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Numerical simulation of whole core squeezer radon pore water profiles: Methodological considerations and evaluation of benthic fluxes and rates of bio-irrigation and advection
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Numerical simulation of whole core squeezer radon pore water profiles: Methodological considerations and evaluation of benthic fluxes and rates of bio-irrigation and advection
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NUMERICAL SIMULATION OF WHOLE CORE SQUEEZER RADON PORE WATER PROFILES: METHODOLOGICAL CONSIDERATIONS AND EVALUATION OF BENTfflC FLUXES AND RATES OF BIO-IRRIGATION AND ADVECTION By Steven Laurence Colbert A Thesis Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree MASTER OF SCIENCE (GEOLOGICAL SCIENCES) May 2001 Copyright 2001 Steven Laurence Colbert R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . UMI N um ber: 1 4 0 6 4 4 3 Copyright 2001 by Colbert, Steven Laurence All rights reserved. UMI UMI Microform 1406443 Copyright 2001 by Bell & Howell Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. Bell & Howell Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . UNIVERSITY OF SOUTHERN CALIFORNIA THE GRADUATE SCHOOL UNIVERSITY PARK LOS ANGELES. CALIFORNIA SO 0O 7 This thesis, written by Steven Laurence Colbert under the direction of hJ&.— Thesis Committee, and approved by all its members, has been pre sented to and accepted by the Dean of The Graduate School, in partial fulfillment of the requirements for the degree of Master of Science Bern D a te „ -m x S X ± J M k .. THESIS COMMITTEE R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . ACKNOWLEDGEMENTS ii The following research was completed with the following financial and intellectual support. Funding came from USC Earth Sciences Department teaching assistantships, Tyler Environmental Award Fellowship, and from the National Science Foundation. This thesis was developed under the careful guidance of Doug Hammond. His unpretentious attitude and zeal for quality science have made him an outstanding mentor. Thank you to Will Berelson for providing me with research opportunities and an outlet for my musical passions. Thank you Richard Ku for your kindness and input on my research. Thanks to those past and present members of the geochemistry group for their valuable discussions and continual encouragement: Mike Neumann, Tim Townsend, Chris Hill, Masha Prokopenko, Tonya Bunn and Kathy Cummins. Thanks to the crew of R/V Atlantis and R/V Sonne, as well as those at Oregon State University and GEOMAR who provided sediment cores and helped in processing, specifically Jim McManus, Marta Torres, Olaf Pfannkuche, Gerhard Bohrmann, Dale Hubbard, Mike Tryon, Franzi Gutthann, Dirk Rickert, and Alex Heuser. My warmest thanks go to my family and friends for their immense support and encouragement. Finally, I am grateful for the unconditional love and support of my dearest Sara, the cricket to my cicada. R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . iii TABLE OF CONTENTS PAGE ACKNOWLEDGEMENTS.................................................................ii TABLE OF CONTENTS.................................................................... iii LIST OF FIGURES.............................................................................v LIST OF TABLES................................................................... ...........vi ABSTRACT...................................................................................... viii INTRODUCTION........................................................................... 1 Radon ................................................................................. 4 Whole Core Squeezer....................................................... 5 Study Area and Regional Geology.................................. 6 M ETH ODS....................................................................................... 14 Core Recovery................................................................... 14 Selection Criteria for Sites to Simulate........................... 14 Pore Water Extraction and Depth Assignment................. 16 Pore Water Analysis........................................................ 19 Rn Emanation Analysis.................................................... 20 Carbon A nalysis................................................................. 21 RESU LTS......................................................................................... 23 S orption................................................................................. 23 Pore Water R n.................................................................. 27 Additional Sorption of Pore Water Rn ............... 27 Rn Production Rate Function ............................... 30 ANALYTICAL AND NUMERICAL MODELS......................... 35 Diffusive Rn M odel......................................................... 35 Diffusive Rn Flux................. .................................... 39 Bio-Irrigation M odels....................................................... 39 Radial Diffusion-Reaction Model ............................ 43 Radial Diffusion Model Flux......................................... 51 One-Dimensional Reaction-Transport-Non-Local Exchange M odel............................................................... 54 One-Dimensional Model Flux........................................ 60 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . TABLE OF CONTENTS (continued) D ISC U SSIO N ................................................................................. 62 Bio-Irrigation Rates.................................................. ......62 Rn F lux............................................................................... 69 A dvection............................................................................. 70 Additional Sorption.......................................................... 77 CO NCLUSIONS............................................................................. 83 BIBLIOGRAPHY.............. ............................................................ 8 8 APPENDIX A .............................................................................. 96 APPENDIX B ................................................................................ 101 APPENDIX C .................. 110 APPENDIX D ................................................................................ 118 APPENDIX E ................................................................................ 122 APPENDIX F ................................................................................ 131 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . LIST OF FIGURES v FIGURE PAGE 1. Bathymetric map of Hydrate Ridge (within dashed box) and surrounding area (modified from Bohrmann et al., 2000).............. 7 2. Diagram of whole core squeezer.................................................. 17 3. Bulk sediment mobile Rn data, estimated diffusive Rn profile and Rn production rate vs. depth............................................................. 29 4. Cross-sectional diagram of radial diffusion model............................44 5. Radial diffusion model fit to mobile Rn data and Rn producion rate vs. depth.............................................................................................50 6 . Model derived fluxes plotted against water depth compared with the flux chamber measurement.................................................................. 53 7. Non-local exchange without advection model fit to mobile Rn data and Rn producion rate vs. depth ..... ...................................... 57 8 . Non-local exchange with advection model fit to mobile Rn data and Rn producion rate vs. depth............................................................... 58 A l. Rn concentration normalized to the initial tap water concentration for the nylon tubing and WCS experiments....................................... 98 B 1. Schematic diagram of the distribution of Rn in slurry effect experiments.......................................................................................... 1 0 2 C l. Schematic diagram of sorption model........................................... 112 C2. Sorption model for core 13MC for various fractions of organic carbon...................... ............................................................................ 116 C3. Sorption model results................................................................... 117 D l. Comparison and sensitivity of models to the use of a linear vs. exponential production rate and diffusivity.................................. 1 2 0 E l. Cross section diagram for radial diffusion model.......................... 124 E2. Radial diffusion model result for burrow depth = 5cm.......................126 E3. Sensitivity analysis for radial-diffusion model.............................. 129 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . LIST OF TABLES vi TABLE PAGE 1 . Table of variables.......................................................................... 1 2 2. Core locations and porosities and flux chamber result................... 15 3. Average parameters for each core................................................. 24 4. Sediment carbon measurements summary......................................26 5. Pore water and mobile radon-222 summary.................................. 28 6 . Rn emanation rate and production rate summary............................31 7. Fluxes (atoms/m2-sec) calculated for each model-derived pore water profile................................................................................................... 40 8 . Radial diffusion model parameters ..............................49 9. One-dimensional model-derived non-local exchange and advection rates.......................................................................................59 10. Literature values for dissolved solute transport in nearshore and estuarine sediments caused by non-diffusive mechanisms................63 11. Calculated non-local exchange rate based on Boudreau's relationship between the average concentration radius from the radial diffusion model and the non-local exchange rate (Equation 21)........................ 67 12. One dimensional transport-reaction model results before and after Rn profiles are moved 2 mm deeper in sediments...................... 73 13. Decrease in porosity due to settling required to match uppermost pore water sample with the diffusive Rn profile..............................74 14. Fraction of deep water in uppermost sample required to produce the observed pore water concentration ........ :. 75 15. Bulk sediment mobile Rn and mobile Rn adjusted for additional sorption................................................................................................. 78 16. Comparison of radial diffusion model burrow half-spacing calculated for mobile Rn data and mobile Rn adjusted for additional sorption. ...80 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . LIST OF TABLES (continued) 17. Comparison of non-local exchange and advection rates calculated for mobile Rn data and mobile Rn adjusted for additional sorption... 81 18. Comparison of fluxes (atoms/m2-sec) calculated for mobile Rn data and mobile Rn adjusted for additional sorption...................................82 B l. Slurry effect experiment summary................... 107 E 1. Radial diffusion model variability calculated using the parameters for core 13MC..................... 128 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . ABSTRACT viii Distributed advective flow through sediments is anticipated at Hydrate Ridge, Cascadia Margin. Advection of water through near-surface sediments should have a predictable effect on the near-surface Rn concentration profile. High-resolution Rn profiles were measured in near-surface pore waters extracted with a whole core squeezer from five cores collected in the vicinity of Hydrate Ridge. After squeezing, the cores were sectioned and the sediment Rn emanation rates and organic carbon fractions were analyzed. Emanation rates ranged between G.23 and 0.55 dpm/g. The fraction of organic carbon (w/w) in these sediments ranged between 1 . 2 and 2 .8 %, and modeling indicates that about 20% of the mobile Rn pool is sorbed to organic carbon. After accounting for sorption, the mobile Rn concentrations were 35-45% deficient relative to the calculated diffusive mobile Rn profile. The deficiency was attributed to bio-irrigation, and several models are presented to identify rates of bio- irrigation and advection. First, a radial diffusion-reaction model qualitatively estimates bio-irrigation. Second, a one-dimensional model calculates a non-local exchange term, both with and without an advection term. Model results indicate more efficient bio-irrigation at Hydrate Ridge than at surrounding sites, and comparable rates to previous work further inland. The one-dimensional model with R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . ix advection generated similar non-local exchange rates at all the sites, and advection rates of 0.2-0.5 cm/day. Estimated diffusive Rn fluxes were less than the result of a nearby deployed flux chamber, implying that irrigation is important in these sediments. Radial diffusion model fluxes were the most similar to the flux chamber result. One-dimensional model fluxes were significantly greater than the flux chamber result. Several lines of evidence suggest that the advection rates are over-estimated. These include a stiff clay at the bottom of the cores, significantly lower advection rates measured with flow meters, and overestimates of the flux in comparison that measured with a benthic flux chamber. This may be the result of extracting pore waters preferentially from burrows. An additional loss of Rn may occur as high Rn pore waters from deeper in the core come in contact with sediments that were in equilibrium with low Rn pore water in order to maintain sorption equilibrium. A model to assess the maximum effect of additional sorption estimated a loss of as much as 11% pore water Rn. Re examining the data showed that this significantly decreased the irrigation rates (-25%), but had little effect on the advection rates and Rn flux. To extract accurate Rn pore water profiles with a whole core squeezer, it is best to avoid bio-irrigated sediments with a high fraction of organic carbon. R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 1 INTRODUCTION Not all of the water trapped in the pore spaces and mineral structures of a subducting plate is transported back into the mantle. Compressive forces acting on the sediments reduce their porosity, and at greater depths, dewatering and volume reduction continues by dehydration and metamorphic reactions (Bray and Karig, 1985). The bulk transport of water, or advection, returns this water to the seafloor. This process, known as tectonic dewatering, will occur in the sediments on the subducting plate as well as those accreted onto the over-riding plate. Quantifying this water flux and its path is necessary to define regional and global biogeochemical budgets. The objective of this thesis is to explore whether naturally-occurring radon- 222 (Rn) can be used to solve this problem. The Cascadia Margin is a convergent margin where the Juan de Fuca oceanic plate is subducting beneath the North American Plate. For nearly two decades, research has been underway in the Cascadia Margin to locate active vents and quantify the volume of water released by tectonic dewatering. Cold seeps have been observed based on the presence of specific vent biota and geochemical tracers of fluid advection (Kulm et al., 1986; Carson et al., 1990). Researchers have returned to the fluid vents with sensitive flow meters and confirmed the release of fluids (Carson et al., 1990; Linke et al., 1994). Very sensitive flow meters are required to measure the low flow rates of these cold seeps, making this region a proving ground for new developments in flowmeter technology (Linke et al., 1994; Try on et al., 1999). Comparison of these site locations with geophysical evidence correlated the vents with the surface R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 2 traces of the frontal thrust, the back thrust, and along an erosional exposure of sandy strata (Carson et al., 1990; Moore et al., 1990). While the correlation with faults provides a mechanism for fluid from tectonic dewatering to reach the surface, evidence of deep-source water, such as reduced salinity and thermogenic methane, have not been observed at vents in the Cascadia Margin (Kulm et al., 1986, Carson et al., 1990). This may indicate a shallow source for these fluids, and a relatively fast cycling of seawater through the sediments. Several research groups have observed inflow of water near clam colonies and have presented possible mechanisms to explain this circulation. These include density gradients that develop beneath clam colonies that drives convection (Henry et al., 1992), or a significant change in the flow pattern in the immediate area of the clams as a result of biological pumping (Wallmann et al., 1997; Suess et al., 1998). Try on and co-workers (1999) propose a model that is driven by the build-up and release of methane gas as hydrates dissociate at the base of the hydrate stability field. While focused fluid advection has been observed, it is conceivable that there is also an advection of fluids that is evenly distributed across the region of tectonic dewatering. However, the fine-grained mud that makes up oceanic sediments may inhibit distributed advection. By increasing the area that advection may occur, large volumes of water could be expelled at low flow rates. Only recently has a flow meter been designed to measure these small flow rates (Tryon et al., 1999). Advection will have a predictable effect on the gradient of solutes in near-surface sediment pore waters. For a solute that is produced in the sediments, advection will either carry high concentration deep pore waters closer to the sediment-water interface or push low concentration bottom water into the sediments. A mathematical model that describes the pore water solute distribution can be used to quantify the advection rate. R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . 3 To minimize the uncertainty when calculating the advection rate, a sufficient pore water sampling density is required, and the production and reaction terms for the solute must be well characterized. While flow meters are limited by their availability and deployment time, pore water sampling is only limited by the ability to make pore water analyses. Plus, using near-surface pore water profiles to estimate advection is much less expensive than flow meters and many locations can be sampled in a short period of time. This method has been attempted with several different solutes, however the results were highly dependent on poorly understood sediment compositions and early diagenetic reactions (Mahn and Gieskes, 1999). Radon-222 is a solute that may circumvent these problems. For this study, near-surface pore waters were extracted with a whole-core squeezer (WCS) to generate Rn pore water profiles from the Cascadia Margin. All cores were collected in areas where presumably no localized advection was occurring. Using these profiles and a model that simulates the WCS process, the effects of sorption of Rn to organic matter and artifacts that may arise from the WCS process are examined. Then, two different models that account for the affect of bio-irrigation on pore water concentrations are used to generate pore water profiles. The first is a radial diffusion model and does not include advection (Aller, 1980). The second is a one dimensional reaction-transport-non-local exchange model that includes a term for advection. Parameters quantifying advection and bio-irrigation were derived from comparing simulated and observed profiles, and the derived results were compared to values in the literature. As an additional model constraint, the Rn flux was calculated for each of these models and compared to the results from a nearby benthic flux chamber deployment. R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . 4 Radon: Radon-222 (Rn), a naturally occurring radioactive noble gas with a mean life of 5.5 days, was first recognized by Broecker (1965) as a useful tracer of sediment- water exchange. Rn is an intermediate in the 238U decay series: 238j j 4.5j:109>ct ^234 7 TAdays ^2 3 4 \ - 2 m i n ) 234^y 2.5x10s/rs ^ Th -L gf*°3 -..daughter products Moderate quantities of 234U dissolved in seawater provide a source for 2 3 0Th. Particles falling through the water column will readily strip out insoluble 230Th and carry it to the sediments. 226Ra is also relatively insoluble and remains associated with the solid phase. Only a fraction of the total Rn produced enters the pore water because a substantial fraction of the Rn produced recoils into the solids. Rn that is available for diffusion in pore waters is called mobile Rn, and its release rate per gram of dry sediments is called the emanation rate. Rn is known to be readily soluble in organic solvents and to adsorb to charcoal (Ramstedt, 1911; Schulze, 1920; Wright and Smith, 1915). Wong and co-workers (1992) have shown that Rn will also sorb to organic carbon in the sediment. Mobile Rn includes both the Rn in pore waters as well as Rn that is sorbed to organic matter. Sorption will reduce the distance Rn can be transported before it decays. The distribution of Rn in pore waters reflects the effect of transport averaged over about two mean lives. Three different transport mechanisms control the interactions between bottom waters and pore waters. Diffusion, the transport of a solute based on random molecular movement, will transport Rn from regions of high to low concentration, moving it upward because the Rn concentration in the sediments is often more than three orders of magnitude larger than in bottom water. Advection, R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm ission . depending on the direction, will either carry Rn upward or downward. Finally, macrofauna living in the sediments will affect the distribution of Rn in the sediments. Bioturbation affects the Rn production rate by making the surficial sediments homogeneous by mixing older, deeper sediments with younger, shallower sediments. Since the mean life of 2 2 6 Ra is much longer than the time scales for bioturbation, the Rn emanation rate per unit of dry sediment should be nearly constant in near-surface sediments. Bio-irrigation will strip the Rn out of the sediments as low-concentration bottom water is pumped through the sediments. Each of these transport mechanisms will be examined in this thesis. Whole Core Squeezer: In order to accurately measure diffusion and to possibly measure advection, the curvature of the Rn pore water profile in the top few centimeters of the sediment must be accurately measured. The standard method for measuring Rn in pore waters involves sectioning the core, providing at best 0.5 cm resolution. Plus, sectioning exposes a core to the atmosphere, increasing the chance for gas exchange. A desire to improve the resolution of pore water profiles in surficial sediments led to the development of a technique to squeeze the water out of the top of a sediment core in sequential aliquots, known as the whole core squeezer (WCS) (Bender et al., 1987). Assuming that the pore waters travel with pipe flow, the depth a sample originated can be calculated based on the sediment porosity profile. While only a few cm can be sampled, mm scale resolution is achieved. An additional benefit of the WCS technique is that samples are isolated from the atmosphere, making the WCS an ideal method for sampling dissolved gases in pore waters such as Rn, oxygen, and methane. This method has been used to obtain Rn and oxygen pore R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 6 water profiles from equatorial Pacific sediments (Berelson et al., 1990; Hammond et al., 1996). The WCS method has been identified to only work for "particle-unreactive pore water constituents" (Bender et al., 1987). Wong and coworkers (1992) raise the question of the importance of sorption to organic matter during the squeezing process. Rn sorption is insignificant in sediments with little organic material, such as the equatorial Pacific, but does become significant in organic-rich sediments that often characterize continental shelf and rise settings. Study Area and Regional Geology: This research was centered around Hydrate Ridge on the Cascadia Margin. Along the Cascadia Margin, the Juan de Fuca plate is subducting beneath the North American plate at approximately 16 mm/yr (Carson et al., 1994). The boundary between these two plates is marked by a deformation front approximately 1 2 0 km off the coast; to the west are undisturbed abyssal plain sediments of the Juan de Fuca plate and to the east are deformed sediments and rugged topography. Hydrate Ridge is the second ridge east of the deformation front and formed as sediments from the Juan de Fuca Plate were scraped onto the overriding North American Plate (Silver, 1972; Carson et al., 1974; Kulm et al., 1974; Seely et al., 1974). Hydrate Ridge is dumbbell shaped and is divided by a saddle into Hydrate Ridge North (HRN) and Hydrate Ridge South (HRS) (Figure 1). The ridge extends about 24 km longitudinally, and is about 11 km wide at the northern summit. Hydrate Ridge was named after the discovery of massive accumulations of gas hydrates in surficial sediments (Suess and Bohrmann, 1997). Gas hydrates are a Nid phase containing gas and water that is stable at temperature and pressure conditions found along the continental rise and the deep sea, below about 500 m and 5°C. During R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 7 Figure 1: Bathymetric map of Hydrate Ridge (within dashed box) and surrounding area (modified from Bohrmann et al., 2000). 