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  • Radium isotopes  (6)
  • Barium  (4)
  • Glacier
  • 1
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    Isotope tracing of submarine groundwater discharge offshore Ubatuba, Brazil : results of the IAEA–UNESCO SGD project (2008)
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    Publication Date: 2022-05-25
    Description: Author Posting. © Elsevier B.V., 2008. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Journal of Environmental Radioactivity 99 (2008): 1596-1610, doi:10.1016/j.jenvrad.2008.06.010.
    Description: Results of groundwater and seawater analyses for radioactive (3H, 222Rn, 223Ra, 224Ra, 226Ra, 228Ra) and stable (2H, 18O) isotopes are presented together with in situ spatial mapping and time-series 222Rn measurements in seawater, direct seepage measurements using manual and automated seepage meters, pore water investigations using different tracers and piezometric techniques, and geoelectric surveys probing the coast. This study represents first time that such a new complex arsenal of radioactive and non-radioactive tracer techniques and geophysical methods have been used for simultaneous submarine groundwater discharge (SGD) investigations. Large fluctuations of SGD fluxes were observed at sites situated only a few meters apart (from 0 cm d-1 to 360 cm d-1; the unit represents cm3/cm2/day), as well as during a few hours (from 0 cm d-1 to 110 cm d-1), strongly depending on the tidal fluctuations. The average SGD flux estimated from continuous 222Rn measurements is 17±10 cm d-1. Integrated coastal SGD flux estimated for the Ubatuba coast using radium isotopes is about 7x103 m3 d-1 per km of the coast. The isotopic composition (δ2H and δ18O) of submarine waters was characterised by significant variability and heavy isotope enrichment, indicating that the contribution of groundwater in submarine waters varied from a small percentage to 20%. However, this contribution with increasing offshore distance became negligible. Automated seepage meters and time-series measurements of 222Rn activity concentration showed a negative correlation between the SGD rates and tidal stage. This is likely caused by sea level changes as tidal effects induce variations of hydraulic gradients. The geoelectric probing and piezometric measurements contributed to better understanding of the spatial distribution of different water masses present along the coast. The radium isotope data showed scattered distributions with offshore distance, which imply that seawater in a complex coast with many small bays and islands was influenced by local currents and groundwater/seawater mixing. This has also been confirmed by a relatively short residence time of 1-2 weeks for water within 25 km offshore, as obtained by short-lived radium isotopes. The irregular distribution of SGD seen at Ubatuba is a characteristic of fractured rock aquifers, fed by coastal groundwater and recirculated seawater with small admixtures of groundwater, which is of potential environmental concern and has implications on the management of freshwater resources in the region.
    Description: This research was supported by IAEA and UNESCO (IOC and IHP) in the framework of the joint SGD project. Science support for some U.S. investigators was provided by grants from the National Science Foundation (OCE03-50514 to WCB and OCE02-33657 to WSM).
    Keywords: Submarine groundwater discharge ; Groundwater ; Seawater ; Stable isotopes ; δD ; δ18O ; Tritium ; Radium isotopes ; Radon ; Coastal zone ; Ubatuba ; Brazil
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  • 2
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    Shelf-derived iron inputs drive biological productivity in the southern Drake Passage (2010)
    American Geophysical Union
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    Publication Date: 2022-05-25
    Description: Author Posting. © American Geophysical Union, 2009. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Global Biogeochemical Cycles 23 (2009): GB4014, doi:10.1029/2008GB003406.
    Description: In the Southern Ocean near the Antarctic Peninsula, Antarctic Circumpolar Current (ACC) fronts interact with shelf waters facilitating lateral transport of shelf-derived components such as iron into high-nutrient offshore regions. To trace these shelf-derived components and estimate lateral mixing rates of shelf water, we used naturally occurring radium isotopes. Short-lived radium isotopes were used to quantify the rates of shelf water entrainment while Fe/228Ra ratios were used to calculate the Fe flux. In the summer of 2006 we found rapid mixing and significant lateral iron export, namely, a dissolved iron flux of 1.1 × 105 mol d−1 and total acid leachable iron flux of 1.1 × 106 mol d−1 all of which is transported in the mixed layer from the shelf region offshore. This dissolved iron flux is significant, especially considering that the bloom observed in the offshore region (0.5–2 mg chl a m−3) had an iron demand of 1.1 to 4 × 105 mol Fe. Net vertical export fluxes of particulate Fe derived from 234Th/238U disequilibrium and Fe/234Th ratios accounted for only about 25% of the dissolved iron flux. On the other hand, vertical upward mixing of iron rich deeper waters provided only 7% of the lateral dissolved iron flux. We found that similarly to other studies in iron-fertilized regions of the Southern Ocean, lateral fluxes overwhelm vertical inputs and vertical export from the water column and support significant phytoplankton blooms in the offshore regions of the Drake Passage.
