±.01 3 - Summer June-Aug. (2 cores) Z=143±20 0-3 0.45±.09 2 3 .6 U .3 0 50±4 3-6 0 . 72±.05 1 4.26+.21 8±5 6-9 0.81± .07 2 4.61±.09 22±3 9-15 0.89+.07 0 4.62± .11 25±1 15-21 0.98±.02 2 4 .63±.06 5±2 21-33 0 . 96±.07 0 4.83±.26 19± 12 33-36 0 . 94±.07 1 5 . 10±.25 8±3 36-39 0 . 97±.07 0 5 . 27±.32 4±4 39-70 1 .00±.01 4 5 . 44±.20 - 2=141±15 Fall Sept.-Dec, (8 cores) 0-3 0.56±.02 7 3.91± . 13 43±1 3-6 0.80±.09 6 4.17±.15 21 ±4 6-9 0 . 92±.07 6 4.12±.10 8±3 9-12 0 . 88±.09 0 4 .23±.24 13±3 12-21 0 . 84±.05 8 4 .34±.22 52±9 21-24 0.97±.06 0 4.45±.30 11 ±4 24-30 0.96±.04 6 4 .56±.21 9±6 30-33 0.94±.04 0 4 . 71±.26 7±3 33-42 0 . 92±.02 3 4 .87±.15 29±5 42-81 1.04±.06 7 4 .99±.14 - 2=193±14 o o - i n > cu ~ j n > cu K > o o 3 w ---- T | - p > n > c u ■ a — I O r+ _l o • 5 o ( / > n > '— o ro ro —» — • co— *cocncocncoo i i i i i i i i r o r o r o — >— >cocnco cn co — ■ oo cn o o o o o o o o C O 00 C O • ^ J c n c n c n C O co c n o 00 -o — i 4* 1 + i+ 1 + 1 + i+ l+ i+ 1 + o o o l_l L . !_i o ''J <n <n ro ro 4* ro 4* —1— • — * O C O C O 4* 4* 4* ro C O C O C O C O C O O o 0 0 L i cn cn c n L 4* 4* C O c n o — • 4* c n 1 + 1 + 1 + i + i+ 1 + 1 + l + ro ro L i 4* 4* C O C O ro o o 4* C O 0 0 ro c o c n II _ i _ i ro C O C O cn 4* -o -o C O 4* 00 ro 1 + i+ i+ i+ 1 + 1 + l+ ro ro cn cn cn cn C O " - v l \l 5 > ro cn 03 00 c+ I - ro 3> C U m 0 0 - c+ a _!. C O ro O 00 3 i ro o C -. cn ~n z : cn cn c c cn ro _i, C D ,—» — ■ 2 cr 3 C U o o << 3 o • rt- u> o O 1 C D O 1 ri) o z 2 > 3 3 2 - i 3 H n 5 c r t > c u 1 — i c n m w p z i — < c z m a C O ro —i cn ro ro _ i 3 0 1 i 00 1 co cn co i i i 0 1 cn i cn i i cn co cn co i i i i 0 1 « — ' C + O C D 4* C O ro _ i co cn C O cn C O ro ro — • co <n C O 3 3 cn o —1 o o o cn cn _ i cn — < C U _ i o O O o o o o o o o o o o o 30 • • • • • • • • • • • • • • • 3 o co 00 -o cn 4* C O co 00 00 00 4* cn cn 4* \ — i co cn C O C O C O — 1 4* - '- J 4* — 1 ''J 4* C O 30 i+ i+ i+ 1 + i+ 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + i+ 1 + c u • • • • • • * • • • • • • • 1 + o o o o o O o o o o o o O o o cn 00 C O cn cn ro ro -o C O C O ro cn ro 4* c n a> C O ro o 4* cn 4* cn -■ ro o ro 4* cn cn cn = » cn 4* 4* C O 4* C O C O cn C O C O C O 4* 4* C O C O 30 • • • • • • • • • • • • • • c u c n co ro 'O ro -o o -o C O 4* cn ro ro 00 C O ^ - -V o — j cn 4* o C O o 00 o — 1 ro cn o 00 QL13- i+ l+ i+ 1 + i+ 1 + 1 + 1 + 1 + 1 + i+ i+ i+ 1 + 1 + ro ro 4* ro ro L L ro L 0 0 0 0 — • L L ro cn C O O -o o o — 1 C O cn cn cn o 00 o cn ♦ i + M M C D II II . n > ro C O —i 31 > -+i C O — ■ 4* 4* cn 4* C O —t C O — i 4* 4* 4* N c+ -*• $ 4* cn cn C O 00 ro C O cn 00 C O C O 00 ''J 00 1 O O 1 + i+ i+ 1 + 1 + i+ 1 + i - t - 1 + 1 + 1 + 1 + 1 + 1 + l /> 3 — * • — ■ 4* cn co ro C O — j ro _ i —1 _ 1 cn ro ro co n > < / » n > 4* o co cn o 3 Q Rn/RaJ A T CHANNEL STATIONS (27 S 28) o CD O O C V J + 1 ro C T > o C V J o fO o o lO o CD o N - O O CD O ID O o o C V J O O ro O in o o 0 D CVJ _l O 2 -* C V J Q Q0 CVJ o' O (D O O ID O C V J o ro O ao CVJ < 1 ^ C V J CO < I— CO < o X CO o ao o C D o o C V J CO ro CVJ Es I 5 ^ a o CVJ o ro o o » n o CD O O ao CVJ - H ro o o C V J o o C V J o ro o o in o o c r tz cr a o CVJ + 1 ro ro C V J o in o o ro O O o cvj (■WO) H Xd3G ( ujo) H X d 3Q Figure 3-5. Radon to radium a c t iv it y ra tio s in composite cores fo r each sampling season fo r the channel and shoal areas. Each data point is the mean {t lse ) of a ll samples co llec ted in the indicated depth in te r v a l. Shaded area indicates radon deficiency. The numbers in boxes give the integ rated d e ficien c ies in atoms/m -sec and were computed from the average Rn/Ra and average radon emanation ra te in each depth in te r v a l. 78 radon emanation rates from sediments. Key et a l . (1979), and Berelson et a l . (1982) have shown that emanation rates determined j | from slurries of fine-grained marine sediments are enhanced by 10% to 20% above in-situ rates. A similar result was reported by j Smethie et a l . (1981) for shelf sediments. However, equilibrium I ratios ( i . e . , Rn/Ra = 1) were observed by our group in the Potomac i j River estuary (Hammond and Fuller, 1983) using the slurry method. | The implication from these data is that the accuracy of emanation | rates determined by the slurry method appears to depend upon the | sediment type and grain size as suggested previously by Hammond and Fuller (1979). While application of the slurry method for I measuring emanation rates in marine sediments is doubtful based on i i | these results, i t appears valid for estuarine sediments. | j Radon fluxes across the sediment-water interface measured i in-situ are presented in Table 3-3. Values measured in the stirred chambers have been separated from values measured in unstirred chambers to fa c ilita te comparison. The tabulated fluxes are mean fluxes ( ±1 se) for all chamber deployments for each sampling period (individual fluxes for all deployments are given in Table j j AI-3). The two values marked with asterisks are addressed in the ! i discussion section. | | Gas transfer coefficients computed from the floating chamber method are given in Table 3-4. The transfer coefficients are means (+ lse)of 2 or 3 deployments for most periods (individual fluxes TABLE 3-3. In-situ Fluxes of Radon Across the Sediment-Water Interface Measured with Stirred and Unstirred Chambers, n represents the number of samples for the mean values given in the subsequent column. Stirred Unstirred Deployment Flux (atoms \ Flux (atoms) Date Station n m z-sec n m z-sec 6/79 Channel(28) 2 198+43 3 63+14 2/80 Channel(28) 3 268±12 7 It 5 West Shoal(28C) 1 211 2 28± 4 6/80 Channel(27) 3 74± 5 4 67±28 West Shoal(28C) 3 261+46 2 190+ 6 10/80 Channel(27) 6 66+12 3 46+17 West Shoal(28C.28D) 6 302+45 East Shoal(28A,28B) 5 229+66 E Shoal 11 269+38 2/81 Channel(27) 7 112+19 Channel(27) 3 153+18* 2 42+4* l Channel 10 124+15 2 42+ 4 West Shoal(28C) 4 209+21 3 159+14 ^Denotes experiments using a chamber equipped with a switched stirrer. See text for discussion. TABLE 3-4. Gas Transfer C o efficien ts Computed From the Across The Air-Water In te rfac e. In -S itu Radon Flux Date Stati on Wind Speed (m/sec) Current Speed (cm/sec) Kl (m/day) 7-17-78 28 2 .2 a 5 .3 b 47c 1.7± 0.5 11-5-80 27 - 4.0 0C 1. 6± 0. 5 11-6-80 27 - 2.0 15d 0.4±0.1 2-23-81 27 - 5.3 40d 5.6 28C - 5.3 l l d 4.7 2-25-81 27 - 2.7 26d 0.9 2-26-81 28C - 2.4 33d 2.2 2-27-81 27 - 2.2 37d 2.1 28C - 2.2 40d 1.7 27 - 2.2 17d 0.4 10-31-81 26 1.9 3.3 13c 1.9±.12 28C 1.4 3.1 25c 1 . 5± .07 27 1.1 2.0 6C 0.6±.03 11-1-81 27 0.5 2.7 26c 0 .9 *. 06 28B 0.3 2.7 35c 0 .2 *.0 2 11-2-81 27 1.4 1.8 12c 0.4±.06 27 2.2 2.0 l l c 1.1—. 24 27 1.4 2.0 27c 0.7±.08 27 0.8 1.8 3C 0.4* .03 11-3-81 27 1.1 1.8 20c 0.3 *.04 27 1.1 1.8 20c 1.2e a - values in th is column from measurements made on station using a hand-held anemometer, corrected to a 10m reference height, b - values in th is column from measurements at S.F. a ir p o r t, 10m above the water surface, c - values calculated from t id a l current data, d - values from USGS current meter records, e - tethered chamber. for all deployments are listed in Table AI-4). The values vary by as much as a factor of 4 over the period of one day and range from 0.2 m/day to 2.0 m/day for all dates except 2/23/81. These la tte r values were measured during extremely rough surface conditions, and may be in error because of additional turbulence generated by the j rocking chambers. The measured rates are of similar strength to values measured in streams (Rathbun, 1977), lakes ( Broecker et a l . , 1980), and estuaries (Juliano, 1969; Hammond and Fuller, 1979; Hammond and Fuller, 1983), but are at least a factor of two lower than rates measured in the coastal and deep ocean (Broecker and Peng, 1974; Peng et a l . , 1978; Tsunogai and Tanaka, 1980). During November, 1981, an experiment was performed to investigate the effect of tethering the chambers on the measured | fluxes. The tethered flux value was a factor of 4 higher than ! j values measured in concurrent free-drifting chambers (Table 3-4, j 11-3-81), presumably a result of the increased turbulence within I the chamber created by the passing current. This experiment suggests that in-situ measurements should be restricted to free-floating chambers. j i A n additional estimate of the transfer coefficient can be made ! by constructing a radon budget for the study section and computing ! the air-water exchange term as a forced value. This was done using | a thirteen-box model to represent the study section (Figure 3-6). The use of a multi-box model was preferable to a one-box model, because it provided a better representation of bottom topography and also allowed horizontal transport across the bay to be modeled. 82 c y > Representation of the 13-box model used to bottom topography across the center of the construct a mass balance for radon and of the study section. Vertical exaggeration is 500 to For each box, radon was supplied by the sedimentary column, by radium decay in the water column, and by exchange with neighboring boxes. Radon was lost by decay, by exchange with neighboring boxes, and by exchange across the air-water interface. The exchange terms between boxes and across the air-water interface were modeled as diffusive processes, with a characteristic horizontal eddy d iffusivity (Dh) and transfer coefficient (KL), respectively. These parameters were assumed to be constant over each side of the bay, but the east side and west side were allowed to have different values. For any box, the mass balance equation is: dcw = PROD + JSED + DIFFIN - DECAY - JATM - DIFFOUT (3-5) “ cPt where: PROD is the radon input from radium decay, JSED is the radon flux per unit area of sediments divided by the water depth, DIFFIN is the radon input by diffusive exchange with the neighboring box of higher concentration, equal to: (ACw) “ X Z T x DECAY is the radon lost by decay, JATM is the radon exchange across the air-water interface, equal to: (Cw-Co)/h, 84 DIFFOUT is the radon lost by diffusive exchange with the neighboring box of lower concentration, equal to: Dr (A ^ w ) , X a5T X is the box width, h is the box depth, ACW is the concent rati on difference between two successive boxes, and AX is the distance between the centers of two successive boxes. A total of seventeen parameters were unknown: the radon concentrations in each box, K |_ and for the west side of the bay, and K |_ and for the east side of the bay. K |_ for the channel box was assumed to be equal to the average of the east and west values. A mass balance for each box gave thirteen equations, thus four boundary conditions were required to solve the model. Three were obtained by setting the concentrations in the outermost and center boxes to the measured values. The fourth boundary condition was obtained by requiring that the net transport of radon be from the shallow boxes to the deeper boxes. This is a reasonable constraint since the channel box loses more radon by decay than i t receives from the sediments, and thus i t must receive radon by horizontal transport from the shoal areas. The fourth boundary condition allows a range of possible solutions, since the required radon could be supplied by just one of the two sides or by combinations of both. 85 The model was solved by choosing values for the transfer coefficient and solving the mass balance equations numerically, assuming steady state. Iterations continued using new values for the transfer coefficients until the boundary conditions were satisfied. It was assumed that the study section acted as a closed system with respect to axial transport and that C0 = 0. A more detailed description of the algorithm is given in Appendix I I . For two sampling periods, August 1976 and June 1980, the radon concentration in the eastern shoal area was less than in the channel (Table 3-1). This situation did not f i t the fourth boundary condition, hence a solution was not possible with the thirteen-box model. Transfer coefficients for these two periods were calculated by constructing a mass balance for the entire system based on a three-box model representation, without considering the influence of horizontal transport. The difference in the computed K |_ values between this approach and the thirteen box model for all other periods was less than 10%. Transfer coefficients and horizontal d iffu s iv itie s , computed for the individual sets of water column data for all sampling periods for which channel and shoal data exist (Table 3-1) are presented in Table 3-5. The listed values are the midpoints of the range of possible solutions f u lfillin g the fourth boundary condition. Typical ranges relative to the midpoint values were approximately 10% for K |_ and a factor of 2 for D^. For February 86 TABLE 3-5. Gas Transfer Coefficients and Horizontal D i f f u s i v i t ie s Computed From a Radon Mass Balance. Current Wind Speed V e lo c ity ________ K \ (m/day) Peri od (m/sec) (cm/sec) East Side West Side Bay East West Aug. 76 5.5 48 - - 1.42* - - Mar. 77 5.0 48 1.45 1.0 1.33 - - Feb. 80 4.9 49 1.01 0.45 0.87 6.5 5.2 June 80 6.4 50 - - 1.78* - - Oct. 80 3.2 40 0.63 0.25 0.53 6.4 5.2 Feb. 81 3.8 33 - - 1.08** - - Nov. 81 4.1 36 1.25 0.85 1.03 6.5 5.5 6-YR . PER. . 1.29 0.70 1.13 6.5 5.6 *Values calculated using a 3-box model **Value calculated assuming [Rn]£^ST = [R^WESt/ 1*^ 1981, the radon concentration in the east shoal was estimated from I | the west shoal value by using the average concentration ratio (1.5) observed for all periods with comparative data. Sediment fluxes for the shoal and channel areas were taken as the average value of the integrated deficiency and in-situ fluxes for each season (Table 3-6). A final calculation was performed using averages of all the water concentration and benthic flux data collected since 1976 I (final rows of Tables 3-1 & 3-6). One immediate observation from the model results is that larger values of K j_ were required for the eastern side than for the western side of the bay to satisfy the observed concentration profiles. Since the predominant wind direction is from the west, this suggests that a relationship exists between gas exchange and fetch. The transfer coefficients (in m/day) computed by this method range from 0.25 to 1.0 on the western side, from 0.63 to 1.45 on i the eastern side, and from 0.53 to 1.78 for the entire study section. W hen averaged over the six-year period during which experiments were peformed, these values are 0.70, 1.29, and 1.13 for the west side, east side, and entire segment, respectively. Exchange rates reach a peak in the summer; the season of highest wind velocity. j Horizontal eddy di ffusi vities (in 1 0 5 cm2 /sec) computed from j the model range from 1.5 to 4 for the western side and 2 to 32 for ! I the eastern side. These diffusivity ranges match values determined j i 88 earlier for South Bay of 4 x 105 cm2/sec to 1 x 106 cm2/sec by Glenne and Selleck (1969), as well as values of 105 cm2/sec to 106 cm2/sec predicted from the scale of the system (Okubo, 1971). The average values of the gas transfer coefficient and horizontal eddy d iffusivity on the east side of the bay are approximately a factor of 2 and 10 higher respectively, than the west side. 89 DISCUSSION Sediment-Water Exchange Fluxes measured in the unstirred chambers are systematically lower than corresponding values in stirred chambers for all periods, although the magnitude of this reduction varies widely. These large discrepancies in the measured fluxes from the two types of chambers contrast with results reported by Hale (1974) and by j our group in the Potomac River (Hammond and Fuller, 1983). Lower fluxes in unstirred chambers can occur i f the chamber water s tra tifie s during the deployment period. The effects of stratification would be an increase in the possibility of drawing a non-representative sample, since the sampling port was located near the top of the chambers, and possibly a reduction in benthic flux. These effects are most likely to occur during February when the salinity in the water column is lower than in in te rs titia l i waters. j In an attempt to explore this hypothesis, a chamber fitted with a s tirre r controlled by an external switch was deployed during February 1981. After nearly 24 hours of deployment without ! stirring , a sample was taken, the switch was turned on for one hour, and another sample was drawn. The results of these experiments are presented in Table 3-3 (marked with asterisks). For three t r ia ls , the flux determined after stirring was nearly a factor of 4 higher than the pre-stirring flux (one of the pre-stirred samples was lost) and of similar strength to fluxes 90 measured concurrently in stirred chambers. The implications of this experiment are that stratificatio n ( i . e . , heterogeneity of the trapped water) can be a significant problem in unstirred chambers j under certain conditions and that the measured fluxes in these j chambers are probably lower than the true values. i ! Considering only the fluxes measured in stirred chambers, a I I few general trends appear. Fluxes from the western shoal areas are of similar strength to fluxes from the eastern shoal areas and remain relatively uniform over the 1 1/2 years of measurements. In contrast, fluxes from the channel vary by a factor of 2 from year i to year and by a factor of 3 over the period of one year. The i I reason for this variation is not clear. I Table 3-6 summarizes the fluxes determined by both the integrated deficiency and in-situ methods. Stirred fluxes from j Table 3-3 have been averaged by season in a similar manner to the core data. The agreement between the two methods fa lls within i 2se for 4 of 6 comparisons at the two stations (shoal, winter; channel, f a l l ) . For these la tte r two comparisons, the core i deficiency method gives higher values than the in-situ chambers. i ; Since the response time of the core deficiency method is i I j approximately seven to ten days, the discrepancy between the ! methods could be due to a period of increased benthic exchange just 91 TABLE 3-6. Summary of Measured Radon Fluxes Across the Sediment-Water Interface and Flux Expected by Molecular Diffusion. Radon Flux j^tomsj m^-sec Core In-Situ Season Station Deficiency Chambers Mean Flux Di f fusi on (< t> ) Winter Channel 143±20 157 ±21 150±14 63 2.4 Shoal 343±24 209+16 250+13 60 4.2 Sum m er Channel 141+15 124±33 138 ±14 64 2.2 Shoal 238+11 261±46 23 7 ±10 55 4.3 Fall Channel 193+14 66±12 120± 9 65 1.8 Shoal 191+12 269±38 198+11 53 3.7 I Channel 159+17 116±27 136± 9 64 2.1 Shoal 257+45 246+19 228 ±16 56 4.1 prior to chamber deployment. O n a yearly basis, the fluxes from the two methods agree within 15% and 35% for the shoal and channel stations, respectively. The reason for the larger discrepancy in | the channel fluxes is unclear. Since i t cannot be determined whether the integrated deficiencies or the in-situ measurements are better estimates of the true benthic exchange rate, we have taken the weighted mean (based upon the standard error) of both methods as the best ; estimate (Table 3-6). The mean fluxes remain relatively uniform over the course of a year, with the shoal fluxes nearly two times j i greater than fluxes in channel areas. These fluxes are compared to | fluxes expected by simple molecular transport in the last column in j Table 3-6. Molecular diffusion fluxes were computed using the j expression given by Hammond and Fuller (1983), assuming a radon i | d iffusivity in the sediments of 9 x 10~5 cm /sec. The measured fluxes are 2 and 4 times higher than fluxes expected solely by : molecular transport for the channel and shoal areas, respectively, i The likely mechanism for these enhanced fluxes is the action of burrowing organisms. Models of the exchange processes and the ^application of these exchange rates to the nutrient dynamics in | South Bay will be presented in a subsequent paper (Hammond et a l . , I 1983). Air-Water Exchange Dependencies of Gas Exchange on Current Velocity and Wind Speed in Estuarine Systems ~ Turbulence is presumably generated by both wind and current shear, however, a lack of field data has precluded determination of the relative importance of these processes in controlling exchange rates. Juliano (1969) concluded that wind shear controlled gas exchange in the Sacramento-San Joaquin delta. Previous measurements suggest that processes other than wind shear may control gas exchange in South Bay (Hammond and Fuller, 1979) and in the Potomac River (Hammond and Fuller, 1983), although the data base is limited. To investigate these dependencies, stepwise multiple regression analyses were performed on the computed gas transfer coefficients with current velocity and wind speed as the independent variables. The goal was to determine the functional relationships in a form: KL = B v V (3-6) Where B is a constant, V is current velocity, W is wind speed, and x and y are exponents. Current velocities were estimated from tidal current tables, assuming a sinusoidal velocity curve, or from USGS current rneter records. Wind speeds were taken from measurements made at three-hour intervals by the National Weather Service at San 94 Francisco Airport at a height of ^10m above the water surface. j i For some periods, wind speeds were measured on-station at ^2m height using a hand-held anemometer. These la tte r values were corrected to a 10 m reference height assuming a logarithmic velocity profile. The data from Tables 3-4 and 3-5 were divided into three groups for regression analysis for the following reasons. Chamber i data were regressed separately from mass balance data because of j j the large difference in time scales of the transfer coefficients j computed from the two methods (one hour vs. 3 to 6 days). Chamber | i data were regressed separately against airport wind speeds and j i against on-station (anemometer) wind speeds since i t was doubtful j that the values estimated from each method would be the same. Wind speeds and current velocities used for correlation with the mass balance data were averaged over a period commencing six days prior s to sampling through the end of the sampling period, to match the response time of the method. The relationships between the transfer coefficients and current velocity and wind speed are illustrated for the chamber data in Figure 3-7 and for the mass balance values in Figure 3-8. The plotted values have not been corrected for temperature differences, since the functional dependence between exchange rates and temperature has yet to be resolved. If it is assumed that K |_ depends linearly upon the ratio of the diffusivity over the kinematic viscosity (the inverse Schmidt number), then the maximum temperature correction would be 15% of the plotted values. 