Sedimentation and drag in drifting macrophytes and plastic objects: A model

Predicting macroalgal sedimentation and drag sensitivity is essential for ecological and geochemical modeling, and for optimizing seaweed cultivation. However, despite the diversity of macrophyte forms, models incorporating their specific morphology and hyd rodynamic effects are largely lacking. To develop a broadly applicable model, we tested whether the drag response of diverse macrophyte morphologies and plastic objects can be accurately predicted by approximating them as ellipsoids and accounting for the ir specific shapes. A set of simple shape descriptors (wet weight, volume, thallus thickness, thallus projection area) and an empirical solution for the drag equation , enabled relative accurate prediction s of the sinking velocity for 26 morphologically div erse macroalgae species, as well as the eelgrass Zostera marina, another major source of drifting biomass in many shallow seas . Additionally, we identified a second simpler empirical solution that incorporates shape and, while slightly less accurate, can be applied to a broader range of particles, including plastics. .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity.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 The copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint 4

Drifting macroalgal blooms are a global problem, with some of the largest blooms being caused by floating species such as Sargassum natans and S. fluitans in the Great Atlantic Sargassum Belt or Ulva prolifera in the Yellow Sea (Smetacek and Zingone 2013). When blooms of that magnitude beach, they often cause severe problems for the coastal communities and environment (Zhang 2019, Bartlett and Elmer 2021) . In the SW Baltic Sea the macroalgae blooms are of a smaller scale, but more diverse than in many other environments (Weinberger et al. 2021). These blooms can be dominated by a single species, but more often several species are found blooming together, and in most blooms in the SW Baltic, the eelgrass Zostera marina (littered leaves, fragments and whole specimens) also constitutes a significant part of the biomass (Weinberger et al. 2020). The ways in which hydrodynamic factors affect the sp ecies composition of macroalgal blooms are still poorly known. Unattached macrophytic biomass in the Baltic can be floating (Rothäusler et al. 2015), or negatively buoyant, but drifting (Bonsdorff 1992, Weinberger et al. 2008) . Problematic blooms are often found in sheltered, relatively shallow waters, where they may degrade and cause nuisance and envir onmental problems locally (Mossbauer et al. 2012, Weinberger et al. 2020, 2021). Accumulations of algal biomass can have great impact on the environment in deeper waters as well (Vahteri et al. 2000) . It has been proposed that significant portions of biomass produced in photic coastal waters may even reach deep anoxic zones of the ocean through drift and sedimentation, where they could then provide an important component of global carbon sequestration (Krause-Jensen and Duarte 2016, Ortega et al. 2019, Kokubu et al. 2019) . Such transport of particulate biomass over long distances obviously requires drifting velocities that exceed the speed of biomass degradation during the transport process. Possible maximum drift velocities of seaweeds are typically predicted using Lagrangian particle transport models .CC-BY 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint 5 (Rothäusler et al. 2015, Kwon et al. 2019, Garbossa et al. 2021, Zhou et al. 2021). These models do usually no t consider the specific resistance of seaweeds to drag, as suitable generalized descriptors for predicting the hydrodynamic drifting behavior of seaweeds are so far largely missing. The lack of models that can accurately describe the drifting and sinking b ehavior of seaweeds also affects the development and design of land -based seaweed aquaculture systems, which target the cultivation of unattached macroalgae. One important goal of such systems is to achieve maximally homogenous exposure of the cultivated organisms to sun light and nutrients with a minimum of energy investment (Sahoo and Yarish 2005). Typical solutions are raceways (Mata et al. 2003), aerated tank (Israel et al. 2005) or pond systems (Msuya and Neori 2008) or bioreactors (Savvashe et al. 2021) that are usually developed based on trial and error, as the drifting and sedimentation behavior of different seaweed species is difficult to predict. In addtion to macroalgae and eelgrass, plastic particles represent another large group of drifting particles in the ocean (Eriksen et al. 2014). These particles can become problematic for example by remaining within the ecosystem and slowly degrading (Gewert et al. 2015), being ingested by marine organisms as microplastic (Galloway et al. 2017) , or accumulating on beaches (Barnes et al. 2009). Plastic litter, to some degree, resembles seaweeds as it exhibits a similar diversity of shapes and sizes. These similarities suggest that a model developed to predict sedimentation velocities of seaweeds may also be applicable for plastic particles of similar size. Established approaches for predicting sedimentation velocity As predicted by Stokes (1851) , the sedimentation of particl es in water is driven by the gravitational acceleration g. It also depends on the particle buoyancy, i.e. the particle mass density ρ relative to the mass density of the seawater ρsw. Other factors that determine the sedimentation velocity ω are the diameter d of the particle and the drag coefficient C D. CD is a .CC-BY 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint 6 dimensionless indicator of the resistance of a particle to current. CD is not a constant, but varies as a function of flow speed, flow direction, object position, object size, fluid density and the kinematic viscosity of the medium. ω may be calculated for spherical particles as ω = √4 3 ( 𝜌 𝜌𝑠𝑤 −1) 𝑔 𝑑 𝐶𝐷 (Eq. 1) Equation 1 is based o n the assumption that the sedimentation velocity can be calculated by equating the effective weight force with the drag force (Riazi and T ürker 2019) . For non - spherical particles, the nominal diameter dn - describing the diameter of a sphere with the same volume as the particle - can be used instead of the diameter d. However, ex act analytical solutions of Eq. 1 only exist for spheres (Stokes 1851) and spheroids (Oseen 1927) in laminar flows, because turbulence on the particle surface strongly influences CD and irregularly shaped particles must be expected to generate turbulences that are virtually impossible to predict. To resolve this problem, different empirical solutions of Eq. 1 that used shape factors to correct CD for non-sphericity have been proposed for sediment grains (e.g., Swamee and Ojha 1991, Cheng 1997, She et al. 2005, Camenen 2007) . Particle shape could be expressed in various ways, for example by use of sphericity factors that put the volume of a particle in relation with its surface area (Wadell 