Calcite carbonate sinks low-density plastic debris in open oceans

Domain: earth_science
Published: 2024-06-06
Editorial outcome: accept

Abstract
The vertical settling of plastic debris in oceans is poorly understood. A large share of low-density microplastics (LDMPs) are largely absent from sea surfaces. The present study employs a model that considers the potential of an overlooked microbially induced calcium carbonate precipitation (MICP) process and new motion equations for irregular LDMPs. Here we show that the motion of LDMPs in the present model, exhibiting a damped oscillation pattern, is quite different from that in biofouling models. Furthermore, LDMPs in the size range of 10–200 µm are most likely to gain sufficient density at the biofouling/MICP stage to independently sink to the ocean floor with relatively small drag coefficients, potentially explaining the selective enrichment of LDMPs in the oceanic sediment. The size and shape exhibit strong non-linear effects on the settling patterns of LDMPs. Overall, the present study highlights the importance of calcite-mediated sinking of LDMPs in open oceans.

Introduction
Marine plastic pollution has been a global concern, but plastic fate in deep seas has remained mysterious1. Low-density plastics, such as polyethylene (PE) and polypropylene (PP), account for over 50% of the total plastic waste, which can float on the sea surface, drift through the ocean currents, and spread into the global ocean2. Plastic debris conform to a fractal process through aging and fragmentation upon photolyzation and abrasion, breaking into smaller pieces3. However, field measurements confirmed that the estimated amount of low-density plastic debris discharged into the global ocean was much greater than that observed on the oceanic surface, especially for plastic debris with size below 5mm, also known as low-density microplastics (LDMPs)4,5. For instance, LDMPs in the range of 0.33–1.00mm were roughly 40% fewer in numbers than larger LDMPs (1.01–4.75mm)6. “Missing plastics” and “lost plastics” have led to broad investigations into the potential inventories or sinks of LDMPs in the ocean7.

Although field investigations regarding deep-sea LDMPs are still challenging, scientists have managed to obtain samples of deep ocean water and sediment from multiple locations since 20138–10. Considerable amounts of LDMPs were detected from the twilight zone to the abyssal seafloor11,12. In seawater, LDMPs were detected at the 1000m depth, in depth, peaking at 200−400m at an off-shore site close to California, USA13. Li et al.14 collected LDMPs at a spate of vertical depths up to 2000m at six locations in the Pacific Ocean and the Indian Ocean. Nakajima et al.15 also reported the widespread occurrence of benthic plastic debris in the deep-sea basin of the Northwest Pacific (3500–6500m), upto 70% of which are LDMPs. In oceanic sediment, abundant LDMPs were found at the Southwest Indian Ocean (900–1000m)8, the Northeast Atlantic Ocean (1400–2200m)8, the Arctic Ocean (2783–5570m)9, and the western Pacific Ocean (5108–10,908m) at the Mariana Trench10. A tentative “whole ocean” mass balance theory suggested that a large share of LDMPs have settled on the seafloor7, but rational explanations on LDMPs vertical settling remain challenging. Laboratory tests were deemed impossible to simulate LDMP settling in the deep ocean16, and modeling had become a viable alternative. Kooi et al.17 built the first idealized 1D, depth-dependent LDMP vertical settling model, considering biofouling as the density shifter18. Simulated LDMPs exhibited a repeated oscillation pattern near the upper water column17. Although the outcome has never been observed19, the biofouling model could explain the low concentration of LDMPs in the ocean surface4, as well as the accumulation of LDMPs within 200m beneath the ocean surface12.

However, the biofouling model encounters an enormous challenge to explain the enrichment of LDMPs in the oceanic sediment. Modeled LDMPs were impossible to approach the ocean floor due to the continuing loss of biofilm20. Fischer et al.19 evaluated LDMP settling under another biofilm dynamic, assuming frustule attachment on LDMPs after settling beneath the twilight zone. Ingestion by marine organisms (fecal pellets) merely sinks a negligible fraction (0.13–0.19%) of LDMPs21. Aggregation with biogenic particles (marine snow) could sequestrate another 0.06–8.8% of LDMPs22. Lobelle et al.23 and Fischer et al.19 incorporated oceanographic processes with a settling model, including large-scale 3D advection, small-scale vertical turbulence, dynamic grazing, and wind-induced mixing etc. The updated model allowed LDMPs to sink below the euphotic zone and mixed layer; however, only 15 of 10,000 LDMPs reached the ocean floor (>5000m) under favorable conditions19.

Microbially induced calcium carbonate precipitation (MICP) is commonly observed under calcium-rich and high pH environments, such as ocean surface and soil matrix24,25. The present study considers MICP accompanied by biofouling (autotrophic path)26. Most algae have negative surface charges27, and continue attracting oversaturated Ca2+ in the upper seawater column27,28. Some biological processes, such as photosynthesis and hydrolysis of urea, can increase pH levels in surrounding water25, triggering CaCO3 to precipitate near the biofilm and become part of the biofilm exoskeleton24,29. Different types of CaCO3, including calcite and aragonite30, can be produced by MICP. However, aragonite formation requires temperatures over 30°C31. Thus, calcite is considered the primary precipitate on LDMPs. With a density over 2.63 g cm−3, calcite could perform as an effective ballast to sink LDMPs to ocean sediments.

In the present study, a new one-dimensional hydrodynamic model is designed to evaluate the impact of MICP on LDMP settling. The MICP is controlled by the algal photosynthetic intensity. The target LDMPs have a density of 0.85–1.00 g cm−3 with an equivalent size range between 1µm and 5mm (see “Methods”), following an exponential distribution32. Sphere, fiber (57–13,000µm in length), and film (0.1–100µm in thickness) are evenly distributed. New hydrodynamic equations are introduced to improve the model’s performance on irregular LDMPs. The settling dynamics of LDMPs with and without MICP are compared, and the impact of size and shape on settling behaviors of LDMPs are discussed. The observed enrichment of LDMPs in the ocean subsurface and sediment is also discussed by simulating the vertical settling of a group of randomly generated LDMPs using the Monte Carlo approach (see “Methods”).

Results
Impacts of calcite precipitation on the settling of LDMPs
The essence of LDMP settling is to increase its density by binding with high-density substances, and heavy and steady fouling is always beneficial. Calcite (2.63 g cm−3) is an efficient ballast in increasing and maintaining the density of LDMPs compared to biofilm (1.15–1.18 g cm−3)18, algal frustules (1.80 g cm−3)33, marine snow (1.02–1.03 g cm−3)20, and fecal pellets (1.02–1.06 g cm−3)34. A 10µm sphere PE with an initial density of 0.92 g cm−3 only needs 0.35µm thick calcite precipitates to approach a density of over 1.1 g cm−3, which has already exceeded the highest known seawater density of 1.09 g cm−335. Moreover, calcite precipitates are difficult to come off plastic surfaces25. Laboratory studies revealed that the binding between calcite and LDMPs is so strong that calcite can be used as a coat to strengthen plastics in cementitious materials36.

To fully evaluate the settling patterns of LDMPs, we use the Monte Carlo method to generate 500 random LDMPs, calculate their vertical trajectories with and without MICP using the present model, and record their depths in a time series of 200 days (Fig. 1). The settling patterns of LDMPs in the deep ocean can be substantially altered by MICP, as compared to the results by Kooi’s model, which only considered biofouling process (Fig. 1A). Shortly after being released to simulated seawater, algae begin to collide and attach on the LDMP surface. Depending on the algal concentration and kernel encounter rate2,37, biofilm forms within minutes to hours38. During the process, MICP delivers calcite on the plastic surface. With growing ballast (biofilm and calcite), the density of LDMPs surpasses the density of surrounding seawater, triggering initial settling of LDMPs to the water column. Due to light intensity attenuation with increasing depth, biofilm decays through dying, shrinking, and shedding39. Although MICP also fades due to reduced pH caused by weakened algal photosynthesis24, calcite precipitates are more difficult to detach from the plastic surface than biofilms. Thus, LDMPs can retain most of the gained density and continue to settle until the negative buoyancy is balanced with the vertical drag. Depending on the settling conditions, most LDMPs could sink to the seafloor within tens to hundreds of days (Fig. 1B). Microbially induced calcium carbonate precipitation may serve as one of the critical factors in depleting LDMP concentrations at the ocean subsurface and enhancing LDMP accumulation at the oceanic sediment12.

The present model also considers the impact of calcite dissolution during LDMPs settling, especially after penetrating the calcite saturation depth (CSD)24. Seawater saturation state and oxygen consumption are the driving forces behind calcite precipitation or dissolution40. The level of calcite saturation decreases in cold deep water. Because the solubility of calcite increases with increasing seawater depth/pressure, the concentration of dissolved inorganic carbon is elevated relative to total alkalinity levels in the deep ocean41. Oxygen consumption due to biological respiration generates carbon dioxide and organic acids, enhancing calcite dissolution40. Yet, our model simulation indicates that most LDMPs only suffer slight calcite loss and settling velocity deceleration, even after passing the CSD. The impact of calcite dissolution is relatively small for three reasons. First, oxygen consumption is largely inhibited during the MICP process because of the high pH environment near the LDMP surface created by photosynthesis25. Second, the settling velocity of LDMPs is relatively high. Previous studies reported little CaCO3 dissolution was observed on particles at a canonical sinking rate of 100 m day−1, so the sinking flux at 4000 m is almost identical to the surface flux40. Based on our model simulation, most LDMPs can reach the seafloor within less than one year, leading to insufficient dissolution. Third, the CSD varies regionally from 1000 m to 4600 m24. Calcite dissolution is limited when the seafloor is above the CSD. For instance, the CSD in most regions of the Atlantic Ocean is below 3500 m24. In comparison, the average depth of the Atlantic Ocean is 3646 m.