95 Airport Wind Speed (m/sec) Current Velocity (cm /sec) X <2.0 A 2.0- 2.9 ■ 3.0-3.9 • > 4.0 6.0 5.0 40 o ID E 3.0 til * 2.0 <1 1 .0 - A • I X 0 -9 A 10-19 ■ 20-29 • >30 10 20 30 40 50 CURRENT VELOCITY (cm/sec) 6.0 5.0 T3 4.0 _l 3.0 2.0 1.0 2.0 3.0 4.0 5.0 6.0 AIRPORT WIND SPEED (m/sec) Figure 3-7a. Relationships between the gas transfer coefficient and current velocity and airport wind speed observed for the chamber experiments. U D CT) KL(m /day) Anemometer W ind Speed (m/sec) 0 — 0.9 X 1.0 — 1.5 ▲ 1.5 — 2.2 ■ Current Velocity (cm/sec) 0 - 9 X 10-19 ▲ 2 0 - 2 9 ■ > 3 0 • 2.0 .0 ▲ X ▲ * A * ■ , * 10 20 30 40 CURRENT VELOCITY(cm/sec) ^ 2 . 0 r o T> E 1.0 X? X 1 .0 2.0 ANEMOMETER WIND SPEED (m/sec) Figure 3-7b. Relationships between gas transfer coefficient with current velocity and with anemometer wind speed for the chamber measurements. K, (m/day) 2.0 2.0 >% D T3 \ E _j * 30 40 50 1.0 2.0 3.0 4.0 5.0 6.0 7.0 CURRENT VELOCITY(cm/sec) AIRPORT WIND SPEED (m/sec) c o Figure 3-8. Relationships between the gas transfer coefficient with current velocity and with airport wind speed for coefficients computed from the radon mass balance. Symbol legend as in Figure 3-7a. The general conclusions from the regression analyses are similar for all three groups of data. Gas exchange does not show any statis tic a lly significant dependence upon current velocity, but is strongly related to wind speed. The computed exponents (y in equation 3-6) relating the transfer coefficient and wind speed are 1.6, 0.8, and 1.7 for the data in Figures 3-7a, 3-7b and 3-8, respectively. However, there is no s ta tis tic a lly significant difference in the goodness of f i t given by these computed power dependencies and by simple linear dependencies. Additional measurements over a wider range of wind speed are necessary to select between these relationships. The computed slopes for the b e s t-fit linear expressions are 0.83, 0.66, and 0.37 for the data in Figures 3-7a, 3-7b and 3-8, respectively. If the two questionable measurements made on 2/23/81 are ignored in Figure 3-7a, the computed slope drops to 0.46. Considering the differences in the time scales of the two methods and the uncertainty of the wind speed data, the agreement between the 3 data groups is remarkably good. The computed slopes change by less than 1 0 % i f the data are corrected for temperature I differences as described previously. The lack of a dependence between K [_ and current velocity is ! i surprising, especially for the data presented in Figure 3-7b. All I I but one of these data were collected in November, 1981. Surface j i conditions during this period were exceptionally calm and the | primary process generating turbulence in the water column appeared I 99 to be tidal currents. Whether this lack of dependence is real or i perhaps due to inaccurate current velocity data is not clear. j I i However, the similar lack of dependence observed for the mass | balance data (Figure 3-8) supports the fir s t possibility. Comparison of Gas Exchange Rates Determined by the Mass Balance and Fi oati ng Chambers MethdoTs Comparison of the transfer coefficients computed from the mass balance and floating chamber methods is shown in Figure 3-9 for the s three sampling periods for which comparative data exists. The questionable chamber measurements from February 1981 have been neglected in this analysis. Perfect agreement between the two methods would follow the solid line in Figure 3-9. Uncertainty in j the K |_ values computed from each approach is indicated by the error bars. The agreement between the methods for two of the three sampling periods (2/81, 11/81) is quite good. For the remaining period (11/80), a lack of chamber data (four measurements) could be j i the reason for the poor agreement. J Although good agreement between the two methods exists when compared for a given sampling period (Figure 3-9), the agreement is not good when compared on a wind speed basis. For the two periods j (2/81, 11/81), showing good agreement, the average airport wind | i speed during chamber deployments was approximately 50% lower than the average value over the time period of the mass balance. j i Assuming that the mass balance values are representative of the ! j true exchange rate and that airport wind speeds are good estimates j i i 100 I ▼ CHAMBERS • O’CONNOR a DOBBINS 2.0 T D C 7 > T D m 0.5 2.0 1.5 1,0 0.5 K l ( m /d a y ) Figure 3-9. Comparison of transfer coefficients computed from a radon m ass balance to values computed from chamber measurements and to values predicted by the O'Connor and Dobbins current velocity model. Perfect agreement between the values would follow the solid line. of the station wind speeds, these data suggest that fluxes measured in the floating chambers are higher than true values. At high wind speeds, this result seems reasonable since the wind tends to push the chamber through the water, generating turbulence around the chamber walls. However, for the low wind speeds observed during these periods (^ 2 -3 m/sec), it does not seem likely that this effect should be important. If the lack of agreement between the two methods is due to inaccurate wind speed data, continuous, on-station wind speed data during future comparisons may help to resolve this discrepancy. Comparison with Models of Gas Exchange The transfer coefficients computed from the mass balance may be used to test previously proposed relationships for gas exchange rates in natural systems. Gas transfer coefficients were calculated from four of the predictive models discussed in Chapter 1 : (1) The stagnant film model (equation 1-5), computing the film thickness from the measured wind speed using the empirical data summarized by Broecker et a l . , (1980), (2) the surface renewal model of 01Connor and Dobbins (1958) (equation 1-9), (3) the large eddy model of Fortesque and Pearson (1967) (equation 1 - 1 1 ) and 102 (4) the viscous sublayer model of Deacon (1977) (equation 1-15). The assumptions and simplifications used in the calculation of the transfer coefficients from these models are as follows. Radon d iffu s ivities were taken from Broecker and Peng (1974), assuming water temperature of 13° in winter, 20° in summer, and 16° in f a ll. Gas phase friction velocities were calculated from the airport wind speeds using the relationship given by Hicks (1973). The mean depth of the study area was estimated to be 2.3m from a nautical chart. Comparison of the transfer coefficients predicted from the O'Connor and Dobbins model to the measured values is shown in Figure 3-9. The agreement is quite good for transfer coefficients between 1.0 m/day and 1.5 m/day, but poor for values outside this range. In fact, for this model to adequately predict the lowest and highest transfer coefficients listed in Table 3-5, the average current velocity required would be approximately 10 cm/sec and 90 cm/sec, respectively. Current velocities of these magnitudes are unlikely in the study section, thus i t seems doubtful that this model is accurately representing the process of gas exchange in this system. The predicted values from the three wind dependent models and the values derived from the mass balance are plotted against wind friction velocity in Figure 3-10, for a water temperature of 15°C. 103 The mass balance values for the winter and summer periods have been j corrected to 15°C assuming both square root and linear dependencies of K j_ with the inverse Schmidt number. The range of values corresponding to and lying between these dependencies is shown in ! i Figure 3-10 for the four periods requiring correction. The values j for October 1980 and November 1981 did not require correction since they were measured at 15° and are shown as single points (open circles) on Figure 3-10. Best-fit lines, determined by linear regression, through the corrected points are shown for both the square root and linear Schmidt number dependencies. Over the limited wind speed range observed in this study, the stagnant film model gives the best f i t to the measured values. The average difference between the predicted and observed transfer coefficients is 15%. The predictions from the other models are not nearly as good as the film model. The large eddy model gives reasonable estimates at low wind speeds, however, the difference in j I functional dependence with friction velocity causes increasingly | poor agreement as U* increases. Although the viscous sublayer j model predicts a similar functional dependence between K [_ and U* as ; observed with the measured values, the absolute values are far j i below the observed values. The average difference between the predicted and observed transfer coefficients is 65% for the large eddy model and a factor of 3 for the viscous sublayer model. j i i I 104 i K L ( m /day) STAGNANT FILM • Sc Sc 12 - LARGE EDDY 0 8 0 6 VISCOUS SUBLAYER 0.4 LABORATORY 0.2 20 Figure 3-10. Dependencies o f the tr a n s fe r c o e ff ic ie n ts computed from a radon mass balance, p re d icte d from th re e gas exchange models, and p re d ic te d by the la b o ra to ry re la tio n s h ip w ith wind f r i c t i o n v e lo c ity a t a w ater tem perature o f 15°C. Budget values f o r the w in te r and summer seasons have been co rrected to 15°C f o r both a lin e a r and square ro o t dependence w ith the inverse Schmidt number. The dashed lin e s are the b e s t - f it s to the co rre cte d p o in ts f o r the two fu n c tio n a l dependencies. 105 Also shown on Figure 3-10 are the values given by the 1aboratory-derived relationship (Equation 2-15), estimating q and L from U* and water depth as done for the other models. The predicted values follow the same trend as the large eddy model, but are a factor of 3 lower. The results from this comparison neither prove nor disprove any of the proposed models of gas exchange, since i t is not clear whether the discrepencies between the observed and predicted rates are due to errors in the estimation of the required parameters ( 5 , s) or to inaccurate representation of the gas exchange process. However, this comparison does show that at present, the best estimates of gas exchange rates in natural systems in which the fluid turbulence is primarily generated by wind shear are given by the stagnant film model, using the empirical relationship between film thickness and wind speed given by Broecker et a l . (1980), (Figure 3-2). 106 CHAPTER 4 j MEASUREMENT AND PREDICTION O F G AS EXCHANGE RATES IN ; WIND-DOMINATED SYSTEMS The results from the laboratory experiments (Chapter 2) | suggest that gas exchange can be adequately represented by a | surface renewal model, at least for conditions prior to deformation | of the interface. However, the fie ld studies (Chapter 3) indicate i that surface renewal models in which the relevant parameters are i estimated from current velocity, wind speed, and water depth do not | adequately represent the exchange process. Assuming that the gas | transport process was the same during both the laboratory and field | studies, these results imply that present methods for estimating i turbulent velocities and turbulent length scales from wind speed, current speed, and water depth are not satisfactory. Thus, application of surface renewal models for the prediction of gas i I exchange rates in natural systems will not be practical until field | measurements of the pertinent turbulence parameters are possible. J In the meantime, empirical relationships between gas exchange | rate and some parameter characteristic of the fluid turbulence must i suffice. As discussed in Chapters 1 and 3, the common approach is to relate the exchange rate to easily measured hydraulic and , meteorological parameters which generate fluid turbulence. Because of the d iffic u ltie s of trying to characterize the fluid turbulence j | by this approach an appealing alternative is to estimate the I intensity of the fluid turbulence and to relate the exchange rate to this parameter. Estimation of Fluid Turbulence from Salt Dissolution , One technique that has been proposed to estimate turbulence intensity is to measure the dissolution rate of a material suspended in the water column. Assuming that turbulence controls i both the dissolution rate and gas exchange rate, a relationship should exist between these two rates. To test this idea, dissolution rates of a moderately soluble j salt, NaSO^, were measured in some of the laboratory and field experiments. Salt tablets (3 cm diameter x 0.5 cm) were made in a hydraulic press and encased in an aluminum cap such that only one side of the tablet was exposed to the water. This insured a nearly constant surface area throughout the experimental period. The I i tablets were suspended at various distances from the interface, ; with the exposed side parallel to the water surface and facing the j grid. Tablets closest to the surface were generally suspended within 2 cm of the interface. The results from these experiments are given in Table 4-1. In the laboratory experiments, the dissolution rate decreased with i ! increasing distance from the grid ( i . e . , turbulence velocity) for tablets suspended below the grid. However, the same result was not ; observed for tablets suspended above the grid. The reason for this ! observation becomes clear upon examination of the relationship i between dissolution rate and surface renewal rate (Figure 4-1). While a positive correlation appears to exist between these two i parameters, large differences in renewal rate are required to see a TABLE 4-1. Results from the sodium sulfate dissolution experiments in the laboratory. Numbers in parentheses are the number of tablets used in the computation of the dissolution rate. Distance From Dissolution Rate q L q/L Run # Grid (cm)* (g/min x 1 0 0 ) (cm/sec) (cm) (see” 1 -3.0 5.1 (i) 3.6 1 . 2 3.0 -12.3 4.4 (i) 1.7 2.7 .64 3 +12.7 8 . 7±1.5 ( 2 ) 1 . 2 3.3 .36 +8 . 0 8 . 6 ± . 6 ( 2 ) 1 . 6 1 . 6 1 . 0 -12.7 4.0 0 ) 1.4 3.2 .45 -30.0 1.6± .3 ( 2 ) 0.9 6.5 .14 4 +18.0 8.7± .4 (6 ) 1 . 0 5.0 . 2 +13.6 8.4± .4 (5) 1 . 2 4.5 .27 -7.2 7.2± . 6 ( 6 ) 1.9 .7 2 . 6 -24.0 5 .2± .4 (6 ) 0 . 8 4.6 .18 5 +18.0 7.3± .7 ( 2 ) 1.4 5.0 .28 +13.6 7.1± .3 ( 2 ) 1 . 6 4.5 .35 -7.2 6.3± .5 ( 2 ) 2 . 2 1 . 1 2 . 0 -24.0 4.7± .3 ( 2 ) 1 . 2 3.6 .33 *Negative values refer to distances below grid. Positive values refer to distances above grid. 109 V RUN No. I A RUN No. 3 O RUN No. 4 □ RUN No. 5 8 6 o » 4 2 0.2 0.4 0.6 0.8 1 .0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 (?) Figure 4-1. Relationship between N aS C > 4 dissolution rate and surface renewal rate observed in the laboratory experiments. Solid symbols represent values below the grid. Open symbols represent values above the grid. ! significant change in the dissolution rate relative to the analytical precision. For the measurements above the grid (runs 3,4,5), the variation in the renewal rate between tablets was too small to see a change in dissolution rate. In the field I experiments, no significant relationship was observed between dissolution rate and distance from the interface, possibly due to small variations in the surface renewal rate. ! The relationship between the gas transfer coefficient and j dissolution rate near the interface is shown in Figure 4-2. The plotted dissolution rates are only for the tablets closest to the interface and are mean values of all tablets suspended under identical conditions. No relationship appears to exist between these two parameters for either the laboratory or field measurements. This result is not surprising following the preceding discussion and implies that for the limited range of j turbulence conditions observed in the laboratory and in the fie ld , this method is not sensitive enough to show significant differences. Thus, the u t ilit y of this salt and possibly this method for estimating gas exchange rates in natural systems is ! doubtful. j Laboratory Comparison of Exchange Rates Measured with Floating j 'Chambers' | The accuracy of gas exchange rates measured with floating | enclosures has been questioned due to the potential influence of 1 j J the enclosure on the turbulent regimes in both the air and water. I Consequently, this technique has only been employed in a limited • FIELD ▲ LABORATORY >t o "O \ E _i 0 .8 - 0.6 0.4 0.2 0.2 0.4 0.6 0.8 1.0 SALT LOSS (% /min.) Figure 4-2. Relationship between the gas transfer coefficient and NaSC^ dissolution rate observed in the laboratory and field experiments. j number of studies (for example, Sugui ra et £l_., 1963; Copeland and Duffer, 1964; Kremer, 1978; Nixon et a l . , 1980; Murphy and Kremer, | 1983). Comparison of rates measured by this method to rates j determined by the mass balance approach in San Francisco Bay i S (Chapter 3) showed that the rates given by the chambers are higher I | than values computed by a mass balance. A similar result was i ! observed by Hammond and Fuller (1983) in the Potomac River estuary. j Since the rates deduced from the mass balance approach in these two systems agree well with values measured in other systems (see following section), the apparent conclusion is that rates measured with chambers are higher than true values. In an attempt to test the validity of the chamber method, a small "chamber" (volume a , 2 &) was constructed from a thick plastic bowl and deployed in the laboratory tank. The changes in concentration of C02 and CH4 in the chamber and in the tank water were measured simultaneously through time and transfer coefficients determined using equations 3-3 and 2-11, respectively. Coefficients for the chambers were also computed using equation 3-4 to test the difference in values obtained by assuming that the chamber gas concentration did not increase sufficiently to change the concentration gradient, i . e . , d e ficit from saturation. Since equations 3-3 and 3-4 were derived assuming constant water concentration, average values of Cw were computed for the time period of the experiment by averaging the in itia l and final values. 113 Transfer coefficients were computed from the time-series j measurements of chamber gas and water concentrations from the slope ; of the b e st-fit lines to equations 3-3, 3-4, and 2-11. The results from this experiment are summarized in Table 4-2. Coefficients for the 2 gases computed from the change in water concentration agree within 1 0 % and are similar to values measured previously under similar turbulence conditions (Run #4, Table 3-4), Transfer coefficients computed from the chambers, including the j correction for the chamber gas concentration (equation 3-3), show ! excellent agreement with the values computed from the water j concentrations. Chamber values computed neglecting the influence of the chamber gas concentration (equation 3-4) agree well with the other values for CH^, but are a factor of two lower for C02. This ! result is not surprising since the chamber gas concentration at the conclusion of the experiment was within 25% of saturation for i C02, but only within 95% for CHk (Table 4-2). j I The results from this experiment suggest that floating chambers j should be a valid technique for measuring gas exchange rates. j i However, this conclusion should be applied cautiously. In natural systems, chambers are disturbed by wind and wave motions which can I cause additional turbulence to be generated in the enclosed water ! column. In addition, the chamber may suppress turbulence generated by the wind. Neither of these conditions were produced in these j laboratory experiments. Thus, additional laboratory comparisons are required under more general conditions before the validity of I 114 Table 4-2. Comparison of gas transfer coefficients measured in floating chambers and computed from the change in tank water concentration in laboratory experiments. Method Gas KL(m/day) [(C0 -Cw)/Cw1 (% ) Tank Water (Eq. 2-11) CH^ .61 Chamber (Eq. 3-3) .59 5% Chamber (Eq. 3-4) .55 Tank Water Run # 4 .62 Tank Water (Eq. 2-11) C02 .70 Chamber (Eq. 3-3) .71 75% Chamber (Eq. 3-4) .36 Tank Water Run # 4 .59 115 exchange rates measured with chambers in natural systems can be assessed. Prediction of Gas Exchange Rates in Wind Dominated Systems Until methods to estimate fluid turbulence intensity or to measure the characteristic turbulence parameters are developed, prediction of gas exchange rates in natural systems must continue to be made using empirical relationships based upon parameters characteristic of the turbulence generating processes, e .g ., wind speed and current speed. Since the turbulent flow field appears to depend upon the scale of the system, empirical relationships based upon measurements in natural systems are preferable to 1 aboratory-derived relationships. Table 4-3 summarizes the measurements of gas exchange rates in natural systems in which the fluid turbulence is presumably dominated by wind shear. These data can be used to derive an empirical relationship between exchange rate and wind speed. Broecker et a l . , (1980) applied the stagnant film model to the majority of these measurements and derived a relationship between film thickness and wind speed (Figure 3-3). However, the results from the laboratory experiments (Chapter 2) suggest that a surface renewal model gives a better representation of the transport process. Assuming this la tte r model to be valid, hypothetical renewal rates can be computed for the data in Table 4-3 as: 116 Table 4 -3 . Measurements of gas exchange rates and wind speed in wind dominated systems. Chamber data are averages of a number of deployments. Location Method (°C) W i nd Speed (m/sec) D m (1° cm /s e c ) kl (m/day) s , (sec- 1 ) Symbol i n Fig. 4-3 Ref OCEANS Whol e Natural 1‘*C 20 8 1.64 4.7 1.80 M0 1 N. A tla n tic Bomb 11+ C 20 8 1.64 5.4 2.38 NA 5 A t ! . & Pac. Rn diseq uilib riu m 20 8 1.20 2.8 0.87 AP 1 N. Pac.