    Description: This work was funded by the National Science Foundation (ANT-0443869 to M.A.C.).
    Keywords: Radium isotopes ; Iron ; Natural iron fertilization
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  • 3
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    Molecular characterization of dissolved organic matter associated with the Greenland ice sheet (2010)
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    Publication Date: 2022-05-25
    Description: Author Posting. © The Author(s), 2010. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Geochimica et Cosmochimica Acta 74 (2010): 3768-3784, doi:10.1016/j.gca.2010.03.035.
    Description: Subsurface microbial oxidation of overridden soils and vegetation beneath glaciers and ice sheets may affect global carbon budgets on glacial-interglacial timescales. The likelihood and magnitude of this process depends on the chemical nature and reactivity of the subglacial organic carbon stores. We examined the composition of carbon pools associated with different regions of the Greenland ice sheet (subglacial, supraglacial, proglacial) in order to elucidate the type of dissolved organic matter (DOM) present in the subglacial discharge over a melt season. Electrospray ionization (ESI) Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry coupled to multivariate statistics permitted unprecedented molecular level characterization of this material and revealed that carbon pools associated with discrete glacial regions are comprised of different compound classes. Specifically, a larger proportion of protein-like compounds were observed in the supraglacial samples and in the early melt season (spring) subglacial discharge. In contrast, the late melt season (summer) subglacial discharge contained a greater fraction of lignin-like and other material presumably derived from underlying vegetation and soil. These results suggest (1) that the majority of supraglacial DOM originates from autochthonous microbial processes on the ice sheet surface, (2) that the subglacial DOM contains allochthonous carbon derived from overridden soils and vegetation as well as autochthonous carbon derived from in situ microbial metabolism, and (3) that the relative contribution of allochthonous and autochthonous material in subglacial discharge varies during the melt season. These conclusions are consistent with the hypothesis that, given sufficient time (e.g., overwinter storage), resident subglacial microbial communities may oxidize terrestrial material beneath the Greenland ice sheet.
    Description: This research was supported by: the National Science Foundation (CAREER-OCE- 0529101 (EBK), ARC-0520077 (SBD)), National Atmospheric and Space Administration (SBD), the WHOI Clark Arctic Research Initiative (EBK, SBD, MAC), the WHOI Ocean Ventures Fund (MPB), and the National and Science Engineering Research Council of Canada (MPB).
    Keywords: Glacier ; Ultrahigh resolution mass spectrometry ; FT-ICR ; Organic carbon ; DOM
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  • 4
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    Preparation of Mn-fiber standards for the efficiency calibration of the delayed coincidence counting system (RaDeCC) (2011)
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    Publication Date: 2022-05-25
    Description: Author Posting. © The Author(s), 2010. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Marine Chemistry 121 (2010): 206-214, doi:10.1016/j.marchem.2010.04.009.
