{"paper_id":"16adf24a-72d7-43bf-9dca-01e9f1e2aeb7","body_text":"1 \n \nSedimentation and drag in drifting macrophytes and plastic \nobjects: A model \n \nAuthors: Friederike Gronwald1#, Florian Weinberger 1#*, Tjeerd J. Bouma2, Rolf Karez3 \n# These authors contributed equally to this work \n*Corresponding author:  Florian Weinberger , G EOMAR Helmholtz Centre for Ocean \nResearch Kiel, Düsternbrooker Weg 20, 24105 Kiel, Germany, telephone: +49 431 600 4516, \nE-Mail: fweinberger@geomar.de \nAffiliations \n 1 Department of Marine Ecology, GEOMAR Helmholtz Centre for Ocean Research Kiel, \n24105 Kiel, Germany.  \n2 NIOZ Royal Netherlands Institute for Sea Research, Department of Estuarine and Delta \nSystems, 4401 NT Yerseke, the Netherlands.  \n3 State Agency for the Environment Schleswig-Holstein, 24220 Flintbek, Germany.  \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint \n\n2 \n \nGraphical abstract \n  \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint \n\n3 \n \nAbstract \nPredicting macroalgal sedimentation and drag sensitivity is essential for ecological and \ngeochemical modeling, and for optimizing seaweed cultivation. However, despite the diversity \nof macrophyte forms, models incorporating their specific morphology and hyd rodynamic \neffects are largely lacking.  To develop a broadly applicable model, we tested whether the drag \nresponse of diverse macrophyte morphologies and plastic objects can be accurately predicted \nby approximating them as ellipsoids and accounting for the ir specific shapes. A set of simple \nshape descriptors (wet weight, volume, thallus thickness, thallus projection area) and an \nempirical solution for the drag equation , enabled relative accurate prediction s of the sinking \nvelocity for 26 morphologically div erse macroalgae species, as well as the eelgrass Zostera \nmarina, another major source of drifting biomass in  many shallow seas . Additionally, we \nidentified a second simpler empirical solution that incorporates shape and, while slightly less \naccurate, can be applied to a broader range of particles, including plastics. \n  \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint \n\n4 \n \nIntroduction \nDrifting macroalgal blooms are a global problem, with some of the largest blooms being caused \nby floating species such as Sargassum natans and S. fluitans in the Great Atlantic Sargassum \nBelt or Ulva prolifera in the Yellow Sea (Smetacek and Zingone 2013). When blooms of that \nmagnitude beach, they often cause severe problems for the coastal communities and \nenvironment (Zhang 2019, Bartlett and Elmer 2021) . In the SW Baltic Sea the macroalgae \nblooms are of a smaller scale, but more diverse than in many other environments  (Weinberger \net al. 2021). These blooms can be dominated by a single species, but more often several species \nare found blooming together, and in most blooms in the SW Baltic, the eelgrass Zostera marina \n(littered leaves, fragments and whole specimens) also constitutes a significant part of the \nbiomass (Weinberger et al. 2020). The ways in which hydrodynamic factors affect the sp ecies \ncomposition of macroalgal blooms are still poorly known. Unattached macrophytic biomass in \nthe Baltic can be floating (Rothäusler et al. 2015), or negatively buoyant, but drifting (Bonsdorff \n1992, Weinberger et al. 2008) . Problematic blooms are often found in sheltered, relatively \nshallow waters, where they may degrade and cause nuisance and envir onmental problems \nlocally (Mossbauer et al. 2012, Weinberger et al. 2020, 2021).  \nAccumulations of algal biomass can have great impact on the environment in deeper waters as \nwell (Vahteri et al. 2000) . It has been proposed that significant portions of biomass produced \nin photic coastal waters may even reach deep anoxic zones of the ocean through drift and \nsedimentation, where they could then provide an important  component of global carbon \nsequestration (Krause-Jensen and Duarte 2016, Ortega et al. 2019, Kokubu et al. 2019) . Such \ntransport of particulate biomass over long distances obviously requires drifting velocities that \nexceed the speed of biomass degradation during the transport process. Possible maximum drift \nvelocities of seaweeds are typically predicted using Lagrangian particle transport models \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint \n\n5 \n \n(Rothäusler et al. 2015, Kwon et al. 2019, Garbossa et al. 2021, Zhou et al. 2021). These models \ndo usually no t consider the specific resistance of seaweeds to drag, as suitable generalized  \ndescriptors for predicting the  hydrodynamic drifting behavior  of seaweeds are so far largely \nmissing. \nThe lack of models that can accurately describe the drifting and sinking b ehavior of seaweeds \nalso affects the development and design of land -based seaweed aquaculture systems, which \ntarget the cultivation of unattached macroalgae. One important goal of such systems is to \nachieve maximally homogenous exposure of the cultivated organisms to sun light and nutrients \nwith a minimum of energy investment (Sahoo and Yarish 2005). Typical solutions are raceways \n(Mata et al. 2003), aerated tank (Israel et al. 2005) or pond systems (Msuya and Neori 2008) or \nbioreactors  (Savvashe et al. 2021)  that are usually developed based on trial and error, as the \ndrifting and sedimentation behavior of different seaweed species is difficult to predict. \nIn addtion to macroalgae and eelgrass, plastic particles represent another large group of drifting \nparticles in the ocean (Eriksen et al. 2014). These particles can become problematic for example \nby remaining within the ecosystem and slowly degrading (Gewert et al. 2015), being ingested \nby marine organisms  as microplastic (Galloway et al. 2017) , or accumulating on beaches  \n(Barnes et al. 2009). Plastic litter, to some degree, resembles seaweeds as it exhibits a similar \ndiversity of shapes  and sizes. These similarities suggest that a model developed to predict \nsedimentation velocities of seaweeds may also be applicable for plastic particles of similar size.  \nEstablished approaches for predicting sedimentation velocity \nAs predicted by Stokes (1851) , the sedimentation of particl es in water is driven by  the \ngravitational acceleration g. It also depends on the particle buoyancy, i.e. the particle mass \ndensity ρ relative to the mass density of the seawater ρsw. Other factors that determine  the \nsedimentation velocity ω are the diameter d of the particle and the drag coefficient C D. CD is a \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint \n\n6 \n \ndimensionless indicator of the resistance of a particle to current. CD is not a constant, but varies \nas a function of flow speed, flow direction, object position, object size, fluid density and the \nkinematic viscosity of the medium. ω may be calculated for spherical particles as \nω = √4\n3\n( 𝜌\n𝜌𝑠𝑤\n−1) 𝑔 𝑑\n𝐶𝐷\n     (Eq. 1) \nEquation 1 is based o n the assumption that the sedimentation velocity can be calculated by \nequating the effective weight force with the drag force (Riazi and T ürker 2019) . For non -\nspherical particles, the nominal diameter dn - describing the diameter of a sphere with the same \nvolume as the particle  - can be used instead of the diameter d.  However, ex act analytical \nsolutions of Eq. 1 only exist for spheres (Stokes 1851) and spheroids (Oseen 1927) in laminar \nflows, because turbulence on the particle surface strongly influences CD and irregularly shaped \nparticles must be expected to generate turbulences that are virtually impossible to predict. To \nresolve this problem, different empirical solutions of Eq. 1 that used shape factors to correct CD \nfor non-sphericity have been proposed for sediment grains (e.g., Swamee and Ojha 1991, Cheng \n1997, She et al. 2005, Camenen 2007) . Particle shape could be expressed in various ways, for \nexample by use of sphericity factors that put the volume of a particle in relation with its surface \narea (Wadell 1935). Yet, exact measurements of the surface area of irregularly shaped particles \nare often hardly possible, which makes the application of sphericity factors to them difficult. \nThe shape factor most commonly used instead is the Corey factor S f  (Komar and Reimers \n1978), which expresses the deviation of particle shape from sphericity independent of its size \nas \n𝑆𝑓 =\n𝑐\n√𝑎𝑏       (Eq. 2) \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint \n\n7 \n \nwhere a, b, and c are the diameters in the longest, the intermediate and the shortest mutually \nperpendicular axes of the particle, respectively. An improved empirical solution of Eq. 1 was \nrecently proposed by Riazi and Türker (2019), who investigated the sedimentation behavior of \nsediment particles with diameters in the approximate range between 0.5 and 7 mm. The authors \nproposed to treat such particles as ellipsoids and introduced S f raised to the power of 2/3 into \nEq. 1 to account for their non-spherical shapes: \nω = √4\n3\n( 𝜌\n𝜌𝑠𝑤\n−1) 𝑔 𝑑𝑛 𝑆𝑓\n2\n3 \n𝐶𝐷\n    (Eq. 3) \nRiazi and Türker (2019) (Riazi and Türker 2019) further proposed to calculate the drag factor \nin Eq. 3 as  \n𝐶𝐷 = (\n𝑋2 𝜈\n𝑑𝑛1.5𝑔0.5 +𝑋3)\n𝑋1\n     (Eq. 4) \nwhere ν is the kinematic viscosity of the medium, X 1 is a dimensionless constant and X 2 and \nX3 are also dimensionless constants that both depend on S f and describe the behavior of the \ndrag coefficient with respect to particle shape in laminar  and turbulent flow conditions, \nrespectively. \nThe need to transfer these equations towards seaweed-like particles \nDrifting macrophytes exhibit highly variable morphologies that range from unbranched \nfilamentous forms over branched or unbranched leaf shapes to three-dimensionally branched or \nunbranched irregularly tangled forms (Fig. S 4 to S10). Macrophytes are usually much larger \nand mechanically more flexible than sediment grains, which may also be expected to affect \ntheir response to drag. The question th erefore arises whether generalized approaches to the \ndetermination of CD and ω are possible that allow for the prediction of sedimentation velocities \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint \n\n8 \n \nand drag across species without tedious experimental setups. We hypothesized that approximate \npredictions may be possible if drifting macroalgae and eelgrass litter are treated as ellipsoids, \nsimilar as proposed by Riazi and Türker (2019) for sediment particles.  \nThe approximately ellipsoidal character of unbranched mac rophytes is fairly obvious. \nHowever, in macrophytes exhibiting branching of several orders typically the longest, shortest, \nand middle perpendicular thallus axes cannot be readily identified  and measured . It was \ntherefore necessary to develop a suitable method for the determination of these axes and Sf in \nmacrophytes. Sedimentation velocities of two different sample sets of seaweeds and eelgrass  \nand a set of plastic objects, with variable particle properties were then measured. Measures \nobtained with seaweed sample set 1 allowed for the identification of an empirical solution for \nEq. 4 and the resulting model was successfully tested with seaweed sample set 2. Subsequently, \nit was tested whether the optimal solution for seaweeds would be applicable to plastic particles. \nMaterial and methods \nCollection and maintenance of algae \nThis study includes 73 specimens of drifting marine macrophytes belonging to 26 different  \nspecies (Fucus vesiculosus, Fucus serratus, Chorda filum, Saccharina latissima, Gracilaria \nvermiculophylla, Ceramium virgatum, Vertebrata fucoides, Polysiphonia stricta, \nSpermothamnion repens, Ahnfeltia plicata, Furcellaria lumbricalis, Coccotylus truncatus, \nDelesseria sanguinea, Cladophora flexuosa, Cladophora sp., Rhodomela confervoides, \nPyropia leu costicta, Ulva clathrata, Ulva linza, Ulva compressa , Kornmannia leptoderma, \nBryopsis hypnoides, Acrosiphonia centralis, Zostera marina, Ascophyllum nodosum and Ulva \ngigantea). The specimens were selected to represent a wide range of morphologies  (Fig. S4 to \nS10) and were taxonomically identified based on these traits , following Nielsen et al. (2023) . \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint \n\n9 \n \nTen of the specimens were collected from drift material in January 2023 at a location between \nStrande and Bülk light house (Kiel Fjord/Germany ; 54°26'57.4\"N 10°11'37.6\"E). On the 26th \nof June 2024, 56 more specimens were collected a t the same site and at two other locations in \nthe Kiel Fjord area ( Schilksee, 54°25'16.3\"N 10°10'43.1\"E and Mönkeberg, 54°21'20.92\"N \n10°10'41.97\"E). Six specimens of A. nodosum and one of U. gigantea were collected in July \n2024 from a beach at Yerseke/Netherlands (51°30'09.0\"N, 4°02'39.7\"E). Salinities and water \ntemperatures at the collection sites and during subsequent maintenance and experiments were \nmeasured using a WTW Multi3630IDS conductometer. Prior to use, material collected in 2023 \nwas maintained for 3 d at 13.6 °C in Baltic Sea seawater with a salinity of 18.8 psu, which was \nthe salinity at the collection site. All subsequent measurements were conducted in