## Abstract

Phytoplankton biovolume can be measured or calculated through the calculation of similar geometric models. A set of geometric models is suggested for calculating cell biovolume and surface area for 284 phytoplankton genera in China Sea waters. Thirty-one geometric shapes have been assigned to estimate the biovolume and surface area of phytoplankton cells. Reductions of error and microscopic effort are also discussed. The model has been verified by its application in the China Seas regions. The software to make these calculations is available at http://www.ouc.edu.cn/csmxy/sunjun/biovolume.htm

## INTRODUCTION

The biovolume of marine phytoplankton cells is important to the study of phytoplankton ecology. The related parameters, such as cell size and conversion of carbon content from biovolume, and physiology functions are also important for marine ecosystem studies (Malone, 1980; Sournia, 1981; Chisholm, 1992).

Phytoplankton cell size varies greatly among different genera or even between different individuals. Sizes range from a few micrometres (or even less than 1 μm) to a few millimetres. Hence, there is a wide range of nine orders in magnitude for cell biovolume of phytoplankton. Several automated and semi-automatic methods for biovolume estimation have been described in the literature, such as the Coulter Counter (Hasting et al., 1962; Maloney et al., 1962; Boyd and Johnson, 1995), the micrographic image analysis system (Gordon, 1974; Krambeck et al., 1981; Estep et al., 1986; Verity and Sieracki, 1993; Sieracki et al., 1998), flow cytometry (Olson et al., 1985; Wood et al., 1985; Steen, 1990; Cunningham and Buonnacorsi, 1992) and holographic scanning technology (Brown et al., 1989). However, the general method for calculating phytoplankton cell biovolume is based on geometric assignation (Kovala and Larrance, 1966; Willén, 1976; Sicko-Goad et al., 1977; Smayda, 1978; Edler, 1979; Rott, 1981; Kononen et al., 1984; Vilicic, 1985; Hillebrand et al., 1999). The methods mentioned above have advantages and/or disadvantages. Microscopic observation is a direct, convenient way to obtain species level information on phytoplankton taxa, whereas biovolume calculation based on geometric models of phytoplankton cells and their related conversion biomass are popular in phytoplankton ecology studies (Kuuppo, 1994; Snoeijs, 1994; Sommer, 1994, 1995; Tang, 1995; Hillebrand, 1997; Young and Ziveri, 2000). Some references (Smayda, 1978; Baltic Marine Environmental Protection Commission–Helsinki Commission, 1988; Hansen, 1992; Kramer et al., 1992) list the biovolume calculations and their conversion biomasses as a routine method when studying phytoplankton.

Phytoplankton cell geometric models for biovolume calculation have been discussed in the literature (Kovala and Larrance, 1966; Willén, 1976; Edler, 1979; Rott, 1981; Kononen et al., 1984; Hansen, 1992; Hillebrand et al., 1999; Sun et al., 2000a; Young and Ziveri, 2000). The method applies the principle of geometric models or shapes that are most similar to the real shape of the organism. Often there is the dilemma of whether to assign a phytoplankton cell shape to a complex but similar geometric model or to a simple, conveniently measurable, but inadequate model or shape. Most of the above studies pay attention to special regions or microalgae classes. Although different geometric equations used in the literature were dependent on dominance of the respective species in the local plankton communities, routine phytoplankton analysis would benefit from a series of standardized geometric models.

Hillebrand et al. recommend a standard set of 20 geometric shapes for over 850 genera and provide equations to be used for accurate estimates of cell volume and surface area for phytoplankton and microbenthic algae from linear dimensions measured microscopically (Hillebrand et al., 1999). Its extensive listing of cell shapes will be a valuable resource for experimental and literature-based studies of relationships between cell size, surface area and biovolume for a wide variety of physiological characteristics. This comprehensive study will help set consistent parameters for evaluating the dynamics of phytoplankton standing stocks in terms of biovolume for ecological studies, and will be evaluated as a primary research reference in this field for studies of phytoplankton by physiologists and ecologists (Wheeler, 1999). Although it is comprehensive and extensive, its applicability is in need of expansion.

In the present study, based on earlier work of Hillebrand et al. (Hillebrand et al., 1999), and focusing on phytoplankton species in the China Sea, a set of 31 geometric shapes is proposed for routine analysis of marine phytoplankton in China Sea waters. After consultation with the literature on phytoplankton studies in China’s seas, we found that nearly 2000 taxa were recorded, belonging to 10 diverse groups and 284 genera (due to the volume of references, they cannot all be cited in this paper). Although the old nomenclature system is still in use in China, the checklist was modified according to Tomas (Tomas, 1997) (Table I). In order to improve the applicability of Hillebrand’s geometric models, we reduced the number of microscopically measured line parameters, improving the previous shapes and updating the models. Furthermore, considering the fact that identifications of phytoplankton taxa need expert knowledge, we used the linear dimensions for length, width and height instead of apical axis, transapical axis and pervalvar axis. For example, when phytoplankton samples were observed under the light microscope, in most circumstances, the length (may be the pervalvar axis in some diatoms, e.g. Leptocylindrus spp.) and width were measured, then the cell volume and surface area were calculated from the geometric models discussed in this paper. The models were checked with a set of phytoplankton counter data and a Visual Basic for Applications (VBA) program was written in Microsoft Excel for calculations.

Table I:

Shape codes of phytoplankton genera found in China Sea waters according to the geometric models in Table II

