Impact of the Artificial Strait in the Vistula Spit on the Hydrodynamics

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Article Impact of the Artiﬁcial Strait in the Vistula Spit on the Hydrodynamics of the Vistula Lagoon (Baltic Sea)

Michał Szydłowski * , Tomasz Kolerski and Piotr Zima Faculty of Civil and Environmental Engineering, Gda´nskUniversity of Technology, Narutowicza 11/12, 80-233 Gda´nsk,Poland; [email protected] (T.K.); [email protected] (P.Z.) * Correspondence: [email protected]; Tel.: +48-58-347-1809

Received: 25 March 2019; Accepted: 8 May 2019; Published: 10 May 2019

Abstract: In the Vistula Lagoon, storm surges are induced by variable sea levels in the Gulf of Gdańsk and wind action. The rising of the water level in the southern part of the basin, exceeding 1.0 m above mean sea level, can be dangerous for the lowland area of Zuławy˙ Elbl ˛askie,causing the inundation of the polders adjacent to the lagoon. One of the potential possibilities to limit the flood risk is to decrease the water level in the lagoon during strong storm surges by opening an artificial canal to join the lagoon with the Gulf of Gdańsk.The decision to build a new strait in the Vistula Spit was made in 2017. In order to analyze the impact of the artificial connection between the sea and the lagoon during periods of high water stages in the southern part the lagoon, mathematical modelling of the hydrodynamics of the Vistula Lagoon is required. This paper presents the shallow water equations (SWEs) model adapted to simulate storm surges driven by the wind and sea tides, and the numerical results obtained for the present (without the new strait) and future (with the new strait) configuration of the Vistula Lagoon.

Keywords: Vistula Lagoon; storm surges; mathematical modelling; ﬂood risk; artiﬁcial strait

1. Introduction Coastal lagoons are defined in [1] as inland and shallow water bodies (depths not exceeding a few meters), separated from the ocean by a barrier. They are connected to the ocean by at least one restricted inlet. The orientation of the lagoon may vary, but the parallel to the shore is dominant. According to [2], coastal lagoons occur on about 12% of the length of the world’s coastline. The formation of lagoons could be caused by alluvial progradation, the transgression of barriers in response to a sea level rise, or be formed behind storm-build barriers. A good example of this last type of formation can be found on the southern shores of the Baltic Sea. These semi-closed water areas are very calm and have the same salinity as the open sea, making them ideal for aquaculture. Some lagoons have been extensively converted for brackish-water fish ponds (e.g., the lagoons south of Madras), shellfish aquaculture (i.e., lakes on Hokkaido Island [3]), or cage culture, which is widespread around the world [4]. Changing climatic conditions [5,6] over the next century are likely to increase marine influences in lagoons, by the action of wind and storm surges. The paper presents some possibility of flood relief by the example of the proposed cut channel on the Vistula Lagoon transboundary water body. The Vistula Lagoon is located on the southern coast of the Baltic Sea, in the east part of the Gulf of Gda´nsk (Figure1). The length of the lagoon is 90.7 km and its width varies from almost 6 km up to 13 km. The mean width is 8.9 km. The lagoon is a very shallow basin with a mean depth of only 2.75 m. It is separated from the Gulf of Gda´nsk by the Vistula Spit of a length of about 65 km. The only connection between the Vistula Lagoon and the Baltic Sea is through the Strait of Baltiysk, which is 2 km long, 440 m wide, and approximately 8.8 m deep. The Vistula Lagoon, which developed about 6000 years ago, was created by being cut off from the Baltic Sea by the Vistula Spit. Since the digging of the canal

Water 2019, 11, 990; doi:10.3390/w11050990 www.mdpi.com/journal/water Water 2019, 11, 990 2 of 19 only connection between the Vistula Lagoon and the Baltic Sea is through the Strait of Baltiysk, which Water 2019, 11, 990 2 of 18 is 2 km long, 440 m wide, and approximately 8.8 m deep. The Vistula Lagoon, which developed about 6000 years ago, was created by being cut off from the Baltic Sea by the Vistula Spit. Since the digging of(artificial the canal strait) (artificial across thestrait) Vistula across Spit the in 1497Vistula in the Spit vicinity in 1497 of Baltiysk,in the vicinity the Vistula of Baltiysk, Lagoon the has Vistula been in Lagoonconstant has contact been with in constant the sea [ 7contact]. The lagoon with the represents sea [7]. aThe transboundary lagoon represents area divided a transboundary into two parts area by dividedthe state into border two between parts by Poland the state and border Russia. between The total Poland area of and the Russia. lagoon The measures total area 838 kmof the2, of lagoon which measures472.5 km2 838belongs km2,to of Russia. which 472.5 The shore km2 linebelongs is 270 to km Russia. long, The with shore a water line volume is 270 km of 2.3 long, km 3with[8]. a water volume of 2.3 km3 [8].

Figure 1. LocationLocation of of the the Vistula Vistula Lagoon.

Unsteady flows flows in the Vistula Lagoon are usually caused by changes of the sea level in the Gulf of Gda Gdańskandńsk and by wind action on the water surface of the lagoon. When When the the water stage of the Gulf of Gda Gdańskrises,ńsk rises, a difference difference in sea level in relation to the lagoonlagoon appears. This This results results in in a strong water current directed into the lagoon. The The decrease decrease of of the the water water table table in in the Baltic Sea causes the lagoonlagoon water water to to flow flow into into the the sea, sea, creating creating a strong a strong current current in the in thestrait strait in the in opposite the opposite direction. direction. The 3 totalThe totalvolume volume of sea of seawater water inflowing inflowing into into the the lagoon lagoon equals equals about about 17 17 km km3 perper year. year. In In extreme 3 1 conditions, the water inflowinflow reaches 10,00010,000 mm3 s−-1. .Such Such a asituation situation can can occur occur several several times times per per year, year, mainly in autumn andand winter,winter, whenwhen storm storm surges surges in in the the sea sea reach reach a watera water level level of overof over 0.8 0.8 m a.s.l.m a.s.l. [9]. 3 1 [9].The The total total outflow outflow from allfrom the all rivers the enteringrivers entering into the into lagoon the is lagoon about 180is about m s− 180, and m has3 s-1 no, and significant has no significantinfluence on influence changes inon the changes water stagein the in water this basin. stage Except in this for basin. the water Except exchange for the through water exchange the Strait throughof Baltiysk, the theStrait hydrodynamic of Baltiysk, the conditions hydrodynamic of the lagoon conditions depend of the on thelagoon wind depend action. on In the the wind region action. of the 1 InVistula the region Lagoon, of the SW Vistula (from South-West Lagoon, SW direction) (from Sout windsh-West with direction) a velocity winds from 4 with to 6 ma velocity s− (wind from velocity 4 to 6measurements m s-1 (wind velocity at a height measurements of 10 m) prevailat a height [8]. of These 10 m) winds prevail can [8]. cause These a risewinds of can the cause water a level rise of in thethe water Gulf of level Gdańskand in the Gulf in theof Gda Vistulańsk Lagoonand in the of upVistula to 0.8 Lagoon m over of the up mean to 0.8 sea m level. over However,the mean sea NE level.(from However, North-East NE direction) (from North-East winds in particular direction) cause winds a dangerous in particular water cause level a risedangerous in the southern water level part 1 riseof the in the Vistula southern Lagoon. part Forof the long Vistula periods Lagoon. (12 h Fo andr long more) periods of strong (12 h NE and winds more) (10 of mstrong s− and NE winds more), (10a rise m ofs-1 theand water more), level a rise exceeding of the water+1.0 level m and exceeding in extremes +1.0 reachingm and in +extremes1.5 m above reaching the mean +1.5 m sea above level can be observed [9]. The total tidal vertical range in the southern part of the lagoon is about 3.0 m (from –1.5 up to +1.5 m a.s.l.). Although NE winds are relatively rare, they can be very dangerous for Water 2019, 11, 990 3 of 19 Water 2019, 11, 990 3 of 19 Waterthe mean2019, 11sea, 990 level can be observed [9]. The total tidal vertical range in the southern part of the lagoon3 of 18 theis about mean 3.0 sea m level (from can –1.5 be upobserved to +1.5 [9].m a.s.l.). The total Alth tidalough vertical NE winds range are in relatively the southern rare, part they of can the be lagoon very isdangerous about 3.0 form (fromthe polders –1.5 up adjacent to +1.5 m to a.s.l.). the lagoon, Although resulting NE winds in extensive are relatively inundation rare, they of the can lowland be very the polders adjacent to the lagoon, resulting in extensive inundation of the lowland areas of Zuławy˙ dangerousareas of Żu łforawy the Elbl poldersąskie. adjacent to the lagoon, resulting in extensive inundation of the lowland Elbl ˛askie. areasFigures of Żuławy 2 and Elbl 3 presentąskie. the correlation between the mean wind direction and the sea level in the Figures2 and3 present the correlation between the mean wind direction and the sea level in the Gulf Figuresof Gdań 2sk. and As 3 seen present from the the correlation plots, the seabetween level on th ethe mean southern wind shoredirection of the and Baltic the seaSea level is strongly in the Gulf of Gdańsk.As seen from the plots, the sea level on the southern shore of the Baltic Sea is strongly Gulfaffected of Gda by windsńsk. As blowing seen from from the the plots, SW the direction. sea level on the southern shore of the Baltic Sea is strongly affected by winds blowing from the SW direction. affected by winds blowing from the SW direction.