Two settling patterns of LDMPs
Depending on how much calcite precipitates remain and how the seawater density varies, LDMPs can either undergo damped oscillation at the epipelagic zone or settle into the oceanic sediment (Fig. 2). Using the tropical Pacific Ocean profiles as an example, we conducted a series of sensitive analyzes to study the two settling patterns of LDMPs by tracking the trajectory, settling velocity, vertical drag coefficient, and density of a series of typical spherical LDMPs.

For relatively large LDMPs with a shape factor close to the sphere (the smallest specific surface area under the same volume), the damped oscillation pattern is frequently observed in the model simulation results (Fig. 2A, B). For large LDMPs with relatively small specific surface areas, the vertical drag coefficients are small. A slightly higher density of large fouled LDMPs than that of surrounding seawater would trigger the settling process (e.g., >500µm spheres), with a settling velocity over 200 m day−1. A slight loss of biofilm during settling would lead to density reduction, creating positive buoyancy. With a small vertical drag coefficient, LDMPs would rise quickly toward the sea surface, where biofilm and calcite can grow and accumulate again. Unlike the biofilm model, LDMP cannot approach its previous depth due to the existing calcite participates, resulting in a damped oscillation. During this time, calcite precipitates would slowly accumulate on each cycle. It is speculated that LDMPs would reach a suspension state when nearly no algae exist on the LDMP surface or are substituted by other microorganisms.

In contrast, the vertical drag coefficient of small (<500µm) and non-spherical LDMPs (e.g., film, fragments, and fiber) is quite, which could slow down the LDMP motion (Fig. 2C, D). Established biofilms and calcite precipitates can be developed on the LDMP surface, leading to a much higher density of fouled LDMP than seawater density. In some cases, the density can grow up to 2.40 g cm−3 (Fig. 2D) before fouled LDMPs could leave the epipelagic zone. For fouled LDMPs with established biofilms and calcite precipitates, the vertical settling is straightforward, because the extra ballast of calcite could assist LDMPs to overcome seawater density gradient and resist calcite dissolution (Fig. S1).

The simulation results also indicate a transitional state between the two settling patterns (Fig. 2E). With proper vertical drag coefficient, the LDMP settling would neither follow an oscillation pattern nor sink quickly to the ocean floor. These particles would accumulate just enough biofilm and calcite to gain negative buoyancy, but they cannot maintain negative buoyancy upon increased seawater density and biofilm loss. Furthermore, the LDMP density with remaining calcite precipitates and biofilms balances with the seawater density, allowing LDMPs to enter the suspension state directly without other oceanographic processes involved.

Impacts of MICP on sinking patterns of LDMPs
The settling of LDMPs is controlled primarily by negative buoyance created by biofilm and calcite, as well as the vertical drag coefficient affected by the physical properties of LDMPs. We evaluate the initial density, shape, and size of LDMPs and their impact on settling patterns. The shape categories of LDMPs (Fig. 3A–I) are evenly assigned as sphere, film, and fiber. Simulation results indicate that the settling of LDMPs exhibits essentially no relevance to the initial density of LDMPs, which is determined mainly by MICP and biofilm growth (Fig. 3A–C).

The shape of LDMPs plays an important role in determining the specific surface area of LDMPs (Fig. 3D–F). Fibers and films have larger specific surface areas than spheres, leading to higher vertical drag coefficients (Fig. 4A). Under the same volume, spheres are more sensitive to negative buoyance with larger settling velocities than films and fibers. Due to the high vertical drag coefficient, films and fibers have relatively enough time for biofouling and MICP and therefore higher densities than spheres. Spheres are more concentrated at 100–200 m, where fibers and films distribute in a much deeper and broader region of 100–400 m (Fig. 3D–F). The wider distribution of fibers and films compared to spheres can be explained by the uncertainty of the shape factor due to the extra degree of freedom of motion. Unlike spheres, fibers and films can twist and flip naturally during settling, so the projection areas towards the settling direction could vary accordingly, which creates deviations in the vertical drag coefficient42. Our simulation also exhibit that fibers and films require a much longer time to reach a steady state than spheres. Sphere-shaped LDMPs are most likely to accumulate on the seafloor. A close examination of simulated LDMPs sized below 1mm indicates that fibers and films need much longer time than spheres to reach the seafloor, especially for those with equivalent diameters smaller than 100µm. This trend has been observed in several previous studies, and the present model may provide a viable explanation for the high abundance of fibers and films in the water column43.

The size of LDMPs is another crucial factor governing the specific surface area (Fig. 3G–I). A larger size with the same shape category means a smaller specific surface area, which corresponds to a lower vertical drag coefficient and density difference and higher settling velocity. For spheres (shape factor close to 1), LDMPs at a size range below 500µm could stack enough calcite ballast to settle into the oceanic sediment without aggregation with fecal pellets and marine snow44 (Fig. 4B). The maximum sizes for these sinking fibers and films can be one order of magnitude larger than those for sinking spheres at equivalent diameters (equivalent in volume to sphere diameter). When large, LDMPs sink below the minimum light intensity depth, their density can approach at least 1.04 g cm−3 for a 500µm sphere (up to 2.60 g cm−3 for nanoplastics; Fig. 4C). It is noted that the upper size limit for LDMPs to independently sink to the seafloor depends on the specific seawater conditions. The current upper size limit of 500µm is only for spherical LDMPs settling under the tropical Pacific Ocean profile, where seawater has a maximum density of 1.035 g cm−3.

Sphere-shaped LDMPs in a size range of 100–500µm can directly settle to the oceanic sediment, and their settling velocities (100–300 m day−1) are much higher than marine snow (68 m day−1)45 and fecal pellet (25–67 m day−1)46. For sphere-shaped LDMPs in the size range of 10–100µm, the settling velocity is reduced to 10–20 m day−1. Increased vertical drag coefficient for LDMPs in the size range below 10µm would further decrease the settling velocity to less than 1 m day−1 (Fig. 4D). The high abundance of LDMPs in the simulated water column with the size range below 10µm is inconsistent with field measurements. Moreover, LDMPs in the size range of 1–5mm cannot settle to the seafloor, which is consistent with the observed size distribution of LDMPs at the oceanic sediment.

In previous studies, aggregation has been demonstrated as one of the important processes assisting the settling of ocean particles37, which may also boost the settling of LDMPs with the size ranges of <10µm and 1–5 mm26,47. The simulation results indicate that such aggregation could sink a significant amount of LDMPs in the size range below 10µm, aggregating them with portions of LDMPs in the size range of 1–5mm. On one hand, oscillating large-sized LDMPs have more chances to collide with other LDMPs. On the other hand, small-sized LDMPs are much more abundant according to the exponential size distribution of LDMPs. With high-density fouling, these small-sized LDMPs are the perfect ballast to aggregate with large-sized LDMPs. Aggregation of LDMPs with marine snow and fecal pellets also occurs, and the aggregates could settle to the seafloor under a small vertical drag coefficient.

Two sinking patterns of LDMPs
Figure 5 summarizes the field measurements of LDMPs in the seawater column (13 sampling sites) and oceanic sediment (6 sampling sites) in the Indian Ocean, Pacific Ocean, Atlantic Ocean, and Arctic Ocean13,14,48,49. High concentrations of LDMPs were found in the subsurface water column and oceanic sediment. With new motion equations, MICP, and designated ocean data from the National Oceanic and Atmospheric Administration (NOAA)50, the present model has successfully reproduced the distribution patterns of LDMPs, explaining the settling dynamics behind the field observations, especially the enrichment of LDMPs in the size range of 10–200µm in the oceanic sediment.

Under consideration of MICP, two LDMP accumulation zones along the vertical direction are formed. The first accumulation zone occurs at the upper water column near the sea surface (60–400m), coinciding with assumed static seawater conditions. Fischer et al.19 and Lobelle et al.23 demonstrated that incorporating oceanographic processes such as large-scale 3D advection, small-scale vertical turbulence, dynamic grazing, and wind-induced mixing could spread LDMPs to much deeper waters (up to 5,500m), but the maximum concentration of LDMPs remains in the upper water column51. It seems that the oceanographic processes can assist in creating dynamic and complex scenarios for LDMPs.

The subsurface accumulation zone commonly appears in subtropical oceans13,14, where the light intensity and chlorophyll concentration are consistent throughout the year (Fig. 5A–E), creating relatively stable conditions for biofouling and MICP52,53. As seawater density increases with increasing depth, it is difficult for large-sized (>500µm) spherical LDMPs to settle as they cannot accumulate enough ballast and are sensitive to density gradients (Fig. 4D). Most of these LDMPs stop settling and concentrate at the subsurface zone51. In contrast, the model simulation suggests that LDMPs with a size range below 10µm can accumulate much heavier ballast (nearly 2.5 g cm−3); however, the high vertical drag coefficient trap these LDMPs in the upper water column for a long time due to extremely slow settling velocity54. Although aggregation among LDMPs can accelerate the settling process, it is entirely by chance. It is positively correlated with the concentration of LDMPs in the water column, which further assists informing the subsurface accumulation zone26,37,47.