-PAPA Rn diseq uilib riu m - - 12 0.83 3.6 2.09 PA 9 Atl.-BOMEX Rn diseq uilib riu m — 7 1.33 1.8 0.33 B0 8 Antarctic-GEOSEC Rn disequilibrium — 10.5 1.1 3.5 1.50 AG 1 Funka Bay ^2 balance - summer 15 3 1.75 3.35 0.86 FB 10 02 balance - winter 7 5 1.40 10.3 10.1 FB 10 LAKES Mono Bomb 1*+C 15 4 1.43 8.3 6.45 M0 3 Pyramid Bomb & Natural l “ *C 15 3.2 1.43 0.9 0.08 PY 2.3 Walker Bomb l*+C 15 3.2 1.43 3.3 1.02 M A 3 ELA 224 Tracer l “ *C 22 3.4 1.74 0.95 0.07 ELA 4 Rn spike 22 3.4 1.37 0.61 0.04 4 Rn spike-corral 22 3.4 1.37 0.65 0.04 4 ELA 226 Rn spike 20 2.5 1.20 0.62 0.04 6 Rn spike-corral 20 2.5 1.2 0.82 0.075 6 3 He 20 2.5 3.5 2.3 0.202 6 3He-corral 20 2.5 3.5 3.3 0.417 6 ELA 227 Rn spike 22 3.4 1.37 0.5 0.024 7 ESTUARIES Potomac Rn mass balance 20* 4.0 1.2 0.66 0.049 P0 11 Rn-chambers 20* 2.4 1.2 2.5 0.70 11 S.F. Bay Rn mass balance 20 5.5 1.2 1.42 0.225 SF 12 Rn mass balance 12 5.0 1.0 1.33 0.237 12 Rn mass balance 12 4.9 1.0 0.87 0.101 12 Rn mass balance 20 6.4 1.2 1.78 0.354 12 Rn mass balance 16 3.2 1.1 0.53 0.034 12 Rn mass balance 16 4.1 1.1 1.03 0.129 12 Rn-chambers 16 3.0 1.1 1.0 0.122 12 Rn-chambers 12 2.3 1.0 1.5 0.301 12 Rn-chambers 16 2.3 1.1 1.8 0.395 12 Narragansett Bay 0 2 -chambers 20* 1.8 2.03 1.0 0.066 N B 17 0 2 -chambers 20 2.8 2.03 2.3 0.349 17 0 2 -chambers 20 3.3 2.03 3.1 0.034 17 117 Table 4 -3 . Measurements of gas exchange rates and wind speed in wind dominated systems. (Continued) Locati on Method Temp (°C) Wind Speed (m/sec) D m ( l o - 5 cm /sec) KL (m/day) s . (sec ) Symbol in F ig .4-3 Ref. Colorado Lagoon ^2 -chambers 20* 1.0 2.03 0.22 .003 CL 13 20* 1.5 2.03 0.30 .006 13 20* 1.9 2.03 0.25 .004 13 20* 2.4 2.03 0.35 .008 13 20* 2.8 2.03 0.7 .032 13 20* 3.8 2.03 1.0 .066 13 L.A. Harbor •^-chambers 20 3.0 2.03 0.7 0.032 LA 14 Sacramento Delta 0 2 -chambers 20* 3.6 2.03 18.8 23.3 SD 15 20* 3.6 2.03 23.3 35.8 15 20* 0.9 2.03 24.4 39.3 15 0 2 -c o rral s 20* - 0 2.03 8.16 4.32 15 20* 5.4 2.03 8.71 5.01 15 20 0.9 2.03 16.3 17.5 15 20* 1.8 2.03 28.6 54.0 15 20* 2.7 2.03 26.8 47.4 15 Chipperton Lagoon 0 2 -chambers 20* 5 2.03 0.13 C H 16 ‘ Estimated Values Peng et a l . , 1979. 10. Tsunogai and Tanaka, 1981 BroecTcer and Walton, 1959. 11. Hammond and F u lle r , 1983. Peng and Broecker, 1980. 12. This work. Hess!ein et a l . , (1980). 13. Kremer (unpublished). Broecker et a l . , 1978. 14. Kremer, 1978. Torgerson et al . , 1982. 15. Ju lian o , 1969. Emerson et^ a l . , 1973. 16. Murphy and Kremer, 1983 Broecker and Peng, 1971. 17. Ni xon et a l . , 1980. Peng et a l . , 1974. (Ki measured) 2 s = --------------------- (4-1) These values are given in Table 4-3. i i The computed renewal rates are plotted in Figure 4-3 against wind speed for all of the water bodies listed in Table 4-3. The plotted values are averages of all measurements made for each system by any one method, except for Funka Bay where the large variation in wind speed between the two sampling periods precluded averaging. Rates measured in chambers and corrals have been plotted separately (open symbols) from rates measured by other methods (fille d symbols). If all the data in Figure 4-3 are considered, a simple dependence between renewal rate and wind speed is not apparent. However, many of the data are unreliable as discussed subsequently and are best excluded in the determination of the dependence between these two parameters. The chamber values from the Potomac River and San Francisco Bay are probably overestimates of the true | i rates as discussed in the previous section. In addition, exchange rates measured with corrals in the ELA are higher than rates I j measured by other methods during the same time period (Emerson et_ j i a l . ; Torgerson et al . , 1982), supporting the idea that rates j determined with chambers or enclosures may be higher than true ! rates. Thus, all values measured with floating chambers or corrals | (Juliano, 1969; Kremer, 1978; Nixon et a l . , 1980; Kremer, j unpublished; Murphy and Kremer, 1983) may be in error. Rates | i calculated by Torgerson et a l . (1982) for helium are suspect 119 SD □ 20.0 - 10.0 - 8. 0 - FB ■ 6. 0 - 4.0 - ▲ PA 2. 0 - wo • ▲ AG WA • FB ■ 1.0 - . 8 - AP ▲ P O A ELA V .4 - ▲ BO A SF NB □ ELA ▼ .2 SF ▲ ICH .08 - PY • .06- ELA ▲ PO C O ▲ ELA .0 4 - □ LA Rn He □ CL .0 2 - .01 -i------------------------- 1 -------------------------1 ------------------------- 1 ------------------------- 1 -------------------------1 — 2 4 6 8 10 12 WIND SPEED (m /sec) Figure 4-3. Relationship between the computed surface renewal rate and wind speed observed from measurements of gas exchange rates in natural systems. Open symbols represent measurements made in chambers and corrals. Location abbreviations given in Table 4-3. 120 because of the uncertainty in the molecular d iffusivity of helium. The wind speeds reported for Mono and Walker Lakes were not measured on location. In addition, gas exchange in these systems might be effected by the high salinity as discussed by Broecker et a l'. (1980). There is no obvious explanation for the high values determined in Funka Bay. These values were computed by constructing an oxygen budget, with the biological effects estimated from measurements of dissolved phosphate. Clearly, this approach is subject to numerous complications. An alternative explanation is that some other process besides wind speed is important for controlling gas exchange in Funka Bay. The best f i t equation to the remaining data (10 points) is: Kl 2 .45W = s = .019e (4-2) D m where s is in sec-1 and W in m/sec. Since rates determined by natural and bomb 13C methods represent long-term averages, inclusion of these data assumes that the wind speed has remained nearly constant over long time periods. If only the values obtained from radon measurements are considered, the equation becomes: .43W s = .017e (4-3) which is nearly identical to the previous expression. Considering the large variation in the size and type of systems from which these data were obtained, the good description is surprising. In tu itively , i t seems likely that fluid turbulence should also 121 depend upon system scale, fetch, and wave height; yet the data seem to be well represented by wind speed alone. It is doubtful that these parameters were constant for all the data shown. Note that the rates measured in the L.A. Harbor and Colorado Lagoon with chambers show good agreement with the exponential relationship. Although i t is possible that these la tte r values are overestimates of the true exchange rate, these data raise the possibility that the accuracy of rates measured with chambers is a | function of the chamber design and environmental conditions. The average deviation between the ten observed renewal rates and rates given by Equation 4-2, computed by dividing the root-mean-square of the deviations by the number of observations, is approximately 30%. Since the exchange rate is dependent upon the square root of the renewal rate, the 30% error in s translates to approximately a 15% error in Kj_. Thus, despite the fact that our understanding of the processes controlling gas exchange in natural systems is incomplete, i t appears that predictions of the average exchange rates in wind-dominated systems can be made to within 15% of measured values using the empirical relationship j derived from available field data. ; 122 CONCLUSIONS From the data collected in the laboratory and fie ld experiments, the following conclusions have been reached: (1) Gas exchange across an undeformed air-water interface appears to depend upon the square root of the molecular d iffusivity of the gas of interest and upon the square root of the quotient of the turbulent velocity near the interface and the turbulent length scale near the interface. This is in accordance with the surface renewal model of gas exchange. (2) Exchange rates predicted from previously proposed surface renewal models are ^ 2 times higher than rates observed in the laboratory. This discrepancy is presumably due to differences in the measurement of the relevant turbulence parameters. (3) Benthic exchange rates of radon for the channel and shoal areas of south San Francisco Bay are greater than rates expected by simple molecular diffusion by factors of 2 and 4 respectively, most likely due to the actions of benthic organisms. 123 (4) Radon fluxes across the sediment-water interface determined by in-sltu chambers and by integrating the depth deficiency of radon in cores show no systematic differences and agree within ± 2se in 4 of 6 comparisons of seasonal fluxes at two stations. Averages of fluxes on an annual basis are quite close. Both methods probably give representative estimates of the true fluxes. (5) Gas transfer coefficients for radon exchange across the air-water interface in South Bay range from 0.2 m/day to 2.2 m/day for all sampling periods, with a six-year average of 1.1 m/day. Exchange across this interface depends primarily upon wind shear stresses, and both wind speed and fetch appear to be important. Exchange rate is linearly related to the wind speed for speeds ranging from 0.2 m/sec to 5.0 m/sec. Current velocity has no apparent effect on exchange rate. (6) The use of an empirical relationship relating gas exchange rates and wind speed from the data given by Broecker et a l . (1980) based on observations in lakes and the oceans, predicts radon exchange rates for south San Francisco Bay which are within 15% of the values determined by a radon mass balance. 124 (7) Surface renewal models based on wind speed, current velocity, and water depth predict exchange rates for south San Francisco Bay which are two to three times lower than measured rates and do not show the same trend with wind speed. This discrepancy is most likely due to errors in the estimation of the required turbulence parameters from common meteorologic and hydrodynamic parameters. Application of these models to the prediction of gas exchange rates in natural systems requires direct measurements of the turbulent velocity and integral length scale. (8) Gas exchange rates measured with floating chambers in natural systems are often higher than rates given by other methods, presumably due to increased turbulence created by the chambers. (9) Characterization of the fluid turbulence intensity by NaS04 dissolution does not appear to be a promising method for estimating gas exchange rates in natural systems. 10) At present, empirical relationships between gas exchange rates and turbulence generating processes (such as wind speed and current velocity) yield more accurate estimates of gas exchange rates than present theoretical models. Compilation of all existing field measurements from wind-dominated systems suggests that predictions of average exchange rates can be made to within 15% of measured values based upon wind speed alone. REFERENCES Aller, R. C. and J. Y. 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Engr., 29, 146-148, 1923. 132 APPENDICES The following appendices present additional data and information which are related to this study, yet are not required by the majority i of readers to gain an understanding of the project. The goal is to present the detailed information and data required by future workers I involved in similar or related studies as well as by those interested in checking the results from this work. These appendices have been divided into three sections for cla rity and to fa c ilita te referencing. Appendix I contains a complete lis t of the data collected in the fie ld and laboratory. It is these data which have been reworked and modeled to yield the graphs and tables presented in the main body of the thesis. Appendix II contains a listing and brief description of the computer programs used for the modeling, processing, and presentation of the raw data. Appendix I I I is intended to serve as a laboratory manual. Included are detailed descriptions of the laboratory apparatus and procedures for the operation and maintenance of the equipment. APPENDIX I LABORATORY AND FIELD DATA This appendix contains a complete lis t of the data collected in the field and in the laboratory experiments. The data are presented as follows: Table: AI-1. Radon activity in the water column of San Francisco Bay. AI-2. Radon and radium activities in the sedimentary column of south San Francisco Bay. AI-3. In-situ fluxes of radon across the sediment-water interface measured with benthic chambers. AI-4. In-situ fluxes of radon across the air-water interface measured with floating chambers. AI-5. Gas transfer coefficients from the laboratory experiments. AI-6. Turbulence data from the laboratory experiments. 134 TABLE AI-1. Radon a c t iv it y in the water column of San Francisco Bay. Stati on/Depth Date Time (m) January, 1976 1-29 10:00 23/1 /15 1-29 11:00 21/1 /12 1-29 11:40 18/1 /12 1-29 12:45 15/1 /8 1-29 13:30 13/1 /8 1-29 14:15 11/1 / 12 1-29 15:15 9/1 / 15 1-29 16:45 6/1 / 6 1-29 17:45 3/1 /6 1-30 7:20 3/2 1-30 8:00 6/2 1-30 8:50 10/2 1-30 9:40 13/2 1-30 1:00 16/1 /9 1-30 11:15 17/2 1-30 12:00 19/2 / 5 0 1-30 12:20 20/2 1-30 13:00 21/1 /12 1-30 13:40 23/2 1-30 14:10 25/2 1-30 14:40 27/2 1-30 15:30 30/2 [Rn] Salinity [Ra] (dpm/ z) ( °/oo) (dpm/ & ) 1.31 1.16 1.53 1.00 29.3 1.01 0.89 31.7 1.18 1.26 27.2 1.32 1.15 25.2 1.26 20.9 1.10 1.25 20.6 1.47 1.29 8.9 1.64 0.08 1.86 4.5 1.51 1.66 9.3 1.22 14.9 0.10 1.12 24.0 1.23 30.3 1.29 1.21 31.5 1.10 0.93 32.2 0.15 0.87 31.4 1.60 1.23 29.9 1.64 29.4 0.11 1.63 28.6 1.70 27.9 2.21 27.2 0.23 135 TA B LE AI-1. R adon activity in the water column o f S a n Francisco Bay. 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C U O c E O ' • r — ■P < o -P L T ) C N J o C N J C O ^ + > > a d a d C 3 C N J r-H C 3 C O r-H i —1 < —I i—I i— - I r-H C N J C Z 3 i—I C N J (— 1 C N J C N J r-H C N J C O C O i-H r-H 0 0 -4fc O N r-H O N r-H LO r-H r — t i-H C O C N J C O r-H C " ^ ^ i-H C N J i-H i— H r-H C O C O C N J 0 0 i— H N n v s v s ' ss v s v n v > w w o n v v s ^ j : | u (D J 3 U ' N ' N V . W . V . W ' N ' V c o c o c o c o c o c r i c r i o c o c o c o < O L i _ < o o o c x 5 c r i c r i < - H r - i « d - « ^ - L O L O L n < o c o o o o o o o o o o o o o o o o o o o o o o o o o o i-H i—I r-H r-H i— I (/) r— I i- H r-H r-H i C N J C N J C N J C N J C N J C N J C N J C N J C N J C N J C N J C N J C N J C N J C N J C N J C N J C N J CO CO CO CO CO CO CO < D ■P n 3 O NO on -p c o 0 3 CD 3 C 0 0 LO o LO r - 0 0 C N J o LO VO LO LO o o LO LO LO o o LO CO ON LO o o LO o LO 0 0 LO O CO r ^ . LO LO LO O LO LO o LO LO LO LO CO r-H CO CO C N J i— H C N J o CO o C N J o LO i-H o LO CO LO LO CM CO i- • CM i-H i-H CM o o CM LO CM CO LO i— H VO r - ^ VO LO 0 0 ON o ON r-H ON i-H i-H ON 0 0 CO CO CO CO o o o i-H I-H CO ON ON 0 0 0 0 o VO LO CM CM ON VO 1 — 1 i-H i-H i-H rH r-H r-H i-H r-H r-H i-H I — H r-H r-H r-H i-H i-H i-H i-H i-H i-H i-H i-H r-H r-H i-H I — H o i-H o o r-H o o i— H i—4 o i-H o o i-H o o i-H i-H i-H i-H o o CM CM CM CM CM CM CM o i-H CM CM o 1 — 1 i-H i-H r-H i-H i-H i-H i—l i-H i-H i-H r-H i-H i-H i-H r-H r-H r-H i-H I — H i-H r-H r-H r-H i-H ON ON ON ON ON i- H i-H i-H ON i-H ON ON r-H r-H i-H r-H ON I — H l CO 1 CO 1 CO 1 CO ■ I 0 0 0 0 1 0 0 1 CO 1 CO 1 0 0 1 0 0 1 0 0 1 CO ■ I i ■ i 0 0 0 0 0 0 0 0 0 0 ■ ■ ■ ■ ■ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 CO 00 I I CO CO 1 00 1 00 1 00 0 0 CO CO ____ _______________ ____ ___ — — — TABLE AI-1. Radon a c t iv it y in the water column of San Francisco Bay. (Continued) [Ra] (dpm/ l) Date Time Stati on/Depth (m) [Rn] (dpm/ Z ) Sal i nv ( °/oo March, 3-7 1977 10:55 30/1 1.36 3-7 10:30 30/8 1.26 29.75 3-8 11:35 30/1 1.47 29.83 3-8 11:25 30/10 1.17 3-11 12:15 30/2a 1.52 29.6 3-11 12:25 30/2b 1.23 3-7 17:40 29/1 1.30 30.08 3-7 13:48 28c/I 2.90 30.23 3-7 12:15 28/1 1.18 30.4 3-11 9:50 28C/1 2.79 3-11 9:35 28C/1 1.69 3-11 9:10 27C/1 2.50 3-8 13:25 27/1 1.10 30.32 3-8 13:15 27/10 1.15 30.31 3-11 10:40 27/1 0.95 30.0 3-11 10:23 27/8 0.93 29.93 3-8 15:50 27B/1 1.29 3-11 11:00 27B/1 1.30 3-8 14:40 27A/1 2.69 3-11 10:45 27A/1 1.54 3-7 15:55 26D/1 1.30 30.44 3-7 13:35 26C(1)/1 1.58 3-7 14:20 26C(2)/1 1.59 3-7 16:16 26A/1 1.46 30.55 3-8 17:25 24/1 1.27 30.65 3-8 17:20 24/8 1.36 30.69 3-11 7:45 23/1 1.05 31.2 3-11 7:35 23/14 1.13 3-9 8:55 21/1 1.37 30.65 3-9 8:45 11/15 1.35 30.92 3-9 10:02 19/1 1.10 31.64 3-9 9:40 19/40 0.91 3-9 10:30 19/50 1.14 3 9 11:10 18/1 1.06 30.78 3-9 11:02 18/9 1.21 30.99 3-10 12:35 18/2 1.23 30.68 3-10 12:20 18/30 1.01 31.32 3-10 13:00 18A/2 1.03 30.8 3-10 13:10 18A/2 0.87 3-11 6:45 20/1 0.94 31.35 3-11 6:30 20/15 0.74 31.98 3-9 11:55 16/1 0.95 28.86 3-9 11:45 16/9 1.02 28.79 3-10 11:25 15/1 0.66 26.6 0.20 0.13 137 TABLE AI-1. Radon a c t iv it y in the water column of San Francisco Bay. (Conti nued) Station/Depth [Rn] Salinity [Ra] Date Ti m e (m) (dpm/ l) ( °/oo) March, 1977 (Cont.) 3-10 11:10 15/14 0.66 3-10 9:50 14C/3 0.52 26.3 3-9 12:55 13/1 0.78 26.05 3-9 12:45 13/7 0.84 26.08 3-10 9:33 13/1 0.63 26.0 3-10 9:22 13/8 0.75 3-10 8:55 11/1 0.79 23.8 3-10 8:40 11/12 0.79 24.50 3-9 14:30 10/1 0.94 20.59 3-9 15:15 7/1 0.94 15.39 3-9 15:05 7/12 1.04 15.28 3-10 7:30 6/2 1.00 14.0 3-9 15:45 5/2 1.25 10.06 3-9 16:15 3/2 1.00 6.24 3-9 17:25 RV/2 1.48 0.27 3-10 4:55 RV/1 1.35 0.04 0.23 0.08 138 TABLE AI-1. Radon a c t iv it y in the water column of San Francisco Bay. (Conti nued) Date Time Stati on/Depth (m) [Rn] (dpm/ ji) July, 1977 7-9 8:47 Transect: A/1 1.19 7-9 9:01 B/l 1.24 7-9 9:13 C/1 0.95 7-9 9:30 D/1 1.30 7-9 9:50 E/1 1.10 7-8 18:14 Pi er/1 1.39 7-8 18:43 1.24 7-8 19:10 1.21 7-8 20:47 1.14 7-8 22:40 1.20 7-9 1:15 1.22 7-9 2:45 1.23 7-9 4:05 1.13 7-9 5:35 1.22 7-9 7:05 1.34 7-9 8:40 1.20 7-9 10:10 1.26 7-9 11:40 1.27 7-9 13:15 1.17 7-9 14:50 1.21 7-9 16:15 1.18 7-9 17:45 1.17 7-9 19:15 1.03 7-9 20:45 1.10 7-9 22:20 1.22 7-9 23:49 1.30 7-10 2:10 1.22 7-10 3:20 1.20 7-10 4:30 1.12 7-10 6:15 1.12 7-10 9:15 1.21 7-10 12:15 1.03 7-10 13:45 (1.27) 7-10 14:15 0.88 7-10 16:10 (1.60) 7-10 18:40 0.97 7-10 19:00 1.19 T Pier 1.17 139 TABLE AI-1. Radon a c t iv it y in the water column of San Francisco Bay. (Continued) Stati on/Depth Date Time_______ (m _)_____ October, 1977 10-14 16:35 Pier 10-14 16:00 Pier 10-14 16:08 Pier 10-14 18:10 Pier 10-14 20:25 Pier 10-14 20:45 Pier 10-14 21:20 Pier 10-16 10:00 27/0 10-16 10:13 27-28/0 10-16 10:25 28/0 10-16 10:35 Pier 10-16 10:43 Pier 10-16 10:50 29-30/0 10-17 10:00 28/0 10-17 10:17 Pier 10-17 9:50 27-28/0 10-17 10:28 29-30/0 10-17 9:45 27-28/0 10-22 10:50 27-28/0 10-22 11:05 27-28/0 [Rn] (dpm/ i) 1.99 1.64 1.59 ( 1. 68) 1.81 2.11 2.01 1.49 1.54 1.76 1.85 1.62 (1.61) 1.61 1.70 1.48 1.28 1.36 1.05 1.22 1.57 July, 1978 7-18 11:30 7-18 11:35 27 27 1.23 June, 6-10 6-10 6-11 6-12 6-12 6-13 6-13 6-13 6-15 6-15 1979 14:30 11:50 13:25 8:45 13:00 10:00 13:30 7:34 10:20 8:15 28C 28C 28 28 28C 28 28C 28C 28 28C 2.53 2.15 1.16 1.18 1.55 1.28 1.91 0.90 0.97 1.14 140- TABLE AI-1. Radon a c t iv it y in the water column of San Francisco Bay. (Conti nued) Date Time Stati on/Depth (m) [Rn] (dpm/ i February, 1980 2-12 0:20 28/1 1.17 2-12 6:39 28/1 2.16 2-12 11:00 28/1 2.14 2-12 16:15 28/1 1.60 2-12 13:30 28C/1 3.53 2-13 14:53 29/1 2.28 2-13 14:20 26/1 2.05 2-13 14:35 28/1 1.90 2-14 16:30 28A/1 2.38 2-15 8:04 28/1 1.39 2-15 10:15 28A/1 2.04 2-20 12:30 29-30/1 1.31 2-20 13:00 29-28/1 0.88 2-20 13:45 28-29/1 0.79 2-20 14:00 28-CP/l 1.20 2-21 10:15 CP-28a/l 1.11 2-21 10:30 CP-28b/l 1.00 2-21 10:45 28-29/1 1.17 [Ra] (dPm / ri 0.13 0.11 0.13 TABLE AI-1. Radon a c t iv it y in the water column of San Francisco Bay. (Continued) Station/Depth [Rn] Date Time (m) (dpm/ *) March, 1980 i i South Bay 3-4 8:50 30-31/0 1.48 3-4 11:42 30/2 1.27 3-4 11:53 no 1.35 3-4 12:30 29-28/0 0.99 3-4 13:00 27/2 0.68 3-4 13:17 /9 0.82 3-4 13:50 26-25/0 0.99 i 3-4 14:27 24/2 1.15 ; 3 - 4 14:46 /8 1.47 3-4 15:44 21/2 1.27 : 3-4 16:00 no (1.16) ! 3-4 16:15 /17 1.00 26/0 0.81 / o 0.81 : 28/0 0.79 t Central Bay ! / o 0.81 ; 3-4 16:36 20-19/0 1.42 i 3-4 17:15 19/0 1.09 ! 3-5 7:30 19/0 1.36 i 3-5 9:00 17/2 1.49 ! 3"5 8:34 /25 1.12 i i San Pablo Bay | 3-5 10:24 15/2 1.85 : 3-5 10:34 /5 1.91 ; 3-5 10:45 no 1.50 ! 3-5 11:05 /14 1.49 ' 3-5 10:57 /1 8 1.36 ! 3-5 12:10 13/2 2.10 3-5 12:20 / 8 1.76 3-5 12:50 12/0 2.93 3-6 15:38 14/0 2.08 3-6 15:13 12-13/0 (2.08) 3-6 14:55 12/0 2.63 3-6 15:50 (2.22) TABLE AI-1. Radon a c t iv it y in the water column of San Francisco Bay. (Conti nued) Date Time Stati on/Depth (m) [Rn] (dpm/ I) March, 3-6 1980 (Cont.) 12:05 334/0 2.27 3-6 13:25 324/0 1.25 3-6 14:20 318/0 1.22 3-6 15:17 312.2/0 3.04 3-7 17:00 13/0 2.37 3-7 17:00 /o 2.30 3-7 17:00 /o (2.72) 3-5 13:20 Suisan Bay 10/0 3.13 3-5 13:45 9/2 3.79 3-5 14:10 / 25 3.41 3-5 15:20 6/2 3.82 3-5 15:30 /9 3.22 3-5 16:55 3/2 3.51 3-5 18:00 /8 3.87 3-5 11:00 3/0 (3.08) 3-5 11:00 /o 3.38 3-5 11:00 /o 3.97 i 3-5 11:00 /o 3.51 3-6 18:00 3 (Ai r Equi1.) 