1935). Yet, exact measurements of the surface area of irregularly shaped particles are often hardly possible, which makes the application of sphericity factors to them difficult. The shape factor most commonly used instead is the Corey factor S f (Komar and Reimers 1978), which expresses the deviation of particle shape from sphericity independent of its size as 𝑆𝑓 = 𝑐 √𝑎𝑏 (Eq. 2) .CC-BY 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint 7 where a, b, and c are the diameters in the longest, the intermediate and the shortest mutually perpendicular axes of the particle, respectively. An improved empirical solution of Eq. 1 was recently proposed by Riazi and Türker (2019), who investigated the sedimentation behavior of sediment particles with diameters in the approximate range between 0.5 and 7 mm. The authors proposed to treat such particles as ellipsoids and introduced S f raised to the power of 2/3 into Eq. 1 to account for their non-spherical shapes: ω = √4 3 ( 𝜌 𝜌𝑠𝑤 −1) 𝑔 𝑑𝑛 𝑆𝑓 2 3 𝐶𝐷 (Eq. 3) Riazi and Türker (2019) (Riazi and Türker 2019) further proposed to calculate the drag factor in Eq. 3 as 𝐶𝐷 = ( 𝑋2 𝜈 𝑑𝑛1.5𝑔0.5 +𝑋3) 𝑋1 (Eq. 4) where ν is the kinematic viscosity of the medium, X 1 is a dimensionless constant and X 2 and X3 are also dimensionless constants that both depend on S f and describe the behavior of the drag coefficient with respect to particle shape in laminar and turbulent flow conditions, respectively. The need to transfer these equations towards seaweed-like particles Drifting macrophytes exhibit highly variable morphologies that range from unbranched filamentous forms over branched or unbranched leaf shapes to three-dimensionally branched or unbranched irregularly tangled forms (Fig. S 4 to S10). Macrophytes are usually much larger and mechanically more flexible than sediment grains, which may also be expected to affect their response to drag. The question th erefore arises whether generalized approaches to the determination of CD and ω are possible that allow for the prediction of sedimentation velocities .CC-BY 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint 8 and drag across species without tedious experimental setups. We hypothesized that approximate predictions may be possible if drifting macroalgae and eelgrass litter are treated as ellipsoids, similar as proposed by Riazi and Türker (2019) for sediment particles. The approximately ellipsoidal character of unbranched mac rophytes is fairly obvious. However, in macrophytes exhibiting branching of several orders typically the longest, shortest, and middle perpendicular thallus axes cannot be readily identified and measured . It was therefore necessary to develop a suitable method for the determination of these axes and Sf in macrophytes. Sedimentation velocities of two different sample sets of seaweeds and eelgrass and a set of plastic objects, with variable particle properties were then measured. Measures obtained with seaweed sample set 1 allowed for the identification of an empirical solution for Eq. 4 and the resulting model was successfully tested with seaweed sample set 2. Subsequently, it was tested whether the optimal solution for seaweeds would be applicable to plastic particles.

Collection and maintenance of algae This study includes 73 specimens of drifting marine macrophytes belonging to 26 different species (Fucus vesiculosus, Fucus serratus, Chorda filum, Saccharina latissima, Gracilaria vermiculophylla, Ceramium virgatum, Vertebrata fucoides, Polysiphonia stricta, Spermothamnion repens, Ahnfeltia plicata, Furcellaria lumbricalis, Coccotylus truncatus, Delesseria sanguinea, Cladophora flexuosa, Cladophora sp., Rhodomela confervoides, Pyropia leu costicta, Ulva clathrata, Ulva linza, Ulva compressa , Kornmannia leptoderma, Bryopsis hypnoides, Acrosiphonia centralis, Zostera marina, Ascophyllum nodosum and Ulva gigantea). The specimens were selected to represent a wide range of morphologies (Fig. S4 to S10) and were taxonomically identified based on these traits , following Nielsen et al. (2023) . .CC-BY 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint 9 Ten of the specimens were collected from drift material in January 2023 at a location between Strande and Bülk light house (Kiel Fjord/Germany ; 54°26'57.4"N 10°11'37.6"E). On the 26th of June 2024, 56 more specimens were collected a t the same site and at two other locations in the Kiel Fjord area ( Schilksee, 54°25'16.3"N 10°10'43.1"E and Mönkeberg, 54°21'20.92"N 10°10'41.97"E). Six specimens of A. nodosum and one of U. gigantea were collected in July 2024 from a beach at Yerseke/Netherlands (51°30'09.0"N, 4°02'39.7"E). Salinities and water temperatures at the collection sites and during subsequent maintenance and experiments were measured using a WTW Multi3630IDS conductometer. Prior to use, material collected in 2023 was maintained for 3 d at 13.6 °C in Baltic Sea seawater with a salinity of 18.8 psu, which was the salinity at the collection site. All subsequent measurements were conducted in sea water of the same salinity and temperature at the GEOMAR laboratories in Kiel. Material collected from the Kiel Fjord in 2024 was kept for 4 days in seawater with salinity 15.0 psu (mean salinity at the collection sites: 14.0 psu) and 16 °C (mean temperature at collection sites: 20 °C) and then packed in cooler boxes and transported within 7 h to the NIOZ laboratories at Yerseke in the Netherlands. There the material was maintained for 1 to 3 weeks at 18 °C in Oosterschelde water (salinity: 33 psu) diluted with tap water to a salinity of 14.4 psu. Material collected from the Oosterschelde was acclimatized at the NIOZ laboratories to a salinity of 15 psu by stepwise decrease of salinity by 4-5 psu every two to three days. Aeration was provided to all specimens during the maintenance and they were kept in artificial light (80 µmol photons m-2 s-1 for 12 h d-1). Water was exchanged every other day. In addition to the seaweeds, 16 negatively buoyant plastic objects were tested, including eight circular foil cutouts (disks), three table tennis balls, two plastic nets and three rubber bands (Fig. S11). The foil disks were cut to different diameters and some were punched with different numbers of small holes. The nam e of the foil circles indicates both their diameter and perforation level. For example , “Disk 40-1” had a diameter of 40 mm and was unpunched, .CC-BY 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint 10 where “1” denotes unpunched, “2” partially punched, and “3” heavily punched, “4” extremely heavily punched. The three table tennis balls shared identical dimension and therefore had the same shape parameters. To increase their mass density air inside the balls was replaced with sea water, using an injection syringe. To increase the mass density further different nubers of glass beads (2 mm diameter) were pressed into the balls through small holes, which were then sealed with Scotch tape. Descriptors of thallus shape and density Particle traits were determined for all specimens. To