Genera Shape code
1. Cyanobacteria
Anabaena Bory de St.-Vincent
Aphanothece Näegeli
Arthrospira Stizenbberger 28
Borzia Cohn 28
Calothrix Agardh 28
Camptylonemopsis Desikachary 28
Chlorogloea Wille
Chroococcus Näegeli
Chroothece Hansgirg 28
Dichothrix Zanardini 28
Enthophysalis Kützing
Gardnerula de Toni 28
Gomphosphaeria Kützing
Homoeothrix (Thuret) Kirchner 28
Hormathonema Ercegovic
Hydrocoleum Kützing 28
Hyella Bornet & Flahault 28
Isactis Thuret 28
Johannesbaptista de Toni
Kyrtuthrix Ercegovic 28
Lyngbya Agardh 28
Merismopedia Meyen 10
Microchaete Thuret 28
Microcoleus Desmazières 28
Microcystis Kützing
Nodularia Mertens 28
Oscillatoria Vaucher 28
Phormidium Kützing 28
Pleurocapsa Thuret ex Hauck 28
Richelia Schmidt 28
Rivularia (Roth) Agardh 28
Schizothrix Kützing 28
Sirocoleum Kützing 28
Scytonema Agardh 28
Spirulina Turpin 28
Symploca Kützing 28
Synechococcus Näegeli
Synechocystis Sauvageau
Tolypothrix Kützing 28
Trichodesmium Ehrenberg 28
Campylosira Grunow ex Van Heurck 14
Cerataulina Peragallo 28
Cerataulus Ehrenberg 28
Chaetoceros Ehrenberg 29
Chrysanthemodiscus Mann
Cistula Cleve 11
Climacodium Grunow 23
Climacosphenia Ehrenberg 31
Cocconeis Ehrenberg 11
Corethron Castracane
Coscinodiscus Ehrenberg emend. Hasle & Sims
Cyclotella Kützing ex de Brébisson
Cymatodiscus Hendey
Cymatoneis Cleve 13
Cymatosira Grunow 29
Cymatotheca Hendey 17
Cymbella Agardh 17
Dactyliosolen Castracane 28
Delphineis Andrews 11
Denticula Kützing 11
Detonula Schütt 28
Diatoma Bory de St.-Vincent 29
Dictyoneis Cleve 12
Dimeregramma Ralfs 29
Diploneis Ehrenberg ex Cleve 12
Ditylum Bailey ex Bailey 30
Endictya Ehrenberg
Entomoneis Ehrenberg 12
Ethmodiscus Castracane
Eucampia Ehrenberg 29
Eunotia Ehrenberg 15
Eunotogramma Weisse 14
Eupodiscus Bailey
Fallacia Stickle & Mann 11
Fragilaria Lyngbye 29
Fragilariopsis Hustedt emend. Hasle 29
Frustulia Rabenhorst 11
Gephyria Arnott 11
Gomphonema Agardh 21
Gomphonitzschia Grunow 21
Gossleriella Schütt
Plagiogrammopsis Hasle, von Stosch & Syvertsen 29
Plagiotropis Pfitzer 11
Planktoniella Schütt
Pleurosigma Smith 13
Pleurosira Trevison 28
Podocystis Bailey 11
Podosira Ehrenberg
Proboscia Sundström 28
Psammodictyon Mann 12
Psammodiscus Round & Mann
Pseudoeunotia Grunow
Pseudo-nitzschia Peragallo 13
Pseudosolenia Sundström 28
Pseudostaurosira (Grunow) Williams & Round 20
Pyxidicula Ehrenberg 11
Rhabdonema Kützing 10
Rhaphoneis Ehrenberg 13
Rhizosolenia Brightwell 28
Rhoicosphenia Grunow 21
Rhopalodia Müller 17
Rocella Hanna
Roperia Grunow ex Pelletan 11
Rossia Voigt 11
Schroederella Pavillard 28
Scoliopleura Grunow 11
Sellaphora Mereschkowsky 10
Skeletonema Greville
Stauroneis Ehrenberg 29
Stauropsis Meunier 29
Staurosira (Ehrenberg) Williams & Round 29
Stellarima Hasle & Sims
Stenopterobia de Brébisson ex Van Heurck 13
Stephanodiscus Ehrenberg
Stephanopyxis (Ehrenberg) Ehrenberg
Stictodiscus Greville
Striatella Agardh 29
Surirella Turpin 11
Synedra Ehrenberg 10
Synedrosphenia (Peragallo) Azpeitia 21
Tabellaria Ehrenberg 20
Dinophysis Ehrenberg
Diplopelta Stein ex Jörgensen
Diplopsalis Bergh
Dissodinium Pascher
Gloeodinium Klebs
Goniodoma Stein
Gonyaulax Diesing
Gymnodinium Stein
Gyrodinium Kofoid & Swezy
Heteraulacus Diesing
Heterodinium Kofoid
Histioneis Stein
Karenia Daugbjerg, Hansen, Larsen, Moestrup
Kofoidinium Pavillard
Lingulodinium Dodge
Noctiluca Suriray
Ornithocercus Stein 26
Ostreopsis Schmidt
Oxytoxum Stein
Peridiniopsis Lemmermann
Peridinium Ehrenberg
Phalacroma Stein
Podolampas Stein
Polykrikos Bütschli
Preperidiunium Mangin
Prorocentrum Ehrenberg
Protoperidinium Bergh
Xenococcus Thuret
2. Chrysophyceae
Chromulina Cienkowski
Dictyocha Ehrenberg
Dinobryon Ehrenberg
Mallonmonas Perty
Ochromonas Wyssotski
Synura Ehrenberg
3. Bacillariophyceae
Acanthoceras Honigmann 29
Achnanthes Bory de St.-Vincent 12
Achnanthidium Kützing 11
Actinocyclus Ehrenberg
Actinoptychus Ehrenberg
Amphipleura Kützing 11
Amphiprora Ehrenberg 11
Amphora Ehrenberg ex Kützing 17
Aneumastus Mann & Stickle 11
Anomoeoneis Pfitzer 11
Anorthoneis Grunow 11
Arachnoidiscus Deane ex Pritchard
Arcocellulus Hasle, von Stosch & Syertsen 29
Ardissonea De Notaris 10
Asterionella Hassall 10
Asterionellopsis Round 10
Asterolampra Ehrenberg
Asteromphalus Ehrenberg
Aulacodiscus Ehrenberg
Auliscus Ehrenberg 11
Auricula Castracane 17
Azpeitia Peragallo
Bacillaria Gmelin 10
Bellerochea Van Heurck emend. von Stosch 30
Biddulphia Gray 29
Bleakeleya Round 10
Caloneis Cleve 11
Campylodiscus Ehrenberg ex Kützing 11
Campyloneis Grunow 11
Grammatophora Ehrenberg 10
Guinardia Peragallo 28
Gyrosigma Hassall 13
Hantzschia Grunow 10
Helicotheca Ricard 29
Hemiaulus Ehrenberg 29
Hemidiscus Wallich 17
Hyalodiscus Ehrenberg
Hydrosera Wallich 18
Isthmia Agardh 29
Lauderia Cleve 28
Leptocylindrus Cleve 28
Leudugeria Tempère ex Van Heurck 17
Licmophora Agardh 16
Lioloma Hasle 10
Lithodesmium Ehrenberg 30
Luticola Mann 11
Lyrella Karajeva 11
Martyana Round 11
Mastogloia Thwaites ex Smith 11
Mastogonia Ehrenberg 11
Melosira Agardh 28
Meuniera Silva 29
Minidiscus Hasle
Minutocellus Hasle, von Stosch, & Syvertsen 11
Navicula Bory de St.-Vincent 11
Neidium Pfitzer 11
Nitzschia Hassall 13
Nitzschiella Rabenhorst 13
Odontella Agardh 29
Opephora Petit 29
Östrupia Heiden ex Schmidt 11
Palmeria Greville 17
Paralia Heiberg
Perissonoë Andrews & Stoelzel 10
Petrodictyon Mann 29
Phaeodactylum Bohlin 14
Pinnularia Ehrenberg 10
Plagiodiscus Grunow & Eulenstein 14
Plagiogramma Greville 11
Tabularia (Kützing) Williams & Round 10
Tetracyclus Ralfs 20
Thalassionema Grunow 10
Thalassiosira Cleve emend. Hasle
Thalassiothrix Cleve & Grunow 10
Toxarium Bailey 24
Trachyneis Cleve 11
Triceratium Ehrenberg 18
Trigonium Cleve 18
Trinacria Heiberg 18
Tropidoneis Cleve 11
Tryblioptychus Hendey 11
Xanthiopyxis (Ehrenberg) Ehrenberg 11
4. Raphidophyceae
Chattonella Biecheler
5. Prymnesiophyceae
Acanthoica Lohmann emend. Schiller and
Kleijne
Calyptrolithia Heimdal
Emiliana Hay & Mohler
Gephyrocapsa Kamptner
Hayaster Bukry
Syracosphaera Lohmann
6. Cryptophyceae
Chroomonas Hansgirg
Cryptomonas Ehrenberg
7. Dinophyceae
Alexandrium Halim
Amphidinium Claparède et Lachmann
Amphisolenia Stein
Balechina Loeblich J & Loeblich III
Blepharocysta Ehrenberg
Ptychodiscus Stein
Pyrocystis Murray ex Haeckel
Pyrophacus Stein
Scrippsiella Balech ex Loeblich III
Schuettiella Balech
Spiraulax Kofoid
Symbiodinium Freudenthal
Triposolenia Kofoid 27
Centrodinium Kofoid
Ceratium Schrank 25
Ceratocorys Stein 26
8. Euglenophyceae
Euglena Ehrenberg 22
Eutreptia Perty 22
9. Prasinophyceae
Halosphaera Schmitz
Mantoniella Desikachary
Micromonas Manton & Parke
Nephroselmis Stein
Pyramimonas Schmarda
10. Chlorophyceae
Actinastrum Lagerheim
Ankistrodesmus Cord 16
Brachiomonas Bohlin
Carteria Diesing
Chlamydomonas Ehrenberg
Dunaliella Teodoresco
Pediastrum Meyen 11
Scenedesmus Meyen
Tetraëdron Kützing 10
Genera Shape code
1. Cyanobacteria
Anabaena Bory de St.-Vincent
Aphanothece Näegeli
Arthrospira Stizenbberger 28
Borzia Cohn 28
Calothrix Agardh 28
Camptylonemopsis Desikachary 28
Chlorogloea Wille
Chroococcus Näegeli
Chroothece Hansgirg 28
Dichothrix Zanardini 28
Enthophysalis Kützing
Gardnerula de Toni 28
Gomphosphaeria Kützing
Homoeothrix (Thuret) Kirchner 28
Hormathonema Ercegovic
Hydrocoleum Kützing 28
Hyella Bornet & Flahault 28
Isactis Thuret 28
Johannesbaptista de Toni
Kyrtuthrix Ercegovic 28
Lyngbya Agardh 28
Merismopedia Meyen 10
Microchaete Thuret 28
Microcoleus Desmazières 28
Microcystis Kützing
Nodularia Mertens 28
Oscillatoria Vaucher 28
Phormidium Kützing 28
Pleurocapsa Thuret ex Hauck 28
Richelia Schmidt 28
Rivularia (Roth) Agardh 28
Schizothrix Kützing 28
Sirocoleum Kützing 28
Scytonema Agardh 28
Spirulina Turpin 28
Symploca Kützing 28
Synechococcus Näegeli
Synechocystis Sauvageau
Tolypothrix Kützing 28
Trichodesmium Ehrenberg 28
Campylosira Grunow ex Van Heurck 14
Cerataulina Peragallo 28
Cerataulus Ehrenberg 28
Chaetoceros Ehrenberg 29
Chrysanthemodiscus Mann
Cistula Cleve 11
Climacodium Grunow 23
Climacosphenia Ehrenberg 31
Cocconeis Ehrenberg 11
Corethron Castracane
Coscinodiscus Ehrenberg emend. Hasle & Sims
Cyclotella Kützing ex de Brébisson
Cymatodiscus Hendey
Cymatoneis Cleve 13
Cymatosira Grunow 29
Cymatotheca Hendey 17
Cymbella Agardh 17
Dactyliosolen Castracane 28
Delphineis Andrews 11
Denticula Kützing 11
Detonula Schütt 28
Diatoma Bory de St.-Vincent 29
Dictyoneis Cleve 12
Dimeregramma Ralfs 29
Diploneis Ehrenberg ex Cleve 12
Ditylum Bailey ex Bailey 30
Endictya Ehrenberg
Entomoneis Ehrenberg 12
Ethmodiscus Castracane
Eucampia Ehrenberg 29
Eunotia Ehrenberg 15
Eunotogramma Weisse 14
Eupodiscus Bailey
Fallacia Stickle & Mann 11
Fragilaria Lyngbye 29
Fragilariopsis Hustedt emend. Hasle 29
Frustulia Rabenhorst 11
Gephyria Arnott 11
Gomphonema Agardh 21
Gomphonitzschia Grunow 21
Gossleriella Schütt
Plagiogrammopsis Hasle, von Stosch & Syvertsen 29
Plagiotropis Pfitzer 11
Planktoniella Schütt
Pleurosigma Smith 13
Pleurosira Trevison 28
Podocystis Bailey 11
Podosira Ehrenberg
Proboscia Sundström 28
Psammodictyon Mann 12
Psammodiscus Round & Mann
Pseudoeunotia Grunow
Pseudo-nitzschia Peragallo 13
Pseudosolenia Sundström 28
Pseudostaurosira (Grunow) Williams & Round 20
Pyxidicula Ehrenberg 11
Rhabdonema Kützing 10
Rhaphoneis Ehrenberg 13
Rhizosolenia Brightwell 28
Rhoicosphenia Grunow 21
Rhopalodia Müller 17
Rocella Hanna
Roperia Grunow ex Pelletan 11
Rossia Voigt 11
Schroederella Pavillard 28
Scoliopleura Grunow 11
Sellaphora Mereschkowsky 10
Skeletonema Greville
Stauroneis Ehrenberg 29
Stauropsis Meunier 29
Staurosira (Ehrenberg) Williams & Round 29
Stellarima Hasle & Sims
Stenopterobia de Brébisson ex Van Heurck 13
Stephanodiscus Ehrenberg
Stephanopyxis (Ehrenberg) Ehrenberg
Stictodiscus Greville
Striatella Agardh 29
Surirella Turpin 11
Synedra Ehrenberg 10
Synedrosphenia (Peragallo) Azpeitia 21
Tabellaria Ehrenberg 20
Dinophysis Ehrenberg
Diplopelta Stein ex Jörgensen
Diplopsalis Bergh
Dissodinium Pascher
Gloeodinium Klebs
Goniodoma Stein
Gonyaulax Diesing
Gymnodinium Stein
Gyrodinium Kofoid & Swezy
Heteraulacus Diesing
Heterodinium Kofoid
Histioneis Stein
Karenia Daugbjerg, Hansen, Larsen, Moestrup
Kofoidinium Pavillard
Lingulodinium Dodge
Noctiluca Suriray
Ornithocercus Stein 26
Ostreopsis Schmidt
Oxytoxum Stein
Peridiniopsis Lemmermann
Peridinium Ehrenberg
Phalacroma Stein
Podolampas Stein
Polykrikos Bütschli
Preperidiunium Mangin
Prorocentrum Ehrenberg
Protoperidinium Bergh
Xenococcus Thuret
2. Chrysophyceae
Chromulina Cienkowski
Dictyocha Ehrenberg
Dinobryon Ehrenberg
Mallonmonas Perty
Ochromonas Wyssotski
Synura Ehrenberg
3. Bacillariophyceae
Acanthoceras Honigmann 29
Achnanthes Bory de St.-Vincent 12
Achnanthidium Kützing 11
Actinocyclus Ehrenberg
Actinoptychus Ehrenberg
Amphipleura Kützing 11
Amphiprora Ehrenberg 11
Amphora Ehrenberg ex Kützing 17
Aneumastus Mann & Stickle 11
Anomoeoneis Pfitzer 11
Anorthoneis Grunow 11
Arachnoidiscus Deane ex Pritchard
Arcocellulus Hasle, von Stosch & Syertsen 29
Ardissonea De Notaris 10
Asterionella Hassall 10
Asterionellopsis Round 10
Asterolampra Ehrenberg
Asteromphalus Ehrenberg
Aulacodiscus Ehrenberg
Auliscus Ehrenberg 11
Auricula Castracane 17
Azpeitia Peragallo
Bacillaria Gmelin 10
Bellerochea Van Heurck emend. von Stosch 30
Biddulphia Gray 29
Bleakeleya Round 10
Caloneis Cleve 11
Campylodiscus Ehrenberg ex Kützing 11
Campyloneis Grunow 11
Grammatophora Ehrenberg 10
Guinardia Peragallo 28
Gyrosigma Hassall 13
Hantzschia Grunow 10
Helicotheca Ricard 29
Hemiaulus Ehrenberg 29
Hemidiscus Wallich 17
Hyalodiscus Ehrenberg
Hydrosera Wallich 18
Isthmia Agardh 29
Lauderia Cleve 28
Leptocylindrus Cleve 28
Leudugeria Tempère ex Van Heurck 17
Licmophora Agardh 16
Lioloma Hasle 10
Lithodesmium Ehrenberg 30
Luticola Mann 11
Lyrella Karajeva 11
Martyana Round 11
Mastogloia Thwaites ex Smith 11
Mastogonia Ehrenberg 11
Melosira Agardh 28
Meuniera Silva 29
Minidiscus Hasle
Minutocellus Hasle, von Stosch, & Syvertsen 11
Navicula Bory de St.-Vincent 11
Neidium Pfitzer 11
Nitzschia Hassall 13
Nitzschiella Rabenhorst 13
Odontella Agardh 29
Opephora Petit 29
Östrupia Heiden ex Schmidt 11
Palmeria Greville 17
Paralia Heiberg
Perissonoë Andrews & Stoelzel 10
Petrodictyon Mann 29
Phaeodactylum Bohlin 14
Pinnularia Ehrenberg 10
Plagiodiscus Grunow & Eulenstein 14
Plagiogramma Greville 11
Tabularia (Kützing) Williams & Round 10
Tetracyclus Ralfs 20
Thalassionema Grunow 10
Thalassiosira Cleve emend. Hasle
Thalassiothrix Cleve & Grunow 10
Toxarium Bailey 24
Trachyneis Cleve 11
Triceratium Ehrenberg 18
Trigonium Cleve 18
Trinacria Heiberg 18
Tropidoneis Cleve 11
Tryblioptychus Hendey 11
Xanthiopyxis (Ehrenberg) Ehrenberg 11
4. Raphidophyceae
Chattonella Biecheler
5. Prymnesiophyceae
Acanthoica Lohmann emend. Schiller and
Kleijne
Calyptrolithia Heimdal
Emiliana Hay & Mohler
Gephyrocapsa Kamptner
Hayaster Bukry
Syracosphaera Lohmann
6. Cryptophyceae
Chroomonas Hansgirg
Cryptomonas Ehrenberg
7. Dinophyceae
Alexandrium Halim
Amphidinium Claparède et Lachmann
Amphisolenia Stein
Balechina Loeblich J & Loeblich III
Blepharocysta Ehrenberg
Ptychodiscus Stein
Pyrocystis Murray ex Haeckel
Pyrophacus Stein
Scrippsiella Balech ex Loeblich III
Schuettiella Balech
Spiraulax Kofoid
Symbiodinium Freudenthal
Triposolenia Kofoid 27
Centrodinium Kofoid
Ceratium Schrank 25
Ceratocorys Stein 26
8. Euglenophyceae
Euglena Ehrenberg 22
Eutreptia Perty 22
9. Prasinophyceae
Halosphaera Schmitz
Mantoniella Desikachary
Micromonas Manton & Parke
Nephroselmis Stein
Pyramimonas Schmarda
10. Chlorophyceae
Actinastrum Lagerheim
Ankistrodesmus Cord 16
Brachiomonas Bohlin
Carteria Diesing
Chlamydomonas Ehrenberg
Dunaliella Teodoresco
Pediastrum Meyen 11
Scenedesmus Meyen
Tetraëdron Kützing 10