sea water of \nthe same salinity and temperature at the GEOMAR laboratories in Kiel. Material collected from \nthe Kiel Fjord in 2024 was kept for 4 days in seawater with salinity 15.0 psu (mean salinity at \nthe collection sites: 14.0 psu) and 16 °C (mean temperature at collection sites: 20 °C) and then \npacked in cooler boxes and transported within 7 h to the NIOZ laboratories at Yerseke in the \nNetherlands. There the material was maintained for 1 to 3 weeks  at 18 °C in Oosterschelde \nwater (salinity: 33 psu) diluted with tap water to a salinity of 14.4 psu. Material collected from \nthe Oosterschelde was acclimatized at the NIOZ laboratories to a salinity of 15 psu by stepwise \ndecrease of salinity by 4-5 psu every two to three days. Aeration was provided to all specimens \nduring the maintenance and they were kept in artificial light (80 µmol photons m-2 s-1 for 12 h \nd-1). Water was exchanged every other day. \nIn addition to the seaweeds, 16 negatively buoyant plastic objects were tested, including eight \ncircular foil cutouts (disks), three table tennis balls, two plastic nets and three rubber bands (Fig. \nS11). The foil disks were cut to different diameters and some were punched with different \nnumbers of small holes. The nam e of the foil circles  indicates both  their diameter and \nperforation level. For example , “Disk 40-1” had a diameter of 40 mm and was unpunched, \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint \n\n10 \n \nwhere “1” denotes unpunched, “2” partially punched, and “3” heavily punched, “4” extremely \nheavily punched. The three table tennis balls shared identical dimension and therefore had the \nsame shape parameters. To increase their mass density air inside the balls was replaced with \nsea water, using an injection syringe. To increase the mass density further different nubers of \nglass beads (2 mm diameter) were pressed into the balls through small holes, which were then \nsealed with Scotch tape.  \nDescriptors of thallus shape and density \nParticle traits were determined for all specimens. To determine volume V a graduated cylinder \nmeasure of suitable size was filled with a defined volume of sea water and the specimen was \ncompletely immersed in this volume. Any air bubbles were carefully removed and the increase \nof volume was recorded as particle volume. Wet weights were measured after the macrophytes \nhad been carefully blotted with paper. All measurements of volume and weight were repeated \ntwo times and in case of data divergency by more than 5 % three t imes. The particle mass \ndensity ρ could then be calculated as the ratio of mean blotting weight and mean volume. The \nnominal particle diameter dn was also derived from the mean volume and determined as twice \nthe radius of a sphere with the volume of the measured macrophyte: \n𝑑𝑛 = 2 √ \n3 𝑉\n4 𝜋\n3\n      (Eq. 5) \nProjection images of all specimens were used to determine measures for the calculation of \nCorey shape factors. To generate such images the specimens were scanned on a flatbed scanner \ntogether with a size standard . The resulting images were analyzed using the Fiji software \npackage (Schindelin 2012). In the case of specimens with flattened morphologies (A. nodosum, \nF. vesiculosus, F. serratus, S. latissima phylloid, P. leucosticta, C. truncatus, U. compressa, U. \ngigantea, K. leptoderma, Z. marina leaves) and also of the unbranched cylindrical C. filum the \ndetermined parameter was the t hallus projection area (using the “adjust color threshold” and \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint \n\n11 \n \n“measure particles” procedures implemented in Fiji). This projection area obviously represents \nthe product of the longest and the intermediate perpendicular thallus axes a * b of flattened \nthalli (see Eq. 2). The shortest intermediate perpendicular axis c is in these cases equal to the \nthallus thickness. It could be subsequently calculated by division of the thallus volume V by \nthe projection area a*b, because V = a*b*c. All remaining specimens exhibited three -\ndimensional morphologies, often with branches that partly overlapped and masked each other \nin projection images. In these cases, ten independent measurements of the width of youngest \nthallus branches were conducted and the mean was consider ed as a representative measure of \nc. Division of volume V by c allowed then to calculate corresponding values for a*b. \nMeasurements of sinking velocity \nMaximum sinking velocities in sea water were determined for all non -buoyant specimens \ndirectly before or  after the determination of particle traits . After their release at the water \nsurface, sinking particles initially accelerate until they reach their maximum sinking speed. It \nwas therefore necessary to first determine a water depth below which a maximum sinking speed \nof the macrophytes could be assumed. It was found that a water depth of 15 cm is required for \nthe acceleration phase. To verify this, the sinking speeds of 22 samples were measured in two \ndifferent ways (Fig. S1). In both cases, the samples were released at the water surface and only \nafter they had sunk to a depth of 15 cm was their speed measured during the further descent. In \nthe first case, however, the sinking speed was only measured over the depth segment from 15 \ncm to 41 cm and in the seco nd case over the depth segment from 15 cm to 76 cm. If the \nmaximum speed is not reached at a depth of 15 cm and thus a further acceleration takes place \nbelow 15 cm, this should lead to higher mean sinking speeds for measurements at a greater \ndepth (i.e. over a distance of 61 cm) than for measurements at a lesser depth (i.e. over a distance \nof 26 cm). However, a significant difference between the two measurements was only observed \nfor two specimens (Welch corrected t -tests, p = 0.05), and in only one of thes e cases was the \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint \n\n12 \n \nmeasured velocity higher when the measuring distance was longer.  