The second accumulation zone (seafloor zone) is at the oceanic sediment. The presence of abundant LDMPs in the oceanic sediment has been confirmed by a number of field investigations8–10,48,55. Previous LDMP settling models fail to account for the occurrence of abundant LDMPs in the oceanic sediment. Some of these sites are located far from high-density populations and major river outflows, so LDMPs should have deposited to the sediment from the seawater column. Considering MICP, the present model successfully reproduces the vertical settling of LDMPs, especially for the size range of 10–500µm under various shapes.

The vertical distribution of LDMPs in the Arctic Ocean is unique compared to those in other oceans, and this unique distribution of LDMPs can be well explained by the present model. The concentration of LDMPs in the Arctic Ocean is higher at both the sea surface and oceanic sediment (seafloor) and lower in the upper water column (Fig. 5A)1,9,48. No subsurface accumulation zone is observed, which could be attributed to the dramatic seasonal variations in light intensity and chlorophyll concentration. In summer, light intensity and chlorophyll concentration at the Arctic Ocean reach their maximums, and biofouling and MICP quickly uplift the density of LDMPs (Fig. 5B). Once overcoming the vertical drag coefficient, LDMPs can settle to the seafloor. The seawater density of the Arctic Ocean is almost consistent from the surface to the bottom (Fig. 5C), posing the least hindering effect on the settling of LDMPs56.

There are also vertical downward currents in the Arctic Ocean, which further promote the settling of LDMPs, especially those with a size below 10µm. In winter, however, light intensity is almost zero. LDMPs in the subsurface zone would ascend due to the lack of biofouling and MICP, which explain the high abundances of LDMPs on the ocean surface1 (Fig. 5A, D, E). Seasonal alternation creates a relatively long period of time with no light, which means that the aggregation of LDMPs is insufficient due to inadequate ballast. As a result, the most favorable size range for vertical settling of LDMPs should be 10–500µm based on the present model, which is consistent with the results from sediment core analyzes8,9 (Fig. 5F) that the most abundant LDMPs were in the 11–200µm size class48. The aging and fragmentation may also explain the absence of large LDMPs during long-range transport through the global ocean circulation44,50,57.

Simulating vertical settling of LDMPs in a time series
Figure 6 shows the settling distribution of a group of typical LDMPs in a time series with a size range of 1–5000μm, density range of 0.85–1.00 g cm−3, and shape categories of sphere, film, and fiber. The simulation conditions are reported as the tropical Pacific Ocean profiles. The normalized histogram represents the vertical distribution of LDMPs in sphere, film, and fiber. Most LDMPs sink toward deep seas after 30 days of biofouling and MICP. Concentrations of LDMPs at various depths of the upper 1500m water column decreased dramatically with increasing settling time. The density increment of LDMPs relies on the attached calcite precipitates and biofilms, and the accumulation of LDMPs in the seafloor requires a considerable amount of time58,59. Under the same oceanic conditions, the distribution of LDMPs continuously evolves along the time series.

In the first 20th days, the vast majority of LDMPs remain at the sea surface to a depth of 1500m, while a few LDMPs have begun to settle into the deep water column (Fig. 6A). At this point, strong size-selective characteristics are observed between the sizes of LDMPs and settling depths (Fig. 3G–I). Fibers and films with equivalent sizes close to those of spheres exhibit similar distribution patterns as spheres. As the settling time passes the 100th day, most LDMPs begin to diffuse into the deep water column, and the subsurface accumulation zone begins to fade away due to lack of continuous supply of LDMPs (Fig. 6B). Spheres occur less commonly in the seafloor than fibers and films. Starting from the 200th day, most LDMPs have already sunk to the seafloor (Fig. 6C). On the 300th day, the distribution of LDMPs shows a gradually dispersed trend, with few LDMPs remaining in the water column (Fig. 6D).

In summary, LDMPs can concentrate in the upper water column beneath the ocean surface and seafloor. LDMPs in the size range of 100–500μm are more likely to settle independently to the seafloor; settling larger and smaller LDMPs may need to involve aggregation1,59. Because efficient aggregation usually requires relatively high concentrations of LDMPs to increase collision probability, LDMPs would stagnate at the epipelagic and twilight zones, boosting the formation of the subsurface accumulation zone. Moreover, the formation of the subsurface accumulation zone seems to rely on a continuous supply of LDMPs from emission sources. Settling of LDMPs on the seafloor creates the second accumulation zone, one of the ultimate sinks for LDMPs. These modeling results are consistent with recent observations11–14. Onink et al.57 also confirmed these patterns through a Lagrangian model. The aggregation and settling of small-sized LDMPs into deep waters lead to low near-sea surface concentrations despite their high total abundances.

Implications for future projections
The present study shows that MICP is vital in the vertical settling of LDMPs in open oceans. It dramatically alters the distribution and motion of LDMPs in the water column. The outcome explains the “missing plastic” or “lost plastic” puzzle in the global ocean, as well as the abundant and uneven occurrence of LDMPs in the oceanic sediment4. The simulation results suggest that the seafloor is likely the ultimate destiny of LDMPs. If LDMPs with calcite precipitates eventually sink to the seafloor, it might impact the ocean benthic ecosystem, global carbon cycle, and ocean calcite cycle. All these potential risks require adequate assessments and systematic studies. We thus call for further strengthening the field measurement of LDMPs in deep-seawater and sediment and searching for LDMPs covered with precipitates under natural conditions. These LDMPs are likely widely distributed in sediment and deep-sea water and deserve further comprehensive investigations.

Methods
Model design principles
The vertical settling of LDMPs is mainly dependent on seawater density, current (vertical and horizontal), nutrition conditions, and biological activity17,55,58. The present model calculates the vertical settling speed and trajectory of LDMPs, considering the initial density, shape, and size of LDMPs and designated ocean conditions. The present model is a one-dimensional depth-dependent calcium carbonate (CaCO3) precipitation model using dynamic seawater conditions in a quiescent ocean based on Kooi’s model, which is explicitly designed to examine the impact of MICP during plastic settling.

Low-density microplastics under investigation are sized between 1μm and 5mm following an exponential distribution, which was adjusted to meet previous observations that the quantity of LDMPs with a size between 100–500μm is ten times compared to the number of LDMPs generated between 500μm–5mm60. For fiber-like LDMPs, a length range between 100μm and 1.3mm is selected. The thickness of film-like LDMPs varies between 0.1–100μm. Each simulated LDMPs is randomly assigned with an initial density from 850 to 1000 kg m−361. A random plastic generator was added to the model, generating LDMPs following the above-mentioned conditions. For simulation purposes, the ratio of plastic debris of different shapes is assumed as fiber: sphere: film = 1:1:1. The model can describe the vertical distribution of a group of random LDMPs using the Monte Carlo method in specific vertical profiles at a given site. The seawater profiles are acquired from the global real-time ocean forecasting system (RTOFS).

The present model includes three complementary sub-models: An updated vertical settling model, a MICP model, and a biofouling model. The vertical settling model based on fluid dynamic principles describes the settling speed and motion of unregulated LDMPs under a wide range of Reynolds numbers, taking into account the temporary density of LDMPs and ocean profiles. The MICP model was designed to estimate calcite precipitates on the plastic surface, considering the activity level of algal photosynthesis and dissolution rate under CSD. The biofouling model simulates biofilm growth on LDMPs, established by Kooi et al.17, which includes algae attachment, growth, mortality, and respiration under specific nutrition conditions and light intensity. Key parameters are listed in the supplementary materials (Table S2).

The vertical settling model
Motion equations for a wider range of Reynolds numbers. Previous studies calculated the settling speed or vertical settling velocity using a modified Stokes equation17, a linearized form of the Navier-Stokes equations for LDMPs with small Reynolds numbers.

dz/dt = v settling(z,t) (1)

The Reynolds number may become significantly large for numerous LDMPs with irregular shapes and sizes, and the current Stoke equation may not be accurate for estimation. In 2018, a new one-equation model considering the fluid drag was presented by Dioguardi and Dellino42, which is suitable for irregularly shaped LDMPs over a wider range of Reynolds numbers:

Cd = 24/Re * (1 + 0.1806Re^0.6459) + 0.4251 / (1 + 6880.95Re^-1) (2)

v settling = sqrt(8g(ρ pl - ρ sw)rESD / 3Cd ρ sw) (3)

Re = 4ρ sw * v settling * rESD / u (4)

where Cd is the drag coefficient of LDMPs, Ψ is the shape factor, Re is the Reynolds number, g is the gravitational acceleration (ms−2), ρ pl is the density of LDMPs (kgm−3), ρ sw is the seawater density (kgm−3), rESD is the equivalent spherical radius (m), and v settling is the vertical settling velocity (ms−1). Equations (2)–(4) show that each one of Cd, v settling, and Re is affected by the other two factors, which mean that an estimate of the Re value should be made to start the calculation procedure.

In each cycle, the Reynolds number approaches the actual value. An error estimation function is provided to determine the termination of the calculation:

τ = (Re n - Re n-1) / Re n-1 (τ < 0.001) (5)

The density of LDMPs ρ pl at the given moment t can be calculated as below:

ρ tot(t) = (m pl + m bf(t,z) + m Ca(t)) / (V pl + V bf(t,z) + V Ca(t)) (6)

where ρ tot(t) is the density of the LDMP and its attachment (kgm−3), m pl is the mass of pure LDMP (kg), m bf(t,z) is the mass of biofilms (algae only, kg), m Ca(t) is the mass of calcite precipitates (kg), V pl is the volume of pure LDMP (m3), V bf(t,z) is the volume of biofilm (algae only, m3), V Ca(t) is the volume of calcite precipitates (m3).