determine volume V a graduated cylinder measure of suitable size was filled with a defined volume of sea water and the specimen was completely immersed in this volume. Any air bubbles were carefully removed and the increase of volume was recorded as particle volume. Wet weights were measured after the macrophytes had been carefully blotted with paper. All measurements of volume and weight were repeated two times and in case of data divergency by more than 5 % three t imes. The particle mass density ρ could then be calculated as the ratio of mean blotting weight and mean volume. The nominal particle diameter dn was also derived from the mean volume and determined as twice the radius of a sphere with the volume of the measured macrophyte: 𝑑𝑛 = 2 √ 3 𝑉 4 𝜋 3 (Eq. 5) Projection images of all specimens were used to determine measures for the calculation of Corey shape factors. To generate such images the specimens were scanned on a flatbed scanner together with a size standard . The resulting images were analyzed using the Fiji software package (Schindelin 2012). In the case of specimens with flattened morphologies (A. nodosum, F. vesiculosus, F. serratus, S. latissima phylloid, P. leucosticta, C. truncatus, U. compressa, U. gigantea, K. leptoderma, Z. marina leaves) and also of the unbranched cylindrical C. filum the determined parameter was the t hallus projection area (using the “adjust color threshold” and .CC-BY 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint 11 “measure particles” procedures implemented in Fiji). This projection area obviously represents the product of the longest and the intermediate perpendicular thallus axes a * b of flattened thalli (see Eq. 2). The shortest intermediate perpendicular axis c is in these cases equal to the thallus thickness. It could be subsequently calculated by division of the thallus volume V by the projection area a*b, because V = a*b*c. All remaining specimens exhibited three - dimensional morphologies, often with branches that partly overlapped and masked each other in projection images. In these cases, ten independent measurements of the width of youngest thallus branches were conducted and the mean was consider ed as a representative measure of c. Division of volume V by c allowed then to calculate corresponding values for a*b. Measurements of sinking velocity Maximum sinking velocities in sea water were determined for all non -buoyant specimens directly before or after the determination of particle traits . After their release at the water surface, sinking particles initially accelerate until they reach their maximum sinking speed. It was therefore necessary to first determine a water depth below which a maximum sinking speed of the macrophytes could be assumed. It was found that a water depth of 15 cm is required for the acceleration phase. To verify this, the sinking speeds of 22 samples were measured in two different ways (Fig. S1). In both cases, the samples were released at the water surface and only after they had sunk to a depth of 15 cm was their speed measured during the further descent. In the first case, however, the sinking speed was only measured over the depth segment from 15 cm to 41 cm and in the seco nd case over the depth segment from 15 cm to 76 cm. If the maximum speed is not reached at a depth of 15 cm and thus a further acceleration takes place below 15 cm, this should lead to higher mean sinking speeds for measurements at a greater depth (i.e. over a distance of 61 cm) than for measurements at a lesser depth (i.e. over a distance of 26 cm). However, a significant difference between the two measurements was only observed for two specimens (Welch corrected t -tests, p = 0.05), and in only one of thes e cases was the .CC-BY 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint 12 measured velocity higher when the measuring distance was longer. Moreover, a non- significantly higher mean sinking velocity was found for 1 3 specimens when measured over the shorter depth distance, and only for 7 specimens over the longer distance. Therefore, sedimentation velocities were measured in such a way that the specimens were submerged just below the water surface and released, so that they could accelerate from the water surface to a depth of 15 cm before the velocity was measured with a stop-watch until the specimens made first contact with the bottom. In 2024 the measurements with small algae were carried out in a glass cylinder (diameter 40 cm), which allowed for lateral observation. In this case, the length of the fall distance was 87 cm and the monitoring distance was 72 cm. For larger algae, a plastic barrel was used, in which an underwater video camera and corresponding depth marks allowed for observation of the algae reaching the water depth of 15 cm. In these cases, the monitoring distance was 61 cm. All measurements were repeated five times. In 2023 sedimentation velocities were measured in an aquarium that was filled to a height of 26 cm with sea water and the monitoring distance was 11 cm . The macrophytes were filmed outsi de the aquarium, with a ruler attached to the window pane, and sedimentation times were determined by single frame analysis. These measurements were repeated 7 times. The plastic particles were measured in a plastic cylinder (diameter: 19 cm) with a fall distance of 48 cm and a monitoring distance of 33 cm. Water temperature and salinity in the measuring vessels changed slightly from day to day. Both parameters were therefore determined repeatedly between the speed measurements, in order to derive mass density ρH2O and kinematic viscosity ν (Sharqawy et al. 2012) . These parameters are listed in Tab. 1 .CC-BY 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint 13 Statistics and model development Data were visualized and correlations were analyzed using the Prism9 software package (GraphPad, Boston, USA). Differences in sedimentation velocities among specimens or groups of specimens were detected by Kruskal -Wallis-ANOVA and Sidak-corrected pairwise Dunn- tests using the same software. All other statistical treatment was conducted in R version 4.2.2. The sedimentation velocity equation (see Eq. 3 and 4) was optimized for the particles using genetic algorithm as implemented in R library GA (Scrucca 2013). For this purpose, the data sets of sedimenting macrophytes were divided into two groups. The first group was selected to include a wide range of different morphologies and particle properties, and this group was used for the actual modeling. The employed genetic algorithm started with an initial population of 5000 randomly generated individuals, with a crossover probability of 0. 8, a mutation probability of 0.1 and an elitism of 250. The optimization process continued for maximally 500 000 generations and ended when no convergence toward a lower mean square error was obtained over 5000 generations. The accuracy of the resulting equations was then verified , using the second group of seaweed data sets as well as the plastic particle data set.