Figure 2. Monthly distribution of the percentage of SW (225°–285°) and NE (15°–75°) winds [9]. Figure 2. Monthly distribution of the percentage of SW (225 –285 ) and NE (15 –75 ) winds [9]. Figure 2. Monthly distribution of the percentage of SW (225°–285°)◦ ◦ and NE (15°–75°)◦ ◦ winds [9].

Figure 3. Monthly mean sea level measured at the Hel station (Gulf of Gdańsk)[9]. Figure 3. Monthly mean sea level measured at the Hel station (Gulf of Gdańsk) [9]. Table1 presentsFigure 3. Monthly the maximum mean sea probable level measured storm at surges the Hel in station the Gulf(Gulf ofof Gda Gdańsk,basedńsk) [9]. on the probabilityTable 1 calculations presents the of themaximum highest annualprobable Baltic storm Sea surges levels onin thethe PolishGulf of coast Gda [10ńsk,]. Computationsbased on the wereprobabilityTable performed 1calculations presents taking the into of themaximum consideration highest probableannual observational Baltic storm Sea surges data levels of on thein the highest PolishGulf annual of coast Gda sea[10].ńsk, levels Computationsbased in Gdańsk.on the probabilitywere performed calculations taking ofinto the considerationhighest annual observat Baltic Seaional levels data on of the the Polish highest coast annual [10]. Computations sea levels in wereGdań sk.performed Tabletaking 1. Probabilityinto consideration of the maximum observat seaional levels data in the of Gulf the of highest Gdańsk[ annual10]. sea levels in Gdańsk. Table 1.Probability Probability (%) of the maximum sea levels in the Level Gulf (mof Gda a.s.l.)ńsk [10]. Table 1. Probability99 of the maximum sea levels in the Gulf 0.41 of Gdańsk [10]. 95Probability (%) Level (m a.s.l.) 0.49 90Probability (%) Level (m a.s.l.) 0.55 8099 0.41 0.62 709995 0.410.49 0.67 509590 0.490.55 0.78 309080 0.550.62 0.91 20 0.99 8070 0.620.67 10 1.12 57050 0.670.78 1.23 25030 0.780.91 1.37 13020 0.910.99 1.47 0.12010 0.991.12 1.78 105 1.121.23 There is a concept to create a new52 connection between1.231.37 the Polish part of the Vistula Lagoon and the Gulf of Gdańsk[11]. The aim is to21 significantly shorten1.371.47 and improve the sea route to the Baltic Sea. The idea to build a new strait between0.11 the sea and the1.471.78 lagoon is not new; it was first proposed in 1577. Over the years, the idea was0.1 often returned to [121.78,13], but the final decision was made in

Water 2019, 11, 990 4 of 18

2017 when the President of Poland signed a special act regarding the Vistula Spit cut. Nowy Swiat´ (Figure1) was chosen as the location of a new canal with a lock. According to this act, the canal is to be 1.1 km long, up to 80 m wide, and 5 m deep. In addition to the creation of an independent connection of the Polish part of the Vistula Lagoon with the Baltic Sea, there are some additional arguments for building the Strait of Nowy Swiat.´ The first is the increased possibility of using the sea port in Elbl ˛ag.Moreover, due to the possibility of opening the canal for outflowing water in case of an accumulation and rise of water in the southern part of the Vistula Lagoon, the flood risk for the polders of the lowland areas of Zuławy˙ Elbl ˛askiecan be potentially limited. In order to assess the impact of the artificial strait in the Vistula Spit on the storm surges in the Vistula Lagoon, a numerical simulation is needed. This paper presents the mathematical modelling of the hydrodynamics of the Vistula Lagoon, based on the solution of shallow water equations (SWEs) considering wind stresses.

2. Mathematical Model and Solution Method Mathematical modelling of the Vistula Lagoon hydrodynamics and mass transport has been developed over the last 35 years. In the first period, two-dimensional models were built and used to predict floods that can occur in the Zuławy˙ Elbl ˛askielowland areas during the winter storm season. They were useful prediction tools for water level forecasts in the lagoon [14,15]. In the next period, from 1994 to 2001, complex 2D models composed of hydrodynamics, water quality, and eutrophication modules were used for the modelling of hydrobiological and hydrochemical processes in the Vistula Lagoon [16–19]. Starting from the beginning of the 21st century, 3D water flow and mass transport models were applied to simulate the Vistula Lagoon hydrodynamics and migration phenomena [8,20,21]. These models were used for cases when the vertical variability of flow currents and the distribution of mass had to be considered. Such an approach can be necessary to model the hydro-sedimentary processes in lagoons and enclosed bays, for example, sand transport or contaminant migration [22]. However, in the case of storm surges driven by winds, mass (water volume) conservation plays the main role and the vertical variation of flow parameters can be neglected. Therefore, a 2D model seems to be sufficient to simulate the problem described in this paper. Moreover, the problem of the influence of a second connection between the Gulf of Gdańskand the Vistula Lagoon has not been investigated intensively so far. The first numerical approach to this problem was proposed in [23]. Recently, some numerical simulations of the hydrodynamics of the lagoon in view of the artificial canal through the Polish part of the Vistula Spit have been analyzed in [21]. In the numerical analysis presented in this paper, the 2D SWEs model is used to simulate the impact of the artificial canal in the vicinity of Nowy Swiat,´ where the Vistula Spit cut is planned. The application of this model is reasonable since the assumption of a uniform vertical distribution of horizontal velocities is satisfied. Although the measurements carried out in the lagoon [8] show that due to strong winds the vertical velocity distributions are not quite uniform, the SWEs model is sufficient to describe the water surface movement and horizontal circulation neglecting the vertical accelerations, which was confirmed with the previous satisfactory simulation results [14,24,25]. The set of shallow water equations can be written as:

2 2 2 ! ∂U ∂ U ∂U ∂ h gn ∂ U ∂ U Tx + U + V + g + U W νo + = 0, (1) ∂ t ∂ x ∂ y ∂ x H4/3 | | − ∂ x2 ∂ y2 − H

2 ! ∂V ∂ V ∂V ∂ h gn ∂ 2V ∂ 2V Ty + U + V + g + V W νo + = 0, (2) ∂ t ∂ x ∂ y ∂ y H4/3 | | − ∂ x2 ∂ y2 − H ∂ h ∂(UH) ∂(VH) + + = 0, (3) ∂ t ∂ x ∂ y where: x, y—spatial coordinates; t—time; U, V—depth-averaged components of velocity in the x- and y-direction, respectively; |W| = (U2 + V2)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 Water 2019, 11, 990 5 of 18

coefficient; v0—coefficient of horizontal turbulent viscosity; Tx—wind stresses in the x-direction; Ty —wind stresses in the y-direction. The system of partial differential Equations (1)–(3) for the imposed initial and boundary conditions can be solved by different numerical techniques. Some applications of the finite difference method (FDM) [26], finite element method (FEM) [27], and finite volume method (FVM) [28] were used, for example, to numerically integrate the SWE in space. In general, the main disadvantages of numerical methods used to solve 2D problems are the large dimension of the system of algebraic equations if implicit time integration schemes are applied, or the long computational time (small time integration step) if explicit schemes are used. In order to avoid these disadvantages, the two-dimensional problem can be split into a sequence of two one-dimensional problems, which can be solved efficiently in an implicit way. Here, the idea of the splitting technique presented in [24] was adapted. For this approach, the set of Equations (1)–(3) can be written in the matrix notation as follows:

