870 Hamm, C. E. 2002. Interactive aggregation and sedimentation of diatoms and clay-sized lithogenic material. Limnology and Oceanography **47**: 1790--1795.

872 Hilborn, R., and M. Mangel. 1997. The Ecological Detective: Confronting Models with Data. Princeton University Press.

874 Honjo, S., S. J. Manganini, and J. J. Cole. 1982. Sedimentation of biogenic matter in the deep ocean. Deep Sea Research Part A. Oceanographic Research Papers **29**: 609--625, doi:10.1016/0198-0149(82)90079-6

877 Iversen, M. H., N. Nowald, H. Ploug, G. A. Jackson, and G. Fischer. 2010. High resolution profiles of vertical particulate organic matter export off Cape Blanc, Mauritania: Degradation processes and ballasting effects. Deep Sea Research Part I: Oceanographic Research Papers **57**: 771--784, doi:10.1016/j.dsr.2010.03.007

881 Iversen, M. H., and H. Ploug. 2010. Ballast minerals and the sinking carbon flux in the ocean: carbon-specific respiration rates and sinking velocity of marine snow aggregates. Biogeosciences **7**: 2613-2624, doi:10.5194/bg-7-2613-2010

884 Iversen, M. H., and M. L. Robert. 2015. Ballasting effects of smectite on aggregate formation and export from a natural plankton community. Marine Chemistry **175**: 18 - 27, doi:10.1016/j.marchem.2015.04.009

887 Jackson, G. A. 2001. Effect of coagulation on a model planktonic food web. Deep Sea Research Part I: Oceanographic Research Papers **48**: 95--123, doi:10.1016/S0967-0637(00)00040-6

890 Jackson, G. A. 2005. Coagulation theory and models of oceanic plankton aggregation, p. 271-292. Flocculation in natural and engineered environmental systems. CRC Press, doi:10.1201/9780203485330.ch13

893 Jackson, G. A., R. Maffione, D. K. Costello, A. L. Alldredge, B. E. Logan, and H. G. Dam. 1997. Particle size spectra between 1 µm and 1 cm at Monterey Bay determined using multiple instruments. Deep Sea Research Part I: Oceanographic Research Papers **44**: 1739--1767, doi:10.1016/S0967-0637(97)00029-0

897 Jackson, G. A., A. M. Waite, and P. W. Boyd. 2005. Role of algal aggregation in vertical carbon export during SOIREE and in other low biomass environments. Geophysical Research Letters **32**: L13607, doi:10.1029/2005GL023180

900 Jagt, H. v. d., C. Friese, J. B. W. Stuut, G. Fischer, and M. H. Iversen. 2018. The ballasting effect of Saharan dust deposition on aggregate dynamics and carbon export: Aggregation, settling, and scavenging potential of marine snow. Limnology and Oceanography **63**: 1386--1394, doi:10.1002/lno.10779

904 Jansen, H., R. E. Zeebe, and D. A. Wolf-Gladrow. 2002. Modeling the dissolution of settling CaCO3 in the ocean. Global Biogeochemical Cycles **16**: 11-11--11-16, doi:10.1029/2000GB001279

907 Johnson, C. P., X. Li, and B. E. Logan. 1996. Settling velocities of fractal aggregates. Environmental Science & Technology **30**: 1911-1918, doi:10.1021/es950604g

This article is protected by copyright. All rights reserved.

Author Manuscript
909 Jokulsdottir, T., and D. Archer. 2016. A stochastic, Lagrangian model of sinking biogenic
910 aggregates in the ocean (SLAMS 1.0): model formulation, validation and sensitivity.
911 Geoscientific Model Development **9**: 1455--1476, doi:10.5194/gmd-9-1455-2016

912 Jouandet, M.-P. and others 2011. Optical imaging of mesopelagic particles indicates deep
913 carbon flux beneath a natural iron-fertilized bloom in the Southern Ocean. Limnology
914 and Oceanography **56**: 1130-1140, doi:10.4319/lo.2011.56.3.1130

915 Jouandet, M. P., S. Blain, N. Metzl, C. Brunet, T. W. Trull, and I. Obernosterer. 2008. A
916 seasonal carbon budget for a naturally iron-fertilized bloom over the Kerguelen
917 Plateau in the Southern Ocean. Deep-Sea Research Part Ii-Topical Studies in
918 Oceanography **55**: 856--867, doi:10.1016/j.dsr2.2007.12.037

919 Kajihara, M. 1971. Settling velocity and porosity of large suspended particle. Journal of the
920 Oceanographical Society of Japan **27**: 158-162, doi:10.1007/BF02109135

921 Karperien, A. 2005. FracLac Advanced User's Manual.

922 Kaye, B. H., G. G. Clark, J. E. Leblanc, and R. A. Trottier. 1987. Image Analysis Procedures
923 for Characterizing the Fractal Dimension of Fineparticles. Particle & Particle Systems
924 Characterization **4**: 63--66, doi:10.1002/ppsc.19870040113

925 Kelbaliyev, G. I. 2011. Drag coefficients of variously shaped solid particles, drops, and
926 bubbles. Theoretical Foundations of Chemical Engineering **45**: 248--266,
927 doi:10.1134/S0040579511020084

928 Kilps, J. R. 1993. Fractal dimensions of aggregates formed under natural and engineered fluid
929 environments. University of Arizona.

930 Kilps, J. R., B. E. Logan, and A. L. Alldredge. 1994. Fractal dimensions of marine snow
931 determined from image analysis of in situ photographs. Deep Sea Research Part I:
932 Oceanographic Research Papers **41**: 1159-1169, doi:10.1016/0967-0637(94)90038-8

933 Klaas, C., and D. E. Archer. 2002. Association of sinking organic matter with various types
934 of mineral ballast in the deep sea: Implications for the rain ratio. Global
935 Biogeochemical Cycles **16**: 1116, doi:10.1029/2001GB001765

936 Komar, P. D., A. P. Morse, L. F. Small, and S. W. Fowler. 1981. An Analysis of Sinking
937 Rates of Natural Copepod and Euphausiid Fecal Pellets. Limnology and
938 Oceanography **26**: 172--180, doi:10.2307/2835816

939 Kriest, I., and A. Oschlies. 2008. On the treatment of particulate organic matter sinking in
940 large-scale models of marine biogeochemical cycles. Biogeosciences **5**: 55--72,
941 doi:10.5194/bg-5-55-2008

942 Kriest, I., and A. Oschlies. 2013. Swept under the carpet: organic matter burial decreases
943 global ocean biogeochemical model sensitivity to remineralization length scale.
944 Biogeosciences **10**: 8401--8422, doi:10.5194/bg-10-8401-2013

945 Laurenceau-Cornec, E. C. and others 2015a. The relative importance of phytoplankton
946 aggregates and zooplankton fecal pellets to carbon export: insights from free-drifting

This article is protected by copyright. All rights reserved.