Moreover, a non-\nsignificantly higher mean sinking velocity was found for 1 3 specimens when measured over \nthe shorter depth distance, and only for 7 specimens over the longer distance. \nTherefore, sedimentation velocities were measured in such a way that the specimens were \nsubmerged just below the water surface and released, so that they could accelerate from the \nwater surface to a depth of 15 cm before the velocity was measured with a stop-watch until the \nspecimens made first contact with the bottom. In 2024 the measurements with small algae were \ncarried out in a glass cylinder (diameter 40 cm), which allowed for lateral observation. In this \ncase, the length of the fall distance was 87 cm and the monitoring distance was 72 cm. For \nlarger algae, a plastic barrel was used, in which an underwater video camera and corresponding \ndepth marks allowed for observation of the algae reaching the water depth of 15 cm. In these \ncases, the monitoring distance was 61 cm. All measurements were repeated five times. In 2023 \nsedimentation velocities were measured in an aquarium that was filled to a height of 26 cm with \nsea water and the monitoring distance was 11 cm . The macrophytes were filmed outsi de the \naquarium, with a ruler attached to the window pane, and sedimentation times were determined \nby single frame analysis. These measurements were repeated 7 times. The plastic particles were \nmeasured in a plastic cylinder (diameter: 19 cm) with a fall distance of 48 cm and a monitoring \ndistance of 33 cm. \nWater temperature and salinity in the measuring vessels changed slightly from day to day. Both \nparameters were therefore determined repeatedly between the speed measurements, in order to \nderive mass density ρH2O and kinematic viscosity ν (Sharqawy et al. 2012) . These parameters \nare listed in Tab. 1 \n \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint \n\n13 \n \nStatistics and model development  \nData were visualized and correlations were analyzed using the Prism9 software package \n(GraphPad, Boston, USA). Differences in sedimentation velocities among specimens or groups \nof specimens were detected by Kruskal -Wallis-ANOVA and Sidak-corrected pairwise Dunn-\ntests using the same software. All other statistical treatment was conducted in R version 4.2.2.  \nThe sedimentation velocity equation  (see Eq. 3 and 4) was optimized for the particles using \ngenetic algorithm as implemented in R library GA  (Scrucca 2013). For this purpose, the data \nsets of sedimenting macrophytes were divided into two groups. The first group was selected to \ninclude a wide range of different morphologies and particle properties, and this group was used \nfor the actual modeling.  The employed genetic algorithm started with an initial population of \n5000 randomly generated individuals, with a crossover probability of 0. 8, a mutation \nprobability of 0.1 and an elitism of 250. The optimization process continued for maximally 500 \n000 generations and ended when no convergence toward a lower mean square error was \nobtained over 5000 generations.  The accuracy of the resulting equations was then verified , \nusing the second group of seaweed data sets as well as the plastic particle data set. \n \nResults \nParticle traits \nParticle traits of all investigated specimens are summarized in Tab.1, for images of all \nspecimens see Figs. S4 to S11. Nominal diameters of these specimens ranged from 0.5 76 cm \nto 4.844 cm, volumes from 0.1 cm³ to 59.5 cm³ and blotting weights from 0.1 1 g to 46.10 g. \nThe shape factor Sf varied beween 0.00029 and 0.0689 (Fig. 1), with the exception of some of \nthe plastic particles with higher shape factors, especially the table tennis balls, which had an Sf \nof 1 due to their perfectly round shape. As to be expected, Sf was particularly low in specimens \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint \n\n14 \n \nwith pronounced thin and flattened morphologies, such as U. gigantea, K. leptoderma, or P. \nleucosticta, but also in specimens characterized by very thin and dense lateral branches, such \nas A. centralis, C. flexuosa or S. repens. Sf was the highest in macrophyte specimens exhibiting \nrelatively thick branched or unbranched morp hologies, such as  C. filum, A. nodosum or S. \nlatissima rhizoid. A particularly large variability of S f was detected for Z. marina, \ncorresponding with the circumstance that the investigated specimens were morphologically \nvariable and included littered leafs , as well as whole plants bearing or not bearing rhizoid or \ninflorescence. In F. vesiculosus floating specimens - characterized by presence of gas -filled \nvesicles - exhibited a larger Sf than non-floating specimens. A trend towards larger Sf in floating \nspecimens gets also apparent if different species are compared: in none of the negatively \nbuoyant seaweed specimens was Sf larger than 0.0278 and in none of  the buoyant specimens \nsmaller than 0.00116 (Fig.1). \nFig. 1: Shape factors of 73 specimens of driftin g marine macrophytes.  Red dots indicate \npositively buoyant (floating) specimens, blue dots negatively buoyant (sinking) specimens.  \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint \n\n15 \n \nTable 1: Shape descriptors of the investigated specimens. Non-buoyant specimens were grouped and used either for development or for testing of 1 \nthe sedimentation models, while buoyant specimens could obviously not be used for this purpose. Weight is the blotting weight [g], V is the volume 2 \n[cm³], dn [cm] is the nominal diameter. c [mm], a and b [cm] are thallus diameters in the  shortest, longest and intermediate mutually perpendicular 3 \naxes, respectively, that were used to calculate the Corey shape factor S f (see Eq. 2). Bold values listed under c and a b were measured directly, while non -bold 4 \nvalues listed under c and a b were determined by division of V by the bold value. Figure refers to pictures in the online supplement. ρH2O and ν are seawater density 5 \nand kinematic viscosity during measurements of the mean sedimentation velocity . 6 \nSpecimen Group \nWeight \n[g] \nV \n[cm³] \ndn \n[cm] \nc \n[mm] \na b \n[cm²] Sf Figure ρsw [kg/m³] v [m2 s-1]  [m s-1] \nAcrosiphonia centralis 36 Modeling 12.98 12.25 2.86 0.102 1205.7 0.00029 S4 1009.446 1.0494E-06 0.0208 \nAhnfeltia plicata 47-1 Modeling 0.66 0.50 0.98 0.455 11.0 0.01371 S5 1009.862 1.0917E-06 0.0347 \nAhnfeltia plicata 47-2 Modeling 7.07 5.63 2.21 0.492 114.4 0.00460 S5 1009.862 1.0917E-06 0.0466 \nBryopsis hypnoides 1-2 Modeling 0.95 0.88 1.19 0.104 84.5 0.00113 S4 1009.862 1.0917E-06 0.0144 \nCoccotylus truncatus 24-2-1 Modeling 0.50 0.45 0.95 0.142 31.6 0.00253 S5 1009.710 1.0915E-06 0.0277 \nDelesseria sanguinea 26-2 Modeling 1.62 1.25 1.34 0.144 86.6 0.00155 S5 1009.446 1.0494E-06 0.0181 \nFucus serratus 9 Modeling 6.15 5.50 2.19 0.492 111.8 0.00465 S4 1009.446 1.0494E-06 0.0290 \nFucus vesiculosus 54 Modeling 17.88 17.00 3.19 0.653 260.2 0.00405 S4 1009.446 1.0494E-06 0.0256 \nFurcellaria lumbricalis 43-1 Modeling 1.31 1.08 1.27 0.606 17.9 0.01433 S5 1009.564 1.0727E-06 0.0450 \nFurcellaria lumbricalis 44-1 Modeling 2.39 2.00 1.56 0.530 37.8 0.00862 S5 1009.564 1.0727E-06 0.0525 \nGracilaria vermiculophylla 16-1 Modeling 0.45 0.42 0.93 0.351 12.1 0.01007 S5 1009.710 1.0915E-06 0.0306 \nGracilaria vermiculophylla 49 Modeling 5.23 5.00 2.12 0.279 179.2 0.00208 S5 1009.488 1.0726E-06 0.0237 \nKornmannia leptoderma 1-1 Modeling 0.29 0.27 0.81 0.052 52.4 0.00073 S4 1009.724 1.0835E-06 0.0084 \nPolysiphonia stricta 37-2-1 Modeling 1.69 1.58 1.45 0.094 168.8 0.00072 S4 1009.745 1.0862E-06 0.0124 \nSaccharina latissima rhizoid K9B Modeling 0.98 0.70 1.10 0.815 8.6 0.02779 S4 1013.900 1.1939E-06 0.0492 \nSpermothamnion repens 14 Modeling 0.47 0.40 0.91 0.078 51.4 0.00109 S5 1009.862 1.0917E-06 0.0169 \nUlva clathrata 21-1 Modeling 0.30 0.25 0.78 0.323 7.7 0.01163 S4 1009.710 1.0915E-06 0.0097 \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint \n\n16 \n \nTab. 1, continued. 