∂ C = F, (4) ∂ t where: C = (U, V, h)T; and F—vector containing all the terms of (1-3) except time derivatives. The solution of this equation can be obtained by integration in the time increment (t, t + ∆t). The general integration formula is: tZ+∆t Ct+∆t = Ct + Fdt. (5) t In the mentioned splitting method, the vector, F, is expressed as a sum of vectors:

F = F(1) + F(2), (6) where:  2  ∂ U ∂ h gn ∂ 2U Tx  U g U W + νo +   − ∂ x − ∂ x − H4/3 | | ∂ x2 H  (1)  ∂ V ∂ 2V  F =  U + νo , (7)  ∂ x ∂ x2   − ∂(UH)  − ∂ x  2  V ∂ U + ν ∂ U  ∂ y o ∂ y2   − 2   gn 2 Ty  F(2) =  V ∂ V g ∂ h V W + ν ∂ V + . (8)  ∂ y ∂ y H4/3 o ∂ y2 H   − − − | |   ∂(VH)  − ∂ y Finally, Equations (1)–(3) can be written as:

∂ C = F(1) + F(2). (9) ∂ t Following [24], for the time increment (t, t + ∆t), one can obtain a solution of Equation (4) by the successive solution of the following equations:

∂ C(1) = F(1), (10) ∂ t

(1) with the initial condition, Ct = Ct, and:

∂ C(2) = F(2), (11) ∂ t Water 2019, 11, 990 6 of 18

(2) = (1) = (2) with the initial condition, Ct Ct+∆t. The final solution at the time (t + ∆t) is Ct+∆t Ct+∆t. The accuracy of the method depends on the accuracy of the methods applied for the solution of the Equations (10) and (11). Here, they were integrated using the method to solve the 1D unsteady flow equations proposed in [29]. In order to solve the set of Equations (1)–(3) the initial and boundary conditions are needed. In general, the following initial conditions are prescribed: For time, t = t0, in the functions, U(x,y,t0) = U0(x,y), V(x,y,t0) = V0(x,y), h(x,y,t0) = h0(x,y). The boundary conditions depend on the boundary type. At open boundaries, where flow occurs, a velocity normal (N) to the boundary, WN = W(t), or the water level, h = h(t), is forced (the second condition was used in the simulations presented in the paper). At the same time, a velocity tangential (T) to the boundary is forced equal to zero (WT = 0) and a ‘free slip’ exists (δWT/δn = 0). At closed (impermeable) boundaries, normal velocity is set to zero, WN = 0, and tangential velocity can be zero, WT = 0, or a ‘free slip’ can be assumed. The SWE model (1–3), solved by the described technique, was applied to simulate an unsteady flow in the Vistula Lagoon. A structured square numerical mesh of grid dimensions, ∆x = ∆y = 400 m, was applied to represent the lagoon (the lowland areas of Zuławy˙ Elbl ˛askieare not included directly in the model). The contour of the mesh representing the flow area is shown in Figure4. The archival bathymetry data [9] (Figure4) was used for the simulations. The coordinate system with a vertical datum based on the Baltic Sea level (0.0 m a.s.l., Kronstadt) was rotated 45◦ clockwise. For all numerical cases, the initial conditions were determined by the hydrostatic state, with the horizontal water table corresponding to the initial water level in the Gulf of Gdańskand the Strait of Baltiysk. The boundary conditions were chosen in the following way. At open boundaries, where connections of the Vistula Lagoon with the Gulf of Gdańskexist, the sea water level (representing storm surges) was forced together with null velocity tangential to the boundary. Such a condition represents the variation of the sea level. The water discharge in a direction normal to the cross-section of the strait was always calculated based on the actual value of normal velocity and the water depth. The same type of boundary condition was imposed for the existing Strait of Baltiysk (Figure4, point A) as well as for the artificial canal in Nowy Swiat´ (Figure4, point E) while it was analyzed. The other boundaries are located along the shore line of the lagoon and they were treated as closed boundaries with a ‘free slip’ condition.Water 2019, 11 The, 990 inflow of rivers entering into the lagoon was neglected. 7 of 19

Figure 4. Bathymetry of the Vistula Lagoon (dimensions in meters), point A—Strait of Baltiysk, point Figure 4. Bathymetry of the Vistula Lagoon (dimensions in meters), point A—Strait of Baltiysk, point B—Nowakowo, point C—Tolkmicko, point D—Kaliningrad, point E—Nowy Swiat.´ B—Nowakowo, point C—Tolkmicko, point D—Kaliningrad, point E—Nowy Świat. 3. Results and Discussion 3. Results and Discussion There are 10 numerical simulations presented in this section for different conditions and scenarios. The overallThere dataare 10 for numerical each case studysimulations is shown presented in Table2 .in this section for different conditions and scenarios.To investigate The overall the data influence for each of case sea tidesstudy on is shown the water in Table exchange 2. between the Gulf of Gdańsk and the Vistula Lagoon, and to test the boundary conditions imposed at the open boundaries of the Table 2. Numerical simulations of storm surges in the Vistula Lagoon. strait, a numerical experiment was carried out for the hypothetical change in sea level without wind action. Two variants, first without and then with the new openingNew in the strait Vistula Spit,Simulation were simulated. time Sea level Wind The variationNumber of the sea level forced as a boundary condition is shown(point in FigureE) 5. Such a boundary

hypothetical 1 No No 72 hours 0.0–0.6 m a.s.l. hypothetical 2 No Yes 72 hours 0.0–0.6 m a.s.l. hypothetical hypothetical 3 No 24 hours const. 0.0 a.s.l. from NE/12 m s-1 hypothetical hypothetical 4 Yes 24 hours const. 0.0 a.s.l from NE/12 m s-1 hypothetical hypothetical 5 No 24 hours const. 0.0 a.s.l. from SW/12 m s-1 hypothetical hypothetical 6 Yes 24 hours const. 0.0 a.s.l from SW/12 m s-1 observed observed 7 9 April–13 April 9 April–13 April No 120 hours 1986 1986 observed observed 8 9 April–13 April 9 April–13 April Yes 120 hours 1986 1986 observed observed 9 1 January–6 1 January–6 No 144 hours January 2019 January 2019 observed observed 10 1 January–6 1 January–6 Yes 144 hours January 2019 January 2019