Author Manuscript
947 sediment trap deployments in naturally iron-fertilised waters near the Kerguelen
948 Plateau. Biogeosciences **12**: 1007--1027, doi:10.5194/bg-12-1007-2015

949 Laurenceau-Cornec, E. C., T. W. Trull, D. M. Davies, C. L. De La Rocha, and S. Blain.
950 2015b. Phytoplankton morphology controls on marine snow sinking velocity. Marine
951 Ecology Progress Series **520**: 35--56, doi:10.3354/meps11116

952 Le Moigne, F. A. C., M. Gallinari, E. Laurenceau, and C. L. De La Rocha. 2013. Enhanced
953 rates of particulate organic matter remineralization by microzooplankton are
diminished by added ballast minerals. Biogeosciences **10**: 5755--5765,
955 doi:10.5194/bg-10-5755-2013

956 Le Moigne, F. A. C., K. Pabortsava, C. L. J. Marcinko, P. Martin, and R. J. Sanders. 2014.
957 Where is mineral ballast important for surface export of particulate organic carbon in
958 the ocean? Geophysical Research Letters **41**: 8460-8468, doi:10.1002/2014GL061678

959 Le Moigne, F. A. C. and others 2012. On the proportion of ballast versus non-ballast
960 associated carbon export in the surface ocean. Geophysical Research Letters **39**:
961 L15610, doi:10.1029/2012GL052980

962 Lee, C. and others 2009. Particulate organic matter and ballast fluxes measured using time-
963 series and settling velocity sediment traps in the northwestern Mediterranean Sea.
964 Deep Sea Research Part II: Topical Studies in Oceanography **56**: 1420--1436,
965 doi:10.1016/j.dsr2.2008.11.029

966 Lerman, A., D. Lal, and M. F. Dacey. 1974. Stokes' settling and chemical reactivity of
967 suspended particles in natural waters, p. 17-47. *In* R. J. Gibbs [ed.], Suspended solids
968 in water. Plenum Press, doi:10.1007/978-1-4684-8529-5_2

969 Logan, B. E., and J. R. Kilps. 1995. Fractal dimensions of aggregates formed in different
970 fluid mechanical environments. Water research **29**: 443--453, doi:10.1016/0043-1354(94)00186-B

972 Logan, B. E., and D. B. Wilkinson. 1990. Fractal geometry of marine snow and other
973 biological aggregates. Limnology and Oceanography **35**: 130-136,
974 doi:10.2307/2837345

975 Loth, E. 2008. Drag of non-spherical solid particles of regular and irregular shape. Powder
976 Technology **182**: 342-353, doi:10.1016/j.powtec.2007.06.001

977 Maggi, F. 2007. Variable fractal dimension: A major control for floc structure and
978 flocculation kinematics of suspended cohesive sediment. Journal of Geophysical
979 Research: Oceans **112**, doi:10.1029/2006JC003951

980 ----. 2013. The settling velocity of mineral, biomineral, and biological particles and aggregates
981 in water. Journal of Geophysical Research: Oceans **118**: 2118--2132,
982 doi:10.1002/jgrc.20086

983 ----. 2015. Experimental evidence of how the fractal structure controls the hydrodynamic
984 resistance on granular aggregates moving through water. Journal of Hydrology **528**:
985 694 - 702, doi:10.1016/j.jhydrol.2015.07.002

This article is protected by copyright. All rights reserved.

Author Manuscript
986 Maioli Castilho, M. S., and M. S. Arcifa. 2000. Production of the rotifer *Brachionus plicatilis* (Ploimida: Brachionidae) in a Brazilian coastal lagoon. *Revista de biologia tropical* **48**: 859--865.

989 McCave, I. N., and T. F. Gross. 1991. In-situ measurements of particle settling velocity in the deep sea. *Marine Geology* **99**: 403--411, doi:10.1016/0025-3227(91)90052-6

991 Meakin, P. 1988. Fractal aggregates. *Advances in Colloid and Interface Science* **28**: 249 - 331, doi:10.1016/0001-8686(87)80016-7

993 Miklasz, K. A., and M. W. Denny. 2010. Diatom sinking speeds: improved predictions and insight from a modified Stokes' law. *Limnology and oceanography* **55**: 2513--2525, doi:10.4319/lo.2010.55.6.2513

996 Moriceau, B., M. Garvey, U. Passow, and O. Ragueneau. 2007. Evidence for reduced biogenic silica dissolution rates in diatom aggregates. *Marine Ecology Progress Series* **333**: 129--142, doi:10.3354/meps333129

999 Moriceau, B. and others 2009. Si-C interactions during degradation of the diatom *Skeletonema marinoi*. *Deep Sea Research Part II: Topical Studies in Oceanography* **56**: 1381--1395, doi:10.1016/j.dsr2.2008.11.026

1002 Nowald, N. and others 2009. In-situ sinking speed measurements of marine snow aggregates acquired with a settling chamber mounted to the Cherokee ROV, p. 1286--1291. *Oceans 2009 - Europe, Vols 1 and 2*. doi:10.1109/OCEANSE.2009.5278186

1005 Nowald, N., M. H. Iversen, G. Fischer, V. Ratmeyer, and G. Wefer. 2015. Time series of in-situ particle properties and sediment trap fluxes in the coastal upwelling filament off Cape Blanc, Mauritania. *Progress in Oceanography* **137**, Part A: 1 - 11, doi:10.1016/j poccean.2014.12.015

1009 Pabortsava, K. and others 2017. Carbon sequestration in the deep Atlantic enhanced by Saharan dust. *Nature Geoscience* **10**: 189--194, doi:10.1038/ngeo2899