Particle traits Particle traits of all investigated specimens are summarized in Tab.1, for images of all specimens see Figs. S4 to S11. Nominal diameters of these specimens ranged from 0.5 76 cm to 4.844 cm, volumes from 0.1 cm³ to 59.5 cm³ and blotting weights from 0.1 1 g to 46.10 g. The shape factor Sf varied beween 0.00029 and 0.0689 (Fig. 1), with the exception of some of the plastic particles with higher shape factors, especially the table tennis balls, which had an Sf of 1 due to their perfectly round shape. As to be expected, Sf was particularly low in specimens .CC-BY 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint 14 with pronounced thin and flattened morphologies, such as U. gigantea, K. leptoderma, or P. leucosticta, but also in specimens characterized by very thin and dense lateral branches, such as A. centralis, C. flexuosa or S. repens. Sf was the highest in macrophyte specimens exhibiting relatively thick branched or unbranched morp hologies, such as C. filum, A. nodosum or S. latissima rhizoid. A particularly large variability of S f was detected for Z. marina, corresponding with the circumstance that the investigated specimens were morphologically variable and included littered leafs , as well as whole plants bearing or not bearing rhizoid or inflorescence. In F. vesiculosus floating specimens - characterized by presence of gas -filled vesicles - exhibited a larger Sf than non-floating specimens. A trend towards larger Sf in floating specimens gets also apparent if different species are compared: in none of the negatively buoyant seaweed specimens was Sf larger than 0.0278 and in none of the buoyant specimens smaller than 0.00116 (Fig.1). Fig. 1: Shape factors of 73 specimens of driftin g marine macrophytes. Red dots indicate positively buoyant (floating) specimens, blue dots negatively buoyant (sinking) specimens. .CC-BY 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint 15 Table 1: Shape descriptors of the investigated specimens. Non-buoyant specimens were grouped and used either for development or for testing of 1 the sedimentation models, while buoyant specimens could obviously not be used for this purpose. Weight is the blotting weight [g], V is the volume 2 [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 axes, 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 values 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 and kinematic viscosity during measurements of the mean sedimentation velocity . 6 Specimen Group Weight [g] V [cm³] dn [cm] c [mm] a b [cm²] Sf Figure ρsw [kg/m³] v [m2 s-1]  [m s-1] Acrosiphonia centralis 36 Modeling 12.98 12.25 2.86 0.102 1205.7 0.00029 S4 1009.446 1.0494E-06 0.0208 Ahnfeltia plicata 47-1 Modeling 0.66 0.50 0.98 0.455 11.0 0.01371 S5 1009.862 1.0917E-06 0.0347 Ahnfeltia plicata 47-2 Modeling 7.07 5.63 2.21 0.492 114.4 0.00460 S5 1009.862 1.0917E-06 0.0466 Bryopsis hypnoides 1-2 Modeling 0.95 0.88 1.19 0.104 84.5 0.00113 S4 1009.862 1.0917E-06 0.0144 Coccotylus 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 Delesseria sanguinea 26-2 Modeling 1.62 1.25 1.34 0.144 86.6 0.00155 S5 1009.446 1.0494E-06 0.0181 Fucus serratus 9 Modeling 6.15 5.50 2.19 0.492 111.8 0.00465 S4 1009.446 1.0494E-06 0.0290 Fucus vesiculosus 54 Modeling 17.88 17.00 3.19 0.653 260.2 0.00405 S4 1009.446 1.0494E-06 0.0256 Furcellaria lumbricalis 43-1 Modeling 1.31 1.08 1.27 0.606 17.9 0.01433 S5 1009.564 1.0727E-06 0.0450 Furcellaria lumbricalis 44-1 Modeling 2.39 2.00 1.56 0.530 37.8 0.00862 S5 1009.564 1.0727E-06 0.0525 Gracilaria vermiculophylla 16-1 Modeling 0.45 0.42 0.93 0.351 12.1 0.01007 S5 1009.710 1.0915E-06 0.0306 Gracilaria vermiculophylla 49 Modeling 5.23 5.00 2.12 0.279 179.2 0.00208 S5 1009.488 1.0726E-06 0.0237 Kornmannia leptoderma 1-1 Modeling 0.29 0.27 0.81 0.052 52.4 0.00073 S4 1009.724 1.0835E-06 0.0084 Polysiphonia 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 Saccharina latissima rhizoid K9B Modeling 0.98 0.70 1.10 0.815 8.6 0.02779 S4 1013.900 1.1939E-06 0.0492 Spermothamnion repens 14 Modeling 0.47 0.40 0.91 0.078 51.4 0.00109 S5 1009.862 1.0917E-06 0.0169 Ulva clathrata 21-1 Modeling 0.30 0.25 0.78 0.323 7.7 0.01163 S4 1009.710 1.0915E-06 0.0097 .CC-BY 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint 16 Tab. 1, continued. 