Water 2019, 11, 990 8 of 19

To investigate the influence of sea tides on the water exchange between the Gulf of Gdańsk and theWater Vistula2019, 11 ,Lagoon, 990 and to test the boundary conditions imposed at the open boundaries of the strait,7 of 18 a numerical experiment was carried out for the hypothetical change in sea level without wind action. Two variants, first without and then with the new opening in the Vistula Spit, were simulated. The condition makes the Vistula Lagoon fill with sea water starting from the mean sea level (0.0 m a.s.l.) variation of the sea level forced as a boundary condition is shown in Figure 5. Such a boundary and then empty to the initial state. In the same figure, the evolution of the water surface elevation at condition makes the Vistula Lagoon fill with sea water starting from the mean sea level (0.0 m a.s.l.) Nowakowo (point B, Poland) and Kaliningrad (point D, Russia) is presented while only one strait is and then empty to the initial state. In the same figure, the evolution of the water surface elevation at considered (point A). It can be observed that the whole lagoon fills with water up to 0.6 m a.s.l. after Nowakowo (point B, Poland) and Kaliningrad (point D, Russia) is presented while only one strait is 24 h. The same effect was presented in [9]. Moreover, it is visible that the Russian end of the lagoon considered (point A). It can be observed that the whole lagoon fills with water up to 0.6 m a.s.l. after (point D) fills and empties quicker than the Polish end (point B), which is a result of the difference in 24 hours. The same effect was presented in [9]. Moreover, it is visible that the Russian end of the the distance from the Strait of Baltiysk. lagoon (point D) fills and empties quicker than the Polish end (point B), which is a result of the difference in the distanceTable 2. fromNumerical the Strait simulations of Baltiysk. of storm surges in the Vistula Lagoon. The change in the simulated water discharge through the Strait of Baltiysk is also shown in New Strait Simulation FigureNumber 5. The negative Seaand Level positive values of the flow rate Wind represent the inflow to and outflow from (Point E) Time the lagoon, respectively. The total volume of inflow was estimated to equal 420,031,200 m3 and the 1 hypothetical 0.0–0.6 m a.s.l. No No 72 h 3 total outflow2 was hypothetical 420,733,800 0.0–0.6 m m. a.s.l.The difference between No the volumes is about Yes0.17%, which 72 proves h 1 the good3 mass hypotheticalconservation const. in 0.0 the a.s.l. model. Unfortunathypotheticalely, from it NEis /12not m possible s− to Noverify the discharge 24 h 1 calculation4 for hypotheticalhypothetical const. cases 0.0 a.s.l nor real flowhypothetical events, from due NE to/12 mthe s− lack of flowYes rate or 24velocity h 1 5 hypothetical const. 0.0 a.s.l. hypothetical from SW/12 m s− No 24 h measurements in the strait. However, the total volume exchange can be1 compared to the volume of 6 hypothetical const. 0.0 a.s.l hypothetical from SW/12 m s− Yes 24 h the lagoon7 for observed the given 9 April–13 water Aprildepth. 1986 The area observed of the structural, 9 April–13 April rectangular 1986 numerical No mesh 120 applied h in the8 simulation observed is equal 9 April–13 to 698,960,000 April 1986 m2. If observed the water 9 April–13 layer Aprilof a 1986thickness ofYes 0.6 m is considered, 120 h 9 observed 1 January–6 January 2019 observed 1 January–6 January 2019 No 144 h the total volume of water in the lagoon is equal to 419,376,000 m3. This value is close to the volume 10 observed 1 January–6 January 2019 observed 1 January–6 January 2019 Yes 144 h of inflow and outflow during the filling and emptying processes.

Figure 5. (a) Imposed boundary condition (point A–Baltiysk), and calculated (points B–Nowakowo Figure 5. (a) Imposed boundary condition (point A–Baltiysk), and calculated (points B–Nowakowo and D–Kaliningrad) water levels and (b) calculated water discharge at point A in the Strait of Baltiysk. and D–Kaliningrad) water levels and (b) calculated water discharge at point A in the Strait of Baltiysk. The change in the simulated water discharge through the Strait of Baltiysk is also shown in Figure5. The negativeIn the second and positive numerical values simulation, of the flow two rate straits represent were theconsidered. inflow to The and new outflow strait from (point the lagoon,E) was assumedrespectively. to have The a total cross-sectional volume of inflow area equal was estimatedto 400 m2. toThe equal same 420,031,200 boundary m condition3 and the was total imposed outflow forwas the 420,733,800 new strait m (point3. The diE)ff aserence for the between existing the one volumes (point isA). about It can 0.17%, be observed which proves (Figure the 6) good that masswith theconservation same situation in the in model. the sea,Unfortunately, the full filling of it isthe not lagoon possible is faster to verify than before the discharge (after about calculation 18 hours). for hypothetical cases nor real flow events, due to the lack of flow rate or velocity measurements in the strait. However, the total volume exchange can be compared to the volume of the lagoon for the given Water 2019, 11, 990 9 of 19

WaterThis is2019 due, 11 ,to 990 the additional opening in the spit. Moreover, it can be seen that for the given boundary8 of 18 condition, the lagoon stays fully filled with water for a longer time than for the previous situation. Finally, it can be found that the different parts of the lagoon fill at the same time. water depth. The area of the structural, rectangular numerical mesh applied in the simulation is equal The influence of the new connection between the gulf and the lagoon can be investigated in to 698,960,000 m2. If the water layer of a thickness of 0.6 m is considered, the total volume of water in Figure 6 as a variation of the water discharge through the straits. A similar flow rate time distribution the lagoon is equal to 419,376,000 m3. This value is close to the volume of inflow and outflow during for both straits can be observed. However, because of the greater cross-sectional area, the discharge the filling and emptying processes. through the Strait of Baltiysk is always greater than through the hypothetical new canal. For the In the second numerical simulation, two straits were considered. The new strait (point E) was maximum inflow to and outflow from the lagoon, the ratio of the flow rates is 0.27 and 0.16, assumed to have a cross-sectional area equal to 400 m2. The same boundary condition was imposed respectively. Of course, the division of the discharge is not constant and depends on the actual for the new strait (point E) as for the existing one (point A). It can be observed (Figure6) that with the situation in the sea and the lagoon. Moreover, the hydraulic characteristics of the new strait as an same situation in the sea, the full filling of the lagoon is faster than before (after about 18 h). This is due artificial hydraulic structure, and its mode of work are not known at this moment because there is to the additional opening in the spit. Moreover, it can be seen that for the given boundary condition, only a general concept of the canal with no information about the construction details. Because of the lagoon stays fully filled with water for a longer time than for the previous situation. Finally, it can this, the calculated flow rate ratio can be considered as an approximate value. be found that the different parts of the lagoon fill at the same time.

