Physical Drivers of Salinity in a Southern Baltic Coastal Lagoon: A Selective Modeling Approach

Abstract

Coastal lagoons provide vital ecological functions, supporting diverse flora and fauna while being highly sensitive to environmental changes. In the southern Baltic Sea, the Puck Lagoon is a hydrologically distinct subregion of the Gulf of Gdańsk characterized by variable exchange of water with the outer bay and substantial freshwater inflows. Its benthic communities are particularly sensitive to salinity, yet the processes shaping this parameter remain insufficiently understood. In situ measurements in summer 2020 revealed relatively high salinity in the lagoon (up to 7.7 PSU) compared to the adjacent outer bay (7.2–7.4 PSU), with localized reductions near the Kuźnica Passage and the Reda River mouth. As a first step toward explaining the hydrodynamic processes responsible for these anomalies, we applied a high-resolution, two-dimensional model focused on three fundamental physical drivers: river inflows, open-boundary exchange, and wind forcing. These processes represent the primary controls on salinity in shallow lagoons and provide a basis for evaluating additional mechanisms. The model reproduced observed patterns with a mean absolute error of 0.15 PSU, confirming that this selective framework captures the key features of salinity variability and establishes a baseline for future three-dimensional modeling that will incorporate further processes such as vertical mixing, precipitation, and evaporation.

1. Introduction

Coastal lagoons are shallow water bodies, often separated from the sea by sandbanks or barrier islands, with salinity levels ranging from brackish to hypersaline due to interactions between freshwater inflows, evaporation, and seawater exchange [1,2,3]. The Baltic Sea, which is one of the world’s largest brackish water bodies [4], has several lagoons on its southern coast, including the Vistula and Szczecin Lagoons [5,6] and the Darß-Zingst Bodden chain [7]. These systems are characterized by low salinity and limited tidal influence, creating distinct brackish environments primarily shaped by river discharge and wind-driven water exchange. Among them, the Puck Lagoon (the inner Puck Bay) is the smallest and can be classified as a leaky system [1] due to its seasonally modified water exchange with the outer Puck Bay through a wide-open boundary (Figure 1). Its unique hydrographic setting—in particular, the absence of tides—makes it an appropriate natural laboratory for investigating how individual physical drivers shape the hydrodynamics of the lagoon. Southern Baltic lagoons play an important ecological role by sustaining diverse biological communities. But at the same time, they are highly vulnerable to environmental pressures. Anthropogenic impacts are especially pronounced, driven by nutrient and pollutant inputs that alter ecological functioning [7,8,9]. Over recent decades, nutrient loads in these lagoons have increased markedly, leading to elevated trophic states [7].

Puck Bay is located on the southern coast of the Baltic Sea, in the southwestern part of the Gulf of Gdańsk (Figure 1). It is divided into an inner part (Puck Lagoon, also called Inner Puck Bay) and an outer part (Outer Puck Bay), which differ in bottom morphology and genesis [10,11]. As noted in [12,13], the two parts exhibit significant hydrological differences. Puck Lagoon receives water from more than 75% of the entire Puck Bay catchment, and the surrounding land is characterized by a denser river network. These factors, combined with restricted water exchange with the open sea, justify treating the Puck Lagoon as a distinct hydrological subregion.

The Puck Lagoon is an important area from a biological and ecological perspective. It supports a rich variety of benthic fauna and flora, including species rarely observed elsewhere along the southern Baltic coast. Key representatives include seagrass meadows, stoneworts [14,15], bivalves, and shrimps, which, together, form habitats of high ecological value. Due to this biodiversity, the lagoon is protected as part of the European Ecological Network Natura 2000 [16]. The biological diversity, along with specific hydrological conditions, makes the Puck Lagoon highly sensitive to variations in marine environmental parameters such as temperature and salinity.

The present study focuses on salinity, which is a fundamental physical property of seawater, and its spatial and temporal dynamics significantly influence the distribution of flora and fauna in coastal lagoons [7]. In addition, salinity is often used as an indicator for evaluating the accuracy of hydrodynamic models. Accurate reproduction of salinity patterns provides a basis for studying biogeochemical processes, including the dispersion of pollutants [17].

The salinity of the waters of Puck Bay is mainly influenced by the inflow of marine and freshwater sources, as well as the varying depths of the bay. The surface layer of the Gulf of Gdańsk, with a depth of approximately 50–60 m, is characterized by relatively uniform salinity. The depth of Puck Bay ensures that it is located within this surface layer, with only the deepest northeastern part of the bay near the bottom reaching the pycnocline. Outer Puck Bay is directly affected by saline waters flowing in from the Gdańsk Basin. Additionally, the inflow of freshwater from the Vistula River, particularly in the surface layer, plays a significant role. The hydrological conditions of Puck Lagoon are shaped by the inflow of water from the outer bay and freshwater input from three rivers and several streams. The shallow depths of the lagoon facilitate complete mixing throughout its entire volume. A distinct hydrological regime characterizes the transitional zone between Puck Lagoon and outer Puck Bay. At the interface between these water bodies, significant horizontal and vertical density gradients are observed, forming a frontal zone [18]. Compared with other processes in the Gulf of Gdańsk, the salinity of Puck Lagoon is less frequently discussed in the scientific literature. In recent years, research has, instead, focused on submarine groundwater discharge (SGD) in the outer bay [11,19,20], with studies showing its influence on the chemical composition of coastal waters [21]. Research on the impact of SGD rarely includes salinity measurements in the inner lagoon [19,20,22].

Results from the measurement campaign completed in June and August 2020 revealed unexpectedly high salinity in the inner bay during summer, reaching 7.5 PSU, compared to 7.3 PSU in the outer part of the bay. Building on this dataset, monitoring has continued since 2021 to provide a broader temporal perspective. Preliminary analyses suggest that the tendency toward higher salinity in the inner bay persists, but results have not yet been formally published and will be addressed in future work. These findings are supported by the analysis of diatoms from Puck Lagoon sediments by Hetko et al. [23], who identified species preferring higher salinity conditions, particularly in the northern part of the basin. Such differences in salinity between the inner and outer parts of Puck Bay were not reported in previous studies on the salinity of the entire bay [18]. This suggests that Puck Lagoon exhibits higher salinity than outer Puck Bay, which may affect the composition of phytoplankton species [21,23].