Estimation of the shape factor
A previous study indicated that the partial hydrodynamic area is critical in settling LDMPs, closely related to the projection area towards the settling direction62. A new shape factor is introduced from a recent study considering irregular-shaped particles62. The shape factor Ψ is defined as:

Ψ = Φ/χ (7)

where Φ is the sphericity of LDMPs and χ is the circularity of LDMPs. Φ is defined as the ratio of the surface area of an equivalent sphere and the surface area of LDMPs:

Φ = A sph / A p (8)

where A sph is the surface area of the equivalent sphere (m2), and A p is the surface area of LDMPs (m2). χ is the circularity of LDMPs, defined as

χ = P mp / P c (9)

where P mp is the maximum projection perimeter (m), and P c is the perimeter of a circle with the same area as the maximum projection area of the LDMPs (m). It is noted that for sphere-shaped LDMPs, Ψ ≈ 1.

The MICP model
Microbially induced calcium carbonate precipitation relies on biological processes, which are highly dependent on the presence of bacteria28. Kooi et al.17 pointed out that the number and weight of bacteria are much less than algae. Thus, the present study only considers autotrophic MICP and calcite as modeling processes. The calcium flux (J; μmol cm−2 s−1) at the plastic surface is estimated using Fick’s first law of diffusion29:

J = D Ca2+ * d Ca T / dz (10)

where d Ca T / dz is the concentration gradient in the region adjacent to the plastic surface and D Ca2+ is the ionic diffusion coefficient for MICP.

This equation is functional under steady-state flux conditions since the concentration gradient mainly occurs within 500μm above the biofilm surface25. In a typical saturation state of 1.71, the precipitation rate of calcite is estimated as 5 μmol cm−2 s−125. The MICP rate is adopted under the assumption of the similar biofilm formation for buoyant plastics, which are polyethylene (PE) and polypropylene (PP). Due to their similar composition and structure, the biofilm formation conditions on most PE and PP surfaces are identical. However, the MICP rate cannot be directly adopted as a constant. A linear relationship between the light intensity and the MICP rate is established, which is highly related to photosynthetic strength. When the light availability decreases with increasing water depth, photosynthesis is weakened and the MICP concentration gradient becomes insignificant, which terminates the MICP.

P z = I z / I 0 * J Ca (11)

where P z is the MICP rate at depth z and J Ca 0 is the MICP rate at the sea surface.

Oversaturated calcite in seawater cannot dissolve easily. With increasing depth, the increment of dissolved inorganic carbon content relative to total alkalinity enhances the solubility of calcite, leading to an unsaturated state24. The calcite saturation depth (CSD) is defined as the depth where the calcite unsaturation state first occurs42. Calcite on the LDMPs may partially dissolve when sinking under CSD and may regain buoyancy accordingly. However, CSD is often located in deep oceans where the seafloor is higher than CSD in many places. To study the impact of CSD, we introduce the calcite dissolution process when the adopted seawater condition shows the sinking depth is below the CSD24.

The biofouling growth model
Biofouling formation in open oceans. The biofouling formation on the material surface is a combination of microorganisms, including bacteria, algae, and/or fungi. For LDMPs, the biota types on the biofouling cover may be related to the original size, shape, and surface roughness of LDMPs. The biofouling process, according to previous studies, can be described as follows63,64:
(1) Mass transfer of macromolecules to the surface and formation of an adsorbed layer, or EPS;
(2) Transport of microorganisms to the absorbed layer;
(3) Establishment of a strong binding between the microorganisms and surface layers;
(4) Cell metabolism, including reproduction, growth, and mortality.

To simplify the above-mentioned processes, biofilms comprise three main groups: Slime, non-shell organisms, and calcareous-type fouling64. The slime includes absorbed inorganic and organic matter, trapped silt and detritus, and other unidentified slimes. Non-shell organisms refer to most microorganisms and non-shell macroorganisms64. Calcareous fouling is a new type of modeled fouling, accompanied by biofouling, which is quantitated by the calcification model. These calcite precipitates are formed in a weakly alkaline environment created by the photosynthesis process and supersaturated calcium environment25. The formed CaCO3 can attach tightly to plastic surfaces even after the mortality and decomposition of photosynthesized organisms.

Modeling the biofouling process. The biofouling on the material surface has been formulated, assuming all environmental conditions available for simulation and quantification. Equation (12) is used to evaluate the growth and thickness of biofouling attachment on the prospected targets64,65.

BG = f(SST, psu, pH, ν, I, S, t, m t, σ, θ c, R t) (12)

where BG is the growth rate of biofouling on a given surface, SST is the seawater temperature, psu is salinity (dissolved salt content of seawater), pH is acidity, ν is the speed of the water flow, I is light intensity, S is the concentration of nutrients, t is the time of the exposure to water, m t is the micro-texture of the surface, σ is the surface potential, θ c is the contact angle, which is a wettability measurement, and R t is the time of the exposure to water. Because the relationship is not well-established63.

The behavior of LDMPs upon biofouling is quite different from that of floating vessels. As biofouling grows on plastic surfaces, LDMPs accumulate weight and form a mixed batch of particles covered by calcite precipitates and biofilms58. Once LDMPs’ density exceeds surrounding seawater density, settling begins, and the particles submerge below the sea surface17. Temperature, salinity, and seawater density vary with increasing depth, and the growth and bio-activity are gradually constrained by decreased light intensity and temperature66. Eventually, biofilms stop growing and even fade away. LDMPs may become suspended, float up, or sink depending on the surrounding seawater density.

Furthermore, Eq. (12) is just a conceptual model that includes all possible biofouling variables under marine conditions. However, this type of model cannot be used for real-time predictions since validation of Eq. (12) with all parameters in the conceptual model requires enormous field measurements and laboratory tests, which are challenging to realize. We aim to evaluate the long-term settling of LDMPs in the marine environment, describing the vertical distribution of LDMPs in seawater. Thus, a simplified biofouling model is necessary to eliminate parameters and conditions that have little impact on the vertical settling of LDMPs.

The previous model for LDMPs’ biofouling growth and density is presented below17

ρ tot(z,t) = (r pl^3 ρ pl + (r pl + t bf)^3 - r pl^3) ρ bf / (r pl + t bf)^3 (13)

where ρ tot(z,t) denotes the density of LDMPs with biofouling attachments at a given depth z and time t of seawater exposure; r pl is the radius of LDMPs (assuming a sphere shape); t bf is the average thickness of biofouling; and ρ bf represent the density of biofouling attachment. Based on Eq. (13), the impact of plastic shape is considered in the present model. LDMPs can be in various forms, and three basic shapes are commonly found in field measurements: fragment (near sphere), film, and fiber. For simplification, the film shape is standardized as a round shape with uniform thickness; the fiber shape is modeled as a cylinder with uniform lines and constant radius; and the fragment shape is modeled as a sphere. Thus, the ρ tot(z,t) would be transformed as below:

ρ tot(z,t) = (ρ pl t pl + 2t bf ρ bf) / (t pl + 2t bf) (film) (Neglected edges) (14)

ρ tot(z,t) = (r pl^2 ρ pl + (r pl + t bf)^2 - r pl^2) ρ bf / (r pl + t bf)^2 (fiber) (Neglect both ends) (15)

ρ tot(z,t) = (r pl^3 ρ pl + (r pl + t bf)^3 - r pl^3) ρ bf / (r pl + t bf)^3 (sphere) (16)

where t pl represents the thickness of the plastic firm. The surface area is calculated using separate equations according to the given shapes.

Film. The thickness of biofouling (t bf) on film is calculated by

t bf = V tot / (π r pl^2) - t pl (17)

V tot = V pl + V bf (18)

V pl = t pl π r pl^2 (19)

S pl = 2π r pl^2 (20)

where V tot, V pl, and V bf are the total, plastic, and biofouling volumes, respectively; S pl is the surface area of LDMPs; and t pl is the thickness of the plastic film. Here, only algae are considered the primary fouling objects since bacteria are much smaller than algae, and the number is twice as small as algae.

Fiber. The thickness of biofouling (t bf) on fiber is calculated by

t bf = sqrt(V tot / (π l pl)) - r pl (21)

V tot = V pl + V bf (22)

V pl = l pl π r pl^2 (23)

S pl = 2π r pl l pl (24)

where l pl represents the fiber length, and r pl is the radius of the cross-section.

Sphere. The thickness of biofouling (t bf) on a sphere is calculated by

t bf = (3 V tot / 4π)^(1/3) - r pl (25)

V tot = V pl + V bf (26)

V pl = 4/3 π r pl^3 (27)

S pl = 4π r pl^2 (28)

Here, only algae are considered as the primary fouling objects since bacteria are much smaller than algae, and the number is twice less than that of algae. Furthermore, the biomass of algae in global oceans is used as a proxy to scale the overall biofouling potential from microbes, phytoplankton, zooplankton, marine snow, and ingestion in the feces, which is calculated by the calcification model67. V bf is

V bf = (V A A A) S pl + V minerals (29)

where V A represents the average volume of algae, A A represents the number of algae attached to the plastic surface; and V minerals is the volume of attached calcite precipitates. To simplify the calculation, we assume that the attachment and algal growth are independent of MICP. Thus, the algal growth is calculated as17

dA A / dt = β A A A + μ(T,I)A A - m A A - Q(T-20)/10 R A (30)

where A A (no.m-3) and encounter kernel rate (m3s-1). Algal concentration is calculated through the chlorophyll-a profile using the chlorophyll-a/carbon ratio and carbon/algal cell ratio, which depends on the temperature (T) and light-dependent (I z) equation:

Chla:C = 0.003 + 1.0154e^0.050T e^-0.057Iz = 10^6 μ0 (31)

where nutrients are assumed to be sufficient for algal growth. A well-accepted Gaussian methodology is applied to quantify the vertical chlorophyll-a profile68:

Chl(z) = Chla(z) = C b - sz + C max e^(-((z-Zmax)/Δz)^2) (32)

where C b is the normalized surface concentration; s is the normalized slope; C max is the normalized maximum concentration; Z max represents the maximum concentration depth; Δz is the width of the peak concentration; and Chla is the average chlorophyll-a concentration of the vertical profile. As Equation (32) is executed by a piecewise function with nine ranges based on the Chla surface concentration, which is acquired from NASA52,68 (Table S3).