0.05 3-6 18:00 li 0.04 3-7 18:00 ll 0.03 3-7 18:00 li 0.06 143 TABLE AI-1. Radon a c t iv it y in the water column of San Francisco Bay. (Conti nued) Station/Depth [Rn] S alinity Date Time (m)________ (dpm/j) (°/oo) June, 1980 South Bay 6-4 9:00 32/1 1.64 6-4 9:44 30/1 1.43 6-4 10:04 30/10 1.30 6-6 17:45 30/1 1.17 6-4 11:10 27/1 1.11 6-4 11:35 27/8.5 1.12 6-6 17:05 27/1A 1.12 6-6 17:05 27/IB 1.08 6-4 12:24 24/1 0.97 6-4 12:43 24/5 0.97 6-6 16:30 24/1A 1.04 6-6 16:30 24/IB 0.99 6-4 13:35 21/1A 1.12 6-4 13:35 21/IB 1.31 6-4 13:40 21/1C 1.14 6-4 13:40 21/ID 1.18 6-4 13:57 21/10 1.37 6-4 9:02 150/1 1.08 25.2 6-4 9:30 156/1 0.75 6-6 15:15 SL/1 0.95 25.0 6-9 13:05 27/0 1.02 S W 6-9 13:05 27/0 0.97 D H 6-9 13:05 27/0 0.98 DH 6-9 12:05 28C 1.92 6-11 15:20 27-28 0.80 6-11 15:15 CP 0.91 6-11 14:00 28C 1.31 6-12 14:43 27/0 0.92 6-12 14:31 27/8 1.02 6-12 17:15 CP 1.61 6-12 16:40 28C 1.56 144 TABLE AI-1. Radon a c t iv it y in the water column of San Francisco Bay. (Continued) Station/Depth [Rn] Salinity ( °/oo) Date Time (m) (dpm/ *) dune, 1980 Central Bay 6-4 15:06 19/1 1.05 6-4 15:15 19/38 1.04 6-5 6:30 17/1 1.01 6-5 7:15 17/30 1.17 6-6 15:20 17/1 1.09 San Pablo Bay 6-5 8:15 15/1 1.33 6-5 8:40 15/15 1.44 6-5 9:13 14/1 0.65 6-6 14:25 14/1 0.84 6-5 9:40 13/1 (0.52) 6-5 10:00 13/5 1.12 6-6 13:05 13/1 0.78 6-5 11:00 12/1 0.73 6-6 12:40 12/1 0.86 6-5 7:35 306/1 0.61 6-5 7:45 308-310/1 0.90 6-5 8:00 312/1 0.95 6-5 8:30 318/la (0.70) /lb 0.84 6-5 9:15 324/la (1.74) /lb 1.22 6-6 11:26 13-2.0/1 0.88 6-6 11:56 13-3.6/1 1.45 6-6 12:32 14-3.5/1 0.95 6-6 12:15 14-5.0/1 1.24 Suisan Bay 6-5 12:05 9/1 0.77 6-5 12:40 no 0.92 6-5 14:05 6/1 1.06 6-5 14:30 /5 0.87 6-5 15:50 3/la 1.00 CF 6-5 15:50 /lb 1.08 DH 6-5 15:50 /lc 0.87 D H 15.9 16.6 17.5 17.4 145 TABLE AI-1. Radon a c t iv it y in the water column of San Francisco Bay. (Conti nued) Station/Depth [Rn] Date Ti m e (m) (dpm/£) October, 1980 10-28 10:45 30/0 2.30 10-28 11:15 30/9 1.95 10-30 14:43 30/0 2.18 10-28 11:50 29/0 1.70 10-30 13:15 27/0 1.56 10-30 13:15 27/0 1.57 10-28 12:15 27/0 1.54 10-28 12:40 27/10 1.42 10-28 13:00 26/0 1.62 10-28 13:30 24/0 1.66 10-28 13:53 24/6 1.51 10-30 12:45 24/0 1.64 10-30 12:25 23/0 1.26 10-28 10:21 142/0 2.97 10-28 13:17 180/0 2.33 10-28 11:21 156/0 1.73 10-28 11:56 162/0 2.24 10-28 16:10 19/0 1.11 10-28 16:28 19/40 1.02 10-29 6:15 17/0 1.21 10-29 6:45 17/40 1.45 10-29 7:40 15/0 1.62 10-29 - 8:00 15/20 1.67 10-30 10:55 15/0 1.69 10-29 8:50 13/0 2.31 10-29 9:10 13/7 1.48 10-30 9:55 13/0 1.23 10-30 9:55 13/0 1.31 10-29 9:45 12/0 2.65 10-29 10:28 10/0 1.22 10-30 9:00 10/0 1.39 10-29 16:15 657/0 2.57 10-29 8:33 318/0 1.64 10-29 7:53 312/0 1.95 10-29 9:10 324/0 1.75 10-31 13:55 29-Bridge/O 1.91 10-31 17:10 C.P./0 3.33 10-31 16:25 28C/0 5.48 10-31 14:26 27/0 1.39 11-4 14:14 27A/0 2.88 11-2 15:20 28D/0 3.32 11-2 9:00 27/0 2.08 11-5 12:46 28C/0 3.97 11-5 13:20 28/0 1.68 11-5 8:55 28A/0 2.93 11-6 11:15 27/0 1.72 11-4 12:45 27B/0 2.00 146 TABLE AI-1. Radon a c t iv it y in the water column of San Francisco Bay. (Conti nued) Station/Depth [Rn] Date Time (m) (dpm/ i) Sali ni ty ( t/oo) February, 1981 2-23 10:00 28/0 1.47 2-23 10:40 27/0 1.03 2-23 13:05 27/9 1.14 2-23 14:05 28C/0 2.37 2-24 9:40 28/0 1.01 2-24 9:40 27/0 0.88 2-24 9:40 27/6 1.01 2-24 9:40 28C/0 1.94 2-26 9:40 28C/0 2.72 2-27 9:40 28/0 2.03 2-27 9:40 27/0 0.88 2-27 9:40 27/7 0.95 2-27 9:40 26/0 0.86 2-27 9:40 28C/0 2.48 2-27 9:40 27/0 0.83 November , 1981 0-31 8:48 26/0 1.00 0-31 15:15 27/0 1.11 0-31 10:30 28C/0 1.82 1-1 12:10 27/0 1.01 1-1 13:16 28B/0 1.46 1-2 12:08 27/0 1.08 1-2 16:24 27/0 1.07 1-3 10:50 27/0 1.55 26.2 26.6 TABLE AI-2. Radon and radium a c tiv itie s in the sedimentary column in south San Francisco Bay. Station Date 28 3-08-77 28 10-22-77 28 12-12-77 28 12-14-77 27 02-24-78 Ra-226 Ra-226 Ra- Rn Interval (cm) (Rn/Ra) dpm % (cm3) dpni (“ 9” ) (iPJH) ____ C £_ _ 0-1.5 0.37 6.60 0.31 4.16 1.5-3 0.78 6.59 0.30 1.45 3-4.5 0.75 6.76 0.27 1.69 4.5-6 0.81 7.81 0.30 1.48 6-8 0.84 10.40 0.24 1.66 0-3 0.58 10.28 ±0. 3 4.32 3-6 0.33 12.83 ±0. 13 8.59 6-9 0.59 12.29 ±0. 04 5.05 12-15 0.83 11.41±0. 21 1.90 17-20 0.92 10.36 20. 14 0.80 0-3a 0.52 11.18±1. 18 5.32 0-3b 0.59 11.7320. 79 4.81 3-6a 0.88 13.3620. 91 -1.62 6-9a 1.12 13 . 4 2 20. 86 -1.60 6-9b 0.96 12.27 0.47 18-21a 0.97 14 . 6 5 20. 68 0.44 18— 2 lb 0.87 15.52 1.97 27-30b 0.98 15.23 0.31 42-45b 1.38 13.76 -5.24 51-54a 1.15 15.06 ±1. 62 -2.21 51 — 5 4b 1.00 17.05 0 0-3a 0.60 13.64 5.50 3-6a 0.92 13.98 1.19 6-9a 0.98 13.01 0.21 15— 18b 0.82 12.18 2.24 24-27a 0.93 12.93 0.88 24-27b 1.00 14.05 -0.05 33-36b 0.90 14.45 1.47 39-42a 0.93 13.95 0.97 42-45b 1.10 14.80 -1.57 60-63b 1.03 14.59 -0.40 78-81b 1.00 15.00 -0.07 0-3a 0.77 10.71 2.46 0-3b 0.35 12.58 8.15 : 3-6a 0.86 14.34 2.02 j 3-6b 0.74 11.76 3.11 ! 6-9b 0.87 12.50 1.67 : 15-18a 0.99 14.11 0.17 ; 30-33b 0.80 14.87 2.99 1 31-34a 1.01 15.46 - 0 . 0 9 : 45-48a 1.01 15.31 -0.15 ; 50-53b 0.96 14.96 0.64 | 60-63a 0.97 18.39 148 ! TABLE AI-2. Radon and radium a c tiv itie s in the sedimentary column in south San Francisco Bay (Continued). Ra-226 Ra-226 Interval dpm Station Date (cm) (Rn/Ra) (cm3' ( 9 ) 07-18-78" 28 09-21-78 27 02-11-80 (cm) (Rn/Ra) (cm3' 0-3'a 0.55 11.75 0-3b 0.36 9.92 3-6b 0.72 12.78 6-9a 0.88 14.10 6-9b 0.74 13.55 15— 18b 0.96 13.69 18-21a 1.00 14.07 33-36a 0.94 15.10 39-42b 0.99 17.14 50-53b 0.99 15.12 51-54a 1.00 15.48 66-69a 1.00 17.51 0-3 0.65 11.79 +0.24 3-6 0.86 12.24+0.09 6-9 0.97 11.64 ±1.47 16-19 0.98 14.95 +0.28 25-28 1.11 14.81 ±1.22 37-40 0.93 15.48 +0.48 55-58 1.02 15.14 +0.14 0-3b 0.46 10.29 3-6a 0.74 11.52 6-9b 0.87 11.40 9-12a 1.00 10.38 15-20b 0.88 19.76 21-24a 0.89 13.01 30-35b 0.93 22.88 45-50b 1.04 20.35 57-60a 0.86 14.66 0-3a 0.48 11.43 0-2b 0.49 08.08 2-4b 0.84 07.89 3-6b 0.96 10.95 6-9a 0.91 11.54 10-12b (0.77) 08.07 12-15a 0.56 13.01 24-26b 0.82 17.65 25-30a 0.93 20.12 55-60a 1.00 22.06 28 11-1/2-80 0-3a 0.48 11.43 5.52 4.15 1.30 0.38 1.03 (1.87) 1.78 3.09 1.34 .06 149 STABLE AI-2. Radon and radium a c tiv itie s in the sedimentary column in I south San Francisco Bay (Continued). Station Date Interval (cm) (Rn/Ra) Ra-226 dpm (air3) Ra-226 ( T i Ra-Rn ,dpmv v c c ' 27 02-23/24-81 0-3a 0.62 11.42 4.37 0-3b 0.64 07.72 2.78 i 3-6a 0.69 11.24 3.44 3-6b 0.92 09.96 0.77 6-9a 0.76 11.15 2.77 j 9-12b 0.90 12.09 1.17 12-15a 0.65 13.71 4.78 i 15-20b 0.98 17.17 0.34 I 25-30a 0.96 18.96 0.80 J 30-35b 0.99 16.56 0.17 40-45a 1.04 26.18 -1.03 50-55b 0.90 18.93 1.87 28C 08-09-76 0-2 0.33 5.23 2-4 0.25 6.29 (6.55) i 4-6 0.71 7.79 (7.46) 6-8 0.66 9.41 12-14 0.83 7.55 ; 25C 08-12-76 0-2 0.23 5.42 2-4 0.40 7.94 (6.39) 4-6 0.45 7.96 (8.08) 8-10 0.45 7.58 14-16 0.61 5.97 ; 28C 03-07-77 0-2 0.31 8.65 ±78 5.96 2-3 0.30 6.70 ±20 4.69 | 3-4 0.43 6.54 ±06 3.70 i 4-6 0.66 8.82 ±88 3.00 1 6-8 0.61 9.62 ±19 3.72 1 | 28C 07-12-77 0-3 0.25 8.79 ±79 i 3-6 0.49 10.80 ±79 6-9 0.42 13.95 ±22 9-12 0.79 11.72 ±24 150 TABLE AI-2. Radon and radium a c tiv itie s in the sedimentary column in south San Francisco Bay (Continued). Stati on Date Interval (cm) (Rn/Ra) Ra-226 dpm (cmd ) Ra-226 Ra-Rn (S g ) 28C 10-17-77 0-3 0.46 10.04 30 5.46 3-6 0.85 12.48 ±.09 1 .90 6-9 0.89 12.38 ±. 16 2.42 12-15 0.82 13.05 ±03 2.29 21-24 0.86 12.13 ±. 29 1.67 28E 10-18-77 0-3 0.26 07.68 ±69 5.67 3-6 0.70 07.77 ±.21 2.34 6-9 0.48 09.17 ±.03 4.74 9-12 0.77 08.05 ±.02 1.82 12-15 0.79 09.19 A . 38 1.84 28D 10-20-77 0-3 0.32 08.86 ±.07 6.03 3-6 0.37 11.11 ±.70 7.00 6-9 0.46 10.08+26 5.42 28C 07-14-78 0-3a 0.33 8.17 + 06 5.50 0-3b 0.37 9.33+11 5.85 3-6a 0.55 11.47+59 5.19 6-9a 0.70 11.84+37 3.54 6-9b 0.71 11.81 + 68 3.48 15— 18b 0.71 12.93 + 01 3.73 24-27a 0.91 15.61 + 74 1.42 27-30b 1.07 13.87 +19 -.93 33-36a 1.02 15.99 + 54 -.26 42-45a 1.09 17.39 ±.28 -1.54 42-45b 0.91 17.07 ±.49 1.48 28C 09-21-78 0-3 0.31 11.18 ±68 7.74 3-6 0.36 11.17 ±46 7.16 9-12 0.43 10.37 ±64 5.89 18-21 0.90 08.48 ±28 0.86 23-26 0.99 12.12 ±62 0.08 28C 02-12-80 0-3 0.51 11.47 5.61 3-6 0.62 11.89 4.55 6-9 0.55 12.56 5.59 12-17 0.48 20.77 10.76 25-30 0.84 17.31 2.73 55-60 0.94 28.91 1.75 151 TABLE AI-2. Radon and radium a c tiv itie s in the sedimentary column in south San Francisco Bay (Continued). Stati on 28A ! 28C i Date 02-14-80 02-25/26-81 [nterval (cm) (Rn/Ra) Ra-226 dpm Ra-226 dpm nr) Ra-Rn (dpm j 0-3 0.52 7.79 3.71 3-6 0.53 10.48 4.92 6-9 0.54 11.79 5.48 9-12 0.63 12.35 4.52 18-21 0.84 13.10 2.10 32-35 0.90 9.42 0.98 0-3a 0.59 9.07 3.75 3-6a 0.40 12.36 7.44 6-9a 0.49 11.25 5.76 12-15a 0.39 12.65 7.66 15-19a 0.79 10.70 2.30 0-3b 0.23 10.91 8.36 3-6b 0.44 11.80 6.55 6-9b 0.51 12.97 6.37 12— 15b 0.37 13.67 8.60 152 t |TABLE AI-3. i Deplovment ! Date 6/79 2/80 6/80 In -s itu Fluxes of Radon Across the Sediment- Water Interfaces. Incubati on Station Radon Flux ^atoms ^ rrrsec Comments 27 27 28C 27 28C 25.7 242 Sti rred 47.9 155 ll 19.9 89 Not Stirred 25.8 39 ll 47.3 62 ll X 117±37 15.5 252 Sti rred 8.8 292 ll 18.2 261 ll 9.4 12 Not Stirred 8.9 4 ll 7.8 24 ll 7.1 18 ll 11.7 11 ll 7.7 -14 ll 11.3 -3 ll X 268±12 20.7 211 Sti rred 20.5 24 Not Stirred 20.3 33 it X 211 22 66 Sti rred 23.6 82 ll 21.7 75 2-day incubation 22.0 149 Not Stirred 23.5 41 ll 24.0 21 2-day incubation 22.3 58 Not Stirred X 70± 15 23.5 170 Sti rred 18.3 292 ll 18.3 320 Not Stirring W hei Retri eved 18.0 197 Not Stirred 20.8 184 X 233± 31 153 TABLE AI-3. (Cont.) In -s itu Fluxes of Radon Across the Sediment- Water Interface. Depl oynent Date Station Incubation Time (Hrs) Radon Flux /atoms\ m ? sec Comments 10/80 27 10/80 2/23/81 2/24/81 2/25/81 18.0 19.2 23.2 22.9 22.1 18.0 23.0 23.0 22 J ) X 52 35 62 67 120 36 79 59 23 59± 10 Sti rred Not Stirred ii May Have Stopped Sti rri ng Not Stirred 28C 19.5 440 Sti rred 19.4 386 ll 24.3 160 " 24.8 263 H 28D 23.5 208 23.9 358 ll 28A 21.7 97 ll 21.6 127 ii 21.8 218 17.3 472 28B 22.1 232 X 269±38 27 23.9 47 Sti rred 23.6 58 Not Stirred (Switch Off) 23.7 183 Switch O n for 1 Hour 27 27.3 85 Sti rred 22.7 76 ii 21.8 38 Not Stirred (Switch Off) 21.9 120 Switch O n for 1 Hour 27 24.1 134 Sti rred 24.4 93 ii 19.3 176 ll 19.7 173 ii 25.1 156 Switch O n for 1 Hour X 124 ±15 154 TABLE AI-3. (Cont.) In -s itu Fluxes of Radon Across the Sediment-Water i nterface. Deploynent Date Station Incubation Time (Hrs) Radon Flux (atoms) m 2 sec 2/81 28C Comments 24.7 250 Sti rred 23.7 173 ll 16.7 172 ll 24.2 241 ii 24.3 145 Not Stirred 23.8 186 ii 17.0 145 ll X 187±16 155 TA B LE AI-4. In-S1tu Radon Fluxes Across the A1r-Water Interface. Date-T1me Station Float Time (Min) Current Speed (cm/sec) Wind Speed (m/sec) [Rn]w (djwn/i) Chamber Rn (dpm) JRn* (Atoms) m 7 -m1 n K C (m/day) Comments 7/18/78 11:35 27 40 0 2 . 2a 1.23 11.78 14725 2.15 Only used 2nd 11:30 27 50 0 2 . 2a 1.23 8 . 0 8000 1.17 M ii ii 11/5/80 11:30 27 83 0 4.0* 1.70 28.36 17040 1 . 8 Stirred 11.30 27 80 0 4.0* 1.70 25.7 16020 1.7 Unstlrred 11/6/80 11:30 27 43 15m 2 . 0* 1.70 3.05 3540 0.4 Unstirred 11:30 27 50 15m 2 . 0 * 1.70 6 . 1 0 6060 0 . 6 St1rred 2/23/81 1 1 : 2 0 27 59 40m 5.3* 1.09 4.0 33840 5.6 Black Chamber 15:05 28C 41 l l m 5.3* 2.37 50.7 61680 4.7 n ii 2/25/81 12:35 27 74 26m 2.7* 0.95 7.2 4860 0.9 Black Chamber 2/26/81 10:05 28C 52 33m 2.4* 2.72 35.7 34260 2.3 2/27/81 09:15 27 55 37m 2 . 2* 0.92 1 1 . 6 10500 2 .1 10:30 28C 45 40m 2 . 2* 2.48 21.4 23700 1.7 1 2 : 0 0 27 97 17m 2 . 2* 0.92 4.2 2160 0.4 10/31/81 08:30 26 65 13* 1.9a 1 .0 0 14.95 11500 2 .1 Chamber #5 08:30 26 60 13t 1.9a 1 .0 0 14.88 12400 2 . 2 Chamber #7 08:30 26 64 13t 1.9a 1 .0 0 12.93 1 01 00 1 .8 Chamber #8 10:30 28C 65 25t 1.4a 1.82 20.67 15900 1.58 Chamber #5 10:30 28C 67 25t 1.4a 1.82 24.0 17900 1.77 Chamber #7 10:30 28C 64 25* 1.4a 1.82 19.58 15300 1.52 Chamber 18 14:30 27 70 6* l . l a 1 .1 1 6 . 2 0 4430 0.72 Chamber #5 14:30 27 77 6* l . l a 1 .1 1 7.25 4710 0.77 Chamber #8 11/1/81 11:30 27 62 26* 0.5a 1 .0 1 7.17 5780 1.03 Chamber #5 11:30 27 58 26* 0 . 5a 1 .0 1 7.74 6670 1.19 Chamber 17 11:30 27 60 26* 0.5a 1 .0 1 8.29 6910 1.24 Chamber #8 13:00 28B 66 35* 0 . 3a 1.46 3.85 2920 0.36 Chamber #5 13:00 28B 68 35* 0 . 3a 1.46 4.26 3130 0.39 Chamber #7 13:00 28B 68 35* 0 . 3a 1.46 3.62 2660 0.33 Chamber #8 TABLE AI-4. In-SItu Radon Fluxes Across the Alr-Water Interface. Date-Time Station Float Time (Min) Current Speed (cm/sec) Wind Speed (m/sec) [Rn]w _(dpmAj^_ Chamber R n (dpm) JRn* (Atoms mT^min K C _lra/dajr)_ 0.54 Comments 11/2/81 10:00 27 73 121 1.4a 1.08 4.72 3230 Chamber #7 10:00 27 72 12l 1,4a 1.08 5.50 3820 0.64 Chamber #8 11:30 27 52 l i t 2.2a 1.28 9.46 9100 1.52 Chamber #7 11:30 27 53 l i t 2.2a 1.28 6.57 6200 1.04 Chamber #8 12:45 27 49 27t 1.4a 0.92 5.86 5980 1.00 Chamber #7 12:45 27 48 M " 0.92 4.86 5060 0.85 Chamber #8 16:00 27 57 3t 0.8a 1.07 4.06 3560 0.60 Chamber #7 16:00 27 59 3t 0.8a 1.07 3.82 3240 0.54 Chamber #8 16:00 27 56 3t 0.8a 1.07 3.38 3020 0.50 Kremer's Chamber 11/3/81 11:00 27 52 20t l . l a 1.55 11.54 11100 1.29 Tied to Boat 11:00 27 72 20t l . l a 1.55 5.49 3810 0.44 Chamber #8 11:00 27 - - 20t l . l a 1.55 0.80 "Blank" R un 11:00 27 72 20t l . l a 1.55 5.03 3490 0.41 Chamber #4 11:00 27 - - 20t l . l a 1.55 0.71 — . . "Blank" R un 11:00 27 69 20t l . l a 1.55 9.54 6910 0.81 Kremer's Chamber a - Values from hand-held anemometer, 2 5 meters above water surface. t - Current velocitie s estimated from tid a l v e lo c ity tables; wind velo citie s taken from S.F. a irp o rt readings, m - Values from U S G S current meters from stations 26 S 27. * j^atoms , m - m i n ' & Chamber A c tiv ity (dpm) Afmin*1 ) * Chamber Area (m; * flo a t time (min) c - uncorrected for exchange during deploynent, with = 0. Table A I-5. Summary o f the gas tra n s fe r c o e ffic ie n ts from the laboratory experiments. Values in parentheses are considered questionable and are not used in mean c a lc u la tio n s . K |_ (m /day) ± 1 se Gas * Run Picture Run S ! Grid Depth (cm) O s c illa tio n Speed (Hz) o2 n 2 co2 ch4 Rn 4 — 9 3.5 (4 .0 ) (5 .7 ) (0 .9 0 ) 1.25 — 6 — - « 1 . 19±. 08 1.14+.10 1.33+.04 1 .1 2±.05 1 .2 2 i.2 6 7 1* - - 1.54±.16 (3 .0 ) 1.43± .15 1.41±.07 — 17 — « - — — — — 1.07+.26 18 « - __ 1.49+.14 __ __ X 1 . 26±. 07 1.26+.08 1 . 34±. 04 1.26+.04 1 .1 5 i .18 a - - 31.6 3.5 0.51+. 06 0. 56±. 02 0. 54+. 06 0.45+.05 0 .3 6 i.0 8 9 — « « 0.37+. 08 0 . 38±.06 0. 52+.03 0.42+.04 — 10 2 - - 0.56+.04 0.64+. 05 0.49+. 04 0.59±.04 0 . 44± .02 7 0. 50+. 06 0 . 55±. 02 0.51+.02 0.491.02 0 .4 3 i.0 2 11 3 13 3.5 0 . R8±.06 0. R5±. 09 0.86+.03 0 .9 4 i.0 3 (1 .0 5 ) ? n fi 13 4.5 — — 1.22+.04 0.991.05 0.911.24 l? - - i s . a 3.5 0.63+ .07 O.8 6 1 . 0 8 0 . 57±. 06 0.631.04 - - 13 - - - - 0.64+ . 08 0.84± .07 0.58+ .03 0.681.04 — Id 4 •• - 0.70+ . 08 0.89+. 09 0.65+. 06 0.601.02 0 . 4 6 i . l l 19 - - __ 0.88+ .10 _ __ 0.80+ .15 X 0.66+ . 04 0 . 87±. 05 0. 59+ .02 0.62+. 02 0.58+ .09 IS 5 1 6 .a 4.5 0. 97+. 12 1.07+.13 0. 73+ .07 0. 72+. 01 0.74+.07 16 6 3.5 2.01+. 16 2.10+.30 2.09+. 06 2.00+.01 1.751.22 * Pictures taken on d iffe re n t day then gas analyses. 158 TABLE AI-6. Summary of the turbulence data from the laboratory experiments, lis te d by run number. Heading abbreviations as follows: ~w and Tj are the vertical and horizontal mean velocities (cm/sec), respectively; w'^ and u ' 2 are the vertical and horizontal fluctuating velocities (cm/sec), respectively; R is the ratio of the vertical to horizontal fluctuating ve lo c ities ; TKE is the turbulent kinetic energy (cm2/s e c 2); q is the three-dimensional turbulent velocity (cm/sec); is the turbulent velocity at a specified reference height; L is the integral length scale (cm); e is the turbulent energy dissiptation (cm2/s e c 3); and Lk is the Kolmogorov length scale (cm). Values in parentheses are interpolated from bordering values. RUN #1 Di stance From Grid (cm) Depth (cm) # of Streaks w u i F * R ' TKE 5.70 3.30 | 421 0.006 -0.742 6 . ^ 0 1.637 2.122 3.56 5.44 352 0.520 -0.448 1.701 1.603 1.078 2.453 1.42 7.58 22 -0.054 -0.434 0.955 0.418 1.754 0.895 -0.72 9.72 3 0.182 -0.198 0.023 0.002 1.637 0.132 -2.85 11.85 8 0.869 -0.035 0.644 0.030 6.963 0.352 -4.99 13.99 103 -0.237 0.005 2.764 1.862 1.330 3.244 -7.13 16.13 539 0.191 0.134 2.834 2.544 1.052 3.961 -9.27 18.27 1195 0.756 0.070 2.235 1.669 1.150 2.786 -11.41 20.41 1604 0.987 0.106 1.559 1.152 1.140 1.932 -13.55 22.55 1976 1.034 0.087 1.019 0.667 1.226 1.177 -15.69 24.69 1937 1.055 0.076 0.719 0.531 1.170 0.891 -17.83 26.83 2193 1.058 0.076 0.578 0.414 1.192 0.703 -19.97 28.97 2079 1.009 0.095 0.563 0.365 1.255 0.647 -22.11 31.11 2090 0.954 0.124 0.495 0.354 1.180 0.602 -24.25 33.25 2107 0.972 0.103 0.470 0.356 1.138 0.591 -26.39 35.39 2031 0.863 0.078 0.460 0.331 1.165 0.561 -28.53 37.53 501 0.840 0.077 0.364 0.346 1.039 0.528 15 TABLE A I - 6 (CONTINUED) R U N #1 Dist. From Grid (cm) Depth (cm) # o f Streaks q q/q 0 q J q V q o 3 L Rei_ e l k " 5770 I7T<7 421 2.06 0.976 3.74T~ 0.929 5.00 4.00 (2.111) 1.0 9.407 1.0 3.56 5.44 352 2.215 10.867 1.42 7.58 22 1.338 2.395 -0.72 9.72 3 0.514 0.136 (1.11) 57.1 0.008 0.106 -2.85 11.85 8 0.839 0.591 (1.43) 120.0 0.028 0.077 -4.99 13.99 103 2.547 16.526 (1.75) 445.7 0.630 0.036 -5.00 14.00 (2.704) 1.0 19.771 1.0 (1.75) 473.2 0.753 0.034 -7.13 16.13 539 2.815 1.041 22.297 1.128 (2.07) 582.7 0.718 0.034 -9.27 18.27 1195 2.360 0.873 13.153 0.666 (2.39) 564.3 0.367 0.041 -10.00 19.00 1269 2.505 -11.41 20.41 1604 1.966 0.727 7.596 0.384 (2.71) 532.8 0.187 0.048 -12.00 21.00 1452 2.266 -13.55 22.55 1976 1.534 0.567 3.612 0.183 (3.04) 466.3 0.079 0.060 -14.00 23.00 1397 3.258 -15.69 24.69 1937 1.335 0.494 2.379 0.120 (3.36) 448.6 0.047 0.068 -16.00 25.00 1641 3.246 -17.83 26.83 2193 1.186 0.439 1.667 0.084 (3.68) 436.5 0.030 0.076 -19.97 28.97 2079 1.138 0.421 1.472 0.074 (4.00) 455.2 0.025 0.080 -22.11 31.11 2090 1.097 0.406 1.321 0.067 (4.32) 473.9 0.020 0.084 -24.25 33.25 2107 1.087 0.402 1.285 0.065 (4.64) 504.4 0.019 0.085 -26.39 35.39 2031 1.059 0.392 1.188 0.060 (4.96) 525.3 0.016 0.089 -28.53 37.53 501 1.028 0.380 1.085 0.055 (5.29) 543.8 0.01410.092 160 TABLE AI-6 (Continued) RUN #2a 01 stance from Grid (cm) Depth (cm) # of Streak w u u r R TKE 30. $ 4 " 132 0.072 -0 .3 l? 0.109 C ). >25 6.388 0.780 25.94 2.66 1159 0.2B5 -0 .270 0.432 0.583 0.856 0.799 26.94 4.66 1204 0.553 -0.221 0.462 0.386 1.087 0.617 24.94 6.66 1225 0.702 0.229 0.545 0.355 1.234 0.629 27.94 R. 66 1114 0.721 0.265 0.437 0.335 1.144 0.554 20.94 10.66 1170 0.692 -0.277 0.422 0.329 1.139 0.540 IB . 94 12.66 1105 0.695 -0 .290 0.397 0.302 1.176 0.500 16.94 14.66 1102 0.644 -0 .265 0.405 0.321 1.137 0.523 14.94 16.66 1137 0.5RR -0.251 0.434 0.369 1.101 0.586 12.94 IB. 66 1100 0.509 0.219 0. 535 0.390 1.173 0.660 10.94 90.66 9B1 0.377 -0 .190 0.764 0.456 1.296 0.838 B. 94 22.66 771 0.211 -0 .156 0.995 0.812 1.127 1.309 6.94 24.66 3RB 0.1 BO -0 .0 5 8 1.091 1.137 0.996 1.683 4.94 26.66 133 -O.B25 0.040 1.356 1.336 1.013 2.014 2.94 2R.66 22 0. 204 -0.157 0.761 0.457 0.801 0.837 0.94 30.66 0 0 0 0 0 0 0 161 TABLE AI-6 (Continued) R U N #2a Di stance from Grid (cm) Depth (cm) # Of Streak q q/q 0 q 3 93/q 0 3 L ReL E k 30. 94 0.65 132 1.244 0.604 1.967 0.281 0 0 0 0 2R.94 2.65 1159 1.262 0.613 2.027 0.289 3.86 487.1 0.035 0.073 26.94 4.65 1204 1.108 0.53R 1.382 0.197 4.39 486.4 0 .0 2 1 0.083 24.94 6.65 1225 1.116 0.542 1.440 0.206 3.66 408.5 0.026 0.079 22.94 R. 65 1114 1.050 0.510 1.174 0.168 4.01 421.1 0 .02 0 0.084 20.94 10.65 1170 1.036 0.503 1.131 0.161 3.80 393.7 0 .0 2 0 0.084 IB. 94 12.65 1105 0.999 0. 485 1.006 0.144 3.67 366.6 0.018 0.086 16.94 14.65 1 1 0 2 1 .0 2 2 0.496 1.075 0.153 3.87 395.5 0.019 0.085 14. 94 16.65 1137 1 .0R1 0.525 1.275 0.182 3.39 366.5 0.025 0.080 12.94 IB .65 1 1 0 0 1.147 0.557 1.523 0.217 2.91 333.8 0.035 0.073 10.94 20.65 9R1 1.293 0.62R 2.176 0.311 2.20 284.5 0.066 0.062 R. 94 22.65 771 1.613 0.7R3 4.279 0.611 1.40 225.8 0.204 0.047 6.94 24.65 3R5 1.R2R 0.RR7 6.242 0.891 0 .66 1 2 0 .6 0.631 0.035 4.94 26.65 133 2.007 0.974 8.08R 1.155 0.62 124.4 0.870 0.032 2.94 2R.65 2 2 1.091 0.530 2.827 0.404 0 0 0 0 0.94 30.65 0 0 0 0 0 0 0 0 0 162 TABLE A I - 6 (CONTINUED) RUN #3 Di stance From Grid _ (cm) . _ _ Depth (cm) . # of Streaks w ll w' 1 T T ? R TKE r r : 5 2 — 1.16 0.020 0.023 0.261 0.706 0.610 0.837 9.48 3.30 1643 0.028 0.052 0.737 0.819 0.962 1.188 7.34 5.44 1157 0.230 -0.053 1.105 1.067 1.032 1.619 5.20 7.58 328 0.482 0.019 1.166 1.026 1.066 1.609 3.06 9.72 23 0.568 0.084 0.257 0.294 3.920 0.422 0.93 11.85 2 -0.006 -0.287 -0 - -0- - 0 - -0- -1.21 13.99 9 0.084 -0.309 0.187 0.657 0.368 0.751 -3.35 16.13 95 -0.206 -0.012 1.304 0.883 1.228 1.535 -5.49 18.27 716 0.032 0.116 1.756 1.508 1.083 2.386 -7.63 20.41 1346 0.570 0.086 1.525 1.208 1.136 1.970 -9.77 22.55 1731 0.844 0.022 1.157 0.822 1.154 1.400 -11.91 24.69 1945 0.911 0.072 0.859 0.648 1.122 1.077 -14.05 26.83 2126 0.965 0.173 0.679 0.479 1.167 0.818 -16.19 28.97 2040 0.971 0.222 0.557 0.414 1.146 0.692 -18.33 31.11 2119 0.923 0.300 0.522 0.424 1.105 0.686 -20.47 33.25 1968 0.904 0.380 0.490 0.447 1.052 0.692 -22.61 35.39 688 0.865 0.328 0.354 0.381 1.002 0.558 163 TABLE A I - 6 (CONTINUED) RUN #3 Dist. From Grid (cm) Depth (cm) # of Streaks q q/q 0 q3 q 3 /q 0 3 L Rej_ £ Lk 12.00 (). 78 1022 3.10 11.62 1.16 420 1.294 0.673 2.166 0.305 (2.88) 372.7 0.05 0.067 10.00 2.78 512 2.12 9.48 3.30 1643 1.541 0.801 3.662 0.515 (2.46) 379.1 0.099 0.056 8.00 4.78 60 1.65 7.34 5.44 1157 1.799 0.936 5.827 0.819 (0.32) 57.6 1.214 0.030 5.20 7.58 328 1. 794 0.933 5.773 0.812 5.00 7.78 (1.923) 1.0 7.111 1.0 3.06 9.72 23 0.919 0.775 0.93 11.85 2 -0 - -0 - -1.21 13.99 9 1.226 1.841 (0.35) 42.9 0.351 0.041 -3.35 16.13 95 1.752 5.379 (0.87) 152.4 0.412 0.040 -5.00 17.78 (2.213) 1.0 10.838 1.0 (1.27) 281.1 0.569 0.036 -5.49 18.27 716 2.184 0.987 10.424 0.961 (1.39) 303.6 0.500 0. 038 -6.00 18.78 1062 1.29 -7.63 20.41 1346 1.985 0.897 7.821 0.722 (1.92) 381.1 0.272 0.044 -8.00 20.78 1272 2.40 -9.77 22.55 1731 1.673 0.756 4.685 0.432 (2.44) 408.2 0.128 0.053 -10.00 22.78 1425 2.51 -11.91 24.69 1945 1.468 0.663 3.161 0.292 (2.96) 434.5 0.071 0.061 -12.00 24.78 1528 2.96 -14.00 26.78 1581 3.50 -14.05 26.83 2126 1.279 0.578 2.093 0.193 (3.48) 445.1 0.04 0.071 -16.00 28.78 1533 3.98 -16.19 28.97 2040 1.176 0.531 1.628 0.150 (4.01) 471.6 0.027 0.078 -18.00 30.78 1531 4.16 -18.33 31.11 2119 1.171 0.529 1.607 0.148 (4.53) 530.5 0.024 0.080 -20.00 32.78 1584 5.01 -20.47 33.25 1968 1.176 0.531 1.628 0.150 (5.05) 593.9 0.022 0.082 -22.00 34.78 923 4.24 -22.61 35.39 688 1.056 0.477 1.179 0.109 (5.57) 588.2 0.014 0.092 164 TABLE A I - 6 (CONTINUED) RUN #4 Di stance From Grid (cm) Depth (cm) # O f Streaks w u w7** R TKE 15.26 1.54 596 r - o . o ? o ' -0.127 0.144 0.503 0.564 0.575 13.12 3.68 2049 -0.182 -0.113 0.417 0.471 0.951 0.680 10.98 5.82 2251 -0.224 -0.102 0.478 0.419 1.068 0.658 8.84 7.96 2041 -0.184 -0.146 0.616 0.529 1.079 0.837 6.70 10.1 1466 0.073 -0.137 0.783 0.727 1.051 1.119 4.57 12.23 500 0.356 -0.065 0.870 0.794 1.082 1.228 2.43 14.37 37 0.065 -0.047 0.392 0.248 0.905 0.444 0.29 16.51 -0- -0- -0- -0 - -0- -0 - -0 - -1.85 18.65 1 0.005 -0.126 -0 - -0- -0- -0 - -3.99 20.79 40 0.108 -0.084 1.038 0.699 1.345 1.218 -6.13 22.93 553 -0.369 0.112 1.096 1.263 0.996 1.811 -8.27 25.07 1281 0.159 0.045 1.225 1.102 1.057 1.714 -10.41 27.21 1818 0.477 0.018 0.999 0.746 1.146 1.245 -12.55 29.35 1998 0.599 -0.002 0.833 0.567 1.202 0.984 -14.69 31.49 2066 0.679 -0.003 0.639 0.394 1.277 0.713 -16.83 33.63 2120 0.620 -0.035 0.484 0.310 1.248 0.551 -18.97 35.77 1913 0.510 -0.049 0.390 0.239 1.274 0.434 -21.11 37.91 107 0.496 -0.026 0.272 0.219 1.198 0.355 TABLE A I - 6 (CONTINUED) RUN #4 Dist. From Grid (cm) Depth (cm) § of Streaks q q /q 0 q 3 q ¥ q 0 ' 3 L Rej_ £ k ! i 1 17.00 -(T.2 1619 4.89 i 15.26 1.54 596 1.072 0.693 1.233 0.332 (4.77) 511.3 0.017 0.088 15.00 1.8 1723 4.74 13.12 3.68 2049 1.166 0.753 1.586 0.427 (4.35) 507.2 0.024 0.080 ! 