Understanding the salinity distribution in Puck Bay is crucial for characterizing its hydrodynamic regime, including current circulation and water mass exchange. However, as in many other coastal systems, these processes remain insufficiently understood [3]. In Puck Bay, resolving hydrodynamic processes is particularly important in terms of interpreting chemical fluxes and ecological conditions. While in situ measurements provide valuable information, they are inherently limited in space and time. Numerical modeling allows for reconstruction of salinity variability at higher spatial and temporal resolution. Such models are particularly important for examining hydrodynamic drivers and predicting ecological responses.

Although numerical models exist for the entire Baltic Sea or the Gulf of Gdańsk [24,25,26,27], their spatial resolution is insufficient to capture the detailed salinity variations and underlying processes in Puck Bay. Currently, the only openly available model specifically developed for this area is the WaterPUCK model [28]. However, as discussed in Section 4, its salinity predictions deviate significantly from in situ measurements.

In this study, we develop a dedicated high-resolution model for Puck Lagoon, designed to reproduce the observed anomalies in salinity and provide insight into the underlying physical processes. Following a selective modeling strategy, the model includes a limited set of dominant physical drivers—riverine inflows, open-boundary exchange, and wind forcing—while secondary processes such as precipitation, evaporation, and vertical mixing are neglected. This approach emphasizes process attribution rather than full system complexity, allowing us to assess the importance of the main mechanisms shaping salinity patterns. Such a conceptual model improves understanding of basic lagoon hydrodynamics, while future extensions will allow for examination of additional factors. The performance of the model is evaluated against in situ measurements.

This paper is organized as follows: In Section 2, we describe the model’s construction, highlighting the underlying assumptions. Section 3 presents the current flow and salinity field results for summer 2020. A detailed discussion, including validation against in situ measurements, is provided in Section 4. Finally, Section 5 summarizes our findings and outlines potential directions for further model development.

2. Materials and Methods

2.1. Study Site

Puck Bay is located on the southern coast of the Baltic Sea, in the southwestern part of the Gulf of Gdańsk. To the north, it is separated from the open sea by a sandy barrier—the Hel Peninsula—while to the southeast, it borders the waters of the Gulf of Gdańsk [29]. This relatively small water body accounts for slightly more than 1% of the total area of the Gulf of Gdańsk, with an average depth of 15.5 m [10]. Based on its morphology and formation process, Puck Bay is divided into an outer and an inner part. Outer Puck Bay, of post-glacial marine origin, reaches a maximum depth of 58 m near the tip of the Hel Peninsula, with an average depth of 20.5 m [10]. In contrast, the inner part of Puck Bay (Puck Lagoon) is significantly shallower, with its formation linked to terrestrial influences. The maximum depth of Puck Lagoon is 9.7 m, while the average depth is only 3.13 m, approximately seven times shallower than the Outer Puck Bay [10] (see Figure 2).

The boundary between the outer and inner parts of Puck Bay is defined by Seagull Sandbar to the north and Rewa Cape to the south. Seagull Sandbar is a sandy bar approximately 12 km in length. This barrier renders Puck Lagoon almost a closed water body, with water exchange occurring through two straits: Głębinka and Kuźnica Passage. The average depth of Głębinka is 3–4 m, with a width of 2 km, while the average depth of Kuźnica Passage is 0.6 m, with a width of approximately 1 km [30,31]. The main structural features of Puck Lagoon include the Puck Basin and the Kuźnica Basin. Between these two basins, sandy nearshore bars—namely, the Western Sands and Virgin Sands—are present. Another distinctive feature of the inner structure of Puck Bay is the presence of several depressions. One of these, the Rzucewo Hollow, is located in the southern part of the bay, with a maximum depth of 5.8 m. Two additional pits, the Kuźnica Hollow and the Chałupy Hollow, are situated within the Kuźnica Basin, with maximum depths of 9.7 m and 4.0 m, respectively [10,30,31] (see Figure 3).

One of the characteristic features of the hydrodynamics in the study area is the seasonal variation of water level, which affects water depth around the Seagull Sandbar. During periods of low water levels, the sandbar becomes partially exposed, resulting in a significant decrease in water depths. This seasonal phenomenon plays an important role in regulating water exchange between Inner and Outer Puck Bay. Historical estimates from the 1990s indicate that Seagull Sandbar becomes fully submerged during spring and summer at a sea level of 520 cm in Puck Bay accordign to the Kronstadt datum, corresponding to approximately 533 cm in the Amsterdam datum [30,31].

The first water balance of Puck Bay was developed by Cyberski and Szefler [13], who highlighted significant hydrological differences between the inner and outer parts of the bay. In Outer Puck Bay, precipitation and evaporation (vertical exchange) are several times greater than horizontal exchange, which includes freshwater inflow from the catchment and net water exchange between the two sections of the bay. In contrast, in Inner Puck Bay, horizontal exchange is three times greater than vertical exchange. The water balance for the entirety of Puck Bay, initially established by Cyberski and Szefler [13] and later updated using more recent data by Chlost and Cieśliński [32], confirms the predominance of horizontal exchange over vertical exchange.

2.2. In Situ Measured Salinity in Puck Lagoon

The salinity measurements used for calibration and validation of the model were conducted during two research cruises in the summer of 2020 in Puck Lagoon. For this purpose, a measurement grid consisting of 23 stations (labeled Z1–Z23) was established, with points spaced approximately 2 km apart in both meridional and zonal directions within the bay. The depths at these stations ranged from 0.9 m in shallow areas (Virgin Sands) to 7.5 m in depressions (Kuźnica Hollow).