The collision between algae and LDMPs is calculated through the existing aggregation model for marine algal flocs69. The encounter kernel rate β includes three compartments: the Brownian motion (β ABrownian), differential settling (β Asettling), and advective shear (β AShear) collision frequencies. These different encounter kernel rates are expressed as

β ABrownian = 4π(D A + D pl)(r A + r tot) (33)

β Asettling = 0.5π(r A + r tot)^2 |V sA - V s pl| (34)

β AShear = 1.3γ(r A + r tot)^3 (35)

where D A and D pl are the diffusivities of LDMPs and algal cells, and γ is the shear rate. For various shapes of LDMPs, r tot cannot be directly calculated. Thus, the equivalent spherical diameter (ESD) is introduced to approximate r tot in Eqs. (33), (34), and (35)26:

rESD = (6V tot / π)^(1/3) (36)

Based on this conversion, the diffusivity of LDMPs and algae is calculated as follows:

D pl = k(T+273.16) / 6πμ sw rESD (37)

D A = k(T+273.16) / 6πμ sw r A (38)

where k is the Boltzmann constant (m2kgs-2K-1), μ sw is the dynamic water viscosity (kgm-1s-1). Based on Eqs. (33)–(38), the collision of algae with LDMPs can be calculated.

The algal growth (term 2 in Eq. (28)) is modeled as:

μ(T z, I z) = μ opt(I z) Φ(T z) for T z ∈ [T min, T max] (39)

where μ opt(I z) is the algal growth rate under optimal temperature with a specific light intensity I z, and Φ(T z) is the temperature influence on growth rates66.

μ opt(I z) = μ max (I z / I opt) exp(1 - I z / I opt) (40)

Φ(T z) = [(T z - T min)(T z - T max)] / [(T z - T min)(T z - T max) - (T z - T opt)^2] (41)

In Eq. (41), I z is the light intensity at depth z, I opt is the optimal light intensity for algal growth, μ max is the maximum growth rate under optimal conditions, and α is the initial slope. In Eq. (42), T max, T min, and T opt are the maximum, minimum, and optimal temperatures to sustain algal growth. For temperatures outside the boundary of [T min, T max], μ is zero. The light intensity at a given depth z is calculated according to the law of Lambert-Beer:

I z = I 0 e^(-ϵz) (42)

where I 0 is the surface light intensity, and ε is the extinction coefficient. Light availability at the sea surface is expressed using a sinusoidal function:

I 0 = I m sin(2πt) (43)

where I m is the light intensity at noon. As I 0 never becomes negative, I 0 = 0 when sin(2πt) < 0. The light extinction is assumed to be dominated by water and algae-induced extinctions and can be expressed as:

ϵ = ϵ w + ϵ p Chla (44)

where ϵ w and ϵ p are constant values to quantify water and chlorophyll-a extinction coefficients, respectively.

Profiles of seawater salinity, temperature, and density
Seawater properties are critical for model simulation. Previous studies calculated vertical seawater salinity and temperature distribution using a fifth-order polynomial function against seawater depth. However, it is a rather mechanical and linear simulation that cannot reflect the reality of seawater at different locations. As a result, the RTOFS is introduced to acquire more practical and localized data to estimate seawater salinity and temperature from the surface to the seafloor under the National Centers for Environmental Prediction, which is based on an eddy-resolving 1/12° global hybrid coordinate50,53. The RTOFS provides seawater temperature and salinity nowcasting and forecasting the current date and next seven days’ predictions. The data types assimilated include in situ temperature and salinity profiles from various sources and remotely sensed SST, SSH, and sea-ice concentrations. The operational ocean model configuration has 41 hybrid layers and a horizontal grid size of (4500×3298). The grid has an Arctic bi-polar patch north of 47°N and a Mercator projection south of 47°N through 78.6°S53.

In the present study, only the nowcasting dataset is adopted. We have collected the nowcasting dataset from December 18, 2021, to December 18, 2022, using an auto-web crawler programmed by Python 3.7. Both salinity and temperature profiles include 33 available depths from the sea surface to the seafloor. For a continuous simulation, the salinity and temperature at a given depth z are assumed to vary linearly within each layer:

T z = (T up - T down) / (z down - z up) * z + T up, z ∈ [z up, z down] (45)

S z = (S up - S down) / (z down - z up) * z + S up, z ∈ [z up, z down] (46)

For Eq. (45), T up and T down are estimated temperatures on the top and bottom of a given layer, respectively, and z up and z down are the top and bottom depths for that layer. For Eq. (46), S up and S down are the salinity estimations on the top and bottom of a given layer, respectively.

Seawater density. According to Sharqawy et al.70, the best-fit model with measured seawater density under atmosphere pressure is constructed by salinity and temperature:

ρ sw,z = a 1 + a 2 T z + a 3 T z^2 + a 4 T z^3 + a 5 T z^4 + b 1 S z + b 2 S z T z + b 3 S z T z^2 + b 4 S z T z^3 + b 5 S z T z^4 (47)

a 1 = 9.999×10^2, a 2 = 2.034×10^-2, a 3 = -6.162×10^-3, a 4 = 2.261×10^-5, a 5 = -4.657×10^-8, b 1 = 8.020×10^2, b 2 = -2.001, b 3 = 1.667×10^-2, b 4 = -3.060×10^-5, b 5 = -1.613×10^-5

where a 1–a 5 and b 1–b 5 are constant values, T z (°C) is the temperature at a given depth z (m), and S z is the salinity at z (m). The temperature and salinity range for Eq. (35) are 0 < T < 180°C and 0 < S < 16%, respectively, and the accuracy errors are expected to remain within 1.5%.

Seawater viscosity. The seawater viscosity (μ sw, kgm-1s-1) is also calculated by seawater temperature (t, °C), salinity (S, unitless), and pure water viscosity (μ w, kgm-1s-1) given by IAPWS 2008 with an error of ±0.05%. The expression for the calculation is:

u sw = u w (1 + AS + BS^2) (48)

A = 1.541 + 1.998×10^-2 t - 9.52×10^-5 t^2
B = 7.974 - 7.561×10^-2 t + 4.724×10^-4 t^2
u w = 4.2844×10^-5 + (0.157(t+64.993)^2 - 91.296)^-1 (49)

The accuracy error of Eq. (49) is expected to maintain within 1.5%.

Simulation of observed LDMP distribution in open oceans
The Monte Carlo simulation methodology was introduced, and a group of simulated LDMPs was used to study the distribution patterns of LDMPs along the vertical direction based on available field investigations (Table S1). Because the exact number of LDMPs imported to the specific geographic location is almost impossible to acquire, the comparison mainly focused on the characteristics of LDMPs vertical settling patterns rather than the exact concentration distribution of LDMPs. To maximize the proximity to reality, the vertical seawater salinity and temperature profiles are acquired with latitude and longitude as the sampling location given by the available field measurements13,14,48,49 through the global real-time ocean forecasting system (RTOFS)53,56,65.

