# Analysis of the Water Level Variation in the Polish Part of the Vistula Lagoon (Baltic Sea) and Estimation of Water Inflow and Outflow Transport through the Strait of Baltiysk in the Years 2008–2017

^{*}

## Abstract

**:**

^{3}.

## 1. Introduction

^{3}per year [6,7]. Unfortunately, there are no full, continuous, and current data (measurements) on the seawater transport between the Gulf of Gdańsk and the Vistula Lagoon. Recently, Russian researchers started to measure the flow through the strait, but so far only two series of measurements of approximately one month are available [8]. The annual volume of marine water inflow is usually cited and estimated by researchers like [4,5,9,10,11,12] using only data from historical sources such as [6,13]. This identified knowledge gap in the water balance of the Vistula Lagoon is also investigated in this paper.

- a statistical analysis of the water level variation at Tolkmicko station to identify the factors of water damming in the southern part (Polish) of the Vistula Lagoon (the measurements of the water stages in the lagoon and in the Gulf of Gdańsk, as well as wind observations at Nowa Pasłęka meteorological station were used for this research),
- a validation of the shallow water equations model [4] adopted to simulate the hydrodynamics of the lagoon over a long period of time (the water stage field measurements from Tolkmicko were used for comparison with the calculations),
- a computational estimation of the marine water transport between the Baltic Sea and the Vistula Lagoon (a numerical simulation of the hydrodynamics of the Vistula Lagoon was carried out for the period 2008–2017).

^{3}s

^{−1}[6,7]. The total inflow from all the rivers entering into the lagoon is about 180 m

^{3}s

^{−1}[6,7], yet this was not investigated in this case study due to the lack of continuous measurements. However, in order to make a full hydrological balance of the water exchange in the lagoon, each of the hydrological elements such as river inflow, ground inflow, precipitation and evaporation should be considered.

## 2. Materials and Methods

#### 2.1. Study Area

^{2}, of which 472.5 km

^{2}belongs to Russia, and the shoreline is 270 km long [5,6,7,10].

^{3}to 0.7 km

^{3}. Since that time, the hydrological and sedimentation regimes of the lagoon have changed. The lagoon has evolved from a freshwater plain estuary to an estuarine lagoon significantly influenced by the Baltic Sea [10].

^{3}s

^{−1}[6,7]. Some correction of this component of the lagoon water budget was made in [11].

^{3}per year) and freshwater gain, which consists of catchment runoff (4.97 km

^{3}per year), precipitation (0.55 km

^{3}per year), and evaporation (a loss of 0.53 km

^{3}per year). The total outflow from the Vistula Lagoon to the sea is estimated to be equal to 23.69 km

^{3}per year. The water balance is complemented by the groundwater flow.

^{−1}prevail [3,6,7]. These winds cause a rise in the water level in the Gulf of Gdańsk and in the Vistula Lagoon of even 0.8 m above the mean sea level. However, NE winds in particular cause a dangerous water level rise in the southern part of the Vistula Lagoon. For long periods of strong NE winds, a rise in the water level can be observed exceeding +1.0 m and in extreme conditions reaching +1.5 m above the mean sea level [4].

#### 2.2. Hydro-Meteorological and Bathymetric Data

#### 2.3. Statistical Method

^{2}-independence test [18]. The equality of the empirical probability density functions of water levels was tested with the Kolmogorov–Smirnov test [19]. The time series comparison was performed using a correlation analysis [20]. The statistical analysis was performed using the Anaconda distribution of Python 3.8 [21,22].

#### 2.4. Mathematical Model

^{2}+ V

^{2})

^{1/2}—modulus of the velocity vector; h—water elevation above some plane of reference; H—water depth; g—acceleration due to gravity; n—Manning friction coefficient; ν

_{0}—coefficient of horizontal turbulent viscosity; T

_{x}—wind stresses in x-direction; T

_{y}—wind stresses in y-direction.

^{–1/3}s [7].