1011 Passow, U. 2004. Switching perspectives: Do mineral fluxes determine particulate organic carbon fluxes or vice versa? *Geochemistry Geophysics Geosystems* **5**, doi:10.1029/2003gc000670

1014 Passow, U., and A. L. Alldredge. 1995. A dye-binding assay for the spectrophotometric measurement of transparent exopolymer particles (TEP). *Limnology and Oceanography* **40**: 1326-1335, doi:10.2307/2838691

1017 Passow, U., and C. L. De La Rocha. 2006. Accumulation of mineral ballast on organic aggregates. *Global Biogeochemical Cycles* **20**: GB1013, doi:10.1029/2005gb002579

1019 Passow, U., C. L. De La Rocha, C. Fairfield, and K. Schmidt. 2014. Aggregation as a function of $P_{CO_2}$ and mineral particles. *Limnology and Oceanography* **59**: 532--547, doi:10.4319/lo.2014.59.2.0532

1022 Ploug, H., H. P. Grossart, F. Azam, and B. B. Jørgensen. 1999. Photosynthesis, respiration, and carbon turnover in sinking marine snow from surface waters of Southern

This article is protected by copyright. All rights reserved.

Author Manuscript
1024 California Bight: implications for the carbon cycle in the ocean. Marine Ecology
1025 Progress Series **179**: 1--11, doi:10.3354/meps179001

1026 Ploug, H., M. H. Iversen, M. Koski, and E. T. Buitenhuis. 2008. Production, oxygen
1027 respiration rates, and sinking velocity of copepod fecal pellets: Direct measurements
1028 of ballasting by opal and calcite. Limnology and Oceanography **53**: 469--476,
1029 doi:10.4319/lo.2008.53.2.0469

1030 Ploug, H., A. Terbruggen, A. Kaufmann, D. Wolf-Gladrow, and U. Passow. 2010. A novel
1031 method to measure particle sinking velocity in vitro, and its comparison to three other
1032 in vitro methods. Limnology and Oceanography: Methods **8**: 386-393,
1033 doi:10.4319/lom.2010.8.386

1034 Reynolds, O. 1883. An Experimental Investigation of the Circumstances Which Determine
1035 Whether the Motion of Water Shall Be Direct or Sinuous, and of the Law of
1036 Resistance in Parallel Channels. Philosophical Transactions of the Royal Society of
1037 London **174**: 935--982.

1038 Russ, J. C. 2011. The Image Processing Handbook, Sixth Edition, 6th ed. CRC Press, Inc.

1039 Schindelin, J. and others 2012. Fiji: an open-source platform for biological-image analysis.
1040 Nature Methods **9**: 676--682, doi:10.1038/nmeth.2019

1041 Schmidt, K., C. L. De La Rocha, M. Gallinari, and G. Cortese. 2014. Not all calcite ballast is
1042 created equal: differing effects of foraminiferan and coccolith calcite on the formation
1043 and sinking of aggregates. Biogeosciences **11**: 135--145, doi:10.5194/bg-11-135-2014

1044 Schneider, C. A., W. S. Rasband, and K. W. Eliceiri. 2012. NIH Image to ImageJ: 25 years of
1045 image analysis. Nature Methods **9**: 671--675, doi:10.1038/nmeth.2089

1046 Shanks, A. L., and E. W. Edmondson. 1989. Laboratory-made artificial marine snow: a
1047 biological model of the real thing. Marine Biology **101**: 463-470,
1048 doi:10.1007/BF00541648

1049 Shanks, A. L., and J. D. Trent. 1980. Marine snow: sinking rates and potential role in vertical
1050 flux. Deep Sea Research Part A. Oceanographic Research Papers **27**: 137-143,
1051 doi:10.1016/0198-0149(80)90092-8

1052 Smayda, T. J. 1970. The Suspension and Sinking of Phytoplankton in the Sea. Oceanography
1053 and Marine Biology Annual Review **8**: 353--414.

1054 Stokes, G. G. 1851. On the effect of the internal friction of fluids on the motion of
1055 pendulums. Transactions of the Cambridge Philosophical Society **9**: 8-106.

1056 Syvitski, J. P. M., K. W. Asprey, and K. W. G. Leblanc. 1995. In-situ characteristics of
1057 particles settling within a deep-water estuary. Deep Sea Research Part II: Topical
1058 Studies in Oceanography **42**: 223-256, doi:10.1016/0967-0645(95)00013-g

1059 Trull, T. W. and others 2008. In situ measurement of mesopelagic particle sinking rates and
1060 the control of carbon transfer to the ocean interior during the Vertical Flux in the
1061 Global Ocean (VERTIGO) voyages in the North Pacific. Deep-Sea Research Part II:
1062 Topical Studies in Oceanography **55**: 1684--1695, doi:10.1016/j.dsr2.2008.04.021
This article is protected by copyright. All rights reserved.
1063 Villa-Alfageme, M. and others 2016. Geographical, seasonal, and depth variation in sinking
1064 particle speeds in the North Atlantic. Geophysical Research Letters **43**: 8609--8616,
1065 doi:10.1002/2016GL069233

1066 Waite, A. M., P. A. Thompson, and P. J. Harrison. 1992. Does energy control the sinking
1067 rates of marine diatoms? Limnology and Oceanography **37**: 468-477,
1068 doi:10.2307/2837978

1069 White, F. M. 1974. Viscous fluid flow. McGraw-Hill, New York.

1070 Witten, T. A., and L. M. Sander. 1981. Diffusion-Limited Aggregation, a Kinetic Critical
1071 Phenomenon. Phys. Rev. Lett. **47**: 1400--1403, doi:10.1103/PhysRevLett.47.1400

1072 Yoon, W., S. Kim, and K. Han. 2001. Morphology and sinking velocities of fecal pellets of
1073 copepod, molluscan, euphausiid, and salp taxa in the northeastern tropical Atlantic.
1074 Marine Biology **139**: 923-928, doi:10.1007/s002270100630