Table II:

Geometric shapes and equations for the calculation of biovolume and surface area

Shape code Simulated shape Volume (V) and surface area (A) model
1-H
$$\begin{array}{l}V\ =\ \frac{{\pi}}{6}{\cdot}a^{3}\\A\ =\ {\pi}{\cdot}a^{2}\end{array}$$

2-H
$$\begin{array}{l}V\ =\ \frac{{\pi}}{6}{\cdot}b^{2}{\cdot}a\\A\ =\ \frac{{\pi}{\cdot}b}{2}\left(b+\frac{a^{2}}{\sqrt{a^{2}{-}b^{2}}}\mathrm{sin}^{{-}1}\frac{\sqrt{a^{2}{-}b^{2}}}{a}\right)\end{array}$$

3-H
$$\begin{array}{l}V\ =\ \frac{{\pi}}{6}{\cdot}a{\cdot}b{\cdot}c\\A\ {\approx}\ \frac{{\pi}}{4}{\cdot}\left(b+c\right){\cdot}\left[\left(\frac{b+c}{2}\right)+\frac{2a^{2}}{\sqrt{4a^{2}{-}\left(b+c\right)^{2}}}\mathrm{sin}^{{-}1}\frac{\sqrt{4a^{2}{-}\left(b+c\right)^{2}}}{2a}\right]\end{array}$$

4-H
$$\begin{array}{l}V\ =\ \frac{{\pi}}{4}{\cdot}a^{2}{\cdot}c\\A\ =\ {\pi}{\cdot}a{\cdot}\left(\frac{a}{2}+c\right)\end{array}$$

5-H
$$\begin{array}{l}V\ =\ {\pi}{\cdot}b^{2}{\cdot}\left(\frac{a}{4}{-}\frac{b}{12}\right)\\A\ =\ {\pi}{\cdot}a{\cdot}b\end{array}$$

6-H  Suppose the height of cones is half of b:
$$\begin{array}{l}V\ =\ \frac{{\pi}}{4}{\cdot}b^{2}{\cdot}\left(a{-}\frac{b}{3}\right)\\A\ =\ {\pi}{\cdot}b{\cdot}\left(a{-}\frac{4{-}\sqrt{3}}{4}b\right)\end{array}$$

7-H
$$\begin{array}{l}V\ =\ \frac{{\pi}}{12}{\cdot}a{\cdot}b^{2}\\A\ =\ \frac{{\pi}}{4}{\cdot}b{\cdot}\left(b+\sqrt{4a^{2}+b^{2}}\right)\end{array}$$

8-H
$$\begin{array}{l}V\ =\ \frac{{\pi}}{12}{\cdot}a{\cdot}b^{2}\\A\ =\ \frac{{\pi}}{2}{\cdot}b{\cdot}\sqrt{a^{2}+b^{2}}\end{array}$$