Overall model structure and verification
The model program, as described in a general flowchart (Fig. S3), is composed of four basic modules corresponding to four critical processes regarding the sinking process of LDMPs. The red module describes the surface changes of LDMPs under MICP and biofouling. The blue module represents designated seawater conditions given a specific geographic location and depth. The green module presents light intensity variation for photosynthesis. The purple module represents the position and velocity of given LDMPs under calculation based on given conditions, such as seawater conditions, LDMP properties and postures, MICP, biofilm growth, and so on. After settling the initial configuration, the model utilizes a Markov Chain procedure to calculate the trajectory of all LDMPs along a continuous time interval. The final results include the trajectories of randomly generated LDMPs, whose characteristics matched with observations.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "By Reviewer Michiel Van Melkebeke:\nThe authors of the manuscript fitled “Sinking the unsinkable: Ballast effects of calcite on low-density plasfic debris in open oceans” have provided a sensible and well-structured rebuftal. The arficle itself is carefully wriften with a strong and fifting fitle. The manuscript proposes a new model to describe the sinking behavior of low-density plasfic debris in the marine environment by explicitly accounfing for calcite precipitafion. The authors claim that, next to biofouling, calcite precipitafion greatly impacts the sinking paftern of plasfic debris.\nThe presented results are interesfing and parficularly relevant as the discrepancy between the observed and the esfimated amount of plasfic debris on the oceanic surface is sfill only parfially understood. Figure 3 in parficular provides an excellent graphical summary of the simulafions, where a comparison is made between the results of the model with and without accounfing for calcite precipitafion. From this, the improvement of the newly presented model in predicfing the verfical trajectory of plasfic debris in oceanic waters appears evident. However, much of their work is based on the assumpfion that calcite precipitates are much more difficult to detach from the plasfic surface than biofilms. While this does seem reasonable, addifional confirmafion or validafion aside from the single reference made originafing from 1996 by the efforts of Hartley et al. would definitely strengthen their work. In addifion, the authors menfion the inconsistency of field measurements with the first model that accounted for biofouling on plasfic surfaces proposed by Kooi et al. in 2017, which they in fact also employed as a basis to account for biofouling in their new model. There are, however, various improvements made on this first model such as the one proposed by Fischer et al. (2022) in their work fitled “Modelling submerged biofouled microplasfics and their verfical trajectories” and related efforts put forward by Lobelle et al. (2021) in the arficle fitled “Global Modeled Sinking Characterisfics of Biofouled Microplasfic”.\nNevertheless, I find the explicit inclusion of calcite precipitafion in a model to describe the verfical trajectory of plasfic parficles in a marine environment intriguing. The potenfial significance of the effect of calcite precipitafion on the sinking behavior of plasfic debris in oceanic waters could greatly affect the marine ecosystem and its global carbon cycle beyond the current understanding.\nFinally, in general, the described methodology is safisfactory and the discussion highlights some interesfing insights. Yet, I do have some specific comments:\nLine 20-21: I would suggest to modify: “It further reveals that plasfic debris can distribute at all depths after years of drifting with two accumulafion zones at 60-400 m of the water column andat theseafloor”\nLine 86-87: Missing word: “The verfical seawater densityvariafionis a crifical factor during plasfic seftling (…)”\nLine 123-124: Reformulafion: “But calcite precipitates are more difficult todetach fromplasfic surfaces than algae, as they are embedded within EPS”\nLine 128-129: Correcfion: “Some plasfic debris (e.g. 20 μm film) seftle slowly and steadily,whosedensity can grow much higher than seawater density, overcoming the high viscosity caused by large specific surface area.”\nLine 208-209: Correcfion: “But the dispersion ofthisplasfic debris was much quicker than those in the size range of 0-200 µm.”\nLine 227: Figure 5: It is confusing that the legend in the top right corner uses different colors to label the shapes of the plasfic parficles, while only the point shape is in fact relevant for this descripfion.\nLine 237-238: Correcfion: “In the first 100 days, the vast majority of plasfic debrisremains atthe sea surface to a depth of 200 m, while a few large-sized plasfic debris (> 400 µm) have begun to seftle into the deep water column (Figs. 5A-5B).”\nLine 251-252: This statement is unclear or wrong. I advise the authors to clarify or recfify: “Our simulafion results also indicate that small-sized plasfic debris have entered the upper 100-m water column in less than 300 days.”\nLine 342 and 344: What does “angle only” mean? Perhaps the authors meant to write “algaeonly”? If so, please correct.\nLine 431: Correcfion: “reparameterizafions”", "reviewer_2": "Review report for Sun et al., “Sinking the unsinkable: Ballast effects of calcite on low-density plasfic debris in open oceans”\nThis arficle presents simulafion results of the impacts of a previously overlooked phenomenon: calcite precipitafion on plasfic surface. The authors present simulafion results showing that calcite precipitafion may explain a large part of the sinking of posifively buoyant plasfics. They aftempt an evaluafion of their model results by comparing verfical profiles of measured plasfic debris with their simulafion results. Then, the authors compare the simulated impacts of calcite precipitafion on various plasfics shapes, sizes and densifies and conclude by affirming that calcite precipitafion explains the “missing plasfic” puzzle in the surface ocean.\nThis arficle studies an overlooked process that could significantly impact plasfic distribufion in the global ocean. While the quesfion of whether calcificafion is a significant process to plasfic’s fate in the ocean is interesfing and the methodology employed (numerical modeling) is adapted to the quesfion, the authors fail to jusfify in the arficle the importance of such study. Overall, the arficle lacks references to jusfify that calcite precipitafion may be an important phenomenon, or that it has been observed at all on plasfic debris. The methods are also poorly described. It is not even clear whether the model presented here was enfirely designed for the study, or if it’s based on previous work. There is no reference for the data used to force the model (physical and biogeochemical condifions). Overall, there are very few references in the manuscript and enfire paragraphs are given without referencing any arficle, or even some of this study’s results. Therefore, the whole arficle reads as a thought experiment and remains too theorefical to recommend publicafion in the current state.\nI am detailing below some of my major comments to improve this manuscript.\nMajor comments:\nIn the introducfion, a paragraph is missing to explain why calcite precipitafion is important for plasfic debris distribufion. References are needed here to jusfify that this phenomenon is worth invesfigafing and exploring in a model. This would jusfify the present study.\nMany sentences lack references, as a result, a lot of the arguments presented remain pure speculafion. For instance, lines 89-94 “The distribufion of plasfic debris within the second accumulafion zone is a dynamic interplay, intricately influenced by mulfifarious variables such as incident light intensity, nutrient level, prevailing seawater condifion, distance from emission sources, and the disfincfive aftributes of said sources. Consequently, one may observe a spectrum of concentrafions ranging from several to hundreds of plasfic parficles per cubic meter.” But also lines 109-115, 190-200.\nOne thing I found parficularly confusing is that the dimensions of the plasfic debris of interest in this study are not described unfil line 118. As a results, we do not know what kind of plasfic debris are simulated and measured.\nLines 75-80: what data are you referring to? You also state that “The fifting performance indicates that improvements are achieved in simulafing the verfical seftling dynamics of plasfic debris in open oceans.” compared to what? How can you affirm that the verfical dynamics are improved ?\nIn general, the figures could be improved. Many lack some units or informafion to help interpret their results. Moreover, the text describing the figures presents things that we can’t see on them. For instance lines 103-104: “Once the density of plasfic debris surpasses the seawater density and overcome the seawater viscosity, plasfic debris can seftle on the seafloor (Fig. 1)” There is no menfion of seawater density or viscosity in the figure.\nLines 177-179 (describing Fig.4): “This trend reveals that the seftling of plasfic debris is increasingly dependent on calcite precipitafion and biofilm growth as the equivalent diameter of plasfic debris becomes smaller due to photolyzafion and abrasion.” No menfion of photolyzafion and abrasion anywhere in the figure (or the MS).\nFigure 1: What’s “ss” on the plots? How were the curves calculated? They seem far from the dots at some sites (e.g. North Pacific Ocean). No units on the x axis.\nFigure 4. What’s the shape category of the parficles in A,B,C,G,H and I. How does this choice affect the results?\nFigure 5 must be modified. As presented, we cannot disfinguish the 3 shapes. What’s the density of the parficles? What’s the simulafion condifions?\nLines 184-189: “Moreover, sphere-shaped plasfic debris are most likely to accumulate on the seafloor. Hence fibers and films are more abundant than spheres in the water column. A close examinafion of plasfic debris sized below 1 mm indicates that fibers and films need much longer fime than spheres to reach the seafloor, especially for those with equivalent diameters smaller than 100 m, even though they take a shorter fime to submerge into the water column.” While this may be shown in your simulafions, such results are not new and where seen by other authors. References and discussion of your results with regards to these previous studies is lacking here.\nLine 253: “In summary, large plasfic debris (> 200 m) are concentrated at 60400 m and on the seafloor” This conclusion (which is a major result of the study since it’s also highlighted in the abstract) seems supported by none of the figures presented. Maybe in Figure 4 which presents results from theorefical simulafions.\nThe sentence line 258-261 “However, such deplefion of plasfic debris in the upper 100 m water column can hardly be field-measured, because increasing plasfic producfion and insufficient plasfic waste management constantly supplement plasfic debris to the sea surface.” is awkward. It seems to jusfify that the results of this study may not be supported by data.