    Description: Precise measurements of the short lived radium isotopes 223Ra and 224Ra by means of the delayed coincidence counting system (RaDeCC) rely on an efficiency calibration of this system using Mn-fiber standards for which radium activities are exactly known. We prepared seventeen different standards by placing Mn-fibers in seawater spiked with various amounts of 227Ac (with 223Ra in radioactive equilibrium), 228Th (in radioactive equilibrium with 232Th and 224Ra) and 226Ra. We tested for quantitative adsorption of 227Ac and 228Th on the Mn-fibers by: (1) measuring 227Ac and 232Th in the residual solutions after preparing the Mn-fiber standards and (2) monitoring their 223Ra and 224Ra activities over a period of ~100 days. In the residual solutions, the activities of 227Ac and 232Th were 〈 1.0 % and 〈 5.3 %, respectively, of the activities initially added to the Mn-fibers. Our results indicate that Milli-Q water washing of the Mn-fibers is the major source of our observed losses of thorium. Measurements of 227Ac standards over 1½ years indicate a significant decrease of measurable 223Ra with time prohibiting the long-term use of 227Ac Mn-fiber standards. We found the 224Ra efficiency to be independent of the range of 227Ac, 228Th and 226Ra activities on the Mn-fibers standards used. The efficiency determination for 223Ra, however, may be biased in the case of relatively high 224Ra activities due to insufficient correction of chance of coincidence. Thus we suggest using a single 227Ac Mn-fiber standard for the efficiency determination for 223Ra.
    Description: M. Charette and H. Dulaiova were supported by a grant from the National Science Foundation (OCE- 0751461).
    Keywords: Radium isotopes ; Mn-fiber standards ; RaDeCC system ; Efficiency determination
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  • 5
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    Isotopic, geophysical and biogeochemical investigation of submarine groundwater discharge : IAEA-UNESCO intercomparison exercise at Mauritius Island (2011)
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    Publication Date: 2022-05-25
    Description: Author Posting. © The Author(s), 2011. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Journal of Environmental Radioactivity 104 (2012): 24-45, doi:10.1016/j.jenvrad.2011.09.009.
    Description: Submarine groundwater discharge (SGD) into a shallow lagoon on the west coast of Mauritius Island (Flic-en-Flac) was investigated using radioactive (3H, 222Rn, 223Ra, 224Ra, 226Ra, 228Ra) and stable (2H, 18O) isotopes and nutrients. SGD intercomparison exercises were carried out to validate the various approaches used to measure SGD including radium and radon measurements, seepage-rate measurements using manual and automated meters, sediment bulk conductivity and salinity surveys. SGD measurements using benthic chambers placed on the floor of the Flic-en-Flac Lagoon showed discharge rates up to 500 cm/day. Large variability in SGD was observed over distances of a few meters, which were attributed to different geomorphological features. Deployments of automated seepage meters captured the spatial and temporal variability of SGD with a mean seepage rate of 10 cm/day. The stable isotopic composition of submarine waters was characterized by significant variability and heavy isotope enrichment and was used to predict the contribution of fresh terrestrially derived groundwater to SGD (range from a few % to almost 100 %). The integrated SGD flux, estimated from seepage meters placed parallel to the shoreline, was 35 m3/m day, which was in a reasonable agreement with results obtained from hydrologic water balance calculation (26 m3/m day). SGD calculated from the radon inventory method using in situ radon measurements were between 5 and 56 m3/m per day. Low concentrations of radium isotopes observed in the lagoon water reflected the low abundance of U and Th in the basalt that makes up the island. High SGD rates contribute to high nutrients loading to the lagoon, potentially leading to eutrophication. Each of the applied methods yielded unique information about the character and magnitude of SGD. The results of the intercomparison studies have resulted a better understanding of groundwater-seawater interactions in coastal regions. Such information is an important pre-requisite for the protection management of coastal freshwater resources.
    Description: The financial support provided by the IOC and IHP of UNESCO for travel arrangements, and by the IAEA’s Marine Environment Laboratories for logistics is highly acknowledged. MAC and MEG were supported in part by the US National Science Foundation (OCE-0425061 and OCE-0751525). PPP acknowledges a support provided by the EU Research & Development Operational Program funded by the ERDF (project No. 26240220004), and the Slovak Scientific Agency VEGA (grant No. 1/108/08). The International Atomic Energy Agency is grateful to the Government of the Principality of Monaco for support provided to its Marine Environment Laboratories.
    Keywords: Submarine groundwater discharge ; Groundwater ; Seawater ; Seepage meters ; Stable isotopes ; δD ; δ18O ; Tritium ; Radium isotopes ; Radon ; Nutrients ; Coastal zone ; Volcanic island ; Mauritius Island
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  • 6
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    Utility of Rn-222 as a passive tracer of subglacial distributed system drainage (2017)
    Elsevier
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    Publication Date: 2022-05-25
    Description: This paper is not subject to U.S. copyright. The definitive version was published in Earth and Planetary Science Letters 462 (2017): 180-188, doi:10.1016/j.epsl.2016.12.039.