7 \nSpecimen Group \nWeight \n[g] \nV \n[cm³] \ndn \n[cm] \nc \n[mm] \na b \n[cm²] Sf Figure ρsw [kg/m³] v [m2 s-1]  [m s-1] \nUlva gigantea 10 Modeling 5.98 5.50 2.19 0.079 698.2 0.00030 S4 1009.446 1.0494E-06 0.0149 \nUlva linza 8-1 Modeling 0.23 0.20 0.73 0.151 13.3 0.00413 S4 1009.745 1.0862E-06 0.0119 \nZostera marina leaf 40-2 Modeling 0.16 0.13 0.62 0.168 7.4 0.00618 S4 1009.446 1.0494E-06 0.0108 \nAhnfeltia plicata K1 Testing 1.26 1.00 1.24 0.190 52.8 0.00261 S8 1013.900 1.1939E-06 0.0287 \nCeramium virgatum 6-2 Testing 2.41 2.38 1.66 0.079 299.5 0.00046 S7 1009.745 1.0862E-06 0.0119 \nCeramium virgatum 7-2 Testing 1.47 1.25 1.34 0.186 67.3 0.00226 S7 1009.710 1.0915E-06 0.0132 \nCeramium virgatum 8-2 Testing 0.91 0.88 1.19 0.146 60.6 0.00187 S7 1009.745 1.0862E-06 0.0122 \nCeramium virgatum K6 Testing 0.12 0.10 0.58 0.054 18.4 0.00127 S7 1013.900 1.1939E-06 0.0100 \nCladophora flexuosa 34 Testing 4.97 4.50 2.05 0.152 296.4 0.00088 S6 1013.900 1.1939E-06 0.0087 \nCladophora sp. K3 Testing 0.11 0.10 0.58 0.076 13.1 0.00211 S6 1013.900 1.1939E-06 0.0149 \nCoccotylus truncatus 24-2-2 Testing 0.39 0.35 0.88 0.354 10.0 0.01121 S8 1009.598 1.0967E-06 0.0276 \nDelesseria sanguinea 27 Testing 18.74 16.50 3.16 0.376 438.3 0.00180 S7 1009.446 1.0494E-06 0.0281 \nDelesseria sanguinea 27-2-2 Testing 10.69 9.41 2.62 0.297 317.2 0.00167 S7 1009.598 1.0967E-06 0.0282 \nFucus serratus 12 Testing 9.90 8.88 2.57 0.512 173.2 0.00389 S6 1009.446 1.0494E-06 0.0384 \nFucus serratus K5 Testing 9.37 8.30 2.51 0.443 187.5 0.00323 S6 1013.900 1.1939E-06 0.0321 \nFurcellaria lumbricalis 41-1 Testing 2.00 1.58 1.45 0.659 24.0 0.01345 S8 1009.564 1.0727E-06 0.0499 \nFurcellaria lumbricalis K8 Testing 0.73 0.60 1.05 0.422 14.2 0.01118 S8 1013.900 1.1939E-06 0.0380 \nGracilaria vermiculophylla 26-1 Testing 4.64 4.25 2.01 0.253 168.1 0.00195 S8 1009.446 1.0494E-06 0.0226 \nGracilaria vermiculophylla 49-2 Testing 2.62 2.50 1.68 0.328 76.4 0.00375 S8 1009.598 1.0967E-06 0.0209 \nKornmannia leptoderma 4-2 Testing 0.11 0.10 0.58 0.038 26.2 0.00074 S6 1009.724 1.0835E-06 0.0080 \nPolysiphonia stricta 37-2-2 Testing 1.06 1.00 1.24 0.110 90.9 0.00115 S7 1009.598 1.0967E-06 0.0118 \nPolysiphonia stricta 39-2 Testing 1.28 1.25 1.34 0.117 106.5 0.00114 S7 1009.745 1.0862E-06 0.0143 \nPyropia leucosticta 32 Testing 0.92 0.88 1.19 0.087 100.7 0.00087 S7 1009.488 1.0726E-06 0.0111 \nRhodomela confervoides 4-1 Testing 3.60 3.50 1.88 0.385 90.9 0.00404 S7 1009.724 1.0835E-06 0.0200 \nRhodomela confervoides 4-1-2 Testing 2.47 2.40 1.66 0.373 64.3 0.00465 S7 1009.598 1.0967E-06 0.0201 \nSaccharina latissima phylloid K9A Testing 2.01 1.60 1.45 0.263 60.9 0.00337 S6 1013.900 1.1939E-06 0.0167 \n 8 \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint \n\n17 \n \nTable 1, continued. 9 \nSpecimen Group \nWeight \n[g] \nV \n[cm³] \ndn \n[cm] \nc \n[mm] \na b \n[cm²] Sf Figure ρsw [kg/m³] v [m2 s-1]  [m s-1] \nSpermothamnion repens 16-2 Testing 0.24 0.20 0.73 0.050 39.7 0.00080 S7 1009.710 1.0915E-06 0.0164 \nUlva clathrata 24-1 Testing 0.19 0.18 0.69 0.245 7.1 0.00918 S6 1009.710 1.0915E-06 0.0074 \nUlva linza 6-1 Testing 0.52 0.43 0.93 0.156 27.2 0.00300 S6 1009.745 1.0862E-06 0.0330 \nVertebrata fucoides K2 Testing 0.29 0.20 0.73 0.077 25.8 0.00152 S6 1013.900 1.1939E-06 0.0139 \nZostera marina leaf 40-1 Testing 0.48 0.43 0.93 0.222 19.1 0.00509 S6 1009.446 1.0494E-06 0.0137 \nZostera marina leaf K7 Testing 0.23 0.20 0.73 0.156 12.8 0.00435 S6 1013.900 1.1939E-06 0.0168 \nAscophyllum nodosum 21 Buoyant 8.39 8.63 2.54 1.756 49.1 0.02505 S10 1009.446 1.0494E-06 0 \nAscophyllum nodosum 29 Buoyant 46.10 59.50 4.84 3.384 175.8 0.02552 S10 1009.446 1.0494E-06 0 \nAscophyllum nodosum 2 Buoyant 3.38 4.33 2.02 2.138 20.3 0.04751 S10 1009.446 1.0494E-06 0 \nAscophyllum nodosum 46 Buoyant 1.85 2.58 1.70 2.307 11.2 0.06893 S10 1009.446 1.0494E-06 0 \nAscophyllum nodosum 5 Buoyant 4.81 4.83 2.10 1.747 27.7 0.03323 S10 1009.446 1.0494E-06 0 \nAscophyllum nodosum 68 Buoyant 12.17 13.00 2.92 1.820 71.4 0.02153 S10 1009.446 1.0494E-06 0 \nChorda filum 41-2 Buoyant 0.61 0.88 1.19 1.230 7.1 0.04614 S9 1009.564 1.0727E-06 0 \nChorda filum 42-2 Buoyant 0.98 1.17 1.31 1.086 10.7 0.03313 S9 1009.745 1.0862E-06 0 \nChorda filum 43-2 Buoyant 0.42 0.58 1.04 1.025 5.7 0.04296 S9 1009.564 1.0727E-06 0 \nChorda filum 44-2 Buoyant 0.77 1.42 1.39 1.633 8.7 0.05544 S9 1009.564 1.0727E-06 0 \nFucus vesiculosus 13 Buoyant 6.70 9.50 2.63 1.192 79.7 0.01335 S10 1009.446 1.0494E-06 0 \nFucus vesiculosus 15 Buoyant 6.04 6.50 2.32 0.861 75.5 0.00990 S10 1009.446 1.0494E-06 0 \nFucus vesiculosus 3 Buoyant 7.80 8.88 2.57 1.185 74.9 0.01370 S10 1009.488 1.0726E-06 0 \nFucus vesiculosus 35 Buoyant 6.17 7.38 2.42 1.102 66.9 0.01347 S10 1009.488 1.0726E-06 0 \nFucus vesiculosus 38 Buoyant 4.82 5.50 2.19 1.018 54.0 0.01385 S10 1009.446 1.0494E-06 0 \nFucus vesiculosus 51 Buoyant 10.33 10.75 2.74 1.237 86.9 0.01327 S10 1009.446 1.0494E-06 0 \nFucus vesiculosus 53 Buoyant 14.70 17.50 3.22 0.905 193.3 0.00651 S10 1009.446 1.0494E-06 0 \nUlva compressa 48-2 Buoyant 0.89 1.00 1.24 0.142 70.3 0.00170 S10 1009.862 1.0917E-06 0 \nZostera marina 25 Buoyant 3.69 3.75 1.93 0.171 219.0 0.00116 S9 1009.446 1.0494E-06 0 \nZostera marina 37-1 Buoyant 3.15 3.50 1.88 0.298 117.5 0.00275 S9 1009.745 1.0862E-06 0 \nZostera marina 39-1  Buoyant 0.37 0.50 0.98 0.311 16.1 0.00774 S9 1009.745 1.0862E-06 0 \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint \n\n18 \n \nTable 1, continued. 