\nLine 265: “ Since it requires a considerable amount of fime for plasfic debris to build up calcite precipitates and biofilms” This sentence lacks a reference, and is not true. Biofilms form within minutes to hours (see Paul-Pont et al., 2018)\nPaul-Pont I, Tallec K, Gonzalez-Fernandez C, Lambert C, Vincent D, Mazurais D, Zambonino-Infante J-L, Brotons G, Lagarde F, Fabioux C, Soudant P and Huvet A (2018) Constraints and Priorifies for Conducfing Experimental Exposures of Marine Organisms to Microplasfics. Front. Mar. Sci. 5:252. doi: 10.3389/fmars.2018.00252\nLines 267-273: “By analyzing the verfical distribufion pafterns of plasfic debris, we can diagnose possible emission sources and their geographic locafions (Fig. S3). If plasfic debris collected at a given geographic locafion originate from nearby emission sources, the surface concentrafion of plasfic debris would be higher than that resulfing from distant emission sources. If plasfic debris are derived from mulfiple emission sources with numerous distances, their verfical distribufion pafterns would contain mulfiple overlapping peaks. “ Again, no reference for these affirmafions. Moreover, these affirmafions completely ignore the fact that ocean currents may also be verfical! Verfical currents have been shown to significantly influence plasfic distribufion in 3D (Richon et al., 2022, Mounfford et al., 2019, Huck et al., 2022). Also, these sentences overlook the potenfial influence of fish and other animals on plasfic verfical distribufion through ingesfion-migrafion-excrefion (Jusfino et al., 2020).\nJusfino, A. K. S., Ferreira, G. V. B., Schmidt, N., Eduardo, L. N., Fauvelle, V., Lenoble, V., Sempéré, R., Panagiotopoulos, C., Mincarone, M. M., Frédou, T., & Lucena-Frédou, F. (2022). The role of mesopelagic fishes as microplasfics vectors across the deep-sea layers from the Southwestern Tropical Atlanfic. Environmental pollufion (Barking, Essex : 1987), 300, 118988. hftps://doi.org/10.1016/j.envpol.2022.118988\nRichon C, Gorgues T, Paul-Pont I and Maes C (2022) Zooplankton exposure to microplasfics at global scale: Influence of verfical distribufion and seasonality. Front. Mar. Sci. 9:947309. doi: 10.3389/fmars.2022.947309\nHuck T, Bajon R, Grima N, Portela E, Molines J-M and Penduff T (2022) Three-Dimensional Dispersion of Neutral “Plasfic” Parficles in a Global Ocean Model. Front. Anal. Sci. 2:868515. doi: 10.3389/frans.2022.868515\nMounfford, A. S., & Morales Maqueda, M. A. (2019). Eulerian Modeling of the Three-Dimensional Distribufion of Seven Popular Microplasfic Types in the Global Ocean. Journal of Geophysical Research: Oceans, 124, 8558–8573. hftps://doi.org/10.1029/2019JC015050\nOne major quesfion that I have is if biofilm detaches when plasfic sinks, why would calcite precipitates remain on plasfic surface? This is not jusfified anywhere in the manuscript.\nMethods\nIn general, the methods (except for the model descripfion and equafions) lack important informafion. There is no informafion on whether the model used in this study was built specifically, or if it existed before. Again, there is no reference to calcite precipitafion being a significant process (lines 309-311 have no reference).\nLine 364-365: “Calcite precipitates are much denser than seawater and are difficult to detach, thus they are much more efficient than algae in increasing the density of plasfic debris. “ Needs a reference. Is there any study showing calcite precipitafion on plasfic debris?\nLines 387-406: what locafion did you use? How did you select the sampling sites?\nLine 395-397: “We may move the coordinate of simulated seawater profiles a liftle bit from the original posifion if the depth of the RTOFS dataset at the original site cannot approach the measured depth” Since we have no idea of the locafions you are referring to, this sentence makes no sense.\nThe informafions of size and density of the plasfics should also be menfioned in the main manuscript.\nLines 405-406: “The floafing plasfic debris which are denser than the seawater may be caused by trapped air, hydrophobicity, and surface tension.” So, you simulated bubble formafion?\nLines 409-420: Again, no menfion of the observafions, what observafions? Where?, Who sampled? How was it sampled? I don’t understand the organisafion of the model with colored modules.\nLines 421-422: “The verfical distribufion pafterns of plasfic debris are esfimated via the interpolafion method to create smooth curves for comparison.” Comparison with what? What interpolafion method?\nThe most problemafic with the methods secfion is that there is no menfion of how the simulafions where performed. How log did they run for? Is that 0D, 1D, 2D, 3D? What data is used for forcing? Is there a control simulafion? Did you simulate all processes separately? Did you simulate biofouling & calcite precipitafion? Did you perform a simulafion without calcite precipitafion for comparison? As presented, it seems not. Thus, there is no way to know whether calcite precipitafion is the process actually impacfing plasfic export.\nMinor correcfions:\n- Line 50: “Indian Ocean”\n- Line 146: What’s the “plasfic debris simulator”?\n- Lines 191-193: “Because spheres have the lowest specific surface areas among all shape categories, calcite precipitates and biofilms are much thicker on spheres than on fibers and films when similar overall density is achieved.” Needs a reference", "reviewer_3": "Review of “Sinking the unsinkable: Ballast effects of calcite on low-density plasfic debris in open oceans”\nIn this study, the authors develop a new model of explicit calcite biofouling of microplasfics to invesfigate the transport potenfial of calcite ballast for moving plasfic parficles into the deeper ocean and away from the sea surface. They find that the combinafion of organic and calcite biofouling transports microplasfics into the deeper ocean levels and leads to the accumulafion of debris in the mesopelagic and near the seafloor. Deeper transport of microplasfics is more consistent with observafions. Their implementafion of mulfiple plasfic parficle characterisfics in addifion to organic and calcite biofouling makes this a novel study that could be interesfing to a broad audience. However, some of the arguments put forth are not fully convincing and more informafion is needed. Furthermore, the organizafion of the manuscript could be improved for readability. Starfing the results secfion with the Monte Carlo simulafions (from L141). Move Fig. 3 to Fig. 1 and remove panel A (or, consider moving Fig. 3 to the supplement and adding non-calcite ballast to current Fig. 2). Make current Fig. 1 new Fig. 2. Add density and chlorophyll profiles to that figure panels. Remove the red curve, add in the no-calcite profile to clearly demonstrate the impact. Move current Fig. 4 up to new Fig. 3. Rearrange text accordingly. I think these changes could improve the flow of the Results secfion and make it more understandable.\nGeneral comments:\nIntroducfion: The size range of plasfic debris should be introduced in the first paragraphs of the manuscript, to make it clear which plasfics are being considered. This is also true for the discussion of the Kooi study (from L39), so that the reader understands this is a relevant study to the present topic. Also the paragraph from L44, explicitly stafing the size ranges of the observed plasfics to make it clear these are fairly compared to the Kooi oscillafion mechanism.\nModel validafion secfion:\nFigure 1: It would be very helpful to see an annual average chlorophyll map in Fig. 1. This could replace the current map, with the observafional points sfill overlaid. Please remove the red lines from Figure 1 as they do not add any insight into the model assessment. Are the observafions down the water column taken at the same fime as the surface observafions? Please also define the size range of the plasfic debris used in this model-obs comparison. And, are the units parficles per m^-3?\nThe Fréchet distance is not terribly convincing, as the observafional curves are not convincingly similar to the observafions themselves in many locafions. I would prefer a more direct/less derived comparison method.\nParagraph starfing at L81 is not well jusfified by the figures. Clarity could be improved by moving Fig. 4 to Fig. 3, which then demonstrates the 2 major accumulafion zones for different parficle types in context. If chlorophyll is added to Fig. 1 then this would help to demonstrate how biological acfivity is shaping water column plasfic distribufions. Why not also add density profiles to the panels of Fig. 1, and then you can remove Fig. S1A and also directly see how the density gradient is affecfing accumulafion zones? Fig. S1B is not very useful and can be removed.\nLast 2 sentences from L89 “The distribufion of plasfic debris...” are vague and not demonstrated clearly from looking at the figures. Fig. 1 appears to show typically lower concentrafions.\nParagraph starfing from L95 is also not completely convincing. Parficularly, L98 “No second accumulafion zone...”. What about seasonal deep mixing (e.g. Fischer et al. 2022), and the strongly seasonal biomass? Could seasonality be determining the homogeneous distribufion? And from the next sentence (L99) Kvale et al. (2020) hftps://www.nature.com/arficles/s41598-020-72898-4 Supplement has a sensifivity analysis showing that surface concentrafions in the Arcfic are highly sensifive to the buoyant fracfion advecfing from lower lafitudes, where parficles biofouled and in the subsurface below 40N tend not to escape to the Arcfic. Can a figure strengthen the arguments put forth in this paragraph?\nParagraph from L109: Reference to a figure would help here. Befter sfill would be overlaying density and chlorophyll on the panels of Fig. 1.\nL160&L281: “It seems that...” this sentence is too conclusive, as other mechanisms are not tested, for example marine snow aggregafion and fecal pellet sinking. These other mechanisms have been simply parameterized in another model and have similar results (mesopelagic accumulafion), e.g. Kvale et al. (2020) hftps://www.nature.com/arficles/s41598-020-72898-4. Likewise, biofouling was demonstrated to be able to distribute plasfic parficles deep into the water column (hundreds of meters) in slow oscillafions by Fischer et al. (2022) hftps://doi.org/10.5194/bg-19-2211-2022. Can you explain why your biofouling model does not behave similarly to that of Fischer et al.?\nParagraph from L180. I really like this paragraph and associated Fig. 4. These are a highlight of the paper.\nParagraph from L219. Are there observafions that can be used to validate these simulated pafterns? Perhaps Zhao et al. (2022) hftps://doi.org/10.1111/gcb.16089.\nDiscussions: Kvale et al. (2020) hftps://www.nature.com/arficles/s41598-020-72898-4 Supplement had a whole sensifivity test (Figs. S6, S9) that demonstrated the role of biologically mediated (fecal pellet and marine snow aggregates) in sinking microplasfic parficles into the mesopelagic and in accumulafion of plasfic debris at these depths, but this is never discussed. Likewise, comparison to the Fischer et al. (2022) hftps://doi.org/10.5194/bg-19-2211-2022 study and the Lobelle et al. (2021) hftps://doi.org/10.1029/2020JC017098 study is not done.