22MC PACIFIC (if u i 44 ’ 40’ 44“ 35 44*30' 44’ 2S' 125’ 20W 125’ 10*W 125’ OQ'W 124’ 50'W R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm ission . 8 the Ocean Drilling Program's (ODP) Leg 146, two cores (ODP 891 at the first ridge and ODP 892 at Hydrate Ridge north) were drilled to investigate the vertical distribution and chemical composition of hydrates. The hydrates collected were in small pieces dispersed throughout the pore spaces of the sediments to a depth of 71 mbsf (Kastner et al., 1995a; Whiticar et al., 1995). No hydrates were observed below 71 mbsf because the increased temperature at depth prevents hydrates from being stable. Below the hydrate stability field, methane can become concentrated and form free gas in the sediment. This free gas layer produces a bottom simulating reflector on geophysical seismic profiles and can be used to identify the presence of hydrates as well as the base of the hydrate stability field. Chemical analyses have been made on these hydrates. The gas phase consists primarily (90-99%) of biogenic methane (Suess et al., 1999). The internal fabric of the pure hydrate showed a peculiar structure with large filled pores not unlike bubble wrap material, implying the importance of free gas in the formation of hydrates (Suess et al., 1999). When free gas is available, hydrates have been observed to form very quickly in situ (Torres et al., 1999) and other gasses can be incorporated into the hydrate structure. Hydrogen sulfide-rich hydrates (<10% H2 S) were found to a depth of 19 m in ODP 892 (Kastner et al., 1995b; Kastner et al., 1998). Rn may be incorporated into the hydrate structure because like methane, it is non-polar and has a similar atomic radius. If Rn is quickly incorporated into the hydrate structure, then hydrates may be a sink for Rn. Hydrate formation in near-surface sediments would then reduce the Rn flux to the overlying water column. During a series of D.S.R.V. Alvin dives along the first deformation ridge, localized fluid venting was first identified based on the presence of vent-specific organisms, such as tube worms and the giant clam, Calyptogena sp. (Kulm et al., R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 1986). Water samples collected above these sites contained chemical and physical indicators of fluid venting: increased methane, Rn and temperature relative to bottom water. Comparison of these site locations with geophysical evidence correlated the vents with the surface traces of the frontal thrust, the back thrust, and along an erosional exposure of sandy strata (Carson et al., 1990; Moore et al., 1990). Subsequent Alvin dives deployed a benthic barrel fitted with both a Bernoulli-type and a thermistor flow meter, and advective flow rates ranging from 9-177 cm/day depending on the vent were observed. (Carson et al., 1990; Linke et al., 1994). At Hydrate Ridge, a benthic flux meter capable of measuring fluid velocities on the order of cm/year observed an advection rates between 80 cm/yr out of the sediments to > 6 cm/yr into the sediments (Tryon et al., 1999). These researchers also observed decreasing advection rates with increasing radial distance from the center of a clam field. Gas seeps have been observed and sampled near the topographic highs of Hydrate Ridge (Torres et al., 1998b; Torres et al., 1999; Colbert et al., 1999). Chemical analysis of the vent gas confirmed that it consisted of almost pure methane; no hydrogen sulfide was sensed with an olfactory test (Torres et al., 1998; Torres et al., 1999). High Rn to methane ratios indicate that the gas had recently been in contact with sediments characterized by a high solid to gas ratio (Colbert et al., 1999). Flow rates from the vents are variable in time, with an estimated maximum observed flow rate from a single vent of up to 5 L of gas/min (Torres et al., 1999). One hypothesis for the formation of these gas seeps is that hydrate is dissolved at the base of the stability field and the methane collects in cracks and pore spaces. When the methane is released, free gas travels to the surface in hydrate-lined conduits (Suess et al., 1999). A methane source below the hydrate stability field is supported by a) the correlation of R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 1 0 the seeps with faults that extend from the surface through the hydrate stability field, and b) the high Rn/methane ratios (> 1 dpm/cc). The build up of methane deep in the sediments that outgasses at the methane seeps may also explain the observed pumping of water into and out of the sediments (Tryon et al., 1999). Formation of authigenic carbonates have been identified as indirect evidence of fluid venting (Kulm et al., 1986; Ritger et al., 1987; Suess et al., 1990). Large regions of HRN are covered with a pavement of diagenetic carbonate-cemented sediments, preventing any cores from being collected at HRN. HRS does not have this pavement, but a carbonate pinnacle on the western flank of HRS was recently discovered, with active fluid flow at its top (Torres et al., 1999). The association of authigenic carbonates and hydrates indicate that carbonate formation may be related to the mechanism controlling the formation and decomposition of gas hydrates (Bohrmann et al., 1998). Detailed investigation of gas hydrate/sediment intercalcations from HRS has shown that the carbonate fabric is related to the gas hydrate formation (Bohrmann et al., 1998). Across Hydrate Ridge, benthic fauna change drastically over the scale of centimeters (Sahling et al., 1999). It is believed that different rates of fluid advection or fluid venting control the benthic diversity (Kulm et al., 1986). Specifically, regions with the highest fluxes support bacterial mats, lower fluxes support dense chemotrophic clam communities, and more typical, disperse heterotrophic benthic communities of tiny bi-valves, giant foraminifers, and diverse polychaetes in no-flow regions (Sahling et al., 1999). The presence of high concentrations of methane in near-surface sediments provides a metabolizable carbon source that prevents deep diffusion of oxygen into the sediments. Evidence of microbial CH4 oxidation via R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 11 reduction of sulfate has been observed in the dissolved nutrient patterns in the pore waters of sediments of the Oregon deformation front (Kulm et al., 1986). The oceanic setting is strongly influenced by regional meteorological systems and the Columbia River, which is the predominant supplier of fresh water and sediments to the northern Oregon continental shelf (Gross et al., 1967; Barnes et al., 1972). Circulation is controlled by prevailing winds that change with season. North winds during the summer cause currents to flow southward, creating offshore Ekman transport which results in upwelling of cool, nutrient-rich water onto the shelf (Hopkins, 1971; Smethie et al., 1981). Organic matter that falls below the mixed layer is degraded in the water column, generating an oxygen minimum zone in the water column that is concurrent with the depth of Hydrate Ridge. R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 12 Table 1: Table of variables. Concentrations with volume units of ml represent aqueous concentrations, and cm3 represents bulk sediment concentrations. C = Total mobile Rn per volume o f wet sediments (atoms/cm3 ) Cs = number o f atoms sorbed per unit weight o f sediments (atoms/g) Cw = number o f atoms per volume o f pore water (atoms/ml) C0l = Rn concentration o f overlying water (atoms/ml) C = Average radial concentration (dpm/cm3 ) Cr(r) = Radial Rn concentration (dpm/cm3 ) ACe q = P = mobile Rn equilibrium concentration in bulk sediments (dpm/cm3 ) E = Rn emanation rate (dpm/g) P = ( l-(J))Eps = mobile Rn production rate per unit o f bulk sediments (dpm/cm3 ) P(z) = exponential production rate function (dpm/cm3 ) ?iaf = production rate at infinite depth (dpm/cm3 ) Po = mobile Rn production rate at sediment-water interface (exponential profile) (dpm/cm3 ) p = mobile Rn production rate exponential scale coefficient (cm'1 ) P’(z) = linear production rate function (dpm/cm3 ) P0’ = mobile Rn production rate at sediment-water interface (linear profile) (dpm/cm3 ) P' = slope o f Rn production rate vs. depth in core (dpm/cm4 ) Kd = Kocfoc = distribution coefficient (ml/g) = distribution coefficient for organic carbon (ml/g) fo c = fraction o f organic carbon in sediments < j ) = porosity ps = sediment density (g/cm3 ) R = 1 + -------— = organic carbon adsorption retardation coefficient (unitless) 0 Dm = molecular diffusivity of Rn at in situ temperature (cm2 /sec) 02 = tortuosity (unitless) Ds = Dm/02 = effective diffusivity o f Rn (cm2 /sec) a = non-local exchange constant (m in 1 ) X = Rn decay constant (m in 1 ) T ] = radial mobile Rn scaling constant (cm'1 ) b = Rn profile scaling constant (cm'1 ) r = radial coordinate measured from cylinder axis (cm) r0 = center o f the burrow r5 = radius o f the burrow wall (cm) r2 = burrow half-spacing (cm) r = radius where concentration equals the average Rn concentration (cm) t = time u = pore fluid velocity in the z direction (cm/min) z = vertical space coordinate, positive axis into the sediment (cm) J = Rn flux across the sediment-water interface (atoms m'2 sec-1 ) Jto t = Sum o f diffusive and irrigation flux (atoms m'2 s e c 1 ) Jr = Rn flux into the burrow (atoms m'2 sec'1 ) Jz = Rn flux out the top of the cylinder of sediments (atoms m2 s e c 1 )_______________ ; ____ R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 13 Table 1 (Continued): h,j = vertical coordinate box number, sub-cylinder number i = box number (i= l,2,...) ai = depth to top o f box i (cm) « t > i = porosity o f box i (cm) V w ,i = volume of pore water in box i Vi = total volum e Of box i Cw ,i = pore water concentration in box i (atoms/cm3 ) c * ^w,i = new pore water concentration in box i (atoms/cm3 ) Chj = mobile Rn concentration in box h,j (atoms/cm3 ) ch = mobile Rn concentration in layer h (atoms/cm3 ) c = Rn gas phase concentration (atoms/cm3 o f gas) H = Cg/Cw (z=0) =Henry's Law constant (cm3 of water/ cm3 o f gas) Ms = mass o f sediments K = total thickness of unit n (cm) = depth in unit n (cm) S = subscript n sediment unit w = subscript n water unit g = subscript n gas unit R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 1 4 METHODS Core Recovery: Cores were collected during two cruises organized by the TECFLUX research program. TECFLUX is an international effort to determine effect of widespread hydrate formation on element mobilization, transport, and release at the sea floor (Torres et al., 1998). The focus of this research is Hydrate Ridge and the surrounding area on the Cascadia Margin. Cores were collected with multicores aboard the R/V Atlantis (AT9906) in July, 1999, and aboard the RF Sonne (S0143) in August, 1999. Ten sediment cores were collected from water depths ranging between 700 m and 1800 m. No cores were collected at HRN because a carbonate pavement prevented core penetration. Before squeezing, each core was examined visually, and afterwards each was extruded and split for a closer look. Evidence of macrofauna was found in all of the cores, including burrows observed on the core surface, burrows (radius = 0.25 cm) intersected by the core liner, and live polycheates found once the core was split. All of the cores except the deepest one, 22MC, had a similar coloration and sediment composition: a brown mud at the surface, frequently with black speckles, which abruptly changed to a stiff olive-colored clay near the bottom of the core. This clay presumably prevented further penetration of the core. Core 22MC did not have this stiff clay at the bottom. Selection Criteria for Sites to Simulate: Of these cores, only five (Figure 1; Table 2) matched the following qualifications and are presented in this work: (a) undisturbed sediment-water interface, (b) accurate pore water profile, (c) constant emanation rate (dpm/g) with depth, and (d) constant sediment organic carbon concentration with R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . Reproduced w ith perm ission o f th e copyright owner. Further reproduction p rohibited w ithout permission. Table 2: Core locations and porosity and flux chamber result. Core Date Collected latitude <N) longatude (W ) Location Water Depth <m) (j)o o Porosity do < t > l 22MC 7/7/99 44° 50.40 125° 08.40 Basin; Paleo-1 1826 0.836 0.907 -0.541 35MC 7/11/99 44° 35.95 124° 55.39 Slope 732 0.794 0.886 -0.353 13MC 7/5/99 44° 35.20 125° 07.00 HRS 912 0.688 0.765 -0.492 143-91 8/4/99 44° 33.90 125° 08.31 HRS 848 0.643 0.759 -0.332 143-139 8/12/99 44° 34.08 125° 08.40 HRS 826 0.631 0.782 -0.589 FLUX CHAMBER 7/8-9/1999 44° 34.25 125° 08.99 HRS:Soft Seds 791 FLUX (atoms/m2/sec) 50 ± 11 1 6 depth. Each of these factors is discussed below. Unfortunately, cores collected near localized fluid vents or containing hydrates were not analyzed. The methane degassed as the cores decompressed and warmed during core recovery. This destroyed the sediment water interface, altered the distribution of chemical species in the top of the core, and stripped dissolved gases from the pore fluids. Pore Water Extraction and Depth Assignment: Cores were processed within two hours of collection in a cold room within 1°C of in situ temperature, using a whole core squeezing (WCS) technique (Bender et al., 1987). The WCS technique works by placing a piston/filter pack at the top of a core and a plug at the bottom to keep all sediment within the core liner (Figure 2). Water escapes through a hole in the center of the piston as it is driven down onto the sediments. Once the sediment-water interface is reached, as the piston advances, surficial solids are compressed, and pore waters are expressed out through the piston. The sediment-water interface is initially defined visually when the piston is lying flat against the sediment-water interface. Sequential aliquots of water were then squeezed from the core and their volumes were recorded. The depth of sampling depends on the firmness of the sediments. The depth each sample originated can be derived using the porosity profile of another core from the same multicore deployment. The function, b (z )= < t> in f + (4>0- <{>inf)exp(-01z ) (1 ) provided an excellent fit through the top 4cm of porosity data, where < j ) j nf is an equilibrium porosity at depth, ( j > 0 is the porosity at the sediment-water interface, and < j > i is a scaling constant (Table 2). Heterogeneous sediments may result in different R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . Figure 2: Diagram of whole core squeezer. 17 Oxygen Electrode Squeezing Piston 0.4 pm ■ Filter Polyester Screen ~ Filter Overlying Sample Water Exit [Seaiment I ■ ■ ■ - — Piston R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 18 porosity profiles between cores of the same multicore. In addition, water-filled voids in the sediments, which are avoided when the porosity is measured, may cause the porosity to be underestimated. The porosity is estimated to vary by as much as 0.02 between cores in a multicore. To minimize the uncertainty in the placement of the sediment-water interface, especially in cores with surficial relief, the interface was later identified by using a least-squares fit of Equation 12, discussed in the Results section, to the mobile Rn data. A curve fit, with the production rate function and scaling constant as independent variables, was made for the initial data set and by adding and subtracting 7 ml of water (the volume of water in the line between the core top and the sampling syringe) to the Rn data. The quality of each curve fit was assessed based on a chi- squared test. All curve fits presented in this work were done using the software KaleidaGraph v.3.08d by Synergy Software. Rn could interact with the WCS tubing. Rn adsorbs to and diffuses through Tygon and silicon tubing, but nylon was thought to be less likely to interact with the Rn. Between the piston and the sampling syringe is 75 cm of 0.125" OD nylon tubing and 9 cm that consists of a flow-through oxygen electrode and a 0.4 pm filter with small pieces of Tygon and silicone tubing as connectors. A series of experiments was performed to test if Rn was being lost through the nylon tubing and the rest of the WCS tubing (Appendix A). No sorption or diffusive loss of Rn was observed for the type of nylon used in the WCS. Plus, passing water with a known Rn concentration through the WCS line, including the oxygen electrode and filter, had a negligible effect on the Rn concentration. R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . 19 Pore Water Analysis: In addition to Rn, cores were analyzed for nutrients, oxygen, total C 02 , and some cores also had methane and total H2 S measured. Depending on the depth of sampling, five or six Rn samples were collected into 5 ml glass syringes. Bottom water samples were measured from Niskin bottles within a benthic barrel during short (~1 hour) deployments (Linke et al., 1994; Torres et al., 1999). Samples were stored in syringes in the cold room until processing. Most samples were analyzed within six hours of collection, but some samples waited up to 48 hours. Laboratory tests confirmed that any loss of Rn from glass syringes during storage is negligible. Corrections were made for decay during storage. Rn was analyzed using a rapid radon extraction system (Berelson et al., 1987b). In brief, the sample is injected into a stripping cchamber in an evacuated system. A single pass of He through the solution strips out the Rn, and the gas is carried over anhydrous CaS04 to remove water vapor followed by a NaOH impregnated clay to remove C 02. A Lucas scintillation cell, coated with a ZnS phosphor, collects the gas as the pressure is returned to ambient. The cell is then placed in a detector as outlined by Mathieu and others (1988). The stripping efficiency was calculated to be 95% based on running a second extraction for several samples at this sample volume. The Rn in the scintillation cell is measured by assessing its activity, a count of the number of atoms that decay over a known period of time, or disintegrations per minute (dpm). The absolute number of atoms in a sample can be calculated by dividing the activity by the Rn decay constant, X= 1.26xl0"4 min'1 . The concentration of Rn in a sample (Cs a m p le ) is the total number of Rn atoms divided by the sample volume. However, since the activity is measured, and provides a more practical unit than the absolute number of Rn atoms, the units for the data presented in this work are activity per unit volume, A ,C s a m p le . R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 20 Rn Emanation Analysis: After each core was squeezed, the top three cm of compacted sediment were sectioned, stored at 5°C, and later analyzed in the laboratory for Rn emanation analysis and organic carbon concentration. The Rn emanation rate, the number of Rn atoms released to pore fluids per gram of dry sediment per unit of time, was measured using a slurry technique (Hammond and Fuller, 1979; Key et al., 1979b; Mathieu et al., 1988). For this method, a known mass of sediment (about 20 g wet sediment) was sealed in ajar with 1 0 0 ml of sea water, homogenized, and flushed with helium to remove all the Rn. Afterwards, the jar was stored to allow Rn to grow into equilibrium at a rate that is defined by the half-life of Rn. After sitting for at least 14 days, samples were analyzed, and the radon emanation from solids was calculated after accounting for the fraction of disequilibrium. Rn analysis followed the procedure outlined by Hammond and Fuller (1979). In brief, helium was circulated in a closed loop for two hours, stripping Rn out of the slurry and passing through a column of anhydrous CaS0 4 to remove water vapor and a NaOH/clay mixture that removes CO2 . The gas stream passes through a charcoal trap chilled to -40°C that readily strips out the Rn and then loops back through the sample. After the sample was flushed, the charcoal trap was connected to a transfer board and heated to 450°C to release the Rn. Helium was passed through the charcoal to carry the Rn to an evacuated Lucas cell. The scintillation cell was placed in a detector as outlined by Mathieu and others (1988). The efficiency of stripping the Rn out of the mud and transferring the Rn to the scintillation cell based on previous work is >99% (Hammond et al., 1977). This method should remove all of the dissolved and sorbed Rn because of the long extraction times. For each sample, emanation measurements were repeated until the standard deviation in this parameter was less than 5%. R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm ission . 21 The slurry technique has been shown to overestimate the Rn emanation rate by 10-20% (Key et al., 1979a; Smethie et al., 1981). Excess Rn produced by this method has been attributed to the increased porosity of the slurry over the original sediment, which allows a larger fraction of the Rn produced to enter the pore fluids (Hammond and Fuller, 1979). Berelson and coworkers (1982) tested this hypothesis on a series of samples from the California borderland basins and found the average increase in Rn from slurrying was 13.0± 7.7% for these cores. Their results suggested a depth dependence with 7.8±5.5% for sediments in the upper 8 cm of sediment, increasing to 13.3±10.1% for samples below 8 cm (Berelson et al., 1987a). An independent test of the slurry effect was also attempted (see Appendix B for details). Briefly, a known volume (and mass) of sediment with a known porosity and emanation rate was sealed in ajar. Assuming a closed, purely diffusive system, the Rn emanation rate can be calculated based on the Rn concentration in the headspace gas. The observed head-space Rn activity correlated with the estimated head-space gas activity before adjusting for the slurry effect. This result may reflect that the porosity of the mud was equivalent to the porosity of the slurry. However, the result was strongly dependent on the adsorption and tortuosity parameters, producing a large uncertainty in the results. Because of the uncertainty in the results of this experiment, the published value of 7.8±5.5% (Berelson et al., 1987a) was assumed to be more accurate and used to account for the slurry effect. Carbon Analysis: A split of the sediments was dried at 60°C for a week and stored for carbon analysis. Splits were analyzed for their concentration of CaC03 using a coulometric method (UIC CM 5130 acidification module in line with a UIC CM5012 C02 Coulometer). The standard deviation for duplicate measurements is typically R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . ±0.1 wt% CaC03 . Total carbon was measured using a CHNS elemental analyzer (CE Instruments NC2500). The relative standard deviation based on duplicate total carbon measurements is about ±10% of the measured value. The difference between the fraction of total carbon and fraction of carbonate carbon is the percent of organic carbon in each sample. Using propagation of errors, the uncertainty in the fraction of organic carbon is about 15% of the measured value. Reproduced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . RESULTS 23 The distribution of Rn in sediments is influenced by several factors. Some of these can be directly measured or predicted from previous work, including sorption, the Rn emanation rate, and the effect of molecular diffusivity (Summarized in Table 3). Others must be deduced from modeling observed data, including the effects of bio irrigation and fluid advection. Each of the first set of factors will be evaluated from measurements and a survey of the literature, followed by a discussion of computational work to define the second group. Sorption: A solute may fractionate between the dissolved phase and sorbed to a solid phase as a result of the physical and chemical properties, such as polarity or charge, of the solute and the solid phase. Mobile Rn is either dissolved in pore waters or sorbed to organic matter in the sediments. The ratio of the number of atoms sorbed per unit weight of sediments, Cs (atoms/g), to the atoms in solution, Cw (atoms/ml) is called the distribution coefficient, (ml/g). For a solute at low concentration the distribution coefficient will be constant (Langmuir, 1997). A distribution coefficient for organic carbon (K^; ml/g) has been defined as the ratio of atoms adsorbed per gram of organic carbon to the concentration of atoms in solution. The distribution coefficient K ^j is related to through the following expression, where f^ is the weight fraction of organic carbon in the sediment (Langmuir, 1997): (2) R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . Reproduced w ith perm ission o f th e copyright owner. Further reproduction prohibited without permission. Table 3: Average parameters for each core. Core Water Depth (m ) Effective Diffusivity @5°C: Ds (X10-6 cm 2 /sec) Ave. Organic Carbon: foe (% ) Average Retardation Coeff. @5°C: R Ave. Rn Emanation: E (d p m /g) Exponential Prod. Rate Constants Pinf Po P1 (dp m /cm 3) (d p m /cm 3 ) 1 /cm Linear Prod. Rate Constants Po* P' (dp m /cm 3) (dp m /cm 4) 22MC (Basin) 18 2 6 4 .8 6 2.83 ± 0.11 1.22 0.554 ± 0.059 0 .2 3 8 0 .1 0 5 -0.520 0 .1 5 2 0.021 35MC (Slope) 7 3 2 4 .6 2 2.59 ± 0 .1 0 1.24 0.332 ± 0.036 0 .1 7 5 0 .0 7 6 -0.389 0 .1 0 7 0 .0 1 5 13MC (HRS) 9 1 2 3.3 9 1.51 ± 0.06 1.29 0.297 ± 0.031 0.241 0 .0 6 0 -0.478 0.191 0 .0 1 2 143-91 (HRS) 8 4 8 3 .2 5 1.21 ± 0.05 1.25 0.232 ± 0.030 0 .2 1 7 0 .0 7 2 -0.324 0 .1 5 2 0 .0 1 2 143-139 (HRS) 8 2 6 3.0 9 1.28 ± 0.05 1.28 0.278 ± 0.029 0.269 0 .1 1 0 -0.580 0.181 0 .0 2 3 N > 25 Wong and coworkers (1992) studied the effects of Rn sorption to organic carbon in three sediment cores with a range of organic carbon contents. From this work, they empirically derived to be 18.9 m l/g oc at 5°C and 23 m l/go,, at 2 0 ° C . They also noted that sorption equilibrium is not instantaneous, and estimated that equilibrium is achieved in about 15 minutes based on experimental data. The mobile Rn concentration in bulk sediments (C; atoms/cm3 ) is the sum of the dissolved pool and the sorbed pool: where < j ) is the porosity and ps is the sediment density. Equation 2 and Equation 3 can then be combined: The organic carbon fraction (foe) was measured to assess the importance of Rn sorption to organic matter to the mobile Rn pool and is presented in Table 4. The two cores from the region surrounding HRS had foc > 2%, which is consistent with previous measurements of organic carbon on the slope of the Cascadia Margin (Gross et al., 1972; Archer and Devol, 1992). The fraction of organic carbon in the sediments at Hydrate Ridge was significantly lower, averaging 1.35%. Using the average C = $ > C W + ( 1 - $ ) P SCS (3 ) <7=(4> + ( i - 4 0 p - W C w (4) where R = retardation coefficient = 1 + R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm ission . 