1075
1076
1077 Figure captions

1078 **Fig. 1.** Theoretical expectations for porosity and drag ($C_D$) variations with the equivalent
1079 spherical diameter (ESD) for fractal aggregates. **(a)** Porosity calculated as a function of ESD
1080 for different values of coefficient $a$ and fractal dimension $D_3$ using the formula proposed by
1081 Logan and Wilkinson (1990) and following Laurenceau-Cornec et al. (2015b). **(b)** Drag
1082 coefficient calculated as a function of size following Laurenceau-Cornec et al. (2015b) using
1083 a bisection algorithm to solve numerically the White function (White 1974) and the Stokes'
1084 assumption as a starting point ($Re_0 = 24 / C_{D0}$); the initial drag coefficient $C_{D0}$ was calculated
1085 at two 'specific drag conditions' with arbitrarily fixed ESDs and corresponding sinking
1086 velocities using the Navier-Stokes' drag equation (1: $ESD_0 = 0.5$ mm, $SV_0 = 50$ m $d^{-1}$; 2:
1087 $ESD_0 = 0.5$ mm, $SV_0 = 300$ m $d^{-1}$); solid fractions of the aggregate were set at 60 %
1088 Particulate Organic Matter ($\rho = 1060$ kg m$^{-3}$) and 40 % biogenic silica ($\rho = 2000$ kg m$^{-3}$);
1089 fractal porosity is calculated as in panel a with different values of $a$ and $D_3$. Grey lines
1090 represent $C_D$ obtained with the same calculations using Stokes' law.

1091
1092 **Fig. 2.** Photographs of aggregates formed in the rolling tanks on day 4 (a-d) and 8 (e-h) in

1093 the different treatments. P: Phytoplankton; PZ: Phytoplankton + Micro-Zooplankton

1094 (rotifers); PM: Phytoplankton + Mineral (calcite); PMZ: Phytoplankton + Mineral + Micro-

1095 Zooplankton. Addition of mineral and micro-zooplankton influenced aggregate size, shape

1096 and general aspect. Most of the differences marked on day 4 seemed to attenuate on day 8.

1097 Note the formation of small tails on day 8 in the PM and PMZ treatments for which the

1098 highest sinking velocities were recorded (white arrows).

1099
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**Fig. 3.** Evolution of aggregate size spectra over the course of the experiment in the four treatments. (a) P: Phytoplankton; (b) PZ: Phytoplankton + Micro-Zooplankton (rotifers); (c) PM: Phytoplankton + Mineral (calcite); (d) PMZ: Phytoplankton + Mineral + Micro-Zooplankton. Small bar plots in the top right corner of each panel indicate particle number variations in each of the 14 size classes (see Table 1 for details) from day 2 to 4 (light grey) and from day 4 to 8 (dark grey). Size classes at which particle transfer operates via aggregation and disaggregation processes are indicated in bold. Aggregation processes illustrated by fewer particles in the small size classes and more in the large ones took place between days 2 and 4 in all treatments (no data on day 2 in the P treatment for which visible aggregates formed later). Disaggregation revealed by more particles in the small size classes and fewer in the large ones occurred between days 4 and 8. Note the occurrence of both disaggregation and aggregation in the two time periods in the PM treatment.
1112 **Fig. 4.** Box plots of aggregate equivalent spherical diameter (ESD) (a), circularity (b), and
1113 boundary fractal number $D_B$ (c) in the four treatments on day 2, 4 and 8. P: Phytoplankton;
1114 PZ: Phytoplankton + Micro-Zooplankton (rotifers); PM: Phytoplankton + Mineral (calcite);
1115 PMZ: Phytoplankton + Mineral + Micro-Zooplankton. Largest ESD variations over the
1116 experiment duration were observed in the P treatment while aggregates formed in presence of
1117 mineral and micro-zooplankton were more uniform in size and presented the highest
1118 circularities and lowest $D_B$. Only particles larger than 1 mm ESD were included in the
1119 analysis which required particle volume inferred from images.
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**Fig. 5.** Sinking velocities (SV) versus equivalent spherical diameter (ESD) for aggregates formed in each tank of the four treatments and comparison with theoretical expectations from different parameterizations of Stokes' law and the general Navier-Stokes' drag equation. P: Phytoplankton; PZ: Phytoplankton + Micro-Zooplankton (rotifers); PM: Phytoplankton + Mineral (calcite); PMZ: Phytoplankton + Mineral + Micro-Zooplankton. (a) Model 1, Stokes' law with constant porosities of 0 % (dashed lines) and 99 % (solid lines). (b) Model 2, general Navier-Stokes' drag law with constant drags of 1 (dashed lines) and 5 (solid lines), and a constant porosity of 99 %. (c) Model 3, Stokes' law with a porosity scaled on a fractal geometry with coefficient *a* = 0.03 and *D*<sub>3</sub> = 1.4 (dashed lines) and *D*<sub>3</sub> = 1.8 (solid lines). (d) Model 4, general Navier Stokes' drag law with a porosity scaled on a fractal geometry with coefficient *a* = 0.03 and *D*<sub>3</sub> = 1.4 (solid lines) and 1.8 (dashed lines). See the text for details on drag calculation.
**Fig. 6.** Sinking velocity (SV) versus equivalent spherical diameter (ESD) from various studies for natural and experimentally-made aggregates and comparison with different model parameterizations (dark orange lines indicate the best fit to the data). (a) Aggregates without added minerals and Navier-Stokes' drag law (model 4, see text for details) with different fractal numbers $D_3$ (black lines: extreme values, grey lines: intermediate values), coefficient $a$ (dashed lines: $a = 0.1$; solid lines: $a = 0.01$) and three initial drag conditions indicated on the figure by numbers 1, 2, and 3 (1: ESD$_0$ = 0.1 mm, $SV_0$ = 300 m d$^{-1}$; 2: ESD$_0$ = 0.5 mm, $SV_0$ = 50 m d$^{-1}$; 3: ESD$_0$ = 1 mm, $SV_0$ = 5 m d$^{-1}$). Slopes and offset of the data best fit are reproduced by the model via variations of aggregate fractal dimension, coefficient $a$ and initial drag conditions. a: this study; b: Kajihara (1971); c: Shanks and Trent (1980); d: Alldredge and Gotschalk (1988); e: Alldredge and Gotschalk (1989); f-g: Azetsu-Scott and Johnson (1992), Bedford Basin and Diatom culture respectively; h: Diercks and Asper (1997); i: Ploug et al. (1999), one outlier removed (ESD = 1.14 mm; $SV = 172 m d^{-1}$); j-m: Engel et al. (2009), Diatoms Adriatic Sea, non-calcifying *E. huxleyi* culture, Diatoms Baltic Sea, and *N. closterium* culture respectively; n-p: Iversen and Ploug (2010), *S. costatum*, mix of *E. huxleyi* and *S. costatum*, *E. huxleyi* respectively; q: Jouandet et al. (2011); Laurenceau-Cornec et al. (2015b); s-w: Iversen and Robert (2015), Diatoms North Sea at 48, 91, 156, 187, and 380 h of incubation. (b) Aggregates with added minerals (except Engel et al., 2009) and the Stokes' law (model 3, see text and Fig. 5 caption) with different $D_3$ (grey dashed lines: $D_3$ = 1.4; black solid lines: $D_3$ = 1.8; grey solid lines: $D_3$ = 2.2) and coefficient $a$ (three groups of three grey dashed, black solid and grey solid lines with highest: $a = 0.1$; intermediate: $a = 0.01$; lowest: $a = 0.001$). Slopes and offset of data best fit are well reproduced by Stokes' law parameterized with $D_3$ values around 1.8 and coefficient $a$ varying between 0.1 and 0.001. a: this study; b: Carder et al. (1982); c: Gibbs (1985); d: Syvitski et al. (1995); e: Nowald et al. (2009); f: Engel et al. (2009); g: Iversen et al. (2010); h-l: Iversen