7 Specimen Group Weight [g] V [cm³] dn [cm] c [mm] a b [cm²] Sf Figure ρsw [kg/m³] v [m2 s-1]  [m s-1] Ulva gigantea 10 Modeling 5.98 5.50 2.19 0.079 698.2 0.00030 S4 1009.446 1.0494E-06 0.0149 Ulva linza 8-1 Modeling 0.23 0.20 0.73 0.151 13.3 0.00413 S4 1009.745 1.0862E-06 0.0119 Zostera 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 Ahnfeltia plicata K1 Testing 1.26 1.00 1.24 0.190 52.8 0.00261 S8 1013.900 1.1939E-06 0.0287 Ceramium virgatum 6-2 Testing 2.41 2.38 1.66 0.079 299.5 0.00046 S7 1009.745 1.0862E-06 0.0119 Ceramium virgatum 7-2 Testing 1.47 1.25 1.34 0.186 67.3 0.00226 S7 1009.710 1.0915E-06 0.0132 Ceramium virgatum 8-2 Testing 0.91 0.88 1.19 0.146 60.6 0.00187 S7 1009.745 1.0862E-06 0.0122 Ceramium virgatum K6 Testing 0.12 0.10 0.58 0.054 18.4 0.00127 S7 1013.900 1.1939E-06 0.0100 Cladophora flexuosa 34 Testing 4.97 4.50 2.05 0.152 296.4 0.00088 S6 1013.900 1.1939E-06 0.0087 Cladophora sp. K3 Testing 0.11 0.10 0.58 0.076 13.1 0.00211 S6 1013.900 1.1939E-06 0.0149 Coccotylus 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 Delesseria sanguinea 27 Testing 18.74 16.50 3.16 0.376 438.3 0.00180 S7 1009.446 1.0494E-06 0.0281 Delesseria 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 Fucus serratus 12 Testing 9.90 8.88 2.57 0.512 173.2 0.00389 S6 1009.446 1.0494E-06 0.0384 Fucus serratus K5 Testing 9.37 8.30 2.51 0.443 187.5 0.00323 S6 1013.900 1.1939E-06 0.0321 Furcellaria lumbricalis 41-1 Testing 2.00 1.58 1.45 0.659 24.0 0.01345 S8 1009.564 1.0727E-06 0.0499 Furcellaria lumbricalis K8 Testing 0.73 0.60 1.05 0.422 14.2 0.01118 S8 1013.900 1.1939E-06 0.0380 Gracilaria vermiculophylla 26-1 Testing 4.64 4.25 2.01 0.253 168.1 0.00195 S8 1009.446 1.0494E-06 0.0226 Gracilaria vermiculophylla 49-2 Testing 2.62 2.50 1.68 0.328 76.4 0.00375 S8 1009.598 1.0967E-06 0.0209 Kornmannia leptoderma 4-2 Testing 0.11 0.10 0.58 0.038 26.2 0.00074 S6 1009.724 1.0835E-06 0.0080 Polysiphonia 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 Polysiphonia stricta 39-2 Testing 1.28 1.25 1.34 0.117 106.5 0.00114 S7 1009.745 1.0862E-06 0.0143 Pyropia leucosticta 32 Testing 0.92 0.88 1.19 0.087 100.7 0.00087 S7 1009.488 1.0726E-06 0.0111 Rhodomela confervoides 4-1 Testing 3.60 3.50 1.88 0.385 90.9 0.00404 S7 1009.724 1.0835E-06 0.0200 Rhodomela 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 Saccharina latissima phylloid K9A Testing 2.01 1.60 1.45 0.263 60.9 0.00337 S6 1013.900 1.1939E-06 0.0167 8 .CC-BY 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint 17 Table 1, continued. 9 Specimen Group Weight [g] V [cm³] dn [cm] c [mm] a b [cm²] Sf Figure ρsw [kg/m³] v [m2 s-1]  [m s-1] Spermothamnion repens 16-2 Testing 0.24 0.20 0.73 0.050 39.7 0.00080 S7 1009.710 1.0915E-06 0.0164 Ulva clathrata 24-1 Testing 0.19 0.18 0.69 0.245 7.1 0.00918 S6 1009.710 1.0915E-06 0.0074 Ulva linza 6-1 Testing 0.52 0.43 0.93 0.156 27.2 0.00300 S6 1009.745 1.0862E-06 0.0330 Vertebrata fucoides K2 Testing 0.29 0.20 0.73 0.077 25.8 0.00152 S6 1013.900 1.1939E-06 0.0139 Zostera 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 Zostera marina leaf K7 Testing 0.23 0.20 0.73 0.156 12.8 0.00435 S6 1013.900 1.1939E-06 0.0168 Ascophyllum nodosum 21 Buoyant 8.39 8.63 2.54 1.756 49.1 0.02505 S10 1009.446 1.0494E-06 0 Ascophyllum nodosum 29 Buoyant 46.10 59.50 4.84 3.384 175.8 0.02552 S10 1009.446 1.0494E-06 0 Ascophyllum nodosum 2 Buoyant 3.38 4.33 2.02 2.138 20.3 0.04751 S10 1009.446 1.0494E-06 0 Ascophyllum nodosum 46 Buoyant 1.85 2.58 1.70 2.307 11.2 0.06893 S10 1009.446 1.0494E-06 0 Ascophyllum nodosum 5 Buoyant 4.81 4.83 2.10 1.747 27.7 0.03323 S10 1009.446 1.0494E-06 0 Ascophyllum nodosum 68 Buoyant 12.17 13.00 2.92 1.820 71.4 0.02153 S10 1009.446 1.0494E-06 0 Chorda filum 41-2 Buoyant 0.61 0.88 1.19 1.230 7.1 0.04614 S9 1009.564 1.0727E-06 0 Chorda filum 42-2 Buoyant 0.98 1.17 1.31 1.086 10.7 0.03313 S9 1009.745 1.0862E-06 0 Chorda filum 43-2 Buoyant 0.42 0.58 1.04 1.025 5.7 0.04296 S9 1009.564 1.0727E-06 0 Chorda filum 44-2 Buoyant 0.77 1.42 1.39 1.633 8.7 0.05544 S9 1009.564 1.0727E-06 0 Fucus vesiculosus 13 Buoyant 6.70 9.50 2.63 1.192 79.7 0.01335 S10 1009.446 1.0494E-06 0 Fucus vesiculosus 15 Buoyant 6.04 6.50 2.32 0.861 75.5 0.00990 S10 1009.446 1.0494E-06 0 Fucus vesiculosus 3 Buoyant 7.80 8.88 2.57 1.185 74.9 0.01370 S10 1009.488 1.0726E-06 0 Fucus vesiculosus 35 Buoyant 6.17 7.38 2.42 1.102 66.9 0.01347 S10 1009.488 1.0726E-06 0 Fucus vesiculosus 38 Buoyant 4.82 5.50 2.19 1.018 54.0 0.01385 S10 1009.446 1.0494E-06 0 Fucus vesiculosus 51 Buoyant 10.33 10.75 2.74 1.237 86.9 0.01327 S10 1009.446 1.0494E-06 0 Fucus vesiculosus 53 Buoyant 14.70 17.50 3.22 0.905 193.3 0.00651 S10 1009.446 1.0494E-06 0 Ulva compressa 48-2 Buoyant 0.89 1.00 1.24 0.142 70.3 0.00170 S10 1009.862 1.0917E-06 0 Zostera marina 25 Buoyant 3.69 3.75 1.93 0.171 219.0 0.00116 S9 1009.446 1.0494E-06 0 Zostera marina 37-1 Buoyant 3.15 3.50 1.88 0.298 117.5 0.00275 S9 1009.745 1.0862E-06 0 Zostera marina 39-1 Buoyant 0.37 0.50 0.98 0.311 16.1 0.00774 S9 1009.745 1.0862E-06 0 .CC-BY 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint 18 Table 1, continued. 