Figure 6. (a) Imposed boundary conditions (points A–Baltiysk and E–Nowy Swiat),´ and calculated Figure 6. (a) Imposed boundary conditions (points A–Baltiysk and E–Nowy Świat), and calculated water levels (points B–Nowakowo and D–Kaliningrad) and (b) calculated water discharges at point A water levels (points B–Nowakowo and D–Kaliningrad) and (b) calculated water discharges at point in the Strait of Baltiysk and at point E in the new canal (Nowy Swiat).´ A in the Strait of Baltiysk and at point E in the new canal (Nowy Świat). The influence of the new connection between the gulf and the lagoon can be investigated in FigureIn6 theas asecond variation step, of thein order water to discharge assess the through impact the of straits. the new A similarartificial flow connection rate time between distribution the lagoonfor both and straits the cansea beon observed.the variation However, of the water because level of thein the greater lagoon, cross-sectional several numerical area, the simulations discharge withthrough wind the action Strait were of Baltiysk carried is out. always First, greater two hy thanpothetical through case the studies hypothetical of strong new constant canal. For winds the blowingmaximum along inflow the to andlagoon outflow axis fromwere the simulated. lagoon, the Two ratio scenarios of the flow of ratesa storm is 0.27 surge and 0.16,were respectively. analyzed, inducedOf course, by the constant division NE of theand discharge SW winds, is not respectively. constant and Calculations depends on were theactual madesituation for the following in the sea data—theand the lagoon. water level Moreover, in the theGulf hydraulic of Gdań characteristicssk is constant at of the the mean new straitsea level as an (0.0 artificial m a.s.l.) hydraulic and the windstructure, has anda constant its mode velocity of work of are12 notm s known-1 from atNE this and moment SW, respectively, because there over is onlythe whole a general area concept of the lagoonof the canal for the with first no 18 information hours of simulation. about the Then, construction the wind details. stops and Because the total of this,time the of flow calculated simulation flow israte 24 ratiohours. can For be each considered scenario as of an the approximate synthetic hydr value.o-meteorological situation, two variants of lagoon configurationIn the second were step, considered—without in order to assess the and impact with the of the new new opening artificial in connectionthe Vistula betweenSpit. The the results lagoon of theand computations the sea on the after variation 12 hours of the ofwater flow simulation level in the are lagoon, shown several in Figures numerical 7–15. simulations with wind action were carried out. First, two hypothetical case studies of strong constant winds blowing along the lagoon axis were simulated. Two scenarios of a storm surge were analyzed, induced by constant Water 2019, 11, 990 10 of 19 Water 2019, 11, 990 10 of 19 In Figures 7 and 8, the calculated water levels and flow velocity fields for a NE wind with no straitIn in Figures the Polish 7 and part 8, ofthe the calculated lagoon are water present levelsed. andThe flowvery regularvelocity shape fields offor the a NEwater wind table with can no be straitseen asin thethe Polishcurrent part state. of theA significant lagoon are increase present ed.of theThe water very regularlevel is shapeobserved of the in waterthe SW table part can of thebe seenlagoon, as theexceeding current 0.8state. m Aa.s.l. significant near points increase B and of E the (Figure water 7), level which is observed makes flooding in the SW in thepart Ż ofuł awythe lagoon,Elbląskie exceeding polder area 0.8 possible.m a.s.l. near At the points NE end B and of theE (Figure lagoon, 7), a waterwhich table makes decrease flooding below in the –0.5 Ż muł awya.s.l. Elblis calculatedąskie polder at the area same possible. time. AtThe the flow NE circulation end of the islagoon, the result a water of the table water decrease inflow below through –0.5 the m Straita.s.l. isof calculated Baltiysk (point at the A).same The time. main The stream flow circulationof sea water is is the split result and of circulations the water inflow occur inthrough each part the Straitof the oflagoon. Baltiysk It can (point be seenA). The that main in the stream main partof sea of waterthe lagoon, is split the and water circulations flows in occura SW directionin each part along of thethe lagoon.shore and It can returns be seen in athat NE in direction the main along part theof the main lagoon, axis. theAn waterarea of flows water in flow a SW stagnation direction alongwith very the shorelow velocities and returns can in be a seenNE direction in the Polish along part, the mainin the axis. vicinity An areaof Elbl of ąwaterg (point flow B) stagnation and the Vistula with very Spit low velocities can be seen in the Polish part, in the vicinity of Elbląg (point B) and the Vistula Spit Water(point2019 E)., 11 , 990 9 of 18 (pointFigures E). 9 and 10 present the situation for a NE wind and when considering the new strait (point E). IfFigures the additional 9 and 10 presentconnection the situationbetween forthe a seNEa windand lagoon and when is implemented, considering the the new hydrodynamic strait (point NEE).conditions andIf the SW additional winds,of the Vistula respectively. connection Lagoon Calculations between are changed. the were se Again,a made and the forlagoon regular the followingis implemented,shape data—theof the water the water hydrodynamic surface level can in the be Gulfconditionsobserved, of Gdańskis butof the the Vistula constantdamming Lagoon at of the water meanare atchanged. seathe levelPolish Again, (0.0 side m ofthe a.s.l.) the regular lagoon and the shape is wind less of than hasthe apreviously.water constant surface velocity However, can be of 1 12observed,the m lowering s− from but NEofthe the anddamming water SW, respectively,table of water in the at Russian overthe Polish the part whole si (pointde areaof the D) of lagoonis the greater. lagoon is less The for than thenew firstpreviously. strait 18 results h of simulation. However, in a local Then,thewater lowering the surface wind of depression stopsthe water and table thearound total in thepoint time Russian E of and flow part a simulationsignific (pointant D) modificationis is 24greater. h. For The each of newthe scenario flow strait circulation. results of thesynthetic in a In local this hydro-meteorologicalwaternew situation, surface depression the lagoon situation, around has become two point variants open,E and with ofa signific lagoon the possibilityant configuration modification of water were of inflowthe considered—without flow through circulation. the Strait In andthis of withnewBaltiysk thesituation, new(point opening the A) lagoon and in the outflowhas Vistula become through Spit. open, The thewith results new the of possibilitycanal the computations (point of waterE). Moreover, afterinflow 12 through h ofthere flow isthe simulation no Strait water of areBaltiyskstagnation shown (point in in Figures the A) lagoon and7–15 outflow.and flow through velocities the are new higher. canal (point E). Moreover, there is no water stagnation in the lagoon and flow velocities are higher.

Figure 7. Water surface elevation (m a.s.l.) after 12 hours of a NE wind at a speed of 12 m s-1 and 1 Figure 7. Water surface elevation (m a.s.l.) after 12 h of a NE wind at a speed of 12 m s and without-1 Figurewithout 7. the Water new surface artificial elevation strait at point(m a.s.l.) E (dimensions after 12 hours in meters). of a NE wind at a speed of− 12 m s and thewithout new artiﬁcialthe new straitartificial at point strait Eat (dimensions point E (dimensions in meters). in meters).

Figure 8. Water ﬂow velocity (m s 1) after 12 h of a NE wind at a speed of 12 m s 1 and without the Water 2019Figure, 11, 8.990 Water flow velocity (m −s-1) after 12 hours of a NE wind at a speed of 12− m s-1 and without11 of 19 new artiﬁcial strait at point E (dimensions-1 in meters). -1 Figurethe new 8. artificialWater flow strait velocity at point (m E s(dimensions) after 12 hours in meters). of a NE wind at a speed of 12 m s and without the new artificial strait at point E (dimensions in meters).

1 Figure 9. Water surface elevation (m a.s.l.) after 12 h of a NE wind at a speed of 12 m s− and with the Figure 9. Water surface elevation (m a.s.l.) after 12 hours of a NE wind at a speed of 12 m s-1 and with new artiﬁcial strait at point E (dimensions in meters). the new artificial strait at point E (dimensions in meters).

Figure 10. Water flow velocity (m s-1) after 12 hours of a NE wind at a speed of 12 m s-1 and with the new artificial strait at point E (dimensions in meters).

Figure 11. Water surface elevation (m a.s.l.) after 12 hours of a SW wind at a speed of 12 m s-1 and without the new artificial strait at point E (dimensions in meters).

Figure 12. Water flow velocity (m s-1) after 12 hours of a SW wind at a speed of 12 m s-1 and without the new artificial strait at point E (dimensions in meters).

Water 2019, 11, 990 11 of 19 Water 2019, 11, 990 11 of 19 Water 2019, 11, 990 11 of 19

-1 Figure 9. Water surface elevation (m a.s.l.) after 12 hours of a NE wind at a speed of 12 m s and with Figurethe new 9. artificialWater surface strait atelevation point E (m(dimensions a.s.l.) after in 12 meters). hours of a NE wind at a speed of 12 m s-1 and with theFigure new 9. artificial Water surface strait at elevation point E (dimensions(m a.s.l.) after in 12 meters). hours of a NE wind at a speed of 12 m s-1 and with Water 2019, 11, 990 10 of 18 the new artificial strait at point E (dimensions in meters).

-1 -1 Figure 10. Water flow velocity (m s ) after 12 hours of a NE wind at a speed of 12 m s and with the Figurenew artificial 10. Water strait flow at pointvelocity E (dimensions (m s-1) after in12 meters).hours of a NE wind at a speed of 12 m s-1 and with the 1 1 Figure 10. Water ﬂow velocity (m s− ) after 12 h of a NE wind at a speed of 12 m s− and with the new newFigure artificial 10. Water strait flow at point velocity E (dimensions (m s-1) after in 12 meters). hours of a NE wind at a speed of 12 m s-1 and with the artiﬁcial strait at point E (dimensions in meters). new artificial strait at point E (dimensions in meters).

Figure 11. Water surface elevation (m a.s.l.) after 12 hours of a SW wind at a speed of 12 m s-1 and Figure 11. Water surface elevation (m a.s.l.) after 12 h of a SW wind at a speed of 12 m s 1 and without Figurewithout 11. the Water new artificialsurface elevation strait at point (m a.s.l.) E (dimensions after 12 hours in meters). of a SW wind at a speed −of 12 m s-1 and the new artiﬁcial strait at point E (dimensions in meters). withoutFigure 11. the Water new artificial surface elevationstrait at point (m a.s.l.) E (dimensions after 12 hours in meters). of a SW wind at a speed of 12 m s-1 and without the new artificial strait at point E (dimensions in meters).

Figure 12. Water ﬂow velocity (m s 1) after 12 h of a SW wind at a speed of 12 m s 1 and without the Water 2019Figure, 11 ,12. 990 Water flow velocity (m −s-1) after 12 hours of a SW wind at a speed of 12− m s-1 and without12 of 19 new artiﬁcial strait at point E (dimensions in meters). Figurethe new 12. artificial Water flowstrait velocity at point (m E (dimensions s-1) after 12 hours in meters). of a SW wind at a speed of 12 m s-1 and without theFigure new 12. artificial Water straitflow velocityat point (mE (dimensions s-1) after 12 hoursin meters). of a SW wind at a speed of 12 m s-1 and without

the new artificial strait at point E (dimensions in meters).