13.00 3.8 1581 4.35 ! 11.00 5.8 1276 3.56 1 10.98 5.82 2251 1.148 0.742 1.511 0.408 (3.70) 424.8 0.027 0.078 j 9.00 7.8 837 2.08 i 8.84 7.96 2041 1.294 0.836 2.165 0.584 (2.47) 319.6 0.058 0.064 ! 7.00 9.8 172 0.87 6.70 10.1 1466 1.496 0.966 3.348 0.903 5.00 11.8 (1.548) 1.0 3.710 1.0 4.57 12.23 500 1.567 3.849 2.43 14.37 37 0.943 0.837 0.29 16.51 -0- -0 - -0 - -1.85 18.65 1 -0 - -0 - -3.99 20.79 40 1.561 3.802 -5.00 21.3 (2.041) 1.0 8.502 1.0 (0.22) 44.9 2.575 0.025 -6.13 22.93 553 1.903 0.932 6.893 0.811 (0.48) 91.3 0.957 0.032 -8.27 25.07 1281 1.851 0.907 6.347 0.746 (0.99) 183.3 0.427 0.039 -9.00 25.8 1263 1.14 -10.41 27.21 1818 1.578 0.773 3.929 0.462 (1.49) 235.1 0.176 0.049 -11.00 27.8 1455 1.63 -12.55 29.35 1998 1.403 0.687 2.760 0.325 (1.99) 279.2 0.093 0.057 -13.00 29.8 1485 2.20 -14.69 31.49 2066 1.194 0.585 1.704 0.200 (2.50) 298.5 0.045 0.069 -15.00 31.8 1548 2.52 -16.83 33.63 2120 1.050 0.514 1.158 0.136 (3.00) 315.0 0.026 0.079 -17.00 33.8 1557 2.96 -18.97 35.77 1913 0.932 0.457 0.809 0.095 (3.50) 326.2 0.015 0.090 -19.00 35.8 1526 3.55 -21.11 37.91 107 0.842 0.413 0.598 0.070 (4.00) 336.8 0.010 0.100 166 TABLE A I - 6 (CONTINUED) RUN #5 Di stance From Grid (cm) Depth (cm) # of Streaks w u w'2 u'2 R TKE 15.26 1.54 530 -0.043 0.294 0.259 1.200 0.474 1.33 13.12 3.68 1811 -0.248 0.396 0.759 0.919 0.942 1.299 10.98 5.82 2269 -0.343 0.365 0.857 0.728 1.098 1.157 8.84 7.96 2147 -0.151 0.337 0.988 0.802 1.114 1.296 6.70 10.1 1171 0.224 0.292 1.231 1.180 1.022 1.795 4.57 12.23 265 0.840 0.183 1.713 1.211 1.231 2.067 2.43 14.37 11 -0.158 0.316 0.718 0.846 194.2 1.205 0.29 16.51 -0- -0- -0 - -0 - -0- -0 - -0 - -1.85 18.65 2 0.217 0.481 -0 - -0- -0 - -0 - -3.99 20.79 11 0.113 0.041 0.476 0.315 1.122 0.553 -6.13 22.93 234 -0.161 0.247 1.499 1.582 0.981 2.332 -8.27 25.07 1012 0.093 0.398 1.776 1.547 1.046 2.435 -10.41 27.21 1789 0.572 0.350 1.488 1.186 1.101 1.931 -12.55 29.35 2389 0.824 0.327 1.257 0.856 1.200 1.485 -14.69 31.49 2676 0.915 0.263 0.954 0.737 1.116 1.214 -16.83 33.63 2868 0.956 0.234 0.740 0.585 1.140 0.955 -18.97 35.77 1908 0.895 0.226 0.633 0.472 1.167 0.788 -21.11 37.91 24 0.685 0.006 0.206 0.236 1.066 0.339 TABLE A I - 6 (CONTINUED) Run #5 Dist. From Grid (cm) Depth (cm) # of Streaks q q/q 0 qJ q J/q 0 J L e Lk i/'.OO -0.2 l46l 4.19 15.26 1.54 530 1.631 0.804 4.338 0.519 (4.63) 755.2 0.063 0.063 15.00 1.8 1665 4.49 13.12 3.68 1811 1.612 0.795 4.188 0.502 (4.34) 699.6 0.064 0.063 13.00 3.8 1631 4.46 11.00 5.8 1X76 3.53 10.98 5.82 2269 1.521 0.750 3.52 0.421 (3.65) 555.2 0.064 0.063 9.00 7.8 518 2.67 8.84 7.96 2147 1.610 0.793 4.173 0.500 (2.58) 415.4 0.108 0.055 6.70 10.1 1171 1.895 0.934 6.802 0.815 5.00 11.8 (2.029) 1.0 8.353 1.0 4.57 12.23 265 2.033 8.405 2.43 14.37 11 1.552 3.741 0.29 16.51 -0 - -0 - -0 - -1.85 18.65 2 -0 - -0- (0.07) -0 - -0- -3.99 20.79 11 1.051 1.162 (0.42) 44.1 0.184 0.048 -5.00 21.8 (2.537) 1.0 16.329 1.0 (0.59) 149.7 1.845 0.027 -6.13 22.93 234 2.160 0.851 10.073 0.617 (0.78) 168.5 0.861 0.033 -8.27 25.07 1012 2.207 0.870 10.747 0.658 (1.13) 249.4 0.634 |0.035 -9.00 25.8 1228 1.29 -10.41 27.21 1789 1.965 0.775 7.590 0.465 (1.49) 292.8 0.340 0.041 -11.00 27.8 1571 1.76 -12.55 29.35 2389 1.723 0.679 5.118 0.313 (1.84) 317.0 0.185 0.048 -13.00 29.8 1898 1.8 -14.69 31.49 2676 1.558 0.614 3.783 0.232 (2.19) 341.2 0.115 |0.054 -15.00 31.8 1974 2.45 -16.83 33.63 2868 1.382 0.545 2.641 0.162 (2.55) 352.4 0.069 0.062 -17.00 33.8 2101 2.23 -18.97 35.77 1908 1.256 0.495 1.979 0.121 (2.90) 364.2 0.046 0.068 -19.00 35.8 1646 2.94 -21.11 37.91 24 0.823 0.234 0.558 0.034 (3.25) 267.5 0.012 0.096 168 '1 I j TABLE A I - 6 (CONTINUED) RUN #6 Oi s t a n c e From G r i d (cm) D e p t h (cm ) # o f S t r e a k s w u W1 2 IT7! R TKE 11 . 8 6 l . l 6 240 -0.G T 3 H 0.091 0 . 3 5 3 1 . 6 7 0 0.493 1 . 8 5 0 9.72 3.3 835 -0.184 0.048 1.211 1.313 0.969 1.918 7.58 5.44 696 0.218 -0.113 1.270 1.782 0.868 2.418 5.44 7.58 119 0.497 -0.175 1.261 1.873 0.947 2.503 3.30 9.72 2 0.087 0.047 0.103 0.260 0.281 0.312 1.17 11.85 -0 - -0 - -0- -0 - -0- -0- -0- -0.97 13.99 1 0.136 0.174 -0 - -0- -0- -0 - -3.11 16.13 6 0.271 0.216 0.132 0.186 0.488 0.252 -5.25 18.27 245 -0.363 0.243 2.132 2.321 0.964 3.387 -7.39 20.41 884 0.194 0.394 2.071 1.664 1.164 2.699 -9.53 22.55 1638 0.707 0.388 1.609 1.231 1.179 2.036 -11.67 24.69 2173 0.973 0.350 1.153 0.858 1.158 1.435 -13.81 26.83 2502 1.041 0.252 0.977 0.684 1.221 1.172 -15.95 28.97 2806 1.051 0.233 0.786 0.566 1.228 0.959 -18.09 31.11 2938 1.044 0.212 0.688 0.470 1.247 0.814 -20.23 33.25 2787 0.988 0.150 0.610 0.387 1.311 0.691 -22.37 35.39 399 0.710 0.014 0.496 0.302 1.404 0.550 TABLE A I - 6 (CONTINUED) RUN #6 Dist. From Grid (cm) Depth (cm) # of Streaks q -Q O q 3 q 3/q 0 3 L * eL e k 12.00 1.02 569 2.60 11.86 1.16 240 1.924 0.835 7.117 0.582 (2.89) 556.0 0.164 0.050 10.00 3.02 190 2.71 9.72 3.3 835 1.959 0.850 7.513 0.614 (2.06) 403.6 0.243 0.045 8.00 5.02 3 0.67 7.58 5.44 696 2.199 0.954 10.635 0.868 (0.43) 94.6 1.649 0.028 5.44 7.58 119 2.237 0.971 11.200 0.914 5.00 8.02 (2.305) 1.0 12.247 1.0 3.30 9.72 2 0.790 0.493 1.17 11.85 -0- -0 - -0- -0.97 13.99 1 -0 - -0 - -3.11 16.13 6 0.710 0.358 (0.39) 27.7 0.061 0.064 -5.00 18.02 (2.501) 1.0 15.644 1.0 (0.72) 180.1 1.450 0.029 -5.25 18.27 245 2.603 1.041 17.631 1.127 (0.81) 210.8 1.451 0.029 -6.00 19.02 764 1.70 -7.39 20.41 884 2.323 0.929 12.541 0.801 (1.23) 285.7 0.680 0.035 -8.00 21.02 1182 1.96 -9.53 22.55 1638 2.018 0.807 8.217 0.525 (1.65) 333.0 0.332 0.042 -10.00 23.02 1505 1.85 -11.67 24.69 2173 1.694 0.677 4.862 0.311 (2.07) 350.7 0.157 0.050 -12.00 25.02 1811 2.08 -13.81 26.83 2502 1.531 0.612 3.589 0.229 (2.49) 381.2 0.096 0.057 -14.00 27.02 1914 2.51 -15.95 28.97 2806 1.385 0.554 2.656 0.170 (2.91) 403.0 0.061 0.064 -16.00 29.02 2116 2.83 -18.00 31.02 2166 3.16 -18.09 31.11 2938 1.276 0.510 2.077 0.133 (3.33) 424.9 0.042 0.070 -20.00 33.02 2109 3.91 -20.23 33.25 2787 1.176 0.470 1.625 0.104 (3.74) 439.8 0.029 0.077 -22.00 35.02 638 4.07 -22.37 35.39 399 1.049 0.419 1.154 0.074 (4.16) 436.4 0.01910.085 170 APPENDIX II COMPUTER PROGRAM S Computers were used for processing the data collected in the laboratory experiments and for modeling the radon data collected in the fie ld . Programs were run on two computer systems, the Geophysics PDP-11 and the University IBM 370/185. A brief description and listing of these programs follows. The computer system each program was written for is designated in parentheses. Gas Data Processing Programs GASRUN (PDP11). GASRUN accepted the gas chromatograph settings and peak areas for an experimental run from a computer terminal and stored these data in a data file by run number (e.g.: GASRUN05.DAT). GA5CAL (PDP11). GASCAL read the data from a specified GASRUN f il e and performed a series of calculations, including gas concentration, time change between samples, and change in concentration through time. Gas concentrations were calculated using equation A III-12 and concentration changes using equation 2-11. The results were output in tabular form and stored in an additional data f ile by run number (GASCAL05.DAT). Loading the gas chromatograph and chart-area data into a separate data f ile (GASRUN.DAT) as opposed to direct input into GASCAL, allowed greater fle x ib ility in data manipulation. This approach enabled unlimited changes to be made in the data f ile with only a minimum of retyping effort. GASRUN 1 l o 20 30 3 5 40 55 70 95 130 IPO 190 195 2 CO 2C5 2 15 ?i 0 22 0 D I M E N S I O N GAS ( 4) «YTE RF1LE ( 1 5 ) * DDATE <15) DATA G A S / * 0 2 * * * N 2 * • * C 0 ? » . * C H % * / TYPE * * • ENTER 6 AS R UN " I L l MAKE: { E X : GA S RUM* * ) • ACCEPT 1 0 » V P » R F I L E FQ9M AT { Q « 3A 1 ) CALL A S S I GN! Cl * R F I L E . U P ) T Y ° E * * • ENTER RUN NUMBER AND D A T E : • READ (5 * 2 0 ) I RUM* RDATE FOR MA T ( 1 2 , 1 5 A 1 I WRITE (1 * 3 0 ) IRUN»RDATE F O R M A T ( 5 X . I 2 * 1 0 X * 1 5 A 1 1 D O 7 0 I G = I * 4 WRITE ( 5 , 3 5 ) G A S ( I G ) FORM AT ( * ENTER NUMBER AND A T T . OF » , A 3 , * S T AN DA RD S: •) ACCEPT * , N * I A T T WRITE (1 * 4 0 ) N . I A T T F O R M A T ( S X » I ? * 1 0 X , 1 5 ) I F ( N . E Q . O ) GOTO 70 DO 6 5 I S T A N D = 1 , N TYPE * , * ENTER AREA: * ACCEPT * , A R WPI TE ( 1 * 5 5 ) AR FORMAT ( 5X * F 6 . 0) CONTINUE CONTINUE DO 1 9 0 I G = 1 * 4 W R I T E ( 5 * 9 5 ) 3 A S ( I G ) F O R M A T (• ENTER THE N U " 3 E R AND A T T . DF * . A 3 , * SAMPLES: •) ACCEPT * * f : S . I A T WRITE ( 1 * 4 0 ) N S , I AT I F ( N S . E Q . 0) GOT D 1 9 0 PO 18 0 I SAM PL =1 * NS TYPE * , • ENTER T IM E ( H R . M N ) * AND AREA: • ACCEPT * * T I ME * A R W R I T E (1 *1 3 0 ) T I M E * AR F O R M A T ( 5 X , F 5 . 2 , 1 O X , F b . 0 ) CONT IN UE CONTINUE TYPE ■ * • ENTER THE NUMBER DF RADON S AM PL ES : • ACCENT *,NR ADO M WRITE (1 . 1 9 5 ) NRADOS FO R M A T (5 X , 1 2 ) I F ( N R A D O N . E Q . 0) GOTO 2 1 5 DO 3 0 5 I S A M P L - 1 * N R A D D N TYPE * * • ENTER RADON T IM E AND C O N C E N T R A T I O N : • ACCEPT * , P T I M E , R C 3 N C WRITE ( 1 , £ 0 0 ) R T I « E . R C O N C F P P M A T ( 5 X , 9 5 . 2 * 1 0 X * F 7 . 4 ) CONTINUE CALL CLPSE ( 1 ) W R I T E ( 5 * 2 1 0 ) R F I L E F O R M A T ( IX * 8 A 1 * • I S READY FQR G A S C A L . * ) TYPE * , * ANY MORE RUNS 7 : • R E A D ( 5 * 2 2 0) IA BC F O R M A T ( A 21 I F ( I A 5 C . E Q . 2 H Y E ) GOTO 1 END 172 GASCAL PI M E N S T O N PRATAR(4),X(A),3AS(5),?TiyF(5),0TlMFt:5,5f)*TIME(3*5D) DIM ENSIO N NSAM P(5)»CONC<3,5 0),9Fi_CDNC5,SO).CAIR<5>,XL:>3l5,:>0) 9Y T F RFILt (IE) ,DrILE US) ,R D A TE (lb) P A T a G A S/*02» * • N ?' * • C 0? • , • C b4» , • R N » / * FILE H A N D LIN G A N D INITIALI 7ATI 0N • TY P - *,» E N T E R RUN-FIlE T O B E R E A 3: • A C C E N T 30,NP»RFILE F O R M A T (Q * B A 1 ) C A L _ A E E I& N ! U.RrIL") T Y P E *.* E N TE R ? Ir T O D A T A FILE / 3 IF T O TERMIvM: * A C C E P T • * L IF (L.EQ.1) G O T ) 20 T Y P E *,» E N T E R 0® T A PILE N A M E : (EX:3A SC A L##)• ACCFPT 10,NR*JFILE C A L L A SSIG N (2,DPILE,N=) X(1)=0.R3b X (?)-3. 1 X (■ » ) =3.9R X ( A 5 C A I R ( 3 ) = 0 . 0 1 C A I Q ( 3 ) - 9 . 0 T Y p £ *,» E N T E R E Q U ILT E R I U M V A L U E 3 "O R 02,N2. A N D C H A : • A C C E P T * *C A IQ (1 ) *CMR (?) »CAIR(4) R E ' A O C 1 * 30 II R U N * R O A T E r O P v,6 T ( S X • I 2 * 1 0 X . 1 5 a 1 ) W R IT E (L*40) I P U N .R P A TE F O R M A T (' 1 ', 14X, * P A S D A T A r0R R U N U• ,I 2,?X,1S A 1 ,//1 * S T A N D A R D INPJT and C A LC . O r A TT*A R E A « r .! 7 0 ISA 3=1. A p p A D C 1.SO )NST,I A T T r o P R A T ( S X , I ? , 1 0 X . I S ) I r (NST.FC.OI G U TD 70 A R A T S M = 9 R Q 65 ISTCNT-] ,NPT P E A * ( I , 6 0>S T A T:A F0 PyA T ( S X . F b . O ) /! p / T' vr^iTCM . I f, T T * s T A R E A CCNTI RUE PRATAR(IG-S) = A P A TS « / N 3 T co^tinul * sample INPJT A N D C O N C E N TR A TIO N C A LC . • D R IO C IG^S=I,Q P E A ? (l.LO) N S A W P (T G A S J *1 A T T T F ( m 5 A A P ( 1 0 A S ) . F 0 . 9 ) G 0 T 0 1 C 0 DO DO ISABEL = I , NSAMP ( I GA S) R E A O ( 1 ,N O } TIM E(TGAS.ISAM PL).AREA rQ P M A T ( F X • F F • ? • 1 0 X . F 6 . P ) C O N C (IGAS.ISAVPL) = X(ISAS) * IA T T * A R E A / P R A T A Q ( I G A 5) ruNTi\ur F O N T I S U E • R A D O N IN P U T (IF A N Y ) * R E A D (] ,]1 0) N S A M P C S 1 ^O R maT f c X , I 2 ) Tr (N S A M P ( ) ,F0.0 ) R O T O 140 D O 1?0 NPADO N^I.N S A M P (d) P f A D ( 1 ,120) TIF (3,N R A D O N ) ,C O N C (>,N R A ^O N ) F O R M A T (SX*Fb.2.10X,F7.A1 C O N IT I D U E • L U O C A LC U LA TIO N S F O R A L L S A M P L E S • r J O 150 IGA5=1*S IF(NSAMP(I3AS).P Q.C) G O T O 160 D O ISO ISAYPL=]SAYP<13*3) DELC0N(IGAS*ISAMPL)=C0NCII3A3,I3A«3L) - CAIR(ISAS) X L 0 0(ISA 3,1S A M P L) = V Q G < L 0 G 1 0 C0ELC0N(I34S,I>AMPL>/DELCDN(I3 4;>,1)) ) C C N TIN U E C C N T I > N U F ♦ TIM E A N D IN TER VA L C A LC U LA TIO N S * D O 1B 0 IG A S = 1 * S IF (N S A M P (I G A S ) . r C . 0 ) G O T O 1*0 7 T I M E (I G A S ) = IN T ( TIM E ( I G A 8.1 ))*l.bbbbb» (TIM F (I 3A3.1 ) 1-INI (T IM F ( I G A S » 1 )) ) D 0 170 ISAYPl = 1 ,'’S A M P ( I S A S ) D T I M F (I G A S,TSA M PL)=5 0 * ((INT ( T I M F (I 3AS•ISA M PL) ) l*!.355b5*(TIME(IGAS,ISAM^L)-INT(TI<4E(I 3AS.ISAM PL) ) ) ) 1— 7 TIM E (IGAS) ) CONTINUE C O N TIN U E • O U T P U T D A T A « W R ITE (L *2 00) 173| POO ?1 0 P P O ? 3 0 P A O C P S O P E 0 FORMAT C 15X, • GAS* • SX* • TIME* ,9X , , DTIME, * b X * , C3MCEN.* ,7X, *L 0 3 R * . 1 / , ! 5X» • = = = • *BX, « = = = = « , 9 X , •==== = • x,* = = = = = = = • , 7X* •= = - = « | L I M t = E DO PAO IGAS=-2 *b IF (NSAMP (IGA S ).E O .O) SOTO PAO DO ? 3 0 ISAMPL=1 .MSAMPCI3AS) L I M t = L l N F * l W R I TE (L*P10)GA3 (ISAS) .TIME (IGAS.ISAMPL) • DTI WE Cl GAS .ISAWPL) * 1CO.MC (IG A 3.IS A M P L 1 . XLOG (I GAS. ISAMPLI FOQMAT(1SX*A3»9X.pS . P * 3 X , F S . 1 * S X . F 7 # A , & X . F 6 . 3 I IF ( L IM E .L T .7 P ) GOTO P30 WRITE CL.PPO) FORMAT C•1») LI M E = 0 COMTIMUE CONTIMUf * CLOSIM3 OF FILES AMD OPTIOM « IF CL.EQ.S) GOTO PSD CALL CL OSc (?) CAL_ CLOSE(1) T Y P E **• A M Y M 3R F R U M S ?r * READ Cb.PfcO) I ABC FORMAT(A?) IF (IABC.EG.PHYE) GOTO 1 EMD 174 GASPLOT (PDP11). GASPLOT is a plotting program which was designed to read the data from a specified GASCAL data f ile and construct a plot of the logarithmic concentration ratio vs. time for all gases on a Hewlett-Packard XY plotter. In addition, this program performed a linear regression of the data for each gas, drew the best straight line f i t through the points, and printed the computed slope (in units of m/day) and error in the slope on the plot (see Figure 2-4). Turbulence Data Processing Programs DIGIT (PPP11). Digit accepted the output data from the d igitizer and stored these data in a pre-specified data f i l e . Data filenames took the form: RaTb.Dat where a was the picture-run number, and b the f il e number, A new f il e was set up each time digitizing commenced by advancing the f ile number. The data file contained four columns of information: for each streak an I.D. number (1 for a streak " ta il" , 2 for a streak " ta il" , and 3 for a fiducial point), x-coordinate, y-coordinate, and event counter. These file s were edited for stray or incorrect data (e .g ., clerical transmission noise) and combined into a single f il e for each set of turbulence conditions ( i . e . , picture-run). Each combined DIGIT f ile consisted of approximately 40,000 rows of data, corresponding to approximately 20,000 streaks. A copy of DIGIT is not included. 175 c c 2 57 4 0 0 4 1 0 4 2 0 4 3 0 4 4 0 4 5 0 GASPLOT PLOTTING PROGRAM FOR GAS EXCHANGE LABORATORY DATA GRAPH SI 21 WILL 3E 7 . 5 3Y 4 . 5 INCHE5 Q Y TE F I L EN M (13) • RNO(5) DIMENSION A (90>« 3 ( 0 0 ) . 3 A S C 9 0 ), D T IM E C 9 0 ). CONCC90) D IM EN SIO N ' XC2) • Y ( 2 ) . YIMT C5) • SL03 EC5) • XKC51 DIMENSION V ( 2 ) . WW(?) .S.N<(5) CALL I N I T I A CALL COLOUR Cl) CAL. OFFSET C l . 5* 1 . 7 5 ) CALL ORIGIN CO.O. 0 . 0 ) CALL SI7E C 7 • 5 * A . 5) V ( 1) = 0 . 0 VC?) = 0 . 0 W tf (1 ) = 0.0 WW(2) = 4 . 5 CALL PLOT ( V . * W . ? . N O CALL P L IF T W w (2) = 0.0 WW(l) = 0.0 V (?) =7 .5 V(1) = 0.0 CAL_ DL OT (V .W W .2.N C ) CALL PL IF T TVPE * • * WHAT IS THE NAME OF THE DATA F IL E THAT YOU WISH 1 td HAVE PLOTTED?* ACCEPT 4 , NP.FILENM FCP**AT CQ * 1 3 A ] ) TYPE * . * WHAT RUM NUMBER I S TH IS?* ACCEPT 5 . NO. RNO FORMAT CQ. 4A1) P N O ( N Q * l ) = • « * CALL TEXT CO.4 . 4 . 3 . *RUN NUMBER:**) CALL TEXT Cl.fa. 4 . 3 . RNO) CALL TEXT ( 0 . 4 . 4 . 1 . * 3 A S XL ( M /D A Y ) a • ) CAL- TEXT CO.4, 4 . 0 2 , * 6 * ) ?6 = 3 . 3 COMMAX =0.0 T MVAX = 0 .0 CALL ASSIGN C2.FTLENM.NP) READ C? *57) FORMAT < / / / / ) DO 250 K = 1 •9 9 PLAO ( 2 , 6 0 , ENO = 270,E R R = 2£>0) SAS (K) * DTI ME ( K ) * CONC(K) BB3 = BB ♦ .Ofa IF C K .E Q . l) GOTO 400 IF C3AS(K) . E Q . G A S ( K - l ) ) 3DT0 500 IF C3ASCK).EQ.*OP • ) SOTO 410 IF ( G * S ( K ) . EQ .*N? * ) SOTO 420 IF ( G A S ( K ) . E D . * C D 2 * ) 3DT0 430 IF (GAS ( K ) . EQ. * C H 4 * ) GOTO 440 IF (3ASCK) • E Q . • R M • ) 30TD 450 CALl. TEXT ( 0 . 4 . 9 3 . • OXYG£ N ( ) » • ) CALL s y m b o l Cl) CALL PLOT C l . 12 • BBB.l .NIC) CALL P L IF T PB = 33 - 3 . 2 GOTO 500 CALL TEXT CO.4. B B * • NITR03EN C ) « CALL SYMBOL 12) i>AL L PLOT C l . 32 . 3 3 3 * 1 . N O CALL PL IF T 99 - 93 - 0 . 2 GOTO 500 CALL TEXT CO.4, 93.»C0?C > * • ) CALL 5YM30L (3) CALL PLOT CO.32 .9 8 3 .1 . NO CALL PLIFT 9B = 33 - 0 . 2 S~TO 500 CALL TEXT CO.4, 9 3 * * ME THA ME C > *• CAL. SYM3DL C 4) CALL PLOT C l . 22 . 9 3 3 . 1 , N O CALL PLI FT 33 = 33 - 0 . 2 GOTO 500 CALL TEAT CO.4. 9 3* * RADON C I ® * ) CALL SYM3DL C 5) CAL- PLOT ( 1 . 0 2 . 9 3 3 . I . »C) CALL PLI FT 500 220 25 0 25 0 270 2 5 0 2 5 5 290 20 25 30 4 0 50 6 o 11 0 75 IF (CONIC (<) . L T . CONMAX 1 GOTO 2 2 0 CD ' H A X = CONIC C O IF O T I M E m . L T . T M ^ X ) GOTO 25 0 TMMAX = DTIME ( < ) CONTI NUE TYD£ * , * ERROR IN I N I T I A L READ EX ECUTION* CALL C L O S E ( 2) WRITE ( 5 * 2 8 0 ) CONMAX r 0 R M A T ( * TMMAX = * , F 5 . 1 , 3 X , ' C O N M A X = * , F 6 . 3 > INTTM = N I N T ( T M M A X / 3 0 . 0) TRUNIM = TMMAX - INTTM I F ( T R U N T M . L T . 0 ) GOT 0 2 3 5 INTTM = I N T T M + l TM^AX = I N T T M * 3 0 . 0 INTCDN = NlNTCCONHAX/ D .051 TRUNCD = ( C O N M A X / 0 . 8 5 ) - I NT CON I F (TRUN'CO.LT . 0 ) GOTO 290 IMTCON = INTCDN * 1 CONMAX = INTCDN * . 0 5 YA = - 0 . 0 5 YB = CONMAX YT = 0 . 0 5 YY = Y3 - YA AY = 4 • 5 / YY NT = N I N T ( Y Y / Y T ) NZ = NT - 1 DO 2 0 I = 1 * \ !T C = I * YT * AY CALL TEXT ( 0 . 0 , C * « . a M DO 30 I = 1 » N T » 2 C = ( I * YT * A Y ) - 0 . 0 5 I F ( I . N E . 1) GOTO 25 CALL TEXT r - - 5 , C * • D . 0 0 B » ) GOTO 30 D = ( I * Y T ) ♦ YA C 4 L l HPNUMD( - . 5 , C , D , 2 ) CONTINUE XA = 0 . 0 X B = TMMAX XT = 3 0 . 0 XX - X3 - XA AX = 7 .5 /XX CALL TEXT ( 1 . 9 , - . 5 , • O S C I L L A T I O N T I M E ( M I N U T E S ) B * ) C AL _ AN G LE ( 9 0 . ) CAI TEXT ( - . 7 , 0 . 7 5 , * LOG I ( C W - C A I R ) / ( C l - C A I R ) 3 a • I NT = NI NT ( X X / X T ) NZ = NT - 1 DO 4 0 I = 1 , N T C = I * ( A X * X T ) CALL TEXT ( C , 0. 0 , » . B • ) CALL A N G L E ( 0 . ) DO 50 I = 1 * NT * 2 D = ( I * X T ) ♦ XA C = I * ( A X * X T ) - . 2 0 CALL RP;MUt;D ( C , - . 3 , 0 , 0 ) CALL A S S I - N ( 2 , F I L E N M , N P ) READ ( 2 , 5 7 ) SU'^LOG = 0 . 0 SU**TM = 0 . 0 SUM2TM = 0 . 0 SU‘^LGT = 0 . 0 SU^ZLO = 0 . 0 I 3 A S = 1 I GROUPED W = 4 . 0 DO 1 0 0 J = ! * Q0 READ ( 2 , 6 0 , E NO = I 1 0 , E R R = 15C) G A S ( J ) , D T I M E ( J ) , CDNC(J) FORMAT ( I 5 X , A 3 , 2 I X , F 5 . 1 , 1 9 X , F 6 . 3) I F ( J . E Q . l ) 30 T D 70 T F ( G A S ( J ) . E Q . G A S ( J - l ) ) GOTO 73 GOT j 75 WWW = 3 . 7 12 = ( I 3 R SJ P * S U v ? T M - SUMTM*SU*TM> Z Z 7 = ( S U mL 0 G * 5 U * ? T M - S J M T M * 3U M L 3 7 ) ZZZZ = ( IGROUP*SUMLCT - SJMLO3 * SUMTM1 * » 2 S L D 3 E ( I *3 A S) = ( ( I GROJP*S JML5T - SUML0 3 * SUMTM) / Z Z I Y I N T ( I 3 A S ) = 2 7 . 2 / 2 1 X < ( 1 3 A S ) = S L 3 P E ( I 3 4 S ) * 1 443 .0 « 3 . 6 3 5 « 2 . 3 0 3 X K (5 ) = X K (5 ) - 0 . 1 1 4 SY = ( I GROUP * SUM2L3) - (SUVLDG »* 2) - ( Z Z Z Z / Z Z l ] JJ SY = ( S v * * 0 . 5 ) / I G P 3UP S N K ( I b A S ) - ( CTosQU^ * SY ) / ( ( I GROUP - 2) * ZZ) * * D . 5 ) B? 1 0 5 . 9 D WPITE ( 5 , 8 5 ) SUYT Y, 5JY L0 6»S U YL GT ,S U W 2T M» S U M? L G D 85 FORMAT C1 X , « SUMTM=» , 1 P E 1 1 . 3, • SUMLOG = *♦1 PE 1 1 . 3 , » SJMLGT = • * I P E 1 1 . 3 , D 1 / , 1 X • « Sl)V?TMs », 1 PEI 1 . 3 , « 3 U W ? L 3 = » * 1 P E 1 1 . 3 ) D WPITE ( 5 * 3 6 ) Z Z . 7 Z 7 . 7 Z Z Z D 86 r O P Y A T ( IX , » ZZ = » , T P E l l . 3 * • Z Z Z = ’ * 1 PE 1 I . 3 , » ZZZZ = »* 1 PE 1 1 . 3 ) Y d ) = ( Y IN T ( IG A S ) - Y A ) *A Y X (1 ) = 0 . 0 X ( 2 ) = (DTI ME ( J-T ) - X A ) • AX Y (2 ) = C ( Y I N T (1 GAS) ♦ (DTI WE( J - l ) *S L D P E (I GAS)) ) -YA) *AY CALL SYMBOL(0) CALL PLOT C X ,Y ,2 ,N C ) CALL P L IF T W = W - 0 .? CALL HPNUMD ( 1 . 5 , W, X K C IS A S ) ,? ) CALL TEXT ( 2 . 0 9 , W*C.02» CALL TEXT ( 2 . 0 9 , * - " . 0 5 , » -® * > CALL HPVUMD ( 2 . 1 , W, S N K ( IG A S ) * 2 ) WPITE ( 5 * 9 0 ) p A S f J - D * Y I N T ( I SA 5 ) * X K ( I 3 A S ) , SMKCIGASI 93 FORMAT (1X ,« F O R * , A 3 ,* YINT I S « , F 7 . 3 , » AMD KL I Si • ,1 PEI 0 . 3 . 1 * A NO SN I S : ». 1 PE 1 3 . 3 ) IF (WWW. EU. 3 . 7 ) GOTO 330 91 TYPE * , * APE YJJ PE AD Y FDR THE NEXT GAS?1 PE AD ( 5 , 9 2 ) I A3 D 92 FORMAT (A 2) IF ( IABD .EQ.2HM0) GOTO 91 SU^LOG = 0 . 0 SUM2T’* = 0 . 0 SUMTY = 0.0 SU^LGT = 3 .0 I GROUP = 0 5UM2LG = 3 .0 I GROUP = 0 70 IF ( 3 A S ( J ) . E Q . , 0 ‘> * ) I3AS=1 IF (GAS ( J) . EG).'* M2 * ) I 3A 3 = 2 IF (3ASCJ) . E G . * C O ? * ) IGA 3 = 3 IF ( G A S ( J ) . E Q . * C H 4 « ) IGA5 = 4 IF ( 3 A S ( J ) . E Q . ' P N «) IGAS=5 73 I GROUP = ISPOIJP ♦ 1 A (1) = (DTTME(J) - XA) * AX 9 ( 1 ) = (CEiVCCJ) - YA I * AY WRITE ( 5 , 6 0 ) G A S ( J ) . D T I W E I J ) , CDMCCJ) I F (1 GROUP.EC.1) GOTO 3 9 GUILDS = SU^L 03 ♦ COMC(J) SU^T.H = SUYTY ♦ DTlM EfJ) SU v2 T M = SJM2T* ♦ C[ I I v L ( JI * * 2 ) S U v L G T = SLM'LGT ♦ ( C1 ! ME( J ) *CONC( J ) ) 51' M ? L G - 50 M 2 L G ♦ ( C D N C ( J ) « * 2 ) 8 C CALL SYMPOL (IGA S) CALL PLOT ( A , 3 , l ,fJC) CALL P L IF T 9? \'CP = N CP ♦ NC 100 CONTI MUE GOTO 300 l c0 TYPE • * • EPPOk IM RFAD ATTEKPT* GOTO 140 3 nD WPITE ( 5 , 3 1 0 ) IMTTW. IM TC0 M. Y 3 , YY, AY, X3 • XX, AX 310 FORMAT ( I 2 , 2 X , I ? , ? X , F 5 . 3 , 2 X , F 5 . 3 , ? A , F 7 . 3 , 2 X , F 4 . 0 , 2 X , F ' , . 