10 Specimen Group Weight [g] V [cm³] dn [cm] c [mm] a b [cm²] Sf Figure ρsw [kg/m³] v [m2 s-1]  [m s-1] Zostera marina 45 Buoyant 2.84 3.50 1.88 0.498 70.3 0.00594 S9 0 Zostera marina 48-1 Buoyant 1.69 2.00 1.56 0.300 66.8 0.00367 S9 1009.862 1.0917E-06 0 Zostera marina 69 Buoyant 1.71 1.88 1.53 0.856 21.9 0.01830 S9 0 Disc 40-1 Plastic 0.25 0.18 0.71 0.14 12.7 0.00406 S11 998.15 9.7629E-07 0.0225 Disc 59-1 Plastic 0.55 0.40 0.92 0.15 27.6 0.00279 S11 998.15 9.7629E-07 0.0187 Disc 59-2 Plastic 0.25 0.18 0.71 0.15 12.5 0.00417 S11 998.15 9.7629E-07 0.0260 Disc 70-1 Plastic 0.8 0.59 1.04 0.15 39.9 0.00236 S11 998.15 9.7629E-07 0.0217 Disc 70-2 Plastic 0.56 0.41 0.92 0.15 27.7 0.00280 S11 998.15 9.7629E-07 0.0234 Disc 70-3 Plastic 0.25 0.18 0.71 0.15 12.5 0.00417 S11 998.15 9.7629E-07 0.0507 Disc 84-1 Plastic 1.13 0.83 1.17 0.15 55.4 0.00202 S11 998.15 9.7629E-07 0.0283 Disc 84-4 Plastic 0.26 0.19 0.71 0.15 12.7 0.00413 S11 998.15 9.7629E-07 0.0298 Ball 1 Plastic 33.62 33.51 4 26.67 12.6 1 S11 998.37 9.92893E-07 0.0971 Ball 2 Plastic 33.97 33.51 4 26.67 12.6 1 S11 998.37 9.92893E-07 0.1622 Ball 3 Plastic 35.17 33.51 4 26.67 12.6 1 S11 998.37 9.92893E-07 0.2536 Net-large Plastic 1.13 1 1.24 0.13 80.0 0.00140 S11 998.37 9.92893E-07 0.0493 Net-small Plastic 1.02 0.8 1.15 0.13 64.0 0.00156 S11 998.37 9.92893E-07 0.0605 Rubberband-small Plastic 0.38 0.27 0.8 1.34 2.0 0.09510 S11 998.37 9.92893E-07 0.0769 Rubberband-medium Plastic 0.4 0.31 0.84 1.22 2.5 0.07627 S11 998.37 9.92893E-07 0.0778 Rubberband-large Plastic 0.69 0.53 1.0 1.38 3.8 0.07045 S11 998.37 9.92893E-07 0.0819 11 12 .CC-BY 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint 19 Sedimentation velocities Alltogether 49 specimens of macrophytes were negatively buoyant and could be used to determine sedimentation velocities. This group only included single leafs and no whole plants of Z. marina. The sedimentation speed of the 49 specimens varied over a relatively wide range (Fig. 2). The S. latissima phylloid sank considerably slower than the S. latissima rhizoid and one of the two specimens of U. linza – containing some air entrapped in its tubular thallus – sank less than half as fast as the second, which contained no air. In most other cases specimens belonging to the same species sank with more similar velocities. Particularly fast velocities were recorded for the rhizoid of S. latissima, as well as for the specimens of F. lumbricalis and one of the specimens of A. plicata. Particularly low velocities were observed with specimens of K. leptoderma, C. flexuosa and U. clathrata, which are all members of the Ulvophyceae . Indeed, green algal specimens generally exhibited si gnificantly lower mean sinking velocities (Kruskal-Wallis-ANOVA; ² = 13.91; df = 3; p = 0.003) than brown algal specimens (Dunn - test; p = 0.0069) or red algal specimens (p = 0.0441), while other differences among major taxonomic groups were insignificant (p > 0.05). Further, specimens exhibiting flattened branched morphologies (i.e., fucoids, C. truncatus , D. sanguinea ) sank significantly faster (Kruskal-Wallis-ANOVA; ² = 8.476; df = 2; p = 0.014) than specimens exhibiting flattened unbranched morphologies (i.e., P. leucosticta, U. gigantea, U. linza, K. leptoderma, S. latissima phylloid, Zostera leaves; Dunn -test, p = 0.0112). No significant difference was detected between sinking velocities of non-flattened and either flattened unbranched or flattened branched morphologies (p > 0.05). The sedimentation velocities were found to correlate significantly and non -linearly with both the nominal particle diameter of the macrophytes and their mass density relative to the density of the water at the time of measur ement (Fig. 3). However, the strongest correlation was observed between the velocity and the shape factor of the particles. .CC-BY 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint 20 Fig. 2: Sedimentation velocity  of 49 specimens of macroalgae. Brown bars: Phaeophyceae, red bars: Rhodophyceae, green bars: Ulvophyceae and black bars: eelgrass. Median ± quartiles (n = 5; n = 7 for specimens with numbers beginning with „K“). .CC-BY 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint 21 Figure 3: Correlations between sedimentation and morphological traits of macrophytes. Sedimentation velocity  of 49 macrophyte specimens was correlated with (A) their nominal diameter, (B) their relative density and (C) their shape factor. Best fitting semilogarithmic functions and their 95 % confidence intervals are shown (in all three cases p < 0.0001). Modeling sinking velocity Alltogether 20 macrophyte specimens (Tab. 1, “modeling“ group) were used for the computation of models predicting sedimentation velocity. Resulting models were then tested for accuracy with the remaining 29 specimens (Tab. 1, “testing“ group). The best -fitting sedimentation model that could be obtained without consideration of particle shape (Sf) was ω = √ 4 3 ( 𝜌 𝜌𝑠𝑤 −1) 𝑔 𝑑𝑛 (4567661 ∗ 𝜈 𝑑𝑛 𝑔 ) (Model A) The sedimentation velocities predicted by this model correlated positively with the velocities observed, but the divergence between observed and predicted data was in many cases relatively large (Fig. 4A, r² = 0.3576, p < 0.0001). In particular, the mean sedimentation rate of the S. latissima rhizoid was significantly underestimated in the modeling dataset, placing it well outside the 95 % prediction interval. On the other hand, the velocity of specimen