Version 4.1.1 of the WRF-ARW atmospheric mesoscale model (https://github.com/wrf-model/WRF/releases, last access: 14 March 2020) was used in this study for ensemble hindcasting. A region slightly larger than the Baltic Sea was used with a horizontal resolution of about 0.063∘, and output was written every 5 min. Vertically, 89 pressure levels were applied up to 50 hPa, corresponding to levels 2 to 90 in the ERA5 reanalysis . Initial and lateral boundary conditions originated from the ERA5 reanalysis. tested different ensemble generation strategies with WRF-ARW driven by ERA5 and compared the outcome with the uncertainty measure provided by the ERA5 reanalysis. As demonstrated in , stochastic perturbations, namely stochastically perturbed parameterization tendencies SPPT; and stochastic kinetic energy backscatter SKEB;, were used here to produce a small ensemble of 30 members to study the impact of the uncertainty in the atmospheric forcing on the transport patterns, which includes random perturbations of the lateral boundary conditions . Instead of validating the atmospheric data against observations, the wind data were validated indirectly by the wave model output. A visual comparison of the WRF-ARW wind fields against UERRA/HARMONIE-v1 and ERA5 data can be found in .

Sources of uncertainty in atmospheric model predictions originate from the initial conditions and from the model physics; for a regional model, they also originate from lateral boundary conditions. compared different ensemble generation methods and proposed the use of the ERA5 data from the Ensemble of Data Assimilations as initial conditions to allow for a spread from the start of the simulation. The initial conditions in the presented study are based on the high-resolution ERA5 reanalysis, and the model approach includes perturbations of the model physics and the lateral boundary conditions. In contrast, the desired spread needs to develop in the model ensemble in the method chosen here. We selected this method to keep our results comparable with a potential future application in forecast mode. While we ran the model for a storm event in the past, the same could be done for a predicted storm, possibly based on a deterministic forecast product.

Wave-induced bottom shear stress is an important driver for the resuspension of bottom sediments and, potentially, of high-density MPs on the seafloor, as investigated in this study. To be able to prescribe wave parameters at high spatial and temporal resolution, the WAVEWATCH III v6.07^® (https://github.com/NOAA-EMC/WW3 third-generation spectral wind wave model, last access: 14 March 2020) was applied in a three-level one-way nested configuration. The model domain with the highest resolution is based on the same grid as in the GETM model . Dissipation and wind input were based on the formulation of , and the SHOWEX bottom friction scheme was applied following . For the latter, a map of the D50 (median diameter of the particle size distribution) sediment grain size was prescribed based on the European Marine Observation and Data Network (EMODnet; http://www.emodnet-geology.eu/, last access: 14 March 2020) data. The wave spectrum was discretized in the same way as in the ERA5 reanalysis: 24 directions starting at 7.5∘ with a 15∘ direction increment, and 30 frequencies starting at 0.03453 Hz geometrically distributed with a step of 1.1. A set-up with a 0.1∘ resolution covering the North Sea and a small part of the eastern Atlantic Ocean was used to produce boundary conditions for the Baltic Sea set-up at the border with the North Sea. The 0.1∘ model was nested into a set-up for the Atlantic Ocean with a 0.5∘ resolution. The GEBCO_2014 Grid, version 20150318 (http://www.gebco.net, last access: 14 March 2020), was used as bathymetry for the Atlantic and North Sea set-ups. The Baltic Sea set-up had a resolution of 1 nautical mile with a bathymetry based on the work of . The 0.5∘ set-up is driven by ERA5 winds and the ERA5 sea ice cover fraction. For the 0.1∘ set-up, UERRA/HARMONIE-v1 winds and the ERA5 sea ice cover fraction were used because of their higher spatial resolution. The Baltic Sea set-up was driven by two data sets: the UERRA/HARMONIE-v1 wind for a reference simulation, and the wind produced with the WRF-ARW wind ensemble for the MP ensemble simulations. Sea ice was taken from the Ostia reanalysis (http://marine.copernicus.eu/services-portfolio/, last access: 29 November 2020). An obstruction grid based on the GSHHS (Global Self-consistent, Hierarchical, High-resolution Shorelines) coastline data set has been generated with the Gridgen software (https://github.com/NOAA-EMC/gridgen, last access: 14 March 2020) to take unresolved orography into account.