0 , 2 X , F 7 . A ) C AL ^ PAGE TYRE 1 2 0 , MCF 129 FORMAT (* MU^E.ER OF OFFPLOT POTMTS I S : » , I 3) 1^*0 CALL CLOSE (2) FNP 178 STREAK (UCC). This program read the combined streak-data files for a specified picture-run , ignored anomalous points, and calculated the horizontal and vertical mean and turbulent velocities, j the ratio of these turbulent velocities, and the turbulent kinetic energy throughout the water column. Anomalous points consisted of ! streak coordinates falling outside pre-specified acceptable values or streak points lacking either "head" or "tail" coodinates. Two parameters had to be changed for each run; the photographic exposure time and the grid depth. The turbulence parameters were calculated throughout the water column using equations 2-1 through 2-5 by dividing the tank into five columns and eighteen rows and computing the values of the parameters in each grid element using both 1 x 18 and 5 x 18 matricies. LENGTH (UCC). ! This program was written to compute the parallel turbulence velocity correlations required for computation of the integral length scales. The program read a pre-specified streak data f i l e , j i ! considered only streak points falling within a pre-specified depth range, and computed the correlations at 2 cm streak separation intervals over a total separation range of 0 to 20 cm. A separate ! program was set up for each set of turbulence conditions ( i . e . , j picture-run) and was designated as LENGTH #, where # referred to the t i picture-run number. The only parameters changed for a series of ; i ; computer runs were the depth range of interest and the bin number. J The program output for each streak separation interval consisted i of the number of streak images compared, the summation of the ; 179 ! STREAK / / E>£C FORTGCLG, REGION-1024K, T irC -(0 ,30) ,RG-256K C P R O G R A M ■ C TE1 Ol <TL C THIS PRO G RAM COMFJTES U(X,Y), V(X,Y), AND TURBULENCE DIMO'SION H (44000), >F( 44000 ),YP( 44000) DIMTCION >W(??000),VW(?70BR),DX(?70BR)<DV(?aWB) DIMO'SIQN ASLM(1 8 ),SU(1 8 ),SV(18), SLM(5,18),U (5,18),V(5,18) DPC6ICN L P (5,18),^ (5,18),Q (5,18),S L F (18),S V ^ (18),G P (10) DINJ€ION DEFTH(l8),UAVE(18),VAVEC18),QPVE(18),a32AS€(l8) DIfO€ION QP32(18),Q32(5,18),W =RT(5,18),RATAVE( 18) INTEGER 2RO ,O f€, TW O , TWEE DATA ZERO/'0 V DATA O TC/'l V DATA TW0/'2 V DATA TVREZ/'3 V C D-POSLFE TIPC IS 'T'. C MACHIfC UNITS TO CENTIMETERS COWERSION IS 'CCVST'. C SCALE FACTOR CONSTANT IS 'SCALE'. C 'GRID' IS HEIGHT OF GRID (01. ) A BO VE FIDUCIAL AXIS. T - 0.740 CONST-4.937 SCALE-5.628 GRID-15.24 WRITE (6,999) T, SCALE, GRID 999 FORMAT(IX, 'DPOSLRE TIME - \F 6 .4 ,2 X , 2'9CALE FACTOR COT6TANT - \F 6 .4 , ' GRID POSITION (CM)-',F6.4) C TVE VARIABLES WIQ-TT, XLEFT, WANGE, YBOT, YTOF, A ND YRANG E C ARE USED TWOUGOJT TVE P R O G R A M TO INDICATE TAW DIMEV6IONS FO R C EA Q H RLN. ajEFT-0.4 W IO fT-9.6 YBOT— 1.0 YTOP-6.0 WANGE-(W IG*T-*JEFT) / 5 . YRANGE-(YTOP-YBOT)/ I S . C DETEW1IME BIN DISTANCE FR O M GRID (CM.) CSTART- CONST* (YBOT-0.5*YRANGE) D O 350 JP-1,18 DEPTH(JP)- CSTART+( JP*COf€T*YRANGE) DEPTH(JP)- ABS(GRID-DEPTH( JP)) 350 CONTINUE C TVE MACHIME SET DISTANCE BETW EEN FIDUCIAL POINTS A A N D B IS C 10.0 UNITS. TVE ACTUAL DISTANCE IS 19.4375 INCHES. THJS, A C SCALE FACTO R O F 1.94375 IS REQUIRED TO TAKE MACHIME COORDINATES C TO 'AIR' COORDINATES. IN CENTIMETERS, THIS IS 'CONST' (4.937125) C TVERE IS ALSO A MAGNIFICATION FACTOR D UE TO W A TER A N D GLASS C B ETW EEN FRONT R J *€ OF TAW AN D TEST SECTION AT CENTER OF TAW. C TVE MAGNIFICATION FACTOR IS 1.14 . C TVE SCALE FACTOR REQUIRED IS THEN DETERMINED TO BE 5.675 . C W E CALL THIS 'SCALE'. C REA D TVE DATA WT5 • 44000 r€GL-0 rCND - 0 r+CADS-0 NTAILS-0 M<l>-TWEE > P (l)-0 .0 Y P (l)-0 .0 WRITE(6,303) 303 FCW *T(/,1X, 'FIRST AN) LAST 100 POINTS:') D O 254 L-2, WTS READ(5,1000, 157,ERR-311) M(L),tf»(L),YP(L) 1000 FOfWAT(lX,Al,2X,F9.5,1X,F9.5) IF ((L .G T .100).AND.(L.LT.43000)) G O T O 313 W FITE(6,305)M (L),)P(L),YP(L),L 305 F0RMAT(1X, A l,2X ,F9.5,1X ,F9.5, IX , 16) G O T O 313 180 311 M<L)"ZERO WITE<6,1100) 1100 FO R M AT d X , ' « * * ERRO R IN DATA SET ! • * * * ’ ) 313 IF <(M(L) .EQ.OtC ).OR. (M(L).EQ.TWO).OR. <M(L). EQ. THREE) )GOTO 253 HCGL-fCGL+1 WITEC6,1006)L,M(L) 1006 FORMATdX, 'POINT * ', 1 6 , 2X, 'HEGLECTED; N «\A 1) G O TO 254 253 HEM)-HEND+1 M<H£M))-M<L) >R(IEM))->P(L) YP<r€N))-YP(L) 254 CONTINUE 157 HRITE(6,257)HEGL,L 257 FORMAT( IX, 1 6 ,' ILLEGAL CHARACTERS (HEGLECTED) OUT OF ',1 6 ) C OECK FO R 9CREW-UPS IN HEADS AT® TAILS (SET M TO ZERO) D O 100 L -l,fE M ) L l-L-1 IF<<M(Ll).EQ.OrE).AM>. (M(L).EQ.OHE)) G O TO 301 IF<<M(Ll).EQ.OHE).AM>. <M(L) .EQ.THREE)) G O TO 301 IF((M(Ll).EQ.TVIO).AM). (M(L) .EQ.TVIO)) G O TO 302 IF<<M<Ll).EQ.2RO).AM>. (M(L).EQ.TWO)) G O TO 302 IF((M(L1).EQ.THREE).AM). (M(L).EQ.TWO)) G O TO 302 G O TO 100 301 M(Ll)-ZERO MEADS-MEADS+1 G O TO 100 302 N(L)-SRO NTAILS-NTAILS+1 100 CONTINLE C GET RID O F FIDUCIALS, 9CREHHJPS, ETC. N-0 HF-0 NEGL-0 D O 101 M<«1,NEM) IF(M(MO. EQ.THREE) G O TO 102 |^ B 0 IF<f1(M*).EQ.2RO) G O T O 104 N-N+l M(N)-M(hN) >R<N)->R<MO YP<N)-YP(MI) G O TO 101 102 CONTINUE C FIDUCIAL POINT CHECKS H F-IE d IF(HF.GT.l) G O TO 920 IF<ABS(>R<MO).GT.0.1) G O TO 900 905 IF<ABS<YP<MO).C T .0 .1 ) G O TO 901 G O TO 101 920 IF(H f .GT.2) G O TO 902 IF<ABS<YP<MO) .G T .0.1) G O TO 903 AA")R<MO-10.0 IF(ABS<AA).GT.0.1) G O TO 904 G O TO 902 900 HRITE<6,1001) Mi,)R<MO 1001 FORMAT<2X,'FIDK1 OUT OF TCL',ZX, 'MH»', I5,2X , 'FID K 1»',F9.5) G O TO 902 901 IRITE<6,1002) M<, YP(MO 1002 FORMAT(2X,'FIDY1 OUT OF T C L ',2 X ,'M < -\I5 ,2 X ,'F ID Y 1 -',F 9 .5 ) G O TO 902 903 HRITE<6,1003) M^,YP(M^) 1003 FORMAT(2X, 'FIDY2 OUT OF T0L',2X, 'M i-',I5 ,2 X , 'F ID Y 2-',F 9 .5 ) G O TO 902 904 HRITE(6,1004) Mi,)R<MO 1004 FORMAT(2X, 'FIDK2 OUT OF T0L',2X, ' N S - \ I5 ,2 X ,'F ID X 2 -',F 9 .5 ) 902 CONTINUE G O TO 101 104 CONTINUE rCGL-fCGL+1 M IT E (6,1005) W ,tf» (W ),Y P (W ) 1005 F0RMAT(1X,'fCGL PT; M (HN)-0',2X, 2 'H N -',I5 ,2 X , 'M -',F 9 .5 ,2 X ,'Y P -',F 9 .5 ) 101 CONTINUE M ITE (6,407) NEGL, NEH), NCADS, NTAILS 407 FORMAT( IX, 16,2X, 'POINTS fCGLECTED O UT OF ',1 6 ,ZX, 'READ.', 2 ( ',1 6 ,' REPEATED ► C A D S AM) ', 1 6 ,' REPEATED TAILS ) ') C COM’UTE STREAK MIDPOINT AM) LENGTH. DISPLAY ANY LO NG STREAKS. M4-0 SLMAK-0.0 M>N-1 do 200 m - i,r c ,z MW-N+1 r til-ftH l »«► *)• 0 .5 *(M (rti)-» » M (m i)) YMcrtH)- 0.s*cYP(rti)-*-YP(frti)) DK(ft>0- M (M 1)-M (W 11) DX(f'N)- DX(HN) * SCALE DY(MO- YPChM)-YP(ftll) DY(f'W)- DY(MH) * SCALE SLNGTH-(DX ( ) **2+DY (W ) « 2 ) **0 .5 IF(SLNGTH.LT.5.0) G O TO 314 M IT E (6 ,317) W , SLN6TH, M ( t t l ) , Y P (ftl), M (ft11), YP(ft11) 317 FORMAT( IX, 'LONG STREAK (IGNORED): W - ', I 6 , ' LENGTH-', 1PE10.3, 2 / , ' HEAD-',FB.5, ', ', F 8 .5 ,' T A IL -',F B .5 ,' , ',F B .5 ) Hurt-o-B.B YM(hN)-0.0 314 IF(SLNGTH.LT.SLMAX) G O TO 200 SLMAX-SLNGTH 200 CONTINUE SV41AK-SLMAK/T M ITE (6,1007) W,SLMAX,SVMAX 1007 FO R M A T ( / / , IX, 'A TOTAL OF ', 1 6 ,' STREAKS W E R E U S E D .',/, 2 IX,'LONGEST STREAK IS ',1 P E 1 0 .3 ,' C M .',/, 2 IX ,'IT S VELOCITY IS \1 P E 1 0 .3 ,' CM/SEC . ' ) C INITIALIZE MATRICES (BINS) D O 703 JP-1,18 ASUM(JP)-0. SU(JP)-0. SV(JP)-0. D O 704 IP -1 ,5 9UM(IP, JP)-0. U (IP ,JP )-0. V (IP ,JP )-0. 704 CONTINUE 703 CONTINUE LIERS-0 D O 700 LL-1,MS C CHECK FO R OUTLYING STREAKS IF(ttt(LL).LT.>4_EFr) G O TO 701 IF(HI(LL).GT.M IG HT) G O TO 701 IF(YM(LL) .LT.YBOT) G O TO 701 IF(YM(LL).GT.YTOP) G O TO 701 C SORT STREAKS INTO BINS AM) COMVTE MAN VELOCITIES IN EACH BIN; C THE FIRST MATRIX IS X-5 BY Y-18; C THE SECOM) MATRIX IS X -l BY Y-18 IP - INT( (XM(LL >->4_EFT)/MANGE )+l JP- INT((YM(LL)-YBOT)/YRANGE)+l 9UM( IP, JP)-SUM( IP , JP)+1.0 U (IP ,JP )- DX(LL)/THJ(IP,JP) V (IP ,JP )- DY(LL)/T+V(IP,JP) ASUM(JP)- ASUM(JP)+1.0 SU(JP)- DX(LL)/T+SU(JP) SV(JP)- DY(LL)/T+SV(JP) G O TO 700 701 CONTINUE LIERS-LIERS+1 W ITE(6,263)LL,»1(LL),YM(L1.) 263 FORMAT( IX, 'OUTLIER; LL- ',I6 ,2 X , 'W -',F 9 .5 ,2 X , 'Y M -',F 9.5) 700 CONTINUE W?ITE<6,1008) LIERS 1006 FORMATdX, 'NUMBER OF OUTLIERS - ',1 6 ) D O 1900 JP-1,18 IF(ASUM( JP) .LT. 1.0) ASUM(JP)-1.0 9U(JP)-SU<JP)/ASUM(JP) S V C JP) -SV( JP)/ASUM< JP) UAVE(JP)- 0 VAVE(JP)- 0 D O 1901 IP -1 ,5 IF(SUh(IP,JP).LT. 1.0) SLM (IP,JP)-1.0 U(IP,JP)-U(IP,JP)/SUM (IP,JP) V( IP, JP)-V( IP, JP)/SUM( IP , JP) UAVE(JP)-UAVE(JP)HJ(IP, JP) VANE( JP)-VANE( JP)+V( IP , JP) 1901 CONTINUE UAVE(JP)-UAVE(JP)/5 VANE( JP)-VANE( JP)/5 1900 CONTINUE C kRITE O UT MilflN VELOCITIES AM) N UM BER OF 9AMPLES. W IT E (6 ,1059) 1059 FORM AT( / / , 2X ,'*#C flN VELOCITIES AND SATRLE S IZ E S ',/) D O 1902 JJP-1,18 JP-19-JJP W ITE(6,1050) JP,DEPTH(JP),ASLfKJP),SU(JP),SV(JP) 1050 FORMAT( IX, 'B IN -', 1 2 ,' GRID D IS T .-',F 6.2 ,'C M . ASI*1-',1PE10.3,2X, 2'SU»',1PE10.3,2X, 'SV-',1PE10.3) 1902 CONTINUE H?ITE(6,1054) 1054 FORMAT(/,IX, 'S U M ',/) D O 1903 JJP-1,18 JP-19-JJP H?ITE(6,1150) JP, DEPTH (JP), (S U i(IP ,JP ), IP -1 ,5 ) 1150 FORMATdX,'BIN-', 1 2 ,' GRID DIST.■ ',F6.2,'C M . ',5 (1 X , 1PE11.3)) 1903 CONTINUE kRITE(6,1053) 1053 F0RMAT(/,1X, 'L fE A N ',/) D O 1904 JJP-1,18 JP-19-JJP kRITE(6,1051) JP,DEFTH(JP),(U(IP,JP),IP-1,5),UAVE(JP) 1051 FORMAT( IX, 'B IN -', 1 2 ,' GDIST. - ',F 6 .2 , 'CM. ', 2 5(1X, 1PE11.3),' AV€R.-',1PE11.3) 1904 CONTINUE W ITE(6,1055) 1055 F0RMAT(/,1X,'WCAN',/) D O 1905 JJP-1,18 JP-19-JJP H?ITE(6,1051) JP,DEPTH(JP),(V(IP,JP),IP-1,5),VAVE:(JP) 1905 CONTINUE D O 803 JP-1,18 RSUM(JP)-0. SUP(JP)-0. SVRCJP)-0. D O 804 IP -1,5 SUM(IP,JP)-0. UP(IP,JP)-0. VR(IP,JP)-0. 804 CONTINUE 003 CONTINUE D O 800 L -1 ,W C GET OUTLIERS O U T (AGAIN) IFO^i(L).LT.)C-EFT) G O TO 801 IFOG1(L).GE.>RIGHT) G O TO 801 IF(YM(L).LT.YBOT) G O TO 801 IF(YMCL).GE.YTOP) G O TO 801 C SORT STREAKS A N D COM PUTE *A N TURBULENT VELOCITIES IN EACH BIN; C THE FIRST MATRIX IS X-5 BY Y-18 C THE SECOM) MATRIX IS X -l BY Y-18 IP - INT((»1(L)->E£FT)/>«ANGE)+1 JP- INTCCYHCL)-YB0T)/YRANGEH1 SUMCIP, JP)-5UM( IP, JP)+1.0 ASU1CJP)- A S U M C JP)+1.0 RB- DK(L)/T-U(IP,JP) UPCIP,JP)- UPCIP, JP)+AB**2 9AB- DKCL)/T-SUCJP) SUPCJP)- SUPCJP)49AB**2 AC- D Y(L)/T-V(IP, JP) V*>(IP,JP)- Vff>CIP,JP)4AC**2 SAC- DY(L)/T-SV(JP) SVP(JP)- SVP(JP)+SAC**2 G O TO 800 801 CONTINUE 800 CONTINUE D O 805 JP-1,18 IF(A5UH(JP).LT.1.0) ASLfICJP)-1.0 SUPCJP)- SUPCJP)/ASUMCJP) SVPCJP)- SVPCJP)/ASUMCJP) OP(JP) ■ 0.5*C2*SUPC JP)+SVPC JP)) GP32CJP)- 2*CQPCJP)**1.5) U A P v E C JP)-0 VAVECJP)-0 RATAVECJP)-0 QAVECJP)-0 G32AVE(JP)-0 D O 80S IP -1 ,5 IFCSLMCIP,JP).LT.1.0) SU1CIP,JP)-1.0 UPCIP,JP)- IFC IP, JP)/SUMCIP, JP) VPCIP,JP)- \0> C IP, JP)/SUMCIP, JP) VPUPRTCIP,JP)- \*>CIP,JP) / CUPCIP,JP)+1.0E-15) QCIP,JP)- 0.5*C2*JPCIP,JP)+VPCIP,JP)) G32CIP,JP)- 2*CGCIP,JP)**1.5) UAVE C JP) -U AfVE C JP) H F C IP , JP) V A V E C JP) -V#*C C JP) +VP C IP , JP) R A TAVEC JP) -RATA^C JPHVPUFRTC IP, JP) G AVE C JP) -QANE C JP) *Q C IP , JP) Q32AVE C JP) -Q32AVE C JP)+032 C IP , JP) 806 CONTINUE UNECJP)-UAVECJP)/5 V A VE C JP)-VAVE(JP)/5 RATPYECJP)-RATPVECJP)/5 G A VE CJP)-GAVE (JP )/5 Q 32AYEC JP)-Q32AVEC JP )/5 805 CONTINUE WRITE C 6 1069) 1069 FORMATC//,2X, '**TURBULENT VELOCITIES, EJCRGY, AND SAMPLE S IZ E ',/) D O 850 JJP-1,18 JP-19-JJP WRITE(6,1060) JP, DEPTH CJP) ,ASUMCJP) ,SLF(JP), SVPCJP) ,QPCJP), QP32CJP) 1060 FORMATCIX, 'B IN -', 1 2 ,' G D IS T.-',F 6.2, 'CM. ASUM-', 1PE10.3, 2 ' 9LF-',1P E 10.3,' S V P -M P E 10.3,' Q P-M PE11.3, 2 ' 2»«PA 3 /2 - M P E 1 1.3) 850 CONTINUE WRITE (6,1063) 1063 FORMATC/,IX,'UPRIfE SQUARED',/) D O 954 JJP-1,18 JP-19-JJP WRITEC6,1051) JP,DEPTHCJP), CUPCIP, JP), IP-1,5),UAVECJP) 954 CONTINUE WRITE(6,1065) 1065 FORMATC/,IX,'VPRIfE SQUARED',/) D O 955 JJP-1,18 JP-19-JJP WRITEC6,1051) JP,DEPTHCJP),CVPCIP,JP),IP-1,5),VAVECJP) 184 955 CONTINUE H?ITEC6,1066) 1068 FORMAT(/, IX,'RATIO W’R IIC SQUARED/UPRHC SQUARED',/) D O 958 JJP-1,IB JP-19-JJP W ITE(6,1051) JP,EEFTH(JP),<VPUPRT(IP,JP),IP-1,5),RATAV£(JP) 958 CONTINUE bf?ITE(6,1066) 1066 F0RMAT(/,1X,'TKE',/) D O 956 JJP-1,IB JP-19-JJP «?ITE(6,1051) JP,D EFTH (JP),(Q (IP,JP),IP-1,5),Q A \€(JP) 956 CONTINUE WRITE (6,1067) 1067 FORMAT(/,lX,'2*TKEA 3 / 2 ', / ) D O 957 JJP-1,IB JP-19-JJP WRITE(6,1051) JP,DEFTH(JP),(Q32CIP,JP),IP-1,5),Q32AVE(JP) 957 CONTINUE STOP END //CO.FT05F001 D D DSNAME-RLW5T0P.DAT,DISP-(,KEEP), / / UNIT-TAPE9, / / VOL-SEP-STREAK, / / LABEL-(ll,fi_), / / DCB- (DEN-3, RECFN-FB,LRECL -80, BLKSI2E-4000,OPTCD-Q) END OF DATA LENGTH //OK D£C OKTAPE, MSG-' STREAK-AAYB' / / D€C FORTGCLG, REGION-1024K, TIME-(1 ,0 0 ), RG-1024K C P R O G R A M STTREAK1.CNTL C THIS P R O G R P M COftUTES CORRELATION FOR STREAK RUN *1 . DIMENSION >41(150,200) ,YM( 150,200), U( 150,200) DIMENSION V(150,200),NSTRK(150) DIMENSION a u m il),S L H K (ll),S L O T P (ll) DIMENSION SL0TN(11),SUN(11) INTEGER ZERO, O ft, TW O , THREE DATA ZERQ/'0 V DATA O f t / 'l V DATA TWO/'2 V DATA THREE/'3 V C E >43 O SURE T if t IS 'T '. C DIGIT UNITS TO CENTIICTERS COffvtRSION IS 'CONST'. C SCALE FACTOR CONSTANT IS 'SCALE'. C HEIGHT X GRID ARM! FIDUCIALS IS 'GRID'. T - 0.700 CO NST - 4.937 SCALE - 5.628 GRID - 27.66 M A K SL - 150 DEPTH - 3.0 WIN - 1 YBO T - 0.0 YTOP - 6.0 WRITE(6,999 )T, 9CALE, GRID, YBOT, YTOP 999 FORM AT( ' DTOSURE T if t - ',F 6 .4 ,' SCALE FACTOR CONSTANT 2 F 6 .4 ,' GRID POSITION - \ F 6 . 3 , ' BIN RANGE- \F 6 .2 , 2'CM. TO ',F 6 .2 ,'C M .') HJEFT - 0.4»CONST XRIGHT • 9.&IC0NST C INITIALIZE ALL SLMS FOR ALL SLIDES. fFTS - 43000 NEG L - 0 N RH - 0 W R T ■ 0 LIERS - 0 NSLIDE - 0 Ml - THREE W >1 - 0.0 TP1 - 0.0 ASLtl - 0.0 u ri - 0.0 V M - 0.0 D O 60 NSL-1,MAKSL NSTRK(NSL) - 0 60 CONTINUE D O 100 L -i,fP T 5 READ(5,1000, EM)-95B, ERR-310) M,>^,YP 1000 F0RMAT(1X,R1,2X,F9.5,1X,F9.5) G O TO 315 310 M - ZERO WRITE (6,1100) 1100 FORM AT( ' w * ERROR IN DATA SET * * * * ') G O TO 100 315 IF((M.EQ.Oft).OR. (M.EG.TWO).OR. (M.EQ.THREE)) G O TO 320 ftGL - ftGL + 1 WRITE(6,1005) L,M 1005 F0RMAT(' POINT # ',1 6 ,' ftGLECTED; M- ',A 1) G O TO 100 320 CONTINUE CHEC K FO R 9CREW HJPS IN HEADS PTC TAILS. IF((Ml.EQ.THREE).Aft). (M.ft.THREE)) NSLIDE-NSLIDE+1 IF((M l.E G .O ft).A ft). (M.EQ.TWO)) G O TO 300 IF((Ml.EQ.OfE).Aff>. (M.EQ.Oft)) M RH-NRHf+1 IF ((M l.E Q .O ft).A ft). (M.EQ.THREE)) HRH-HRH+1 IF((M1.EQ.TWO).Aft). (M.EQ.TWO)) W RT-W RT+1 IF((M1.EQ.T>REE) .AND. (M.EQ.TWO)) MTT-MTr+l G O TO 50 300 CONTIMJE C ELIMINATE LONS STREAKS AH) OUTLIERS XG - 0.5*O *W 1)*9C A L E YG • (0.5*(YP+YP1)*SCALE) - GRID ir<(XC.LT.XLEFT).OR. (XC.GT. WIGHT)) G O TO 110 H) • (*>-*>1 )*9CAL£ YD • (YP-YP1 )*9CALE SLNGTH - C Xfr«2 ♦ YE**2 ) « € .5 IF(SLNGTH.CT.5.0) G O TO 120 C CALCULATE U AND V FOR EACH STREAK / SLIDE. IF((YG.L£.YBOT).OR. (YG.GE.YTOP)) G O TO 110 NSTRK(NSLIDE) • NSTRK(NSLIDE) ♦ 1 LSTR • NSTRK(NSLIDE) A S U M - A6UM + 1.0 > 0 1 (NSLIDE, LSTR) ■ XG YM(NSLIDE,LSTR) ■ YG U(NSLIDE,LSTR) • V(NSLIDE,LSTR) • YD/T U M - IN + XD/T Vtl ■ Vtl + YD/T G O TO 50 120 UHTE(6,1015) SLNGTH,tf>l,YPl,>^,YP 1015 FORMAT(' LO N G STREAK (IGNORED); LENGTH- M P E 1 0 .3 ,' CM . V 2 ' HflD- ',F 9 .5 ,', ',F 9 .5 ,' TAIL- ',F 9 .5 ,', ',F 9 .5 ) 110 LIERS-LIERS+1 50 Ml - M »> 1 • V P YP1 ■ YP 100 CONTINUE 950 U*ITE(6,1010) NEGL,L 1010 FORMAT( / , IX, 1 6 ,' ILLEGAL CHARACTERS (hCGLECTED) OUT OF ',1 6 ,/) H?ITE(6,1020) r«H,hRT,LIERS 1020 FORMAT( / , ' N U M B E R OF REPEATED HEADS (IGNORED) • ', 1 6 ,/, 2 ' N U M B E R OF REPEATED TAILS (IGNORED) - ', 1 6 ,/, 2 ' MJHER OF OUT-LIERS (NOT USED) - ',1 6 ) C FIND IHCAN A N D V-fCAN FO R EACH BIN AND CALCULATE U-PRirt C AND V-PRirt FO R EACH STREAK. IF(ASm.LT. 1.0) ASUM-1.0 LM - Ifl/AGUM vti ■ vti/Asm D O 400 NSL-1,NSLIDE LSTR ■ NSTRK(NSL) D O 420 NST-1,LSTR U(NSL,NST) ■ U(NSL,NST) - U M V(N5L,N5T) • V(NSL,NST) - VM 420 CONTINUE 400 CONTINUE C INITIALIZE CORRELATION SLOTS AH) S U M S D O 430 K-1,11 SLOTP(K) • 2 .0 *(K -1 ) - 1.0 SLOTP(l) - 0.0 SLOTM(K) • SLOTP(K)/5.00 COUNT(K) • 0.0 SUMUKK) - 0.0 430 CONTINUE CALCULATION O F CORRELATIONS FOR EACH BIN. D O 600 NSL-1,NSLIDE LSTR • NSTRK(NSL) IF(LSTR.LE.l) G O TO 600 D O 550 I-1,LSTR D O 560 J-1,LSTR IF (J .L T .I) G O TO 560 IF (I.E Q .J ) G O TO 570 W ? • W(NSL,J) - W (N S L ,I) YR ■ YM(NSL,J) - YM(NSL,I) R ■ ( >R**2 ♦ YR**2 ) « 0 .5 187 IFCR.GE.20.0) G OTO 560 IF(R.LT.1.E-2B) G O TO 560 UI - (XR*U(NSL, I ) + YR*V(NSL,I))/R UJ • (XR<0(NSL, J) ♦ YR*V(NSL,J))/R UU • UI*JJ K • INT(R/2.0) ♦ 2 .0 COUNT(K) - COUNT(K) + 1.0 SUMUKK) - a tU l(K ) + UU G O TO 560 570 UU - (U(N SL,I)**2 + V (N S L ,I)**2) COUNT(l) • COUNT(l) ♦ 1.0 SUMJ1U) ■ 9 U m i(l) ♦ UU 560 CONTItt£ 550 CONTirt£ 600 CONTINUE CALCULATIONS O F AVERAG E CORRELATION SLOTS PER BIN. D O 800 K-1,11 C • COUNT(K) IF (C .L T.l.B ) G O TO 050 E • SUNUK1) / COUNT(l) SUN(K) - SUHUKK) / COE) G O TO 800 850 SUN(K) - 0.0 800 CONTINUE C DISPLAY ALL SUNS FOR EVERY BIN. WRITE(6,1025)NSLIDE 1025 FORM AT( / , ' N U M B ER OF SLIDES READ - ',1 3 ,/) WRITE (6,1030) DEPTH, E, ASUM, NBIN 1030 FORM AT( / , ' DISTANCE FRO M G R ID -',F6.2 , ' E-',1PE10.3, 2'CM. N U M B E R OF STREAKS-',F7.0,' R U M »1 B IN * ',12) D O 720 K-1,11 WRITE (6,1835 )K,SLOTP(K),SLOTM(K), CO UNT (K), SUMUKK), 2SUNCK) 1035 FORM AT( ' K -M 2 , ' SLOTPOS.- ',F5.2,'C M . SLOTfESH-', 2F6.4, 'CM. COUNT-',FI 1 .0 ,' S U U 1-', 1PE10.3,' SUN-', 1PE10.3) 720 CONTINUE STOP ETC //GO.FT05F001 D D DSNAME-RLN1TOP.DAT,DISP- ( , KEEP), / / LNIT-TAPE9, / / VOL-SER-STREAK, / / LABEL-(1,NL), / / DCB-(DEN-3, RECFN-FB, LRECL-80, BLKSIZE-4000, OPTCD-Q) EM) OF DATA 188 ! parallel turbulent velocities, and the velocity correlation, | Correlations were computed using equation 2-6 and plotted for each I j interval (Figure 2-3), I C. Modeling Programs j B0X13 (PDP11). This program computed the radon transfer coefficient across the air-water interface and horizontal i diffusivities for a section of south San Francisco Bay by construct ing a radon budget for the study section using a thirteen-box model to represent the section. A time-step numerical procedure was used i to solve the thirteen mass balance equations for the desired parameters. I The algorithm was set-up as follows. At time t = 0, radon i concentrations in the eastern and western shoal boxes (#1 & . #6) were set to measured values and all other box concentrations were set to | | zero. Values for the sediment fluxes from the shoal and channel I areas and gas transfer coefficients (Kl) for each side of the bay ! were fixed. The program constructed a mass balance for these two boxes over ! the stipulated time interval (generally 50 minutes), solved the equations for the unknown horizontal transport terms, and computed the horizontal d i ffusivities (DHe> 0HW) . These d i ffusivities were ; assumed to be constant for each side of the bay. Mass balances were | i i ! constructed successively for the next channel ward box and solved for j 1 the radon concentration in each box. The radon concentration in the ; j channel box (#13) was computed similarly, except that the mass I : I I balance equation did not include a term for radon loss by horizontal j I tranport and the gas transfer coefficient was assumed to be an____189 j average of the K |_ values on each side of the bay. j After the channel concentration was computed, the program tested for steady state by calculating the ratio of radon inputs to outputs j for the entire study section. A ratio within 1% of unity was set as ! the acceptable steady state condition. If steady state was not reached, the program advanced the time, returned to the outermost boxes, (#1 & #6) and recomputed the mass balances. Since the concentrations in the neighboring boxes (#2 & #7) were different from | the previous time, new values for the horizontal diffusivity for each j side of the bay were computed and used for the successive boxes. I W hen steady state was reached, the program printed the radon l concentrations in all boxes, the horizontal diffusivities for each ! | side of the bay, and the average value of the gas transfer coefficient for the entire section. If the computed channel concentration did not agree to within 1% of the concentration measured in the fie ld , new values for the gas transfer coefficients were requested and the computation sequence ! i repeated. Attempts to include this iteration step into the algorithm j were unsuccessful. Generally, three hundred to four hundred j computational loops were required for time steps of 50 minutes to reach steady state. j A range of acceptable values for the gas tranfer coefficients and horizontal diffusivities was observed to satisfy both the steady state and channel concentration constraints. The range of possible | solutions was reduced by specifying that the radon concentration j could not increase between any two successive boxes in a channelward | direction. 190 L6L 8 b CIOS ( 6 4 C 2 4 6 ) ^ 4 VH6C3S = ( 6 ) C38PX XC 6 * 1=6 66 CC 66 VhSC3S *K3G3S ** lc233V •6V3dV 1?CHS CN V lirsNXhGl MI (C3S-2W/6*C1V) 63XP13 lh3»"IC26 hCCvfc M 3cAl t ** 2cAl 66 C1G3 (3 AH2 4 C 3 *J S V I) 31 (2 \») i ^ t C j *)b 2EVI (Vb 4 6 > CV 3d •2S 3riV A Xnia 2 S 2 M 2SP Cl HSIP PCA OC t 4» 3cAl ( 0 4 6 j * i =S1VGHS M I XP3- lh 2k IC3S a / * C * 6 j * a =33NhV63 M X P l j 1N 3 H C 3 S .) 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S E . 1 2 ) 6 0 T0 96 GOTO 99 XJSED(B) = SEDCH CONTINJE t y p e io o FOPMATC* TYPE IN VALUECM/0 AY) FOP THE GAS EXCHANSE CDE-FICIEKT5 1 *) ACCENT** XKGE* XKGE2 XKGE3 = (XKSE ♦ XK6E2)/ CZ * 14*0) TYPE 120 FORMAT C* DO YOU WTSH TO JSE SAME TIME V ALUES?( TYPE NO I F * / 1« THIS IS YOUP FIRST PUN)*) PE AO (5 * 1 3 0 ) IABC FOP- A T ( A 2) IF ( IA 3C .E 2 .2H T E ) SOTO 145 TYPE 140 F09MAT (* TYPE IN TIME STEP VALUE ( M I N ) * TOTAL PUN TINE I N I N ) * * / I * AMD TIME INTERVAL OF 3 P IN T —OUT I N I N ) *) ACCEPT ♦, OT, TFIN* TYPE WRITE C L .147) P N C !). 9N3EP. PN(fa). SEOCH* SEOSHA. 1 X < G E * XKGE2 FORMAT (• TPN IN NEST SHOAL APEA = * , F 5 . 2 , / * TPNl IN 1 CHANNEL = ■ * F 5 ■ ? * /* TPNl IN EAST SHOAL AREA = » , F 5 . ? , / 1* SEDIMENT FLUX IN CHANNEL = ■ • F S . O * / * SEDIMENT FLUX IN 1 SHOALS = » , F 5 . 0 * / « X V Ai_UE IN WEST SHOAL = » . F 6 . 3 * * X VALJE IN EAST SHOA 1 SHOAL = * , F 6 . 3) WRITE C L .150) FORMAT C' TIM E *»6 X **3 0X 1 » , 2 X , * 3 0 X ? * . 2 X , * 3 0 X 3 » , 2 X . 1»?0X 4 » ,? X ,» 3 0 X 5 » . E X ,* 3 0 X S »*2X ,»30X 7*) DO 144 5 = 1 , BOX X JSE 0 C B) = XJSE0C3) » 6 0 * A ( 3) PROD C 5) = PRO DP N • H C 3) * A ( B ) IF CB.EQ.30X) GOTO 144 DXC3) = (DIST (B) ♦ DIST C 3 * l ) ) / 2 . 0 CONTINUE XT = 0 DO 30 0 T =0 * TFIN, OT XIN = 0 X DU T =0 XT = XT ♦ DT XX = XXGE/1440.3 DO 200 5=1* BOX IF (3.E Q .S ) GOTO 153 IF CB.3T.1) GOTO lbO SOTO 154 X< = X X 3E p /1 4 43 . 