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* Corresponding author. Tel.: 44-171-938-8996; fax: 44-171-938-9277. E-mail addresses: jy@nhm.ac.uk (J.R. Young), zivp @geo.vu.nl (P. Ziveri).

Deep-Sea Research II 47 (2000) 1679 }1700

Calculation of coccolith volume and its use incalibration of carbonate flux estimates

Jeremy R. Young *, Patrizia Ziveri Palaeontology Department, The Natural History Museum, London, SW7 5BD, UK

Vrije Uni versiteit Amsterdam, Faculteit der Aardwetenschapen, Amsterdam, NL, The Netherlands

Received 13 February 1998; received in revised form 22 December 1998; accepted 5 January 1999

Abstract

Estimates of coccolith volume help in determining total coccolith carbonate #uxes and therelative contributions of various coccolith species. It is argued here that the best approach to

deriving such coccolith volumes is to calculate shape factors, k , for each species separatelybased on reconstruction of cross pro " les and to determine mean sizes from measurement of sizevariation in the sample of interest. Then volume " k l . Values of k are given for the mostimportant extant coccolith species based on reconstruction of cross-sections, followed bycalculation of a volume of rotation using an iterative routine implemented in an image analysispackage. Substantial errors, ca. 50%, are inevitable in such calculations, but the resultant dataare nonetheless of value. Coccolith assemblages from North Atlantic (47 3N 20 3W) JGOFS 1989sediment trap samples are analysed as a test case; calculated coccolith PIC #uxes constitute30}80% of the chemically determined total PIC #uxes. 2000 Elsevier Science Ltd. All rightsreserved.

1. Introduction

Calculation of #uxes of matter within the oceanic water column has becomea major research endeavour over the last decade (e.g., Beaufort and Heussner, 1999;Broerse et al., 2000; Ziveri et al., 2000). This re #ects the importance of oceanic #uxes

within global biogeochemical cycles, most notably the carbon cycle. In addition, itre#ects the development of sediment traps that allow sampling of particulate #uxesover " nite time periods. Total #uxes of matter are best determined by chemical or

0967-0645/00/$- see front matter 2000 Elsevier Science Ltd. All rights reserved.

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physical measurement, but to probe the biotic component of the biogeochemicalsystem in any depth we require breakdown of #uxes at least by organismal group. Forthis, an attractive methodology is to convert specimen accumulation rates into mass#uxes. The methodology is attractive since biologists and micropalaeontologistsroutinely conduct per taxon specimen counts to investigate other questions. Forinstance, study of coccoliths in sediment trap samples may be carried out in order tostudy ecological succession, sedimentation processes or biogeography, but in all casesroutine analysis includes counts of the abundance of coccoliths, identi " ed to specieslevel. Converting these count data into per species carbonate #ux estimates is a trivialproblem, if accurate estimates of coccolith volume can be obtained.

In the case of coccoliths, we are particularly interested to quantify mass #uxes sincethey are widely believed to be a major, if not dominant, contributor to open-oceanic

carbonate #uxes. Moreover, since it is di $ cult to separate coccoliths from othersediment particles, conversion of taxon counts seems an obvious approach forcalculation of #ux rates. The methodology is also potentially applicable topalaeoceanographic studies * methods for calculating accumulation rates of cocco-liths in sediment cores (i.e., specimens deposited per unit area per unit time) arebecoming increasingly reliable and widely used (e.g., Su, 1996; Flores et al., 1997).Given reliable estimates of coccolith mass, this data can easily be converted intospecies-speci " c mass #uxes.

Several estimates of coccolith volume have been published (Paasche, 1962; Honjo,

1976; Samtleben and Bickert, 1990; Knappertsbusch and Brummer, 1995; Fagger-bakke et al., 1994; Beaufort and Heussner, 1999). The basic approach used in most of these studies (e.g., Beaufort and Heussner, 1999) is to calculate the surface area of thecoccolith, estimate an average thickness, and calculate the resultant volume makingsome corrections for tube structures, etc. These estimates provide a useful startingpoint, but they exclude several signi " cant species. In addition, estimates vary greatlybetween the sources, errors are unquanti " ed, and the e ! ect of size variation on volumeestimates has barely been discussed.

This paper presents new calculations of coccolith, and nannolith, volume for themost abundant extant species. These estimates are based mainly on calculation of coccolith volume from cross-sectional shape. This is a slightly complex technique, butis the most accurate geometric approach possible. Discussion of the results focuses onanalysis of errors and the extent to which #ux rates can be derived in this way.

2. Material and methods

2.1. Material and microscopy

A set of sediment trap samples from the UK North Atlantic JGOFS 1989 station(483N, 20 3W, 3000 m water depth) has been used here as a case study. Details of thesetraps are given in Newton et al. (1994). The samples have been used to provideestimates of coccolith length applicable to coccolith studies in this region, and toprovide a specimen set of coccolith counts to demonstrate the e ! ect of converting

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species counts into carbonate mass distributions. 1/64 rotary splits were provided byDr.R. Lampitt (Institute of Oceanographic Sciences). Strew preparations were madefrom these using 1 ml micropipette sub-samples, after homogenisation but withoutspecial preparation techniques. Slides were counted by light microscopy with count-ing of 10 " elds of view at ; 1600, followed by extended counting of larger specimens.All counts were converted initially into specimens per unit slide area and then into#uxes (based on slide area, sub-sample size, split size, sampling duration and trapopening size). Coccolith size measurements were carried out at ; 1600 magni " cationusing a double-ruled eyepiece graticule, giving a resolution of 0.32 m or, for thesmallest coccoliths, by using a digital image-capture system, as described by Younget al. (1996).

The use of a pipette rather than a rotary splitter for the " nal sub-sampling may have

introduced sampling errors. In addition, #ocs were present in most samples, whichcontained signi " cant numbers of coccoliths that were not possible to count. So, thecoccolith #ux estimates given for these samples have substantial associated errors.Broerse et al. (2000) describe techniques for reducing these errors.

2.2. Coccolith volume calculation

For any given shape, volume is a cubic function of linear dimension, e.g., for spheres< " 4/3 r , for cubes < " l . Or, more generally, < " k l where k is a constantdependent on the shape and l is a characteristic dimension. If l is maximumlength/diameter, then for a sphere k " /6 " 0.52, and for a cube k " 1.

If we assume that for a given coccolith species the shape is scale invariant (discussedbelow), then volume determination can be separated into two stages: " rst determina-tion of the shape constant k ; second determination of the size, l. As an additional step,volume can be converted to mass by multiplying by the density of calcite(2.7 g/cm " 2.7 pg/ m ).

2.2.1. Determination of k from a coccolith cross-sectionCoccoliths possess a high degree of radial symmetry; hence volume can be cal-

culated from a cross-section parallel to the axis of radial symmetry. A minority of coccoliths are circular, and for them calculation of volume from a cross-section can becarried out as follows: (a) the thickness of the coccolith cross-section is measured ateach of n increments out from the axis of the cross-section; (b) for each increment thevolume is calculated as a hollow cylinder; and (c) these volumes are integrated (Fig. 1).