## 3. Results and Discussion

#### 3.1. Variability of the Vistula Lagoon Water Levels (WSE) at Tolkmicko

^{2}-independence test (p-value ≈ 0). The lag time between events at Hel and Tolkmicko was determined by correlation coefficient maximization and is equal to 6 h 50 min with the Pearson correlation coefficient R = 0.91.

^{−6}). Based on the plot of the wind rose, it can be stated that the most frequent directions from which the wind originates are SE, then SW and SSW. The most frequent wind speed intervals are 0–7.1 m s

^{−1}and 7.1–14.1 m s

^{−1}. It can be noticed that stronger winds (14.1–21.2 m s

^{−1}) more frequently originate from westerly directions (SW, SSW, and W) than from other directions. The wind pattern resembles the wind pattern observed in Baltiysk by Chubarenko et al. [3].

#### 3.2. Validation of the Hydrodynamic Model for the 10-Year-Long Simulation Period

^{2}= 0.796.

_{i}are the observed water levels and c

_{i}are the outcomes of the computation (i = 1,...,n) with n denoting the number of values. The value of RMSE is equal to 0.104 m.

#### 3.3. Water Transport through the Strait of Baltiysk

^{3}per year [3,6,7]. The total outflow from the lagoon was estimated at about 24 km

^{3}[5]. However, researchers working today on hydrological processes of the Vistula Lagoon use historical data only. The most recent source data cited by researchers may be found in [6] and [13]. No more up-to-date studies were identified that would provide scientific data for this research area.

^{3}and 20.5 km

^{3}, respectively. The numerical simulations presented in [13] demonstrated the dynamics of the water exchange in the Vistula Lagoon through the Strait of Baltiysk for a one-year period (1994). The calculation was done using the MIKE21 hydrodynamic model. The accumulative annual inflow of marine water into the Vistula Lagoon in 1994 amounted to about 18.1 km

^{3}; the annual outflow (including the river outflow) toward the Baltic Sea in the same year was about 22.5 km

^{3}.

^{3}in the period 2008–2017, Table 3) is devoid of other hydrological balance components and cannot be compared with the source data (20.5 and 22.5 km

^{3}), where additional hydrological processes (e.g., river flow) were incorporated, forming the total outflow. The total inflow to the Vistula Lagoon, calculated for the period 2008–2017 (Table 3), is in the range of 14.31 km

^{3}to 17.78 km

^{3}. The average accumulative marine inflow amounts to 15.87 km

^{3}.

## 4. Conclusions

- The Vistula Lagoon 2D hydrodynamic model was verified and the simulation results were validated using water stage elevation measurements at Tolkmicko control point. Although the results obtained for the years 2008–2017 are slightly understated in relation to the observations, the calculations should be considered reliable, which was confirmed by statistical measures.
- The application of the validated hydrodynamic model enabled calculations of the flow through the Strait of Baltiysk. The calculated discharges in the strait provided the data to estimate the total accumulative inflow and outflow of seawater entering and leaving the lagoon, respectively.
- The average annual marine water inflow into the Vistula Lagoon between 2008 and 2017 was calculated to be equal to 15.87 km
^{3}. The minimum and maximum total inflows were estimated as 14.31 km^{3}and 17.78 km^{3}, respectively. These values, although different, are consistent with the data given in historical sources and can be used to update the hydrological balance of the waters of the Vistula Lagoon.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Location of the Vistula Lagoon [4].

**Figure 2.**Simplified shape and bathymetry (m a.s.l.) of the Vistula Lagoon (in meters) [4]: A—Strait of Baltiysk, B—Nowakowo, C—Tolkmicko, D—Kaliningrad, E—Nowy Świat.

**Figure 3.**Water level (WSE) variation at Hel and Tolkmicko stations and wind speed and direction observed at Nowa Pasłęka in January of 2008 (raw data; measurement frequency of WSE is 10 (min), wind data 1 (h)).