The research expeditions took place on 24–25 June 2020 and 30 August 2020, with data collection carried out from the workboat of the R/V Oceanograf. The salinity data from June 2020 were collected over two days: on 24 June in the afternoon at stations Z1–Z17 and on 25 June in the morning at stations Z18–Z23. The August salinity data were obtained from 20 stations, with measurements conducted in the morning, excluding stations Z1 and Z2 due to ongoing regattas, and in the afternoon, excluding station Z6 due to technical issues. The locations of the measurement stations are presented in Figure 4.

Measurements of the physical parameters of the water were performed using an automatic RBRconcerto CTD (Conductivity–Temperature–Depth) probe (RBR Ltd., Ottawa, ON, Canada). This device directly measures specific conductivity, water temperature, and variations in total pressure within the water column, including atmospheric pressure. The determination of hydrostatic pressure is based on the measurement of total pressure, which encompasses both hydrostatic and atmospheric components. To calculate the hydrostatic pressure, a predefined atmospheric pressure value—which the submerged sensor cannot measure directly—is subtracted from the total pressure measurement. The initial accuracy of conductivity is ±0.003 [mS/cm], temperature is ±0.002 °C, and pressure is ±0.05 [% full scale]. The resolution of conductivity is 0.0001 [mS/cm], temperature is 0.00005 °C, and pressure is <0.001 [% full scale]. The reported accuracy values correspond to the manufacturer’s specifications for the RBRconcerto CTD probe [33] and represent nominal instrument performance rather than uncertainties estimated from our dataset. Based on these parameters, water salinity, expressed in practical salinity units (PSU), was determined using a standard algorithm [34]. The seawater conductivity, temperature, and pressure were recorded from the sea surface to the bottom at intervals of approximately 0.3 m.

In Puck Lagoon, due to the shallow depths, water can mix effectively throughout the water column, and consequently, the vertical variability of salinity is expected to be small [28]. Indeed, our analysis of the measurement data collected at the stations confirms that, in most cases, salinity profiles exhibit insignificant variation with depth. The results shown in Figure 4 and Figure 5 correspond to measurement campaigns conducted in June and August, 2020. Based on their vertical salinity profiles, the stations were categorized into two groups: (I) those with approximately constant salinity and (II) those with salinity varying with depth. As can be seen, salinity remains nearly constant with depth in the northern, central, and western parts of Puck Lagoon in both cases (except at station Z7. where a slight increase from 7.2 to 7.4 PSU was observed in June). Some variations in vertical structure were observed in the southern part of the bay, which is influenced by freshwater inflow from the Reda River. However, even at the station with the highest observed vertical salinity variability, the range of measured values (maximum minus minimum) did not exceed 9% of the vertically averaged value, and the standard deviation relative to the average was 4%. Therefore, the average salinity value throughout the water column is considered a reasonable approximation for studying horizontal variation, and it is justified to use vertically averaged profiles for 2D model validation.

The point maps of vertically averaged salinity values for June and August 2020 are presented in Figure 6 and Figure 7, respectively. In both cases, lower salinity values were recorded in the southern part of Puck Lagoon, where mixing with freshwater from the Reda River occurs. However, the lowest salinity was not observed at the station closest to the river mouth (z22) but farther away, near Rewa Cape and Głębinka Passage (z23). This offset can be explained by wind-driven transport: during the June 2020 campaign, south-easterly winds displaced the river plume towards the shore, causing the freshest water to bypass station z22 and accumulate in the vicinity of station z23. Such lateral plume displacement highlights the importance of local meteorological conditions in shaping observed salinity distributions. In June, salinity measured 7.320 PSU at z22, compared to 6.984 PSU at z23, while in August, a value of 7.396 PSU was obtained at z22, compared to 6.740 PSU at z23. The highest salinity was recorded in the northern, eastern, and western parts of the bay, with peak values of 7.512 PSU at z6 in June and 7.614 PSU at z3 in August. A comparison of the salinity distribution in June and August reveals a similar pattern, except at coastal stations in the northwestern bay (z7, z12), where a decrease in salinity is observed in the June measurements.

2.3. Wind Field Characteristics and Spatial Variability

The characteristics of the wind field were analyzed based on the ERA5 reanalysis dataset [35], which provides mesoscale resolution suitable for assessing spatial variability. We examined 915 wind fields between 1 November 2019 and 31 August 2020, using data from 12 grid points within the study area. The chosen period corresponds to the temporal scope of the modeling experiment. For each hourly time step, wind components (u, v) at 10 m height were extracted at the 12 locations. A mean wind vector was calculated by averaging u and v across all sites, and wind speed and direction were derived from these components. The root mean square (RMS) deviation of wind speed quantifies the spread of speeds relative to the mean speed. The vector RMS deviation was defined as the root mean square of the Euclidean distance between each vector and the mean, providing a measure of overall dispersion in the u–v plane.

The most frequently observed mean wind speeds were 5.5, 5.0, and 6.5 m/s, with dominant directions from the W, WSW, and SW sectors, consistent with the prevailing westerly regime (

Table 1. Summary statistics of the wind field based on ERA5 12 grid points.

Parameter	Value
Number of analyzed fields	915
Time range	1 Noverber 2019 to 31 August 2020
Number of ERA5 grid points	12
Most frequent mean wind speeds (m/s)
5.5 m/s	71 occurrences
5.0 m/s	65 occurrences
6.5 m/s	61 occurrences
Most frequent wind directions
W (west)	118 occurrences
WSW (west-southwest)	109 occurrences
SW (southwest)	99 occurrences
Spatial variability (mean)
RMS of speed	0.85 m/s (14.8%)
RMS of vector	1.08 m/s (19.9%)

). The average spatial variability across the domain, expressed as RMS differences between sites, was 0.85 m/s for speed (14.8% of the mean) and 1.08 m/s for vector differences (19.9%). The highest relative variability was typically observed during calm conditions (mean speed < 2 m/s), where even small absolute differences produced high percentage variability. In contrast, under stronger wind conditions, the relative spatial variability was notably lower.

To identify representative wind field situations for visualization, we selected two categories of wind fields according to spatial variability (

Table 2. Summary of selected wind field situations.