26 Table 4: Sediment carbon measurements summary SAMPLES DepthA %C %CaC03 %C)org* (cm ) 22MC-1 0-1 2.97 ± 0.28 0.74 ± 0.08 2.88 ± 0.28 22MC-2 1-2 2.77 + 0.26 0.48 ± 0.05 2.71 ± 0.26 22MC-3 2-3 3.00 ± 0.28 0.87 ± 0.10 2.90 ± 0.28 22MC Average 2.83 ± 0.16 35MC-1 0-1 2.76 ± 0.26 1.26 ± 0.14 2.61 ± 0.26 35MC-2 1-2 2.72 ± 0.26 0.96 ± 0.11 2.60 ± 0.26 35MC-3 2-3 2.67 ± 0.25 0.83 + 0.09 2.57 ± 0.25 35MC Average 2.59 ± 0.15 13MC-1 0-1 1.51 ± 0.14 0.56 + 0.06 1.44 ± 0.14 13MC-2 1-2 1.72 ± 0.16 0.55 ± 0.06 1.65 ± 0.16 13MC-3 2-3 1.49 ± 0.14 0.37 ± 0.04 1.45 ± 0.14 13MC Average 1.51 ± 0.08 143-91-1 0-1 1.27 ± 0.12 0.66 ± 0.07 1.19 ± 0.12 143-91-2 1-2 1.27 ± 0.12 0.47 ± 0.05 1.21 ± 0.12 143-91-3 2-3 1.28 ± 0.12 0.50 ± 0.06 1.22 + 0.12 143-91 Average 1.21 ± 0.07 143-139-1 0-1 1.59 ± 0.15 1.64 ± 0.18 1.39 ± 0.15 143-139-2 1-2 1.34 ± 0.13 0.98 ± 0.11 1.22 ± 0.13 143-139-3 2-3 1.36 ± 0.13 1.06 ± 0.12 1.23 ± 0.13 143-139 Average 1.28 ± 0.08 A Depth from surface of sediment brick left after squeezing * Calculated as %C-0.12*%CaCO3 DUPLICATES SAMPLE %C %C)ave %CaC03 %CaC03)ave %C)org 22mc-1 22mc-1 -2 2.93 2.97 ± 0.06 3.01 0.74 0.74 ± 0.01 0.73 2.88 ± 0.06 35mc-1 35mc-1 -2 2.72 2.76 ± 0.06 2.80 1 3mc-1 13mc-1-2 1.41 1.51 ± 0.14 1.61 0.56 0.56 ± 0.00 0.56 1.44 ± 0.14 143-91-1 143-91-1-2 1.31 1.27 ± 0.06 1.22 0.61 0.66 ± 0.06 0.70 1.19 ± 0.06 143-139-1 143-139-1-2 1.51 1.59 ± 0.11 1.66 1.64 1.52 ± 0.17 1.40 1.40 ± 0.11 Max. Fractional Standard Deviat on 9.4% 11.3% 14.7% R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm ission . porosity in the top 4 cm, a density of 2.6 g/cm3, and Ko c at 5°C (18.9 ml/go c ), the average retardation factor in each core can be calculated (Table 3). The retardation factor at the 5 sites is remarkably similar. This occurs because of the compensating effects of organic carbon and porosity. Hydrate Ridge sediments have a low porosity and a low organic carbon fraction; the surrounding sites have a high porosity and a high fraction of organic carbon. Pore Water Radon: Results of the WCS Rn pore water concentrations are presented in Table 5. Five or six Rn pore water samples were collected within the top 3.5 cm of each core. Rn concentrations increase by three orders of magnitude within the top 1.5 cm of each core. Below 1.5 cm, the Rn concentration does not change significantly. Maximum Rn concentrations range between 71 and 152 dpm/L of pore water. Pore water samples collect only the dissolved Rn (Cw ). Using Equation 4, the mobile Rn concentrations in bulk sediments can be calculated (Table 5). In each core, a significant fraction of the total mobile Rn is sorbed to organic matter, accounting for about 20% of the mobile Rn pool. These values are plotted against depth in Figure 3. Additional Sorption of Pore Water Rn: An additional sorption of pore water Rn is a possible artifact of the WCS process due to a chromatographic effect as high Rn pore waters from deep in the core are squeezed up through the sediment column and come in contact with sediments in equilibrium with low Rn pore water. High Rn pore waters have the potential to loose a fraction of their Rn to the low Rn sediments in order to maintain sorption equilibrium. The amount of Rn lost by this process will depend on the pore water Rn concentration, the organic carbon concentration, and whether sorption equilibrium is achieved. To assess the importance of this process, a R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 28 Table 5: Pore water and mobile radon-222 summary. Core Depth Pore water Rn Total Mobile Rn (cm) (dpm/L)pw (dpm/cc)bulk 22MC 0.00 0.10 ± 0.03 0.00010 ± 0.00001 (Basin) 0.34 51 ± 7 0.053 ± 0.010 0.77 69 ± 9 0.072 -f- 0.013 1.47 104 ± 1 1 0.109 ± 0.017 2.05 116 ± 1 3 0.122 4 - 0.020 2.55 113 ± 1 9 0.119 ± 0.024 35 MC 0.00 0.10 ± 0.03 0.00010 ± 0.00001 (Slope) 0.30 29 ± 6 0.030 ± 0.007 0.82 41 ± 3 0.043 ± 0.006 1.40 65 ± 8 0.068 ± 0.011 1.96 71 ± 37 0.075 ± 0.040 2.46 70 ± 22 0.074 ± 0.025 13MC 0.00 0.10 ± 0.03 0.00009 ± 0.00001 (HRS) 0.39 65 ± 7 0.061 ± 0.010 0.88 82 ± 7 0.076 ± 0.011 1.40 122 ± 9 0.113 ± 0.016 1.91 118 ± 9 0.109 ± 0.015 2.44 127 ± 12 0.118 ± 0.018 2.97 126 ± 15 0.116 ± 0.019 143-91 0.00 0.10 ± 0.03 0.00009 ± 0.00001 (HRS) 0.08 5 ± 7 0.004 ± 0.006 0.35 49 ± 7 0.044 ± 0.008 0.64 64 ± 9 0.057 ± 0.010 0.94 82 ± 9 0.073 ± 0.012 1.24 79 ± 1 0 0.070 ± 0.012 1.51 101 ± 12 0.089 ± 0.015 143-139 0.00 0.10 ± 0.03 0.00009 ± 0.00001 (HRS) 0.35 53 ± 7 0.048 ± 0.008 0.90 99 ± 9 0.089 ± 0.013 1.43 123 1 1 0.109 ± 0.016 2.02 140 + 1 6 0.123 ± 0.020 2.56 152 ± 16 0.133 ± 0.021 3.09 144 ± 1 6 0.126 ± 0.020 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . 29 Figure 3: Bulk sediment mobile Rn data, estimated diffusive Rn profile and Rn production rate vs. depth. Solid line is the Rn production rate, dotted line is the estimated diffusive Rn profile. d p n a /c c ) b u l k Rn Production Rate • Mobile Rn Data — Est. Diffusive Rn Profile d p m / c c ) b u l k 0.25 0.3 .05 0 fr 22MC Slope 0.5 I t 4 1 d p m / c c ) h u l k 0.05 0.1 0.15 0.2 0.25 0.3 35 MC Slope 0.5 5 6 a 2.5 0.15 0.2 0.25 0.05 € & a 2.5 13MC HRS d p m / c c ) b u l k 0.15 0.2 0.25 0.3 0.05 0.5 6 a a 143-91 HRS d p m / c c ) b u l k 0.15 0.2 0.25 0.3 0.05 0 ^ r- 0.5 5 6 a 2.5 -143-139 : HRS R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm ission . 30 multi-box model was constructed to simulate the additional Rn sorption that can occur as a parcel of water equilibrates with the sediments as it moves from depth in the core to the surface (Appendix G). Briefly, the model tracks parcels of water as they rise through the sediment column. Beginning with a diffusive Rn pore water profile in equilibrium with the sediments, during each step in the model, the water moves up a finite distance and equilibrates with the surrounding sediment. The model output is the parcel of water that has equilibrated with the top-most sediments. It is likely that equilibrium sorption was not achieved because of limited time for exchange, so quantifying how much of an artifact is present due to additional Rn sorption is impossible. The modeling results show that additional sorption may account for as much as an 11% loss of Rn (Appendix C). Additional sorption will be dismissed for the following discussion of the data because it plays only a small role for Rn loss and cannot be quantified. However, some estimates of its possible importance will be noted in the Discussion section. Similarly, some Rn could have been sorbed to organic matter in the fine-mesh filter. When the piston first reached the sediment-water interface, some of the surficial material was fine enough that it passed through the filter on the piston, only to be stopped by the 0.4 pm filter. If an organic-rich layer developed on the filter, then additional sorption of Rn may have occurred as water passed through. However, this does not appear to be a significant effect because two cores (22MC and 3 SMC) had new filters installed after the second Rn draw and still show the same trend as the other cores. Rn Production Rate Function: The Rn emanation rate (E; dpm/g) is presented for each core in Table 6 . The emanation rate accounts for both Rn released into pore waters as R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . Table 6: Rn emanation rate and production rate summary. Rn emanation rate (E) Core DepthA (cm) Rn Emanation Rate* (dpm/g) 22MC (Basin) 0-1 1-2 2-3 Average 0.571 ± 0.035 0.554 + 0.034 0.538 ± 0.033 0.554 ± 0.017 35MC (Slope) 0-1 1-2 2-3 Average 0.336 ± 0.021 0.314 ± 0.02 0.347 ± 0.022 0.332 ± 0.017 13MC (HRS) 0-1 1-2 2-3 Average 0.284 ± 0.017 0.324 ± 0.02 0.268 ± 0.017 0.297 ± 0.029 143-91 (HRS) 0-1 1-2 2-3 Average 0.219 ± 0.014 0.243 ± 0.015 0.234 ± 0.022 0.232 ± 0.012 143-139 (HRS) 0-1 1-2 2-3 Average 0.274 ± 0.017 0.288 ± 0.017 0.273 ± 0.017 0.278 ± 0.008 A Depth from surface of sedim ent brick after squeezing. * Corrected for slurry effect (7.8%) Rn production rate (P)* Depth Rn Production Rate Core (cm) (dpm/cc)huik 22MC 0-1 0.157 ± 0.017 (Basin) 1-2 0.190 ± 0.020 2-3 0.209 ± 0.022 3-4 0.221 ± 0.023 35MC 0-1 0.112 ± 0.012 (Slope) 1-2 0.132 ± 0.014 2-3 0.146 ± 0.016 3-4 0.155 ± 0.017 13MC 0-1 0.194 ± 0.021 (HRS) 1-2 0.212 ± 0.023 2-3 0.223 ± 0.024 3-4 0.230 ± 0.025 143-91 0-1 0.156 ± 0.020 (HRS) 1-2 0.173 ± 0.022 2-3 0.185 ± 0.024 3-4 0.194 ± 0.025 143-139 0-1 0.185 ± 0.020 (HRS) 1-2 0.222 ± 0.024 2-3 0.242 ± 0.026 3-4 0.254 ± 0.027 ‘Calculated from Equation 5 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 32 well as sorbed Rn. The total depth of sediment sampled is actually deeper than 3 cm because the depth assignment for each sample is the depth from the sediment-water interface after the core had been squeezed. The actual depth of each sample is irrelevant because the Rn emanation rate per gram in each core was relatively constant over the depth sampled. The deepest site, 22MC, had a significantly higher Rn emanation rate then the other cores. Across small spatial scales like this study, a correlation between the Rn emanation rate and water depth is expected. Assuming the concentration of 234U is relatively constant in the water column, than the production of 2 3 0 Th, the grandparent of Rn, will also be constant with depth. 230Th is adsorbed to particles falling through the water column; so the greater distance a particle travels, the more 230Th is adsorbed. More 230Th adsorbed to particles will produce more 226Ra, producing a higher Rn emanation rate. Also, the accumulation rate should decrease with increasing water depth, so that near-surface sediments at deep sites have had more time for 2 2 6 Ra ingowth. The production rate of mobile Rn (P; dpm/cm3 ) is a function of the Rn emanation rate, porosity, and sediment density. In a closed system, such as deep in the sediment column, the production rate should be equal to the equilibrium activity of mobile~Rn in bulk sediments (XCe q ): P = (l-<j))Eps = XCe q (5) Using a constant emanation rate, the production rate will increase with depth in the core as porosity decreases. Ideally, the shape of the Rn production rate function plotted against depth (P(z)) is identical to the porosity profile. By combining Equation 1 and Equation 5, a production rate function can be generated: R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm ission . 33 P(z) = Pin f + (Po-Pinf)exp(-pz) (6) where, Pin f = production rate at infinite depth (dpm/cm3 ) P0 = production rate of mobile Rn at the sediment-water interface (dpm/cm3 ) p = scale length (cm-1 ) z = vertical spatial co-ordinate, increasing with distance into the sediment (cm) The production rate scale length should be equivalent to the porosity scale length. However, incorporating this production rate function into mathematical models to generate pore water profiles generates complicated equations that are difficult to compute (Appendix D). A linear approximation is a convenient simplification for near surface sediments (see Appendix D): Po ' = production rate of mobile Rn at the sediment-water interface (dpm/cm3 ) P! = slope of Rn production rate vs. depth in core (dpm/cm4 ) To define the production rate function for the models presented in the next section, Equation 6 is used in the radial diffusion model, and Equation 7 is used in the one dimensional non-local exchange model. To generate production rate functions that were as similar as possible (P(z)-P’(z)), the parameters for Equation 6 and Equation 7 were calculated based on a least-squares fit through the production rates of mobile Rn P(z) = P0 +P'z (7) where, R ep ro d u ced with p erm issio n o f th e copyright ow ner. Further reproduction prohibited w ithout p erm ission . 34 calculated using the average porosity of each of the top 4 cm. These values are presented in Table 6 and regressions of the model fits can be found in Appendix D. The linear approximation of the Rn production rate is plotted with the bulk sediment mobile Rn data in Figure 3. All of the Rn samples are deficient relative to the Rn production rate, implying that these near-surface pore waters are not in a closed system. As noted in the Methods section, several tests were made to confirm the accuracy of the Rn emanation rate measurements (Appendix B) and verify that there is not a problem with a loss of Rn through the WCS (Appendix A). Additional sorption during squeezing may account for as much as 25% of the difference between the deep Rn samples and the Rn production rate (Appendix C). None of these appear to independently be the source of the Rn deficiency, leaving exchange with the overlying water column as the Rn sink. R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . ANALYTICAL AND NUMERICAL MODELS 35 Diffusive Rn Model: Random molecular motion, or Brownian motion, can transport a solute through a solution. This process, known as diffusion, will distribute a solute evenly throughout a closed system and is favored thermodynamically because it maximizes the entropy of the system. The molecular diffusion coefficient (Dm ) of a solute is the rate at which diffusion will occur in a free solution. The diffusion coefficient depends on the size and charge of the solute, as well as the temperature, salinity, and to a lesser extent, the pressure of the system. In sediments, diffusion is hindered because a solute must travel around sediment grains. The formal relationship between the diffusion coefficient in free solution and in bulk sediment (Ds) can be expressed as where 0 is the geometric tortuosity, the actual distance a molecule must travel through a porous substance per unit length of that medium (Ullman and Aller, 1982). Ullman and Aller estimate for unlithified marine muds with < j ) > 0.7 that 02 = ( j ) '1 5 to < j ) '2 . Since the porosity of surficial sediment changes rapidly as a function of depth, the effective diffusion coefficient will also change. For this work, the Rn molecular diffusion coefficient (Dm) at 5°C is assumed to be 6.5xl0' 6 cm2 sec' 1 (Jahne et al., 1987), and the tortuosity was estimated as suggested by Ulman and Aller (1982). R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . 36 The mathematical theory of diffusion in isotropic substances in one dimension is based on calculating the diffusive flux, the rate of transfer of a diffusing substance through a unit area of a section. Fick's first law, named after the chemist who first quantified diffusion, is based on the hypothesis that the flux of material is proportional to the concentration gradient measured normal to the section through which diffusion is occurring. The diffusive flux across the sediment-water interface (J) (Fick, 1855; Crank, 1975): where z the spatial coordinate measured normal to interface and increasing with depth in the sediments. The negative sign arises because diffusion occurs in the opposite direction of increasing concentration. From Equation 7, Fick also derived the fundamental differential equation of diffusion in an isotropic medium. Fick's second law describes the change in concentration with time (dC/dt) in one dimension in bulk sediments: In near-surface sediments, the porosity, and thus the effective diffusivity and retardation coefficient, changes rapidly with depth and must also be differentiated. (9) v (10) y R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 37 For Rn, the change in concentration with time is also a function of the production and decay rates. The linear production rate (P’(z)) has been measured, and the decay rate is fc= 2 .1x l 0~6 sec'1 . a c = _ a/D d (c/R )^ dt dzl dz + P -AC (11) To solve Equation 11 analytically, several assumptions must be made. First, the system must be in steady-state, which is defined as no change in the Rn concentration with time. Rn pore water profiles should reach steady-state equilibrium after about two mean Rn lives and express the average effects of pore water transport and reaction in the sediments during this period (Smethie et al., 1981). With such a short time required to achieve equilibrium, pore water profiles should be in steady state unless a perturbing episodic event, such as physical stirring of the sediments by currents, can be identified. Sedimentation that occurs during this time period is negligible. Bioturbation, the physical stirring of the sediments by organisms, happens on the scale of years and should not influence Rn pore water profiles (Huh and Kadko, 1992). The second assumption is to simplify the effects of porosity. The porosity of surficial sediments changes rapidly with depth. Diffusive flux, effective diffusivity, retardation coefficient, and Rn production rate are all dependent on porosity. The most important effect of changing porosity is to change the production rate. This is simplified in near-surface sediments by using a constant emanation rate and assuming a linear increase with depth (Equation 7). Otherwise, the diffusion coefficient and retardation factor are assumed to be constant and are calculated based on the average porosity of the top 4 cm in each core. This will introduce a small amount of R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . 38 uncertainty into the profiles. A numerical model was developed to test the assumption of a linear Rn production rate and a constant porosity (Appendix E). The model results are nearly identical to the analytical solution over the depth range which the WCS pore water samples are collected. A third assumption is to assign two boundary conditions to solve Equation 11. First, the Rn concentration of water in the overlying water column, and thus at the sediment-water interface, is generally negligible relative to the Rn concentration in pore waters, so Co l is set at zero. Second, at an infinite depth, the concentration is equal to the particular solution of the differential equation. For a system with no advection or bio-irrigation, the particular solution is equal to the production rate function and XC(°°) = P(co). When advection is important, the particular solution becomes more complex. The solution to Equation 11 is: The production rate, effective diffusivity and retardation coefficient are known for each core and are presented in Table 3. This data can then be used to generate the diffusive Rn profile, which is plotted in Figure 3. The scaling constant due to diffusion alone is approximately -0.7 cm '1 , and at a depth of 4 cm, the Rn concentration is about 95% of the equilibrium value. The first Rn sample, drawn within the first 0.5 cm, is consistent with the expected concentration for a diffusive Rn profile. Instead of converging on the Rn production rate curve, all deep pore water samples are XC(z) = P 0 + P'z - P 0 exp(az) (12) scaling constant (cm_l) where a R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 39 significantly depleted in Rn. The deepest samples, at about 3 cm in most cores, are between 35% and 45% out of equilibrium. The similarity in the fraction of Rn missing in each core is striking since these cores were collected over a two month period and cover over 1 0 0 0 m of seafloor topography. Diffusive Rn Flux: Rn has proven to be a valuable tool for the intercalibration of the different techniques used for estimating benthic fluxes (Berelson et al., 1987a, 1987c, 1990; Hammond et al., 1996). For this work, since it is a new method for extracting pore waters that is being examined, the measurement from a benthic flux chamber will be used as a standard for the estimates derived from the Rn pore water and production rate profiles. During the Atlantis cruise in July, 1999, a benthic flux chamber developed at the University of Southern California was deployed for 24 hours in soft sediments at Hydrate Ridge South, where no advection was anticipated (Hammond et al., 1999). The Rn flux into this chamber was 50±11 atoms n r 2 sec4 (±1 sigma) (D.E. Hammond, unpublished data). Using Equation 10 and 12, the diffusive Rn flux can be calculated (Table 7). The uncertainty in these flux calculations is estimated to be 30%. The calculated diffusive flux for each core is significantly less than the flux chamber result. Bio-Irrigation Models: To account for mobile Rn profiles that are less than equilibrium and an observed flux that is higher than the diffusive flux, another mechanism must be transporting Rn out of the sediments. Two possibilities are advection and bio- irrigation. Advection could bring high-Rn pore waters closer to the sediment-water interface or draw bottom water into the sediments. Bio-irrigation will exchange pore R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . Reproduced w ith perm ission o f th e copyright owner. Further reproduction prohibited without permission. Table 7: Fluxes (atoms/m2-sec) calculated for each model-derived pore water profile. The negative sign indicates a flux out of the sediments. All fluxes are calculated for the top 5cm of sediments. Water Depth Diffusive Radial Diffusion 1-D NLX Model 1-D NLX Model CORE (Location) (m ) Flux Model No Advection With Advection 22MC (Basin) 1826 -37 ± 1 1 -64 ± 19 -76 ± 23 -137 ± 41 35MC (Slope) 732 -24 ± 7 -50 ± 15 -61 ± 18 -92 ± 28 13MC (HRS) 912 -32 ± 10 -93 ± 28 -95 ± 29 -125 ± 38 143-91 (HRS) 848 -27 ± 8 -60 ± 18 -74 ± 22 -98 ± 29 143-139 (HRS) 826 -33 ± 10 -93 ± 28 -103 ± 31 -127 ± 38 Observed Flux Flux chamber (HRS) 791 -50 ± 11 - P - * O 41 waters with overlying water, reducing Rn concentration in the sediments. These possibilities will be explored in the following sections. Advection and bio-irrigation are transport mechanisms that affect the distribution of Rn in the sediments but cannot be measured directly from a sediment core. However, using mathematical models based on the law of mass conservation to describe the Rn distribution, the effect of these transport mechanisms can be quantified. Starting with the fundamental differential equation for diffusion, terms for the Rn production and decay rates can be included (Equation 11). A term for advection can easily be added to the model. Quantifying bio-irrigation, however, is more complicated. Extensive study has gone into developing models which can characterize the transport of solutes by the pumping of overlying water into the sediments by benthic biota, or bio-irrigation. Pressure differentials across empty U-shaped burrows and a vertically sheared current has also been shown to effectively irrigate the sediments (Vogel and Bretz, 1972; Ray and Aller, 1985; Webster, 1992). These effects will be considered negligible for the following discussion. As a biologically-mediated transport mechanism, bio-irrigation cannot be reduced to fundamental physics, like diffusion and advection. Instead, bio-irrigation must be described empirically. Bio irrigation was first described as enhanced vertical molecular diffusion (Goldhaber et al., 1977; Hammond et al., 1977; Berner, 1980; Martens et al., 1980). "Bio pumping" models treat biologically regulated solute transfer as an advective exchange of water between two well-mixed reservoirs: pore water and overlying water (Hammond and Fuller, 1979; Luedtke and Bender, 1979; McCaffrey et al., 1980; Smethie et al., 1981). R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . 42 After this initial work came two approaches to quantify the effects of bio irrigation. Each of these models will be used to assess the importance of bio-irrigation on these pore water profiles. The first model was developed by Aller in an effort to quantify bio-irrigation based solely on diffusion (1980, 1982). This model simplifies the sea floor as a series of evenly spaced burrows with a symmetric cylinder of sediments surrounding each burrow. In this cylindrical diffusion-reaction model, the burrows are pumped with overlying water, so particles can diffuse either into the burrow or out the top of the cylinder. The second model treats bio-irrigation as a non local exchange rate, grouping the effects of the extensive and complex burrow structure by assuming pore waters are a well-mixed reservoir. Non-local exchange is the exchange of a parcel of water at any depth within the irrigated zone with overlying water at a defined rate (Imboden, 1981). Several workers have followed this approach (Christensen et al., 1984; Emerson et al., 1984; Hammond et al., 1985; Martin, 1985; Martin and Sayles, 1987). Boudreau (1984) presents a proof that the non-local exchange model is a one-dimensional simplification of the two-dimensional radial- diffusion model. For different benthic organisms the depth of bio-irrigation may differ, leading to a decrease in bio-irrigation rates with depth and stopping at some finite depth. Below the irrigated zone, the pore water concentrations approach the equilibrium concentration. But bio-irrigation lumps together the effects of all benthic biota on the sediments, each of which form burrows with different shapes, depths, and flushing rates. This has led to the development of several different techniques to explain the changes in the pore water concentration gradients at the base of the irrigated zone. For example, singular or multiple zones of bio-irrigation have been used (Hammond and Fuller, 1979; Hammond et al., 1985; Benoit et al., 1991). Alternatively, an R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . 4 3 exponentially decreasing non-local exchange parameter has been used (Viel et al., 1991). The rate of bio-irrigation in the top few centimeters is expected to be independent of depth, so a constant non-local exchange rate is used. The boundary condition at the base of the irrigated zone will be explained in each model. Radial Diffusion-Reaction Model: Aller's radial diffusion-reaction model (1980, 1982) idealizes the burrow structure so that the effects of bio-irrigation can be described by an analytical solution to a two dimensional formulation. The conceptual model is that the sediment is inhabited by organisms that dig cylindrical burrows with identical diameters and lengths perpendicular to the sediment-water interface at a regular spacing (Figure 4). Surrounding each burrow is a cylindrical volume of sediments extending outward to half the distance to the next burrow. Each cylinder is called a microenvironment because the average chemical composition in the sediment will be equivalent to the average for one cylinder. If the burrows are spaced sufficiently close together, then a sediment core will collect several of these microenvironments, and the pore water squeezed from the core can be represented by calculating the concentration in one microenvironment. The advantage of this model over others is that it provides a mechanistic analysis of the effects of solute transport by benthic organisms (Matisoff and Wang, 1998). However, burrow structures are still much more complicated than the model assumes, such as horizontal burrowing and U-shaped burrows. In addition, estimating the burrow dimensions and spacing is not a trivial task, and these are rarely measured. The model also assumes that burrows are irrigated fast enough to maintain overlying water concentrations, a consideration that is particularly important because the concentration within the burrow depends on the flushing rate. R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . Figure 4: Cross-sectional diagram o f radial diffusion model. 4 4 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . SEDIMENT 45 The diffusion-reaction equation describing solute distributions within a microenvironment is similar to Equation 11. However, the diffusion equation must be converted to radial co-ordinates. The steady state differential equation, modified from Aller (1980) to include sorption, is: dC __ _ Ds d2C | Ds d dt R d z2 R r dr r | ~ j + Pm + (P 0 ~ f\rf)eMPz) ~XC (13> where, C (z,r,t) = mobile Rn concentration (atoms/cm3 ) z = vertical space coordinate, origin at sediment-water interface, positive axis into sediment (cm) r = radial coordinate measured from cylinder axis (cm) and other variables are as previously defined. A steady state Rn distribution within a microenvironment should be quickly achieved if the burrow spacing is significantly less than the depth of the burrow (Aller, 1980). Porosity, and by default, effective diffusivity and the retardation coefficient, are assumed constant. The Rn production rate increases exponentially to a constant rate at depth. The following set of boundary conditions were placed on each microenvironment, where L is the maximum depth of the burrow, r=0 is the center of the burrow, rj is the radius of the burrow cylinder, and r2 is the half-spacing of the burrows: R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . 46 C(0,r) = <|)RC0i, C(z,rx ) = <j)RCo l dC(z,r2J _ Q (1 4 a ) (14b) dC (L,r) _ 3 (14c) These specify that (a) the burrow is efficiently flushed so that the solute concentration in the burrow is equivalent to bottom water, (b) Rn concentration goes through a maximum or minimum halfway between any two burrows, and (c) there is continuity of solute flux between the bioturbated and underlying sediment zones (Aller, 1980). The concentration gradient at the base of the cylinder is fixed at a constant value, B, and must be estimated or specified from direct measurements. The steady-state (dC/dt = 0) solution to equation 13 is modified from Aller's solution (1980, 1982) in order to account for sorption: C (z.r)= W (C < J + B z+ — YJ U / V S ) rn ..2 rr Ai ) -1 sin(kn z )~ (15) sin(k„z) } where, n = 0 , 1 ,2 ,... kn = (n + 0 .5 J j m C ol~Pm t (-1)"AP , { PiexV(pL)(-l)n + kn] n t k 2 ^ nf ° ' n 2 + k 2 K n K n V P n / U/V,r)= Kx(V/2)h(Vf)+ IyfofJKJVf) R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 47 The function Iv(z) and Kv(z) are the modified Bessel functions of the first and second kind, respectively, of order v. This equation gives the Rn concentration at any point within the microenvironment. However, pore water samples are not collected at a specific point within a microenvironment. Instead, pore water samples represent the average concentration of a finite thickness of a microenvironment. The average Rn concentration ( C ) in thickness zx to z2 of the sediments is given by: This is slightly more rigorous than the C presented by Aller (Equation 4,1980) by including the volume and number of atoms in the void in calculating the average concentration. Assuming that the volume of the void is negligible is reasonable for small r]/r2 ratios and is required to make the one-dimensional approximation to this model presented by Boudreau (1984). A Fortran code was developed to solve Equation 15 and 16 and generate a Rn pore water profile fit to the observed Rn pore water data (Appendix E). The parameters ( j > , E, R, C0 l, Ds, and X are known for each core. The concentration gradient at the bottom of the irrigated zone, B, and the geometry of the burrows had to be estimated. The concentration at the base of the irrigated zone (C(L)) was assumed to be the average of the maximum observed mobile Rn concentration and the Rn production rate. The concentration gradient was adjusted to produce C(L), resulting in B values between 150 and 550 atoms/cm4. The length of the burrow (L) was set at 5 cm for each core. This is the depth required to produce the best fit to the pore water (16) rz2 p n fizz fri 2n\ rdrdz-V 2n\ rd rd z R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 48 data and the flux results and is further discussed below. A burrow radius of 0.05 cm was used to generate each profile, and the burrow spacing was adjusted until the best fit to the Rn pore water data was made. This is the same burrow radius used by Aller (Table 1,1980) and represents the average burrow radius for the tube-dwelling polychaete, Heteromastus filiformis. To generate the same pore water profile after increasing the burrow size, the burrow spacing had to be increased. The sensitivity of the model results to the choice of B and rj are explored in Appendix E. The values used in the radial diffusion model to simulate the pore water profiles, including the burrow separation required to generate the best fit to observed pore water data, are presented in Table 8 . The model-generated pore water profiles are plotted with the mobile Rn pore water data in Figure 5. The model-generated profiles fit the data well. However, the model predicts an increase in the mobile Rn concentration at the base of the irrigated zone that was not observed in the data. Consequently, it does not appear that the base of the irrigated zone was sampled. This model requires that the minimum thickness of the irrigated zone is 5 cm so that diffusion from below has only a minor effect on the Rn concentrations in the top 3 cm. In comparing the burrow separation distances, the three cores at HRS (13MC, 143-91,143-139) require a significantly tighter packing of burrows relative to the two cores not collected at Hydrate Ridge (22MC, 35MC). The larger burrow separation at site 143-91 relative to the other HRS sites may be an artifact. Core 143-91 was sampled at a higher resolution and only about half as deep as the other cores. In the other cores, the Rn concentration below 1.5 cm remains fairly constant, and these deep samples have the greatest impact on the model generated burrow spacing. In core 143- 91, samples below 1.5 cm were not collected. If in core 143-91 the concentration remains constant below 1.5 cm, then the burrow spacing would be reduced. R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . Reproduced w ith perm ission o f th e copyright owner. Further reproduction prohibited without permission. Table 8: Radial diffusion model parameters. Core (location) Variable (U nits) 22MC (Basin) 35MC (S lope) 13MC (HRS) 143-91 (H RS) 143-139 (HRS) porosity < ! > 0 .8 6 5 0 .8 4 3 0 .7 2 2 0 .7 0 7 0 .6 8 9 organic C fraction foe (% ) 2 .8 3 2 .5 9 1.51 1.21 1 .2 8 Prod, rate at inf. depth Pinf (dpm /cm 3)bulk 0 .2 3 8 0 .1 7 5 0 .241 0 .2 1 7 0 .2 6 9 Prod, rate at surface Po (dpm /cm 3)bulk 0 .1 0 5 0 .0 7 6 0 .0 6 0 0 .0 7 2 0 .1 1 0 Prod, rate scaling const. P1 (1 /c m ) 0 .5 2 0 0 .3 8 9 0 .4 7 8 0 .3 2 4 0 .5 8 0 Cone. G radient at bottor B (atom s/cm 4) 1 7 0 2 0 5 5 3 0 2 7 0 5 5 5 Diffusion Coefficient Dm (cm 2/m in) 0 .0 0 0 3 9 0 .0 0 0 3 9 0 .0 0 0 3 9 0 .0 0 0 3 9 0 .0 0 0 3 9 Decay R ate X (1/rnin) 0 .0 0 0 1 2 6 0 .0 0 0 1 2 6 0 .0 0 0 1 2 6 0 .0 0 0 1 2 6 0 .0 0 0 1 2 6 Bottom w ater Cone. c t (a to m s/c m 3 ) 0 .7 9 4 0 .7 9 4 0 .7 9 4 0 .7 9 4 0 .7 9 4 burrow depth L (cm ) 5 5 5 5 5 burrow radius r1 (cm ) 0 .0 5 0 .0 5 0 .0 5 0 .0 5 0 .0 5 burrow half-spacing* r2 (cm ) 1.91 1.58 1.14 1.38 1.14 ‘C alculated b a se d on b est model fit to mobile Rn profile Figure 5: Radial diffusion model fit to mobile Rn data and Rn production rate vs. depth. Solid line is the exponential fit to the calculated Rn production rate. The dashed line is the result of the radial diffusion model. — Rn Production Rate • Mobile Rn Data Radial Diffusion Model dpm/cc)bulk 0.15 0.25 0.05 22MC Basin 0.5 a & 0 3.5 d p m / c c ) b u i k 0.05 0.1 0.15 0.2 0.25 35 MC Slope 0.5 & u 2.5 d p m / c c ) b t i l k 0.3 0.05 0.1 0.15 0.5 s 6 & 0 F-f-H 1 SMC HRS d p m / c c ) b u l k 0.2 0.25 0.3 0.05 o *r 0.5 ? u • a & o 2.5 143-91 HRS d p m / c c ) h u l k 0.25 0.3 0.05 0.15 0 R 0.5 S u a Q , 0 143-139 HRS R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . An accurate porosity measurement is imperative for identifying the depth each sample is derived from, as well as calculating the Rn production rate, effective diffusivity, and retardation coefficient. When splits for porosity measurements are sampled, any voids in the sediment are avoided, so that only the bulk sediment is sampled. If burrows constitute a significant fraction of the sediments, then the porosity measurement may underestimate the combined porosity of bulk sediments and burrows. The ratio of the volume of water in a burrow to the total volume of water in the sediments can be calculated using the burrow and microenvironment dimensions. To test this, the burrow radius was increased to 1 cm and then changing T 2 until a reasonable model fit was made to the data. The burrow radius was increased to maximize the fraction of burrow water in the sediments. The ratio of the volume of burrow water to the total volume of water in the sediments ranges between 0 .1 % and 0.3%. This is a minor fraction of the pore waters and within the uncertainty of the porosity measurement. Burrows should not have a significant affect on the porosity of the sediments. Radial Diffusion Model Flux: The Rn flux calculation based on the radial diffusion model is the sum of the Rn flux into the burrow (Jr) and the Rn flux out the top of the cylinder of sediments (Jz). The sum of these two fluxes is then normalized to the surface area of the top of the cylinder so that the total flux can be compared to other flux measurements: J = (17) A R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . 52 where, RL{ dr RAZ dz 2 ri A r = 2ti^Z Az = n t f - r ? J A( = 7uf This is a slightly more rigorous flux calculation than one presented by Aller (Equation 5; 1980) which assumes that the cross-sectional area of the burrow is negligible compared to the surface area of the cylinder of sediments (r!«r2 ). To calculate the flux for each core, a Fortran code was developed to solve Equation 17 (Appendix E), and the results are presented in Table 7. The same parameters used to generate the pore water profiles (Table 8 ) were used for the flux calculation. The one model parameter that has the poorest constraint is the depth of bio-irrigation, which has a significant influence on the flux calculation (Appendix E). Based on the shape of the pore water profile, a 5 cm minimum depth of bio-irrigation is estimated. Therefore, the calculated fluxes are a lower limit for the flux at each site. The uncertainty in the flux is estimated to be 30% and is based on the uncertainty of the pore water gradient at the sediment-water interface. The calculated flux from each core and the flux chamber result are plotted against water depth in Figure 6 a. Three of the calculated fluxes are within the uncertainty of one another and the flux chamber result. Calculated fluxes at two of the three HRS sites (13MC and 143-139) were larger than the other sites. The low flux at the third HRS site (143-91) is a function of a lower Rn production rate and a larger burrow R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 53 Figure 6 : Model derived fluxes plotted against water depth compared with the flux chamber measurement. Solid line is the HRS flux chamber result at 791 m water depth, and the dotted line is the flux chamber result uncertai. a) Radial diffusion model 600 800 ■§ 1000 a 1200 ® 1400 « 1600 £ 1800 2000 0 5 0 21 0 0 , 150 Flux (atoms m sec' ) J ---- 1 * 1 ‘ 1 ‘ 1 1 - — F----- 7 r ; ------------- i • Flux Chamber ■ - A Near HRS - : ; A Al HRS : - * , ---------------------- . f i l l , , , 1 i i i i i i .i b) One dimensional m odel without advection 600 800 1000 1200 1400 1600 1800 2000 • Flux Chamber A Near HRS A At HRS 5 0 100 Flux (atoms m 2 sec'1 ) 150 c) One-dimensional m odel with advection 600 s a Q 4 B I 800 1000 1200 1400 1600 1800 2000 • Flux Chamber A Near HRS A At HRS 50 100 Flux (atoms m 2 sec'1 ) 150 R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm ission . 54 spacing, which may be a modeling artifact (see above). Since these model generated pore water profiles are a good fit to the data and the model derived fluxes are equivalent or greater than the flux chamber result, significant transport due to advection is not required to enhance the flux. In addition, a limit for the depth of bio irrigation of 5 cm is required in order to fit the pore water profiles while minimizing the Rn flux. One Dimensional Reaction-Transport-Non-Local Exchange Model: The second model to describe the distribution of mobile Rn in the sediments is a one-dimensional reaction-transport model with a non-local exchange term included to quantify of bio- inigation. Included in this model is the effect of sorption and advection: u = pore fluid velocity in direction of z (cm/min) a = non-local exchange rate (m hr1 ) and other variables are as previously defined. In Equation 18, the first term defines the diffusive transport of Rn in pore waters. The second term is for the advective transport of Rn. The fluid velocity, u, is the Darcy velocity, and assumes that the flow occurs through the entire cross section of the material without regard to solids and voids. The velocity of water through the pore spaces, the interstitial velocity, can be calculated as u/(j). The third and fourth terms are for the production and decay of d(CIR)\ d(C/R) H + P-XC- -(C-<t>RCol) (18) R — —— - u— — dz J where, R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . 55 mobile Rn, respectively. The last term is the non-local exchange term between pore waters and the overlying water column. The non-local exchange term includes the combined effects of the burrow density, diffusion into burrows, Rn decay which may occur within the burrow before being flushed, and the rate at which burrows are flushed (Hammond et al., 1985). To solve Equation 18, the same assumptions as used in the diffusion-reaction model presented above are used: steady state, a constant porosity with depth, and a linear increasing production rate (P’). For the boundary conditions, the Rn concentration at the sediment-water interface is still assumed to be negligible (C0i = 0), but the Rn concentration at depth is defined as equal to the particular solution to the differential equation. This is done to simplify solving this complex equation. For a system with no bio-irrigation and no advection, the solution simplifies to Equation 12, and if bio-irrigation is negligible then the concentration at depth will equal to the production rate function. But the interactions between the irrigated zone and a predominantly diffusive system below are ignored. The solution to Equation 18 is: XC (z) = X a . — + X R J P z+ P - u P a + Jfh |l - exp^bzjj (19) where b - u - J i f + 4Z>ia + Xr) = ----- ------ 20 --------- = scaling constant (cm 'l) The total mobile Rn bulk sediment concentration, production rate, effective diffusivity and retardation factor are known for each core and are presented in Table 3 and Table 5. The advection rate (u) and non-local exchange rate (a) can then be quantified by Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 56 treating them as independent variables in least-squares curve fits of Equation 19 to the Rn data. Equation 19 is used to calculate two different pore water profiles. First, advection is considered negligible (u = 0 ), and the non-local exchange parameter is the independent variable for a least-squares fit to the mobile Rn data. The least-squares fits of Equation 19 to the pore water data are presented in Figure 7. By including the non-local exchange term, this model was able to recreate the Rn deficiency observed in each core. The bio-irrigation rate estimate is dependent on the constant concentration at depth, so the greatest source of uncertainty originates in the Rn measurements. Estimates for the non-local exchange rate range between llxlO '7 and 21xl0' 7 sec 1 (Table 9). Of the three cores collected at HRS, 13MC and 143-139 have a similar non-local exchange rate, but 143-91 is less, although not significantly. Core 143-91 was only sampled to a depth of 1.5cm which was not deep enough to measure the constant concentration with depth observed below 1.5cm in the other cores. Without these deeper data points to guide the curve fit, it is likely that the non-local exchange rate is underestimated. The similarity between the radial diffusion profile and the non local exchange profile is discussed below. Second, least-squares fits of Equation 19 to the pore water data with both advection and the non-local exchange parameter as independent variables were generated and are presented in Figure 8 . The values for the non-local exchange parameter and advection for each pore water fit are presented in Table 9. For this model, the non-local exchange rate was slightly higher than the previous model and very similar among the cores, ranging between 22x1 O ' 7 and 26x1 O ' 7 sec1 . The estimated advection rates ranged between 0.2 and 0.5 cm/day out of the sediment, with an uncertainty of approximately 50%. Advection out of the sediments increases the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 57 Figure 7: Non-local exchange without advection model fit to mobile Rn data and Rn production rate vs. depth. Solid line is the linear Rn production rate, and the dashed line is the non-local exchange model result. dpm/cc)bulk ~~o~Rn Production Rate • Mobile Rn Data Non-local exchange w/ no advection model tit d p m / c c ) b u l k 0.2 0.25 0.05 22MC Basin 0.5 3 1.5 ■ 5 & a 2.5 0.25 0.3 0.05 0.15 0 fer 0.5 s {J • a & a 2.5 13MC HRS d p m / c c ) b u l k 0.15 0.2 0.25 0.3 0.05 0.5 I 2.5 143-91 HRS 3.5 d p m /c c ) b u lk d p m /c c ) b u lk 0.25 0.3 0.05 0.1 0.15 35MC Slope s € su O J a 3.5 0.15 0.2 0.25 0.3 0.05 0.5 a C J a V a 143-139 HRS 3.5 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 58 Figure 8 : Non-local exchange with advection model fit to mobile Rn data and Rn production rate vs. depth. Solid line is the Rn production rate, and the dashed line is the non-local exchange with advection model fit. d p m / c c ) b u l k —Rn Production Rate Mobile Rn Data ■ -Est. Diffusive Profile d p m / c c ) b u l k 0.05 0.15 0.2 0.25 0.3 0 te r 22MC Basin a tj, a * a 2.5 0.05 13MC HRS d p m / c c ) h u l k 0.05 0.1 0.15 0.2 0.25 0.3 0.5 a a & a 2.5 143-91 HRS d p m / c c ) b n l k d p m / c c ) b u l k 0.05 0.15 0.2 0.25 3.5MC Slope 0.5 a u a & Q 2.5 0.25 0.05 0.15 0 f v 0 a i w a i 2 143-139 HRS 3 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 9: One-dimensional model-derived non-local exchange and advection rates. Uncertainties are derived from least- squares fit of Equation 19 to mobile Rn data. Core Non-Local Exchange Advection (location) rate (x10-7 sec-1) (cm /day) No Advection 22MC (Basin) 1 1 ± 2 35MC (Slope) 17 ± 3 13MC (HRS) 20 ± 2 143-91 (HRS) 1 7 ± 2 143-139 (HRS) 21 ± 2 With Advection 22MC (Basin) 22 ± 3 -0.5 ± 0.1 35MC (Slope) 26 ± 4 -0.4 ± 0.2 13MC (HRS) 26 ± 3 -0.3 ± 0.1 143-91 (HRS) 26 ± 6 -0.2 ± 0.2 143-139 (HRS) 26 ± 2 -0.2 ± 0.1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6 0 concentration in the uppermost zone, improving the fit to the data for the uppermost sample. The dependence of this parameter on the curvature of the profile within the first centimeter of sediments results in the large uncertainty. Most cores only have two data points in this region, making a more accurate assessment of advection impossible. Comparison of these values with other published results is made in the Discussion section. One Dimensional Model Flux: The total Rn flux for the one-dimensional reaction- transport-non-local exchange model is the sum of the diffusive flux (Equation 7) and the non-local exchange flux: £ R 0 (20) where, v j p . P - uF a + Rk u-— *1 if + 4Dj oc + RK 2D, The diffusive flux is dependent on the effective diffusivity and the concentration gradient at the sediment-water interface, which is influenced by advection. The bio irrigation flux is dependent on the non-local exchange rate and the depth of the zone of bio-irrigation, L. Based on the results of the radial-diffusion model, the thickness of the irrigated zone is set at 5 cm. In addition, the linear production rate used in the one dimensional model does not accurately describe the production rate below 5cm. To calculate the flux for each core, the same parameters used to generate the pore water profiles were used for the flux calculation (Table 3, Table 9). The results are Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6 1 presented in Table 7. The uncertainty in the flux is estimated to be 30%. Figure 6 b plots the non-local exchange flux without advection along with the flux observed from the flux chamber result. Figure 6 c plots the non-local exchange flux with advection along with the observed flux chamber result. In both cases, the one-dimensional model flux significantly over-estimates the flux chamber result. The non-local exchange flux without advection is 2 0 - 1 0 0 % greater, and the non-local exchange flux with advection is 75-150% larger than the flux chamber result. Comparison of the one-dimensional model fluxes to the results from the radial-diffusion model and the possible effects of additional sorption are discussed in the following section. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 62 DISCUSSION Bio-Irrigation Rates: Both the radial diffusion model and the one-dimensional model with no advection estimate greater bio-irrigation rates at Hydrate Ridge than at the surrounding sites. The burrow half-separation distance generated with the radial diffusion model provides a qualitative analysis of bio-irrigation. The burrow spacing at Hydrate Ridge was significantly closer than either the basin (22MC) or on the slope (35MC), which implies more efficient bio-irrigation of the sediments at HRS. These burrow spacings can be compared with those observed in sediments from Mud Bay, South Carolina (Aller, 1980). With the exception of 22MC, the burrow spacings are a factor of two closer. This implies more efficient bio-irrigation at Hydrate Ridge than at Mud Bay. The one-dimensional model with no advection estimated non-local exchange rates that are greater at HRS than at the basin and slope sites. The non-local exchange rate calculated for HRS site 143-91 is believed to be underestimated because of a lack of deep pore water samples (>1.5cm) to guide the model pore water fit. Table 10 compares these non-local exchange rates with literature values for dissolved solute transport in nearshore and estuarine sediments caused by non-diffusive mechanisms, updated from Emerson and co-workers (1984). The rates observed at HRS are higher than many estuarine environments, but comparable with other measurements of bio irrigation found further inshore on the Washington continental shelf. The non-local exchange rates generated with the one-dimensional model with advection are slightly higher than the no advection model and do not show any variability between sites. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 63 Table 10. Literature values for dissolved solute transport in nearshore and estuarine sediments caused by non-diffusive mechanisms. The literature-derived transport parameter was converted to the equvalent non-local term when possible (Emerson et al., 1984). None of the Rn measurements (except this study) have been corrected for the effects of adsorption. A correction would increase calculated results by an estimated 10-30%. Transport Equiv. "non-local" Location ('Author! Tracer Model Coefficient term (xlO '2 s_1) Hudson River (Hammond et al., 1977) 2 2 2 r h mixing 1 2 x 1 0 '5 (cm2 s'1) --- Puget Sound. 200 m (Grandmanis & Murray, 1977) Si(OH)4 non-local 0.5-1.0 San Francisco Bav (Hammond & Fuller, 1979) 2 2 2 Rn* pumping (0-4 cm) 3 cm d" 1 87 Narraeansett Bav (Luedtke & Bender, 1979) 22Na pumping (non-local) 0.04-0.11 d' 1 5-13 Mud Bav. South Carolina (Aller. 19801 Si(OH) 4 NH4 + cylindrical diffusion 13 MERL tanks. RI ("Adler. 1981) 22Na diffusion (0-5 cm) 7x 10' 5 (cm2 s'1) — Washington Continental Shelf CSmethie et al.. 1981) 222Rn pumping (0-5 cm) 0.2-4.4 (cm d'1) 4-100 Washineton Continental sulfate irrigation 0.05-0.8 2-31 Shelf ('Christensen et al., 1984) reduction coefficient (2 - 1 0 cm) (cm'2) Washington Continental Shelf (Christensen et al., 1984) 222Rn irrigation coefficient (2 - 1 0 cm) 0.15-0.55 (cm'2) 5-17 San Francisco Bav (Hammond et al., 1985) 222Rn non-localA 2 - 2 0 Pueet Sound. 15m (Emerson et al., 1984) % Si(QH)4 non-local ” 1-5 Buzzards Bav. MA. 15m (Martin & Sayles, 1987) 222Rn non-local (0-5 cm) — 4-30 Po River Delta. 2m Si(OH) 4 non-local- — 80-500 (Viel et al., 1991) NH4 exponentially 8 - 1 0 PO4 decreasing* 1 0 0 Washineton Continental Shelf and Slope (Archer & Devol, 1992) 0 2 pumping 0 - 1 0 (cm d'1) Santa Catalina Basin. (Archer & Devol, 1992) 0 2 pumping 2-4 (cmd"1) “ Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 64 Table 10 (continued): Location (Author) Buzzards Bav. MA. 15m (Martin & Banta, 1992) Laboratory Test (Matisoff & Wang, 1998) Central California Shelf (Townsend, 1997) Borderland Basins (Townsend, 1997) Los Angeles Harbor (Townsend, 1997) H vdrate Ridge (This Study) Tracer 222Rn Br' 22Na B r B r Br' 222r „ Model non-local (0-5 cm) non-local non-local non-local non-local non-local Transport Coefficient Equiv. "non-local" term 1x10 ~ 7s~l) 3-21 2-29** 6-19 5-197 5-125 14-247 10-21 A Pore waters were modeled with two zones of irrigation. Irrigation rate for sediments between the surface and between 9 and 21cm. *The irrigation rate is in the form a(z) =aQ exp(-a1z). Presented here is a Q . **One core had evidence of extremely rapid irrigation: 2 2 2 xlO 7 sec1 . Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 65 There are several factors that may result in higher bio-irrigation rates at Hydrate Ridge relative to the surrounding region. First, there may be a greater supply of food at Hydrate Ridge. Smethie and co-workers (1981) observed higher bio-irrigation rates on the Washington shelf during the summer than in the winter. He attributed these to increased spring/summer upwelling and suggested that the difference in bio-irrigation depends on the annual cycles of food supply. Cores analyzed in this study were all collected in the summer, precluding this interpretation. Spatial variations in the food supply at the sea floor may be the result of heterogeneous primary productivity in the surface ocean or a focused rain of particulates to the sea floor. For example, upwelling may occur primarily at the shelf break, near HRS, generating greater primary productivity above HRS than further up on the shelf (Site MC35). Greater decay of particulates generated in the surface ocean as it travels through the deeper water column to reach site 22MC, resulting in less organic matter reaching the sea floor. Alternatively, fluid venting provides a local food source at Hydrate Ridge. Fluid seeps supply methane and some nutrients to surficial sediments and supports chemotrophs that increase the quantity of organic matter available in the surrounding environment. A second possibility for higher bio-irrigation rates at Hydrate Ridge may be a greater need to flush water through the burrows. The oxygen minimum zone of the water column bathes Hydrate Ridge. Low concentrations of oxygen in bottom waters may require more frequent burrow flushing at Hydrate Ridge. Or, elevated concentrations of reduced chemical species, like H2 S and methane, as a result of fluid advection would also need to be rapidly expelled from the burrows. Finally, different bio-irrigation rates between the sites may be the result of ecological changes. The primary organism irrigating the sediments at Hydrate Ridge may be an entirely Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6 6 different organism, with a different burrow shape, dimensions, and flushing rate than either the deep basin or the shelf sites. An attempt was made to quantify the radial-diffusion model results as a non-local exchange rate. The pore water profiles generated by the one-dimensional non-local exchange model and the radial diffusion model are indistinguishable near the sediment- water interface. Boudreau (1984) has shown that the one-dimensional model, with a non-local exchange parameter and no advection, is an approximation to the radial- diffusion model. The following relationship was derived to relate the non-local exchange term to the burrow radius and half-spacing: where r is the distance from the center of the burrow to where the concentration is equal to the laterally averaged concentration, C (Boudreau, 1984). The value C has already been calculated for each model run, so Equation 15 can be used to back- calculate r . In Table 11, the non-local exchange rate calculated with the radial-diffusion model parameters is compared to the one-dimensional non-local exchange model with no advection. Qualitatively, the results are similar, where Equation 21 estimates the highest and lowest bio-irrigation rates for the same cores as the one-dimensional non local exchange model. However, the non-local exchange rate calculated with Equation 2 1 is an order of magnitude less than the value estimated with the one-dimensional non-local exchange model. (21) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced w ith perm ission o f th e copyright owner. Further reproduction prohibited without permission. Table 11: Calculated non-local exchange rate based on Boudreau's relationship between the average concentration radius from the radial diffusion model and the non-local exchange rate (Equation 21). Core (location) Burrow radius (r1=cm) Burrow half-spacing (r2=cm) Average concentration radius (cm) Est. Non-local exchange rate (x10-7 sec-1) 1-0 Model Non-local exchange rate (x10-7 sec-1) 22MC (Basin) 0.05 1.91 1.09 0.5 11 35MC (Slope) 0.05 1.58 0.91 0.9 17 13MC (HRS) 0.05 1.14 0.65 1.7 20 143-91 (HRS) 0.05 1.38 0.78 0.9 17 143-139 (HRS) 0.05 1.14 0.65 1.3 21 O N 68 This relationship (Equation 21) breaks down because of an invalid assumption. One step in the derivation of Equation 21 is to expand the laterally averaged concentration into a Taylor Series: 'd & d r ' r = r \ &_C d r 1 J r = r \ 2! (22) To arrive at Equation 21, it is assumed that the second and higher order terms in this series can be neglected. To test this assumption, the laterally averaged concentration at a depth of 2.5 cm in core 143-139 was calculated from Equation 22 both with and without the higher order terms and compared to the radial diffusion model result of C . Solving the higher order differential equations of the solution to the radial diffusion model would be, at best, tedious. Instead, a simple equation with a similar shape was curve-fit to the radial Rn concentration at 2.5cm depth: Cr{r)= Cr{r2){\-exp{-W )) (23) where, Cr(r) = radial mobile Rn concentration (dpm/cm3 ) r| = scaling constant (cm) The derivatives of this equation can readily be calculated and should be similar to those calculated for Equation 15. For core 143-139, the radial diffusion model estimated that the average Rn concentration is 0.115 dpm/cc)bulk, which occurs at r = 0.43 cm, and at this radius, the Taylor Series expansion without the higher order terms is 0.258 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6 9 dpm/cc)bulk. Only after summing 9 of the terms in the series can the solution be found to three significant figures, 0.118 dpm/cc)bulk. This is a good correlation with the radial-diffusion model estimate. Therefore, the assumption that the higher order terms in Equation 22 can be ignored is invalid, and Boudreau's (1984) reduction of the radial-diffusion model to a non-local exchange rate cannot be done for these pore water profiles. Rn Flux: The radial-diffusion model generates a flux that is closest to the flux chamber result. The flux calculated with the radial-diffusion model and the non-local exchange model are expected to be similar. Instead, the one-dimensional model without advection exceeds the radial diffusion model fluxes by 2-20%. Two sources can be identified to account for this discrepancy. First, the exponential production rate function used in the radial-diffusion model consistently estimates a lower production rate at the sediment-water interface than the linear production rate. This reduces the Rn concentration gradient at the sediment water interface, and thus the diffusive flux into bottom waters. In addition, each model has a different boundary condition at the base of the bio-irrigated zone. The radial diffusion model defines a flux through the base of the irrigated zone (B), whereas the one-dimensional model does not. Without the constraint of a Rn flux into the bottom of the irrigated zone, the one-dimensional model generates a profile that is probably unrealistic for the transition zone between bio-irrigated and diffusive sediments and overestimates the Rn deficiency (and therefore the net Rn flux) below the interval sampled. The fluxes calculated for the one-dimensional model with advection are 25-80% greater than the one dimensional model without advection flux and about 2 times larger than the radial diffusion model fluxes. By including advection to the model, both the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 70 diffusive flux and the bio-irrigation fluxes are increased. In order to match the relatively high Rn concentration of the uppermost sample, all of the model fits predict an advection of pore water out of the sediments. This increases the concentration gradient between the sediments and the overlying water column, thereby increasing the diffusive flux. The non-local exchange rate is also increased. Since there will be more Rn near the sediment-water interface, bio-irrigation must occur at a faster rate to generate the same Rn deficiency. The validity of this model is questionable because it significantly overestimates the flux relative to the flux chamber result. Advection: As noted above, the one-dimensional non-local exchange model with advection produces the best model fit to the pore water data, as it best accounts for the concentration of the uppermost data point. It is the curvature of the pore water profile in the top 1 cm that might reflect the presence of advection, and for all of the cores, a significant advective velocity out of the sediments has been calculated. However, several inconsistencies suggest that advection at the rates predicted by this model are highly unlikely. First, at the base of all of the cores (except 22MC) below 15 cm depth was a stiff, low porosity, olive-colored clay. This layer prevented further penetration of the sediment cores and should prevent significant fluid advection from occurring. Second, calculated advection rates are significantly greater than the rates observed with seepage meters deployed at Hydrate Ridge during the same period as the cores were collected (Tryon et al., 1999). Calculated advection rates are expected to be the same order of magnitude as their seepage meters deployed on the periphery of clam beds, where rates between 0.0003 cm/day into and 0.0003 cm/day out of the sediment were observed. Instead, they are similar to the focused advection measured at the center of clam beds that ranged between >0 . 0 2 cm/day downward and 0 . 2 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 71 cm/day upward. But these cores analyzed for Rn were collected from regions where no evidence for focused fluid venting (i.e. presence of vent biota, high methane concentrations) was observed. No vent biota were observed in the video documentation of the collection of cores 143-91 and 143-139. Third, the one dimensional model with advection predicts the largest Rn fluxes out of the sediments. These calculated fluxes significantly over-estimate the flux chamber result. A fourth and final question, is it likely to observe an advection signal in surficial sediments that are pitted with burrow structures? Burrows were observed in all cores, and the radial diffusion model suggests that there is a relatively high density of organisms living in burrows irrigating the sediments. Burrows would "short circuit" the hydraulic pressure gradient that drives advection and act like a miniature artesian well, providing a conduit for advecting water to reach the seafloor. Similarly, the burrow would act as an injection well if pressure gradients force water into the sediments. In both cases, the greatest effect of advection would be observed at the base of the burrows, not at the sediment-water interface. The efficiency of burrows to act as a conduit will depend on the sediment's bulk porosity and the dimensions and density of the burrows. Horizontal and the base of U-shaped burrows would provide the greatest surface area in the sediments and be the most effective conduits. Consequently, observing distributed advection in near surface sediments seems implausible. If the calculated advection rate is incorrect and should be closer to zero, then fault must be found in the data or the model. Identifying the cause focuses on the depth assignment and concentration of the uppermost data point. Identifying which factor is the most important based on this data set is not possible and is most likely a combination of the following explanations. First, some mixing between the first few Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 72 mm of pore water and the supernatant water has been observed, especially for cores with surface topography, resulting in an uncertainty of ±1 mm in the depth (Bender et al., 1987). However, any mixing of supernatant water with pore waters would lower the Rn concentration of the first sample, resulting in a lower estimate of the advective rate. Instead, a mechanism is required to bring high Rn pore waters from depth towards the surface. Second, the pore water depth assignments may be incorrect if the sediment-water interface was identified incorrectly or there is a significant difference in porosity between the porosity profiled core and the squeezed core. An uncertainty of 1 mm in the depth of the first pore water sample has a significant impact on the calculated advection rate, introducing an uncertainty of about 50%, increasing the total error in the advection estimate to about 70% by propagation of errors. To test if there was a consistent error in the depth assignment due to incorrectly identifying the sediment- water interface, each Rn sample was relocated 2 mm deeper and the best fit of Equation 19 was found with advection and non-local exchange as independent variables (Table 12). Pushing the pore water profile deeper into the sediment reduced, but did not eliminate, the advection rate and did not significantly improve the model generated fits. The sediment-water interface may be incorrectly identified if the upper sediments were compacted by 2 mm (enough to improve the fit of the pore water profile to that predicted for a no advection system) before the core was processed, and the Rn profile did not have time to re-adjust. The amount of settling required to move the uppermost sample down about 2 mm can be estimated. The volume of sediments between the sediment-water interface and the uppermost sample remains constant. The porosity can be changed until the desired volume of pore water (and therefore sample depth) is Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 73 Table 12: One dimensional transport-reaction model results before and after Rn profiles are moved 2 mm deeper in sediments. Core Non-Local Exchange Advection Model Fits (location) rate (x10-7 sec-1) (cm /day) (Rsquared) Before (same as Table 9) 22MC (Basin) 22 ± 3 -0.5 ± 0.1 0.986 35MC (Slope) 26 ± 4 -0.4 ± 0.2 0.976 13MC (HRS) 26 ± 3 -0.3 ± 0.1 0.974 143-91 (HRS) 26 ± 6 -0.2 ± 0.2 0.974 143-139 (HRS) 26 ± 2 1 o N > 1 + O 0.991 After profile moved down 2mm 22MC (Basin) 24 ± 3 -0.4 ± 0.1 0.990 35MC (Slope) 24 ± 4 -0.3 ± 0.2 0.981 13MC (HRS) 25 ± 3 -0.3 ± 0.1 0.978 143-91 (HRS) 25 ± 6 -0.2 ± 0.2 0.938 143-139 (HRS) 25 ± 2 -0.2 ± 0.1 0.990 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 13: Decreases in porosity due to settling required to match uppermost pore water sample with the diffusive Rn profile. Core Observed Average Porosity Required Initial Average Porosity 22MC (Basin) 0.901 0.938 35MC (Slope) 0.881 0.929 13MC (HRS) 0.758 0.840 143-91 (HRS) 0.753 0.840 143-139 (HRS) 0.767 0.796 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 75 Table 14: Fraction of deep pore water in uppermost sample required to produce the observed pore water concentration. Core Uppermost sample dpm/L Model upper, sample dpm/L Ave. deep pore water dpm/L Fraction of deep water % 22MC (Basin) 51 33 115 22 35MC (Slope) 29 19 71 19 13MC (HRS) 65 43 127 26 143-91 (HRS) 49 33 90 28 143-139 (HRS) 53 41 148 1 1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 76 achieved. The measured average porosity between the surface and the first sample along with the estimated average porosity required to fit the profile are presented in Table 13. The porosity would need to be reduced between 0.03 and 0.08 in order to generate the observed pore water profiles. This significant change in porosity would only generate a small change in core length, which may not be observable. Third, a spike of Ra in near surface sediments could produce these profiles with bio-irrigation and no advection. Rn emanation rate enrichment in the top 0-5 cm has been observed in San Clemente Basin in the California borderlands, generating a positive Rn anomaly near the sediment water interface (Berelson et al., 1987a). The only cores that had a greater Rn emanation rate in the top 0-1 cm than the 1-2 cm interval were 22MC and 35MC, but these values are not statistically different. Bioturbation is expected to keep the sediments well mixed, destroying any fine lenses of Ra enrichment. A fourth possibility is that there is mixing between deep and shallow pore waters before they are expressed, violating the pipe flow assumption. The fraction of deep water required to increase the initial data points from the modeled "no advection" concentration to the observed concentration can be estimated for each core. To characterize the deep pore waters, the average Rn concentration of the deepest two points in each core was used. These values are presented in Table 14. Between 10- 30% of each first Rn sample would need to be derived from deep pore waters. One possible mechanism to quickly bring deep water to the surface is the use of burrows as conduits. In addition, if the water is preferentially expressed from the area surrounding a burrow, then the high Rn pore water that is radially farthest away from the burrow may not be expressed. The result would be a reduced maximum Rn Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 77 concentration at depth, causing the bio-irrigation rate and flux to be overestimated. This artifact is the most likely cause of the high advection rates calculated. Additional Sorption: In these sediments, a significant fraction of the mobile Rn is sorbed to organic carbon. Neglecting sorption would cause the bio-irrigation and flux rates to be greatly overestimated. However, a high organic carbon fraction may preclude an accurate interpretation of these cores because additional sorption may occur before the pore waters are expressed. The extent of additional sorption was unable to be quantified; however an assessment of its possible effects can be made. Based on the results of the sorption model, a new mobile Rn profile for each core was generated using the following guidelines: a) the concentration of pore water within the top 0.5 cm was not affected by additional sorption, b) samples between 0.5 and 1.4cm are assumed to be 8 % deficient in Rn, and c) samples below 1.4cm are 11% deficient in Rn. The mobile Rn activity concentrations adjusted for additional sorption are listed in Table 15. Core 143-91 was not included in this analysis because sampling did not extend below 1.4 cm. Each model was fit to the adjusted Rn data following the same method as previously outlined. For the radial diffusion model, the new values for the burrow spacing are compared to those previously calculated for the un-adjusted Rn data are presented in Table 16. To account for the additional Rn in the sediments, the burrow half-spacing had to be increased between 10-20%. Larger burrow half-spacing implies less efficient sediment bio-irrigation. The one-dimensional reaction-transport model was fit to the adjusted mobile Rn profiles to estimate the non-local exchange rate both with and without advection. These values, along with the values calculated for the un-adjusted mobile Rn data, are Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 78 Table 15: Bulk sediment mobile Rn and the mobile Rn adjusted for additional sorption. Depth Total Mobile Rn Total Mobile Rn Core (cm) (dpm/cc)bulk (dpm/cc)bulk Pore water Data Additional Adsorption Data 22MC 0.00 0.00010 ± 0.00001 0.0001 ± 0.00001 0.34 0.053 ± 0.010 0.053 ± 0.010 0.77 0.072 ± 0.013 0.078 ± 0.014 1.47 0.109 ± 0.017 0.121 ± 0.019 2.05 0.122 ± 0.020 0.136 ± 0.022 2.55 0.119 ± 0.024 0.133 ± 0.027 35MC 0.00 0.00010 ± 0.00001 0.0001 ± 0.00001 0.30 0.030 + 0.007 0.030 ± 0.007 0.82 0.043 ± 0.006 0.046 ± 0.006 1.40 0.068 ± 0.011 0.076 ± 0.013 1.96 0.075 ± 0.040 0.083 ± 0.044 2.46 0.074 ± 0.025 0.082 ± 0.027 13MC 0.00 0.00009 ± 0.00001 0-00009 ± 0.00001 0.39 0.061 ± 0.010 0.061 ± 0.010 0.88 0.076 ± 0.011 0.083 ± 0.012 1.40 0.113 ± 0.016 0.126 ± 0.017 1.91 0.109 ± 0.015 0.121 ± 0.017 2.44 0.118 ± 0.018 0.130 ± 0.020 2.97 0.116 ± 0.019 0.129 ± 0.022 143-139 0.00 0.00009 ± 0.00001 0.00009 ± 0.00001 0.35 0.048 ± 0.008 0.048 ± 0.008 0.90 0.089 + 0.013 0.096 ± 0.014 1.43 0.109 ± 0.016 0.121 ± 0.018 2.02 0.123 ± 0.020 0.137 ± 0.022 2.56 0.133 ± 0.021 0.148 ± 0.023 3.09 0.126 ± 0.020 0.139 ± 0.022 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 79 presented in Table 17. Increasing the deep pore water Rn concentration reduced the non-local exchange rate with no advection by 25-40%. Including advection as an independent variable, the non-local exchange rate is reduced by 25%. The smaller non-local exchange rate generated with the adjusted data is in agreement with previous work done on the Washington Continental Shelf (Table 9). Changing the pore water concentration at depth did not change the advection rate. Finally, the flux from each of the three models was calculated for each core (Table 18). For all the models, the calculated flux was 10% lower than the previous calculations. This result is slightly closer to the flux observed with the benthic chamber and within the estimated uncertainties of the previous estimate. Therefore, if additional sorption did occur, then it would reduce the calculated non-local exchange rates, but have little influence on the estimated advection rates and Rn flux. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 80 Table 16: Comparison of radial diffusion model burrow half-spacing calculated for mobile Rn data and mobile Rn adjusted for additional sorption. Core (location) Burrow Radius (rD Burrow Half-Spacing (r 2 ) 22MC (Basin) 0.05 Pore water Data 1.91 35MC (Slope) 0.05 1.58 13MC (HRS) 0.05 1.14 143-139 (HRS) 0.05 1.14 22MC (Basin) 0.05 Additional Adsorption Data 2.29 35MC (Slope) 0.05 1.68 13MC (HRS) 0.05 1.26 143-139 (HRS) 0.05 1.26 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced w ith perm ission o f th e copyright owner. Further reproduction p rohibited w ithout permission. Table 17: Comparison of non-local exchange rate and advection rates calculated for mobile Rn data and mobile Rn adjusted for additional sorption. Core (location) Non-Local Exchange Advection Rate (x10-7 sec-1) (cm /day) Non-Local Exchange Advection Rate (x10-7 sec-1) (cm /day) Pore water Data (Same as Table 9) No Advection 22MC (Basin) 1 1 ± 2 35MC (Slope) 17 ± 3 13MC (HRS) 20 ± 2 143-139 (HRS) 21 ± 2 Additional Adsorption Data No Advection 6 ± 2 12 ± 2 1 5 ± 2 1 6 ± 1 With Advection 22MC (Basin) 22 ± 3 -0.5 ± 0.1 35MC (Slope) 26 ± 4 -0.4 ± 0.2 13MC (HRS) 26 ± 3 -0.3 ± 0.1 143-139 (HRS) 26 ± 2 -0.2 ± 0.1 With Advection 1 6 ± 2 -0.4 ± 0.1 20 ± 4 -0.3 ± 0.2 20 ± 2 -0.3 ± 0.1 20 ± 2 -0.2 ± 0.1 0 0 82 Table 18: Comparison of fluxes (atoms/m2-sec) calculated for mobile Rn data and mobile Rn adjusted for additional sorption. Negative values represent a flux out of the sediments. CORE (Location) Pore water Data Additional Adsorption Data Flux Chamber (HRS) 1-DNLX Model No Advection (0-5cm) 22MC (Basin) -76 ± 23 -63 ± 19 35MC (Slope) -61 ± 18 -55 ± 1 7 13MC (HRS) -95 ± 29 -86 ± 26 143-139 (HRS) -103 ± 31 -93 1-D NLX Model ± 28 With Advection (0-5cm) 22MC (Basin) -137 ± 41 -121 ± 36 35MC (Slope) -92 ± 28 -82 ± 25 13MC (HRS) -125 ± 38 -118 ± 35 143-139 (HRS) -127 + 38 -118 ± 35 Radial Diffusion Model Total Flux (0-5cm) 22MC (Basin) -64 ± 1 9 -57 ± 1 7 35MC (Slope) -50 ± 1 5 -47 ± 14 13MC (HRS) -93 ± 28 -84 ± 25 143-139 (HRS) -93 ± 28 -86 ± 26 -50 ± 11 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 83 CONCLUSIONS High-resolution Rn profiles were measured in near-surface pore waters extracted with a whole core squeezer from five cores collected in the vicinity of Hydrate Ridge on the Cascadia Margin. After squeezing, the top three cm of each core was sectioned, and the Rn emanation rate and the fraction of organic carbon in the sediments were measured. This information was used as the parameters in several models that assessed the quality of the WCS Rn pore water profiles, constrained bio-irrigation rates, and determined whether the advective flow of pore fluids could be observed. One flux chamber deployed in the same region as three of the cores provides an independent estimate of the Rn flux to assess model accuracy. Based on a diffusion-reaction model, Rn is expected to increase non-linearly from a negligible concentration at the sediment-water interface to a constant concentration at depth that is equivalent to the Rn production rate. At first glance, these profiles fit this model; the concentration increases to a depth of about 1.5 cm, reaching a concentration that remains constant down to the deepest samples at 3.5 cm. However, once the Rn emanation rate was measured, allowing the Rn production rate and diffusive mobile Rn profile to be calculated, these sediments were found to be greatly depleted in Rn. About 20% of the mobile Rn is generated by the sorption of Rn to organic matter in the sediments. The WCS only samples Rn dissolved in pore waters, but the production rate estimates the total mobile Rn concentration, the sum of the dissolved and sorbed Rn. The fraction of organic carbon in the sediments of each core was measured to assess the importance of sorption of mobile Rn. The two cores collected Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 84 adjacent to HRS (22MC, 35MC) had the highest fractions of organic carbon and were consistent with previous measurements of organic carbon from the Cascadia Margin. The cores collected at HRS had half as much organic carbon. The sites adjacent to HRS also had higher porosities than the HRS sites. The affect of sorption on mobile Rn, calculated as the retardation coefficient, was very similar among the cores. Sorption of Rn to organic carbon in the sediment should sequester about 25% of the mobile Rn. After accounting for sorption, the mobile Rn concentrations were 35-45% deficient with respect to the calculated diffusive Rn pore water profile. To begin, the Rn deficiency was assumed to be the result of sediment bio-irrigation. Bio-irrigation was assessed with two models: ( 1) a radial diffusion-reaction model and (2 ) a one dimensional diffusion-advection-reaction model with a non-local exchange term to account for bio-irrigation. The radial diffusion model requires input data about burrow dimensions that were not collected at Hydrate Ridge and had to be estimated and generates a burrow spacings at each site that can be used as a qualitative estimate of bio-irrigation. Sites adjacent to HRS had the greatest burrow half-spacing, implying the less efficient bio-irrigation relative to HRS. Two scenarios were examined with the one-dimensional diffusion-advection- reaction model with a non-local exchange term to account for bio-irrigation. First, it was assumed that the rate of advection was negligible. Non-local exchange rates ranged between 1 0 -2 1 x l 0 ' 7 se c 1 and are comparable to similar measurements made further inland on the Cascadia Margin (Smethie et al., 1981; Christensen et al., 1984). Second, advection was included as an independent variable along with non-local exchange. This produced slightly larger non-local exchange rates, and the calculated Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 85 advection rates ranged between 0.2-0.5 cm/day out of the sediments. These model results produced the best fit to the mobile Rn data for each core. The diffusive Rn flux, the radial diffusion model generated flux, and the one dimensional model both with and without advection were calculated for each core and compared to the observed flux chamber result of 50 ± 11 atoms n r 2 sec1 . The diffusive flux, calculated from the Rn emanation rate, provides the lower limit for the flux and ranged between 24-37 atoms n r 2 sec1 . The presence of bio-irrigation of the sediments, which will tend to increase the Rn flux out of the sediments, is consistent with the flux chamber result. Fluxes generated with the radial diffusion model were closest to flux chamber result and ranged between 50-93 atoms n r 2 sec1 . The flux calculated for the one-dimensional model without advection was about 1 0 % larger than the radial diffusion model fluxes. The increase in flux is a result of different Rn production rates at the sediment-water interface and different boundary conditions at the base of the irrigated zone. The one-dimensional model flux with advection is 40- 100% greater than the radial diffusion model. Along with the different boundary condition, the higher flux is attributed to a steeper concentration gradient at the surface and increased non-local exchange rates. Alternatively, the Rn deficiency may be the result of a systematic problem when using the WCS to generate pore water profiles in bio-irrigated sediments with a high organic carbon fraction. One problem may be the additional sorption of Rn may occur during the WCS process as pore waters rich in Rn come in contact with sediments originally in equilibrium with low-Rn pore water. Model-derived results estimate that as much as 11% of this deficiency may be caused by an additional sorption of Rn. Calculations were made to assess the sensitivity of results to possible sorption artifacts. The data was adjusted for the estimated effects of additional sorption, and Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 86 the data was re-analyzed. The results provide an estimate of the maximum possible affects of additional Rn sorption during squeezing. For the radial diffusion model, the burrow spacing was increased by 10-20%. The results from the non-local exchange model were more dramatic. The non-local exchange rate was reduced by at least 25%. These values are a better match to previous estimates from the Cascadia Margin and other systems (Table 10). Additional sorption had little to no influence on the estimated Rn flux or advection rate. The model generated advection rates are significantly higher than expected, based on several lines of evidence. First, all of the cores, except 22MC from the deep basin, had a plug of stiff, low porosity clay at the bottom that should have prevented any fluid advection. Second, these advection rates are up to two orders of magnitude greater than advection rates observed with flow meter deployed simultaneously at Hydrate Ridge (Tryon et al., 1999). Third, while the one-dimensional diffusion- advection-reaction model with a non-local exchange term produced the best fit to the data, the calculated fluxes were two to three times greater than the flux chamber result. The model estimated advection rates are incorrect and instead represent a flaw in the whole core squeezing methodology. Several tests were made to remove the advection anomaly. A high Rn production layer in surficial sediments should have been mixed by bioturbation. Adjusting the sediment-water interface had little effect on the calculated advection rate. Possible settling of surficial sediments before squeezing is possible, but seems unlikely. The most likely cause of the higher-than-predicted Rn concentration in the uppermost sample is deeper pore waters mixing with near-surface pore water before they are expressed. Burrows may act as a conduit to allow water to freely reach the surface. This would violate the pipe flow assumption for water squeezed out of the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 87 sediments. To extract accurate Rn pore water profiles with a whole core squeezer, it is best to avoid bio-irrigated sediments with a high fraction of organic carbon. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 88 BIBLIO G RA PH Y Adler, D.M., 1981, Tracer studies in marine microcosms: Transport processes near the sediment-water interface: Ph.D. thesis, Columbia University, NY. Aharoni, S.M., 1997, n-Nylons: Their synthesis, structure, and properties.Wiley, New York. pp. 598. Aller, R.C., 1980, Quantifying solute distributions in the bioturbated zone of marine sediments by defining an average microenvironment: Geochim. Cosmochim. Acta, v.44, 1955-1965. Aller, R.C., 1982, The effects of macrobenthos on chemical properties of marine sediments and overlying water, in McCall, P.J., and Teveez, M.J.S., eds, Animal-Sediment Relationships: Plenum, p. 3-52. Aller, R.C., 1983, The importance of the diffusive permeability of animal burrow linings in determining marine sediment chemistry: J. Mar. Res., v.41, p. 299- 322. Archer, D., and Devol, A., 1992, Benthic oxygen fluxes on the Washington shelf and slope: A comparison of in situ microelectrode and chamber flux measurements: Limnol. Oceanogr., v.37, no. 3, p. 614-629. Barnes, C.A., Duxbury, A.C., and Morse, B.-A., 1972, Circulation and selected properties of the Columbia River effluent at sea, in Prater, A.T., and Alverson, D.L., eds, The Columbia River Estuary and adjacent ocean waters: U. Wash. Press, Seattle, p. 41-80. f Bender, M., Martin, W.R., Hess, J., Sayles, F.L., Ball, L. and Lambert, C., 1987, A whole core squeezer for interfacial pore water sampling: Limnol. Oceanogr., v.32, p. 1214-1225. Benoit, J.M., Torgersen, T., O’Donnell, J., 1991, An advection/diffusion model for “ Rn transport in near-shore sediments inhabited by sedentary polychaetes: Earth Planet. Sci. Lett., v.105, p. 463-473. Berelson, W.M., Hammond, D.E., and Fuller, C., 1982, Radon-222 as a tracer for mixing in the water column and benthic exchange in the southern California borderland: Earth Planet. Sci. Lett., v.61, p. 41-54. Berelson, W.M., Buchholtz, M.R., Hammond, D.E, and Santschi, P.H., 1987a, Radon fluxes measured with the MANOP bottom lander: Deep-Sea Res., v. 34, p. 1209-1228. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 89 Berelson, W.M., Hammond, D.E., and Eaton, A., 1987b, A technique for the rapid extraction of Rn-222 from water samples and a case study, in Graves, B., ed, Radon in groundwater: National Water Well Association, p. 271-281. Berelson, W.M., Hammond, D.E., O'Neill, D., Xu, X.-M., Chin, C., and Zukin, J., 1990, Benthic fluxes and pore water studies from sediments of the central equatorial north Pacific: Nutrient diagenesis: Geochim. Cosmochim. Acta, v.54, p. 3001-3012. Berelson, W.M., Hammond, D.E., and Johnson, J.S., 1987c, Benthic fluxes and the cycling of biogenic silica and carbon in two southern California Borderland Basins: Geochim. Cosmochim. Acta, v.51, p. 1345-1363. Berner, R.A., 1980, Early Diagenesis: Princeton University Press, Princeton, NJ, 291 pp. Boudreau, B.P., 1984, On the equivalence of nonlocal and radial-diffusion models for pore water irrigation: J. Mar. Res., v.42, p. 731-735. Bohrmann, G., Greinert, J., Suess, E., and Torres, M., 1998, Authigenic carbonates from the Cascadia subduction zone and their relation to gas hydrate stability: Geology, v.26, no. 7, p. 647-650. Bohrmann, G., Linke, P., Suess, E., and Pfannkuche, O., 2000, FS SONNE, Cruise report S0143:TECFLUX-I-1999, Honolulu-Astoria-San Diego, June 29-Sept. 6 , 1999: GEOMAR Report, Kiel, Germany, v.93, p. 75-85. Bray, C.J. and Karig, D.E., 1985, Porosity of sediments in accretionary prisms and some implications for dewatering processes: J. Geophys. Res., v.90, p. 768- 778. Broecker, W.S., 1965, The application of natural radon to problems in ocean circulation, in Ichiye, T., ed, Symposium on Diffusion in Oceans and Fresh Waters: Lamont-Doherty Geological Observatory, Palisades, NY, p. 116-145. Carson, B., Yuan, J., Myers, P.B., Jr., and Barnard, W.D., 1974, Initial Deep-Sea Sediment Deformation at the Base of the Washington Continental Slope: A Response to Subduction: Geology, v.2, no. 11 p. 561-564. Carson, B., Suess, E., and Strasser, J.C., 1990, Fluid flow and mass flux determinations at vent sites on the Cascadia margin accretionary prism: J. Geophys. Res., v.95, p. 8891-8897. Carson, B., Erol, S., Paskevich, V., and Holmes, M.L., 1994, Fluid expulsion sites on the Cascadia accretionary prism: Mapping diagenetic deposits with processed GLORIA imagery: J. Geophys. Res., v.99, p. 11959-11969. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 9 0 Christensen, J.P., Devol, A.H., and Smethie, W.M., 1984, Biological enhancement of solute exchange between sediments and bottom water on the Washington continental shelf: Continental Shelf Research v.3, no. 1, p. 9-23. Clever, H.L., 1980, IUPAC solubility data series: Volume 2: Krypton, Xenon, and Radon: Pergamon Press. Colbert, S.L., Hammond, D.E., Heeschen, K., and Torres, M., 1999, Application of radon to study fluid dynamics in the Cascadia Margin [abs]: Eos (Transactions, American Geophysical Union), v.80, no. 46, p. 511. Crank, J., 1975, The Mathematics of Diffusion, Second Edition: Clarendon Press, Oxford, pp. 414. Emerson, S., Jahnke, R., and Heggie, D., 1984, Sediment-water exchange in shallow-water estuarine sediments: J. Mar. Res., v.42, p. 709-730. Fick, A, 1855, Uber Diffusion: Ann. Physik Chemie, v.94, p. 59-86. Goldhaber, M.R., Aller, R.C., Cochran, J.K., Rosenfeld, J.K., Marten, C.S., Berner, R.A., 1977, Sulfate reduction diffusion and bioturbation in Long Island Sound sediments: report of the FOAM group: Am. J. Sci., v.277, p. 193-237. Gross, M.G., McManus, D.A., and Ling, H.-Y., 1967, Continental shelf sedment, north-western United States. J. Sediment. Petrol., v.37, p. 790-795. Gross, M.G., Carey, A.G., Fowler, G.A., and Kulm, L.D., 1972, Distribution of organic carbon in surface sediments, Northeast Pacific Ocean, In: The Columbia River estuary and adjacent ocean waters: Bioenvironmental studies, Eds: A.T. Prater and D.L. Alverson, Univ. Washington, Seattle, p. 254-264. Grandmanis, V. and Murray, J.W., 1977, Nitrification and denitrification in marine sediments from Puget Sound: Limnol. Oceanogr., v.22, p. 804-813. Hammond, D.E., Simpson, H.J., and Mathieu, G., 1977,2 2 2 Radon distribution and transport across the sediment-water interface in the Hudson River Estuary: J. Geophys. Res. v.82, p. 3913-3920. Hammond, D.E. and Fuller, C., 1979, The use of radon-222 to estimate benthic exchange and atmospheric exchange rates in San Francisco Bay, in Conomos, T.J., ed., San Francisco Bay: The Urbanized Estuary: Pacific Div. Amer. Assoc. Adv. Sci., p. 213-230. Hammond, D.E., Fuller, C., Harmon, D., Hartman, B., Korosec, M., Miller, L.G., Rea, R., Warren, S., Berelson, W., and Hager, S. W., 1985, Benthic fluxes in San Francisco Bay: Hydrobiologia, v.129, p. 69-90. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 91 Hammond, D.E., McManus, J., Berelson, W.M., Kilgore, T.E., and Pope, R.H., 1996, Early diagenesis of organic material in equatorial Pacific sediments: Stoichiometry and kinetics: Deep-Sea Res. II, v.43, no. 4-6, p. 1365-1412. Hammond, D.E., McManus, J., Colbert, D., Colbert, S.L., deAngelis, M., Heeschen, K. Kohlbry, S., Meredith, C., Rickert, D., and Torres, M.E., 1999, Diagenesis and benthic exchange in the vicinity of fluid vents in the Cascadia Margin [abs]: Eos (Transactions, American Geophysical Union), v.80, no. 46, p. 529. Henry, P., Foucher, J.-P., LePichon, X., Sibuet, M., Kobayashi, K., Tarits, P., Chamot-Rooke, N., Furuta, T., and Schultheiss, P., 1992, Interpretation of temperature measurements from the Kaiko-Nankai cruise: Modeling of fluid flowin clam colonies: Earth Planet. Sci. Lett., v.109, p. 355-371. Hopkins, T.S., 1971, On the circulation over the Continental shelf off Washingtion: Thesis, U. Washington, Seattle, WA, 204 p. Huh, C.-A., Kadko, D.C., 1992, Marine sediments and sedimentation processes: in Ivanovich, M. and Harmon, R.S., eds., Uranium-series Disequilibrium: Applications to Earth, Marine, and Environmental Sciences: Clarendon Press, Oxford, p. 460-486. Imbodel, D.M., 1981, Tracers and mixing in the aquatic environment: A critical discussion of diffusion models and an introduction into concepts of non-Hckian transport: Thesis, Swiss Federal Institute of Technology, 137 p. Jahne, B., Heintz, G., and Dietrich, W., 1987, Measurement of the diffusion coefficients of sparingly soluble gases in water: J. Geophys. Res., v.92, no. CIO, p. 10767-10776. Kastner, M., Kvenvolden, K.A., Whiticar, J.M., Camerlenghi, A., and Lorenson, T.D., 1995a, Relation between pore fluid chemistry and gas hydrates associated with bottom- simulating reflectors at the Cascadia margin, Sites 889 and 892, in Carson, B., Westbrook, G.K., Musgrave, R.J., and Suess, E., eds, Proc. ODP Sci. Results, v. 146 (part 1): College Station, TX (Ocean Drilling Program), p. 175-190. Kastner, M., Sample, J.C., Whiticar, M.J., Hovland, M., Cragg, B.A., and Parkes, J.R., 1995b, Geochemical evidence for fluid flow and diagenesis at the Cascadia convergent margin, in Carson, B., Westbrook, G.K., Musgrave, R.J., and Suess, E., eds, Proc. ODP Sci. Results, v. 146 (part 1): College Station, TX (Ocean Drilling Program), p. 375-384. Kastner, M., Kvenvolden, K.A., and Lorenson, T.D., 1998, Chemistry, isotopic composition, and origin of a methane-hydrogen sulfide hydrate at the Cascadia subduction zone: Earth and Planet. Sci. Lett., v.156, p. 173-183. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 92 Key, R.M., N.L. Guinasso, Jr., and D.R. Schink, 1979a, Emanation of radon-222 from marine sediments: Mar. Chem., v.7, p. 221-250. Key, R.M., Brewer, R.L., Stockwell, J.H., Guinasso, Jr., N.L., and Schink, D.R., 1979b, Some improved techniques for measuring radon and radium in marine sediments and seawater: Mar. Chem., v.7, p. 251-264. Kulm, L. D. and Fowler, G.A., 1974, Oregon continental margin structure and stratigraphy; a test of the imbricate thrust model, in Burk, C.A. and Drake, C.L., eds, The geology of continental margins: Springer-Verlag, New York, p. 261-233. Kulm L.D., Seuss, E., Moore, J.C., Carson, B., Lewis, B.T., Ritger, S.D., Kadko, D.C., Thornburg, T.M., Embley, R.W., Rugh, W.D., Massoth, G.J., Langseth, M.G., Cochrane, G.R., and Scamman, R.L., 1986, Oregon subduction zone: Venting, fauna, and carbonates: Science, v.231, p. 561-3. Langmuir, D., 1997, Aqueous environmental geochemistry: Prentice Hall, Upper Saddle River, NJ, 600 p. Linke, P., Suess, E., Torres, M., Martens, V., Rugh, W.D., Ziebis, W., and Kulm, L.D., 1994, In situ measurement of fluid flow from cold seeps at active continental margins: Deep-Sea Research, v.41, p. 721-739. Luedtke, N.A. and Bender, M.L., 1979, Tracer study of sediment-water interactions in estuaries: Estuar. Coast. Mar. Sci., v.9, p. 643-651. Mahn, C.L. and Gieskes, J.M., 1999, Pore water chemistry in methane-seep sediments: Some comparitive observations [abs]: Eos (Transactions, American Geophysical Union), v.80, no. 46, p.541. Martens, C.S., Kipphut, G.W., and Klump, J.V., 1980, Sediment-water chemical exchange in the coastal zone traced by in situ radon- 2 2 2 flux measurement: Science, v.208, p. 285-288. Martin, W.R., 1985, Transport of trace metals in nearshore sediments [PhD Thesis]: M.I.T./W.H.O.I., WHOI-85-18. Martin, W.R. and Sayles, F.L., 1987, Seasonal cycles of particle and solute transport processes in nearshore sediments: 222Rn/226Ra and 234Th/238U disequilibrium at a site in Buzzards Bay, MA: Geochim et Cosmochim Acta, v.51, p. 927-943. Martin, W.R. and Banta, G.T., 1992, THe measurement of sediment irrigation rates: A comparison of the Mr- tracer and 222Rn/226Ra disequilibrium techniques: J. Mar. Res., v. 50, p. 125-154. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 9 3 Mathieu, G.G., Biscaye, P.E., Lupton, R.A., and Hammond, D.E., 1988, System for measurement of radon-222 at low levels in natural waters: Health Physics, v.55, p. 989-992. Matisoff, G. and Wang, X., 1998, Solute transport in sediments by freshwater infaunal bioirrigators: Limnol. Oceanogr., v.43, no. 7, p. 1487-1499. McCaffrey, R.J., Meyers, A.C., Davey, E., Morrison, G., Bender, M., Luedtke, N., Cullen, D., Froelich, P., Klinkhammer, G., 1980, The relation between pore water chemistry and benthic fluxes of nutrients and manganese in Narragansett Bay, Rhode Island: Limnol. Oceanogr., v.25, no. 1, p. 31-44. Moore, J.C., Orange, D., and Kulm, L.D., 1990, Interrelationship of fluid venting and structural evolution: Alvin observations from the frontal accretionary prism: J. Geophys. Res., v.95, p. 8795-8808. Ramstedt, E., 1911, Sur la solubilite de l'emanation du radium dans les liquides organiques: Radium, v.8 , p. 253-256. Ray, A J. and Aller, R.C., 1985, Physical irrigation of relict burrows: Implications for sediment chemistry: Mar. Geol., v.62, p. 371-379. Ritger, S., Carson, B., and Suess, E., 1987, Methane-derived authigenic carbonates formed by subduction -induced pore water expulsion along the Oregon/Washington margin: Geol. Soc. Am. Bull., v.98, p. 147-156. Sahling, H., Rickert, D., and Suess, E,, 1999, Faunal community structure along a sulfide gradient: Interrelationship between porewater chemistry and organisms associated with gas hydrates, Oregon subduction zone [abs]: Eos (Transactions, American Geophysical Union), v.80, no. 46, p.510. Schulze, A., 1920, Uber die Loslichkeit der Radiumemanation in organischen Flussigkeiten: Z. Physik. Chem., v.95, p. 257-279. Seely, D. R., Vail, P.R., and Walton, G.G., 1974, Trench slope model, in Burk, C.A. and Drake, C.L., eds., The geology of continental margins: Springer- Verlag, New York, p. 249-260. Silver, E.A., 1972, Pleistocene tectonic accretion of the continental slope off Washington: Mar. Geol., v.13, p. 239-249. Smethie, W.M., Jr., Nittrouer, C.A. and Self, R.F.L., 1981, The use of radon-222 as a tracer of sediment irrigation and mixing on the Washington continental shelf: Mar. Geol., v. 42, p. 173-200. Suess, E. and Bohrmann, G., 1997, FS SONNE, Cruise report SO110:SO-RO (SONNE-ROPOS). Victoria-Kodiak-Victoria. July 9, Aug. 19, 1996: GEOMAR Report, v.59, 1-181 p. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 94 Suess E., Bohrmann, G., vonHuene, R., Linke, P., Wallmann K., Lammers, S., Sahling H., Winckler, G., Lutz, R.A., and Orange, D., 1998, Fluid venting in the eastern Aleutian subduction zone: J. Geophys. Res., v.103, p. 2597-2614. Suess, E., Torres, M., Bohrmann, G., Collier, R.W., Greinert, J., Linke, P., Rehder, G., Trehu, A., Wallmann, K., Winckler, G., and Zuleger, E., 1999, Gas hydrate destabilization: Enhanced dewatering, benthic material turnover and large methane plumes at the Cascadia convergent margin: Earth Planet. Sci. Lett., v.170, p. 1-15. Torres, M, Brown, K., Collier, R.W., deAngelis, M., Hammond, D., McManus, J., Rehder, G., and Trehu, A., 1998, Geochemical observations on Hydrate Ridge, Cascadia Margin, during R/V BROWN-ROPOS cruise, August, 1998. TECFLUX 1998. Oregon State University Data Report 171. Reference 98-4. 1- 47 p. Torres M, Bohrmann, G., Brown, K., deAngelis, M., Hammond, D., Khnkhammer, G., McManus, J., Suess, E., and Trehu, A., 1999, Geochemical observations on Hydrate Ridge, Cascadia Margin, July 1999. R/V ATLANTIS, Cruise Report AT3-35b. TECFLUX 1999. Oregon State University Data Report 174. Reference 99-3. 1-88 p. Townsend, T.H., 1997, Numerical simulations of tracer loss from benthic chambers : An investigation of bio-irrigation rates and patterns in marine sediments (Masters Thesis): University of Southern California, Los Angeles, 173 p. Try on, M.D., Brown, K.M., Torres, M.E., Trehu, A.M., McManus, J., and Collier, R.W., 1999, Measurements of transience and downward fluid flow near episodic methane gas vents, Hydrate Ridge, Cascadia: Geology, v.27, no. 12, p. 1075-1078. Ullman, W.J. and Aller, R.C., 1982, Diffusion coefficients in nearshore marine sediments:Limnol. Oceanogr., v.27, no. 3, p. 552-556. Viel, M., Barbanti, A., Langone, L., Buffoni, G., Paltrinieri, D., and Rosso, G., 1991, Nutrient profiles in the pore water of a deltaic lagoon: Methodological considerations and evaluation of benthic fluxes: Estuarine, Coastal, and Shelf Sci., v.33, p. 361-382. Vogel, S. and Bretz, W.L., 1972, Interfacial organisms: Passive ventilation in the velocity gradient: Science, v.175, p. 210-212. Wallmann, K., Linke, P., Suess, E., Bohrmann, G., Sahling, H., Schluter, M., Dahlmann, A., Lammers, S., Greinert, J., and von Mirbach, N., 1997, Quantifying fluid flow, solute mixing, and biogeochemical turnover at cold vents of the eastern Aleutian subduction zone: Geochemica et Cosmochemica Acta, v. 61, p- 5209-5219. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 95 Webster, I.T., 1992, Wave enhancement of solute exchange within empty burrows: Limnol. Oceanogr., v.37, n.3, p. 630-643. Whiticar, M.J., Hovland, M., Kastner, M., and Sample, J.C., 1995, Organic geochemistry of gases, fluids, and hydrates at the Cascadia accretionary Margin: Proc. ODP Sci. Results, v. 146(pt.l), College Station, TX (Ocean Drilling Program) p. 385-397. Wong, C.S., Chin, Y.-P., and Gschwend, P.M., 1992, Sorption of radon-222 to natural sediments: Geochemica et Cosmochemica Acta, v. 56, p. 3923-3932. Wright, J.R. and Smith, O.F., 1915, The variation with meteorological conditions of the amount of radium emanation in the atmosphere, in the soil gas, and in the air exhaled from the surface of the ground, at Manila: Phys. Rev., v.5, p. 459-482. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 9 6 APPENDIX A: WHOLE CORE SQUEEZER EXPERIMENTS Loss of Rn through Nylon Tubing: Rn is known to be readily soluble in organic solvents and to adsorb to charcoal and organic matter in sediments (Ramstedt, 1911; Schulze, 1920; Wright and Smith, 1915; Wong et al., 1992). In addition, certain polymers, such as the Tygon and silicone tubing, are known to allow gasses to readily diffuse through them. Because of their versatility, small pieces of both Tygon and silicone tubing were used as connectors in the WCS set-up. The primary tubing used in the WCS apparatus was Nylaflow, a brand name tubing made of nylon-6 . Nylon-n is an aliphatic polyamide made exclusively from (D-amino acids (AB monomers), with the n standing for the number of main-chain carbon atoms contributed by each monomer (Aharoni, 1997). These polymers are present at ambient temperatures in a semi-crystalline state and have main-chains of carbons that are sufficiently flexible to be capable of tightly bending, twisting, folding, and generating loops. Both nylon- 6 and nylon-11 tubing are available for sale, with nylon-11 advertised as more flexible than nylon-6 . Nylon- 6 has achieved the widest commercial use of all the nylons manufactured because it is inexpensive to make and has a broad range of useful properties at normal use temperatures. Nylon-11 was first synthesized in 1931, 4 years before the Nylon was coined by the E.I. DuPont de Nemours Corporation, and today, at a list price about twice that of nylon-6 , holds about 2% of the total U.S. nylon production (Aharoni, 1997). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 97 The absorption of water and/or non-polar solvents, like Rn, by nylon could affect the Rn concentrations during the WGS process. Water is incorporated into the amorphous part of the nylon, which is a function of the degree of crystallization for an individual nylon. The degree of crystallization generally increases as the monomer carbon chain increases. When saturated at room temperature, nylon- 6 absorbs between 8.5-10.9% water by weight, significantly more water than nylon-11 at 1.6-2.2% (Aharoni, 1997). The 11-carbon alcane in the nylon-11 monomer along with the crystal structure allows non-polar solvents to be readily absorbed. When immersed in a non-polar solvent, both nylons are insoluble, but nylon- 1 1 swells much more than nylon- 6 (Aharoni, 1997). Therefore, when using nylon-6 , the Rn concentration could increase as water is absorbed. When using nylon-11, the Rn concentration could decrease as Rn is absorbed. The importance of the loss of Rn through the nylon tubing was tested by a series of experiments. The first experiment tested whether Rn is lost when stored in different types and thicknesses of nylon. Three nylon tubes with the same outer diameter (3/8 inch) but with different wall thicknesses, 0.03, 0.05, and 0.07 inches, were tested. The tube with a wall thickness of 0.05 in. was made of nylon-11 while the other two were nylon-6 . The three tubes, each approximately 12 feet long, were flushed in series with tap water for approximately 1 0 minutes before being sealed. Tap water was sampled before entering the tubes and at the end to account for any loss of Rn while the lines were filled. The three tubes then sat for 4 hours at room temperature before the water was extracted. All water samples were analyzed by RRES. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 98 Figure A l: Rn concentration normalized to the initial tap water concentration for each nylon tubing and WCS experiment. Solid line is Ctap/Ctap, and the dashed line is the uncertainty in the tap water measurement. a) Normalized Rn conc. in 3/8" OD nylon tubing stored for 4 hours at room temperature 1.2 : .-cr, 0.03 0.072 0.05 Wall Thickness (inches) b) Normalized Rn conc. in 1/8" nylon tubing after 1,2,3 hours 1.4 1.2 1 a 0.8 3 y 0.6 0.4 0.2 0 1 2 3 Hours in Line c) Normalized mock-WCS Rn concentrations at different flow rates Flow Rate (ml/rain) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 9 9 The tap water samples from the beginning and end of the line were indistinguishable (23.9±0.7 dpm/L). Their average was then used to normalize the other data. The two tubes made of nylon- 6 had Rn concentrations that were within the counting uncertainty of the initial tap water (Figure Ala). The nylon-11 lost approximately 27% of its Rn in 4 hours, which corresponds to an effective half-life for Rn in this type of tubing of about 9 hours. The Rn in solution is most likely absorbed by the nylon-11. Nylon- 6 does not appear to sorb or allow Rn to diffuse through. The second experiment was designed to further test the ability of nylon- 6 to prevent the loss of Rn. 100 feet of 0.125 in. OD nylon- 6 tubing with a slightly thinner wall thickness than the Nylaflow used in the WCS was flushed with tap water (~ 1 OOml/minute) for about 10 minutes. Before sealing the tubing, tap water was sampled before entering and at the end of the line to account for any loss of Rn while the line was filled. The tubing was then stored in a refrigerator. Samples (25 ml each) were drawn from the front of the line (i.e. where the tap water entered the line) after 1, 2, and 3 hours. Water leaving the line was not significantly depleted in Rn, so, the average of inlet and exit water was used to normalize the data (20.5±0.7 dpm/L). Again, none of these samples were depleted in Rn relative to the initial tap water, and may even be enriched due to water absorbtion by nylon (Figure Alb). For the last test, a mock-WCS was constructed. For a Rn water source, 20 L of tap water was prepared and refrigerated for six hours. The bottle was then stored on ice during the experiment. The line out (a 3/8" OD nylon tubing that did not show any absorption during previous experiments) fed into another cooler chilled with ice with the mock-WCS line suspended above the ice. This kept the air temperature Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 100 around WCS set-up at approximately cold-room temperatures. At the end of the large-diameter nylon feeder line, a three-way valve connected the mock-WCS and a sampling port to obtain the initial Rn. The mock WCS was identical in geometry and sequence to the WCS tubing assembly; 0.125 inch OD Nylaflow is connected together with small pieces of Tygon and silicon to a flow-through oxygen electrode, a 0.4 pm filter, and finally a collection syringe. All samples were normalized to samples drawn at the 3-way connector at the beginning and end of the experiment to obtain the initial Rn concentration. Water from the reservoir was allowed to flow through the mock-WCS for 10 minutes at a flow rate of about 20 ml/minute. Two samples were drawn at 1 ml/min and one at 2 ml/min from the mock-WCS. Again, there was no noticeable loss of Rn for samples drawn at either an 1 or 2 ml/min flow rate (14.5±1.1 dpm/L) (Figure Ale). The error bars are larger during this trial relative to the last two because of a larger spread of initial Rn sample concentrations. There does not appear to be any appreciable loss of Rn from the tubing leading from the WCS out to the sampling port. Variations in the tap water or possibly by a decrease in the water volume as it is absorbed by nylon- 6 may result in a Rn enrichment of as much as 10%. The effect of a loss of water in the WCS samples is assumed to be negligible. Before squeezing, the WCS line was full of water for at least 45 minutes, providing time for the water to be absorbed into the nylon before the samples were drawn. These tests confirm that Rn is not lost through the Nylaflow used in the WCS. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 101 APPENDIX B: ESTIMATING THE SLURRY EFFECT Introduction: The Rn emanation rate was measured using a slurry technique (Hammond and Fuller, 1979; Key et al., 1979a; Mathieu et al., 1988). The slurry technique has been shown to overestimate the Rn emanation rate by 10-20% (Key et al., 1979b; Smethie et al., 1981). Excess Rn has been attributed to the increased porosity of the slurry over the original sediment, which allows a larger fraction of the Rn produced to enter the pore fluids (Hammond and Fuller, 1979). Berelson and coworkers (1982) tested this hypothesis on a series of samples from the California borderland basins and found the average increase in Rn from slurrying was 13.0± 7.7% for these cores. This estimate was modified to 7.8±5.5% for sediments in the upper 8 cm of sediment, increasing to 13.3±10.1% for samples below 8 cm (Berelson et ah, 1987a). The estimate for the upper 8 cm is used throughout this work. Isolating saturated sediments with a known porosity in ajar and allowing the Rn to grow into equilibrium may also assess the slurry effect. The Rn concentration in the gas phase will depend on the sediment's emanation rate. By measuring the Rn concentration in the head space gas, an estimated emanation rate can be calculated. The estimated emanation rate should be equivalent to the observed emanation rate after accounting for the slurry effect. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure Bl: Schematic diagram of the distribution of Rn in the slurry effect experiment. Rn concentration increases to the right. [Rn] -► Gas ■ 5 Boundary Layer Sedim ents . y . . . y ; . • * * . • * * . ■ . * . • / . ■ . * . • / . • / . • / . * . * • - \ ■ v \ * . L ’ ■ • • . ■ . .•. .• ..■ . . % .•. . ■ . . ■ . * \ • * . • * . . ■ ■ . . • v . • v \.. * ■ . * ■ . * ■ . • • . * ■ • . ■ • . * ■ ; ■ : * • , * « . * * . • * . • * * . • ’ * . • * * . • * % ■ * • . • * ■ . ■ * * . * ■ * . • * . • * . * • * ’ , ■ » •,, * V ' * . * * * " . * • " * . * • * . * « * . „ • . * • • . • . ■ • • . * * • . * ■ ■ . • . * ■ . * ■ ■ . • ■ . * • . * . ■ . • . * . * & . * . • . * * • . * . * . * . • ■ * . ' . % • * • . • • . * ■ . • . * . ’ . I * . '. * . * ■ ” / ■ - . * • • . . * . • • • . • • * . • • • . * % * ■ • . • ■ . ■ * * . * * . * • . * . * . * . . • . * * ■ . • ■ ■ . ■ * • . • * • . * ■ - . ■ ■ ■ . • ; * . * , • . * . • . * . • . v . * . • . * . • . * . * . * . • -v Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 0 3 Methods: About 250 g of wet mud collected at Hydrate Ridge was weighed out and placed in a 550 ml straight-walled jar. A second jar was prepared as a regular slurry in order to measure the Rn emanation rate of these sediments. A split of the mud was taken to assess the volume of water in each sample. As these samples settled, a thin layer of water appeared at the surface (<0.5 cm). Porosity ( ( ( > ) of the mud was 0.50 and was calculated from the known volume of water, minus the volume of overlying water, and the volume of dry sediments. The fraction of organic carbon was 1.3%. Jars were fit with a rubber stopper at the top, with two holes for an inlet and an outlet. The jar gas was sampled by attaching an evacuated 2-L acid bottle to the outlet and two 2-L acid bottles full of helium to the inlet. The evacuated acid bottle was then slowly opened in order to keep the pressure in the jar at atmospheric pressure. The Rn in the gas sample was then extracted using a standard charcoal stripping method. Mathematical Models: The distribution of Rn in a jar can be quantified based on mass balance considerations and dividing the system into three layers: sediments that produce Rn, a boundary layer of Ra-free water characterized by diffusive transport, and a well mixed gas phase (Figure Bl). The dynamics of Rn in the sediment, between the base (at a depth zs=Ls) and the sediment-water interface (zs=0), will be dominated by diffusion and reaction: | r = 0 =:i r f j - ^ C + P (Bl) dt R Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 104 where, C = concentration of mobile Rn (atoms/cm3 of bulk sediment) t =time zs = depth in the sediments (cm) BC — = change in mobile Rn concentration with time 3/ Ds = Dm/02 - effective diffusivity of Rn at room temperature (cm 2 sec4) Dm = molecular diffusivity of Rn at room temperature (cm' 2 sec4) 0 2 = tortuosity X = decay constant for Rn (min'l) P = Eps(l-<j)) = Rn production rate (dpm/cm3 of bulk sediment) E= Rn emanation rate (dpm/g dry sediment) ps = sediment density = 2 . 6 g/cm3 R = retardation coefficient In this equation, the first term defines the diffusive flux of material, the second term is for the decay rate of Rn, and the third term is the production rate function of Rn. By defining C(zs ) and P in terms of bulk sediment, the porosity does not appear. Rn generated in the sediments diffuses up through the boundary layer of water and into the gas phase. The distribution of Rn in this boundary layer, from the gas-water interface to the sediment-water interface at (zw =Lw ), can be described by the following equation: P l f n pi2/” E ht = 0 = ^ l1 ± ^ -X C (B2) df R d 4 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 0 5 where Cw is the Rn concentration in the water. Equation B2 is similar to the Equation B l except that in the absence of solids, R=1 and P=0. Rn that diffuses through the water layer is available for the gas phase. The gas phase has a length of Lg and is assumed to be well mixed and have a homogeneous Rn concentration. The concentration in the gas phase, Cg, will be proportional to the Rn concentration at the gas-water boundary, as stated by Henry's Law. To solve these equations, a constant porosity and diffusivity constant is assumed. The general solutions for Equation B l and B2, respectively, are: where Ai, A2 , Bi, and B2 are all constants, and a = (AR/DS) 0 -5 and b = (A/Dm)0- 5. Each constant can be solved by assigning a series of boundary conditions: P (B5a) (B5c) (B5b) (B5d) (B5e) R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 106 Assuming steady state has been attained and the jar is a closed system, these conditions state that (a) the Rn concentration reaches a maximum at the base of the mud, (b) the Rn concentration at the top of the mud is equal to the concentration in the boundary layer water, (c) the Rn flux into the boundary layer is equal to the flux out of the sediments, (d) the concentration of water at the water-gas interface is proportional to the Rn concentration in the gas phase by the dimensionless Henry's Law constant, H= 3.98 for Rn at room temperature (Clever, 1980), and (e) the total Rn concentration in the jar is equal to the total production rate in the sediments, and A is the cross-sectional area of the jar. Using the first four boundary conditions, the four constants can be calculated: A = 4 ^ ' — v 4 H -R 1[ e b L '* - e K j P X l + e P eb L ” C g < j )Pk H \ - e 7-aL, l + e‘ . 2 at. w m c g a D J f \~ e ‘ . 2 aL , (B6 a) (B6 b) (B6 c) (B6 d) (l + ^ ) / + aD' Using the fifth boundary condition and the relationship, P= Eps( l-< ()), the emanation rate can be calculated: R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 1 0 7 Table B l: Slurry effect experiment summary. Slurry Effect Emanation Rate Predicted Emanation Observed (dpm/g) Rate (dpm/g) 0% 0.263 ± 0.013 0.26 7.8%* 0.242 ± 0.012 13%** 0.228 ± 0.011 * Berelson et al., 1987 ** Berelson et al., 1982 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 1 0 8 A k c \ X N +---- s - g H {e 2 a £ ‘ + l) f W ,1 ^ ^ + \a e w y I b ) + i i ( e2 a £ ’ - l {e2 a £ '+ l j 1 e “- ] + k . - 4 If the dimensions of the chamber (including the sediment, gas, and fluid heights), the mass of sediment, and the activity of the gas phase (A ,N g ) are known, then Equation B7 can be solved to calculate the emanation rate. In Table 1, these parameters are presented, along with the calculated emanation rate and the emanation rate measured with the slurry method. Discussion: The head-space gas from one jar was measured and the emanation rate was measured on a split of this mud. The measured head-space gas was then used to compute the (Table Bl). The observed head-space Rn activity with the head-space gas activity -predicted without a slurry effect correction. This result is a bit of a surprise, and does not definitively prove that the slurry effect should be considered negligible. First, A small amount of mud (<lg) was on the side of the jar, not in the slurry at the bottom. However, >15g of sediment would be required to account for the observed Rn head-space gas concentrations. Second, The mud was well-stirred was in the jar. Therefore the porosity may have been similar to that of the slurry. Or, while the mud appears well-mixed, some grading may have occurred, and a greater portion of fine-grained material may have ended up near the surface. The emanation rate of finer particles is expected to be greater than coarser grains because of the increased surface area of the material. This may have elevated the concentration of Rn near the surface, increasing the concentration in the R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 109 gas phase. Third, if the overlying water were convecting instead of remaining stagnant, then the concentration at the water-gas boundary would be underestimated. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 110 APPENDIX C: THE SORPTION BOX MODEL SUMMARY Introduction: A fraction of the mobile Rn will sorb to organic matter in the sediments. Samples from the WCS represent pore water concentrations; the total mobile Rn concentration can then be calculated if the porosity and the fraction of organic carbon in the sediments is known (Equation 4). However, an additional loss of Rn may occur due to a chromatographic effect unique to the WCS process. As deep, high Rn pore water is squeezed upward, it encounters sediments that were initially in equilibrium with low Rn pore water. In order to maintain sorption equilibrium, a fraction of the Rn from deep samples may be lost to low Rn sediments. How much Rn is lost by this process will depend on the concentration of organic carbon in the sediments, the distribution coefficient, and if equilibrium is reached. Model Concept. A one-dimensional multi-box model was constructed that simulates the additional sorption of Rn as a parcel of water moves from depth to the surface where it is collected as a WCS sample (Figure Cl). The model works as follows. The sediment column is divided into a series of boxes with depth, with the boundaries of each box chosen so that the volume of water in each box is identical. A diffusive Rn profile is used to define the initial Rn pore water concentration in each box, calculated assuming the pore waters are in equilibrium with the solid phase. To simulate squeezing, the water is translated one box upward and allowed to Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. I l l re-equilibrate with the solids. After equilibrating, the water in the box at the top of the sediment column leaves the system and represents the WCS sampled water. The model is finished when the water in the deepest box has been moved out of the top box. Diffusion, production and decay of Rn are negligible during the time it takes to squeeze a core, and these processes are not incorporated into this model. The critical aspect is to calculate the quantity of solids that can exchange with pore fluids, and the history of their interaction with pore fluids. This will be independent of any assumptions about compaction during the squeezing process. This model assesses the greatest loss of Rn by assuming the pore waters come in contact and equilibrate with all of the organic carbon in the sediments before being expressed. However, this may not be realistic, and the model will provide an upper limit for the loss of pore water Rn. This model assumes that equilibrium between the sediments and the pore waters is achieved at all depths before the water is expressed. Sorption equilibrium should be achieved in about 15 minutes at room temperature (Wong et al., 1992), which is less than the 60-90 minutes required to squeeze a core. The time a sample is in contact with low Rn sediments is dependent on its depth in the core. For example, waters from surficial sediments high in porosity are quickly expelled, while deep water is expelled more slowly since it has a greater distance to travel and must flow through compressed surficial sediments. Therefore, the rapid extraction of the first Rn sample drawn may not allow time for sorption to occur. Deeper samples are in contact with relatively low Rn sediments for longer periods of time and may approach sorption equilibrium more closely. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 1 2 Figure Cl: Schematic diagram of sorption model. For each step, water is moved up one box and equilibrates with the sediments. Modeled WCS ^ Result J Water - Sedimen STEP 1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 113 Equations. The physical and chemical parameters were taken from the data collected for each core. The model divides the sediments into 18 boxes, each containing 10 ml of pore water (Vw). This is approximately the volume of water in 2 mm of bulk datum is taken as the sediment water interface, and z increases with depth in the sediments. The boxes are numbered sequentially with depth (i= 1,2,... 18), with the top of the first box located at the sediment water interface (ai= 0 cm). The thickness, ai+i-aj, and average depth of each box is dependent on the porosity profile. The thickness of each box, ai+i-aj was found by solving the following equation and for each box: 2 sediment (cores had A=70 cm and (j)~ 0.80 near the sediment-water interface). The (Cl) a i The average porosity assigned to each box was determined: (C2) Finally, the total volume in each box is calculated: y . v . = (C3) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 114 The concentration of organic carbon and the retardation coefficient, R, had to be calculated for each box using Equation 4. The fraction of organic carbon in the solid phase was constant, but each box had a different porosity and thus a different R. Plugging the Rn production rate for each core into Equation 12 and assuming a purely diffusive system generated the initial mobile Rn pore water profile. The average concentration for each box was then found by applying the Mean Value Theorem to Equation 12 over the depth range of each box. The new concentration of mobile Rn in box i after each step of the model is the sum of atoms in pore waters and adsorbed divided by the total volume of the box. Using Equation 4 to differentiate between the pore water and adsorbed phases, the new pore water concentration in box i (Cfw) can be calculated: (c4) By calculating each step in terms of the pore water concentration, the volume of pore water, a constant, drops out of the equation. The pore water concentration in water expressed by the WCS is the concentration calculated in the top box, ( ? w V Observations and Comparison: Because Rn concentration increases with depth, the pore water moving up in each interval of the model has a concentration exceeding that established by equilibrium with the previous water. Consequently, solids adsorb additional Rn and reduce pore water concentrations. The data from core 13MC is used to illustrate profiles predicted for various solid phase organic carbon fractions (Figure C2). None of these profiles simulate the WCS Rn profile accurately. In the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 115 pore water data, there is almost no sorption in the surficial sediments, consistent with an organic carbon fraction of 0 %, while the deepest sample requires an organic carbon fraction of 10%. At 1.5%, the organic carbon fraction measured in core 13MC, sorption during squeezing can only explain about 10% of the Rn pore water deficiency at depth. Similar results were found when modeling the other cores (Figure C3). If the first 0.6 cm of pore water is expressed with no sorption occuring, and the deeper samples are translated upward 0 . 6 cm before sorption occurs, then the surficial organic carbon will have a greater capacity to sorb Rn as deeper samples flow through these sediments. The concentration of sorbed Rn in this part of the core may be less than the model predicts, resulting in more sorption of Rn from the deep samples. To explore this possibility, the model was slightly altered to reflect no sorption while the water moved up three boxes (approximately 0 . 