**Figure 4.**WSE (raw data) comparison at Tolkmicko (blue) and Hel (red) stations. Histograms and box plots.

**Figure 5.**Water level (WSE) variation at Tolkmicko and Hel, wind speed and direction—the case (1–8 August 2008) in which wind originates from a westerly direction for a long period of time causes the water level at Tolkmicko to decrease in comparison to the water level at Hel (raw data; measurement frequency of WSE is 10 (min), wind data 1 (h)).

**Figure 6.**Water level (WSE) variation at Tolkmicko and Hel, wind speed and direction—the case (9–16 October 2009) in which wind originates from a northerly direction for a long period of time causes the water level at Tolkmicko to increase in comparison to the water level at Hel (raw data; measurement frequency of WSE is 10 (min), wind data 1 (h)).

**Figure 7.**Difference between the average water levels (WSE) at Tolkmicko and Hel versus the wind event duration time. The label denotes the dominating wind direction, the size denotes the observed maximum wind speed.

**Figure 8.**Averaged water levels (WSE) at (

**a**) Tolkmicko, (

**b**) Hel versus wind event duration time. Label denotes the dominating wind direction, size denotes the observed maximum wind speed.

**Figure 9.**(

**a**) Wind speed (m s

^{−1}) histogram and estimated Weibull distribution probability density function and (

**b**) wind rose at Nowa Pasłęka meteorological station (2008–2017).

**Table 1.**Basic statistical characteristics of the WSE (m a.s.l.) at Tolkmicko and Hel stations (raw data).

Parameter | Tolkmicko | Hel |
---|---|---|

mean | 0.088 | 0.095 |

std. dev. | 0.202 | 0.193 |

minimum | −0.760 | −0.800 |

q_{0.25} | −0.040 | −0.030 |

median | 0.090 | 0.090 |

q_{0.75} | 0.210 | 0.210 |

maximum | 1.460 | 1.150 |

**Table 2.**The basic statistical characteristics of the observed daily averaged WSE (m a.s.l.) at Tolkmicko and the simulation outcome.

Parameter | Observations | Computations | Error |
---|---|---|---|

mean | 0.059 | 0.010 | 0.049 |

std. dev. | 0.198 | 0.203 | 0.092 |

minimum | −0.580 | −0.600 | −0.667 |

q_{0.25} | −0.060 | −0.120 | 0.000 |

median | 0.060 | 0.010 | 0.045 |

q_{0.75} | 0.179 | 0.130 | 0.096 |

maximum | 1.319 | 1.250 | 0.620 |

Value/Year | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | Average |
---|---|---|---|---|---|---|---|---|---|---|---|

Annual accumulative inflow (km^{3}) | 17.78 | 15.40 | 15.76 | 16.23 | 16.35 | 15.42 | 14.31 | 16.50 | 15.18 | 15.73 | 15.87 |

Annual accumulative outflow (km^{3}) | 17.60 | 15.66 | 15.68 | 15.95 | 15.97 | 15.57 | 14.43 | 16.75 | 15.38 | 15.94 | 15.89 |

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**MDPI and ACS Style**

Szydłowski, M.; Artichowicz, W.; Zima, P. Analysis of the Water Level Variation in the Polish Part of the Vistula Lagoon (Baltic Sea) and Estimation of Water Inflow and Outflow Transport through the Strait of Baltiysk in the Years 2008–2017. *Water* **2021**, *13*, 1328.
https://doi.org/10.3390/w13101328

**AMA Style**

Szydłowski M, Artichowicz W, Zima P. Analysis of the Water Level Variation in the Polish Part of the Vistula Lagoon (Baltic Sea) and Estimation of Water Inflow and Outflow Transport through the Strait of Baltiysk in the Years 2008–2017. *Water*. 2021; 13(10):1328.
https://doi.org/10.3390/w13101328

**Chicago/Turabian Style**

Szydłowski, Michał, Wojciech Artichowicz, and Piotr Zima. 2021. "Analysis of the Water Level Variation in the Polish Part of the Vistula Lagoon (Baltic Sea) and Estimation of Water Inflow and Outflow Transport through the Strait of Baltiysk in the Years 2008–2017" *Water* 13, no. 10: 1328.
https://doi.org/10.3390/w13101328