Type of Variability	Time	Mean Speed	Direction	RMS Speed	RMS Vector
			[m/s]	[m/s]	[m/s]
Dominant RMS speed	6 November 2019	5.34	273° (W)	0.88 (16.5%)	1.65 (30.8%)
Dominant RMS vector	11 November 2019	5.41	281° (W)	0.83 (15.3%)	1.03 (19.1%)
Extreme case	10 December 2019	10.08	301° (WNW)	2.04 (20.2%)	5.15 (51.1%)
Extreme case	21 February 2020	9.72	268° (W)	1.25 (12.9%)	4.11 (42.3%)
Extreme case	14 November 2019	6.27	293° (WNW)	2.17 (34.7%)	3.57 (57.0%)
Extreme case	16 July 2020	3.97	169° (S)	1.70 (42.8%)	3.27 (82.2%)

):

• Dominant spatial variability (typical cases). These were identified by rounding RMS speed and RMS vector values to the nearest 0.1 m/s and selecting the modal value across the dataset. One example was chosen for each metric to represent the most frequently occurring variability levels.
• Extreme spatial variability (extreme cases). To identify rare but high-variability conditions, the dataset was sorted by RMS vector magnitude, and the four highest values were selected. These represent periods of the strongest spatial variability in the wind field.

The selected wind situations are illustrated in Figure 8: two typical cases corresponding to the modal RMS values for speed and vector and four extreme cases with the highest RMS vector magnitudes. Wind vectors are shown at the 12 grid points, with annotations indicating date, mean speed and direction, and associated variability values.

Although ERA5 provides reanalysis-based observations rather than direct observations, its temporal stability and regional resolution make it appropriate for evaluating wind patterns and variability. For this study, ERA5 provides sufficient accuracy. The relatively low average spatial variability—vector RMS differences typically below 20% of the mean speed—supports approximating the wind field as spatially homogeneous. This simplification is justified for applications where fine-scale wind variability is not a dominant factor.

2.4. Model

To model the salinity field, one has to solve the Reynolds-Averaged Navier–Stokes (RANS) equations governing the dynamics of any water system, which are expressed as follows:

$$\rho {\displaystyle \frac{D\overrightarrow{v}}{Dt}}=-\nabla \mathrm{p}+\mu {\nabla }^2\overrightarrow{v}-2\rho \overrightarrow{\omega }\times \overrightarrow{v}+\rho \overrightarrow{g}$$

(1)

where

• $\rho$ is the density;
• ${\displaystyle \frac{D\overrightarrow{v}}{Dt}}$ is the material derivative of the velocity field;
• $\overrightarrow{v}$ is the velocity vector;
• t is time;
• p is the pressure;
• $\mu {\nabla }^2\overrightarrow{v}$ is the turbulent friction force ($\mu$ being the turbulent viscosity coefficient); $2\rho \overrightarrow{\omega }\times \overrightarrow{v}$ is the Coriolis force;
• $\rho \overrightarrow{g}$ is the gravity force.

Once the velocity field is obtained by solving Equation (1), the advection–diffusion equation can be solved, which describes the transportation of salt and has the following form:

$${\displaystyle \frac{\partial hc}{\partial t}}+\nabla \left(h\overrightarrow{v}c\right)=\nabla \left(h\kappa \nabla c\right)+hs$$

(2)

where

• h is the water depth;
• c is the salt concentration;
• $\overrightarrow{v}$ is the flow velocity;
• $\kappa$ is the turbulent diffusion coefficient;
• s represents additional sources and sinks of salt.

In our calculations, we used Delft3D Flexible Mesh Suite 2019.01 (Delft3D FM) software developed by the Deltares Institute, Delft, The Netherlands. Delft3D FM is an advanced numerical tool designed to simulate hydrodynamic processes in various environments, such as rivers, lakes, and coastal waters, by solving the aforementioned equations for a specified area under given initial and boundary conditions. In these simulations, water is assumed to be incompressible, and vertical accelerations are considered negligible compared to gravitational acceleration (shallow water approximation). Additionally, the Boussinesq approximation is applied. One of the most important features of Delft3D FM is its ability to employ a computational mesh with complex geometries and varying shapes and sizes of individual cells. This allows both for a better adjustment of the grid to irregular borders of the simulated domain (thereby avoiding "staircase" boundaries) and a local increase in the grid density in areas where higher spatial resolution is required. Therefore, we utilized Delft3D FM as a numerical environment to develop a two-dimensional (2D) model, which is described in detail in the following paragraphs.

A computational grid generated for the Gulf of Gdańsk is presented in Figure 9. The grid was smoothed out near the border with the open sea, whereas a local refinement of the mesh was applied in the area of Puck Lagoon to obtain more accurate results with higher resolution for this region. The bathymetric point data with a spatial resolution of 50 m × 50 m were interpolated with the help of the triangulation technique to fit the computational mesh (Figure 2). Additional refinement was implemented around the Seagull Sandbar to accurately represent its shape during bathymetric interpolation and to better resolve local hydrodynamic effects.

The modeling process was based on several assumptions. These should be considered when interpreting the results, as they reflect the selective modeling strategy applied in this study, which emphasizes the dominant physical drivers while deliberately neglecting secondary processes.

• The water level at the open boundary of the Gulf of Gdańsk with the Baltic Sea is assumed to be similar to the level measured at the Hel station.
• The wind field is assumed to be uniform throughout the area of interest. This assumption is justified in Section 2.3.
• The current field is considered to be local within the Gulf of Gdańsk, meaning that wind-driven currents from the open sea have a minimal influence on the formation of currents in Puck Lagoon. This is primarily due to the prevailing frequency of westerly winds. Consequently, they do not significantly affect salinity transport in this region.
• The vertical variability of the salinity field is not significant due to the shallow depths in the Inner Puck Bay. This assumption is justified in Section 2.2 and allows us to limit our calculations to two dimensions. This simplification is consistent with the selective modeling strategy adopted here and is generally justified by the shallow depths (rarely exceeding 4 m) and frequent wind-driven mixing. A more detailed discussion of the limitations of this assumption is provided in Section 4.
• The initial salinity value was taken as constant for the entire area of the Gulf of Gdańsk. This setup allows freshwater transport from rivers to be investigated as an isolated process.
• Precipitation and evaporation were excluded, as the water balance described in Section 2.1 indicates that these processes play only a secondary role in the inner bay.
• The Reda River represents the primary local freshwater source, with an immediate influence on salinity in the Puck Lagoon.
• The Vistula River is the largest freshwater source of the Gulf of Gdańsk but is located at a considerable distance from the study site. It exhibits distinct seasonal variability, with higher flows in spring and early summer due to snow melt and increased precipitation and the lowest flows in late summer and early autumn. Despite interannual fluctuations, flow patterns within the same month remain relatively stable, allowing multi-year averaging to provide a representative seasonal profile. Its averaged seasonal influence on the freshening of outer bay waters is considered an important factor, whereas interannual extremes such as flood events or prolonged low-flow periods are treated as secondary and, therefore, neglected.