Observation data from buoys available from the Copernicus Marine Environment Monitoring Service (http://marine.copernicus.eu/services-portfolio/access-to-products/, last access: 14 March 2020) (CMEMS) were used for validation and calibration. A comparison with station data in Fig.  shows good agreement in the significant wave height as well as verification scores over January 2019 (Table ). The spread in the ensemble is visible at all stations and is expected to provoke differences in the bottom shear stress, leading to differences in the resuspension.

Waves affect the seafloor until a water depth of about half the wave length. The dominant wavelength in the Baltic Sea is between 20 and 70 m and can reach up to 130 m .

GETM General Estuarine Transport Model; is an ocean model specifically designed for the coastal ocean (see review by ). In the present study, GETM was applied to the Baltic Sea with the model set-up of , on the same 1 nautical mile grid as the innermost WAVEWATCH III^® nest. The model domain is shown in Fig. . The original set-up was extended by coupling it to FABM Framework for Aquatic Biogeochemical Models; in order to consider sediment and MP. For an accurate 3-D transport of these quantities, GETM provides high-order advection schemes with reduced spurious mixing , a state-of-the-art second-moment turbulence closure for vertical mixing from GOTM General Ocean Turbulence Model;, and flow-dependent lateral mixing . Numerical mixing leads to an unrealistically high diffusion of transported concentrations, reducing the peak concentrations and overestimating the area in which tracers spread. The accuracy of the model is further increased by adaptive vertical coordinates that guarantee an optimal vertical mesh aligned to the dynamic boundary layers and to the stratified interior . Air–sea fluxes were calculated from the meteorological data provided by the atmospheric model according to the bulk formulas of . Based on the data provided by the wave model, GETM calculated the mean and maximum combined wave- and current-induced bed stress during a wave cycle. The latter was used in FABM for the erosion of sediment and MPs from the bottom pool (see Sect. 2.4). A realistic initial state as the starting condition for the hydrodynamical model was obtained by prolonging the simulations from with the UERRA/HARMONIE-v1 atmospheric data set. Further details about open boundary conditions and river discharge can be found in .

A detailed validation of the model set-up can be found in and . For demonstration purposes, only the spread in sea surface elevation due to the different atmospheric forcing sets is shown here (Fig. ). A verification of the water level at different stations from EMODnet (https://www.emodnet-physics.eu/, last access: 14 March 2020) showed satisfactory performance for both forcing data sets (WRF-ARW and UERRA/HARMONIE-v1). A large spread is also visible in the water level, especially at the peak of the surge.

The ensemble generation in the GETM model in this study is only based on the ensemble hindcasts of the atmospheric and wave parameters driving the model runs. showed that stochastic perturbations in the ocean model are also important for uncertainty estimation. The uncertainty in the ocean currents could therefore be underestimated.

In GETM and FABM, sediment and MPs are represented as Eulerian concentration fields. GETM simulated the 3-D transport of the pelagic concentrations, whereas the FABM model calculated the interaction with the corresponding bottom pools due to erosion and deposition and provided settling velocities to GETM. In FABM, a model for non-cohesive sediments see was used to calculate erosion, settling, and deposition of both sediment and MPs. The different transport was caused by the lower densities of MPs, which exceed that of the ambient water, i.e. we only considered sinking particles. This study focuses on model MPs with the sizes and densities reported by : 10 and 330 µm for both PVC with a density of 1275 kgm-3 and PET with a density of 1400 kgm-3. To study the impact of density and particle size on the uncertainty in the transport, additional densities of 1100, 1200, and 1300 kgm-3 and particle sizes of 200, 250, 300, and 350 µm were tested. As our main aim is to support measurement campaigns and larger particles are easier to sample, we focus our attention on particles above 300 µm.

The simulations in this study started from homogenous bottom pools of 1 kgm-2 as a purely hypothetical reference value as well as zero suspended material in the water column. Rivers and open boundaries were assumed to not import material into the model domain. MP transport in the model is affected by wave activity and different types of currents. Tidal currents are represented, but they only play a role in the Danish straits, as the interior of the Baltic Sea is non-tidal. Turbidity currents cannot be represented in our model, as the concentration of suspended matter has no influence on seawater density in the model. Thermohaline circulation, in contrast, is fully taken into account.