3 XJ4TMC3) = XXM 000*PN (3>.*4 (3) /X9M DCAYCB) = RNCB) * HCB) • 1 000 * A ( B) XMH0DC3) = ( (XJ5ED(3> ♦PRO) (3) ) - C0CAT ( B) ♦ XJATMC3 ) ) ) XJHOP(B) = XMHOPC3 ) * D IS T C 3 ) /C A C 3 ) * H C 3 ) ) DEL9N = RNCB) - P N (3 ^ l) R 99 = 100C * DELPN DHEAST = CXJHOPC?) • XPN * D X ( 3 ) ) / 9 9 P I p (B.EQ.6? 30T0 157 IF ( 3 . EG .6) GOTO 153 DHWE5T = XJH0PC1) *X P N *0 X (1 ) /PP9 IF (DELPN.GT.O) SOTO 501 TF (D E L P N .S T .0) GOTO 135 XMHOP (3) = 0 DHEAST = 0 GOTO 501 SOTO 190 XJATMC3) = X<*PNC3>* 1 3 0 3 » 4 ( 9 ) /YPN IF ( 3 . EG.SOX) GOTO 173 I F C 3 . E Q . 5 ) GOTO 164 Of T 0 166 0 X (5) = ( D I S T (5) ♦ D I 5 T ( 1 3 ) ) / 2 DELPN = RNC5) - PNC 13) GOTO 167 DELPN = PNC3) - 3 N ( 3♦1) IF (DEL9N .3T.0) GOTO 163 DELPN - 3 IF ( 3 . S T . 5) GOTO 130 XJH0PC3) = DHWESTM0 0 3 * D E L 9 N * H f l ) / ( XPM*DX(3)*HC3)> GOTO 183 XJHOP C 9 ) =DH E A ST * ID 00 *D E L P W *H (1 > /(X P M *D X C 3 )*H (3 )) XMHOP (3) = XJH0RC3) * A C 3) * 5 ( 5 ) /DISTC3) 0CAYC3) = P N C 3) * HC3) * 1 003 * A C 3) DCDT(3) = XJSED ( 3 ) ♦PP00C3) «X4HDP(3-1 ) -XJATMC3)-DCAYC3) - 1XMHOP C 3) GOTO 173 XMHOP (BOX) = 0 XJATMC90X) = X<3E3*9NC3DX)*1 000 *4 (3 3 X) f \ 9N OCAT C30X) = PNC3) * H (3 ) * 1030 * 4(3 ) DCDTC3DX) = XJSEO( 3 ) ♦PROD< 3 ) ♦XMHOP( 5 ) ♦XMHOR( 1 2 ) -XJATMC3 ) - 1DCAT (5) 0 CO T (3) = DCDTC3)/(A ( 3 ) *H (B )» 1 3 0 3 ) PNCH = DCDT C3)*0T^XPN 192 V V V V — » p » U v- ( V I ( V I O X • • n o o p| \ x. \ Pi • » 1.1 Kill f t . 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Detailed descriptions are given of the apparatus and procedures used in the laboratory, i ] including the generation of turbulence in the tank, the photography of the turbulent flow fie ld , and the gas analyses. Turbulence Tank Apparatus The turbulence tank apparatus consists of the components required to generate turbulence and the components required to illuminate the tank water for photography. All components were supported on frames constructed of pieces of cast-steel channel i (Superstrut Corp.). I Turbulence Generation Tank. A 62.2 cm x 62.2 cm x 76.2 cm tank was constructed of 2.54 cm thick plexiglas walls with a .95 cm bottom. All pieces were fastened using Weld-on 40, following procedures suggested by the manufacturer. A 1.91 cm hole cut through the bottom was used for both fillin g and draining of the tank. Two of the tank walls were covered with opaque plastic to provide a dark backdrop for streak photography. I Grid. The grid was constructed of 2 planes of .95 cm O.D., type | ------- 304 stainless steel tubing. Each plane consisted of eleven 61 cm lengths of tubing, plugged at each end, and spaced two inches apart from center to center. The rods in each plane were oriented 90° 194 relative to one another. Connecting pieces, approximately 1.2 cm diameter by 2.4 cm high, were located on the lower plane, just insidej i the outermost rod on the upper plane. The entire assembly was vacuum-brazed with a nickel-based brazing alloy (Vac-Hyde Corp). Weld joints were small enough that they did not significantly alter | I the rod diameters. After brazing, the grid was within 0.25 cm of squareness in all dimensions. The primary reason for using tubing as opposed to solid rods was to lower the total mass of the oscillating system, thereby minimizing the torque required for oscillation. Unfortunately, this choice of I material introduced two problems. (1) Most of the braze-joints near the corners fractured during the in itia l testing phase, presumably I due to the excessive stress exerted at these locations during j oscillation. To solve this problem, the fracture joints were j i fastened together using 0.32 cm O.D. X 5 cm screws. The screw heads rested nearly fla t on the upper surface of the tubing. The screw stems protruded approximately 2.5 cm below the tubing and were | secured by a nut. The influence of the screws and nuts on the turbulent flow field was probably small, although this was not I verified. (2) The grid began to bow at the conclusion of the tank j runs. The maximum deviation from a fla t surface was 0.16 cm in a concave-up orientation after the conclusion of the experiment. j i Both of these problems may have been avoided i f the grid had been constructed of solid rods, spot welded or brazed at each j intersection. However, the large increase in torque required to ' 195 ! drive a solid grid might have necessitated a larger motor and support! parts. | i Oscillating mechanism,, The oscillating mechanism consists of the parts required to support and oscillate the grid. These include a motor, gear reduction assembly, drive train, and the support assembly. Each of these parts shall be discussed in succession. j I The motor used to drive the system was a 3/4 HP, Blue Chip TEFC j d.c. motor (Minarek Electric Co.), which produced 30 in-lbs of j torque at full speed (1800 RPM). Motor speed was controlled by a j constant torque, variable speed controller (Minarek Electric ! i i Company). The motor rpm was reduced by a 5 to 1 ratio by a gear j reduction assembly, consisting of a sheave mounted on a 1.9 cm (3/4") O.D. shaft supported by two single roller bearings (Figure A III-1 ). | ! A calibration between the motor controller setting and grid j oscillation frequency was performed using a photodiode connected to a j counter/timer (Global Specialties Corp.). A vane connected to the sheave "chopped" a light beam focused on tne photodiode during eacn revolution. The counter/timer recorded the time interval between subsequent interruptions of the light beam, which enabled computation of the oscillation rate. The results of this calibration are given j in Table A III-1 . This calibration was performed with a grid stroke I of 6 cm and the grid postioned near the interface. Increased drag caused by changing the grid position or stroke length could change j this calibration, thus i t is advised that the oscillation frequency be checked during the course of each experimental run. j The selection of this motor and controller was made based upon COUNTER-WEIGHT ECCENTRIC ARM SHEAVE 3 / 4 INCH SHAFT UPPER SHAFT OIL LITE BUSHING BEARINGS Figure AIII-1. Schematic of the gear reduction assembly. Jam nuts and securing screws not shown. Parts and distances not drawn to scale. TABLE A III- I. Calibration between oscillation frequency and controller setting for a stroke length of 6 cm and grid depth of 6 cm below the interface. Controller Setting Frequency (Hz) 40 1.4 50 2.1 55 2.4 60 2.8 65 3.0 70 3.4 75 3.6 80 3.8 85 4.1 90 4.5 estimates of the torque required to drive the system. TOTAL = rACC + TDRAG + riNERTIA (A III-1) where rACC is the torque required to accelerate the grid, TDRAG is the torque required to overcome drag forces in water, and riNERTIA is the torque required to accelerate the gear reduction assembly. The acceleration torque equals the total system force times the lever arm distance, or The drag torque equals the drag force times the lever arm distance. The drag force was estimated from an empirical relationship given by Batchelor, G. K., 1970. r ACC = (ma) U /2 s) (A III-2 ) Drag Force = 1/2 pw V2 A (A III-3) thus the drag torque becomes: where r DRAG = (1/2 Pw V2 A) (1/2 S) m is the mass of the oscillating system, (A III-4) a is the acceleration, S is the stroke length, p is the density of water, V is the velocity of the grid, and A is the cross-sectional area of the grid. 199 Since the grid moves with a sinusoidal motion, X = X sinoj t O (A111— 5) dX V = cTF = X £ > cosm t (A ll1— 6) o dV a = dt = -X g o 2 sinw t O (A III-7 ) The maximum acceleration is given when sin = 1 or: amax = X0^ where XQ is equal to 1/2 the stroke length, and w is the oscillation frequency in radians/sec, r INERTIA is the torque required to accelerate the gear reduction assembly which is small relative to the other two terms. Thus, the maximum torque is: A summary of the required torques and the torque supplied by a 3/4 horsepower motor is given in Figure All 1-2 for a range of oscillation speeds and stroke lengths. In these calculations, m was taken as 25 lbs, p w as 1.0 g/cc, and A as 200 i n 2 (3/8" O.D. x 24" x 22 rods). One way to reduce the torque required to oscillate the system is i to balance the torques along the rotating shaft. To do this, a j counterweight was placed on the gear reduction shaft on the opposite 1 ' TOTAL = 1/2 S [mx0 c o 2 + ! / 2 p wv 2 A] (A III-8 ) The motor horsepower required to supply this torque is HP = r TOTALw TORQUE (in-lbs.) 400 350 300 - 250 200 50 100 50 - 2 4 6 e .OSCILLATION RATE (HZ) TO O Figure AIII-2. Torque required to oscillate the grid at various frequencies for different stroke lengths (solid lines). The dashed lines show the torque supplied by 3/4 H P and 1 H P motors. end of the grid assembly (Figure A III-1 ). The weight was designed to match the torque requirements of the oscillating assembly, but placed at 180° out of phase along the shaft axis ( i . e . , when the grid rose, the counterweight dropped). Although the addition of this weight did I I balance the required torque along the shaft axis, noted by a smoother i | motor stroke, it added to the torque perpendicular to the shaft in | the vertical direction. The effect on the shaft was much like a see-saw; one end torqued up while the opposite end torqued down. | This created additional strain on the support bearings and caused deflection of the steel cross-members supporting the system, especially at higher oscillation speeds (> 3.5 Hz). The counterweight system has been redesigned to eliminate this problem, i which should enable higher oscillation speeds. | The drive train and grid support assembly were attached to the 3/4" shaft by an eccentric arm. This piece contained four holes which allowed stroke lengths of 3, 6, 9, and 12 cm. The drive train s consisted of two pieces of 2.5 cm O.D., type 440-C stainless steel j shafting (Thompson Industries). The upper shafting was tapped to accept threaded, o i l - l i t e bushing mounts on each end and was connected to the eccentric arm by a bolt and to the lower shaft by a bolt and yoke arrangement (Figure A III-3 ). The lower shaft passed I through two linear ball bushing pillow blocks (Thompson Industries). i This assembly successfully converted the rotational motion of the j eccentric arm into a linear motion of the lower shaft. I j j | 202 UPPER SHAFT OIL LITE BUSHING YOKE LOWER SHAFT i i—i GRID SUPPORT ASSEMBLY CONNECTING PIECES i_i I I GRID Figure A III-3 . Schematic of the drive train and grid support assembly. Jam nuts, securing screws, and linear ball bushings not shown. Diagram not to scale. 203 Bolted and pinned to the end of the lower shaft was a support frame, designed to couple the grid to the oscillating shafts. The support frame consisted of 0.95 cm type 303 stainless steel rod, heli-arc welded into a trapezoidal configuration with connecting pieces at the corners and the apex of the trapezoid (Figure A III-3 ). Holes were bored through the corner pieces vertically to accept 0.95cm O.D. stainless steel rods. The corner pieces were designed to hold these rods at any pre-set position by tightening an alien screw which contracted the piece around the rod. The rods extended into the tank and threaded into the connecting pieces at the four corners of the grid. Two of these 0.95cm rods passed through linear ball bushings (Thompson Industries) to prevent horizontal rotational motion of the grid during oscillation. This support structure design provided two advantages over alternative designs. First, the grid position in the water column could be adjusted to any level simply by sliding the vertical connecting rods through the support frame and securing. Second, effects of the rods on the turbulent flow field were minimized since the rods were perfectly vertical and located at the corners of the grid. At high oscillation rates (^3.5 Hz), small capillary waves were generated by these rods, but the total effect on the interface was negligible. Unfortunately, the design and fabrication of the support frame was not problem free. Three problems were encountered during the experimental runs: 204 (1) The support frame was not welded perfectly level. ! Consequently, the connecting rods had to be adjusted to "take-up" this error to level the grid relative to the tank water. This adjustment put additional stress on the grid and the connecting rods. One rod sheared at the threads and had to be replaced, j (2) The connecting pieces at each corner of the support frame j were not able to hold the connecting rods in position. Separate fasteners were required to achieve this goal. These fasteners were j | clumsy, but did solve the problem. | (3) The submerged portion of the connecting rods began to rust ! and pit in the salty tank water. The rods were type 440-C stainless, which is not as rust resistant as the 300 series of stainless steel, I but is of the hardness required to run through the ball bushings. In an attempt to solve this problem, the two rods which do not pass through bearings were replaced with type 304 stainless rods. The ! remaining two rods (type 440-C) were protected with a .0003 in i I electrolysis nickel plate. The 304 rods resisted corrosion quite | I well, however the plated rods began to rust soon after immersion. | I The solution to this problem is not clear. It is desirable to reduce | | | the rust on these two rods since the rusted portions pass through the j linear ball bushings when the grid is readjusted to a shallower j , depth. One suggestion is to coat the submerged portion of the rods with a teflon spray. W hen the grid is readjusted, the teflon can be j scrapedoff i f necessary to allow passage through the bearings. ‘ i ; Illumination assembly Lamp. The tank was illuminated by a mercury-vapor quartz lamp j 205 (Illumination Industries). This lamp supplied the high brightness light required (40,000cp/cm2) , yet radiated l i t t l e in the infrared so that heating of the tank and surrounding equipment was minimal. The lamp was powered by a 1000 watt (nominal) transformer available from the manfacturer. Specifications from the manufacturer for the nominal current draw by the lamp and transformer primary were 1.4 amps and 10 amps, respectively. Power was supplied to the transformer by 14 gauge running through a 20 am p switch. The circuit was protected by a 15 am p fuse. Early tests of the lamp caused the fuse to blow after approximately 45 minutes of continuous lamp-time. Measurements of the current draw through the switch were 12 to 14 amps during illumination. This value was sufficiently close to the current capacity of 14 gauge wire that the wire was overheating and causing the fuse to blow. During the experiments, this problem was solved by j turning off the lamp before the wire became excessively warm (15-30 minutes of lamp time). A better solution would be to rewire the circuit with 12 gauge wire and a 20 am p fuse holder. | The bulb was mounted on a fixture supplied by the manufacturer which contained two air jets for cooling. Dry air at a delivery ! i pressure of 30-35 psig was required for adequate cooling. It is imperative that the cooling air be dry. Wet air can quench the i | lamp resulting in bulb explosion. Line air available in the laboratory was passed through two water traps before reaching the i bulb to meet these requirements. Purging the air line for three to ! eight hours before illumination considerably reduced the quantity j | of water in the a ir. N o bulbs exploded in over 25 hours of | illumination time. | Lenses & Chopping Wheel. Lamp light was collimated by three 16.5 cm | plano-convex lenses (Edmund Scientific Company) and passed through I a 0.63 s lit immediately before entering the tank. A light chopping j wheel was located at a position where the light rays coverged to a small radius. The chopping wheel was constructed from a 0.31cm i aluminum disk, 61cm in diameter, with a window of 5/8^. The wheel | j was driven by a Brevel , 12V D C motor and the rotation rate | controlled by varying the voltage applied to the motor using a variable D C power supply (Powermate Corporation). A piece of mylar 1/4" wide was placed asymmetrically in the window to dim the light for a short instant. This created streak images with long and short bright sections. | The arrangement of the illumination assembly parts used during I the experimental runs is shown in Figure A III-4 . The positions and orientations of the collimating lenses were chosen to illuminate the entire water column in the vertical dimension. Since the | diameter of the lenses was only 16.5 cm, this necessitated a I j diverging light beam. The primary disadvantage of the diverging beam | is increased light scatter and thus, increased f a ll- o f f in the light | intensity across the tank. The resulting streak photographs showed I this effect (Figure 2-2), however, the images were s till bright enough to enable processing. 207 2 0 3 ECCENTRIC MOTOR > BEARINGS GRID TANK CHOPPING WHEEL LE N S ES XT H g -V A P O R LAMP \ / C D G ' 15 A - CAMERA Figure A III-4. Schematic of the turbulence tank apparatus showing the orientation and distances of the illumination assembly parts. Diagram not to scale. The rotation rate of the wheel controls the exposure time of light to the tank. Exposure times were measured using the same photodiode and counter/timer discussed earlier (see oscillating mechanism section). Ideally, exposure times should be measured during the photographic process, however this was not possible ! | because the mylar piece located in the chopping wheel window dimmed ! the light below the threshold value required by the counter/timer. | Instead, a calibration between exposure time and the voltage j applied to the chopping wheel motor was performed without the mylar | piece in place (Table A III-2 ). During picture sessions, exposure I j times were deduced from the applied voltage. Voltages were I measured with a Kiethley digital multimeter. The illumination assembly parts (lamp, lenses, and chopping wheel) were mounted on support pieces enabling both horizontal and vertical adjustment and were housed in a protective shroud, constructed of 0.32 cm masonite. This design consisted of movable "slats" which provided easy access to all interior components. A piece of 10 cm O.D. flexible, vent-hose extending from the shroud to a window provided an escape route for the cooling a ir. Streak Photography Equipment and Operating Conditions Camera and tracer particles. Photographs of tracer particles were taken with a Nikon FE camera, equipped with a 80-205 Vivitar zoom lens. The particles used as tracers were p lio lite VT beads 209 Table A III-2 . Calibration between exposure time and voltage applied to the chopping wheel motor. Voltages read from a Kiethley digital multi-meter. ied Volts Exposure Time (sec) 3.0 1.32 3.5 1.10 4.0 0.95 4.5 0.83 5.0 0.74 5.5 0.66 6.0 0.60 6.5 0.55 7.0 0.50 7.5 0.47 8.0 0.44 8.5 0.41 9.0 0.39 9.5 0.36 10.0 0.35 210 (Goodyear Chemical Company), crushed and sieved to a diameter of .351±.07 m m . This size was large enough to produce good photographic images, yet small enough to follow all scales of motion. Water density was matched to the p lio lite density (1.026 gfee) to insure neutral buoyancy. One teaspoon of the crushed particles was found to give a sufficient density of streak images on the photographs. Prior to addition to the tank, the particles were added to a 500 m l beaker of tank water containing 25 to 50 m l of Kodak Photo-flo 200 solution and stirred for 1 to 2 hours. This procedure expelled trapped air from the particles. Image distance and zoom setting. The camera rested on a tripod at a distance of approximately 1.75 meters from the center of the tank. At this distance, the maximum zoom setting possible was fixed by the size of the desired photographic fie ld . A window, 46cm x 61cm, was constructed from 0.32 cm masonite and placed in front of the tank. The window dimensions were 7.5 cm shorter on each edge than the correspond!'ng tank dimensions, to reduce the possiblity of photographing particles near the tank walls and bottom. Fiducial lamps were mounted to the masonite around the shorter dimension of the window, approximately 2.0 cm from the edge. Thus, the field of view measured approximately 50cm x 61cm. Capturing the entire field of view in a single photograph did not provide enough magnification of the streak traces. Thus, 211 photographs were confined either to the upper or lower sections of the photographic window. A horizontal orientation of the camera at a lens setting of 105 m m provided sufficient magnification, yet s t ill captured the desired field of view. One complication with this arrangement was that the tripod could not be lowered sufficiently enough to photograph the extreme bottom part of the window. Photographs of this section required that the camera be tilte d slightly away from the horizontal. The distortion introduced by this t i l t was checked by comparing the dimensions of a target board on photographs taken with the camera in both orientations. The target board was constructed from a 46cm x 61cm x 0.32cm plexiglas sheet. A grid pattern, consisting of 5cm x 5cm squares, was etched into the sheet and painted white for high contrast. Deviations in the lengths of the target board squares were less than one-half of one percent between photographs taken with the camera in each orientation. As the distance between the camera and tank decreases, distortion of the object image due to differences in refraction across the field of view can become significant. Falco (1971) discusses this problem in detail. A test of this effect was performed by photographing the target board and comparing the distances across the resulting photograph in both the horizontal and vertical dimensions. The results of this test are presented in Table All 1-3 and show a maximum distortion of 1% from the center to the edges of the photograph. 