1 Figure 13. Water surface elevation (m a.s.l.) after 12 h of a SW wind at a speed of 12 m s− and with the Figure 13. Water surface elevation (m a.s.l.) after 12 hours of a SW wind at a speed of 12 m s-1 and new artiﬁcial strait at point E (dimensions in meters). with the new artificial strait at point E (dimensions in meters).

Figure 14. Water flow velocity (m s-1) after 12 hours of a SW wind at a speed of 12 m s-1 and with the new artificial strait at point E (dimensions in meters).

Water 2019, 11, 990 12 of 19

Figure 13. Water surface elevation (m a.s.l.) after 12 hours of a SW wind at a speed of 12 m s-1 and Water 2019, 11, 990 11 of 18 with the new artificial strait at point E (dimensions in meters).

1 1 Figure 14. Water ﬂow velocity (m s− ) after 12 h of a SW wind at a speed of 12 m s− and with the new Water 2019Figure, 11, 99014. Water flow velocity (m s-1) after 12 hours of a SW wind at a speed of 12 m s-1 and with 13the of 19 artiﬁcial strait at point E (dimensions in meters). new artificial strait at point E (dimensions in meters).

In Figures 11 and 12, the calculated water level and flow velocity fields for a SW wind without the new strait are presented. Similar to the results obtained for the NE wind, the shape of the water free surface (Figure 11) is regular, but for the assumed meteorological conditions, the highest water level (above 0.4 m a.s.l.) is calculated at the Russian (NE) part of the lagoon (point D), while the lowest one (below –0.9 m a.s.l.) is observed at the Polish (SW) side of the lagoon (points B and E). The outflow of water into the sea through the Strait of Baltiysk (point A) was simulated for the given situation (Figure 8). Again, the area of water flow stagnation can be seen at the Polish end of the lagoon (points B, C, E). The results obtained for the same wind conditions, but with the consideration of both straits in the spit are shown in Figures 13 and 14. As in the previous case, after connecting the Vistula Lagoon to the Gulf of Gdańsk with two openings to the sea, the hydrodynamic conditions of the lagoon are stronglyFigure modified. 15. Water First, stage the variation water at table point increases, B (Nowakowo) reaching and for0.7 NEm anda.s.l. SW in windsthe Russian at a speed part of of the lagoon.Figure At 15. 1the Water same stage time, variation the water at levelpoint isB (Nowakowo)raised to about and –0.7 for NEm a.s.l. and SWin the winds vicinity at a speed of Elbl ofą 12g (point 12 m s− and without and with the new artificial strait at point E (Nowy Swiat).´ B). Nearm s-1 andthe withoutnew strait and (point with the E), new the artiwaterficial table strait is at higher point E due (Nowy to the Świat). inflow of sea water through the openIn canal. Figures The7 and transformation8, the calculated of waterthe velocity levels andfield flow is also velocity significant. fields for In acontrast NE wind to with the nocase strait of only in theone Polish Żconnection,uławy part is ofa one thesubstantial lagooncan observe are part presented. the of inflowthe Vistula The and very outflo Delta. regularw It of is water shapea lowland through of the area, water the includingnew table and can existing bea depression seen straits, as the reachingcurrentrespectively. state. almost A Such significant 2 m a below situation increase sea level.allows of theThe the water lowest lagoon level point, to is be observed 1.8 filled m below with in the thefresh SW surface, part sea ofwater is the located lagoon, and avoidby exceeding Dru waterżno Lake0.8stagnation. m (Figure a.s.l. near 1), making points B that and terrain E (Figure the7 ),lowest which poin makest in floodingPoland. Nearly in the Zuławyone˙ third Elbl of the ˛askie overall polder delta area areapossible. liesThe below Atvariation the sea NE level.of end the ofThe water the Ż lagoon,u levelławy indepression a watertime at table the is the decreasePolish most side belowimportant of the0.5 Vistula polder m a.s.l. Lagoon complex is calculated in inthe Poland, area at the of − consistingsameElblą time.g (point of The 122B) flow ispolders presented circulation measuring in is Figure the result 1200 15. ofItkm thecan2, waterabe large seen inflow numberthat throughthe newof embankments, theopening Strait ofbetween Baltiysk 125 theautomatic (point sea and A). pumpingThethe mainlagoon streamstations, reduces of as sea wellthe water amplitude as irrigation is split andof and the circulations drainagewater st occur agesfacilities at in eachthis [30]. location. part The of Ż theu ławyThe lagoon. maximumpolders It can comprise bewater seen levelone that ofinobserved two the mainregions for part ofthe ofthe theNE Polish lagoon,wind coast is the decreased considered water flows by to inabouface a SWthet 0.1 directiongreatest m for threat alongthe assumed of the partial shore conditions, or and full returns land while loss in a and NEthe associateddirectionminimum along materialwater the stage main and in axis. social this An area costs. area is of increasedTherefore, water flow by these stagnation about areas 0.2 with mrequire for very the intensive lowSW velocitieswind. care The can and lowering be protection seen inof thethe efforts.Polishwater part, level in during the vicinity a storm of Elblsurge ˛ag is (point particularly B) and theimportant Vistula Spitat this (point location E). due to the reduction of the floodFigures risk in9 theand polders 10 present on theŻuł situationawy Elblą forskie. a NE wind and when considering the new strait (point E). If the additional connection between the sea and lagoon is implemented, the hydrodynamic conditions of the Vistula Lagoon are changed. Again, the regular shape of the water surface can be observed, but the damming of water at the Polish side of the lagoon is less than previously. However, the lowering of the water table in the Russian part (point D) is greater. The new strait results in a local water surface depression around point E and a significant modification of the flow circulation. In this new situation, the lagoon has become open, with the possibility of water inflow through the Strait of Baltiysk (point A) and outflow through the new canal (point E). Moreover, there is no water stagnation in the lagoon and flow velocities are higher. In Figures 11 and 12, the calculated water level and flow velocity fields for a SW wind without the new strait are presented. Similar to the results obtained for the NE wind, the shape of the water free surface (Figure 11) is regular, but for the assumed meteorological conditions, the highest water level (above 0.4 m a.s.l.) is calculated at the Russian (NE) part of the lagoon (point D), while the lowest one (below 0.9 m a.s.l.) is observed at the Polish (SW) side of the lagoon (points B and E). The outflow of −

Figure 16. Wind parameters observed at Nowa Pasłęka (9 April–13 April 1986), (a) direction, (b) velocity.

