Wave conditions were observed near Tvärminne research station in March and April 2017 using two Datawell Directional Waverider buoys: a larger 90 cm Mk-III at 24 m depth (outer archipelago) and a smaller 40 cm DWR-G4 at 17 m depth (inner archipelago) . Both buoys were located about 3 km east of the Tvärminne research station (Fig. ).

Both wave buoys sampled at a frequency of 1.28 Hz and calculated the wave spectrum up to 0.58 Hz. Low-frequency data below 0.05 Hz were discarded when calculating wave parameters. These observations were used to validate the numerical wave model.

The SWAN model is a spectral wave model that was developed especially for shallow water and nearshore simulations. We implemented SWAN for 1 August–30 September 2014 to catch the spatially extensive sediment measurement campaign , for 1 May–30 November 2015 to cover the temporally extensive sediment measurement campaign , and 1 March–30 April 2017 to cover the period of the wave measurements (for validation purposes). Simulations were forced by data from a numerical FMI-HIRLAM weather prediction system e.g., where the wind speed and direction had been processed to a height of 10 m. The wind data had a spatial resolution of roughly 7.4 km, and a 1 h temporal resolution for the years 2014, 2015, and 3 h for 2017.

The model was implemented to a 0.01 nmi (∼ 20 m) regular grid with lateral boundary conditions taken from a 1 nmi Baltic Sea wide SWAN simulation using the same wind forcing. A 0.01 nmi resolution is finer than what is typically used in wave models, but SWAN has been implemented on a similar resolution before in the Baltic Sea . Another spectral model has also been implemented on the North-American coast with an adaptive resolution as fine as 10 m . The available bathymetric data has been composed of data from nautical charts and the VELMU depth model (https://ckan.ymparisto.fi/dataset/velmu-syvyysmalli, last access: 29 June 2026) by the Finnish Environment Institute (SYKE) and had a resolution of 0.1 nmi. The land–sea mask has been rasterized based on a polygon dataset from SYKE (https://ckan.ymparisto.fi/dataset/ranta10-rantaviiva-1-10-000, last access: 22 June 2026) and was available at a 0.01 nmi resolution. Land points were edited to wet points in the 0.1 nmi bathymetrical grid using the surrounding depth information. Additional depth information from , , and field sampling were used. The final 0.1 nmi grid was bi-linearly interpolated to a resolution of 0.01 nmi and the land-sea mask was applied (Fig. ).

The wave model produced direct hourly gridded estimates of the maximum near-bottom orbital velocity, Ubot (m s⁻¹), and the near-bottom mean periods, Tmbot (s). The near-bottom amplitudes, abot (m), were determined directly by the velocity and period estimates. For a full definition of the wave parameters, see Appendix A.

During the simulation periods, the modelled prevailing wave direction at the outer wave buoy was around 225°, and all waves with a height of 2 m or over came from direction between 175 and 225°. The highest significant wave height of 2.9 m was during a wave event from 195° with mean wave periods (Tm01) up to 5.8 s. The simulation period also captured high waves (up to 1.7 m) from the east (95°), although these were less frequent. This distribution aligns with the dominant directions observed in the Gulf of Finland . Statistics of the modelled near-bottom velocities can be found in Appendix B.

We validated the modelled near-bottom orbital velocities and wave periods by determining them from the measured wave spectrum using the same water depth as in the bathymetrical grid used in SWAN. Near-bottom velocities were modelled accurately at both locations (Fig. a, c) with the more exposed outer location showing a -0.04 cm s⁻¹ bias and 0.47 cm s⁻¹ root-mean-square-error (RMSE). The slightly shallower inner location had a 0.08 cm s⁻¹ bias and 0.49 cm s⁻¹ RMSE. Modelled near-bottom periods (Fig. b, d) agreed well at the inner location with a 0.12 s bias and 0.88 s RMSE. For the outer location, bias was 2.23 s and RMSE 3.31 s, reflecting deeper water where wave orbital motions do not reach the bottom and the period is determined by low-frequency noise in the measurements. As seen in Fig. b, near-bottom periods were well modelled during high near-bottom velocities, but less defined under calm conditions. The validation of bulk surface wave parameters showing the temporal dynamics and scatter are shown on Figs. and in Appendix C.

The wave model SWAN has been extensively used and verified in the Baltic Sea. In the open sea areas, the accuracy of the model was found good e.g.. Closer to the shore, and especially in the archipelago in the northern parts of the Baltic Sea, the accuracy of the numerical wave models depends on the grid size, reflecting the capability of the model to resolve smaller islands and variable bottom topography that influence the wave energy dissipation e.g.. A detailed analysis of the performance of three different numerical wave models, including SWAN, in the archipelago off Helsinki in the Gulf of Finland showed that the models on 0.1 nmi grid resolution are capable of simulating the wave field with good accuracy . In the present study, our grid resolution is 20 m, and the islands and bottom topography are well resolved as the comparison with measurements show (Appendix C and Fig. ). The validation period in 2017 did not include the highest sea states during the study periods in 2014 and 2015, but according to the studies mentioned above, also the high wind events can be expected to be reasonably well simulated.