After a 2 d storm surge event, a rearrangement of particles could be observed in the model with some locations dominated by erosion and others by deposition. This can be seen by the change in the amount of MP stored in the bottom pool (PET and PVC with a diameter of 330 µm). To demonstrate the range of uncertainty in the transported amount of MP, two different grid cells in the Gotland Basin were selected (Fig. ): 57.69∘ N, 21.35∘ E (Fig. a–b) as a net erosion location, and 57.66∘ N, 21.32∘ E (Fig. c–d) as a net deposition location. Relative to the initial concentration, net erosion varied between 39 % and 72 % for PVC and between 16 % and 45 % for PET. Net accumulation varied between -13 % and 38 % for PVC and between 22 % and 34 % for PET. Thus, for PVC in the deposition grid cell (Fig. c), weak erosion is visible in some ensemble members, whereas the majority of the ensemble members show net deposition at this location. For the denser PET, the uncertainty range is smaller than for PVC, implying that its transport is less sensitive to uncertainties in the wind fields and more predictable. Still, the transported amount, even in this particle class, varies by around a factor of 2 between realizations, showing that a realistic quantitative estimation of MP transport is impossible in ocean circulation models, even if the precise sinking, settling, and resuspension properties of the MP particles were perfectly known.

Now we consider the spatial patterns where erosion and sedimentation take place. The spatial pattern in four selected ensemble members and the deterministic runs is shown in Fig. . We chose four members with a considerable spread in the simulated wave height (Fig. g). The overall spatial pattern is very similar between the different realizations. The main impact of the metocean uncertainty lies in the amount of the transported material. The perturbations of the atmospheric model also produce deviations in the track of the storm between ensemble members, which impacts the direction of ocean waves and currents and, in turn, the direction in which the bottom shear stresses are directed. These findings indicate that the bathymetry has a predominant impact on the region where erosion and deposition take place, as the locations are insensitive to changes in the track of the storm. For this specific storm surge event and selected region, net deposition took place on the south-western sides of ridges, and net erosion took place on the north-eastern sides. Model MP with a diameter of 330 µm in deeper regions, below 50 m, was completely unaffected. It is well known that water depth plays a major role in sediment erosion by waves, as deep-water waves (with wavelengths much shorter than the water depth) show an exponential attenuation in their velocity amplitude with depth e.g.. Our findings suggest that this causes stability in the spatial patterns of MP transport against changes in the wind forcing and makes the areas where erosion and deposition take place during a specific storm event predictable.

The uncertainty ranges of the spatial pattern of the model results were further investigated by means of the ensemble statistics composed of the mean, minimum, and maximum of each individual grid cell of all ensemble members (Fig. ). The net effect – whether the location was characterized by deposition or erosion – appeared largely consistent for the entire uncertainty range. Only a few locations showed deviations from this finding where some ensemble members shifted between weak erosional and depositional net effects. The larger extent of the erosional areas was due to more severe representations of the storm event in some ensemble members. Overall, these findings suggest stability in spatial patterns of MP transport against changes in the wind forcing. Areas of erosion and deposition during a specific storm event are predictable.

Next, we investigate the effect of particle size on the uncertainty in the transport by reducing the size of the particles to 10 µm. The small PET particles show a net erosion across almost the whole model domain due to slower resettlement. That is, they are still found in the water column up to 1.5 d after the storm (at the end of the simulation). This partly explains the large difference between the ensemble minimum and maximum (Fig. b, c): When sedimentation takes longer, quantitative differences in erosion strength will result in larger transport deviations, as the material can be advected further. This finding is also supported by theory on sediment transport: smaller particles (if unconsolidated) are suspended under lower shear stress levels and also require calmer metocean conditions to deposit. Thus, the uncertainty in MP transport appears to strongly depend on the particle diameter and density.