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1157 and Robert (2015), Diatoms North Sea + Smectite at 48, 91, 156, 187, and 380 h of

1158 incubation.

1159

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<table><caption>**Table 2.** Number, volume, organic and inorganic solid components, porosity (P) and excess density (Δρ) of all aggregates larger than 1 mm ESD.</caption><thead><tr><th>Treat.</th><th>Tank</th><th>Day</th><th>Agg #</th><th>Tot. agg. vol. (µL)</th><th>Tot. POM (mg)</th><th>Tot. PIC (mg)</th><th>Tot. bSiO<sub>2</sub> (mg)</th><th>Tot. TEP (mg XG eq.)</th><th>%POM (m:m<sub>sol</sub>)<sup>(1)</sup></th><th>%PIC (m:m<sub>sol</sub>)</th><th>%bSiO<sub>2</sub> (m:m<sub>sol</sub>)</th><th>P (% H<sub>2</sub>O) (v:v<sub>agg</sub>)<sup>(2)</sup></th><th>Δρ (kg m<sup>-3</sup>)</th></tr></thead><tbody><tr><td rowspan="3">P</td><td>1</td><td>2</td><td>0</td><td>0</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>5</td><td>4</td><td>81</td><td>1036.4±103.6</td><td>1.69±0.29</td><td>0.128</td><td>0.266±0.018</td><td>12.68±0.31</td><td>81.1±18.2</td><td>6.1±0.9</td><td>12.8±2</td><td>99.83±0.11</td><td>0.3</td></tr><tr><td>9</td><td>8</td><td>27</td><td>866.4±86.6</td><td>2.11±0.03</td><td>0.097±0.003</td><td>1.39±0.038</td><td>25.57±1.86</td><td>58.6±1.1</td><td>2.7±0.1</td><td>38.7±1.2</td><td>99.69±0.11</td><td>0.9±0.1</td></tr><tr><td rowspan="3">PZ</td><td>2</td><td>2</td><td>43</td><td>75.7±7.6</td><td>0.44</td><td>0.03</td><td>0.098</td><td>3.91</td><td>77.6</td><td>5.2</td><td>17.2</td><td>99.37±0.11</td><td>1.1±0.1</td></tr><tr><td>6</td><td>4</td><td>230</td><td>861.5±86.2</td><td>3.17</td><td>0.178±0.011</td><td>1.342±0.053</td><td>25±1.83</td><td>67.6±0.8</td><td>3.8±0.2</td><td>28.6±1.2</td><td>99.57±0.11</td><td>1±0.1</td></tr><tr><td>10</td><td>8</td><td>108</td><td>481.3±48.1</td><td>2.55±0.1</td><td>0.133±0.016</td><td>1.31±0.034</td><td>20.7±2.22</td><td>63.8±3</td><td>3.3±0.4</td><td>32.8±1.2</td><td>99.35±0.11</td><td>1.7±0.2</td></tr><tr><td rowspan="3">PM</td><td>3</td><td>2</td><td>226</td><td>368.4±36.8</td><td>1.38±0.08</td><td>1.376±0.047</td><td>0.259±0.097</td><td>13.5±0.8</td><td>45.8±3.3</td><td>45.6±2.5</td><td>8.6±3.2</td><td>99.47±0.11</td><td>2.8±0.4</td></tr><tr><td>7</td><td>4</td><td>210</td><td>1178.5±117.9</td><td>2.8±0.14</td><td>4.507</td><td>0.616±0.044</td><td>42.23±0.08</td><td>35.3±1.9</td><td>56.9±1.1</td><td>7.8±0.6</td><td>99.61±0.11</td><td>2.7±0.4</td></tr><tr><td>11</td><td>8</td><td>133</td><td>800.6±80.1</td><td>2.64±0.12</td><td>6.248±0.906</td><td>1.195±0.064</td><td>27.53±1.55</td><td>26.1±2.6</td><td>62±10.6</td><td>11.9±1.2</td><td>99.33±0.11</td><td>5.7±0.8</td></tr><tr><td rowspan="3">PMZ</td><td>4</td><td>2</td><td>211</td><td>465.9±46.6</td><td>1.95±0.17</td><td>1.697±0.036</td><td>0.388±0.015</td><td>9.77±0.71</td><td>48.3±4.8</td><td>42.1±2.1</td><td>9.6±0.6</td><td>99.43±0.11</td><td>2.8±0.4</td></tr><tr><td>8</td><td>4</td><td>196</td><td>1382.3±138.2</td><td>3.25±0.19</td><td>4.916±0.214</td><td>0.771±0.013</td><td>28.62</td><td>36.4±2.5</td><td>55±3</td><td>8.6±0.3</td><td>99.62±0.11</td><td>2.6±0.4</td></tr><tr><td>12</td><td>8</td><td>135</td><td>699.9±70</td><td>2.48±0.16</td><td>4.873±0.05</td><td>1.279±0.054</td><td>27.35±1.54</td><td>28.7±1.9</td><td>56.5±1.3</td><td>14.8±0.7</td><td>99.32±0.11</td><td>5.3±0.7</td></tr></tbody></table>