In our calculations, we imposed the following boundary conditions, derived from the adopted assumptions.

• On the border with the open sea (Figure 9), we adopted the sea levels measured at Hel station on each day in the simulated period. The data come from the Institute of Meteorology and Water Management (henceforth abbreviated as IMGW), National Research Institute, Poland.
• The flows at the mouths of two main rivers (Reda and Vistula; Figure 9) were introduced into the model. For the Vistula, monthly averaged modeled flow data for the period of 1981–2010 were applied (https://hypeweb.smhi.se), whereas for the Reda River, measured flows from the Wejherowo hydrological station were used. In both cases, the salinity of river waters was assumed to be 0.5 PSU.
• The wind field at the boundary was specified according to Hel station measurements, consistent with the uniform wind field assumption described above.

The simulation was initialized on 31 October 2019 with a uniform initial salinity of 7.63 PSU, corresponding to the observed average in Outer Puck Bay for that month. All data obtained from IMGW (seawater levels from Hel, wind speed and direction from Hel, and Reda River flow) were recorded every 10 min, while the Vistula River flow data from the SMHI Hypeweb model were averaged for each month. Observation points were also established at the in situ salinity measurement locations and at stations subsequently used for validation (Figure 10), and the results at these points were recorded separately for comparison with the measurements.

2.5. Calibration of the Model

It is hypothesized that the intermittent exposure of the Seagull Sandbar during low-sea-level conditions plays a critical role in modulating water exchange and shaping the salinity distribution in the area (see Section 2.1). However, the model failed to reproduce the exposure of the sandbank under the observed sea-level conditions, even in situations where, according to the literature, it would be expected to occur (sea level of 533 cm in Puck in the Amsterdam datum; Section 2.1). It should be emphasized, however, that this threshold value is based on a single historical source, and no broader dataset exists to determine the precise submergence level. In addition to the approximate nature of the reported threshold, the uncertainty introduced by bathymetric interpolation at local depths may also contribute to this limitation. The bathymetric dataset available for model implementation lacked sufficient spatial resolution in this narrow and shallow region to reliably capture depth variability. Consequently, the representation of bathymetry in the vicinity of the sandbank is largely the result of interpolation, which introduces significant uncertainty. Comparisons with independent bathymetric sources confirm that the dataset is reliable at the basin scale but underestimates local variability at the sandbar.

The seasonal shoaling effect is difficult to capture using interpolated bathymetry, and there is also a lack of systematic studies on its dynamics and the hydro-meteorological conditions under which it can be expected. To address this limitation and introduce the effect of sandbank exposure on salinity dynamics, a calibration of the sea-level boundary conditions was introduced. This adjustment enabled a more realistic representation of the hydrodynamic barrier effect associated with the emergence of the Seagull Sandbar and its implications for salinity gradients and transport processes in the study domain. To implement this correction, we introduced a calibration coefficient, $\alpha$, applied to the input water levels at the open-sea boundary. Based on a series of tests, the optimal value was established as $\alpha$ = −0.8 m, meaning that 0.8 m was subtracted from each recorded sea-level value. This empirical correction is site-specific and should not be generalized, but it allows the model to schematically represent the periodic barrier created by the Seagull Sandbar, thereby capturing its essential role in mixing and water exchange. The resulting shoaling effect cannot be quantitatively validated in the absence of systematic observational data, and a comprehensive assessment lies beyond the scope of this study. Instead, it is incorporated in a qualitative manner to account for its essential role in shaping salinity dynamics.

The next step involved verifying the accuracy of the computed sea levels. The results (Figure 11) show that the modeled sea levels are in close agreement with observations at the Puck, Gdynia, and Gdańsk–Port Północ stations. The statistics of the differences are summarized in

Table 3. Statistics of the differences between modeled and measured sea levels for three selected stations: Puck, Gdynia, and Gdańsk–Port Północ (see: Figure 10).

	Puck	Gdynia	Gdańsk–Port Północ
Minimum difference [m]	0.00	0.00	0.00
Maximum difference [m]	0.26	0.18	0.13
Standard deviation of the differences [m]	0.03	0.02	0.02

. The maximum difference was observed for Puck station (0.26 m), while the minimum difference was 0.00 m, and the standard deviation of the differences did not exceed 0.03 m. We therefore conclude that the model reproduces observed sea levels with satisfactory accuracy.

To model the spatial distribution of salinity and its temporal variation, freshwater inflows from rivers were also taken into account. As described in the model setup, the flows of the Reda and Vistula rivers were imposed as boundary conditions. Initial tests showed that the horizontal spread of river water was overestimated when unscaled discharges were applied. This effect is consistent with the depth-averaged (2D) formulation, in which freshwater is instantaneously distributed over the full water column, thereby enhancing effective lateral spreading relative to a surface-confined plume. Additional factors likely contributed, including numerical diffusion and uncertainties in horizontal diffusivity. To compensate for these simplifications, the river discharge was scaled by a factor of $\beta$, which minimized the median salinity error against in situ data. In the context of the selective modeling strategy, this coefficient can be interpreted as an empirical adjustment that partially accounts for unresolved processes deliberately omitted in the present framework. As the model is extended to include additional physical mechanisms the need for such compensation is expected to diminish, and the value of $\beta$ should converge toward unity.