10 \nSpecimen Group \nWeight \n[g] \nV \n[cm³] \ndn \n[cm] c [mm] a b [cm²] Sf Figure ρsw [kg/m³] v [m2 s-1]  [m s-1] \nZostera marina 45 Buoyant 2.84 3.50 1.88 0.498 70.3 0.00594 S9   0 \nZostera marina 48-1 Buoyant 1.69 2.00 1.56 0.300 66.8 0.00367 S9 1009.862 1.0917E-06 0 \nZostera marina 69 Buoyant 1.71 1.88 1.53 0.856 21.9 0.01830 S9   0 \nDisc 40-1 Plastic 0.25 0.18 0.71 0.14 12.7 0.00406 S11 998.15 9.7629E-07 0.0225 \nDisc 59-1 Plastic 0.55 0.40 0.92 0.15 27.6 0.00279 S11 998.15 9.7629E-07 0.0187 \nDisc 59-2 Plastic 0.25 0.18 0.71 0.15 12.5 0.00417 S11 998.15 9.7629E-07 0.0260 \nDisc 70-1 Plastic 0.8 0.59 1.04 0.15 39.9 0.00236 S11 998.15 9.7629E-07 0.0217 \nDisc 70-2 Plastic 0.56 0.41 0.92 0.15 27.7 0.00280 S11 998.15 9.7629E-07 0.0234 \nDisc 70-3 Plastic 0.25 0.18 0.71 0.15 12.5 0.00417 S11 998.15 9.7629E-07 0.0507 \nDisc 84-1 Plastic 1.13 0.83 1.17 0.15 55.4 0.00202 S11 998.15 9.7629E-07 0.0283 \nDisc 84-4 Plastic 0.26 0.19 0.71 0.15 12.7 0.00413 S11 998.15 9.7629E-07 0.0298 \nBall 1 Plastic 33.62 33.51 4 26.67 12.6 1 S11 998.37 9.92893E-07 0.0971 \nBall 2 Plastic 33.97 33.51 4 26.67 12.6 1 S11 998.37 9.92893E-07 0.1622 \nBall 3 Plastic 35.17 33.51 4 26.67 12.6 1 S11 998.37 9.92893E-07 0.2536 \nNet-large Plastic 1.13 1 1.24 0.13 80.0 0.00140 S11 998.37 9.92893E-07 0.0493 \nNet-small Plastic 1.02 0.8 1.15 0.13 64.0 0.00156 S11 998.37 9.92893E-07 0.0605 \nRubberband-small Plastic 0.38 0.27 0.8 1.34 2.0 0.09510 S11 998.37 9.92893E-07 0.0769 \nRubberband-medium Plastic 0.4 0.31 0.84 1.22 2.5 0.07627 S11 998.37 9.92893E-07 0.0778 \nRubberband-large Plastic 0.69 0.53 1.0 1.38 3.8 0.07045 S11 998.37 9.92893E-07 0.0819 \n 11 \n 12 \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint \n\n19 \n \nSedimentation velocities \nAlltogether 49 specimens of macrophytes were negatively buoyant and  could be used to \ndetermine sedimentation velocities. This group only included single leafs and no whole plants \nof Z. marina. The sedimentation speed of the 49 specimens varied over a relatively wide range \n(Fig. 2). The S. latissima phylloid sank considerably slower than the S. latissima rhizoid and \none of the two specimens of U. linza – containing some air entrapped in its tubular thallus – \nsank less than half as fast as the second, which contained no air. In most other cases specimens \nbelonging to the same species sank with more similar velocities. Particularly fast velocities \nwere recorded for the rhizoid of S. latissima, as well as for the specimens of F. lumbricalis and \none of the specimens of  A. plicata. Particularly low velocities were observed with specimens \nof K. leptoderma, C. flexuosa and U. clathrata, which are all members of the Ulvophyceae . \nIndeed, green algal specimens generally exhibited si gnificantly lower mean sinking velocities \n(Kruskal-Wallis-ANOVA; ² = 13.91; df = 3; p = 0.003) than brown algal specimens (Dunn -\ntest; p = 0.0069) or red algal specimens (p  = 0.0441), while other differences among major \ntaxonomic groups were insignificant (p > 0.05). Further, specimens exhibiting flattened \nbranched morphologies (i.e., fucoids, C. truncatus , D. sanguinea ) sank significantly faster \n(Kruskal-Wallis-ANOVA; ² = 8.476; df = 2; p = 0.014) than specimens exhibiting flattened \nunbranched morphologies (i.e., P. leucosticta, U. gigantea, U. linza, K. leptoderma, S. latissima \nphylloid, Zostera leaves; Dunn -test, p  = 0.0112). No significant difference was detected \nbetween sinking velocities of non-flattened and either flattened unbranched or flattened \nbranched morphologies (p > 0.05). \nThe sedimentation velocities were found to correlate significantly and non -linearly with both \nthe nominal particle diameter of the macrophytes and their mass density relative to the density \nof the water at the time of measur ement (Fig. 3). However, the strongest correlation was \nobserved between the velocity and the shape factor of the particles. \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint \n\n20 \n \n \nFig. 2: Sedimentation velocity  of 49 specimens of macroalgae. Brown bars: Phaeophyceae, \nred bars: Rhodophyceae, green bars: Ulvophyceae and black bars: eelgrass. Median ± quartiles \n(n = 5; n = 7 for specimens with numbers beginning with „K“). \n \n \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint \n\n21 \n \n \n \nFigure 3: Correlations between sedimentation and morphological traits of macrophytes. \nSedimentation velocity  of 49 macrophyte specimens was correlated with (A) their nominal \ndiameter, (B) their relative density and (C) their shape factor. Best fitting semilogarithmic \nfunctions and their 95 % confidence intervals are shown (in all three cases p < 0.0001). \n \nModeling sinking velocity \nAlltogether 20 macrophyte specimens (Tab. 1, “modeling“ group) were used for the \ncomputation of models predicting sedimentation velocity. Resulting models were then tested \nfor accuracy with the remaining 29 specimens (Tab. 1, “testing“ group). The best -fitting \nsedimentation model that could be obtained without consideration of particle shape (Sf) was \nω = √\n4\n3\n( 𝜌\n𝜌𝑠𝑤\n−1) 𝑔 𝑑𝑛\n(4567661 ∗  𝜈\n𝑑𝑛  𝑔 )\n          (Model A) \nThe sedimentation velocities predicted by this model correlated positively with the velocities \nobserved, but the divergence between observed and predicted data was in many cases relatively \nlarge (Fig. 4A, r² = 0.3576, p < 0.0001). In particular, the mean sedimentation rate of the S. \nlatissima rhizoid was significantly underestimated in the modeling dataset, placing it well \noutside the 95 % prediction interval. On the other hand, the velocity of specimen D. sanguinea \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint \n\n22 \n \n27 from the test sample set was overestimated. Alltogether, t his model predicted the sinking \nvelocities of the modeling sample set with a median squared deviation (MSD) of 6.84*10-5 and \nthose of the test sample set with MSD = 4.28*10-5. Velocities of plastic disks were relatively \naccurately predicted, but velocities of nets underestimated and those of balls and rubber bands \nextremely underestimated (Fig. S2). As a consequence, the MSD of observed and predicted \nvelocities of plastic items was relatively high (7.07*10-4). \nMore prediction accuracy was possible when particle shape was considered in the model by \ninclusion of S f into the numerator of the function and by taking into account the general \nellipsoidal character of macrophytes. Under this condition the best fitting model that could be \nobtained was \nω = √4\n3\n( 𝜌\n𝜌𝑠𝑤\n−1) 𝑔 𝑑𝑛 𝑆𝑓\n2\n3\n(4146.337∗ 𝜈\n𝑑𝑛1.5𝑔0.5 )\n        (Model B) \nModel B (Fig. 4B , r² = 0.7210, p < 0.0001) visibly predicted the sedimentation velocities of \nmacrophytes with more accuracy than model A (Fig. 4A). Correspondingly, MSDs obtained \nwith model B ( 2.45*10-5 and 5.87*10-5 for the model sample set and the test sample set, \nrespectively) were 29 % smaller than those obtained with model A.  