9-H
$$\begin{array}{l}V\ =\ \frac{{\pi}}{4}{\cdot}a{\cdot}b^{2}\\A\ =\ \frac{{\pi}}{2}{\cdot}b^{2}{\cdot}\left(b+\sqrt{\frac{2a^{2}{-}ab+b^{2}}{2}}\right)\end{array}$$

10-H
$$\begin{array}{l}V\ =\ a{\cdot}b{\cdot}c\\A\ =\ 2{\cdot}a{\cdot}b+2{\cdot}b{\cdot}c+2{\cdot}a{\cdot}c\end{array}$$

11-H
$$\begin{array}{l}V\ =\ \frac{{\pi}}{4}{\cdot}a{\cdot}b{\cdot}c\\A\ =\ \frac{{\pi}}{2}{\cdot}\left(a{\cdot}b+b{\cdot}c+a{\cdot}c\right)\end{array}$$

12-H
$$\begin{array}{l}V\ {\approx}\ \frac{{\pi}}{4}{\cdot}a{\cdot}b{\cdot}c\\A\ {\approx}\ \frac{{\pi}}{2}{\cdot}\left(a{\cdot}b+b{\cdot}c+a{\cdot}c\right)\end{array}$$

13-H
$$\begin{array}{l}V\ =\ \frac{1}{2}{\cdot}a{\cdot}b{\cdot}c\\A\ =\ a{\cdot}b+\frac{\sqrt{a^{2}+b^{2}}}{4}{\cdot}c\end{array}$$

14-H
$$\begin{array}{l}V\ =\ \frac{{\pi}}{4}{\cdot}a{\cdot}b{\cdot}c\\A\ =\ \frac{{\pi}}{4}{\cdot}\left(a{\cdot}b+b{\cdot}c+a{\cdot}c\right)+a{\cdot}c\end{array}$$

15-H
$$\begin{array}{l}V\ {\approx}\ \frac{{\pi}}{4}{\cdot}a{\cdot}b{\cdot}c\\A\ {\approx}\ \frac{{\pi}}{4}{\cdot}\left(a{\cdot}b+b{\cdot}c+a{\cdot}c\right)+a{\cdot}c\end{array}$$

16-H
$$\begin{array}{l}V\ {\approx}\ \frac{{\pi}}{6}{\cdot}a{\cdot}b^{2}\\A\ {\approx}\ \frac{{\pi}}{2}{\cdot}b{\cdot}\sqrt{a^{2}+b^{2}}\end{array}$$

17-H
$$\begin{array}{l}V\ =\ \frac{2}{3}{\cdot}a{\cdot}c^{2}{\cdot}\mathrm{a}\mathrm{sin}\left(\frac{b}{2c}\right)\\A\ =\ \frac{{\pi}}{2}{\cdot}a{\cdot}c+b{\cdot}\left[c+\frac{a^{2}}{2\sqrt{a^{2}{-}4c^{2}}}{\cdot}\mathrm{sin}^{{-}1}\left(\frac{\sqrt{a^{2}{-}4c^{2}}}{a}\right)\right]\end{array}$$

18-H
$$\begin{array}{l}V\ =\ \frac{\sqrt{3}}{4}{\cdot}c{\cdot}a^{2}\\A\ =\ 3a{\cdot}c+\frac{\sqrt{3}}{2}{\cdot}a^{2}\end{array}$$

19-H
$$\begin{array}{l}V\ =\ \frac{1}{6}{\cdot}a^{2}{\cdot}c\\A\ =\ \frac{1}{2}{\cdot}a^{2}+a{\cdot}\sqrt{a^{2}+8c^{2}}\end{array}$$

20-H
$$\begin{array}{l}V\ {\approx}\ \frac{{\pi}}{4}{\cdot}a{\cdot}b{\cdot}c\\A\ {\approx}\ \frac{{\pi}}{2}{\cdot}\left(a{\cdot}b+b{\cdot}c+a{\cdot}c\right)\end{array}$$

21-H
$$\begin{array}{l}V\ {\approx}\ \frac{a{\cdot}b}{4}{\cdot}\left[a+\left(\frac{{\pi}}{4}{-}1\right){\cdot}b\right]{\cdot}\mathrm{a}\mathrm{sin}\left(\frac{c}{2a}\right)\\A\ {\approx}\ \frac{b}{2}{\cdot}\left(2a+{\pi}{\cdot}a{\cdot}\mathrm{a}\mathrm{sin}\left(\frac{c}{2a}\right)+\left(\frac{{\pi}}{2}{-}2\right){\cdot}b\right)\end{array}$$

22-SL
$$\begin{array}{l}V\ =\ \frac{{\pi}}{3}{\cdot}\left(a_{1}+a_{2}\right){\cdot}b_{1}^{2}+\frac{{\pi}}{4}{\cdot}\left(a_{2}+b_{2}\right){\cdot}b_{2}^{2}+\frac{{\pi}}{12}{\cdot}a_{2}{\cdot}b_{1}{\cdot}b_{2}\\A\ =\ {\pi}{\cdot}a_{1}{\cdot}b_{1}+\frac{{\pi}}{4}{\cdot}b_{1}^{2}+\frac{{\pi}}{2}{\cdot}b_{2}^{2}+\frac{{\pi}}{2}{\cdot}b_{2}^{2}{\cdot}\sqrt{\left(\frac{a_{1}}{b_{1}}\right)^{2}+\frac{1}{4}}{-}\frac{{\pi}}{2}{\cdot}b_{1}{\cdot}\sqrt{\left(\frac{a_{1}{\cdot}b_{2}}{b_{1}}{-}a_{1}\right)^{2}+\frac{b_{1}^{2}}{4}}\end{array}$$

23-SL
$$\begin{array}{l}V\ =\ \frac{{\pi}}{4}{\cdot}a_{1}{\cdot}b_{1}{\cdot}c_{1}+\frac{{\pi}}{3}{\cdot}a_{2}{\cdot}b_{2}^{2}\\A\ =\ \frac{{\pi}}{2}{\cdot}a_{1}{\cdot}b_{1}+\frac{{\pi}}{2}{\cdot}b_{1}{\cdot}c_{1}+\frac{{\pi}}{2}{\cdot}a_{1}{\cdot}c_{1}+{\pi}{\cdot}b_{2}{\cdot}\left(\sqrt{4a_{2}^{2}+b_{2}^{2}}{-}b_{2}\right)\end{array}$$

24-SL
$$\begin{array}{l}V\ {\approx}\ \frac{{\pi}}{4}{\cdot}a{\cdot}b{\cdot}c\\A\ {\approx}\ \frac{{\pi}}{2}{\cdot}\left(a{\cdot}b+b{\cdot}c+a{\cdot}c\right)\end{array}$$

25-SL
$$\begin{array}{l}\mathrm{Suppose:}\ b_{2}=b_{3}=b_{4}\\V\ =\ \frac{{\pi}}{4}{\cdot}a_{2}{\cdot}b_{2}^{2}+\frac{{\pi}}{12}{\cdot}\left(a_{3}+a_{4}\right){\cdot}b_{2}^{2}+\frac{{\pi}}{6}{\cdot}a_{1}{\cdot}b_{1}{\cdot}b_{2}\\A\ {\approx}\ \frac{{\pi}}{4}{\cdot}\left(b_{1}+b_{2}\right){\cdot}\left[\frac{b_{1}+b_{2}}{2}+\frac{a_{1}^{2}}{\sqrt{a_{1}^{2}{-}\left(\frac{b_{1}+b_{2}}{2}\right)^{2}}}{\cdot}\mathrm{sin}^{{-}1}\frac{\sqrt{a_{1}^{2}{-}\left(\frac{b_{1}+b_{2}}{2}\right)^{2}}}{a_{1}}\right]+\frac{{\pi}}{2}{\cdot}b_{2}{\cdot}\left(2a_{2}+\sqrt{a_{3}^{2}+\frac{b_{2}^{2}}{4}}+\sqrt{a_{4}^{2}+\frac{b_{2}^{2}}{4}}{-}b_{2}\right)\end{array}$$

26-SL
$$\begin{array}{l}V\ =\ \frac{{\pi}}{12}{\cdot}a^{3}\\A\ =\ \frac{3{\pi}}{4}{\cdot}a^{2}\end{array}$$

27-SL
$$\begin{array}{l}V\ =\ \frac{{\pi}}{4}{\cdot}a_{2}{\cdot}b_{2}^{2}+\frac{{\pi}}{2}{\cdot}a_{3}{\cdot}b_{3}^{2}+\frac{{\pi}}{12}{\cdot}a_{1}{\cdot}\left(b_{1}^{2}+b_{1}{\cdot}b_{2}+b_{2}^{2}\right)\\A\ =\ \frac{{\pi}}{2}{\cdot}\left(b_{1}+b_{2}\right){\cdot}\sqrt{a_{1}^{2}+\left(\frac{b_{1}{-}b_{2}}{2}\right)^{2}}+\frac{{\pi}}{4}{\cdot}\left(b_{1}^{2}+b_{2}^{2}\right)+2{\pi}{\cdot}\left(a_{2}{\cdot}b_{2}+a_{3}{\cdot}b_{3}\right)\end{array}$$

28-H
$$\begin{array}{l}V\ =\ \frac{{\pi}}{4}{\cdot}b^{2}{\cdot}a\\A\ =\ {\pi}{\cdot}b{\cdot}\left(\frac{b}{2}+a\right)\end{array}$$