Salinity results were compared with in situ measurements from June at the locations in Figure 10, with vertical averaging applied to match the 2D model output. Relative errors were calculated, and

Table 4. Statistics of the relative errors of modeled salinity for different $\beta$ values.

	$\mathit{\beta }=1$	$\mathit{\beta }=\frac{1}{12}$	$\mathit{\beta }=\frac{1}{15}$	$\mathit{\beta }=\frac{1}{18}$
Minimum [%]	29.200	0.049	0.008	0.022
Maximum [%]	60.463	7.798	5.259	3.747
Mean [%]	46.235	1.955	1.409	1.362
Median [%]	48.399	1.370	1.074	1.328

summarizes the results for several tested values of $\beta$. Without scaling ($\beta =1$), river influence was clearly overestimated, while reduced scaling improved accuracy. The optimal value, $\beta ={\displaystyle \frac{1}{15}}$, minimized median error and was adopted for further simulations.

In summary, two calibration coefficients were introduced during model development. The first, $\alpha$ = −0.8 m, was applied to boundary sea levels to reproduce the seasonal exposure of the Seagull Sandbar. The second, $\beta =1/15$, was applied to river inflows to realistically represent their effect on the salinity field.

3. Results

Since the model presented in this work operates in 2D, the calculated salinity values can only be compared with vertically averaged in situ measurements.

3.1. Results of Water Flow Simulation

The flow simulation results provide valuable insights into the general circulation patterns and hydrodynamic conditions within Puck Lagoon, which significantly influence the spatial distribution of salinity. The simulated current fields have a temporal resolution of 10 s. This section presents selected representative flow structures observed during the two analyzed periods.

Between 24 and 25 June, 2020, the maximum water flow velocity reached 0.5 ${\displaystyle \frac{\mathrm{m}}{\mathrm{s}}}$ in the Kuźnica Passage, directed toward the Puck Basin. Similarly high velocities were obtained in the Głębinka Passage (Figure 12). In the central region of Puck Lagoon, the maximum westward velocity reached 0.25 ${\displaystyle \frac{\mathrm{m}}{\mathrm{s}}}$, while most flow speeds ranged between 0.1 ${\displaystyle \frac{\mathrm{m}}{\mathrm{s}}}$ and 0.15 ${\displaystyle \frac{\mathrm{m}}{\mathrm{s}}}$ (Figure 13). The direction of the currents changed significantly between 24 and 25 June, accompanied by the appearance of eddy circulation features (Figure 14). Regardless of whether the Seagull Sandbar was submerged (Figure 12) or exposed (Figure 13 and Figure 14), the prevailing flow directions remained aligned with its longitudinal axis. When submerged, flow was observed to pass over the sandbar, yet retained a trajectory parallel to its orientation. The sandbar undergoes seasonal exposure, and during this period, temporary emergence was also observed following a temporary decrease in sea level (Figure 13 and Figure 14). It is worth noting that the flow patterns in the Głębinka and Kuźnica Passages indicated both inflows from the outer bay into the inner bay (Figure 12 and Figure 13) and outflows from Inner Puck Bay (Figure 14).

On 30 August 2020, the flow velocities ranged from 0.05 ${\displaystyle \frac{\mathrm{m}}{\mathrm{s}}}$ to 0.20 ${\displaystyle \frac{\mathrm{m}}{\mathrm{s}}}$ (Figure 15, Figure 16 and Figure 17) in the central part of the Puck Lagoon. The highest velocities occurred in the Kuźnica Passage, reaching 0.8 ${\displaystyle \frac{\mathrm{m}}{\mathrm{s}}}$ (Figure 17), while flow in the Głębinka Passage reached 0.35 ${\displaystyle \frac{\mathrm{m}}{\mathrm{s}}}$ (Figure 16). In both cases, the flow was directed toward the inner part of Puck Bay. As in June, the current directions varied considerably; however, the appearance of eddy features was much less frequent (Figure 16). Within the region of the Seagull Sandbar, flow remained predominantly aligned with its axis (Figure 17), although transverse currents were present where water crossed the feature (Figure 15 and Figure 16). As in the earlier period, the sandbar exhibited both submerged and exposed states, driven by seasonal and episodic changes in water level. Outflow scenarios are illustrated in Figure 15 and Figure 16, while inflow scenario is shown in Figure 17.

The hydrodynamics of the Puck Lagoon were reconstructed based on simulations forced by wind and water-level conditions. In the Kuźnica Passage, the maximum velocity obtained during the simulation reached 0.8 m/s in August. This value is higher than the range of 0.05–0.1 m/s reported by Dybowski [28], who presented multi-year, monthly mean surface current distributions for the period of 2011–2018. Such differences can be attributed to methodological differences, as long-term averages do not capture episodic maximum values.

At the same time, the maximum velocities obtained in this study are consistent with earlier field observations by Nowacki (1993) and Szymczak and Rucińska (2021), who reported velocities of up to 0.8 m/s in the Kuźnica Passage under storm conditions. This indicates that the model is capable of reproducing episodic circulation patterns and the dynamic response of the Puck Lagoon to extreme wind forcing.

3.2. Modeled Salinity Results

The numerical results of salinity for June and August 2020 are presented in Figure 18 and Figure 19, respectively. These values were obtained by averaging salinity calculations (performed with a temporal resolution of 10 s) over the periods of 24–26 June and 30 August, respectively. According to the model, the lowest salinity values in June (6.935 PSU at z22 and 6.984 PSU at z23) occurred in the vicinity of the Reda River’s mouth. In Rzucewo Hollow, the salinity ranged from 7.203 PSU at z20 to 7.475 PSU (z16), while in Kuźnica Hollow, values ranging from 7.287 PSU at z15 to 7.462 PSU at z6 were obtained. In the central, northern, and western parts of the Puck Basin, salinity showed little variation, ranging from 7.475 PSU (z16) to 7.561 PSU (z2)—the highest value recorded in the simulated period for Puck Lagoon.