6 cm) before sorption occurred. The result of this model is nearly identical to the previous model because there is still sufficient Rn in the sediments to saturate the organic carbon. The additional sorption of Rn accounts for at best 25% of the total Rn deficiency in each core. The actual importance of additional sorption is probably less than this because sorption equilibrium may not be achieved. Since additional sorption is not the principal source of the Rn deficiency and cannot be quantified, it was assumed to be negligible. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. D epth (cm) 1 1 6 Figure C2: Sorption model for core 13MC for various fractions of organic carbon. Circles indicate observed mobile Rn, calculated for the observed foe of 1.5%. The solid line indicates mobile Rn production rate, and broken lines indicate calculated mobile Rn concentrations at various fractions of organic carbon. Mobile Rn decreases with increased foe as a result of additional sorption to the sediments. 0 13MC 1.5% OC .5 1 .5 2 5 0% foe 1.5% foe 6% foe 10% foe 3 5 0.05 0.15 0.2 0.25 dpm/cc)bulk Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 1 7 Figure C3: Sorption model results. Solid line is the Rn production rate. Dotted line is the estimated diffusive Rn profile. Dashed line is the sorption model result. (dpm/cc)bulk 0.05 0.15 0.2 0.25 0.3 O— Rn Production Rate • Mobile Rn Data Diffusive Rn — - Sorption Model Rn V ' 0.5 Q 13IVIC 1.5%OC (dpm/cc)bulk 0.05 0.1 0.15 0.2 0.25 0.3 B w i eu O - Rn Production Rate Mobile Rn Data - Diffusive Rn - Sorption Model Rn 0 1 2 22MC 2.8%OC 3 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 1 8 APPENDIX D: ASSESSING CONSTANT DIFFUSIVITY, LINEAR RADON PRODUCTION RATE ASSUMPTIONS To test the verisimilitude that Ds is constant with depth and a linear production rate is a good approximation, an advanced multibox model was developed for a numerical simulation. This model divides a 10 cm sediment column into 1mm boxes. During each time step, Rn is produced and decays in each box, and the diffusive flux of material between two adjacent boxes was calculated by the difference in concentration between the boxes and is proportional to the effective diffusivity, Ds. This model assumes that there is no sorption. The model was run allowing for only diffusion to occur between the boxes until the system had reached a steady state (less than 1% change in 24 hours). For this exercise, the data from core 13MC was used. For each box, the porosity at the top and the middle of the box is calculated based on the exponential porosity profile generated using Equation 1. The Rn emanation rate per gram of dry sediment was assumed constant with depth, and the production rate for each box was calculated using Equation 5. Therefore, the Rn production rate profile approaches a constant value approximately exponentially with a scaling distance equal to that of the porosity profile (Equation 6 ). The effective diffusivity was calculated using the porosity at the boundary between two boxes, and will decrease nearly exponentially toward a constant value at depth, due to the effect of porosity. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 119 The result of the numerical simulation was compared to that for a one dimensional diffusion-reaction model. This model is a simplification of Equation 14 with no sorption, adveetion, or non-local exchange. The analytical solution to this model calculates the concentration of Rn in bulk sediment based on a Rn production rate that increases linearly with depth. A least-squares line was fit through the Rn production rate calculated for each of the top 4 cm with a constant emanation rate per gram of dry sediment. The effective diffusivity must be assumed to be constant in order to solve this equation. The effective diffusivity was calculated using the average porosity in the top 4cm. Because of the linear production rate and constant effective diffusivity, the analytical model should not be as precise as the numerical model. Results for the top 5 cm were compared. Figure Dla, presents the production rate profile for the numerical model and the analytical solution that assumes a linear increase. The high resolution numerical model predicts a smaller production rate at the sediment water interface than the linear production rate. Between 1 and 3 cm, it predicts a larger production rate. Below 3 cm, it begins to approach an equilibrium value, while the linear production rate continues to increase. The calculated Rn pore water profiles are compared in Figure Dlb. These two profiles are nearly indistinguishable in the top 3.5cm. Between 0.5 and 2.0 cm, the analytical model slightly overestimates the numerical model. This is because of the relatively low porosity used in the analytical model, which underestimated the effective diffusivity in the near-surface sediments. Below 3.0 cm, the analytical solution continues to increase while the numerical model begins to plateau. This can best be seen in the plot of the residuals (Figure Die). The deviation in calculated Rn Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure D l: Comparison and sensitivity of models to the use of a linear vs. exponential production rate and diffusivity. a ) R n p r o d u c t i o n r a t e s . S o l i d l i n e i s t h e l i n e a r p r o d u c t i o n r a t e , a n d t h e d o t t e d l i n e i s t h e e x p o n e n t i a l p r o d u c t i o n r a t e . a a. & 0 1 2 3 4 Exponential P Linear P Estim ate 5 r. , , , \ ,■ . , i i ■ , , , i . , ■ . i . . i ■ , i , .V. t , , , 73 0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 Production Rate (dpm/cc)bulk b ) M o d e l e d d i f f u s i o n - o n l y m o b i l e R n c o n c e n t r a t i o n . S o l i d l i n e is t h e r e s u l t f o r a c o n s t a n t b s a n d a l i n e a r p r o d u c t i o n r a t e , t h e d a s h e d L in e i s t h e r e s u l t f o r a v a r i a b l e D s a n d a n e x p o n e n t i a l p r o d u c t i o n r a t e . g & 0 1 2 3 4 V ariable Ds, Exponential P C onstant Ds, L inear P 5 0.25 0 0.05 0.1 0.15 0.2 Rn (dpm/cc)bulk c ) R e s i d u a l p l o t o f F i g u r e D l b : M o d e l e d d i f f u s i o n - o n l y m o b i l e R n C o n c e n t r a t i o n . 0.25 3 .5 c m 0.2 : 1 : 1 L i n e 0.05 0.05 0.1 0.15 0.25 0 0.2 Variable Ds, Exponential P (dpm/cc)bulk Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 2 1 concentrations with depth is primarily a result of the deviation of the Rn production functions. At a depth of 4cm, the diffusive Rn pore water profile is approximately 95% to equilibrium. Therefore, below this depth, the Rn pore water concentration is closely following the Rn production rate. Therefore, the Rn profiles generated by the numerical simulation and the analytical model are essentially equivalent in the top 3.5 cm. Below 3.5 cm, a linear Rn production rate will cause the Rn concentration to be overestimated as long as the Rn emanation rate per gram of dry sediments remains constant or increases with depth. R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 1 2 2 APPENDIX E: THE RADIAL DIFFUSION-REACTION MODEL SUMMARY Introduction: Aller (1980, 1982) developed a model that relies only on diffusion to transport solutes through sediments affected by bio-inigation. In this model, a solute can diffuse either across the sediment-water interface or into a burrow, where it is immediately flushed out. To develop this model, several assumptions about the physical characteristics of the sediments and bio-irrigation must be made. The model assumes that the sediments are comprised of a series of evenly spaced burrows that extend perpendicular to the sediment-water interface. All burrows have the same diameter and length. Surrounding each burrow, from the burrow wall to half the distance to the next burrow, is a cylindrical volume of sediments with a constant porosity with depth. The entire sea floor is then made up of these cylinders packed together. Each cylinder is called a microenvironment, because the average chemical composition in the sediments will be equal to the average for one cylinder. The burrow must be rapidly flushed to keep the concentration of water in the burrow equal to the concentration of water in the overlying water column. The differential equation to assess the distribution of a solute within the micro environment includes a term for the radial diffusion of a solute between the sediments and the burrow as well as diffusion across top of the cylinder, as well as the reaction kinetics for various solutes (Equation 13). Aller has solved this differential equation analytically and provided an equation for the concentration of a chemical species at any point within the cylinder, incorporating several functional R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 1 2 3 forms that are chosen to represent the depth dependence of the reaction kinetics (Aller, 1980,1982). Presented here is a finite difference model used to solve these equations. Equations: Aller's radial diffusion-reaction model was used to generate pore water profiles to match the mobile Rn data and to calculate the flux of Rn out of the sediments. To do this, a finite difference model was developed that could solve Equations 15, 16, and 17 numerically. To begin, the open cylinder of sediments was divided into 1 0 0 concentric sub-cylinders (j= 1 ,2 ,. ..,1 0 0 ) from the burrow wall, ri, to the half-spacing between burrows, T 2, and 1 0 0 boxes with depth (h= 1 ,2 ,. ..,1 0 0 ), from the sediment-water interface, z=0 to the bottom of the burrow, L (Figure El). The width of each sub-cylinder (dr) and thickness of each box (dz) was calculated as: dr = (r2 -ri) / 1 0 0 (El a) dz = L/100 (Elb) Then, the pore water concentrations were calculated by numerically solving Equation 15. For each box, the pore water concentration was calculated at each intersection of the four surfaces of the box: the inner and outer radii of the sub-cylinder, and at the top and bottom of the box. The concentration for the box was the average concentration of these four measurements. Next, the concentration for each layer of the microenvironment, dz, was calculated by summing the number of atoms in the layer (including the atoms in the center void) and dividing by the total volume of water in that layer: R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . Figure El: Cross section schematic for radial diffusion model. 1 2 4 ▲ 100 1 0 0 2,2 2,2 1 0 0 1 0 0 3,2 3,2 100 1 0 0 L 100,1 100 , 1 0 0 1 0 0 1 0 0 100, 1 0 0 1 0 0 ▼ R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm ission . 125 1 0 0 , 7tr?dxRCo l + n d xY ^r, + jd r f - (rx + (j - Ijdrf^Chj c = -____________ t i ____________________ : _______ (E2) ndx(r?+(r*-r?)) The output for the model is Ch (h=l,2,...,100). The model generated pore water concentrations can be directly compared to the measured WCS pore water activity concentrations presented in Table 5 by multiplying Ch by the Rn decay constant, 1.26x1 O ' 4 m hr1. Using the data in Table 8 , the resulting pore water profile for cores M CI3 and MC22 are shown in Figure E2. Finally, the Rn flux was calculated in two steps. The flux into the burrow was calculated as a linear change in concentration between the burrow wall and the average concentration of each box adjacent to the burrow, and the flux across the sediment water interface was calculated as a linear change in concentration between the overlying water and the average concentration of each box adjacent to the sediment water interface. After normalizing each flux to the surface area of the burrow and the top of the open cylinder, respectively, these two fluxes can be summed and divided by the surface area of the top of the entire cylinder to calculate the total Rn flux escaping from the sediments: 100 sy t~\ 100 , 4,iD . A K , - * c ) + r S K , - « c ) fc + ^ ) + (i + U - 1)*-)' j ________ a r h= 1 _______________________ j = 1 _____________________________________________________ J tot ~ 2 (E3) R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . Figure E2: Radial diffusion model result for burrow depth= 5cm. Solid line is the mobile Rn production rate. Dashed line is the radial diffusion model result. (dpm/cc) bulk 0.25 0.3 0.05 0.15 0 B & f O ) Q 13MC -r1= 0.05 cm r2= 1.14 cm B= 530 atoms/cm' (dpm/cc) bulk 0.15 0.2 0.25 0.05 - 22MC I r1= 0.05 cm r2= 1.91 cm B= 170 atoms/cm R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 127 The mobile Rn concentrations must be converted to pore water concentrations to calculate the flux. The pi term in the area calculations has been canceled out of this equation. Discussion: In a later paper, Aller (1983) reports on the importance of reduced permeability and high organic carbon concentration of the burrow walls which was not factored into this model. If organic carbon or a reduced permeability at the burrow walls is significant, then Rn diffusion into the burrow would be hindered, increasing the Rn concentration in the sediments and reducing the flux into the burrow. This model was tested by recreating the published model sensitivity plots presented for silica (Aller, 1980). Using the same parameters (Aller, 1980, Table 1), variables such as burrow half-spacing and burrow depth, were changed to see how the model reacted. The model results were almost identical to those presented by Aller. This model did deviate from Aller's results at the extremes, such as for very large burrow spacing 10cm) and when the v\ approaches 12 ■ The errors at large radii are generated by the error of the geometrically increasing Bessel function calculation. A deviation from Aller's results when rj approaches T 2 is expected because of the inclusion in this model of the burrow volume for the average concentration calculation. The sensitivity of the generated pore water profiles to variations in the Rn parameters was made. The effect of the burrow radius and burrow spacing on the curvature of the profile was assessed using the parameters and pore water profile for core 13MC. Selecting a value of r\ and adjusting 12 until a fit is made generates a R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . 1 2 8 Table El: Radial diffusion model variability calculated using the parameters for core 13MC. L r1 r2 B Flux (cm) (cm) (cm) (atoms/cm4) (atom s/cm 2/sec) 1 5 0.05 1.08 388 297 15 0.1 1.243 395 301 15 0.2 1.491 400 297 1 5 0.5 2.072 415 274 5 0.05 1.08 388 112 1 0 0.05 1.08 388 205 15 0.05 1.08 388 297 5 0.05 1.08 0 107 5 0.05 1.08 388 112 5 0.05 1.08 600 1 15 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . Figure E3: Sensitivity analysis for the radial-diffusion model. a) Change in burrow half-spacing with a change in burrow radius to maintain a flux of 2.2 I I 0.2 0.3 0.4 Burrow radius (rl=cm) 0.5 b) Change in flux with a change in burrow length. 350 : r l = 0 .0 5 c m 1 r 2 = 1 .0 8 c m - 3- 300 » 250 200 Q c s Burrow length (L=cm) c) Change in total flux with a change in the flux into the base of the burrow. 116 ; r l = 0 .0 5 c m . r 2 = 1 .0 8 c m - L = 5 c m o 114 112 o ta 110 108 106 Flux into burrow (B=atoms/cm4 ) R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 1 3 0 modeled pore water profile that matches the Rn pore water data. The importance of the choice of ri was assessed by systematically changing ri and then adjusting T 2 to generate pore water profiles that matched the Rn pore water profile for 13MC. This was equivalent to maintaining a flux of 300 atoms m' 2 sec"1 . The relation between ri and T 2 was found to be almost linear over the burrow radii of interest and is presented in Table E l (Figure E3a). If the burrow radius is increased, then the burrow spacing would also need to increase to generate a similar profile. Different burrow spacing had only a slight effect on the flux, with about a 5% decrease in flux for large burrows (Table El). Then, setting ri = 0.05 cm and V 2 = 1.08 cm, the burrow depth was increased from 5 cm to 15 cm (Table E l; Figure E3b). As the depth of the burrow increased, the Rn flux increased with an approximately linear relationship. Using these same parameters and burrow depth of 5 cm, the addition of material into the bottom of the cylinder resulted in a maximum flux change of about 5% (Table El; Figure E3c). R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . 13 1 APPENDIX F: FORTRAN CODE FOR MODELS 1. Radial Diffusion C Radial diffusion-reaction model taken from Aller, 1980 C Created by Steven Colbert 3/30/2000 (radr.f); Modified 1/24/01 C Set up for Rn; Output is bulk sediment concentration (dpm/cm3) C at the midpoint of each box C Calculates two fluxes: 1 -D flux assuming no irrigation and linear flux calculated b/w C the ave. conc. of the 1st box from the burrow wall/surface and the bottom water. DIMENSION V(15),DC(101,101),C(100,100),VOL(100),Z(100) DIMENSION CW(100,100),S(100,100) CHARACTER PARA(15)*60 REAL R,R1,R2,L,LI,PRO,CT,B,DS,DECAY,KN REAL MU,G,X,X 1 ,X2,U,U 1 ,XX,XXX,SUM1 ,SUM2 REAL POR,VOLO,DR,DX,ATOMS,RR,FLUXUP,FLUXIN REAL UI0,UK0,UI1 ,UK1,FLUX,ONEFLX,PRO 1 ,PR02 INTEGER I,NFLAG,J,M,K C Functions used REAL bessiO,bessil,besskO,besskl TYPE *, 'radial concentration model' TYPE *, 'ave Rn Cone, at any depth' TYPE *,' ADJUSTABLE PARAMETERS ARE:' PARA(l) = 'Rn Emanation Rate (dpm/g)' V (l) = .33 PARA(2) = 'Rn Overlying water/burrow conc. (atoms/cm3)' V(2) = 0.794 PARA(3) = 'flux into bottom of cylinder (atoms/cm4)' V(3)= 100 PARA(4) = 'Porosity' V(4) = 0.8 PARA(5) = 'Rn Molecular diffusivity (cm2/sec)' V(5) = 6.5e-6 PARA(6 ) = 'Rn decay Const (1/sec)' V(6 ) = 2.1e-6 PARA(7) = 'tube radius (cm)' Y(7) = .05 PARA(8 ) = 'Half Burrow Spacing (cm)' V(8 ) = 1 PARA(9) = 'Burrow Length (cm)' V(9) = 5 PARA(10) = 'Look at x=(cm)' V(10) = 5 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 132 PARA(ll) = 'Organic Carbon Fraction: foe' V(11) = 0 PARA(12) = 'Production rate at depth (dpm/cm3)' V(12) = .2 PARA(13) = Production rate increase with depth (positive)(dpm/cm3)' V(13) = 0 PARA(14) = 'Production rate scaling distance with depth (1/cm)' V(14) = 0 PARA(15) = 'Number of iterations' V(15) = 50 C Adjust model parameters 19 DO 201=1,15 20 TYPE 1 ,1 , V(I), PARA(I) 1 FORMAT (13, ' = ', E10.3, ' ', A60) TYPE *, 'ENTER # OF PARAMETER TO CHANGE, 0=RUN, 99 =EXIT' ACCEPT *, NFLAG IF (NFLAG.EQ.99) GO TO 1000 IF (NFLAG.EQ.0) GO TO 100 IF (NFLAG.GE.16) GO TO 19 TYPE *, 'ENTER NEW VALUE FOR ', PARA (NFLAG) ACCEPT *, V(NFLAG) GO TO 19 C RADIUS AND BURROW LENGTH (in cm) 100 RI = V(7) R2 = V(8 ) LI = V(9) DR = (R2-R1)/100 DX = V(10)/100 C VOLUMES (in cm3): VOLO=burrow vol., VOLUME=vol. of each layer, C VOL(I)=vol. of each annulus, I is boxes away from burrow. VOLO = DX*3.14159*R1*R1 VOLUME = VOLO+DX*3.14159*((R2* *2)-(R 1 * *2)) DO 105 1=1,100 VOL(I) = DX*3.14159*((R1+I*DR)**2-(R1+(I-1)*DR)**2) 105 CONTINUE C PORosity, RRetardation factor, PROduction rate (dps/cm3), C CT=bottom water conc (atoms/cm3) C B=bottom flux, DS=diffusivity,DECAY rate, J=number of iterations POR = V(4) RR = l+(l-POR)*2.6*18.9*V(ll)/POR PRO = V(12)/60 PROl = V(13)/60 PR02 = V(14) CT = V(2) R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 133 B = V(3) DS = P0R*P0R*V(5) DECAY = V(6 ) CEQ = PRO/DECAY J = V(15) C Calculate summations C K is radial box number, M is vertical box number C DC is atoms/cm3 of bulk sediments DO 110 M=l,101 L = DX*(M-1) DO 115K= 1,101 R = R1+DR*(K-1) SUM 1=0 SUM2=0 DO 1201=0,J KN=(I+0.5)*3.14159/Ll MU=SQRT(DECAY*RR/DS+KN* *2) G = (DEC AY*RR*POR*CT-PRO)/KN+((-1 )* *I)*DEC AY*B/KN* *2 1 -PR01*(PR02*(-1**I)*EXP(-PR02*L1)-KN)/(PR02*PR02+KN*KN) X = MU*R XI = MU*R1 X2 = MU*R2 UI0 = bessiO(X) UK0 = besskO(X) UU = bessil(X2) UK1 = besskl(X2) U = UK1*UI0+UI1*UK0 UI0= bessiO(Xl) UK0= besskO(Xl) U1 = UK1*UI0+UI1*UK0 XX = G/(MU**2)*(U/U1-1)*SIN(KN*L) SUM1 = SUM1 + XX XXX = ((4)**I)*U/(KN**2)/U1*SIN(KN*L) SUM2 = SUM2 + XXX 120 CONTINUE DC(M,K)=POR*RR*CT+B *L+2 *RR* SUM 1 /L1/DS -2*B * SUM2/L1 115 CONTINUE 110 CONTINUE C Calculate the average concentration in each box, C(X,R) C S(X,R) = number of atoms in each box DO 1401=1,100 DO 150 K=l,100 C(I,K) = (DC(I,K)+DC(I+l,K)+DC(I,K+l)+DC(I+l,K+l))/4 CW(I,K) = C(I,K)/RR S(I,K) = C(I,K)*VOL(K) 150 CONTINUE 140 CONTINUE R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . C Calculate number of atoms in VOID VOID = VOLO*CT C Calculate concentration with depth = Z(I) DO 1601=1,100 ATOMS = 0 DO 170 K=l,100 ATOMS= ATOMS+S(I,K) 170 CONTINUE Z(I) = (ATOMS+VOID)* 1,26e-4/VOLUME 160 CONTINUE C CALCULATE THE NEW TOTAL FLUX (ATOMS/M2-SEC) C Note that pi has cancelled out FLUXUP = 0 FLUXIN = 0 DO 1801=1,100 C FLUXUP is the change in conc at surface*area/pi FLUXUP = FLUXUP+(CW (1,1)-CT)*(((R 1 +I*DR)**2) 1 -(R1 +(I-1) *DR) * *2) C FLUXIN is the change in conc at burrow FLUXIN=FLUXIN+(CW (1,1 )-CT) 180 CONTINUE C normalize to area/pi FLUXUP=FLUXUP* 2 * DS/DX/RR FLUXIN= FLUXIN*4*R 1 *DX* DS/DR/RR FLUX=(FLUXUP+FLUXIN)* 10000/(R2**2) C Print out average concentration at each interval DO 2001=1,100 PRINT*, ", Z(I) 200 CONTINUE PRINT*," PRINT*,'The Flux is’,FLUX PRINT*," GOTO 19 1000 CONTINUE PRINT*,'I am just a little freaked out' STOP END R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 135 REAL FUNCTION bessiO(x) REAL bessiO, x C Returns the modified bessel fxn Io(x) for any real x REAL ax DOUBLE PRECISION p 1 ,p2,p3 ,p4,p5,p6,p7,q 1 ,q2,q3,q4,q5,q6,q7, 1 qB,q9,y SAVE pl,p2,p3,p4,p5,p6,p7,ql,q2,q3,q4,q5,q6,q7,q8,q9 DATA pl,p2,p3,p4,p5,p6,p7/1.0d0,3.5156229d0,3.0899424d0,1.2067492d0, 1 Q.2659732d0,0.360768d-1,0.45813d-2/ DATA ql,q2,q3,q4,q5,q6,q7,q8,q9/0.39894228d0,0.1328592d-l, 1 0.225319d-2,-0.157565d-2,0.91628 ld-2,-0.2057706d-l, 1 0.2635537d-l,-0.1647633d-l,0.392377d-2/ IF (abs(x).lt.3.75) THEN y=(x/3.75)**2 bessi0=pl+y*(p2+y*(p3+y*(p4+y*(p5+y*(p6+y*p7))))) ELSE ax=abs(x) y=3.75/ax bessiO=(EXP(ax)/SQRT(ax))*(ql+y*(q2+y*(q3+y*(q4 1 +y*(q5+y*(q6+y*(q7+y*(q8+y*q9)))))))) ENDIF RETURN END REAL FUNCTION besskO(x) REAL besskO.x C USES bessiO C Returns the modified bessel fxn Ko(x) for positive real x REAL bessiO DOUBLE PRECISION pl,p2,p3,p4,p5,p6,p7,ql, 1 q2,q3,q4,q5,q6,q7,y SAVE p 1 ,p2,p3,p4,p5,p6,p7,ql,q2,q3,q4,q5,q6,q7 DATA pl,p2,p3,p4,p5,p6,p7/-0.57721566d0,0.42278420d0,0.23069756d0, 1 0.3488590d-l,0.262698d-2,0.10750d-3,0.74d-5/ DATA ql,q2,q3,q4,q5,q6,q7/1.25331414d0,-0.7832358d-l,0.2189568d-l, 1 -0.1062446d-l,0.587872d-2,-0.251540d-2,0.53208d-3/ IF (x.le.2.0) THEN y=x*x/4,0 besskO=(-LOG(x/2.0) *bessiO(x))+(pl+y*(p2+y *(p3+ 1 y*(p4+y*(p5+y*(p6+y*p7)))))) ELSE y=(2 .0 /x) besskO=(EXP(-x)/SQRT(x))*(ql+y*(q2+y*(q3+ 1 y*(q4+y*(q5+y*(q6+y*q7)))))) R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 1 3 6 ENDIF RETURN END REAL FUNCTION bessil(x) REAL bessil, x C Returns the modified bessel fxn Il(x) for any real x REAL ax DOUBLE PRECISION pl,p2,p3,p4,p5,p6,p7,ql,q2,q3,q4,q5,q6,q7, 1 q8,q9,y SAVE pl,p2,p3,p4,p5,p6,p7,ql,q2,q3,q4,q5,q6,q7,q8,q9 DATA pl,p2,p3,p4,p5,p6,p7/0.5d0,0.87890594d0,0.51498869d0, 1 0.15084934d0,0.2658733d-l,0.301532d-2,0.3241 ld-3/ DATA ql,q2,q3,q4,q5,q6,q7,q8,q9/0.39894228d0,-.3988024d-l, 1 -0.362018d-2,0.163801d-2,-0.1031555d-l,0.2282967d-1, 1 -0.2895312d-1,0.1787654d-1 ,-0.420059d-2/ IF (abs(x).lt.3.75) THEN y=(x/3.75)**2 bessi 1 =x* (p 1 +y*(p2+y*(p3+y*(p4+y*(p5+y* (p6+y*p7)))))) ELSE ax=abs(x) y=3.75/ax bessil=(EXP(ax)/SQRT(ax))*(ql+y*(q2+y*(q3+y*(q4 1 +y*(q5+y*(q6+y*(q7+y*(q8+y*q9)))))))) IF (x.lt.O.) bessi l=-bessil ENDIF RETURN END REAL FUNCTION besskl(x) REALbesskl,x C USES bessil C Returns the modified bessel fxn Kl(x) for positive real x REAL bessil DOUBLE PRECISION p l,p2,p3,p4,p5,p6,p7,ql, 1 q2,q3,q4,q5,q6,q7,y SAVE pl,p2,p3,p4,p5,p6,p7,ql,q2,q3,q4,q5,q6,q7 DATA pi,p2,p3,p4,p5,p6,p7/1.0d0,0.15443144d0,-0.67278579d0, 1 -.18156897d0,-0.1919402d-1 ,-0.110404d-2,-0.4686d-4/ DATA q l,q2,q3,q4,q5,q6,q7/l.25331414d0,0.23498619d0,-0.3655620d-l, 1 0.1504268d-l,-0.780353d-2,0.325614d-2,-0.68245d-3/ IF (x.le.2.0) THEN y=x*x/4.0 besskl=(LOG(x/2.0)*bessil(x))+(1.0/x)*(pl+y*(p2+y*(p3+ 1 y*(p4+y*(p5+y*(p6+y*p7)))))) ELSE y=(2 .0 /x) R ep ro d u ced with p erm issio n o f th e copyright ow ner. Further reproduction prohibited w ithout p erm ission . besskl=(EXP(-x)/SQRT(x))*(ql+y*(q2+y*(q3+ 1 y*(q4+y*(q5+y*(q6+y*q7)))))) ENDIF RETURN END R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission .
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Colbert, Steven Laurence
(author)
Core Title
Numerical simulation of whole core squeezer radon pore water profiles: Methodological considerations and evaluation of benthic fluxes and rates of bio-irrigation and advection
Degree
Master of Science
Degree Program
Geological Sciences
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University of Southern California
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University of Southern California. Libraries
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geochemistry,OAI-PMH Harvest
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English
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https://doi.org/10.25549/usctheses-c16-38554
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38554
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Colbert, Steven Laurence
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University of Southern California Dissertations and Theses
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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...
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geochemistry