\nSupersaturated dissolufion of calcite is an observed phenomenon and reponsible for the regulafion of deep ocean calcite fluxes, e.g. Subhas et al. (2022) hftps://doi. org/10.1029/2022GB007388. Choosing to omit this process should be discussed.\nSpecific comments:\nL61: From “Ingesfion by seabirds...” This sentence can be deleted as it is not obviously relevant.\nL77: What is Fréchet similarity (please define)\nL78: “The fifting performance...” this sentence is not jusfified by a comparison to a model without calcite ballast. Could model simulafions that do not include calcite ballast be added to Fig. 1 panels?\nL106: are ageing and fragmentafion represented in this model? If not, please remove this sentence.\nL122: This sentence should be rephrased for clarity. I think ‘resumpfion’ is the wrong word. And is in situ CO2 affecfing calcificafion rate? No dissolufion is included in this model- correct? (please state explicitly)\nA sentence added around L122 to describe how calcite precipitates are modelled to come off the plasfic parficle would be helpful for understanding this secfion.\nFig. 2: Adding biofouling only (no calcite) trajectories,velocifies, and densifies to these panels would enhance understanding of how calcite is uniquely affecfing the results.\nL152: “Due to low light intensity..” the dominant control of light intensity on deep parficle sinking is not clearly demonstrated by the results. Rephrasing to a density difference focus would be more clear.\nL176: “According to the simulafion results...” this sentence does not make sense to me because the inifial density cannot be modified by the seftling fime. Please revise.\nNext sentence (L177) I am confused here because up to now I thought the plasfic parficles are not losing mass. Please explicitly state this somewhere before this point. Also L193, plasfic is warped in the model by biofilm? I am confused.\nL214: “It seems that...” this sentence is self-condtradictory. Could it be “maintain sinking” rather than “floafing”? Or “small” should be “large”?\nL285: “If plasfic debris...” Do you have a citafion for this statement?"}, "author_response": "Reviewer #1:\nThe authors have comprehensively addressed the comments and made the required\nimprovements. In particular, the revised manuscript provides a significantly more elaborated\ndiscussion by including necessary references from literature, which was one of my greatest\nconcerns. In addition, the methods section, which was ultimately incomplete, is dramatically\nimproved in the revised version. Finally, specific comments have also been addressed,\nhowever, I would advise the authors to closely review their manuscript for critical errors. For\nexample, I doubt that the word “breathe” is intended in line 61.\nResponse/action: Thank you very much for your positive feedback and suggestions. The\nreviewer’s concerns are well taken. The entire manuscript was subject to rigorous\nexamination and check. Indeed, “breathe” was a typo. It should be “beneath” (line 62 in the\nrevised manuscript).\nReviewer #1 (Remarks on code availability):\nN/A\n1 / 5\nReviewer #3:\nThe authors have greatly improved the quality of their manuscript since my last reading.\nThere remain some grammar errors that I leave to the editors to correct if the manuscript is\naccepted.\nSpecific comments:\nLine 25-26: Highlights the ‘potential’ importance…Because without model validation with\nobservations of calcite coated microplastics at depth, this study remains a sensitivity study.\nResponse/action: The reviewer’s concerns are well taken. In the revised manuscript, the\nstatement of “potential” has been highlighted as suggested.\n“The present study employs a new model that considers the potential of an overlooked\nmicrobially induced calcium carbonate precipitation (MICP) process and new motion\nequations for irregular LDMPs.” (lines 17)\n“Furthermore, LDMPs in the size range of 10200 µm are most likely to gain sufficient\ndensity at the biofouling/MICP stage to independently sink to the ocean floor with relatively\nsmall drag coefficients, potentially explaining the selective enrichment of LDMPs in the\noceanic sediment.” (lines 2124)\nLine 61: ‘breathe’ should be ‘beneath’\nResponse/action: Thak you for your careful checking our manuscript. Indeed, “breathe”\nwas a typo. It should be “beneath” (line 62 in the revised manuscript).\nLine 63-64: Sentence on marine snow aggregation. Ref 30 show 0.06-8.8% sedimentary\n‘sequestration’ potential, not sinking potential.\nKvale et al. 2020 https://www.nature.com/articles/s41598-020-72898-4 shows that marine\nsnow aggregation + fecal pellet removal can potentially remove all of the microplastics from\nthe upper 50 m, but the model parameters are too poorly constrained to say anything more\ndefinitive.\nResponse/action: The reviewer’s points are greatly appreciated. In the revised manuscript,\nthe statement has been corrected as suggested.\n“Aggregation with biogenic particles (marine snow) could sequestrate another\n0.068.8% of LDMPs22.” (lines 6465)\nLine 130: ‘In our model’ calcite dissolution may never occur… I think the authors\nmisunderstood my comment on supersaturated calcite dissolution, which is a major process in\nthe upper ocean (see Subhas et al.,\nhttps://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2022gb007388). Calcite dissolution\nis better explained by a combination of oxygen consumption and saturation state than\nsaturation state alone. This implies that calcite mediated LDMP transport is less effective\nthan simulations based purely on thermodynamics would indicate.\nResponse/action: Thank you very much for your valuable suggestions. In the revised\nmanuscript, the explanation of calcite dissolution has been revised as suggested. Moreover,\n2 / 5\nwe merge the results of Subhas et al. within the revised manuscript with additional\nreferences.\n“The present model also considers the impact of calcite dissolution during LDMPs\nsettling, especially after penetrating the calcite saturation depth (CSD)24. Seawater saturation\nstate and oxygen consumption are the driving forces behind calcite precipitation or\ndissolution40.” (lines 12224)\n“Oxygen consumption due to biological respiration generates carbon dioxide and\norganic acids, enhancing calcite dissolution40.” (lines 127)\n“First, oxygen consumption is largely inhibited during the MICP process because of the\nhigh pH environment near the LDMP surface created by photosynthesis25. Second, the\nsettling velocity of LDMPs is relatively high. Previous studies reported little CaCO\n3\ndissolution was observed on particles at a canonical sinking rate of 100 m day-1, so the\nsinking flux at 4,000 m is almost identical to the surface flux40. Based on our model\nsimulation, most LDMPs can reach the sea floor within less than one year, leading to\ninsufficient dissolution.” (lines 13137)\nLine 138: ‘series of sensitivity analyses’\nResponse/action: Thank you for chatching the error. “analysis” has been revised to\n“analyse” (line 146 in the revised manuscript).\nLine 148: ‘Unlike the biofilm model’… this is a key sentence, very important to highlight in\nthe abstract. Please consider producing a schematic of this process, as well as those for\nsmaller sized LDMPs.\nResponse/action: The reviewer’s points are well taken. In the revised manuscript, the\nabstract has been revised as suggested.\n“The motion of LDMPs in the new model, exhibiting a damped oscillation pattern, is\nquite different from that in biofouling models.” (lines 1)\nLine 160: ‘increment’-> ‘the sw density gradient’\nResponse/action: Thank you for your valuable suggestion. “increment” has been revised to\n“gradient” (line 169 in the revised manuscript).\nLine 174: ‘Simulation results indicate that the initial density of LDMPs exhibits essentially\nno relevance to their settling, which is determined mainly by MICP and biofilm growth’ (and\nthen you can remove last sentence of paragraph)\nResponse/action: The reviewer’s suggestions are greatly appreciated. In the revised\nmanuscript, the statement has been revised as suggested and the last sentence of the\nparagraph has been deleted.\n“Simulation results indicate that the settling of LDMPs exhibits essentially no\nrelevance to the initial density of LDMPs, which is determined mainly by MICP and biofilm\ngrowth (Figs. 3A3C).” (lines 18385)\nLine 214: ‘The high abundance…’ Sentence is unclear. The high abundance of LDMPs in\nmodel sediments? Simulated water column?\n3 / 5\nResponse/action: The reviewer’s concerns are well taken. In the revised manuscript, “in the\nsimulated water column” has been inserted after “The high abundance of LDMPs” (line\n).\nPage 13: A schematic of the relevant processes in the Arctic could also be a very useful\naddition to a supplement, or to otherwise get onto the internet. I expect this would be a very\nuseful resource for others.\nResponse/action: The reviewer’s points are well taken. We totally agree with the reviewer\nthat adding a schematic of seasonal impacts in the Arctic would be useful for readers. We\nwill integrate such schematics as an extend content and added as demo figures in the Github\npackage at https://github.com/JePhyllis/MICP_Model_v1.0.\nLine 290: I think ‘settled’ is the wrong word. Maybe, ‘reported’?\nResponse/action: Thank you very much for catching the error. “settled” has been replaced\nwith “reported” in the revised manuscript (line 298).\nAn off-track comment: you can potentially simulate a large storm, e.g. cyclone with your\nforcing data and see how this disrupts settling times. This could be very interesting looking at\nregions with consistently high pollution and regular seasonal storm tracks.\nResponse/action: Thank you very much for your valuable suggestions. We totally agree\nwith the reviewer that adding extreme weather conditions not only assists exploring the\nvariation of settling times, but also spurs further interests. We will integrate this good idea\ninto future studies with existing models in the form of online websites or as an additional\nfunctional module.\nLine 313-314: This is an important sentence with policy implications.\nResponse/action: Thank you for your confirmation of our perception. We will continue to\nemphasize policy implications in our future investigations.\nFig 5A: What are the units? Please provide this information in the caption.\nResponse/action: The reviewer’s suggestions are well taken. In the revised manuscript, the\nunits of Fig 5A have been added.\n4 / 5\nReviewer #3 (Remarks on code availability):\nThere is no readme that I could find and I did not try to install and run the code. It was not\nclear how to do so.\nResponse/action: The reviewer’s points are well taken. The original code is uploaded to\nGithub website (https://github.com/JePhyllis/MICP_Model_v1.0). The reviewers can\ndownload the entire model from the website and follow the instructions for model\nreproduction. The code package contains a readme file regarding step-by-step environment\nestablishment, model simulation, and operation details.\n5 / 5\nREVIEWERS' COMMENTS\nReviewer #3 (Remarks to the Author):\nThe authors have safisfied my remaining concerns and I have no further comments on the manuscript.\nReviewer #3 (Remarks on code availability):\nThe authors have now provided clear instrucfions how to download and run their model code."}]

Decision letter