In August 2020, the lowest salinity values were, again, obtained at stations z22 (6.689 PSU) and z23 (6.874 PSU). Similarly to June, a salinity decrease occurred at stations located in Rzucewo Hollow (z18–z21), with values ranging from 7.040 PSU at z20 to 7.267 PSU at z19. In the eastern part of the Puck Basin, particularly in the Kuźnica Hollow, water salinity was relatively low, with values of 7.236 PSU at z10, 7.213 PSU at z11, 7.260 PSU at z14, and 7.214 PSU at z15. Higher salinity values were recorded in the central, western, and northern parts of Puck Lagoon, ranging from 7.289 PSU at Z16 to 7.412 PSU at Z3—the highest simulated value for 30 August.

4. Discussion

4.1. Model Performance and Validation

The model presented in the previous sections was developed as a case study to test whether a simplified, process-focused framework can reproduce the salinity anomalies observed in Puck Lagoon and provide insight into the underlying physical drivers. As described in Section 2.5, the model calibration process involved two steps. In the first step, the model was calibrated to accurately reproduce the observed sea levels, including the seasonal exposure of parts of the Seagull Sandbar—a phenomenon that has a significant impact on water exchange between the inner and outer part of Puck Bay. In the second step of calibration, the inflow of the riverine water was scaled to accurately reproduce salinity measurements conducted in situ in June 2020. After the calibration, the validation process was conducted by comparing the calculated salinity values with those measured in situ on 30 August 2020, at each station. Both in both the calibration and validation processes, we adopted the relative error at each station as a measure of the accuracy of modeled results:

$$\delta ={\displaystyle \frac{S_m-S}{S}}\times 100\%$$

(3)

where

• $S_m$ is the modeled value of vertically averaged salinity at a given station;
• S is the value of vertically averaged salinity at that station obtained from field measurements.

Point maps showing the relative error are presented in Figure 20 and Figure 21 for June and August 2020, respectively. For June, the most accurate results were obtained for station z23, where the relative error was −0.008% (Figure 20). The greatest underestimation of the salinity result was obtained for station z22 (−5.259%), while overestimation was obtained in the area of Rzucewo Hollow (z16, z17, and z18) (Figure 20). At these stations, the error value reached 4.300% (Figure 20).

For the measurement dataset from August used for validation, it can be seen that the model underestimates the salinity values at all stations (Figure 21). The relative error ranged from −0.185% (z19) to −4.898% (z22). The most accurate simulation results were obtained in the area of Rzucewo Hollow, while significant error values occurred in the area of Kuźnica Hollow (z10, z11, z14, and z15) (Figure 21). However, the largest relative error occurred at the same station as in June 2020 and did not exceed −4.900%—a result that we find satisfactory.

These results indicate that, although local deviations exist, the overall accuracy (MAE ≈ 0.15 PSU) is high relative to observed spatial gradients of 0.5–1.0 PSU, supporting the model’s ability to reproduce the main features of the salinity field.

4.2. Comparison with Existing Modeling Efforts

The results discussed above should be compared with the only other model dedicated specifically to the area of Puck Bay, developed within the WaterPUCK project. A key tool is the SWAT model (Soil and Water Assessment Tool), which enables detailed hydrological modeling, as well as the transport of nutrients, pesticides, and sediments, and assesses the impact of agricultural practices on water quality [36]. As part of the project, the EcoPuckBay system was developed to monitor water quality in Puck Bay, analyzing the influence of anthropogenic and natural factors on marine ecosystems. This tool allows for the prediction of several environmental parameters, including, among others, salinity [37].

The salinity simulation results from the WaterPUCK model exhibit substantial discrepancies compared to in situ measurements. During the measurement campaign conducted on 24–25 June 2020, recorded salinity values ranged from 6.936 PSU to 7.512 PSU, while the WaterPUCK model produced values between 5 PSU and 6.2 PSU, with maximum relative error reaching −22.8% at station z6. Similarly, on August 30, 2020, measured salinity values ranged from 6.740 PSU to 7.614 PSU, whereas the WaterPUCK model indicated values between 5.9 PSU and 6.7 PSU, with a maximum relative error of −22.2% at station z5. Therefore, the results obtained within the model presented in this study can be considered to be a notable improvement in simulating the salinity field in the study area.

Our simulation advances beyond the WaterPUCK model in several important respects. It employs a high-resolution, flexible mesh, refined in detail near the mouths of the Reda and Vistula rivers, which allows for a more accurate representation of river widths and the intricate geometry of the inner lagoon. Calibration and validation were performed using observational records of water levels and salinity from reference stations. Additional calibration enabled the progressive shoaling of the Seagull Sandbar, which proved essential for reproducing the seasonal modulation of water exchange between the inner and outer bay.

Moreover, the model introduces a selective modeling strategy. By restricting the formulation to the dominant physical drivers, the approach isolates their respective roles in shaping salinity patterns. This provides a controlled experimental framework that not only improves agreement with observations but also establishes a basis for future model extensions, including the incorporation of vertical mixing, precipitation, and evaporation.

4.3. Uncertainties and Limitations

While model–observation agreement expressed through relative errors is satisfactory, we acknowledge that uncertainties also arise from input data, calibration choices, and structural simplifications of the model. Forcing data such as river inflows and wind speed are subject to measurement and averaging errors, while assumptions regarding uniform wind fields and simplified boundary conditions introduce additional uncertainty. Calibration efforts, particularly the adjustment to represent the progressive shoaling of the Seagull Sandbar, reduced some of these discrepancies but cannot eliminate them entirely. The relative magnitude of these uncertainties can, however, be evaluated by comparing model errors with observed salinity gradients. The mean absolute error of 0.15 PSU is substantially smaller than the salinity differences of 0.5–1.0 PSU observed between the inner and outer bay or between Kuźnica Hollow and adjacent areas, indicating that the processes reproduced by the model exceed the uncertainty range. Furthermore, the Vistula River’s discharge series used as forcing data are based on multi-year averages that capture seasonal variability, with typical interannual deviations smaller than the modeled salinity contrasts.