The near-bottom shear stress was computed as e.g.: 1τw=0.5ρwfwUbot2, where ρw=1003 kg m⁻³ is the water density and fw is the wave friction coefficient. The friction coefficient was determined following as the larger of the rough and smooth bottom estimates: 2fw=max⁡{fwr,fws}, where 3fwr=0.237r-0.52, is the rough bottom friction coefficient, r=abot/ks, ks=2.5d50 is the Nikuradse equivalent sand grain roughness, and 4fws=BRw-N is the smooth bottom friction coefficient. Here Rw=Ubotabot/ν is the Reynolds number, ν is the kinematic viscosity of water (1.3×10-6 m² s⁻¹), abot is the amplitude of the wave-induced near-bottom velocities (see Appendix A for a definition), and B and N are constants that depend on the Reynolds number such that: 5B=2,N=0.5forRw≤5×105(laminar)6B=0.0521,N=0.187forRw>5×105(turbulent)

Environmental data and critical shear stress measurements were available from two field campaigns conducted in the years 2014 and 2015 in the Hanko archipelago. In 2014, samples were gathered from 16 shallow sites (depth < 4 m), covering a sedimentary gradient from mud to sand (median grain sizes 21–570 µm). These sampling locations are illustrated in Fig. . The 2014 field campaign focused on spatial variation in sediment erodibility, maximizing variation in sediment surface characteristics (e.g. bedforms, biofilms) across sites. In 2015, three sites (mud (ID04), mixed (ID09), and sandy (ID14) sediment) from the 2014 study were re-sampled from April to December to capture temporal variation in sediment erodibility. In this campaign, variation in sediment characteristics was minimized to focus solely on temporal changes.

The sampling procedure was consistent across both campaigns. At each site, SCUBA divers collected samples by carefully inserting EROMES cores (10 cm diameter, 10 cm depth) into the sediment . Samples were maintained at in situ temperatures and transported to the laboratory for further measurements. A total of 59 and 73 EROMES cores were collected in 2014 and 2015, respectively. For a detailed description of the sampling procedures, see . The grain size, dry bulk density and chlorophyll a for each measurement site were determined from the combined 2014 and 2015 data as mean of monthly means (Table ).

In the 2014 and 2015 field campaigns , the critical shear stresses from the sediment samples were determined in the laboratory with a portable EROMES device . Bed shear stress on the sediment surface is generated by turbulent fluctuations induced by a propeller and baffle ring. The baffle ring prevents rotational flow and ensures turbulent flow fluctuations mimicking those observed by waves in nature. Suspended solids concentration was monitored with an OBS sensor (optical back-scattering sensor). The propeller revolutions were calibrated to nominal bed shear stresses .

At each run, the bed shear stress was increased every 2 min by 0.1 N m⁻² from 0 to 2.0 N m⁻² in the year 2014 study and from 0 to 1.6 N m⁻² in the year 2015 study. Water samples for gravimetric analysis were collected during each run to calibrate the OBS sensor into suspended solids concentration (SSC; mg L⁻¹) . The critical shear stress (N m⁻²) was defined at the erosion rate of 0.1 (g m⁻² s⁻¹), which describes the erosion after the erosion of unconsolidated “fluffy” material . For a more extensive description of the laboratory procedures, see .

Since the EROMES device is not reliable for large grain sizes, we excluded individual critical shear stress measurements when the median grain size of the sample exceeded 300 µm. Consequently, no reliable measurements were obtained from site ID10 (Table ).

We used EMODnet Seabed Substrates (1 : 100 000) to define seabed classes: Mud to muddy sand, Sand, Mixed sediments, Coarse sediments, and Boulders (see Fig. a). Coarse sediments and Boulders were excluded from this study, since we had no in situ data from those seabed types. For Mud, Sand, and Mixed sediments we determined representative median grain sizes for each seabed type based on the data from Sect. (Table ). The representative values were determined as means of monthly means to not give too much weight to data from the spatial campaign.

The critical shear stress is the threshold shear stress above which particle motion is initiated. The critical shear stress depends on the sea floor properties, and is given by 7τcr=θcr(ρs-ρw)gd50 where τcr (N m⁻²) is the critical shear stress, θcr is the threshold Shields parameter, g is the gravitational acceleration (9.82 m s⁻²), ρs is particle density (2650 kg m⁻³), ρw is the water density (1003 kg m⁻³) and d50 is median grain size (m) .