29-H
$$\begin{array}{l}V\ =\ \frac{{\pi}}{4}{\cdot}a{\cdot}b{\cdot}c\\A\ =\ \frac{{\pi}}{2}{\cdot}\left(a{\cdot}b+b{\cdot}c+a{\cdot}c\right)\end{array}$$

30-H
$$\begin{array}{l}V\ =\ \frac{\sqrt{3}}{4}{\cdot}a{\cdot}b^{2}\\A\ =\ 3a{\cdot}b+\frac{\sqrt{3}}{2}{\cdot}b^{2}\end{array}$$

31-SL
$$\begin{array}{l}V\ {\approx}\ c{\cdot}\left(a_{1}{\cdot}b_{1}+\frac{{\pi}}{4}{\cdot}a_{2}{\cdot}b_{2}\right)\\A\ {\approx}\ c{\cdot}\left(2a_{1}+b_{1}+\frac{{\pi}}{2}{\cdot}a_{2}+\frac{{\pi}}{2}{\cdot}b_{2}\right)+2a_{1}{\cdot}b_{1}+\frac{{\pi}}{2}{\cdot}a_{2}{\cdot}b_{2}\end{array}$$

Shape code Simulated shape Volume (V) and surface area (A) model
1-H
$$\begin{array}{l}V\ =\ \frac{{\pi}}{6}{\cdot}a^{3}\\A\ =\ {\pi}{\cdot}a^{2}\end{array}$$

2-H
$$\begin{array}{l}V\ =\ \frac{{\pi}}{6}{\cdot}b^{2}{\cdot}a\\A\ =\ \frac{{\pi}{\cdot}b}{2}\left(b+\frac{a^{2}}{\sqrt{a^{2}{-}b^{2}}}\mathrm{sin}^{{-}1}\frac{\sqrt{a^{2}{-}b^{2}}}{a}\right)\end{array}$$

3-H
$$\begin{array}{l}V\ =\ \frac{{\pi}}{6}{\cdot}a{\cdot}b{\cdot}c\\A\ {\approx}\ \frac{{\pi}}{4}{\cdot}\left(b+c\right){\cdot}\left[\left(\frac{b+c}{2}\right)+\frac{2a^{2}}{\sqrt{4a^{2}{-}\left(b+c\right)^{2}}}\mathrm{sin}^{{-}1}\frac{\sqrt{4a^{2}{-}\left(b+c\right)^{2}}}{2a}\right]\end{array}$$

4-H
$$\begin{array}{l}V\ =\ \frac{{\pi}}{4}{\cdot}a^{2}{\cdot}c\\A\ =\ {\pi}{\cdot}a{\cdot}\left(\frac{a}{2}+c\right)\end{array}$$

5-H
$$\begin{array}{l}V\ =\ {\pi}{\cdot}b^{2}{\cdot}\left(\frac{a}{4}{-}\frac{b}{12}\right)\\A\ =\ {\pi}{\cdot}a{\cdot}b\end{array}$$

6-H  Suppose the height of cones is half of b:
$$\begin{array}{l}V\ =\ \frac{{\pi}}{4}{\cdot}b^{2}{\cdot}\left(a{-}\frac{b}{3}\right)\\A\ =\ {\pi}{\cdot}b{\cdot}\left(a{-}\frac{4{-}\sqrt{3}}{4}b\right)\end{array}$$

7-H
$$\begin{array}{l}V\ =\ \frac{{\pi}}{12}{\cdot}a{\cdot}b^{2}\\A\ =\ \frac{{\pi}}{4}{\cdot}b{\cdot}\left(b+\sqrt{4a^{2}+b^{2}}\right)\end{array}$$

8-H
$$\begin{array}{l}V\ =\ \frac{{\pi}}{12}{\cdot}a{\cdot}b^{2}\\A\ =\ \frac{{\pi}}{2}{\cdot}b{\cdot}\sqrt{a^{2}+b^{2}}\end{array}$$

9-H
$$\begin{array}{l}V\ =\ \frac{{\pi}}{4}{\cdot}a{\cdot}b^{2}\\A\ =\ \frac{{\pi}}{2}{\cdot}b^{2}{\cdot}\left(b+\sqrt{\frac{2a^{2}{-}ab+b^{2}}{2}}\right)\end{array}$$

10-H
$$\begin{array}{l}V\ =\ a{\cdot}b{\cdot}c\\A\ =\ 2{\cdot}a{\cdot}b+2{\cdot}b{\cdot}c+2{\cdot}a{\cdot}c\end{array}$$

11-H
$$\begin{array}{l}V\ =\ \frac{{\pi}}{4}{\cdot}a{\cdot}b{\cdot}c\\A\ =\ \frac{{\pi}}{2}{\cdot}\left(a{\cdot}b+b{\cdot}c+a{\cdot}c\right)\end{array}$$

12-H
$$\begin{array}{l}V\ {\approx}\ \frac{{\pi}}{4}{\cdot}a{\cdot}b{\cdot}c\\A\ {\approx}\ \frac{{\pi}}{2}{\cdot}\left(a{\cdot}b+b{\cdot}c+a{\cdot}c\right)\end{array}$$

13-H
$$\begin{array}{l}V\ =\ \frac{1}{2}{\cdot}a{\cdot}b{\cdot}c\\A\ =\ a{\cdot}b+\frac{\sqrt{a^{2}+b^{2}}}{4}{\cdot}c\end{array}$$

14-H
$$\begin{array}{l}V\ =\ \frac{{\pi}}{4}{\cdot}a{\cdot}b{\cdot}c\\A\ =\ \frac{{\pi}}{4}{\cdot}\left(a{\cdot}b+b{\cdot}c+a{\cdot}c\right)+a{\cdot}c\end{array}$$

15-H
$$\begin{array}{l}V\ {\approx}\ \frac{{\pi}}{4}{\cdot}a{\cdot}b{\cdot}c\\A\ {\approx}\ \frac{{\pi}}{4}{\cdot}\left(a{\cdot}b+b{\cdot}c+a{\cdot}c\right)+a{\cdot}c\end{array}$$

16-H
$$\begin{array}{l}V\ {\approx}\ \frac{{\pi}}{6}{\cdot}a{\cdot}b^{2}\\A\ {\approx}\ \frac{{\pi}}{2}{\cdot}b{\cdot}\sqrt{a^{2}+b^{2}}\end{array}$$

17-H
$$\begin{array}{l}V\ =\ \frac{2}{3}{\cdot}a{\cdot}c^{2}{\cdot}\mathrm{a}\mathrm{sin}\left(\frac{b}{2c}\right)\\A\ =\ \frac{{\pi}}{2}{\cdot}a{\cdot}c+b{\cdot}\left[c+\frac{a^{2}}{2\sqrt{a^{2}{-}4c^{2}}}{\cdot}\mathrm{sin}^{{-}1}\left(\frac{\sqrt{a^{2}{-}4c^{2}}}{a}\right)\right]\end{array}$$

18-H
$$\begin{array}{l}V\ =\ \frac{\sqrt{3}}{4}{\cdot}c{\cdot}a^{2}\\A\ =\ 3a{\cdot}c+\frac{\sqrt{3}}{2}{\cdot}a^{2}\end{array}$$

19-H
$$\begin{array}{l}V\ =\ \frac{1}{6}{\cdot}a^{2}{\cdot}c\\A\ =\ \frac{1}{2}{\cdot}a^{2}+a{\cdot}\sqrt{a^{2}+8c^{2}}\end{array}$$

20-H
$$\begin{array}{l}V\ {\approx}\ \frac{{\pi}}{4}{\cdot}a{\cdot}b{\cdot}c\\A\ {\approx}\ \frac{{\pi}}{2}{\cdot}\left(a{\cdot}b+b{\cdot}c+a{\cdot}c\right)\end{array}$$

21-H
$$\begin{array}{l}V\ {\approx}\ \frac{a{\cdot}b}{4}{\cdot}\left[a+\left(\frac{{\pi}}{4}{-}1\right){\cdot}b\right]{\cdot}\mathrm{a}\mathrm{sin}\left(\frac{c}{2a}\right)\\A\ {\approx}\ \frac{b}{2}{\cdot}\left(2a+{\pi}{\cdot}a{\cdot}\mathrm{a}\mathrm{sin}\left(\frac{c}{2a}\right)+\left(\frac{{\pi}}{2}{-}2\right){\cdot}b\right)\end{array}$$

22-SL
$$\begin{array}{l}V\ =\ \frac{{\pi}}{3}{\cdot}\left(a_{1}+a_{2}\right){\cdot}b_{1}^{2}+\frac{{\pi}}{4}{\cdot}\left(a_{2}+b_{2}\right){\cdot}b_{2}^{2}+\frac{{\pi}}{12}{\cdot}a_{2}{\cdot}b_{1}{\cdot}b_{2}\\A\ =\ {\pi}{\cdot}a_{1}{\cdot}b_{1}+\frac{{\pi}}{4}{\cdot}b_{1}^{2}+\frac{{\pi}}{2}{\cdot}b_{2}^{2}+\frac{{\pi}}{2}{\cdot}b_{2}^{2}{\cdot}\sqrt{\left(\frac{a_{1}}{b_{1}}\right)^{2}+\frac{1}{4}}{-}\frac{{\pi}}{2}{\cdot}b_{1}{\cdot}\sqrt{\left(\frac{a_{1}{\cdot}b_{2}}{b_{1}}{-}a_{1}\right)^{2}+\frac{b_{1}^{2}}{4}}\end{array}$$