    Description: Water flow beneath the Greenland Ice Sheet (GrIS) has been shown to include slow-inefficient (distributed) and fast-efficient (channelized) drainage systems, in response to meltwater delivery to the bed via both moulins and surface lake drainage. This partitioning between channelized and distributed drainage systems is difficult to quantify yet it plays an important role in bulk meltwater chemistry and glacial velocity, and thus subglacial erosion. Radon-222, which is continuously produced via the decay of 226Ra, accumulates in meltwater that has interacted with rock and sediment. Hence, elevated concentrations of 222Rn should be indicative of meltwater that has flowed through a distributed drainage system network. In the spring and summer of 2011 and 2012, we made hourly 222Rn measurements in the proglacial river of a large outlet glacier of the GrIS (Leverett Glacier, SW Greenland). Radon-222 activities were highest in the early melt season (10–15 dpm L−1), decreasing by a factor of 2–5 (3–5 dpm L−1) following the onset of widespread surface melt. Using a 222Rn mass balance model, we estimate that, on average, greater than 90% of the river 222Rn was sourced from distributed system meltwater. The distributed system 222Rn flux varied on diurnal, weekly, and seasonal time scales with highest fluxes generally occurring on the falling limb of the hydrograph and during expansion of the channelized drainage system. Using laboratory based estimates of distributed system 222Rn, the distributed system water flux generally ranged between 1–5% of the total proglacial river discharge for both seasons. This study provides a promising new method for hydrograph separation in glacial watersheds and for estimating the timing and magnitude of distributed system fluxes expelled at ice sheet margins.
    Description: U.S. National Science Foundation Arctic Natural Sciences Program (ANS-1256669); Woods Hole Oceanographic Institution Arctic Research Initiative, Ocean Ventures Fund, and Ocean Climate Change Institute; United Kingdom Natural Environment Research Council studentship (NE/152830X/1); the Carnegie Trust, Edinburgh University Development Trust.
    Keywords: Radon ; Greenland ; Glacier ; Proglacial river ; Meltwater
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  • 7
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    Relationship between water and aragonite barium concentrations in aquaria reared juvenile corals (2017)
    Elsevier
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    Publication Date: 2022-05-25
    Description: This paper is not subject to U.S. copyright. The definitive version was published in Geochimica et Cosmochimica Acta 209 (2017): 123-134, doi:10.1016/j.gca.2017.04.006.
    Description: Coral barium to calcium (Ba/Ca) ratios have been used to reconstruct records of upwelling, river and groundwater discharge, and sediment and dust input to the coastal ocean. However, this proxy has not yet been explicitly tested to determine if Ba inclusion in the coral skeleton is directly proportional to seawater Ba concentration and to further determine how additional factors such as temperature and calcification rate control coral Ba/Ca ratios. We measured the inclusion of Ba within aquaria reared juvenile corals (Favia fragum) at three temperatures (∼27.7, 24.6 and 22.5 °C) and three seawater Ba concentrations (73, 230 and 450 nmol kg−1). Coral polyps were settled on tiles conditioned with encrusting coralline algae, which complicated chemical analysis of the coral skeletal material grown during the aquaria experiments. We utilized Sr/Ca ratios of encrusting coralline algae (as low as 3.4 mmol mol−1) to correct coral Ba/Ca for this contamination, which was determined to be 26 ± 11% using a two end member mixing model. Notably, there was a large range in Ba/Ca across all treatments, however, we found that Ba inclusion was linear across the full concentration range. The temperature sensitivity of the distribution coefficient is within the range of previously reported values. Finally, calcification rate, which displayed large variability, was not correlated to the distribution coefficient. The observed temperature dependence predicts a change in coral Ba/Ca ratios of 1.1 μmol mol−1 from 20 to 28 °C for typical coastal ocean Ba concentrations of 50 nmol kg−1. Given the linear uptake of Ba by corals observed in this study, coral proxy records that demonstrate peaks of 10–25 μmol mol−1 would require coastal seawater Ba of between 60 and 145 nmol kg−1. Further validation of the coral Ba/Ca proxy requires evaluation of changes in seawater chemistry associated with the environmental perturbation recorded by the coral as well as verification of these results for Porites species, which are widely used in paleo reconstructions.