<footnote>(1) percentage of component in total solid content (m<sub>sol</sub>) taken as the sum of POM, PIC and bSiO<sub>2</sub> masses.</footnote>

<footnote>(2) P = volume of seawater in total aggregate volume (v<sub>agg</sub>).</footnote>
<table><caption>**Table 3.** Statistical results of ANOVA<sub>S</sub>, Kruskal-Wallis and Tukey tests for ESD, circularity and *D*<sub>B</sub> differences between treatments.</caption><thead><tr><th colspan="5">ANOVA</th><th rowspan="2">p-value</th><th colspan="2">Kruskal-Wallis</th><th rowspan="2">Tukey <sup>(2)</sup><br>p-value</th></tr><tr><th>Day</th><th>P</th><th>PZ</th><th>PM</th><th>PMZ</th><th>χ<sup>2</sup></th><th>p-value</th></tr></thead><tbody><tr><td colspan="9" style="text-align: center; font-weight: bold;">Equivalent Spherical Diameter ESD</td></tr><tr><td rowspan="2">2</td><td rowspan="2">-</td><td>1.34;<br>1.5±0.44<br>(43)</td><td>1.45;<br>1.49±0.3<br>(226)</td><td>1.57;<br>1.64±0.44<br>(211)</td><td rowspan="2">&lt;0.001</td><td rowspan="2">13.23</td><td rowspan="2">0.0013</td><td>4: 0.987<br>5: 0.071</td></tr><tr><td>1.91;<br>2.53±1.28<br>(81)</td><td>1.92;<br>1.93±0.51<br>(230)</td><td>2.17;<br>2.21±0.56<br>(210)</td><td>2.32;<br>2.35±0.67<br>(196)</td><td>2: 0.003<br>3: 0.217<br>6: 0.162</td></tr><tr><td rowspan="2">8<sup>(3)</sup></td><td rowspan="2">1.39;<br>1.63±0.69<br>(26)</td><td>1.98;<br>1.99±0.56<br>(108)</td><td>1.98;<br>2.17±0.72<br>(133)</td><td>1.9;<br>2.03±0.74<br>(135)</td><td rowspan="2">0.003</td><td rowspan="2">16.23</td><td rowspan="2">0.001</td><td>1: 0.084<br>2: 0.002<br>3: 0.036<br>4: 0.169<br>5: 0.966<br>6: 0.328</td></tr><tr><td>0.543;<br>0.548±0.13<br>(26)</td><td>0.779;<br>0.75±0.12<br>(105)</td><td>0.666;<br>0.66±0.14<br>(61)</td><td>0.652;<br>0.656±0.113<br>(44)</td><td>0.647±0.11</td></tr><tr><td colspan="9" style="text-align: center; font-weight: bold;">Circularity</td></tr><tr><td rowspan="2">2</td><td rowspan="2">-</td><td>0.461;<br>0.465±0.12<br>(45)</td><td>0.578;<br>0.567±0.14<br>(118)</td><td>0.668;<br>0.656±0.113<br>(73)</td><td>0.659;<br>0.658±0.13<br>(64)</td><td rowspan="2">&lt;0.001</td><td rowspan="2">45.97</td><td rowspan="2">&lt;0.001</td><td>all &lt;0.001</td></tr><tr><td>0.504;<br>0.478±0.11<br>(20)</td><td>0.75;<br>0.714±0.13<br>(69)</td><td>0.6;<br>0.594±0.15<br>(62)</td><td>0.659;<br>0.658±0.13<br>(64)</td><td>5: 0.002<br>6: 0.98</td></tr><tr><td colspan="9" style="text-align: center; font-weight: bold;">Boundary fractal number D<sub>B</sub></td></tr><tr><td rowspan="2">2</td><td rowspan="2">-</td><td>1.113;<br>1.117±0.03<br>(26)</td><td>1.068;<br>1.073±0.03<br>(103)</td><td>1.08;<br>1.084±0.03<br>(060)</td><td rowspan="2">&lt;0.001</td><td rowspan="2">36.7</td><td rowspan="2">&lt;0.001</td><td>6: 0.046</td></tr><tr><td>1.13;<br>1.138±0.04<br>(45)</td><td>1.107;<br>1.114±0.04<br>(118)</td><td>1.082;<br>1.085±0.03<br>(73)</td><td>1.09;<br>1.092±0.03<br>(42)</td><td>1: 0.026<br>5: 0.003<br>6: 0.79</td></tr><tr><td rowspan="2">8</td><td rowspan="2">-</td><td>1.128;<br>1.128±0.03<br>(20)</td><td>1.069;<br>1.08±0.03<br>(68)</td><td>1.101;<br>1.103±0.03<br>(61)</td><td>1.09;<br>1.09±0.03<br>(63)</td><td rowspan="2">&lt;0.001</td><td rowspan="2">41.74</td><td rowspan="2">&lt;0.001</td><td>2: 0.0164<br>5: 0.147<br>6: 0.158</td></tr><tr><td>1.128±0.03<br>(20)</td><td>1.069;<br>1.08±0.03<br>(68)</td><td>1.101;<br>1.103±0.03<br>(61)</td><td>1.09;<br>1.09±0.03<br>(63)</td><td>1: 0.026<br>5: 0.003<br>6: 0.79</td></tr></tbody></table>

<footnote><sup>(1)</sup> X̄: median; X̄: mean; SD: standard deviation to the mean; n: number of observations.</footnote>

<footnote><sup>(2)</sup> Only *p*-values > 0.001 are indicated (*p*-values of all other pairwise comparisons < 0.001); Pairwise comparisons between treatments: 1=PZ-P, 2=PM-P, 3=PMZ-P, 4=PM-PZ, 5=PMZ-PZ, 6=PMZ-PM.</footnote>