23-SL
$$\begin{array}{l}V\ =\ \frac{{\pi}}{4}{\cdot}a_{1}{\cdot}b_{1}{\cdot}c_{1}+\frac{{\pi}}{3}{\cdot}a_{2}{\cdot}b_{2}^{2}\\A\ =\ \frac{{\pi}}{2}{\cdot}a_{1}{\cdot}b_{1}+\frac{{\pi}}{2}{\cdot}b_{1}{\cdot}c_{1}+\frac{{\pi}}{2}{\cdot}a_{1}{\cdot}c_{1}+{\pi}{\cdot}b_{2}{\cdot}\left(\sqrt{4a_{2}^{2}+b_{2}^{2}}{-}b_{2}\right)\end{array}$$

24-SL
$$\begin{array}{l}V\ {\approx}\ \frac{{\pi}}{4}{\cdot}a{\cdot}b{\cdot}c\\A\ {\approx}\ \frac{{\pi}}{2}{\cdot}\left(a{\cdot}b+b{\cdot}c+a{\cdot}c\right)\end{array}$$

25-SL
$$\begin{array}{l}\mathrm{Suppose:}\ b_{2}=b_{3}=b_{4}\\V\ =\ \frac{{\pi}}{4}{\cdot}a_{2}{\cdot}b_{2}^{2}+\frac{{\pi}}{12}{\cdot}\left(a_{3}+a_{4}\right){\cdot}b_{2}^{2}+\frac{{\pi}}{6}{\cdot}a_{1}{\cdot}b_{1}{\cdot}b_{2}\\A\ {\approx}\ \frac{{\pi}}{4}{\cdot}\left(b_{1}+b_{2}\right){\cdot}\left[\frac{b_{1}+b_{2}}{2}+\frac{a_{1}^{2}}{\sqrt{a_{1}^{2}{-}\left(\frac{b_{1}+b_{2}}{2}\right)^{2}}}{\cdot}\mathrm{sin}^{{-}1}\frac{\sqrt{a_{1}^{2}{-}\left(\frac{b_{1}+b_{2}}{2}\right)^{2}}}{a_{1}}\right]+\frac{{\pi}}{2}{\cdot}b_{2}{\cdot}\left(2a_{2}+\sqrt{a_{3}^{2}+\frac{b_{2}^{2}}{4}}+\sqrt{a_{4}^{2}+\frac{b_{2}^{2}}{4}}{-}b_{2}\right)\end{array}$$

26-SL
$$\begin{array}{l}V\ =\ \frac{{\pi}}{12}{\cdot}a^{3}\\A\ =\ \frac{3{\pi}}{4}{\cdot}a^{2}\end{array}$$

27-SL
$$\begin{array}{l}V\ =\ \frac{{\pi}}{4}{\cdot}a_{2}{\cdot}b_{2}^{2}+\frac{{\pi}}{2}{\cdot}a_{3}{\cdot}b_{3}^{2}+\frac{{\pi}}{12}{\cdot}a_{1}{\cdot}\left(b_{1}^{2}+b_{1}{\cdot}b_{2}+b_{2}^{2}\right)\\A\ =\ \frac{{\pi}}{2}{\cdot}\left(b_{1}+b_{2}\right){\cdot}\sqrt{a_{1}^{2}+\left(\frac{b_{1}{-}b_{2}}{2}\right)^{2}}+\frac{{\pi}}{4}{\cdot}\left(b_{1}^{2}+b_{2}^{2}\right)+2{\pi}{\cdot}\left(a_{2}{\cdot}b_{2}+a_{3}{\cdot}b_{3}\right)\end{array}$$

28-H
$$\begin{array}{l}V\ =\ \frac{{\pi}}{4}{\cdot}b^{2}{\cdot}a\\A\ =\ {\pi}{\cdot}b{\cdot}\left(\frac{b}{2}+a\right)\end{array}$$

29-H
$$\begin{array}{l}V\ =\ \frac{{\pi}}{4}{\cdot}a{\cdot}b{\cdot}c\\A\ =\ \frac{{\pi}}{2}{\cdot}\left(a{\cdot}b+b{\cdot}c+a{\cdot}c\right)\end{array}$$

30-H
$$\begin{array}{l}V\ =\ \frac{\sqrt{3}}{4}{\cdot}a{\cdot}b^{2}\\A\ =\ 3a{\cdot}b+\frac{\sqrt{3}}{2}{\cdot}b^{2}\end{array}$$

31-SL
$$\begin{array}{l}V\ {\approx}\ c{\cdot}\left(a_{1}{\cdot}b_{1}+\frac{{\pi}}{4}{\cdot}a_{2}{\cdot}b_{2}\right)\\A\ {\approx}\ c{\cdot}\left(2a_{1}+b_{1}+\frac{{\pi}}{2}{\cdot}a_{2}+\frac{{\pi}}{2}{\cdot}b_{2}\right)+2a_{1}{\cdot}b_{1}+\frac{{\pi}}{2}{\cdot}a_{2}{\cdot}b_{2}\end{array}$$

Simulated shapes were given by a three-dimensional image with a cross-section view or a transapical section view. In the shape code column, H = models from Hillebrand et al. (Hillebrand et al., 1999), amended by ourselves; SL = models from Sun & Liu in this paper; V = volume; A = surface area; a = length; b = width; c = height. Other symbols are marked in the table.

## METHOD

Phytoplankton samples from sample sites covering most of China’s seas (with samples collected from the first comprehensive investigation in 1958 up to now) were selected and analysed using a light microscope. Net samples were collected with a standard net III (76 μm mesh size, simple conical tow net, which is a standard phytoplankton tool used in China) and a vertical haul was made from just off the bottom to the surface. These samples were preserved in 2 or 5% neutral formaldehyde (final concentration) in glass or polyethylene bottles. Samples were observed with an Olympus BH-2 microscope at × 200, × 400 or × 1000 magnification in a phytoplankton counting chamber (a standard tool used in China fabricated in our laboratory, 0.25 ml, similar to a Palmer–Maloney chamber) and identified to species level (Yamaji, 1991; Tomas, 1997). Water samples were preserved initially in 250 ml polyethylene bottles containing 1% Lugol’s iodine solution and ultimately the samples were preserved in 1% neutral formaldehyde (final concentration). Twenty-five millilitres of preserved sample were left for >24 h in settling chambers and then analysed with an American Optical Ltd inverted microscope at × 200, × 200 or × 640 magnification (Utermöhl, 1958) to identify phytoplankton to species level (Yamaji, 1991; Tomas, 1997). The scale bar for the microscopic ocular was calibrated using a standard scale bar (S22-StageMic; Graticules Ltd, UK) mounted on the microscopic objective.

Linear dimensions were measured according to Table II or by obtaining taxonomic information and searching the shape code in Table I. In most cases, it was possible to determine the length and width of the target cell. As the cell settles on the base plate on the posture of synthetic effect of several forces, such as gravitation and buoyancy, the length may not always be the apical axis. The individual analysing the sample need not consider the morphological information when using this set of models, thus the applicability will be improved in the models. The height of the target cell can be measured after rolling the cell by gently touching the coverslip with a pin-like object under routine examination by light microscope.

Twenty or more individual cells should be measured to avoid biasing results (Sournia, 1978; Hillebrand et al., 1999). The information on taxa and linear dimensions were then input into a Microsoft Excel worksheet; cell and community biovolume and surface areas were calculated by a VBA program which compiled data according to the shape code in Table I and the equation in Table II. History samples from which the cell abundance and community information to species level have been derived can also be converted from cell counts to biovolume and surface area. When linear dimensions of 20 typical cells in the sample were measured, individual cells of chain-forming species were measured and calculated. Software enabling these calculations is available from the first author, or at http://www.ouc.edu.cn/csmxy/sunjun/biovolume.htm.

## RESULTS AND DISCUSSION

### Measurement of phytoplankton cell height

Measuring the height of phytoplankton cells under the microscope can be difficult for some species. The algal cell usually keeps a definite position on the slide when the centre of gravity is low, making it difficult to measure the cell height. In most instances, an algal species will keep a fixed position, but on rare occasions the side view of the cell is visible, providing the opportunity to measure the height. If the cell is rotated, it will increase the chances of getting a side view. Using a pin-like object to tip the coverslip, algal cells will roll with the movement of the surrounding medium.

Usually it is not possible to rotate the cell using a pin in order to measure the cell height, either when the sample is examined by the Utermöhl method or when special counting slides such as Sedgwick–Rafter or Palmer–Maloney slides are used. There are two ways to solve the problem: one is to concentrate the sample after observation and follow up with a standard compound microscope; the other is to estimate the height from the width of the cell, because the height of small algal cells is usually approximately equal to the width. Verity et al. also pointed out that there is little variation between the depth and width of nanoplankton cells (Verity et al., 1992). However, as Hillebrand et al. (Hillebrand et al., 1999) suggest, the height of large cells should be measured.

### Error sources in the models

For each genus, the error sources within these models come from the choice of geometric shapes assigned to the algal cell, in addition to the accuracy of measurement and consequent estimation of biovolume.

The selection of geometric shapes in this model was similar to Hillebrand’s model (Hillebrand et al., 1999). It was based on an assumption of similar shapes within each genus. In general, this principle applies, but there are some exceptions within genera, as pointed out by Hillebrand et al. (Hillebrand et al., 1999). The main distinguishing feature between these two models is that some geometric shapes were divided into two similar models for convenience of measurement, each one being the side view of the opposite one, such as ‘prism on elliptic base’ and ‘prism on elliptic base girdle view’ (cf. Table II). Meanwhile, six additional geometric shapes were assigned to additional morphologically complex genera.