To find out whether this is a systematic effect, the uncertainties in the amount of transported material dependent on the particle properties size and density were investigated in more detail. These relationships were studied based on sensitivity runs with 30 ensemble members for (1) PVC with grain sizes of 200, 250, 300, and 350 µm as well as (2) 330 µm MP with different densities of 1100, 1200, 1300, and 1400 kgm-3 (Fig. a, b). The seafloor concentrations at the end of the model run deviate between the ensemble members. Relative deviations from the ensemble mean were calculated. Figure c and d show that the relative uncertainty increases with decreasing density and/or particle diameter, with the exception of the 1100 µm MP class, which shows a smaller uncertainty as it is almost completely resuspended at the chosen location. We conclude that the uncertainty in the amount of transported material on the seafloor at a specific time depends strongly on the properties of the transported material. Thus, the application of an ensemble approach (using more than one model realization to predict transport pathways) is especially important if finer and lighter material is to be represented in future model applications.

In the following, the mechanism by which the atmospheric uncertainty affects the MP transport is identified. In our model, this can be caused (a) by influencing the wave height, which changes the bottom shear stress and, therefore, MP mobilization, or (b) by directly affecting the ocean circulation through factors such as momentum input, thereby influencing both mobilization and transport. We focused on these two major pathways and attempted to distinguish their influence. The possibility of interlinkage by wave–current interaction is neglected in the present model cascade. To estimate the respective uncertainties of MP transport of the two above-mentioned pathways, an ensemble driven with the wave data from the unperturbed WRF-ARW run with the perturbed WRF-ARW atmospheric forcing and vice versa (with perturbed wave data and unperturbed atmospheric data) has been conducted. By comparing (Fig. ) the outcome with the original ensemble, where both perturbed atmospheric and wave data were used, it can be seen that the impact of the wave field depends on the properties of the transported material. The lighter or smaller the MP, the more important the impact of the wave uncertainty on the amount of transported material. For denser and larger MP, the uncertainty in the direct effect of atmospheric uncertainty on hydrodynamics is predominant.

Higher-density MPs of about 300 µm diameter were only transported under severe storm conditions, as demonstrated in Fig. . The continuation of the simulation for the rest of January 2019 caused almost no further erosion or deposition. This confirms the assumption regarding the importance of extreme events for MP transport, which complicates its direct empirical determination. Budget methods will be required to empirically determine quantities of transported MP. A budget method relates (a) the input and (b) the output of a quantity to (c) changes in its mass, e.g. inside an area of interest. If two of the three values are known, the third one can be determined. That is, transport rates might be more reliably derived from observed amounts before and after storm events than by multiplying abundances of suspended MP by instantaneous volume transports, both of which might show strong temporal variation during extreme weather conditions.

The finding that spatial patterns of MP can be reliably predicted by ocean models, while the quantitative estimation of MP is prone to considerable uncertainties shows that additional approaches are required for a more reliable estimation of large-scale MP concentration levels. Here, the recently found MP–sediment proxy postulated by , which is based on correlations between certain high-density polymer size fractions (> 1000 kgm-3, > 500 µm) and sediment grain size fractions, would be an achievable method. Estimations of MP levels can be based on a relatively small in situ data set and extrapolated to larger spatial scales by using the MP–sediment correlates. Lower densities of MP (1000–1600 kgm-3) compared with sediments (quartz: 2650 kgm-3) are offset by a larger size. This relationship was explained by comparable threshold bed shear stresses (and thus erosion rates) between these size fractions, which appeared to be the predominant mechanism determining the sorting in the described study area (Warnow Estuary, Baltic Sea, Germany; ). Although the MP size ranges covered in the present study were below those investigated by , it is assumed that similar patterns can be found for smaller size ranges. Indeed, in the present study, after the storm surge event, model PVC with a diameter of 330 µm co-occurred with 64 µm sediment grains, as apparent by the high correlation coefficient shown in Fig. . This correlation is found to be largely explained by similar erosion rates (Fig. b), whereas bottom concentrations, predominantly determined by deposition, are also influenced by the settling velocity of particles and, thus, differ slightly (higher amounts of PVC). Therefore, it is expected that areas largely influenced by the settling of MP show a larger difference in the expected MP–sediment size relation than described by the current MP–sediment proxy. For instance, larger (and/or heavier) MP particles than 330 µm PVC (such as PET) would be closer to the deposition rate of sediment grains of 64 µm (Fig. a). Existing maps of sediment substrate type, which typically differentiate between median grain sizes above and below 63 µm e.g., may therefore also provide information about the MP concentrations to be expected. However, as this investigation is purely based on our model results with the above-mentioned uncertainties, in situ measurements are inevitable to further research the influences on this MP–sediment proxy.