Although recent years have shown noticeable hydrological changes, such as more frequent low-flow events and a decline in ice phenomena, the use of the 1981–2010 period follows the World Meteorological Organization’s recommendation to apply 30-year reference intervals [38]. This baseline captures both dry and wet years and can therefore be considered a representative climatological framework for the Vistula River, providing stable reference conditions for hydrological modeling.

The spatial distribution of relative errors (Figure 20 and Figure 21) further confirms that maximum deviations remain below 5%, supporting the robustness of the main patterns. This suggests that, although uncertainties remain, they do not outweigh the key spatial patterns identified.

It is worth noting that in our simulations, Kuźnica Hollow was characterized by lower salinity, resulting from the influence of fresher water from Outer Puck Bay through the Kuźnica Passage. This may also be influenced by model limitations, such as mesh resolution, local bathymetric uncertainty, or the uniform wind assumption.

4.4. Ecological Implications

In accordance with the selective modeling strategy, the hydrodynamic model was constrained to a minimal set of dominant processes, thereby providing a rigorous first step toward investigation of the key physical mechanisms shaping the salinity field of Puck Lagoon. The results show that under simplified conditions, spatial patterns of salinity emerge, which have significant ecological implications, influencing the distribution and health of benthic and planktonic communities. Locally elevated salinity levels create conditions that favor specific species, including seagrasses and bivalves, which are integral to the lagoon’s biodiversity [14,16,17,23].

The present study should therefore be seen as a framework for linking physical drivers with biological responses: it highlights which mechanisms are most relevant for structuring the ecological environment while creating a basis for more advanced modeling that will include additional processes such as precipitation, evaporation [39], and vertical exchange. In this way, the results not only inform our understanding of current ecological conditions but also provide a foundation for predicting how the lagoon’s habitats and water quality may respond to future hydrological and climatic changes.

4.5. Future Work and Research Needs

Although the applied calibration coefficients are empirical and site-specific, they enabled the model to reproduce observed salinity patterns with satisfactory accuracy. This supports the hypothesis that river inflows, open-boundary exchange, and wind are dominant drivers of salinity dynamics. However, the coefficients should not be interpreted as universal parameters, as they may partly compensate for unresolved processes or model simplifications.

Future research should include scenario testing and sensitivity analyses to examine how mesh resolution, bathymetric representation, wind forcing, boundary exchange, river discharge, and sea-level calibration affect model performance. Such analyses are needed to clarify whether features such as the simulated freshening in Kuźnica Hollow are robust or artifacts of model configuration.

The selective modeling approach applied in this study neglects vertical salinity variation, an assumption that is generally justified in the shallow and wind-mixed waters of the Inner Puck Lagoon. With depths rarely exceeding 4 m and frequent wind-driven turbulence preventing persistent layering, a two-dimensional representation captures the dominant physical processes under most conditions. Nonetheless, this simplification may not hold in all situations. During periods of high river discharge, buoyant freshwater plumes can generate near-surface gradients; calm summer weather may promote transient haline or thermal stratification; and reduced wind forcing can limit vertical mixing. Even relatively minor vertical differences in such cases have the potential to influence horizontal transport pathways, freshwater residence times, and the dispersal of riverine inputs.

Recognizing these limitations highlights the value of extending the present selective framework into three dimensions. A 3D implementation would allow for the explicit treatment of stratification events and vertical mixing processes, thereby complementing the current focus on horizontal exchanges. It would also enable a more detailed examination of river plume dynamics, including buoyancy-driven spreading and subduction beneath saline waters, processes that cannot be represented in two dimensions. In this way, the selective modeling approach provides both a robust baseline for identifying the dominant drivers of salinity and a flexible foundation for sensitivity analyses that incorporate additional processes. Future 3D applications will therefore not replace but expand the present framework, offering a pathway to quantify how episodic stratification and vertical processes may reinforce or alter the salinity patterns described here.

In the context of sea-level calibration, it is important to note the absence of systematic studies defining the precise ranges at which the Seagull Sandbar becomes exposed or submerged. This limitation makes it difficult to assess the accuracy of hydrodynamic modeling of this phenomenon. In addition, sandbar exposure is likely influenced not only by sea level but also by local hydrodynamic conditions, including currents and wind forcing, which can modify water levels and mixing on short time scales. Future modeling efforts for the Puck Lagoon should therefore include targeted investigations to better constrain these thresholds and to quantify how wind-driven circulation interacts with sea-level variability in controlling sandbar shoaling.

The validation performed in this study was limited to salinity observations from August 2020, without complementary current measurements or longer time series. This constrains the robustness of model testing, as performance may differ under other hydrological and meteorological regimes. For instance, during spring freshets, increased river inflows may enhance plume dynamics and vertical gradients, whereas autumn storm conditions may intensify wind-driven mixing and exchange across the Seagull Sandbar. Future work should therefore test the model against seasonal and interannual datasets, which will provide a stronger basis for assessing whether the current framework remains valid under a broader spectrum of conditions.

5. Summary

We developed a high-resolution 2D hydrodynamics model for Puck Lagoon designed to reconstruct the spatial distribution of salinity and its temporal variability—one of the key parameters influencing biogeochemical processes and the unique flora and fauna of the lagoon. The model accounts for the dominant physical processes shaping the salinity field: water exchange with the outer part of Puck Bay, riverine inflows, and wind forcing.

The simulations provided valuable insights into the hydrodynamics of Puck Lagoon, confirming that the above-mentioned processes are the primary drivers determining salinity patterns in a typical scenario. The results showed satisfactory agreement with in situ measurements conducted in summer 2020, reproducing relatively high salinity levels in Puck Lagoon compared to the outer bay. However, slightly lower salinity values were obtained in Kuźnica Hollow, which can be attributed to a strong current generated by the model in the Kuźnica Passage causing the inflow of less saline water from the outer bay, which contributes to the discrepancy.

Future research should focus on extending the model to three dimensions, which would allow for more detailed studies of hydrodynamics in the vicinity of the river mouths and their influence on the bay’s salinity distribution. Incorporating additional processes such as precipitation and evaporation would also contribute to further refinement of the model.