D. sanguinea .CC-BY 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint 22 27 from the test sample set was overestimated. Alltogether, t his model predicted the sinking velocities of the modeling sample set with a median squared deviation (MSD) of 6.84*10-5 and those of the test sample set with MSD = 4.28*10-5. Velocities of plastic disks were relatively accurately predicted, but velocities of nets underestimated and those of balls and rubber bands extremely underestimated (Fig. S2). As a consequence, the MSD of observed and predicted velocities of plastic items was relatively high (7.07*10-4). More prediction accuracy was possible when particle shape was considered in the model by inclusion of S f into the numerator of the function and by taking into account the general ellipsoidal character of macrophytes. Under this condition the best fitting model that could be obtained was ω = √4 3 ( 𝜌 𝜌𝑠𝑤 −1) 𝑔 𝑑𝑛 𝑆𝑓 2 3 (4146.337∗ 𝜈 𝑑𝑛1.5𝑔0.5 ) (Model B) Model B (Fig. 4B , r² = 0.7210, p < 0.0001) visibly predicted the sedimentation velocities of macrophytes with more accuracy than model A (Fig. 4A). Correspondingly, MSDs obtained with model B ( 2.45*10-5 and 5.87*10-5 for the model sample set and the test sample set, respectively) were 29 % smaller than those obtained with model A. Model B also provided significantly better predictions of the sinking velocities of plastic items (Fig. S2B ; MSD = 8.12*10-5). The best prediction accuracy of the sinking velocity of macrophytes was achieved when Sf was not only included in the numerator, but also in the denominator of Eq. 4 , considering that specific particle shape may also affect the drag coefficient CD. The best fitting model obtained under this condition was .CC-BY 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint 23 ω = √ 4 3 ( 𝜌 𝜌𝑠𝑤 −1) 𝑔 𝑑𝑛 𝑆𝑓 2 3 ( (198.3826+34121.98𝑆𝑓) 𝜈 𝑑𝑛1.5𝑔0.5 +0.8906959−9939.812 𝑆𝑓 2.972455−87764.06𝑆𝑓 52.04557) 5.566767 (Model C) In particular the sedimentation velocities of faster sinking specimens were predicted with even more accu racy by model C (Fig. 4C, 0.7926, p < 0.0001) than by model B (Fig. 4B). Correspondingly, MSD’s obtained with model C (2.12*10-5 and 2.08*10-5 for modeling sample set and test sample set , respectively) were 40 % smaller than those obtained with model B. However, while model C predicted the sedimentation velocities of plastic discs approximately correctly it underestimated the velocities of nets (Fig. S2C). Moreover, model C extremely overestimated the sedimentation velocities of balls and rubber bands . As a consequence, the MSD of observed and predicted velocities of plastic items was only 8.00*10 -4 and thus in the same order of magnitude as with model A, but 10 times larger than with model B. Fig. 4: Correlations between observed and predicted sedimentati on velocities. For the modeling sample set (blue, means ± ranges) and the test sample set (red, means only) with sedimentation velocities predicted for the same sample sets by (A) model A, (B) model B and (C) model C. Lines represent linear functions fitti ng best to data of the modeling sample set (model A: r² = 0.3576, p < 0.0001; model B: r² = 0.7210, p < 0.0001; model C: r² = 0.7926, p < 0.0001), dotted lines represent 95 % prediction intervals. .CC-BY 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint 24 Given that low S f values characterised not only thin, lea f-shaped, but also filamentous, tufted algae (see Fig. 1), and since similar surface interactions with water are not a priori to be expected for such different morphologies, one might possibly expect less accurate predictions of  by model C at low S f. However, macrophytes with lower S f were not those with lower predicted sinking velocities and there was no significant correlation between S f and and the MSD between predicted and observed velocities (Fig. S2A). Likewise, correlations between the relative algal density or the nominal diameter d n and MSD were not observed (Figs. S2B and C). Fig. 5: Predicted sinking velocity  from model C. For macrophytes exhibiting different combinations of shape factor Sf and nominal diameter d n. Kinetic viscosity of sea w ater, macrophyte density and seawater density were considered to be the median conditions observed during our experimental setup, i.e. 𝜈 = 1.0915*10-6 m2 s-1, 𝜌 = 1104.44 kg m -3 and 𝜌𝐻2𝑂 = 1009.45 kg m-3. .CC-BY 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint 25 In order to examine the interactive impact of the size and the specific shape of macrophytes on their sedimentation velocity more closely, fictitious values were entered for dn and Sf in model C, resulting in the dependencies shown in Figure 5. Obviously, the influence of the shape factor increases with particle size. Large macrophytes with a small shape factor sink significantly more slowly than those with a large shape factor, while smaller macrophytes can generally be expected to have lower sinking velocities.