<footnote><sup>(3)</sup> One outlier with an ESD larger than 12 mm removed from the analysis.</footnote>
<table><caption>**Table 4.** Average values, standard deviations (SD), minima and maxima of aggregate equivalent spherical diameters (ESD), sinking velocities (SV), Reynolds numbers (Re), drag coefficient ($C_D$) are indicated for each tank. Coefficients and statistics of the power regression fits (SV = a . ESD$^b$) to the observations are also reported. The number of aggregates sub-sampled from all particles for sinking velocity measurements in each tank is indicated (n).</caption><thead><tr><th>Treat.</th><th>Tank (n)</th><th><span style="text-decoration: overline;">ESD</span>±SD (mm)<br>[min., max.]</th><th><span style="text-decoration: overline;">SV</span>±SD (m d<sup>-1</sup>)<br>[min., max.]</th><th><span style="text-decoration: overline;">Re</span>±SD<br>[min., max.]</th><th><span style="text-decoration: overline;">C<sub>D</sub>s</span> ± SD<sup>(1)</sup><br>[min., max.]</th><th><span style="text-decoration: overline;">C<sub>D</sub>w</span> ± SD<sup>(2)</sup><br>[min., max.]</th><th>a; SE; p-value<br>[95% CI]<sup>(3)</sup></th><th>b; SE; p-value<br>[95% CI]</th></tr></thead><tbody><tr><td rowspan="2">P</td><td>5 (11)</td><td>3.18±0.52<br>[1.99, 4]</td><td>361±76<br>[225, 493]</td><td>11.4±3.6<br>[4.4, 17.3]</td><td>2.4±1.1<br>[1.4, 5.5]</td><td>4.2±1.3<br>[3, 7.8]</td><td>159; 68.7; &lt;0.05<br>[55.7, 378.8]</td><td>0.711; 0.36; 0.082<br>[-0.034, 1.582]</td></tr><tr><td>9 (33)</td><td>4.61±1.64<br>[1.92, 7.51]</td><td>511±125<br>[218, 928]</td><td>22.6±8.6<br>[5.7, 43.8]</td><td>1.3±0.7<br>[0.5, 4.2]</td><td>2.8±0.9<br>[1.7, 6.4]</td><td>667.1; 103.1; &lt;0.001<br>[474.4, 914.4]</td><td>-0.184; 0.1; 0.093<br>[-0.408, 0.043]</td></tr><tr><td rowspan="3">PZ</td><td>2 (6)</td><td>1.43±0.27<br>[1.16, 1.78]</td><td>276±37<br>[234, 317]</td><td>3.9±1.2<br>[2.6, 5.5]</td><td>6.6±1.9<br>[4.4, 9.1]</td><td>9.1±2.1<br>[6.6, 11.7]</td><td>228.9; 22.3; &lt;0.001<br>[171.3, 296.3]</td><td>0.539; 0.24; 0.087<br>[-0.137, 1.205]</td></tr><tr><td>6 (6)</td><td>3.61±0.89<br>[2.44, 4.6]</td><td>404±114<br>[226, 543]</td><td>14±4.9<br>[9.4, 22.4]</td><td>1.9±0.6<br>[1.1, 2.6]</td><td>3.6±0.7<br>[2.5, 4.4]</td><td>706.3; 433.9; 0.179<br>[-498.4, 1911]</td><td>-0.45; 0.5; 0.419<br>[-1.836, 0.9561]</td></tr><tr><td>10 (16)</td><td>4.34±0.86<br>[3.1, 5.92]</td><td>493±132<br>[311, 862]</td><td>21.3±8.5<br>[10.9, 43.4]</td><td>1.3±0.5<br>[0.6, 2.2]</td><td>2.8±0.7<br>[1.7, 4]</td><td>200.7; 97.9; 0.059<br>[69.1, 543.5]</td><td>0.615; 0.32; 0.078<br>[-0.063, 1.31]</td></tr><tr><td rowspan="3">PM</td><td>3 (5)</td><td>1.07±0.34<br>[0.57, 1.49]</td><td>397±60<br>[327, 461]</td><td>4.3±1.8<br>[2, 6.7]</td><td>6.8±3.4<br>[3.6, 12.1]</td><td>9.2±3.7<br>[5.7, 15]</td><td>393.6; 22.7; &lt;0.001<br>[320.4, 465.6]</td><td>0.3; 0.19; 0.205<br>[-0.265, 0.99]</td></tr><tr><td>7 (17)</td><td>1.5±0.37<br>[1.01, 2.38]</td><td>833±184<br>[555, 1305]</td><td>12.7±6.3<br>[6.7, 30.3]</td><td>2.2±0.8<br>[0.8, 3.6]</td><td>4±1<br>[2.1, 5.7]</td><td>617.5; 43.7; &lt;0.001<br>[526.9, 716.8]</td><td>0.742; 0.13; &lt;0.001<br>[0.442, 1.031]</td></tr><tr><td>11 (49)</td><td>1.98±0.37<br>[1.24, 2.8]</td><td>1181±256<br>[698, 1704]</td><td>23.4±8.7<br>[10.7, 44.4]</td><td>1.2±0.4<br>[0.5, 2.3]</td><td>2.6±0.6<br>[1.7, 4.1]</td><td>722.7; 72.2; &lt;0.001<br>[585.7, 884]</td><td>0.723; 0.13; &lt;0.001<br>[0.445, 1]</td></tr><tr><td rowspan="3">PMZ</td><td>4 (5)</td><td>1.68±0.49<br>[1.09, 2.32]</td><td>724±149<br>[543, 941]</td><td>12.3±5.7<br>[5.8, 21.3]</td><td>2.3±1.1<br>[1.1, 4.1]</td><td>4.1±1.4<br>[2.6, 6.3]</td><td>563.7; 100; &lt;0.05<br>[280.2, 916.6]</td><td>0.497; 0.29; 0.186<br>[-0.411, 1.527]</td></tr><tr><td>8 (22)</td><td>1.82±0.43<br>[0.72, 2.63]</td><td>896±254<br>[352, 1385]</td><td>16.7±7.5<br>[3.1, 35]</td><td>2±1.9<br>[0.7, 7.8]</td><td>3.7±2.2<br>[2, 10.4]</td><td>519.5; 72.1; &lt;0.001<br>[377, 678.4]</td><td>0.911; 0.2; &lt;0.001<br>[0.517, 1.362]</td></tr><tr><td>12 (33)</td><td>2.08±0.43<br>[1.41, 3]</td><td>1201±233<br>[759, 1697]</td><td>25±9.4<br>[11.6, 49.6]</td><td>1.1±0.4<br>[0.5, 2.1]</td><td>2.5±0.6<br>[1.6, 3.8]</td><td>763.6; 76.7; &lt;0.001<br>[616.7, 935.5]</td><td>0.622; 0.13; &lt;0.001<br>[0.361, 0.887]</td></tr></tbody></table>