The measurement procedure can potentially be the largest error source when estimating biovolume if the sampler does not follow the standard protocol accurately. The scale bar must be calibrated for each magnification. Light halos affect the measurement of small-sized cells (Montagne et al., 1994), but can be overcome by increasing the magnification of the microscope.

Between the initial field sampling and final interpretation of data, there are several potential sources of bias or variability. They include initial sampling methods, preservation (primary samples), subsampling (including concentration or dilution), counting use of tertiary subsamples, or random field selection, and statistical analyses. Some of these can be minimized or eliminated by following a strictly standardized procedure (Sournia, 1978; Hallegraeff et al., 1995).

It is not possible to measure every cell during routine analysis. Subsamples for line dimension measurement should consider phytoplankton assemblages. For each phytoplankton assemblage, at least 25 randomly selected cells of each species should be measured (Smayda, 1978), and the mean biovolume should be calculated from the mean value of these individual cell biovolumes. Hillebrand et al. propose that biovolume should be calculated from the mean of measured linear dimensions, not as a mean of a set of individually calculated biovolumes (Hillebrand et al., 1999). When the two methods for mean biovolume calculation were compared, we found that although the latter method usually underestimated the variability, its trend has better agreement with increased measurements (Figure 1). Thus, the mean measured linear dimension can be used to calculate biovolume in routine analysis. Although, under most circumstances, the standard error (SE) is <5% of the mean biovolume after the measurement of 10 cells (cf. Figure 1), we suggest that taking as many measurements as possible is better.

Fig. 1.

Comparison of the mean biovolume of four species calculated from the mean of the linear dimension (dashed line) or the mean of individual biovolumes (solid line).

Fig. 1.

Comparison of the mean biovolume of four species calculated from the mean of the linear dimension (dashed line) or the mean of individual biovolumes (solid line).

### Comparison with other models

A comparison between this study and the other three models, Hansen (Hansen, 1992), HELCOM (Helsinki Commission, 2000) and BIOVOL (Kirschtel, 1992), is shown in Figure 2. Five typical species were assigned to five different geometric shapes with a length/width ratio from 1.2 to 25. Sample measurements were conducted under the microscope as described previously. Compared with these models, Hansen’s model underestimated the volume and the BIOVOL model overestimated the biovolume. The HELCOM model had similar results to our study. However, most results have a SE of not more than 30%. With the exception of Ceratium furca, the calculation equations of the other four species in this study were equal to the Hillebrand et al. model (Hillebrand et al., 1999). Hillebrand et al. (Hillebrand et al., 1999) also compared their results with Edler’s model (Edler, 1979), Rott’s model (Rott, 1981) and Kovala–Larrance’s model (Kovala and Larrance, 1966). They pointed out that there were some genera without a geometric model for calculating biovolume. In each model mentioned in this paper, including this study, none can give every phytoplankton species/genera a geometric model for calculating biovolume. Because of the diversity of phytoplankton morphology, it is impossible to calculate biovolume according to a set of geometric models, but all the models determine biovolume by simulation. It is important to focus on how to attain more accurate and available data when we choose appropriate models to calculate biovolume. Thus, for resolving a specific problem we can use different biovolume models. For example, Young and Ziveri use a cubic function, V = Ks × l3, to calculate coccolithophorids (Young and Ziveri, 2000). They assigned a specific shape constant, Ks, to a definite coccolithophorid species, thus they can get a more accurate value of biovolume for the species. If a phytoplankton assemblage is dominated by a microalga that has a more complex geometric shape, such as C. furca, it is important to produce a more complex geometric model or employ the models mentioned above to calculate this particular species.

Fig. 2.

Comparison of calculated biovolume by four models for five typical phytoplankton species.

Fig. 2.

Comparison of calculated biovolume by four models for five typical phytoplankton species.

### Related ecological parameters

Biovolume and surface area calculations for phytoplankton cells are important for many related ecological parameters (Malone, 1980; Sournia, 1981; Chisholm, 1992), such as biomass, growth, photosynthesis, respiration, assimilation, sinking, grazing, etc. Most relationships between these parameters and biovolume follow the allometric theory, i.e. R = a × Vb, where R is a specific rate process or biomass, V is biovolume, and a and b are constants. So the biovolume and surface area of phytoplankton cells are used for conversion of cell counts into many related parameters. Although this procedure is complex and tedious, the conversion parameters provide the opportunity of differentiating between the contribution of different taxonomic groups which cannot be calculated accurately in ‘bulk measurement’.

In these biovolume-related parameters, carbon conversion is obviously important to phytoplankton studies, and is becoming a routine quantity derived from phytoplankton sample analyses. Several relationships between carbon and biovolume have been established in the literature (Mullin et al., 1966; Strathmann, 1967; Eppley et al., 1970; Taguchi, 1976; Rocha and Duncan, 1985; Verity et al., 1992; Montagne et al., 1994; Menden-Deuer and Lessard, 2000). The different phytoplankton assemblages have their own special carbon–biovolume relationship, but this measurement has not been carried out in the China Sea waters until now. Following the calculation of biovolume for 87 commonly found phytoplankton species in China Sea waters, Sun et al. (Sun et al., 2000a) compared four carbon–biovolume relationships (Mullin et al., 1966; Strathmann, 1967; Eppley et al., 1970; Taguchi, 1976) for carbon estimation of net phytoplankton, and proposed using Eppley’s method (Eppley et al., 1970) for carbon conversion in China Sea waters.

### Model applications in China

There are few biovolume studies on phytoplankton in China (Sun et al., 2000a,b,c 1980). In these studies, Jiaozhou Bay was chosen as a case study area, and phytoplankton cell biovolume was calculated for each species by assigning one or several combinations of regular geometric shapes. This is not easily done as we required to consider each species’ morphological information. The new model, as described above, was established at the end of 1999. According to the convenient feature of inputting data in Microsoft Excel, we compiled a VBA program for this model. This model was tested using the conversion carbon estimates from elsewhere (Sun et al., 2001).

In conclusion, the geometric model for estimating phytoplankton cell biovolume is applicable in China and easier to use in routine phytoplankton analyses. It provides taxonomic information while calculating biovolume-related parameters. Its application should be extended to other regions, and should be attempted in many other related fields, such as historical data assimilations, studies on carbon flux at the species level, studies on biovolume and surface area relationship with related parameters, etc.

We are indebted to the National Natural Science Foundation of China (NFSC) which supported the work under contract No. 40206020, 2001CB409702 and the State Oceanic Administration of China (SOA). We thank the following colleagues for useful discussions: Dr Jennifer Martin (Fisheries & Oceans, Canada) and Dr Claus-Dieter Dürselen (Oldenburg University, Germany). The manuscript benefited from comments by Dr Ian Jenkinson, Professor Helmut Hillebrand and one anonymous reviewer.