Morphological differences in sedimentation behavior This comparative study of morphologically very diverse marine macrophytes ma de it possible to identify both differences and similarities in their sedimentation behavior. With few exceptions (namely, U. linza and different thallus parts of S. latissima), specimens of the same species behaved similarly and we observed some tendencies toward different behaviour across major taxonomic groups . That is, b rown and red seaweeds tended to sink fast er than green seaweeds and flattened branched specimens faster than flattened unbranched ones. Predicting seaweed sinking velocity based on thallus volume, weight and shape We identified the most relevant traits for the prediction of sinking velocity and drag impact on marine macrophytes and established protocols for their determination. The relevant parameters are (1) thallus volume, (2) thallus wet weight and (3) thallus shape. Thallus volume allows for the determination of the nominal diameter dn as described in Eq. 5. Thallus volume and thallus wet weight together are required for the determination of thallus mass density ρ. Use of the Corey shape factor Sf proved to be an applicable solution to characterize thallus shape even in very irregularly shaped macrophytes. The assumption of an ellipsoidal particle shape is inherent .CC-BY 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint 26 to use of Sf, given that Sf expresses the ratio of the longest, shortest and intermediate mutually perpendicular particle diameters. Leaving aside the more or less pronounced thallus flexibility, which can lead to consider able deviations, unbranched morphologies of macrophytes appear relatively obviously as ellipsoidal. A longest diameter is usually easy to identify in these cases. In the case of leaf -shaped morphologies the shortest diameter is the thallus thickness, in th e case of cylindrical unbranched morphologies it is any mean diameter perpendicular to the longest axis. The ellipsoidal character of branched thallus morphologies, on the other hand, is less obvious. A longest diameter is often not clearly discernible and - where it becomes visible - in many cases still not easy to measure. In the case of side branches of varying length and thickness, there is also the question of how to determine a representative shortest diameter, not to mention a representative intermediate diameter. The method used in the present work, based on a direct measurement of the more obvious axis lengths (Table 1; a * b in the case of flattened morphologies, c in the case of cylindrical morphologies) and subsequent derivation of less obvious axis lengths (c in the case of flattened morphologies, a*b in the case of cylindrical morphologies) from the volume, proved to be practicable and led to convincing results. The shape factors we found for macrophytes are in the range between 0.00029 and 0.0 69. A value of only 0.0003 was found with Ulva gigantea, which is characterised by particularly large, flat and very thin thalli. The individual we examined had a maximum length of 35 cm and a width of 29 cm with an average thallus thickness of only 79 µm. Individuals about twice or thrice this size exist (own observations) and a minimum value of S f around 0.0001 could therefore be possible. Therefore, the minimum values observed in our study could be close to the actually existing minimum values of Sf in macrophytes. However, the maximum value of 0.069 is still well below the theoretically possible maximum value of 1, which would result for perfect spheres. It is to be expected that species such as Codium bursa or Colpomenia peregrina, which approximately have a spherical morphology but were not available for our study, will exceed the maximum value of Sf that we found. .CC-BY 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint 27 Enhancing accuracy by incorporating Sf as a component of CD The inclusion of S f values determined in this way into the drag equation enable d relatively accurate predictions of the sedimentation rate of macrophytes. Notably, the prediction accuracy increased when Sf was not only considered in the numerator, but also as a component of CD in the denominator, as previously suggested by Riazi and Türker (2019) (Riazi and Türker 2019) for sediment particles. Remarkably, the best model C empirically determined on this premise and on the basis of our modeling data set predicted  with slightly better accuracy for the test sample set than for the modeling data set. Differences in predicting the sedimentation velocity of plastic objects vs. seaweeds In contrast, this model did not have good prediction accuracy for most plastic particles. Instead, it resulted in a significant overestimation of the sedimentation velocity for both balls and rubber bands. Only the velocities of the plastic disks were predicted relatively accurately, pr obably due to the fact that their shape factor is similar to that of macrophytes. Balls and rubber bands had shape factors that were significantly higher than those of all macrophytes. When balls and rubber bands were experimentally integrated into the modeling dataset, no alternative model based on the formula structure of model C could converge (not shown). Models based on this formula structure could therefore be fundamentally unsuitable for accurate predicti ons of the sedimentation velocity of particles with high shape factors. Alternatively, the very poor prediction accuracy of model C for balls and rubber b ands could also result from the fact that the transition between laminar and turbulent conditions at the particle surface is influenced by the material properties (e.g., elasticity or compressibility) at the particle surface. These properties could differ between various plastic particles and macrophyte particles and were not considered further in our study. The observation that model C predict ed the sinking speed of plastic nets with only moderate accuracy, although their form factors were in the same order of .CC-BY 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint 28 magnitude as those of macrophytes, also suggests an influence of surface material properties on CD. Model Performance divergence: C for seaweeds, B for plastic objects On the other hand, the fact that model C worked with better accuracy than the simpler models A and B for all macrophytes tested indicates that the surface material properties of different macrophytes differ significantly less than their form factors in terms of influence on CD. Interestingly, when the shape factor was only included in the numerator and not used to predict CD (Model B), the sedimentation velocity of all plastic and macrophyte particles was predicted with reasonable accuracy and better accuracy than when shape was completely ignored (Model A). This demonstrates the general usefulness of considering Sf.

Our study highlights that the sedimentation behaviour and the sensitivity to drag of marine macrophytes and also of plastic particles can be predicted with significantly increased accuracy if they are regarded as ellipsoids and their specific shape is also considered. Model C performed well for a wide range of macrophyte species, which were characterised by very different morphologies. It can be assumed that the behaviour of macrophytes from other habitats - marine as well as limnic - would also be predicted with similar accuracy. With Model B, we were able to increase the predictive capacity for plastic particle shapes and sizes, although the model was less accurate than model C for macrophytes. Model C therefore appears as better suited for accurate predictions of the velocities of macrophytes, while Model B appears more robust for generalistic predictions, especially for particles with high shape factors. Potentially, our models could even provide sufficiently a ccurate estimates for other particles with sizes and specific .CC-BY 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted May 3, 2025. ; https://doi.org/10.1101/2025.04.29.651208doi: bioRxiv preprint 29 densities similar to those of marine macrophytes, such as leaves shed by terrestrial plants . To accurately predict a higher variability of particles with higher shape factors than macrophytes, more diverse particles should be measured. A next step towards a generalistic model could also be to integrate different particle surface properties for a further model improvement. Thus, o ur results provide the foundation for improving the accuracy of pre dictions of the sinking velocities of morphologically diverse seaweeds – an important step for understanding processes such as carbon sequestration and the delivery of biomass to deeper parts of the ocean. Additionally, they can help refine estimates of ho w fast negatively buoyant plastic objects transition from the surface to being deposited on the seafloor.

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