    Description: M.E.G. was supported by a NDSEG graduate fellowship. Funding for this research came from the NSF Chemical Oceanography program (OCE-0751525) and the Coastal Ocean Institute, the Ocean and Climate Change Institute and the Ocean Ventures Fund at Woods Hole Oceanographic Institution.
    Keywords: Coral Ba/Ca ; Barium ; Aragonite ; Distribution coefficient ; Favia fragum
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  • 8
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    Dissolved and particulate barium distributions along the US GEOTRACES North Atlantic and East Pacific zonal transects (GA03 and GP16): global implications for the marine barium cycle (2022)
    American Geophysical Union
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    Publication Date: 2022-10-26
    Description: Author Posting. © American Geophysical Union, 2022. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Global Biogeochemical Cycles 36(6), (2022): e2022GB007330, https://doi.org/10.1029/2022gb007330.
    Description: Processes controlling dissolved barium (dBa) were investigated along the GEOTRACES GA03 North Atlantic and GP16 Eastern Tropical Pacific transects, which traversed similar physical and biogeochemical provinces. Dissolved Ba concentrations are lowest in surface waters (∼35–50 nmol kg−1) and increase to 70–80 and 140–150 nmol kg−1 in deep waters of the Atlantic and Pacific transects, respectively. Using water mass mixing models, we estimate conservative mixing that accounts for most of dBa variability in both transects. To examine nonconservative processes, particulate excess Ba (pBaxs) formation and dissolution rates were tracked by normalizing particulate excess 230Th activities. Th-normalized pBaxs fluxes, with barite as the likely phase, have subsurface maxima in the top 1,000 m (∼100–200 μmol m−2 year−1 average) in both basins. Barite precipitation depletes dBa within oxygen minimum zones from concentrations predicted by water mass mixing, whereas inputs from continental margins, particle dissolution in the water column, and benthic diffusive flux raise dBa above predications. Average pBaxs burial efficiencies along GA03 and GP16 are ∼37% and 17%–100%, respectively, and do not seem to be predicated on barite saturation indices in the overlying water column. Using published values, we reevaluate the global freshwater dBa river input as 6.6 ± 3.9 Gmol year−1. Estuarine mixing processes may add another 3–13 Gmol year−1. Dissolved Ba inputs from broad shallow continental margins, previously unaccounted for in global marine summaries, are substantial (∼17 Gmol year−1), exceeding terrestrial freshwater inputs. Revising river and shelf dBa inputs may help bring the marine Ba isotope budget more into balance.
    Description: The International GEOTRACES Programme is possible in part thanks to the support from the U.S. National Science Foundation (Grant OCE-1840868) to the Scientific Committee on Oceanic Research (SCOR). This research was supported by the National Science Foundation under Grant No. NSF OCE-0927951, NSF OCE-1137851, NSF OCE-1261214, and NSF OCE-1925503 to A. M. Shiller; NSF OCE-1829563 to R. F. Anderson; NSF OCE-0927064 and NSF OCE-1233688 to R. F. Anderson and M. Q. Fleisher; NSF OCE-0927754 to R. Lawrence Edwards; NSF OCE-1233903 to R. Lawrence Edwards and H. Cheng; NSF OCE-0926860 to L. F. Robinson; NSF OCE-0963026 and NSF OCE-1518110 to P. J. Lam; and NSF OCE-1232814 to B. S. Twining.
    Keywords: Barium ; Excess barium ; Barite ; GEOTRACES ; Th-normalized flux ; Burial efficiency
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  • 9
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    Radium isotopes as tracers of iron sources fueling a Southern Ocean phytoplankton bloom (2008)
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    Publication Date: 2022-05-26
    Description: Author Posting. © Elsevier B.V., 2007. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Deep Sea Research Part II: Topical Studies in Oceanography 54 (2007): 1989-1998, doi:10.1016/j.dsr2.2007.06.003.