<footnote>(1) $\overline{C_D}$ s: average drag coefficient calculated from the Reynolds number using the Stokes' assumption $C_D = 24/Re$.</footnote>

<footnote>(2) $\overline{C_D}$ w: average drag coefficient calculated from the Reynolds number using White's empirical relationship (White 1974) $C_D = 24/Re + 6/(1+Re^{0.5}) + 0.4$.</footnote>

<footnote>(3) Standard Error, p-value and 95 % confidence intervals.</footnote>
<table><caption>**Table 5.** Criteria for inter-comparisons of model performance to predict log-transformed observations. Bold values indicate the model pairwise inter-comparison: model 1 versus 3 for the treatment with calcite and model 2 versus 4 for the treatments without calcite (see text for details on model parameterization). Italicized values indicate the occurrence of a difference in log(Likelihood) larger than 2 points and taken as a criterion for a better fit.</caption><thead><tr><th rowspan="2">Treat.</th><th rowspan="2">Tank</th><th rowspan="2">n</th><th colspan="3">Model 1</th><th colspan="3">Model 2</th><th colspan="3">Model 3</th><th colspan="3">Model 4</th></tr><tr><th>RSS</th><th>RMSE</th><th>log (L)</th><th>RSS</th><th>RMSE</th><th>log (L)</th><th>RSS</th><th>RMSE</th><th>log (L)</th><th>RSS</th><th>RMSE</th><th>log (L)</th></tr></thead><tbody><tr><td rowspan="2">P</td><td>5</td><td>11</td><td>0.61</td><td>0.23</td><td>6.93</td><td><strong>0.12</strong></td><td><strong>0.1</strong></td><td><strong>10.86</strong></td><td>0.65</td><td>0.24</td><td>6.76</td><td><strong>0.1</strong></td><td><strong>0.09</strong></td><td><strong>11.3</strong></td></tr><tr><td>9</td><td>33</td><td>17.59</td><td>0.73</td><td>4.51</td><td><strong>0.72</strong></td><td><strong>0.15</strong></td><td><strong>27.45</strong></td><td>13.97</td><td>0.65</td><td>6.16</td><td><strong>0.39</strong></td><td><strong>0.11</strong></td><td><strong>31.74</strong></td></tr><tr><td rowspan="3">PZ</td><td>2</td><td>6</td><td>0.71</td><td>0.35</td><td>2.77</td><td><strong>0.08</strong></td><td><strong>0.12</strong></td><td><strong>5.61</strong></td><td>0.16</td><td>0.16</td><td>4.71</td><td><strong>0.02</strong></td><td><strong>0.05</strong></td><td><strong>7.79</strong></td></tr><tr><td>6</td><td>6</td><td>1.71</td><td>0.53</td><td>1.64</td><td><strong>0.14</strong></td><td><strong>0.15</strong></td><td><strong>4.92</strong></td><td>1.5</td><td>0.5</td><td>1.8</td><td><strong>0.09</strong></td><td><strong>0.12</strong></td><td><strong>5.46</strong></td></tr><tr><td>10</td><td>16</td><td>5.72</td><td>0.6</td><td>3.58</td><td><strong>0.14</strong></td><td><strong>0.09</strong></td><td><strong>16.54</strong></td><td>5.09</td><td>0.56</td><td>3.98</td><td><strong>0.2</strong></td><td><strong>0.11</strong></td><td><strong>15.24</strong></td></tr><tr><td rowspan="3">PM</td><td>3</td><td>5</td><td><strong>0.68</strong></td><td><strong>0.37</strong></td><td><strong>2.17</strong></td><td>0.06</td><td>0.11</td><td>4.88</td><td><strong>0.04</strong></td><td><strong>0.09</strong></td><td><strong>5.14</strong></td><td>0.02</td><td>0.06</td><td>6.15</td></tr><tr><td>7</td><td>17</td><td><strong>0.71</strong></td><td><strong>0.2</strong></td><td><strong>11.72</strong></td><td>1.29</td><td>0.28</td><td>9.53</td><td><strong>0.06</strong></td><td><strong>0.06</strong></td><td><strong>20.62</strong></td><td>0.13</td><td>0.09</td><td>17.9</td></tr><tr><td>11</td><td>49</td><td><strong>0.91</strong></td><td><strong>0.14</strong></td><td><strong>42.44</strong></td><td>5.15</td><td>0.32</td><td>23.97</td><td><strong>1.31</strong></td><td><strong>0.16</strong></td><td><strong>38.52</strong></td><td>0.5</td><td>0.1</td><td>48.86</td></tr><tr><td rowspan="3">PMZ</td><td>4</td><td>5</td><td><strong>0.28</strong></td><td><strong>0.24</strong></td><td><strong>3.12</strong></td><td>0.36</td><td>0.27</td><td>2.87</td><td><strong>0.02</strong></td><td><strong>0.07</strong></td><td><strong>5.87</strong></td><td>0.03</td><td>0.08</td><td>5.45</td></tr><tr><td>8</td><td>22</td><td><strong>0.58</strong></td><td><strong>0.16</strong></td><td><strong>17.4</strong></td><td>1.64</td><td>0.27</td><td>12.39</td><td><strong>0.4</strong></td><td><strong>0.13</strong></td><td><strong>19.15</strong></td><td>0.43</td><td>0.14</td><td>18.78</td></tr><tr><td>12</td><td>33</td><td><strong>0.67</strong></td><td><strong>0.14</strong></td><td><strong>27.88</strong></td><td>3.74</td><td>0.34</td><td>15.61</td><td><strong>0.74</strong></td><td><strong>0.15</strong></td><td><strong>27.26</strong></td><td>0.28</td><td>0.09</td><td>34.31</td></tr></tbody></table>

RSS: Residual sum of squares; RMSE: Root Mean Square Error; L: Likelihood.