## REFERENCES

Baltic Marine Environmental Protection Commission–Helsinki Commission (
1988
)
Guidelines for the Baltic Monitoring Programme for the Third Stage: Part D. Biological Determinants. Baltic Sea Environmental Proceedings No. 27 D
. BMEPC-HC.
Boyd
,
C. M.
and Johnson, C. W. (
1995
) Precision of size determination of resistive electronic particle counters.
J. Plankton Res.
,
17
,
41
–58.
Brown
,
L. M.
, Gargantini, I., Brown, D. J., Atkinson, H. J., Govindarajan, J. and Vanlerberghe, G. C. (
1989
) Computer-based image analysis for the automated counting and morphological description of microalgae in culture.
J. Appl. Phycol.
,
1
,
211
–225.
Chisholm
,
S. W.
(
1992
) Phytoplankton size. In Falkowski, P. G. and Woodhead, A. D. (eds),
Primary Productivity and Biogeochemical Cycles in the Sea
. Plenum Press, New York, pp.
213
–237.
Cunningham
,
A.
and Buonnacorsi, C. A. (
1992
) Narrow-angle forward light scattering from individual algal cells: implications for size and shape discrimination in flow cytometry.
J. Plankton Res.
,
14
,
223
–234.
Edler
,
L.
(ed.) (
1979
)
Phytoplankton and Chlorophyll: Recommendations on Methods for Marine Biological Studies in the Baltic Sea. Baltic Marine Biologists Publication No. 5
.
Eppley
,
R. W.
, Reid, F. M. H. and Strickland, J. D. H. (
1970
) Estimates of phytoplankton crop size, growth rate and primary production.
Bull. Scripps Inst. Oceanogr.
,
17
,
33
–42.
Estep
,
K. W.
, MacIntyre, F., Hjorleifsson, E. and Sieburth, J. M. (
1986
) MacImage: a user friendly image-analysis system for the accurate mensuration of marine organisms.
Mar. Ecol. Prog. Ser.
,
33
,
243
–253.
Gordon
,
R.
(
1974
) A tutorial on ART (algebraic reconstruction techniques).
IEEE Trans. Nucl. Sci.
,
21
,
78
–93.
Hallegraeff
,
G. M.
, Anderson, D. M. and Cembella, A. D. (eds) (
1995
)
Manual on Harmful Marine Microalgae. IOC Manuals and Guides No. 33
. UNESCO, Paris.
Hansen
,
G.
(
1992
) Biomasseberegninger. In Thomsen, H. A. (ed.),
Plankton i de indre danske farvande
. Havforskning fra Miljøstyrelsen, Miljøministeriet, pp.
20
–34.
Hastings
,
J. W.
, Sweeney, B. M. and Mullin, M. M. (
1962
) Counting and sizing of unicellular marine organisms.
,
99
,
180
–289.
Helsinki Commission (
2000
)
Phytoplankton Species Composition, Abundance and Biomass
. HELCOM. Available at http://sea.helcom.fi/manual/anxc6.html
Hillebrand
,
H.
(
1997
) Response of epilithic microphytobenthos of the Western Baltic Sea to in situ experiments with nutrient enrichment.
Mar. Ecol. Prog. Ser.
,
160
,
35
–46.
Hillebrand
,
H.
, Dürselen, C. D., Kirschtel, D., Pollingher, D. and Zohary, T. (
1999
) Biovolume calculation for pelagic and benthic microalgae.
J. Phycol.
,
35
,
403
–424.
Kirschtel
,
D. B.
(
1992
) Calculating the biovolume and surface area of irregularly shaped diatoms.
Bull. N. Am. Benth. Soc.
,
9
, 159.
Kononen
,
K.
, Forsskaehl, M., Huttunen, M., Sandell, M. and Viljamaa, M. H. (
1984
) Practical problems encountered in phytoplankton cell volume calculations using the BMB recommendation in the Gulf of Finland.
Limnologica
,
15
,
605
–614.
Kovala
,
P. E
and Larrance, J. P. (
1966
)
Computation of Phytoplankton Cell Numbers, Cell Volume, Cell Surface Area and Plasma Volume per Litre, from Microscopical Counts. Special Report, Vol. 38
. University of Washington, Seattle, WA, pp.
1
–91.
Krambeck
,
C.
, Krambeck, H. J. and Overbeck, J. (
1981
) Microcomputer-assisted biomass determination of plankton bacteria on scanning electron micrographs.
Appl. Environ. Microbiol.
,
42
,
142
–149.
Kramer
,
K. J. M.
, Warwick, R. M. and Brockmann, U. H. (
1992
)
Manual of Sampling and Analytical Procedures for Tidal Estuaries
. Electronic Publishing Centre, TNO, Delft.
Kuuppo
,
P.
(
1994
) Annual variation in the abundance and size of heterotrophic nanoflagellates on the SW coast of Finland, the Baltic sea.
J. Plankton Res.
,
16
,
1525
–1542.
Malone
,
T. C.
(
1980
) Algal size. In Morris, I. (ed.),
The Physiological Ecology of Phytoplankton
. University of California Press, California, pp.
433
–463.
Maloney
,
T. E.
, Donovan, E. J., Jr and Robinson, E. L. (
1962
) Determination of numbers and sizes of algal cells with an electronic particle counter.
Phycologia
,
2
,
1
–8.
Menden-Deuer
,
S.
and Lessard, E. J. (
2000
) Carbon to volume relationships for dinoflagellates, diatoms, and other protist plankton.
Limnol. Oceanogr.
,
45
,
569
–579.
Montagne
,
D. J. S.
, Berges, J. A., Harrison, P. J. and Taylor, F. J. (
1994
) Estimationg carbon, nitrogen, protein, and chlorophyll a from volume in marine phytoplankton.
Limnol. Oceanogr.
,
39
,
1044
–1060.
Mullin
,
M. M.
, Sloan, P. R. and Eppley, R. W. (
1966
) Relationship between carbon content, cell volume, and area in phytoplankton.
Limnol. Oceanogr.
,
11
,
307
–311.
Olson
,
R. J.
, Vaulot, D. and Chisholm, S. W. (
1985
) Marine phytoplankton distributions measured using shipboard flow cytometry.
Deep-Sea Res.
,
32
,
1273
–1280.
Rocha
,
O.
and Duncan, A. (
1985
) The relationship between cell carbon and cell volume in freshwater algal species used in zooplankton studies.
J. Plankton Res.
,
7
,
279
–294.
Rott
,
E.
(
1981
) Some results from phytoplankton counting intercalibrations.
Schweiz. Z. Hydrol.
,
43
,
34
–62.
,
L.
, Stoermer, E. F. and Ladewski, B. G. (
1977
) A morphometric method for correcting phytoplankton cell volume estimates.
Protoplasma
,
93
,
147
–163.
Sieracki
,
C. K.
, Sieracki, M. E. and Yentsch, C. M. (
1998
) An imaging-in-flow system for automated analysis for marine microplankton.
Mar. Ecol. Prog. Ser.
,
168
,
285
–296.
Smayda
,
T. J.
(
1978
) From phytoplankton to biomass. In Sournia, A. (ed.),
Phytoplankton Manual. Monographs on Oceanographic Methodology 6
. UNESCO, Paris, pp.
273
–279.
Snoeijs
,
P.
(
1994
) Distribution of epiphytic diatom species composition, diversity and biomass on different macroalgal hosts along seasonal and salinity gradients in the Baltic Sea.
Diatom Res.
,
9
,
189
–211.
Sommer
,
U.
(
1994
) Are marine diatoms favoured by high Si:N ratio?
Mar. Ecol. Prog. Ser.
,
115
,
309
–315.
Sommer
,
U.
(
1995
) An experimental test of the intermediate disturbance hypothesis using cultures of marine phytoplankton.
Limnol. Oceanogr.
,
40
,
1271
–1277.
Sournia
,
A.
(ed.) (
1978
)
Phytoplankton Manual. Monographs on Oceanographic Methodology 6
. UNESCO, Paris.
Sournia
,
A.
(
1981
) Morphological base of competition and succession.
Can. Bull. Fish. Aquat. Sci.
,
210
,
339
–346.
Steen
,
H. B.
(
1990
) Characters of flow cytometers. In Melamed, M. R., Lindmo, T. and Mendelsohn, M. L. (eds),
Flow Cytometry and Sorting
, 2nd edn. Wiley-Liss, New York, pp.
11
–25.
Strathman
,
R. R.
(
1967
) Estimating the organic carbon content of phytoplankton from cell volume or plasma volume.
Limnol. Oceanogr.
,
12
,
411
–418.
Sun
,
J.
, Liu, D. Y. and Qian, S. B. (
2000
) Estimating biomass of phytoplankton in the Jiaozhou Bay, I. Phytoplankton biomass estimated from cell volume and plasma volume.
Acta Oceanol. Sin.
,
19
,
19
–31.
Sun
,
J.
, Liu, D. Y. and Qian, S. B. (
2000
) Study on phytoplankton biomass, II. Net-phytoplankton measurement biomass estimated from cell volume in the Jiaozhou Bay.
Acta Oceanol. Sin.
,
22
,
102
–109 (in Chinese).
Sun
,
J.
, Liu, D. Y. and Qian, S. B. (
2000
) Study on phytoplankton biomass, III. Estimated bulk measurement biomass of phytoplankton in the Jiaozhou Bay.
Acta Oceanol. Sin.
,
22(Suppl.)
,
293
–299 (in Chinese).
Sun
,
J.
, Liu, D. Y. and Qian, S. B. (
2001
) Preliminary study on the seasonal succession and development pathway of phytoplankton community in the Bohai Sea.
Acta Oceanol. Sin.
,
20
,
251
–260.
Taguchi
,
S.
(
1976
) Relationships between photosynthesis and cell size of marine diatoms.
J. Phycol.
,
12
,
185
–189.
Tang
,
E. P. Y.
(
1995
) The allometry of algal growth rates.
J. Plankton Res.
,
17
,
1325
–1335.
Tomas
,
C. R.
(ed.) (
1997
)
Identifying Marine Phytoplankton
. Academic Press, San Diego, CA.
Utermöhl
,
H.
(
1958
) Zur Vervolkommung der quantitativen Phytoplankton-Methodik.
Mitt. Int. Ver. Theor. Angew. Limnol.
,
9
,
1
–38 (in German).
Verity
,
P. G.
and Sieracki, M. E. (
1993
) Use of color image analysis and epifluorescence microscopy to measure plankton biomass. In Kemp, P. F., Sherr, B. F., Sherr, E. B. and Cole, J. J. (eds),
Handbook of Methods in Aquatic Microbial Ecology
. Lewis Publishers, Boca Raton, FL, pp.
327
–338.
Verity
,
P. G.
, Robertson, C. Y., Tronzo, C. R., Andrews, M. G., Nelson, J. R. and Sieracki, M. E. (
1992
) Relationships between cell volume and the carbon and nitrogen content of marine photosynthetic nanoplankton.
Limnol. Oceanogr.
,
37
,
1434
–1446.
Vilicic
,
D.
(
1985
) An examination of cell volume in dominant phytoplankton species of the central and southern Adriatic Sea.
Int. Rev. Ges. Hydrobiol.
,
70
,
829
–843.
Wheeler
,
P. A.
(
1999
) Cell geometry revisited: realistic shapes and accurate determination of cell volume and surface area from microscopic measurements.
J. Phycol.
,
35
,
209
–210.
Willén
,
E.
(
1976
) A simplified method of phytoplankton counting.
Br. Phycol. J
.,
11
,
265
–278.
Wood
,
A. M.
, Horan, P. K., Muirhead, K., Phinney, D. A., Yentsch, C. M. and Waterbury, J. B. (
1985
) Discrimination between pigment types of marine Synechococcus spp. by scanning spectroscopy, epifluorescence microscopy, and flow cytometry.
Limnol. Oceanogr
.,
30
,
1303
–1315.
Yamaji
,
I.
(
1991
)
Illustrations of the Marine Plankton of Japan
. Hoikusha Publishing Co., Osaka.
Young
,
J. R.
and Ziveri, P. (
2000
) Calculation of coccolith volume and its use in calibration of carbonate flux estimates.
Deep-Sea Res.
,
47
,
1679
–1700.