The parametrization of the Shields parameter, as improved by , reads: 8θcr=0.31+1.2D*+0.0551-exp⁡-0.02D* where D* is the dimensionless grain size calculated with 9D*=g(ρsρw-1)ν213d50.

The strength of this model is its simplicity, but we found it to result in estimates of the critical shear stress that were an order of magnitude too small compared to values determined in the laboratory from in situ samples (Fig. b).

developed predictive models for critical shear stress based on physical and biological characteristics in the Celtic Sea and North Sea. Their approach combined principal component analysis (PCA) and multiple linear regression, identifying key predictors such as median grain size, sorting, kurtosis, percentage of fines, bulk density, porosity, chlorophyll a, and organic carbon. Two models were proposed:

Model 1 (Celtic Sea): Included both physical and biological parameters, suggesting that bed stability increases with grain size, better sorting, and greater bulk density, while decreasing with greater proportions of fines and organic carbon.

These models were not applicable in our study for several reasons. First, we lacked key parameters such as grain sorting and kurtosis, and organic carbon content, which are essential for Model 1. Second, the model had a negative coefficient for dry bulk density despite Fig. 3 of showing a positive relationship between bulk density and bed stability. This negative coefficient combined with bulk densities being higher in our data compared to the dataset of , resulted in unphysical values of the critical shear stress. Finally, their models were calibrated for Celtic and North Sea conditions, which differ from our study area in water depth, sediment composition, hydrodynamic forcing, and shear stress history.

We constructed a parsimonious model that couples time-invariant physical factors – median grain size (d50, µm) and dry bulk density (ρB, g cm⁻³) – with a time-varying biological proxy, chlorophyll a (Chl a, µg g⁻¹). To fit the model we returned to the raw in situ measurements reported by . Since EROMES measurements are not reliable for very coarse sands, samples with d50>300 µm were excluded.

The final dataset used for the new regression model contained n = 108 individual observations covering the three sediment classes. The model was determined as a three variable least-squares fit using the individual samples from the raw data. In other words, the model predicts critical shear stress as: 10τcr=β0+β1d50+β2ρB+β3Chla where τcr is critical shear stress (N m⁻²), β0 is the intercept, d50 is median grain size (µm), ρB is dry bulk density (g cm⁻³), and Chl a is chlorophyll a (µg g⁻¹).

The fit made to each sediment class (Sand, Mud, Mixed sediments) separately had only modest predictive power, whereas the combined model (using all observations) explained a substantially larger portion of the variance (R2=0.659, p≤0.01) (Table , Fig. ). The RMSE of the full model was 0.31 N m⁻². Importantly, the combined fit captures the differences between the classes more efficiently than the class-specific models (Table ). Since the primary purpose of the model is to provide class-level critical shear stress estimates for application to the seabed classes (Sect. ), this ability of the model to reproduce the variation between classes is more relevant than its performance within individual classes.

We assessed collinearity among the predictors used in the combined model (n=108) by examining pairwise Pearson correlations and variance inflation factors (VIF) following the protocol of . The two physical variables were strongly correlated (R=0.86 between d50 and ρB), reflecting their expected co-variation in natural sediments, whereas Chl a showed only weak correlations with the physical variables (R=0.10 and R=0.34). VIF values indicated moderate collinearity for the physical variables (VIFd50=4.96, VIFρB=4.44) and low collinearity for Chl a (VIF = 1.33). Despite the moderate collinearity between the d50 and ρB, omitting either variable from the combined model reduced the explained variance R2, confirming that each physical variable contributes unique predictive information and should be retained.

Physical variables explained most of the variation in τcr, but including chlorophyll a increased the explained variance (R2) by approximately 0.1.

Our aim was not to build the most comprehensive model for the τcr but to define a practical model that can be combined with numerical wave model outputs. To use the modelled critical shear stresses with the spatio–temporal wave model data, we determined representative values of d50 and ρB for each of the three classes (Mud, Sand, and Mixed sediments), and monthly values of Chl a for each of the classes. The model is not applied to coarse sediments or boulders because representative values cannot be reliably determined from the available data.

The raw data from the in situ samples were therefore grouped according to the determined seabed classes: Mud={ID04,ID16}, Sand={ID02,ID05,ID06,ID07,ID10,ID11,ID14} and Mixed={ID01,ID03,ID09,ID15} (see Table ). For each site, monthly means were computed while retaining the year (e.g. 6–29 August 2014 and 25–27 August 2015 remain distinct) to avoid overweighting data from the spatial campaign. For d50 and ρB, class-level monthly means were computed and then averaged to obtain time-invariant values (Table ). For Chl a, temporal variability was retained by computing monthly means for each class. Months lacking measurements were filled with the off-season mean (September–April).