    Description: Elevated levels of productivity in the wake of Southern Ocean island systems are common despite the fact that they are encircled by high nutrient low chlorophyll (HNLC) waters. In the Crozet Plateau region, it has been hypothesized that iron from island runoff or sediments of the plateau could be fueling the austral summer phytoplankton bloom. Here, we use radium isotopes to quantify the rates of surface ocean iron supply fueling the bloom in the Crozet Plateau region. A 1-D eddy-diffusion-mixing model applied to a 228Ra profile (t1/2 = 5.75 yr) at a station north of the islands suggested fast vertical mixing in the upper 300 m (Kz = 11-100 cm2 s- 1) with slower mixing between 300 and 1000 m (Kz = 1.5 cm2 s-1). This estimate is discussed in the context of Kz derived from the CTD/LADCP data. In combination with the dissolved Fe profile at this location, we estimated a vertical flux of between 5.6 and 31 nmol Fe m-2 d-1. The cross-plateau gradients in the short-lived radium isotopes, 224Ra (t1/2 = 3.66 d) and 223Ra (t1/2 = 11.4 d), yielded horizontal eddy diffusivities (Kh) of 39 m2 s-1 and 6.6 m2 s-1, respectively. If we assume that the islands (surface runoff) alone were supplying dissolved Fe to the bloom region, then the flux estimates range from 2.3 to 14 nmol Fe m-2 d-1. If the plateau sediments are considered a source of Fe, and conveyed to the bloom region through deep winter mixing combined with horizontal transport, then this flux may be as high as 64 to 390 nmol Fe m-2 d-1. Combined, these Fe sources are sufficient to initiate and maintain the annual phytoplankton bloom.
    Description: This work was funded by grants from the Natural Environment Research Council [NE/B502844/1] and the National Science Foundation (ANT-0443869 to M.A.C).
    Keywords: Radium isotopes ; Iron ; Productivity ; Ocean mixing ; Southern Ocean
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  • 10
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    New perspectives on radium behavior within a subterranean estuary (2008)
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    Publication Date: 2022-05-26
    Description: Author Posting. © Elsevier B.V., 2007. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Marine Chemistry 109 (2008): 250-267, doi:10.1016/j.marchem.2007.12.002.
    Description: Over the past decade, radium isotopes have been frequently applied as tracers of submarine groundwater discharge (SGD). The unique radium signature of SGD is acquired within the subterranean estuary, a mixing zone between fresh groundwater and seawater in coastal aquifers, yet little is known about what controls Ra cycling in this system. The focus of this study was to examine controls on sediment and groundwater radium activities within permeable aquifer sands (Waquoit Bay, MA, USA) through a combination of field and laboratory studies. In the field, a series of sediment cores and corresponding groundwater profiles were collected for analysis of the four radium isotopes, as well as dissolved and sediment associated manganese, iron, and barium. We found that in addition to greater desorption at increasing salinity, radium was also closely tied to manganese and iron redox cycling within these sediments. A series of laboratory adsorption/desorption experiments helped elucidate the importance of 1) contact time between sediment and water, 2) salinity of water in contact with sediment, 3) redox conditions of water in contact with sediment, and 4) the chemical characteristics of sediment on radium adsorption/desorption. We found that these reactions are rapid (on the order of hours), desorption increases with increasing salinity and decreasing pH, and the presence of Fe and Mn (hydr)oxides on the sediment inhibit the release of radium. These sediments have a large capacity to sorb radium from fresh water. Combined with these experimental results, we present evidence from time series groundwater sampling that within this subterranean estuary there are cyclic periods of Ra accumulation and release controlled by changing salinity and redox conditions.
    Description: This work is a result of research sponsored by NSF (OCE- 0425061 to M.A.C.), the WHOI-NOC Student Exchange program (to P.J.M), and the WHOI Postdoctoral Scholar program (to H.D.).
    Keywords: Radium ; Sediments ; Desorption ; Adsorption ; Barium ; Submarine groundwater ; Subterranean estuary ; Redox reactions ; Ion exchange ; Distribution coefficient
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