Model B also provided \nsignificantly better predictions of the sinking velocities of plastic items (Fig. S2B ; MSD = \n8.12*10-5).  \nThe best prediction accuracy of the sinking velocity of macrophytes was achieved when Sf was \nnot only included in the numerator, but also in the denominator of Eq. 4 , considering that \nspecific particle shape may also affect the drag coefficient CD. The best fitting model obtained \nunder this condition was \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint \n\n23 \n \nω = √\n4\n3\n( 𝜌\n𝜌𝑠𝑤\n−1) 𝑔 𝑑𝑛 𝑆𝑓\n2\n3\n(\n(198.3826+34121.98𝑆𝑓) 𝜈\n𝑑𝑛1.5𝑔0.5 +0.8906959−9939.812 𝑆𝑓\n2.972455−87764.06𝑆𝑓\n52.04557)\n5.566767   (Model C) \nIn particular the sedimentation velocities of faster sinking specimens were predicted with even \nmore accu racy by model C (Fig. 4C, 0.7926, p  < 0.0001) than by model B (Fig. 4B). \nCorrespondingly, MSD’s obtained with model C (2.12*10-5 and 2.08*10-5 for modeling sample \nset and test sample set , respectively) were 40 % smaller than those obtained with model B.  \nHowever, while model C predicted the sedimentation velocities of plastic discs approximately \ncorrectly it underestimated the velocities of nets (Fig. S2C). Moreover, model C extremely \noverestimated the sedimentation velocities of balls and rubber bands . As a  consequence, the \nMSD of observed and predicted velocities of plastic items was only 8.00*10 -4 and thus in the \nsame order of magnitude as with model A, but 10 times larger than with model B. \n \nFig. 4: Correlations between observed and predicted sedimentati on velocities.  For the \nmodeling sample set (blue, means ± ranges) and the test sample set  (red, means only) with \nsedimentation velocities predicted for the same sample sets by (A) model A, (B) model B and \n(C) model C. Lines represent linear functions fitti ng best to data of the modeling sample set  \n(model A: r² = 0.3576, p < 0.0001; model B: r² = 0.7210, p < 0.0001; model C: r² = 0.7926, p < \n0.0001), dotted lines represent 95 % prediction intervals.  \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint \n\n24 \n \n \nGiven that low S f values characterised not only thin, lea f-shaped, but also filamentous, tufted \nalgae (see Fig. 1), and since similar surface interactions with water are not a priori  to be \nexpected for such different morphologies, one might possibly expect less accurate predictions \nof  by model C at low S f. However, macrophytes with lower S f were not those with lower \npredicted sinking velocities  and there was no significant correlation between S f and and the \nMSD between predicted and observed velocities (Fig. S2A). Likewise, correlations between the \nrelative algal density or the nominal diameter d n and MSD were not observed (Figs. S2B and \nC). \n \nFig. 5: Predicted sinking velocity  from model C.  For macrophytes exhibiting different \ncombinations of shape factor Sf and nominal diameter d n. Kinetic viscosity of sea w ater, \nmacrophyte density and seawater density were considered to be the median conditions observed \nduring our experimental setup, i.e. 𝜈 = 1.0915*10-6 m2 s-1, 𝜌 = 1104.44 kg m -3 and 𝜌𝐻2𝑂 = \n1009.45 kg m-3. \n \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint \n\n25 \n \nIn order to examine the interactive impact of the size and the specific shape of macrophytes \non their sedimentation velocity more closely, fictitious values were entered for dn and Sf in \nmodel C, resulting in the dependencies shown in Figure 5. Obviously, the influence of the \nshape factor increases with particle size. Large macrophytes with a small shape factor sink \nsignificantly more slowly than those with a large shape factor, while smaller macrophytes can \ngenerally be expected to have lower sinking velocities. \n \nDiscussion \nMorphological differences in sedimentation behavior \nThis comparative study of morphologically very diverse marine macrophytes ma de it possible \nto identify both differences and similarities in their sedimentation behavior. With few \nexceptions (namely, U. linza and different thallus parts of S. latissima), specimens of the same \nspecies behaved similarly and we observed some tendencies toward different behaviour across \nmajor taxonomic groups . That is, b rown and red seaweeds tended to sink fast er than green \nseaweeds and flattened branched specimens faster than flattened unbranched ones.  \nPredicting seaweed sinking velocity based on thallus volume, weight and shape \nWe identified the most relevant traits for the prediction of sinking velocity and drag impact on \nmarine macrophytes and established protocols for their determination. The relevant parameters \nare (1) thallus volume, (2) thallus wet weight and (3) thallus shape. Thallus volume allows for \nthe determination of the nominal diameter dn as described in Eq. 5. Thallus volume and thallus \nwet weight together are required for the determination of thallus mass density ρ. Use of the \nCorey shape factor Sf proved to be an applicable solution to characterize thallus shape even in \nvery irregularly shaped macrophytes. The assumption of an ellipsoidal particle shape is inherent \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint \n\n26 \n \nto use of Sf, given that Sf expresses the ratio of the longest, shortest and intermediate mutually \nperpendicular particle diameters. Leaving aside the more or less pronounced thallus flexibility, \nwhich can lead to consider able deviations, unbranched morphologies of macrophytes appear \nrelatively obviously as ellipsoidal. A longest diameter is usually easy to identify in these cases. \nIn the case of leaf -shaped morphologies the shortest diameter is the thallus thickness, in th e \ncase of cylindrical unbranched morphologies it is any mean diameter perpendicular to the \nlongest axis. The ellipsoidal character of branched thallus morphologies, on the other hand, is \nless obvious. A longest diameter is often not clearly discernible and - where it becomes visible \n- in many cases still not easy to measure. In the case of side branches of varying length and \nthickness, there is also the question of how to determine a representative shortest diameter, not \nto mention a representative intermediate diameter. The method used in the present work, based \non a direct measurement of the more obvious axis lengths (Table 1; a * b in the case of flattened \nmorphologies, c in the case of cylindrical morphologies) and subsequent derivation of less \nobvious axis lengths (c in the case of flattened morphologies, a*b in the case of cylindrical \nmorphologies) from the volume, proved to be practicable and led to convincing results.  \nThe shape factors we found for macrophytes are in the range between 0.00029 and 0.0 69. A \nvalue of only 0.0003 was found with Ulva gigantea, which is characterised by particularly large, \nflat and very thin thalli. The individual we examined had a maximum length of 35 cm and a \nwidth of 29 cm with an average thallus thickness of only 79 µm.  Individuals about twice or \nthrice this size exist (own observations) and a minimum value of S f around 0.0001 could \ntherefore be possible. Therefore, the minimum values observed in our study could be close to \nthe actually existing minimum values of Sf in macrophytes. However, the maximum value of \n0.069 is still well below the theoretically possible maximum value of 1, which would result for \nperfect spheres. It is to be expected that species such as Codium bursa  or Colpomenia \nperegrina, which approximately have a spherical morphology but were not available for our \nstudy, will exceed the maximum value of Sf that we found.  \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint \n\n27 \n \nEnhancing accuracy by incorporating Sf as a component of CD \nThe inclusion of S f values determined in this way into the drag equation enable d relatively \naccurate predictions of the sedimentation rate of macrophytes. Notably, the prediction accuracy \nincreased when Sf was not only considered in the numerator, but also as a component of CD in \nthe denominator, as previously suggested by Riazi and Türker (2019) (Riazi and Türker 2019) \nfor sediment particles. Remarkably, the best model C empirically determined on this premise \nand on the basis of our modeling data set predicted  with slightly better accuracy for the test \nsample set than for the modeling data set.  \nDifferences in predicting the sedimentation velocity of plastic objects vs. seaweeds \nIn contrast, this model did not have good prediction accuracy for most plastic particles. Instead, \nit resulted in a significant overestimation of the sedimentation velocity for both balls and rubber \nbands. Only the velocities of the plastic disks were predicted relatively accurately, pr obably \ndue to the fact that their shape factor is similar to that of macrophytes. Balls and rubber bands \nhad shape factors that were significantly higher than those of all macrophytes. When balls and \nrubber bands were experimentally integrated into the modeling dataset, no alternative model \nbased on the formula structure of model C could converge  (not shown). Models based on this \nformula structure could therefore be  fundamentally unsuitable for accurate predicti ons of the \nsedimentation velocity of particles with high shape factors. Alternatively, the very poor \nprediction accuracy of model C for balls and rubber b ands could also result from the fact that \nthe transition between laminar and turbulent conditions at the particle surface is influenced by \nthe material properties (e.g., elasticity or compressibility) at the particle surface. These \nproperties could differ between various plastic particles and macrophyte particles and were not \nconsidered further in our study. The observation that model C predict ed the sinking speed of \nplastic nets with only moderate accuracy, although their form factors were in the same order of \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint \n\n28 \n \nmagnitude as those of macrophytes, also suggests an influence of surface material properties \non CD. \nModel Performance divergence: C for seaweeds, B for plastic objects \n On the other hand, the fact that model C worked with better accuracy than the simpler models \nA and B for all macrophytes tested indicates that the surface material properties of different \nmacrophytes differ significantly less than their form factors in terms of influence on CD. \nInterestingly, when the shape factor was only included in the numerator and not used to predict \nCD (Model B), the sedimentation velocity of all plastic and macrophyte particles was predicted \nwith reasonable accuracy and better accuracy than when shape was completely ignored (Model \nA). This demonstrates the general usefulness of considering Sf. \n \nConclusions \nOur study highlights that the sedimentation behaviour and the sensitivity to drag of marine \nmacrophytes and also of plastic particles can be predicted with significantly increased accuracy \nif they are regarded as ellipsoids and their specific shape is also considered. Model C performed \nwell for a wide range of macrophyte species, which were characterised by very different \nmorphologies. It can be assumed that the behaviour of macrophytes from other habitats - marine \nas well as limnic - would also be predicted with similar accuracy. With Model B, we were able \nto increase the predictive capacity for plastic particle shapes and sizes, although the model was \nless accurate than model C for macrophytes. Model C therefore appears as better suited for \naccurate predictions of the velocities of macrophytes, while Model B appears more robust for \ngeneralistic predictions, especially for particles with high shape factors.  Potentially, our models \ncould even provide sufficiently a ccurate estimates for other particles with sizes and specific \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint \n\n29 \n \ndensities similar to those of marine macrophytes, such as leaves shed by terrestrial plants . To \naccurately predict a higher variability of particles with higher shape factors than macrophytes, \nmore diverse particles should be measured. 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It is \nThe copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint \n\n32 \n \nZhou, F., Ge, J., Liu, D., Ding, P., Chen, C. and Wei, X. 2021. The Lagrangian-based Floating \nMacroalgal Growth and Drift Model (FMGDM v1.0): application to the Yellow Sea \ngreen tide. - Geoscientific Model Development 14: 6049–6070. \n \nAcknowledgments \nFunding: FG and FW received funding from the State Agency for the Environment Schleswig-\nHolstein.  \nAuthor contributions: FW, FG and TB initiated and designed this study. FG, FW and TB  \ncollected the data. FG and FW analysed the data. FW and FG generated the models. FW wrote \nthe manuscript. All authors contributed to the final version of the manuscript. \nCompeting interests: The authors declare that they have no competing interests.  \nData availability: Data available via the Pangaea Digital Repository (doi will be provided once \npaper is accepted). \n  \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint","source_license":"CC-BY-4.0","license_restricted":false}