The physical variables (d50 and ρB) define the overall magnitude of the critical shear stress for each class, with Mud being lowest and Sand being highest (Fig. b). The variation caused by the monthly variations in Chl a is substantial (Table ), being up to 52 % of the mean value for Mixed sediments, and 29 % and 27 % for Sand and Mud, respectively. Nevertheless, the monthly variation never changes the ordering between the classes.

Modelled shear stresses were estimated based on the near-bottom velocities (Sect. ), the representative grain sizes (Sect. ), and the friction coefficients (Sect. ). The shear stresses were determined for every model time step from all available data (2014, 2015 and 2017). The in situ data doesn't contain samples from categories Boulders or Coarse sediments. Therefore, no representative grain sizes could be determined, and wave-induces near-bottom stresses could not be determined. Results are therefore only given for categories Mud, Sand and Mixed sediments, while the other areas are masked out.

Mean values were generally low, remaining below 1 N m⁻² across the entire area (Fig. a). The 95th percentiles ranged between 0.5 and 1 N m⁻² over extensive areas, especially where the seabed was classified as sand, and exceeded 1 N m⁻² in more exposed locations (Fig. b). The maximum near-bottom shear stress values (Fig. c) shows localised peaks exceeding 2 N m⁻² along several exposed areas of the coastline. These peaks occur mainly in areas classified as mud or muddy sand (compare Figs. and c), because these locations coincide with narrow wave-exposed channels and long fetch, where near-bottom orbital velocities are particularly high (see Fig. in Appendix B). Thus, although sandy areas tend to exhibit moderately larger shear stress values, the largest instantaneous maxima occur over mud bottoms due to local wave-bathymetry interactions rather than sediment type itself. The maximum values also indicate that the area directly south-west of the Tvärminne research station is well sheltered from waves, resulting in small wave-induced near-bottom shear stresses.

Modelled near-bottom shear stresses were compared to critical shear stresses to estimate erosion threshold exceedance probabilities. These probabilities reflects the likelihood that wave-induced shear stress exceeds the critical value, indicating potential sediment resuspension. Exceedance depends on wave conditions, depth, and seabed class. The critical shear stress was determined from the model in Sect. , and therefore varied monthly. Exceedance probabilities were determined simply from the fraction of times the modelled shear stress for a given time exceeded the modelled critical shear stress for the given class and month. The model is not applicable to categories Boulders and Coarse sediments, and those areas are therefore masked out.

Exceedance of the critical shear stress was generally low across the study area (Fig. ). Localized patches in the outer archipelago exhibited exceedance of up to 10 %, indicating that sediment mobilization mostly occurs during episodic high-energy events. These areas were not limited to the coastline but also appeared among groups of islands and islets located about 2–3 km from the shoreline where the water is shallow, and include narrow channels that concentrate wave energy. Sheltered nearshore areas remained below the threshold, suggesting stable sediments and minimal resuspension potential. Even during high-wind events, modeled wave-induced shear stresses rarely exceeded predicted or measured thresholds, indicating that sediment mobilization is episodic and limited to localized areas.

estimated the potential for wave-induced near-bottom velocities using the long-wave (7 s) wave heights from a ray-tracing model as a proxy. The results of were 10 % exceedance values. While they are able to identify some areas that might be vulnerable to higher wave-induced near-bottom velocities, the author noted that they are not a substitute for specifically modelling the near-bottom velocities. The use of wave heights as a proxy can naturally also not account for the variation in the seabed type or the temporal variation of the critical shear stress caused by changing biological activity, as done in this study.

Two late-November 2015 storms illustrate the impact of strong winds on wave forcing and initiation of sediment movement. On 28 November, south-westerly winds (19–20 m s⁻¹) generated significant wave heights of ∼ 3 m offshore and ∼ 2 m within the archipelago (Fig. a). Near-bottom orbital velocities reached 0.5 m s⁻¹ along exposed coastlines (Fig. b), producing localized shear stresses exceeding 2 N m⁻² (Fig. c).

The 30 November event was more severe, with SSE winds of 23–25 m s⁻¹ (gusts up to 26 m s⁻¹) causing offshore wave heights exceeding 4 m and near-bottom velocities approaching 1 m s⁻¹ in shallow exposed areas (Fig. b). Shear stresses surpassed 2 N m⁻² across extensive outer archipelago areas, conditions sufficient to mobilize coarse sediments (Fig. c).

While the strongest shear stresses were mostly concentrated to the same areas in both cases, the areas with sand bottom in the western part of the area were more exposed during the SSE winds on 30 November. These two examples represent typical cases of higher waves propagating towards the shore, with south-westerly winds being the most dominant in the area. Together these two events demonstrate that sediment mobilization is highly episodic, concentrated in exposed shallow areas and constricted channels, with implications for turbidity, nutrient fluxes, and benthic habitats.