Water 2019, 11, 990 12 of 18 water into the sea through the Strait of Baltiysk (point A) was simulated for the given situation (Figure8). Again, the area of water flow stagnation can be seen at the Polish end of the lagoon (points B, C, E). The results obtained for the same wind conditions, but with the consideration of both straits in the spit are shown in Figures 13 and 14. As in the previous case, after connecting the Vistula Lagoon to the Gulf of Gdańskwith two openings to the sea, the hydrodynamic conditions of the lagoon are strongly modified. First, the water table increases, reaching 0.7 m a.s.l. in the Russian part of the lagoon. At the same time, the water level is raised to about 0.7 m a.s.l. in the vicinity of Elbl ˛ag(point B). Near the − new strait (point E), the water table is higher due to the inflow of sea water through the open canal. The transformation of the velocity field is also significant. In contrast to the case of only one connection, one can observe the inflow and outflow of water through the new and existing straits, respectively. Such a situation allows the lagoon to be filled with fresh sea water and avoid water stagnation. The variation of the water level in time at the Polish side of the Vistula Lagoon in the area of Elbl ˛ag(point B) is presented in Figure 15. It can be seen that the new opening between the sea and the lagoon reduces the amplitude of the water stages at this location. The maximum water level observed for the NE wind is decreased by about 0.1 m for the assumed conditions, while the minimum water stage in this area is increased by about 0.2 m for the SW wind. The lowering of the water level during a storm surge is particularly important at this location due to the reduction of the flood risk in the polders on Zuławy˙ Elbl ˛askie. Zuławy˙ is a substantial part of the Vistula Delta. It is a lowland area, including a depression reaching almost 2 m below sea level. The lowest point, 1.8 m below the surface, is located by Dru˙zno Lake (Figure1), making that terrain the lowest point in Poland. Nearly one third of the overall delta area lies below sea level. The Zuławy˙ depression is the most important polder complex in Poland, consisting of 122 polders measuring 1200 km2, a large number of embankments, 125 automatic pumping stations, as well as irrigation and drainage facilities [30]. The Zuławy˙ polders comprise one of two regions of the Polish coast considered to face the greatest threat of partial or full land loss and associated material and social costs. Therefore, these areas require intensive care and protection efforts. In order to investigate and discuss the potential impact of the new strait (point E) in the Vistula Spit on the reduction of high water levels in the lagoon, two numerical simulations were carried out for real (observed) data. These two episodes differ from each other regarding wind parameters and, what is important, the range of sea level changes. In the first case, the sea level changes slightly and remains below the mean sea level, while in the second case, the sea level of the Gulf of Gdańskrises to over 1.0 m a.s.l. In both cases, storm surges were simulated without taking into account tides that are negligibly small. The first example concerns the simulation of the water level variation in the Vistula Lagoon for the period from 9 April to 13 April 1986. This event was numerically investigated in [14] and can be used to verify the mathematical model presented in this paper. The observed wind direction and velocity (Figure 16a,b) measured at the Nowa Pasł˛eka(Figure1) meteorological station and water level variation at point A (Figure 17a) were used as the input data for the simulation. A uniform wind field over the whole surface of the Vistula Lagoon was assumed. The E direction wind is represented by 0 and 360 degrees, N wind 90 degrees, W wind 180 degrees, and S wind 270 degrees, respectively. It can be seen that wind from the N, NE, and E sectors was observed for the first 72 h. The maximum 1 wind velocities, reaching 15 m s− , were measured during this period. After 3 days, the wind direction changed to the SE, and finally the S sector. Such a specific meteorological situation was the reason for the storm surge in the Vistula Lagoon and the rising of the water surface in the southern (Polish) part of the lagoon. The water level was observed to reach almost 1.0 m a.s.l. in the vicinity of Elbl ˛ag (Figure 17b). Water 2019, 11, 990 13 of 19

Figure 15. Water stage variation at point B (Nowakowo) and for NE and SW winds at a speed of 12 m s-1 and without and with the new artificial strait at point E (Nowy Świat).

Żuławy is a substantial part of the Vistula Delta. It is a lowland area, including a depression reaching almost 2 m below sea level. The lowest point, 1.8 m below the surface, is located by Drużno Lake (Figure 1), making that terrain the lowest point in Poland. Nearly one third of the overall delta area lies below sea level. The Żuławy depression is the most important polder complex in Poland, consisting of 122 polders measuring 1200 km2, a large number of embankments, 125 automatic pumping stations, as well as irrigation and drainage facilities [30]. The Żuławy polders comprise one of two regions of the Polish coast considered to face the greatest threat of partial or full land loss and associatedWater 2019, 11 material, 990 and social costs. Therefore, these areas require intensive care and protection13 of 18 efforts.

Figure 16. Wind parameters observed at Nowa Pasł˛eka(9 April–13 April 1986), (a) direction, (b) velocity. Figure 16. Wind parameters observed at Nowa Pasłęka (9 April–13 April 1986), (a) direction, (b) velocity.Two variants of the lagoon configuration were considered (without and with the new strait in the Vistula Spit) and simulated for the described meteorological situation. The results of the computations of the water level variation at the southern part of the lagoon are shown in Figure 17b,c. The comparison between the observed data and the results of the computations obtained for the current state of the lagoon (without the new opening in the spit) confirms that the proposed mathematical model provides reliable results of simulations of storm surges in the Vistula Lagoon. If the new connection of the lagoon with the Gulf of Gdańskis considered, the water level at the southern part of the lagoon is significantly lower. The extreme water level at point B (Nowakowo, near Elbl ˛ag)is reduced from 0.94 m a.s.l. (over the alarm level) to 0.53 m a.s.l. (below the alarm level) (0.41 m decrease). At point C (Tolkmicko), it is reduced from 0.67 m a.s.l. to 0.35 m a.s.l. (0.32 m decrease). Such a significant decrease in the water surface level could limit the flood risk at the polders adjacent to the lagoon in this region. The alarm and warning water levels in Nowakowo and Tolkmicko are equal to 0.82 m a.s.l. and 1.22 m a.s.l., respectively. The second numerical simulation was carried out for the storm surge event observed in the Vistula Lagoon at the beginning of the year 2019. All the hydro-meteorological data used in this case were published online by the Polish Institute of Meteorology and Water Resources (IMGW) on the website, http://monitor.pogodynka.pl/. Again, the observed wind direction and velocity (Figure 18a,b) measured at the Nowa Pasł˛eka(Figure1) meteorological station and water level variation at point A (Figure 19a) were used as the input data for the simulation. At the turn of the year, wind from the S 1 and SW sectors with a velocity reaching 10 m s− was observed. Starting from 2 January 2019 (t = 24 h), the wind direction changed to the E sector. This situation lasted about 48 h. During this period, 1 the wind velocity reached over 18 m s− . From 4 January 2019 (t = 72 h) to 5 January 2019 (t = 96 h), 1 the wind direction changed to the SW sector and blew with a velocity in the range of 6 to 10 m s− . At the beginning of 5 January 2019 (t = 96 h), again, the wind direction changed to the E-NE sectors, 1 but the observed wind velocity was lower than 10 m s− . Finally, during the last day of the analyzed Water 2019, 11, 990 14 of 19

In order to investigate and discuss the potential impact of the new strait (point E) in the Vistula Spit on the reduction of high water levels in the lagoon, two numerical simulations were carried out

Waterfor real2019 (observed), 11, 990 data. These two episodes differ from each other regarding wind parameters14 and, of 18 what is important, the range of sea level changes. In the first case, the sea level changes slightly and remains below the mean sea level, while in the second case, the sea level of the Gulf of Gdańsk rises 1 periodto over (61.0 January m a.s.l. 2019)In both the cases, wind storm velocity surges dropped were belowsimulated 4 m swithout− and the taking wind into direction account changed tides that to arethe negligibly W sector. Thissmall. moment (t = 144 h) was assumed as the ﬁnish time of the surge simulation.

Figure 17. Observed and calculated water level at (a) point A, (b) point B and (c) point C (9 April–13 AprilFigure 1986). 17. Observed The yellow and line calculated represents water the level alarm at water (a) point surface A, (b level.) point B and (c) point C (9 April–13 April 1986). The yellow line represents the alarm water surface level.

The first example concerns the simulation of the water level variation in the Vistula Lagoon for the period from 9 April to 13 April 1986. This event was numerically investigated in [14] and can be used to verify the mathematical model presented in this paper. The observed wind direction and velocity (Figure 16a,b) measured at the Nowa Pasłęka (Figure 1) meteorological station and water level variation at point A (Figure 17a) were used as the input data for the simulation. A uniform wind field over the whole surface of the Vistula Lagoon was assumed. The E direction wind is represented

Water 2019, 11, 990 15 of 19 by 0 and 360 degrees, N wind 90 degrees, W wind 180 degrees, and S wind 270 degrees, respectively. It can be seen that wind from the N, NE, and E sectors was observed for the first 72 hours. The maximum wind velocities, reaching 15 m s-1, were measured during this period. After 3 days, the wind direction changed to the SE, and finally the S sector. Such a specific meteorological situation was the reason for the storm surge in the Vistula Lagoon and the rising of the water surface in the southern (Polish) part of the lagoon. The water level was observed to reach almost 1.0 m a.s.l. in the vicinity of Elbląg (Figure 17b). Two variants of the lagoon configuration were considered (without and with the new strait in the Vistula Spit) and simulated for the described meteorological situation. The results of the computations of the water level variation at the southern part of the lagoon are shown in Figure 17b,c. The comparison between the observed data and the results of the computations obtained for the current state of the lagoon (without the new opening in the spit) confirms that the proposed mathematical model provides reliable results of simulations of storm surges in the Vistula Lagoon. If the new connection of the lagoon with the Gulf of Gdańsk is considered, the water level at the southern part of the lagoon is significantly lower. The extreme water level at point B (Nowakowo, near Elbląg) is reduced from 0.94 m a.s.l. (over the alarm level) to 0.53 m a.s.l. (below the alarm level) (0.41 m decrease). At point C (Tolkmicko), it is reduced from 0.67 m a.s.l. to 0.35 m a.s.l. (0.32 m decrease). Such a significant decrease in the water surface level could limit the flood risk at the Waterpolders2019 adjacent, 11, 990 to the lagoon in this region. The alarm and warning water levels in Nowakowo15 ofand 18 Tolkmicko are equal to 0.82 m a.s.l. and 1.22 m a.s.l., respectively.

Figure 18. Wind parameters observed at Nowa Pasł˛eka(1 January–6 January 2019), (a) direction, (Figureb) velocity. 18. Wind parameters observed at Nowa Pasłęka (1 January–6 January 2019), (a) direction, (b) velocity. The significant storm surge in the Gulf of Gdańsk(water level 1.11 m a.s.l. close to the maximum levelThe of probability, second numerical 10%, Figure simulation 19a, Table was1 ),carried and the out complex for the meteorologicalstorm surge event situation observed with in long the periodsVistula Lagoon of strong at the winds beginning from theof the E andyear NE2019. sectors All the caused hydro-meteorological visible effects indata the used form in ofthis water case accumulationwere published in online the southern by the Polish part of Institute the lagoon of Meteorology (Figure 19b,c). and It Water must beResources underlined (IMGW) that suchon the a coincidencewebsite, http://monitor.pogodynka.pl/. of a very high sea level and NE Again, winds the is aobserved rather unique wind situation direction in thisand areavelocity [9] (Figures (Figure2 and18a,b)3). measured The variation at the of theNowa direction Pasłęka and (Figure velocity 1) ofmeteorological the wind resulted station in aand sequence water oflevel two variation damming at periods in days 2 and 3, and day 5 of the storm event. The former was longer and higher with the water level exceeding the alarm and warning water levels in the vicinity of Elbl ˛agand Tolkmicko, causing a real flood risk for the neighboring polders. The observations and results of the numerical simulations of the water level variation in this region are presented in Figure 19b,c. The computations fit the measurements quite well. However, the simulated water level at point B is significantly lower than the measurements in the period after t = 72 h. It is a result of the specific landform in the vicinity of point B (Nowakowo), which is located in a sheltered area for SW and S winds. It means that assuming a uniform wind field over the whole lagoon surface is appropriate only for winds from the N, NE, and NS sectors, while it results in an underestimation of the calculated water levels in the southern part of the lagoon for winds from the S and SW sectors. This phenomenon was described in [9], but it was not considered in this work. Such an underestimation is not visible at point C (Tolkmicko), which is located outside the sheltered area for winds blowing from the SW and S sectors. The results obtained for the current conditions (without the new strait) have confirmed that the model of storm surges was validated and can be used as a numerical tool for the forecasting of the hydrological situation in the Vistula Lagoon during storm surges and periods of strong winds. The model was also used to analyze the impact of the new strait in the Vistula Spit on the flood risk at the polder area of Zuławy˙ Elbl ˛askieduring the occurrence of a high sea water level. When the hypothetical scenario with an open canal connecting the Gulf of Gdańskand the lagoon is considered, the results of simulations differ in a noticeable way. It can be found that the maximum water levels Water 2019, 11, 990 16 of 19 Water 2019, 11, 990 16 of 18 point A (Figure 19a) were used as the input data for the simulation. At the turn of the year, wind from the S and SW sectors with a velocity reaching 10 m s-1 was observed. Starting from January 2 at points B and C calculated for the concept (future) state (with the new strait) are lower during 2019 (t = 24 h), the wind direction changed to the E sector. This situation lasted about 48 hours. During damming periods than for the current state (without the new strait). Such a situation is a consequence this period, the wind velocity reached over 18 m s-1. From January 4 2019 (t = 72 h) to January 5 2019 of water exchange through the new opening in the spit. However, due to the high water level in the (t = 96 h), the wind direction changed to the SW sector and blew with a velocity in the range of 6 to sea, this impact is limited. In the example presented in Figure 19, the highest water levels at points 10 m s-1. At the beginning of January 5 2019 (t = 96 h), again, the wind direction changed to the E-NE B and C were reduced from 1.51 m a.s.l. to 1.34 m a.s.l. (0.17 m decrease) and from 1.38 m a.s.l. to sectors, but the observed wind velocity was lower than 10 m s-1. Finally, during the last day of the 1.27 m a.s.l. (0.11 m decrease), respectively. Therefore, for this extreme hydro-meteorological event, the analyzed period (January 6 2019) the wind velocity dropped below 4 m s-1 and the wind direction water levels in the southern part of the Vistula Lagoon could not be decreased below the warning or changed to the W sector. This moment (t = 144 h) was assumed as the finish time of the surge the alarm levels. simulation.

Figure 19. Observed and calculated water level at (a) points A and E, (b) point B and (c) point C Figure(1 January–6 19. Observed January and 2019). calculated The yellow water and level red linesat (a represent) points A the and alarm E, (b and) point warning B and water (c) point surface C (1levels, January–6 respectively. January 2019). The yellow and red lines represent the alarm and warning water surface levels, respectively. Discussing the two presented numerical simulations of real storm events, it can be found that the impactThe significant of the new storm artificial surge canal in the on Gulf the of hydrodynamics Gdańsk (water oflevel the 1.11 Vistula m a.s.l. Lagoon, close andto the on maximum flood risk levelmitigation of probability, can be significant. 10%, Figure However, 19a, Table the possible 1), and decreasethe complex in the meteorological water level in situation the southern with part long of periodsthe Vistula of Lagoon,strong winds in the vicinityfrom the of theE andZuławy˙ NE sector Wi´slanepolders,s caused visible strongly effects depends in the on theform actual of water water accumulationlevel in the Gulf in ofthe Gdańsk.The southern part effective of the operation lagoon (Figure of a new 19b,c). connection It must of thebe lagoonunderlined with that the sea,such as a a coincidenceflood protection of a channelvery high during sea level NE winds,and NE will winds bepossible is a rather only unique for low situation storm surges. in this Atarea this [9] moment, (Figure

Water 2019, 11, 990 17 of 18 the inﬂuence of the new strait can be analyzed only when the water gate (lock) in the new canal is considered open. There is no information regarding the construction details of the canal and lock.

4. Conclusions The results of the two-dimensional numerical simulations of the hydrodynamics of the Vistula Lagoon induced by storms and strong winds allow the following conclusions:

A comparison of the calculated and observed water levels in the lagoon shows that the applied • mathematical model and its numerical solution ensure the satisfactory accuracy of the results. The hydrodynamic conditions of the Vistula Lagoon are often driven by strong winds and storm • sea surges. Long-lasting N or NE winds can result in water accumulation in the southern part of the lagoon, • causing a flood risk for Zuławy˙ Elbl ˛askie. The new artificial connection of the Gulf of Gdańskwith the Vistula Lagoon can change the • hydrodynamics of the lagoon, but only if the lock is open during the surge event and a difference exists between water levels in the lagoon and the sea. The new opening can intensify the water exchange between the sea and the lagoon, reducing • water stagnation in the southern part of the lagoon. The new canal in the Vistula Spit can be helpful to limit the flood risk at the polder area near • Elbl ˛agby the reduction of extreme water levels in the southern part of the lagoon during damming driven by N and NE winds; a significant (below the warning and alarm levels) decrease of the water surface level in the lagoon will be possible only when high sea water levels in the Gulf of Gdańskdo not occur.

Author Contributions: Conceptualization, methodology, software, validation M.S.; formal analysis, investigation M.S, P.Z. and T.K.; resources, T.K.; data curation, M.S., P.Z.; writing—original draft preparation, M.S.; writing—review and editing, T.K.; visualization, M.S., T.K. Funding: This research received no external funding. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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