2 1 2 Table A III-3 . Lengths of selected target board squares measured on the photo-digitizer for slide #2 from picture run #1, roll #1. True distance was 2.00 inches. Horizontal Dimension (in) read # le ft center 1 2.021 1.991 2 2.015 2.000 3 2.015 1.993 4 2.028 2.000 5 2.023 2.001 " X 2.021 2.000 se 0.003 0.002 i/X)100 0.12 0.10 Horizontal Distortion: .0195 TTO TFO Vertical Distortion: .0215 179^3 Vertical Dimension (in) right top center bottom 2.024 2.013 1.985 2.004 2.008 1.995 1.975 2.007 2.014 2.014 1.982 2.001 2.024 2.015 1.983 2.015 2.021 1.990 1.992 1.997 2.018 2.005 1.983 2.004 0.003 0.006 0.003 0.004 0.15 0.27 0.13 0.17 ~ .01 ^ .01 213 Film f-stop, and exposure time. Selections of the photographic film, lens f-stop, and exposure time were constrained by the desired quality of the streak images. Desirable images had to be bright, sharp, of sufficient length to differentiate the head and ta il sections, and straight. Kodak Tri-X film was chosen because of its high sensitivity, high contrast, and sharpness (small grain I size ). The brightness of the streak images is controlled by the light intensity and by the lens f stop. Test photographs shot over a range of f-stops indicated that an f-stop of 3.8 was necessary for the best streak images. One problem with the choice of such a low f-stop was that the depth of field was small and increased the possibility for blurred images. Larger f-stops can be used i f the light-collimating lenses are rearranged to focus the light onto a smaller section of the water column. i The optimum exposure time for proper length streak images is j controlled by the velocity of the tracer beads, which in turn j depends upon the turbulent flow fie ld. For the turbulent conditions generated in the experiments, an exposure time o f^ 0 .7 I sec (5.0 V applied to the chopping wheel motor) gave the best j streak image length. The optimal exposure time will not remain ; constant for all turbulence conditions and must be redetermined for experiments with substantially different turbulent flow fields by taking a series of test photographs. 214 Fociising> Sufficient clarty of the streak images necessitated accurate focusing of the lens on the illumination plane. This requirement presented no problems prior to grid oscillation, | i since an object was simply suspended within the illumination plane and the lens focused upon the object. However, the lens required refocusing each time the film was changed and such an approach was not possible with the grid in motion. A refocusing procedure was developed for this situation as follows. The lens was focused upon the target board prior to grid oscillation and the position of the focus ring marked. Refocusing during the oscillation period was accomplished by setting the focus ring to the marked position. The success of this method required that the camera position relative to the tank stay fixed throughout the course of a run. This was tested by comparing photographs of the target board shot before and after refocusing. N o significant difference was observed in the clarity of the photographs, nor in the lengths of the target board squares, thus i t was concluded that this focusing method was acceptable. j FiduClal Lamps. Orientation and calibration of the streak photographs required a set of fiducial points. These were provided j I by a set of small, D.C. lamps (Radio Shack) mounted to the masonite ! window. The lamps were illuminated by a 6VDC power supply. Lam p | brightness was controlled by varying the A C voltage to the D C j supply using an A C powerstat. The optimum powerstat setting was determined from a series of test photographs. A dial position 215 setting at approximately one o'clock was found to give the best fiducial images on the photographs. Developing. Developing procedures for the exposed film were determined by conducting a series of tests with different developing solutions for various developing times. The highest contrast photographs were obtained using D-76 developer for 13 minutes at 20°C. The negatives were mounted into plastic slide holders for processing. Digitizing Procedures. Streak images were measured on a GTCO digitizer in conjunction with a Digital PDP11 computer using the program, DIGIT. The streak photographs were projected onto a digitizing board with a Kodak 650H projector fitted with an Ektanar zoom lens. This arrangement allowed large magnification of the steak images which facilitated the digitization process. In addition, the f a ll-o ff in streak brightness due to the diverging light beam was minimized by this technique. Each photgraphic negative contained 3 to 5 fiducial points (only 2 were digitized) and from 100 to 200 streak images. The fiducial points were digitized fir s t to set the reference length scale. Streaks had to f u lf ill the following crite ria to be read: (1) they had to be clear and relatively straight, (2) head and ta il sections had to be present, and (3) they had to be located away from the slide edge. 216 These crite ria introduce a slight bias towards "middle-sized" i ! streaks since very long streaks and very short streaks are omitted. The result is a slight underestimation of the turbulent velocity. i The negatives were projected onto a background consisting of a sequence of columns which enabled the operator to maintain position, thereby reducing the possibility for duplicating and/or neglecting streaks. Generally, the procedure was to read an entire column and progress from le ft to right across the projected image. Computation of streak length. Conversion of the streak images on the photographic negatives into actual distances was performed as follows. Streak images were digitized relative to the digitized distance between fiducial points for each photograph. The fiducial point digitized distance was calibrated to true distance by digitizing the distance between fiducial points relative to the distance between target board squares on photographs of the target board. These photographs were taken prior to each run. Since the true distance between the target board squares is known, the digitized distances between fiducial points and of the lengths of j ! the target board squares enable the true length of a streak to be computed as: 217 Ys = Xf * 1 Xtb hb Where: Ys is the true streak lengthy is the ratio between the streak length and fiducial distance digitized on the streak photographs, Xf "Xtb is the ratio between the fiducial distance and target board squares digitized on the target board photographs, and Ytb is the true distance between target board squares. Note that corrections for magnification due to refraction are not required since both the streak lengths and target board lengths are measured in water ( i . e . , the effect cancels out). 218 The ratio Xf J tb is a function of the camera position and the lens settings which were held constant for a given run. This ratio remained constant for all runs (Table A III-4 ), implying that the camera positon and lens settings were reproducible from run to run. Using the mean values in Table A III-4 , equation AIII-10 reduced to: Ys (in) = X s _ Xf 22.22 (AIII-11) This equation was used in the STREAK program (see Appendix I I ) to compute the true streak lengths. 219 Table A III-4 . Distances (in inches) between target board squares and fiducial points measured on selected slides. Scale set assuming a distance of one target board square in water of 2.00 inches. SI ide (Run# - Roll# - SIide#) yTB ( Xf ) (XTBy) 1 - 1 2 2.00 11.13 3 - 1 4 2.00 11.14 5 - 1 2 2.00 11.07 6 - 1 2 2.00 11.11 8 - 1 1 2.00 11.08 X se 2.00 11.11 .015 (se/X) 100 ----- 0.12 220 Gas Analysis Chapter 2 gives a good overview of the methods used for the determination of the dissolved gas concentrations. This section i I describes some of the details of the methods and operation of the | equipment. | Gas Chromatography The Carle gas chromatograph is a pleasant instrument to use since i t is relatively simple and quite forgiving. A schematic of the flow system is given in Figure All 1-5. The instrument I contains two-columns and two detectors (thermal conductivity and j flame ionization detectors). With the proper gas flow rates and clean columns, stable and "quiet" baselines at low attenuations (x4 for TCD, x 8 for FID) are com m on for both detectors. The | operating conditions used during this study are given in Table | A111 — 5. i The instrument was prepared for a gas run as follows. The day prior to the experiment, both columns were cleaned at the ; temperatures given in Table A III-5 by reversing the carrier flow j | through the column for 4 to 8 hours. The evening prior to a run, the columns were installed, the flame detector was l i t , the ; thermistors turned on, and the chart recorders turned on (no, not the paper drive.) The instrument was immediately ready for use the i • next day. 2 2 1 R g l a s s s t r i p p e r STANDARD INJEXJQON VALVE STRIPPER -j V A L VE ^ PORT DRIER / FLOW RESTRICTORS He COLUMN-SWITCHING VALVE INJECTION PORT COLUMN OVEN TCD H2 FID AIR VENT ro ro P O Figure All 1-5. Schematic of the gas chromatograph and stripping system used for the gas analyses. Water samples are introduced into the stripper through a rubber septa. Table A III-5 . Operating conditions for gas analyses on the Carle Carle gas chromatograph, A- Pelivery Pressures (psig) Hel i um 20 Hydrogen 2 .0 Air 17 B. Column Temperatures (°C) Column Instrument Setting °C Actual Temp °C Molecular Sieve 5A 43 48 Chromosorb 101 50 5 5 C. Carrier Flow Rates Column Pressure drop across stripper (psig) Molecular Sieve 5A 10 Chromosorb 101 12 0. Column Conditioning Temperatures (°C) Molecular Sieve 5A* 275 Chromosorb 101 175 * Not done on Carle Instrument due to excessive temperature 223 Calculations of gas concentrations in the tank water were made from peak areas using the expression: C .: (m mol / I ) Asam ATTsam Astan ATTstan 1 \ /Vstan) * * * ) f e n (AIII-12) Where: ^w Asam/Astan ATTsam/ A T T sj.an Vsam Vstan is the concentration of gas in the water, are the areas of the sample peak and standard peak, respectively, are the g.c. attenuation settings for the sample and standard peaks respectively, 3 is the volume of water injected (cm ), and is the standard volume injected, equal to ( P i ) ( vi ) {^ 3) wh e re : "TH ") P-j is the partial pressure of gas in the standard (1.0 for CH4 , & CO2 , ~0.79 for N2 , ~ 0 . 2 1 for O 2 ) , V] is the standard loop volume, equal to 105.5^1,and T] is the standard loop temperature (°K) (approximately 5° below the column temperature). 224 Peak areas were determined either by a disk integrator or by reading the areas with a d igitizer. A test on the precision of transfer coefficients computed from the digitizing method was performed by reading the peaks from one run four times and computing the transfer coefficient from the areas. The results are given in Table A III-6 . The precision of coefficients computed from the disk integrator areas should be similar, although this was not checked. Radon Measurements Generally, radon measurements in natural waters are performed on large volumes of water (1 to 20 lite rs ) to reduce the required counting time. However, as the sample volume increases, so does the required stripping time. To reduce the radon analysis time for the tank runs, the tank water was enriched in radon prior to the experimental run. This was done by equilibrating the gas phase above a radium solution (3 x 1 0 10dpm) with ^ 2 liters of tank water. The "hot water" was added to the turbulence tank. After addition, tank activities were generally in the range of 50 to 70 dpm/1. At these activities, a 25 m l water sample was sufficient to give good counting statistics ( ^3%) for reasonable counting times (20 hours). The time required to strip this volume of 99% of the dissolved gas was only 8-10 minutes, significantly shorter than the 60-90 minute stripping periods generally required for radon measurements in natural waters (19£ sample volumes). 225 TABLE A III-6 . Precision of transfer coefficients determined by digitization of peak areas of nitrogen from gas run #9, Read # KL (m/day) ± 1 se 1 0.34 ± ,08 2 0.41 ± .09 3 0.37 ± .08 4 0.43 ± .06 X 0.39 ± .037 (se/X)100 9.50 226 A single pass stripping system was constructed for these analyses (Figure A III-6 ). Operational procedures of the stripping system were as follows. The entire system was flushed three times with helium, evacuated, and an evacuated counting cell 125 cm ) placed on-line. A water sample (25ml) was slowly injected at very low helium gas flow (excessive helium delivery would cause the water sample to degas too violently and pass into the drying column). As the pressure in the cell increased from vacuum to 1 atm, the helium flow rate would progressively decrease, thus it was necessary to increase the He delivery during the stripping period. The cell was removed when the pressure reached 1 atm gauge, generally eight to ten minutes after injection. Results of tests on the stripping efficiency and precision are given in Table A III-7 . Procedures for an Experimental Run The experimental methods consist of the procedures required to prepare the system for an experimental run and the procedures employed during the run. Preparational Procedures Adjustment of the grid. The oscillating system is designed to enable the grid to be positioned at any depth within the tank. The procedure is to loosen the clamps on the vertical support rods (Figure A111-3) and slide the support rods through the support frame corner connectors to the desired height. 227 228 COUNTING CELL INJECTION PORT SWITCHING VALVE DRIER GLASS STRIPPER TO VACUUM PRESSURE GAUGE GLASS FRIT HELIUM IN / ) DRAIN VALVE FLOW RESTRICT OR Figure All 1-6. Schematic of the radon stripping system. Water samples were introduced into the stripper through a rubber septa in the injection port. Stripper volume is approximately 30 ml. TABLE All 1-7. Efficiency and precision test data for the radon stripping system. A. Stripping efficiency tests Sampl e Draw # [RN]o (dpm/1) [RN]/[RN] draw #1 Tap Water 9/26/81 1 1.84 2 .075 .041 Tap Water 9/26/81 1 1.89 2 .08 .042 "Hot Water" 10/17/81 1 57.83 2 0 0 3 0 0 "Hot Water" 10/17/81 1 61.97 2 .08 .001 3 .01 .0002 B. Precision Sampl e # of Runs (se/X)*100 Tap Water 9/23/81 2 2.5 Tap Water 9/26/81 2 2.2 229 It is important that the grid is level with respect to the water surface. To insure this, the tank water was generally set to the desired grid height and the grid adjusted to the water surface. Occasionally, the grid was adjusted by measuring equal distances along the support rods and setting the rods to the marked positions. This method is faster than the firs t method since i t does not necessitate draining and refillin g of the tank, however it is not as accurate. Filling and draining the tank. The tank was fille d with tap water through a hose extending from the faucet tap to the tank. The water passed through a cartridge f il t e r (25 cm by 6.5 cm diameter) prior to entry into the tank. Draining was accomplished with the same hose, however, the hose was repositioned to empty into a drain pipe. Two PVC gate valves enabled the cartridge f il t e r to be bypassed during draining. Generally, the tank water was changed for each new grid location. In addition, the water was replaced when it appeared cloudy. Water preparation. The tank water had to be prepared for streak photography and for gas exchange measurements. Preparation for photography required addition of the tracer beads and adjustment of the water density to match the bead density (1.026 g/cc). This was accomplished by adding solar-coarse grade, NaCl (Leslie Salt Co.). For the range of water temperatures observed during the experiments (18°C to 21°C), a salinity range of 30°/oo to 36°/oo 230 proved sufficient. This required approximately twenty pounds of salt. The tank was mixed by an electric stirrer after the addition of the salt to quicken the dissolution process and insure homogenization. Good agreement between the bead and water densities was apparent by observing the general movement of the beads after stirring ( i. e ., no obvious rising or settling). Preparation of the water for gas analysis entailed reducing oxygen and nitrogen concentrations below saturation and elevating the water concentration of C02 , CH4 , and R n above saturation. Oxygen and nitrogen concentrations were reduced by bubbling helium through the water. At reasonable helium flow rates ( i . e . , so the interface was not violently disturbed), the water concentration could be reduced to half saturation in 4 to 8 hours. Approximately 300-500 psig of helium were generally required for this procedure. Covering the tank with plastic seemed to reduce the required stripping time and amount of helium. Charging with methane required only 10-15 minutes, because of the high sensitivity of the flame ionization detector. Charging with carbon dioxide was not necessary i f the water had just been replaced, due to the high dissolved bicarbonate concentration in the tap water. Conversion of the bicarbonate to C02 was accomplished by acidifying the water to a pH of approximately 4. I f the water had not been replaced, CO 2 charging times of a,30 minutes proved sufficient. 231 Stripping and charging were performed the day prior to a run to insure that bubbles caused by the charging procedure dissolved and that room concentrations of CH^ and C02 returned to atmo spheric values. Tank water was periodically mixed during these preparational procedures with a stirrer. Experimental Run Procedures Streak Photography. Prior to grid oscillation, it was necessary to set-up the camera for photography. The tripod legs were set | onto pre-marked location on the floor, the camera mounted in a horizontal orientation at a zoom lens setting of 105 m m , and the tripod adjusted to photograph the desired field of view. The target board was suspended in the illumination plane, the lens focused as described previously (see Streak Photography Section of Appendix i n l a n d three pictures of the target board (with the fiducial lamps on) taken in a dark room at an f-stop of 8.0 and exposure times of 1/4, 1/2, and 1 second. Three pictures were taken of the target board at different settings to ensure a good exposure. After completion of the target board shots, the target board was removed and the Hg-lamp and fiducial lamps turned off until the beginning of the streak photography. Streak photography did j not begin until at least one hour after the start of grid oscillation, to insure fully developed turbulent, steady-state i conditions within the tank. | 232 ! The photographic procedures consisted of manually depressing and releasing the camera shutter (camera shutter in the bulb position) as the tank was illuminated by the rotating light-chopping wheel. Fiducial lamps were on for all pictures. Generally, four to eight rolls of film (36 exposures) were taken for each run. The rolls were shot throughout the time-period of a run to ensure a representative description of the turbulent flow during the experimental run. The Hg-lamp and chopping wheel were turned off when the elasped time between rolls was longer than 10 minutes to prevent overheating of the switch circuit. Sampling of tank water. Early tests of waters drawn at different tank depths showed no significant variation in concentration, thus i t was concluded that the tank water was nearly perfectly mixed. Sampling for 0 , N , C02 and CH^was done by immersing 1 m l syringes approximately 3-5 cm below the water surface, flushing 5 times, and drawing a volume slightly in excess of the desired amount. Samples for 02 and N2 analysis were drawn into syringes which had been previously flushed 5 times in helium to reduce the possibility of air contamination. Samples for radon analyses were drawn by a similar procedure using a 30 m l syringe equipped with a 5 cm piece of 1/4" (.635 cm) tygon tubing. All waters were run immediately after sampling, except for C02 samples which were stored until later analysis. Despite the care taken during the sampling and injection procedures, considerable scatter was observed in the measured gas concentrations relative to analytical precision. The reasons for the scatter are not clear. Perhaps air contamination was responsible for the oxygen and nitrogen scatter. Generally, methane, radon, and carbon dioxide showed much less scatter. For low exchange rates, the observed scatter introduced considerable error into the calculated value of the gas exhange coefficient (see Table 2-4). Salt dissolution experiments. Salt tablets were suspended in the tank at different depths using 0.32cm O.D. stainless steel tubing for support. Two pieces of tubing were suspended vertically in the tank and the salt tablets attached to the tubing by alligator clips. Salt tablets were oriented to face the grid. For most grid positions, the salt dissolution experiments were performed on separate runs from the turbulence and gas exchange measurements. This procedure was necessary because the salt had to be removed before completion of the gas analyses and the removal procedure required that the grid be stopped. One tablet per experiment was put into a small volume of quiescent tank water to act as a control so that results from different experiments could be compared. Tablets were dried in an oven at 100°C and weighed. Dissolution rate was computed as the change in weight over the immersion time. 234

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Asset Metadata

Creator Hartman, Blayne Alan (author)

Core Title Laboratory and field investigations of the processes controlling gas exchange across the air-water interface

Contributor Digitized by ProQuest (provenance)

Degree Doctor of Philosophy

Degree Program Geological Sciences

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag Geology,OAI-PMH Harvest

Language English

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c29-351802

Unique identifier UC11221122

Identifier DP28564.pdf (filename),usctheses-c29-351802 (legacy record id)

Legacy Identifier DP28564.pdf

Dmrecord 351802

Document Type Dissertation

Rights Hartman, Blayne Alan

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA