Baltic Sea) and the Proposed Artiﬁcial Island

Home , Nogat, Pregolya, Szkarpawa, Vistula, Vistula Lagoon

water

Article Mathematical Modeling of Ice Thrusting on the Shore of the Vistula Lagoon (Baltic Sea) and the Proposed Artiﬁcial Island

Tomasz Kolerski * , Piotr Zima and Michał Szydłowski Faculty of Civil and Environmental Engineering, Gda´nskUniversity of Technology, Narutowicza 11/12, 80-233 Gda´nsk,Poland; [email protected] (P.Z.); [email protected] (M.S.) * Correspondence: [email protected]; Tel.: +48-58-347-2930

Received: 4 October 2019; Accepted: 31 October 2019; Published: 2 November 2019

Abstract: Coastal lagoons are inland and shallow water bodies, separated from the ocean by a barrier. In cold regions, ice phenomena in shallow water coastal lagoons occur every winter season. Ice is predominantly formed on the surface due to density stratification and surface cooling. The ice dynamics in such areas are dominantly affected by winds. Water dynamics also cause ice movement, but due to the large areal scale of lagoons, the effect is usually limited to the direct vicinity of river estuaries. For open lagoons, which are connected to the sea by straits, tides will also cause significant movement of the ice inside the lagoon. Due to the limitation of ice outflow from a lagoon, ice fields will form ridges or hummocks on the shores. In this paper, the case of the Vistula Lagoon, located on the southern Baltic coast, is analyzed. Currently, the project of a new strait connecting the Baltic Sea with the Vistula Lagoon is in progress. As an effect of extensive dredging for the waterway to the port of Elblag, the material will be disposed of at a Confined Disposal Facility (CDF), which will form an artificial island. The island will be located on the western part of the lagoon, limiting the cross-section by about 20%. In consequence, ice cover pushed by winds blowing along the lagoon will create significant force action on the island banks. The DynaRICE mathematical model has been used to evaluate the ice dynamics and to determine the force produced by the ice on the coasts of the lagoon and the artificial island.

Keywords: ice dynamics; ice load; artiﬁcial island; conﬁned disposal facility; ice hummocks

1. Introduction In the contact zone of sea and land waters, coastal lakes and lagoons form as a transition zone of two different water regimes. This zone constantly experiences phenomena and processes of mutual interaction. Coastal lagoons are defined in [1] as inland and shallow water bodies (of depths not exceeding a few meters), separated from the ocean by a barrier and connected to the ocean by at least one restricted inlet. A classic example of a coastal lagoon in the southern Baltic Sea is the Vistula Lagoon. In the 20th century, the Vistula Lagoon experienced major hydrological changes, in particular the reduction of its catchment area by the Vistula River basin, as a result of the Nogat being cut off by a lock near Biała Góra in 1915. Before this, the lagoon was a freshwater reservoir, constantly backfilled and shallow with Vistula sediments, and now it has turned into a saltwater reservoir. Once the huge sedimentation was interrupted, instead of the inflow of Vistula waters, Baltic water became the overwhelming factor, with an easier intrusion through the Strait of Baltijsk, which is 2 km long, 440 m wide, and approximately 8.8 m deep. The length of the lagoon is 90.7 km and its width varies from almost 6 km up to 13 km. The lagoon is a shallow basin with an average depth of only 2.75 m [2]. The largest rivers flowing into the Vistula Lagoon are: the Pregolya (providing 62% of the freshwater) and other small rivers flowing from the Russian part, and the Pasł˛eka,the Elbl ˛ag,the

Water 2019, 11, 2297; doi:10.3390/w11112297 www.mdpi.com/journal/water Water 2019, 11, x FOR PEER REVIEW 2 of 16 Water 2019, 11, 2297 2 of 16 The largest rivers flowing into the Vistula Lagoon are: the Pregolya (providing 62% of the freshwater) and other small rivers flowing from the Russian part, and the Pasłęka, the Elbląg, the Nogat, and the Szkarpawa flowing from the Polish side, as seen in Figure1. The inflow of fresh Nogat, and the Szkarpawa flowing from the Polish side, as seen in Figure 1. The inflow of fresh water waterfrom from the Vistula the Vistula to the to thelagoon, lagoon, as a as result a result of the of thefunctioning functioning of the of thelocks locks on onthethe Nogat Nogat and and the the 3 1 Szkarpawa,Szkarpawa, is is very very limited. limited. TheThe averageaverage annual river water water inflow inflow to to the the lagoon lagoon is isabout about 100 100 m m3·s−1.s − . 3 1 3 1 · Instantaneous flows are in the range of about 40 m 3s −1 to about 1300 m3 s−1 . The maximum daily Instantaneous flows are in the range of about 40 m··s− to about 1300 m ·s· −. The maximum daily changeschanges in in the the water water level level in in the the lagoonlagoon causedcaused by these inflows inflows do do not not exceed exceed 0.1 0.1 m m [3]. [3 ].

FigureFigure 1. Location1. Location of theof Vistulathe Vistula Lagoon; Lagoon; blue trianglesblue triang indicateles indicate water surfacewater surface elevation elevation (WSE) boundary(WSE) stationsboundary in the stations lagoon; in the lagoon; red triangle the red indicates triangle the indicates meteorological the meteorological station in station Frombork. in Frombork.

AA new new project project is currently is currently being being implemented implemented regarding regarding the construction the construction of a waterway of a waterway connecting theconnecting Vistula Lagoon the Vistula with theLagoon Gulf ofwith Gdańsk.The the Gulf of basicGdań elementssk. The basic of the elements waterway of the include waterway the construction include ofthe a navigable construction canal of (artificiala navigable strait) canal through (artificial the strait) Vistula through Spit, the the Vistula construction Spit, the of construction a fairway from of a the mouthfairway of thefrom Elbl the˛agBay mouth to of the thechannel, Elbląg Bay and to athe Confined channel, Disposal and a Confined Facility Disposal (CDF). InFacility the planned (CDF). In CDF, dredgedthe planned material CDF, will dredged be placed material behind will dikes, be placed which behind will contain dikes, andwhich isolate will itcontain from theand surrounding isolate it environmentfrom the surrounding [4]. The typeenvironment of CDF [4]. planned The type for of the CDF Vistula planned Lagoon for the is Vistula an island Lagoon type is andan island will be type and will be constructed offshore, but in relatively shallow water. In the CDF, a mixture of constructed offshore, but in relatively shallow water. In the CDF, a mixture of dredged material and dredged material and water is pumped into an area that is divided into several smaller areas, called water is pumped into an area that is divided into several smaller areas, called cells. As the water moves cells. As the water moves between the cells, it slows; the dredged material settles, and finally, clean between the cells, it slows; the dredged material settles, and finally, clean water is discharged from the water is discharged from the site. The proposed CDF site in the Vistula Lagoon will have a total site. The proposed CDF site in the Vistula Lagoon will have a total volume of 9.2 million m3 and will volume of 9.2 million m3 and will consist of two separate cells which, when filled, will form an island consist of two separate cells which, when filled, will form an island with an area of approximately 180 with an area of approximately 180 ha. The island has been designed in the shape of an ellipse with ha.its The longer island axis has equal been to 1930 designed m and in shorter the shape to 1190 of anm, ellipseas seen within Figure its longer 2a. axis equal to 1930 m and shorterThe to 1190construction m, as seen of inthe Figure proposed2a. CDF site consists of earth dikes with a base width of 25 m reinforcedThe construction with geotextiles of the in proposed Geotube technology. CDF site consists After the of stabilization earth dikes of with the dike a base structure width at of the 25 m reinforcedlevel of the with load-bearing geotextiles soil in Geotube (sand), rip-rap technology. armoring After will the stabilizationbe laid from ofthe the outside, dike structure forming atan the levelexternal of the slope load-bearing inclined soilin the (sand), underwater rip-rap part armoring 3:1 and will the be upper laid frompart 2:1. the The outside, CDF formingsite will anbe externalfilled slope inclined in the underwater part 3:1 and the upper part 2:1. The CDF site will be filled up to 3.0 m above sea level, as seen in Figure2b. After completion of the filling of the island with dredging Water 2019, 11, x FOR PEER REVIEW 3 of 16 Water 2019, 11, 2297 3 of 16 up to 3.0 m above sea level, as seen in Figure 2b. After completion of the filling of the island with dredging material and the stabilization of the soil (draining), it is possible to use the island for other material and the stabilization of the soil (draining), it is possible to use the island for other purposes, purposes, such us a habitat improvement project (HIP) for birds, amphibians, and other aquatic such us a habitat improvement project (HIP) for birds, amphibians, and other aquatic species. species.

FigureFigure 2. 2.Project Project of of the the conﬁned confined disposaldisposal facility (CDF) in in the the Vistula Vistula Lagoon; Lagoon; plane plane view view (a) ( aand) and cross-sectionalcross-sectional view view (b ()[b)4 [4].].

IceIce on on coastal coastal lakes lakes and and shallow shallow water water lagoons lagoons in cold in cold regions regions typically typically forms forms as a resultas a result of thermal of coolingthermal and cooling vertical and water vertical density water stratification. density stratifica Such istion. the caseSuch when,is the duecaseto when, a lack due of turbulence to a lack of and limitedturbulence water and velocity, limited the water surface velocity, layer ofthe water surface quickly layer of cools water and quickly skim icecools is formedand skim [5 ice]. If is conditions formed are[5]. favorable, If conditions the skimare favorable, ice may developthe skim intoice may solid, develop stationary into solid, ice cover, stationary which ice could cover, stretch which overcould the stretch over the entire water body. Once the cover is formed, its movement is limited by the land entire water body. Once the cover is formed, its movement is limited by the land boundaries and the boundaries and the ice dynamics are usually considered as insignificant and neglected; however, ice dynamics are usually considered as insignificant and neglected; however, mechanical ice thrusting mechanical ice thrusting can occur due to wind or the sea water rise effect. Tides or storm surges will can occur due to wind or the sea water rise effect. Tides or storm surges will obviously affect only open obviously affect only open lagoons, which are connected to the sea by straits. Due to the limitation in lagoons, which are connected to the sea by straits. Due to the limitation in displacement, ice pushed by displacement, ice pushed by wind or high water level in the sea will thrust against the banks or windcollapse or high and water accumulate level in on the the sea cracks, will thrust forming against ridges. the These banks forms or collapse are not andcommon, accumulate but can on be the cracks,observed forming on coastal ridges. water These bodies forms in are the not southern common, Baltic, but i.e., can Szczecin be observed Lagoon on or coastal the Vistula water Lagoon bodies in the[6]. southern Piled-up Baltic, ice may i.e., endanger Szczecin Lagooncoastal and or the onshore Vistula structures Lagoon [6such]. Piled-up as lighthouses, ice may navigation endanger coastaland andsignal onshore beacons, structures harbors such or asartificial lighthouses, islands. navigation For hydro-engineering and signal beacons, structures, harbors some or regulations artificial islands. are Forused hydro-engineering to ensure materials structures, strong enough some regulations to resist ice are impact. used toFurthermore, ensure materials the potential strong threat enough of to resistlandslides ice impact. concerns Furthermore, the shores of the the potential Vistula Lagoon threat ofdue landslides to the thrusting concerns of the the ice shores ashore. of As the the Vistula ice Lagoonload on due the to shores the thrusting of coastal of lagoons the ice ashore. is affected As theby many ice load factors, on the it shoresshould ofbe coastal investigated lagoons further. is affected by manyIce factors, monitoring it should in sheltered be investigated water bodies further. of the southern Baltic coast has been summarized in [7],Ice and monitoring for the Vistula in sheltered Lagoon in water [8], but bodies this ofonly the covers southern data Balticfrom a coast period has of been the last summarized century (from in [ 7], and1950 for to the 1990). Vistula More Lagoon recent indata [8 ],for but the this winter only seasons covers 2003/2004–2016/2017 data from a period ofhave the been last presented century (from in 1950[9] toand 1990). ice data More were recent collected datafor from the the winter Swedish seasons Meteorological 2003/2004–2016 Institute’s/2017 haveSea Ice been Service. presented In recent in[ 9] andyears, ice datasatellite were produced collected images from have the Swedishprovided Meteorologicalinformation on the Institute’s distribution Sea Iceof ice Service. cover [10] In recentand years,polynya satellite dynamics produced [11] imagesin the Vistula have provided Lagoon and information are a good on complement the distribution to field of icemeasurements. cover [10] and polynyaBased dynamicson historical [11 ]observations in the Vistula, the Lagoon Vistula and Lagoon are a good freezes complement nearly every to field season measurements. and ice cover Based commonly occurs over its entire extent. During severe winters the Vistula Lagoon freezes for an on historical observations, the Vistula Lagoon freezes nearly every season and ice cover commonly average of four months. In mild winters, the Lagoon froze for no more than 2.5 months (January– occurs over its entire extent. During severe winters the Vistula Lagoon freezes for an average of four March), and the ice only covered parts of the waters offshore or did not occur. The average monthly months. In mild winters, the Lagoon froze for no more than 2.5 months (January–March), and the ice long-term minimum temperature of the lagoon waters is 0.13 °C. The thickness of the ice cover can only covered parts of the waters offshore or did not occur. The average monthly long-term minimum be up to 60 cm. The disappearance of the ice cover usually occurs in March, first from the side of temperatureŻuławy and of the the Elbl lagoonąg Upland, waters and is 0.13then ◦inC. the The middle thickness pool. ofThe the ice ice stays cover the canlongest be upin the to 60northern cm. The ˙ disappearanceRussian part of of the the lagoon, ice cover except usually for the occurs zone inat March,the Piławska first fromStrait, the which side is of afZuławyfected by and the thewarmer Elbl ˛ag Upland,(on average andthen 1–2 °C) in theand middlesaltier waters pool. of The the ice Gulf stays of Gda theń longestsk. Even in though the northern from 2003 Russian there were part five of the lagoon,seasons except without for thecontinuous zone at ice the cover Piławska on the Strait, Vistula which Lagoon, is aff thereected is by no the clear warmer trend (onin the average duration 1–2 of◦ C) andthe saltier ice cover waters or the of thedates Gulf for offreezing Gdańsk.Even and breakup though [9]. The from ice 2003 phenomena there were on the five Vistula seasons Lagoon, without continuous ice cover on the Vistula Lagoon, there is no clear trend in the duration of the ice cover or the dates for freezing and breakup [9]. The ice phenomena on the Vistula Lagoon, understood as the probability of ice occurrence and the number of days with ice, reflect trends observed on the southern Baltic Sea, as described in [12]. Water 2019, 11, 2297 4 of 16

Ice–shore interaction has been studied in many ways. In most cases, the structural load is determined by that required for ice failure. Thus, the common design concept is to slope the structure at the water line to induce a bending failure rather than a crushing failure. For any hydro-engineering structure subjected to ice interaction, the structural force should be analyzed with two goals: to determine the angle of the slope needed to induce a bending failure and to determine the magnitude of the loads. Since the design for the new waterway of the Vistula Lagoon is already set, all the dimensions of the artiﬁcial island will be adopted for the project and the angle of the slope will not be determined here. The magnitude of the loads on the island shore as well as on the harbor and lagoon coasts will be determined using the previously calibrated DynaRICE model [13].

2. Numerical Model Many mathematical models of the Vistula Lagoon have been developed over the last decades, including two-dimensional (2D) hydrodynamic models [14–16], 2D models composed of hydrodynamics, water quality and eutrophication modules [17–19], and recently developed three-dimensional models used for sediment transport and migration [3,20,21]. Despite the signiﬁcant number of applications of numerical models to the Vistula Lagoon, water and ice dynamics during the winter season have not been simulated. In the current study, the ice phenomena are investigated by applying the DynaRICE two-dimensional river ice dynamic model. The model was developed at Clarkson University [5] to simulate river ice processes including ice formation and breakup [22–24], ice jam dynamics [22,25–27] and ice load determination for both vertical [28–30] and sloped structures [31,32]. Even though the model was primarily developed to reproduce ice dynamics in rivers, where the ice movement is mainly driven by water hydrodynamics, it has been successfully applied to a coastal lake subjected to sea tides [33]. The DynaRICE is a coupled model composed of hydrodynamics and ice dynamics solved separately. All information from each module is transferred to the other one at every coupling time step, which for this study was set to 15 min. The water hydrodynamics are calculated by solving a two-dimensional set of shallow water equations [23]: ∂η ∂(qx) ∂ qy ∂ + + = (Nt), (1) ∂t ∂x ∂y ∂t

2 ! ! ∂qx ∂ qx ∂ qxqy 1 1 ∂Txx ∂Tyx ∂η + + = (τsx τ ) + + gH , (2) ∂t ∂x H ∂y H ρ − bx ρ ∂x ∂y − ∂x 2 ! ! ∂qx ∂ qx ∂ qxqy 1 1 ∂Txx ∂Tyx ∂η + + = (τsx τ ) + + gH , (3) ∂t ∂x H ∂y H ρ − bx ρ ∂x ∂y − ∂x in which η = water surface elevation; qx = qux + qlx and qy = quy + qly are components of the total unit width of water discharge; qlx, qly are components of the unit width of water discharge beneath the ice layer; qux and quy are the water discharge in the upper layer; N = ice concentration; t = ice thickness; = ∂qx + ∂qy Txy εxy ∂y ∂x and εxy are generalized eddy viscosity coeﬃcients; τs and τb are shear stresses at the ice–water interface and the river bed; and H is the water depth underneath the equivalent ice–water interface and the bed. Dynamic transport of river ice is mathematically described as the movement of the number of particles carrying all ice properties and being subjected to force balance. Considering the surface ice layer on the water surface as a continuum, the equation of motion can be derived from the momentum balance of an elemental area. The governing equation for ice dynamics can be presented in Lagrangian form as follows [34]: dV M L = R + F + F + G, (4) L dt a w Water 2019, 11, 2297 5 of 16

where: ML = ρiNt is the unit mass (per area) of an ice particle, VL is the ice velocity vector, R is the internal ice resistance force, Fa and Fw are the wind and water drag and G is a gravitational force due to the water surface slope. In the two-dimensional approach, the internal ice resistance force is deﬁned in the following form [34]: → → R = i Rx + j Ry, (5) ∂ ∂ Rx = (σxxNη) + σxyNη , (6) ∂x ∂y ∂ ∂ Ry = σyxNη + σyyNη , (7) ∂x ∂y in which σxx and σyy are the normal internal stresses in ice rubble, and σxy = σyx are the tangential internal ice stresses. All stresses are determined at the point where the considered ice particle is located, 2 and the ice parcel is determined by the vector →r , deﬁned as follows: →r = x2 + y2. The determination of internal stresses is based on a viscoelastic-plastic constitutive model for ice dynamics, as described in [35]. Other components of Equation (4) are presented below [34]:

→ → → → → → Fa = i ρaCw Vi W (u Wx)N + j ρaCw Vi W v Wy N , (8) − − − −     2 2 → ni → →  → ni → →  Fw = i ρ Vi Vw (u uw)N + j  Vi Vw (v vw)N, (9)  1/2 − −   1/2 − −  (αddw) (αddw) ! ! → ∂η → ∂η G = i ML g j ML g . (10) − ∂x − ∂y

In the above equations, Cw ( ) is the wind coefficient Cw = 0.00155 [36], ρa is the air density − 3 → → → 1 → → → 1 (kg m ), Vw = uw i + vw j (m s ) is the water velocity vector, V = u i + v j (m s ) is the surface · − · − i · − → → → 1 ice velocity vector, W = i Wx + j Wy (m s ) is the wind velocity vector at 10 m above the water or ice · − surface, ni is the roughness coefficient of the underside of the ice surface, dw (m) is the water depth, αd ( ) is a parameter describing the proportion of the cross-section area affected by the ice only to the − entire cross-section area. Since it is impractical and not necessary to solve the governing equations for ice dynamics and hydrodynamics simultaneously, a coupled ice dynamic and hydrodynamic model with the proper time integration scheme was developed. The Finite Element Method was used to solve the hydrodynamic equations using the streamline-upwind Petrov–Galerkin weighted residual concept over triangular elements with linear shape functions [37]. The Explicit Finite Element Method was employed to integrate the equations with respect to time. The developed finite element model allows the simulation of two-dimensional transitional flows and the treatment of dry-and-wet bed conditions. The solution to the ice dynamic equation was carried out using the Smoothed Particle Hydrodynamics (SPH) method along with images implemented to land boundaries. The method, applied to dynamic river ice processes, has been described in [38].

3. Results and Discussion The mathematical model (1–3), solved by the described technique, was applied to simulate the unsteady water flow and ice dynamics in the Vistula Lagoon. To include the inflow and outflow effect from the Baltic Sea, the model domain was extended about 50 km into Gulf of Gdańsk,where water surface elevation (WSE) boundary conditions were set up. The freshwater inflow to the model domain was implemented at four locations, representing the four main rivers discharging into the Vistula Lagoon. In these locations, as indicated by red arrows in Figure3, open boundaries were set in the form of water discharge conditions. Since no data on Russian rivers were available, only the discharge from the Pregolya was included in the model. On the Polish side of the lagoon, the Pasl˛eka,the Elbl ˛ag, Water 2019, 11, x FOR PEER REVIEW 6 of 16

to the moment when water surface elevation and water velocity did not change from one time step to another. In the model, ice inflow from the rivers was not simulated because its impact is negligible. WaterFor all2019 simulations,, 11, 2297 the entire lagoon was initially covered by ice cover of a constant thickness. At6 of the 16 beginning of the simulation, the ice cover was broken (defragmented into SPH parcels) and its anddynamics the Nogat were (including subjected to the external Szarpawa) and wereinternal simulated. forces. The initial conditions were obtained from simulationsA triangular of the finite model element set-up whichmesh werewas applied carried outwith at element a steady dimensions state condition varying up to from the moment40 m in whenthe vicinity water of surface the proposed elevation strait and and water artificial velocity isla didnd, not to 3000 change m at from the sea one side time open step boundary to another. (shown In the model,in Figure ice 3). inﬂow The from mesh the for rivers the wascurrent not simulatedcondition, because which itsdoes impact not isinclude negligible. the new For allstrait simulations, nor the theartificial entire island lagoon was was built initially in a similar covered way. by The ice coverbathymetry of a constant of the Vistula thickness. Lagoon At the and beginning the shore ofof the simulation,southern Baltic the iceSea cover were was provided broken by (defragmented the Institute intoof Hydro-engineering SPH parcels) and its of dynamics the Polish were Academy subjected of toSciences. external and internal forces.

Figure 3. Bathymetry of the Vistula Lagoon and the southern Baltic Sea with the finite element mesh usedFigure in 3. the Bathymetry model; the of redthe Vistula oval indicates Lagoon theand artificial the southe island;rn Baltic the Sea thick with blue the line finite represents element mesh WSE boundaryused in the conditions; model; the red red arrows oval representindicates waterthe arti dischargeficial island; boundary the thick conditions. blue line represents WSE boundary conditions; red arrows represent water discharge boundary conditions. A triangular finite element mesh was applied with element dimensions varying from 40 m in the vicinity3.1. Model of Calibration the proposed strait and artificial island, to 3000 m at the sea side open boundary (shown in Figure3). The mesh for the current condition, which does not include the new strait nor the artificial The calibration of the bed and ice roughness was preceded by using hydrodynamic and island was built in a similar way. The bathymetry of the Vistula Lagoon and the shore of the southern meteorological conditions as observed during the winter season 2010/2011. That winter, the lowest Baltic Sea were provided by the Institute of Hydro-engineering of the Polish Academy of Sciences. air temperature recorded in the Polish part of the Vistula Lagoon area reached −24.6 °C and took 3.1.place Model on 24 Calibration February 2011. The winter season 2010/2011 was characterized by severe frosts that started early, in the second half of November 2010, and lasted until mid-January 2011. As a result of such Thelow calibrationand long-lasting of the air bed temperatures, and ice roughness the ice cover was precededdeveloped by over using the hydrodynamicentire extent of andthe meteorologicallagoon. Duringconditions this first cold as observed wave, unusual during and the abnormal winter season snowfalls 2010/2011. triggered That winter,snow cover the lowest reaching air temperature recorded in the Polish part of the Vistula Lagoon area reached 24.6 C and took place on up to 60 cm (see Figure 4). Next, starting from 9 January, the air temperature− increased◦ above zero, 24causing February most 2011. of the The snow winter cover season to melt, 2010 affecting/2011 was an characterizedincreased river by flow severe observed frosts that over started the next early, days. in theAfter second a short half period of November of thaw, 2010,the weather and lasted was untilcooler mid-January again for 10 2011. days. As Starting a result from of such 1 February, low and long-lastinganticyclone circulations air temperatures, with strong the ice winds cover and developed rainfall caused over the the entire breakup extent and of drifting the lagoon. of the During ice on thisthe lagoon. first cold Because wave, unusualthe wind and was abnormal mainly blowing snowfalls from triggered the north snow east cover and reachingeast direction, up to 60see cm Figure (see Figure6b, ice4 was). Next, blown starting towards from the 9 January,southern the shore air temperature of the lagoon increased and extensive above zero,hammocks causing were most formed of the snow[39]. Ice cover movement to melt, was affecting caused an by increased the wind river and flow also observedby the water over inflow the next to days.the lagoon After from a short the period Baltic of thaw, the weather was cooler again for 10 days. Starting from 1 February, anticyclone circulations with strong winds and rainfall caused the breakup and drifting of the ice on the lagoon. Because the wind was mainly blowing from the north east and east direction, see Figure 6b, ice was blown Water 2019, 11, 2297 7 of 16 towards the southern shore of the lagoon and extensive hammocks were formed [39]. Ice movement Water 2019, 11, x FOR PEER REVIEW 7 of 16 was caused by the wind and also by the water inflow to the lagoon from the Baltic Sea due to the high storm surge. The wind speed and direction recorded during the entire season is presented in SeaWater due 2019 to , the11, x high FOR PEER storm REVIEW surge . The wind speed and direction recorded during the entire season7 of 16 is Figurepresented5. Table in Figure1 summarizes 5. Table 1 wind summarizes distribution wind over distribution the entire over season the asentire shown seaso onn the as windshown rose on inthe FigurewindSea rosedue6a. Theto in the Figure wind high data storm 6a. Thewere surge wind measured. The data wind werewith speed 10 measured minand direction intervals with recorded by10 themin Institute intervalsduring the of by Meteorology entire the Instituteseason andis of WaterMeteorologypresented Resources in and Figure in Water Frombork 5. Table Resources (location1 summarizes in shownFrombork wind in Figure distribution(location1). All shown over data the usedin entireFigure in the seaso 1) study. Alln as anddata shown presented used on inthe the in thestudywind paper and rose arepresented in public Figure andin 6a the can. The paper be wind found are datapublic on https: were and // measured dane.imgw.plcan be found with /on. 10 https://dane.imgw.pl/min intervals by the Institute. of Meteorology and Water Resources in Frombork (location shown in Figure 1). All data used in the study and presented in the paper are public and can be found on https://dane.imgw.pl/. 20 Air temperature, daily maximum 15 20 Air temperature, daily average

C] Air temperature, daily maximum 10 Air temperature, daily minimum 15 Air temperature, daily average 5

C] 10 Air temperature, daily minimum

0 5 -5 0 -10-5

-15-10 Air temperature[ Air

-20-15 Air temperature[ Air -25-20 1-Nov-2010-25 1-Dec-2010 31-Dec-2010 30-Jan-2011 1-Mar-2011 31-Mar-2011 1-Nov-2010 1-Dec-2010 31-Dec-2010 30-Jan-2011 1-Mar-2011 31-Mar-2011

18 60 18 60 16 20 16 Air temperature, daily maximum Snow 50 1420 Snow 50 15 AirAir temperature, temperature, daily maximumaverage Rain 1415

C] 1210 AirAir temperature, temperature, daily averageminimum Rain 40

C] 1210 Air temperature, daily minimum Snow cover 40 10 5 Snow cover 5 010 30 8 0 30 -5 8 6 -5 20 -10 6 20 4-10

-15 4 Air temperature[ Air

-15 10 [cm] thickness cover Snow Air temperature[ Air 10 [cm] thickness cover Snow -202 Precipitation intensity [mm/day] intensity Precipitation -202 -25[mm/day] intensity Precipitation 0-250 0 0 1-Nov-20101-Nov-2010 1-Dec-20101-Dec-20101-Dec-20101-Dec-2010 31-Dec-201031-Dec-20101-Jan-20111-Jan-2011 30-Jan-201130-Jan-20111-Feb-20111-Feb-2011 1-Mar-20111-Mar-20111-Mar-20111-Mar-2011 31-Mar-201131-Mar-2011

FigureFigure 4. 4. 4.Air AirAir Temperature, Temperature, Temperature, precipitation precipitation and and snow snow cover cover cover thickness thickness thickness measured measured at at Frombork Frombork meteorologicalmeteorological station station station in in thein the the winter winter winter season season season 2010 2010/2011;/2011; the pinkthe the pinkpink rectangle rectangle rectangle indicates indicates indicates the calibration the the calibration calibration period (1period February–12period (1 (Feb1 Februaryruary February);–12–12 Feb Feb dataruaryruary from);); data data https: fromfrom// dane.imgw.pl https://dane.imgw.pl/https://dane.imgw.pl//. . .

2020 1515 1010

5 5 Wind speed[m/s]Wind Wind speed[m/s]Wind 0 0 1-Nov-2010 1-Dec-2010 31-Dec-2010 30-Jan-2011 1-Mar-2011 31-Mar-2011 1-Nov-2010 1-Dec-2010 31-Dec-2010 30-Jan-2011 1-Mar-2011 31-Mar-2011

Figure 5. Cont.

Water 2019, 11, x FOR PEER REVIEW 8 of 16 Water 2019, 11, 2297 8 of 16 Water 2019, 11, x FOR PEER REVIEW 8 of 16 360 ] º 360

270] º 180270 90180

Wind Wind direction[ 090 1-Nov-2010[ direction Wind 0 1-Dec-2010 31-Dec-2010 30-Jan-2011 1-Mar-2011 31-Mar-2011 1-Nov-2010 1-Dec-2010 31-Dec-2010 30-Jan-2011 1-Mar-2011 31-Mar-2011 Figure 5. Wind speed and direction measured at Frombork in the winter season 2010/2011; the pink rectangleFigureFigure 5. 5.indicatesWind Wind speed speed the andcalib and direction rationdirection period measuredmeasured (1 February at Frombork –12 February); in in the the winter winter data seasonfrom season https://dane.imgw.pl/. 2010/2011; 2010/2011; the the pink pink rectanglerectangle indicates indicates the the calibration calibration period period (1(1 February–12February–12 Feb February);ruary); data data from from https://dane.imgw.pl/ https://dane.imgw.pl. /. Table 1. Distribution of wind directions in percent during the winter season 2010/2011 recorded in Table 1. Distribution of wind directions in percent during the winter season 2010/2011 recorded in FromborkTable 1. withDistribution respect toof fourwind speed directions ranges; in percent data from during https://dane.imgw.pl/. the winter season 2010/2011 recorded in FromborkFrombork with with respect respect to to four four speed speed ranges;ranges; datadata from https://dane.imgw.pl/https://dane.imgw.pl/. . Wind Wind Directions (%) Wind Wind WindDirections Directions (%) (%) SpeedWind Speed (m/s) Speed N NE E SE S SW W NW Σ (m/s) N NNE NEE ESE SES SSW SWW WNW NW  Σ (m/s) 0–5 0–515.40% 13.10%15.40% 13.10%8.61% 8.61%3.18% 3.18%1.34% 1.34% 2.30% 2.30% 5.74% 5.74% 9.19% 9.19% 58.86%58.86% 0–5 15.40% 13.10% 8.61% 3.18% 1.34% 2.30% 5.74% 9.19% 58.86% 5–10 5–10 3.79% 11.54% 3.79% 11.54%12.69% 12.69%4.32% 4.32% 1.55% 1.55% 0.50% 0.50% 0.21% 0.21% 0.46% 0.46% 35.05%35.05% 5–10 3.79% 11.54% 12.69% 4.32% 1.55% 0.50% 0.21% 0.46% 35.05% 10–15 10–150.00% 1.49% 0.00% 1.49%2.37% 2.37%1.58% 1.58%0.37% 0.37% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 5.82% 10–1515–20 0.00% 0.00%1.49% 0.01%2.37% 0.25%1.58% 0.00%0.37% 0.00% 0.00% 0.02% 0.00% 0.00% 0.00% 0.00% 5.82% 0.27% 15–1520– 20 0.00%0.00% 0.01%0.01% 0.25%0.25% 0.00%0.00% 0.00% 0.02%0.02% 0.00%0.00% 0.00%0.00% 0.27%0.27% 0–20 19% 26% 24% 9% 3% 3% 6% 10% 100% 0–200– 20 19%19% 26%26% 24%24% 9%9% 3% 3% 3% 6% 6% 10% 10% 100%100% (b) N 25%

NW 20% NE 15% 10% 5% W 0% E

SW SE

Wind speed in [m/s] 0-5 5-10 10-15 15-20 Wind speed in [m/s] 0-5 5-10 10-15 15- Figure 6. Wind rose for the winter season 2010/2011 (a) and for the calibration period 1–12 February Figure 6. a Figure(b); data 6. WindWind from rosehttps://dane.imgw.pl/ for the winter season . 2010/2011 2010/2011 ( a)) and and for for the calibration period period 1 1–12–12 February February ((b); data from https://dane.imgw.pl/.https://dane.imgw.pl/. Water surface elevation measured in the Hel peninsula was used as the sea side boundary conditionWater surface for the calibrationelevation measured of the model. in the From Hel the peninsula land side, was was for used all the as as inflowing the sea side rivers boundary to the conditionconditionlagoon, forwaterfor thethe discharge calibration calibration boundary of of the the model. conditionsmodel. From From were the the land set. land side,Historical side, for all fordat the aall inﬂowingof the the inflowingwater rivers discharge torivers the existlagoon,to the lagoon,wateronly discharge on water the Elbląg discharge boundary and Pasłękaboundary conditions rivers, co werenditions thus set.historical were Historical set.hydrographs Hi datastorical of the were data water used of dischargethe for watercalibrations. exist discharge only For onthe exist the onlyElblNogat ˛agandon the and Pasł˛ekarivers,Elbl theąg Pregolya and Pas,łę thus theka rivers, historicalaverage thus discharge hydrographs historical was hydrograph usedwere [18] used, s which forwere calibrations. used is a simplification, for calibrations. For theNogat but For the andthe Nogatthecontribution Pregolya, and the the of Pregolya, averagethe rivers dischargethe to theaverage ice was dynamics discharge used [ 18on], the whichwa Vistulas used is a simpliﬁcation,Lagoon[18], which is negligible, is buta simplification, the and contribution limited tobut the of the the contributionriversareas to in the the of ice direct the dynamics rivers vicinity to on of the the ice river Vistula dynamics estuaries. Lagoon on the is negligible,Vistula Lagoon and limited is negligible, to the and areas limited in the to direct the areasvicinity inModel ofthe the direct calibration river vicinity estuaries. was of the done river to estuaries. compare water surface elevations at four locations along the PolishModel shore calibrationcalibration of the lagoon: waswas done done namely to to compare compare Osłonka, water Nowakowo,water surface surface elevations Toklmicko elevations at, fourand at locationsfourNowa locations Pasłęka along (seealong the Polish the the Polishshorelocations ofshore the in lagoon:of Figure the lagoon: namely1). It was namely Osłonka, assumed Os Nowakowo, łthatonka, the Nowakowo, ice covers Toklmicko, the Toklmicko, entire and Nowalagoon and Pasł˛eka(seeand Nowa its initial Pasłę the thicknesska locations(see the locationsinwas Figure 0.2 1in ).m. Figure It The was initial assumed1). It ice was thickness thatassumed the was ice that coverscalculated the theice covers entirewith the lagoonthe freezing entire and lagoondegree its initial dayand thickness methodits initial (F was DD)thickness 0.2 by m. wasThe initial0.2 m. iceThe thickness initial ice was thickness calculated was with calculat the freezinged with degree the freezing day method degree (FDD) day method by using (FDD) the daily by Water 2019, 11, x FOR PEER REVIEW 9 of 16 using the daily average air temperature for the entire season as shown on Figure 4. Ice monitoring in the Vistula Lagoon is rather scattered and there are no systematic ice thickness measurements for the winter season 2010–2011. However, Girjatowicz [6] measured an ice thickness of 21 cm on 8 February 2011 near Frombork, which is consistent with the calculated value. In the model simulation, ice cover of 20 cm initially covered the entire lagoon and at the beginning of the calibration period all ice was assumed to break up and was able to move according to the wind and water flow drag forces. The bed roughness and ice roughness were calibrated by a series of simulation runs. The final results of the calibration are shown in Figure 7, where the red dots represent the observed WSE and the black line is the simulated water level at each of the locations. It is worth noting that the water level increase starting on 12 February was mainly affected by high wind (nearly 20 m/s) but also increased fresh water inflow due to snow melting (see Figure 4). In addition to graphically presented results, the root-mean-square deviation (RMSD) was calculated according to the formula:

1 Water 2019, 11, 2297 RMSD = 𝐻 −𝐻 . 9(11) of 16 𝑛 average air temperature for the entire season as shown on Figure4. Ice monitoring in the Vistula RMSD results for all stations are shown in a Table 2. The objective of limiting inconsistencies Lagoon is rather scattered and there are no systematic ice thickness measurements for the winter between the observed and simulated values was satisfactorily met and the model parameters were season 2010–2011. However, Girjatowicz [6] measured an ice thickness of 21 cm on 8 February 2011 next used for a case scenario analysis. near Frombork, which is consistent with the calculated value. In the model simulation, ice cover of 20 cmTable initially 2. Calculated covered root-mean-square the entire lagoon deviation and at (RMSD) the beginning for the calibration of the calibration period from period 6 February all ice was assumedto 13 toFebruary break up2011. and was able to move according to the wind and water flow drag forces. The bed roughness and ice roughness were calibrated by a series of simulation runs. The final results of the calibrationStation are shown in FigureOsłonka7, where theNowakowo red dots represent theTolkmicko observed WSE andNowa the Pas blackłęka line is theRMSD simulated (m) water level0.065 at each of the locations.0.076 It is worth noting0.065 that the water level0.086 increase starting on 12 February was mainly affected by high wind (nearly 20 m/s) but also increased fresh In addition to the WSE calibration, the length and the thickness of ice thrusting on the lagoon water inflow due to snow melting (see Figure4). In addition to graphically presented results, the shore were analyzed and compared with forms observed in the field. According to [6], the longest ice root-mean-square deviation (RMSD) was calculated according to the formula: thrust observed in 2011 on the Vistula Lagoon was 140 m and the thickness of the ice at the shore was v up to five times the initial thickness of thet ice ncover. The simulation results show ice piled up on the 1 X shore between Frombork and RMSDTolkmicko= and the(H largest thicknessH was)2. up to 1.1 m and occurred (11) on n observed − simulated the night of 11–12 February, which is consistenti=1 with the observations. Satellite images from 9 March 2011 (Landsat 5) showed fractured cover and residual portions of ice hummocks, as seen in Figure 8.

1.2 1 Osłonka 0.8 0.6 0.4 WSE [m] 0.2 0 8-Feb-2011 9-Feb-2011 10-Feb-2011 11-Feb-2011 12-Feb-2011 13-Feb-2011 1.2 1 Nowakowo 0.8 0.6 0.4 WSE [m] 0.2 0 Water 2019, 11, x FOR PEER REVIEW 10 of 16 8-Feb-2011 9-Feb-2011 10-Feb-2011 11-Feb-2011 12-Feb-2011 13-Feb-2011 1.2 1 Tolkmicko 0.8 0.6 0.4 WSE [m] 0.2 0 8-Feb-2011 9-Feb-2011 10-Feb-2011 11-Feb-2011 12-Feb-2011 13-Feb-2011 1.2 1 Nowa Pasłęka 0.8 0.6 0.4 WSE [m] 0.2 0 8-Feb-2011 9-Feb-2011 10-Feb-2011 11-Feb-2011 12-Feb-2011 13-Feb-2011 Figure 7. MeasuredMeasured (red dots) and simula simulatedted (black line) WSE in Februa Februaryry 2011, at locations along the South Polish shore of the Vistula Lagoon.Lagoon.

Figure 8. Simulated ice thickness on 12 February 2011 and a satellite image of the southern part of the Vistula Lagoon (Landsat 5, 9 March 2011; https://eos.com/landviewer/).

3.2. Sensitivity Analysis of Ice Conditions in the Vistula Lagoon In the study, numerical simulations were performed for various flow and wind conditions which cover the most severe conditions for the Vistula Lagoon. The sensitivity analysis was made by varying the model parameters, which are wind speed, wind direction, and water level, in the Gulf of Gdańsk. All simulation cases run for the model domain included the proposed bathymetry and new strait. However, to make the simulations more reasonable, the new lock in Nowy Świat was constantly closed to avoid any water flow through the proposed strait. According to the project, the lock will only be open for navigation purposes, thus the flow exchange will be limited to the amount filled in the lock chamber. A comparison of the maximum ice loads predicted by DynaRICE showed that high wind velocity yielded the highest ice supply from the northern part of the lagoon and produced the most severe ice conditions in the Nowy Świat–Elbląg area. The water level in the southern Baltic Sea also affects the ice dynamics, leading to ice loads on lock harbors inside the lagoon.

Water 2019, 11, 2297 10 of 16

Water 2019, 11, x FOR PEER REVIEW 10 of 16 RMSD results for all stations are shown in a Table2. The objective of limiting inconsistencies between the1.2 observed and simulated values was satisfactorily met and the model parameters were next used for1 a case scenario analysis. Tolkmicko 0.8 0.6 Table 2. Calculated root-mean-square deviation (RMSD) for the calibration period from 6 February to 0.4 WSE [m] 13 February0.2 2011. 0 Station Osłonka Nowakowo Tolkmicko Nowa Pasł˛eka 8-Feb-2011 9-Feb-2011 10-Feb-2011 11-Feb-2011 12-Feb-2011 13-Feb-2011 1.2 RMSD (m) 0.065 0.076 0.065 0.086 1 Nowa Pasłęka 0.8 In addition0.6 to the WSE calibration, the length and the thickness of ice thrusting on the lagoon shore were0.4 analyzed and compared with forms observed in the ﬁeld. According to [6], the longest ice WSE [m] thrust observed0.2 in 2011 on the Vistula Lagoon was 140 m and the thickness of the ice at the shore was up to ﬁve times0 the initial thickness of the ice cover. The simulation results show ice piled up on the shore between8-Feb-2011 Frombork 9-Feb-2011 and Tolkmicko 10-Feb-2011 and the largest 11-Feb-2011 thickness was 12-Feb-2011 up to 1.1 m and 13-Feb-201 occurred1 on the nightFigure of 11–12 7. Measured February, (red which dots) is and consistent simulated with (black the line) observations. WSE in Februa Satellitery 2011, images at locations from along 9 March the 2011 (LandsatSouth 5) Polish showed shore fractured of the Vistula cover Lagoon. and residual portions of ice hummocks, as seen in Figure8.

FigureFigure 8. 8. SimulatedSimulated ice ice thickness thickness on on 12 12 February February 2011 2011 and and a a satellite satellite image image of of the the southern southern part part of of the the Vistula Lagoon (Landsat 5, 9 Marc Marchh 2011; https:https://eos.c//eos.comom/landviewer/)./landviewer/).

3.2.3.2. Sensitivity Sensitivity Analysis Analysis of of Ice Ice Conditions Conditions in in the the Vistula Vistula Lagoon Lagoon InIn the the study, study, numerical numerical simulations simulations were were performed performed for various various flow flow and and wind wind conditions conditions which which covercover thethe mostmost severe severe conditions conditions for for the the Vistula Vistula Lagoon. Lagoon. The sensitivityThe sensitivity analysis analysis was made was by made varying by varyingthe model the parameters, model parameters, which are which wind are speed, wind wind speed, direction, wind direction, and water and level, water in level, the Gulf in the of Gdańsk.Gulf of GdaAll simulationńsk. All simulation cases run cases for therun modelfor the domainmodel do includedmain included the proposed the proposed bathymetry bathymetry and new and strait. new strait.However, However, to make to the make simulations the simulations more reasonable, more thereasonable, new lock the in Nowy new Swiat´lock in was Nowy constantly Świat closed was constantlyto avoid any closed water to flowavoid through any water the flow proposed through strait. the Accordingproposed strait. to the According project, the to lock the willproject, only the be lockopen will for only navigation be open purposes, for navigation thus the purposes, flow exchange thus the will flow be exchange limited to will the be amount limited filled to the in amount the lock filledchamber. in the A lock comparison chamber. of A the comparison maximum of ice the loads maximum predicted ice loads by DynaRICE predicted showed by DynaRICE that high showed wind thatvelocity high yielded wind velocity the highest yielded ice supply the highest from theice northernsupply from part the of the northern lagoon part and producedof the lagoon the mostand produced the most severe ice conditions in the Nowy Świat–Elbląg area. The water level in the southern Baltic Sea also affects the ice dynamics, leading to ice loads on lock harbors inside the lagoon.

Water 2019, 11, 2297 11 of 16

´ Watersevere 2019 ice, 11 conditions, x FOR PEER in REVIEW the Nowy Swiat–Elbl ˛agarea. The water level in the southern Baltic Sea11 of also 16 affects the ice dynamics, leading to ice loads on lock harbors inside the lagoon. The resultsresults of of the the DynaRICE DynaRICE simulations simulations for fourfor hypotheticalfour hypothetical cases arecases presented are presented in the following in the followingsection. The section. first two The cases first representtwo cases typical represent storm typical events storm with even windsts blowingwith winds along blowing the lagoon, along from the lagoon,NE and from from NE SW. and In eachfrom case, SW. theIn each wind case, speed the waswind specified speed was as 12specified m/s with as a12 duration m/s with of a 24duration h. The ofwater 24 h. level The atwater the sealevel is at 0 mthe a.s.l., sea is the 0 m initial a.s.l., ice the thickness initial ice is thickness 0.2 m and is the0.2 dischargem and the fromdischarge the Nogat, from theElbl Nogat, ˛ag,Pasł˛eka,and Elbląg, Pas Pregolyałęka, and rivers Pregolya is equal rivers to the is equal long-term to the average long-term flow. average In all scenarios, flow. In all the scenarios, breakup theice conditionbreakup ice was condition simulated. was The simulated. DynaRICE The model DynaRICE simulates model ice simulates dynamics ice by dynamics using the SPHby using method the SPHwhich method is a pure which Lagrangian is a pure approach. Lagrangian In this approach. method, aIn continuum this method, is simulated a continuum by su isffi simulatedcient number by sufficientof elements number which of are elements referred which to particles. are referred In the to used particles. method, In thethe massused densitymethod, of the any mass point density in the ofspace any ispoint obtained in the by space summing is obtained up the by contributions summing up from the allcontributions particles surrounding from all particles that point. surrounding However, thatto simulate point. However, ice cover, iceto simulate particles areice cover, kept in ice initial particles locations are kept up to in the initial moment locations defined up asto thethe initiationmoment definedof the ice as cover the initiation breakup. of It the could ice cover be a function breakup. of It the could water be surfacea function elevation of the water change, surface but also elevation can be change,arbitrarily but introduced also can be at arbitrarily the time ofintroduced the breakup. at the In time all the of simulationsthe breakup. of In the all sensitivity the simulations study, of since the sensitivitythe ice properties study, since were the not ice known, properties it was were assumed not known, that the it breakup was assumed occurred that at the the breakup beginning occurred of the atsimulation the beginning time. of the simulation time. The results results show show that that wind wind blowing blowing from from the the NE NE causes causes the the drift drift of all of allice icein the in thelagoon lagoon in a inSW a directionSW direction and an and accumulation an accumulation along alongthe shore, the shore,as seen as in seen Figure in Figure9. Three9. main Three jam main sites jam are sites formed, are fromformed, which from the which first thehas first its hastoe itsnear toe Primorkoye near Primorkoye and is and formed is formed from fromthe ice the dragged ice dragged from from the Kaliningradthe Kaliningrad shores shores and andPrim Primorskayaorskaya bay. bay. The Thenext next jam jamsite siteis a isconsequence a consequence of the of narrowing the narrowing of the of lagoonthe lagoon near near the theMamonowo–Nowa Mamonowo–Nowa Pasłę Pasł˛ekaareaka area (Polish–Russian (Polish–Russian border). border). Once Once the ice the passes ice passes the narrowthe narrow area, area, it moves it moves down down to the to the Polish Polish part part of ofthe the lagoon lagoon and and finally finally forms forms the the last last jam jam on on the eastern side of the artificialartificial island and near Osłonka.Osłonka. The The last last jam location is of principle interest because thethe proposedproposed CDF CDF site site is is planned planned to beto transformedbe transformed into into a habitat a habitat improvement improvement project project (HIP), (HIP),and thus and it needsthus it to needs withstand to withstand the force causedthe force by ca theused ice. Theby the results ice. obtainedThe results from obtained the mathematical from the mathematicalmodel show a model 0.8-thick show ice a hummock0.8-thick ice formed hummock at the formed island at after the 24island h of after simulation. 24 h of simulation. This formation This formationcaused an icecaused load an on ice the load entire on eastern the entire shore eastern of the shore island of varying the island from varying 20 to nearly from260 20 to N /nearlym2 asseen 260 N/min Figure2 as seen 10. Sincein Figure the NE10. Since wind the drags NE ice wind from drags the Vistula ice from Spit, the thereVistula is noSpit, load there on theis no harbor load on of the harbornew strait. of the new strait.

FigureFigure 9. SimulationSimulation results results of of ice ice thickness thickness for for wind wind blowing from a North-East direction.

Water 2019, 11, 2297 12 of 16 Water 2019, 11, x FOR PEER REVIEW 12 of 16 Water 2019, 11, x FOR PEER REVIEW 12 of 16

FigureFigure 10. 10.Simulation Simulation results results ofof iceice loadload on the shore of of the the Vistula Vistula Lagoon Lagoon for for the the case case with with wind wind Figure 10. Simulation results of ice load on the shore of the Vistula Lagoon for the case with wind blowingblowing from from a North-Easta North-East direction. direction. blowing from a North-East direction. TheThe case case with with the the opposite opposite windwind directiondirection (blowing from from a a SW SW direction) direction) is isless less critical critical for for the the The case with the opposite wind direction (blowing from a SW direction) is less critical for the proposedproposed CDF CDF site. site. IceIce isis pushedpushed towardstowards the eastern and and northern northern side side of of the the lagoon lagoon and and some some accumulationproposed CDF is site. formed Ice isnear pushed Primorskoye towards and the alongeastern the and dams northern boarded side the of Kaliningrad the lagoon Seaand Canalsome accumulation is formed near Primorskoye and along the dams boarded the Kaliningrad Sea Canal fromaccumulation the lagoon is side,formed as seennear inPrimorskoye Figure 11. There and alongis also the a small dams ice boarded hummock the onKaliningrad the western Sea shore Canal of from the lagoon side, as seen in Figure 11. There is also a small ice hummock on the western shore of thefrom island; the lagoon however, side, due as seen to the in smallFigure ice 11. field, There the is fo alsorce abuilt small up ice at hummockthe CDF shore on the is westernrelatively shore small. of thethe island; island; however, however, due due to to the the small small ice ice ﬁeld, field, thethe forceforce builtbuilt up at at the the CDF CDF shore shore is is relatively relatively small. small.

Figure 11. Simulation results of the ice thickness for a wind blowing from a South-West direction. FigureFigure 11. 11.Simulation Simulation results results ofof thethe iceice thickness for a a wind wind blowing blowing from from a aSouth-West South-West direction. direction. The next scenarios are high and low sea level conditions at +1 m a.s.l. and −1 a.s.l. In these cases, to TheavoidThe next anext multiplication scenarios scenarios are are of high high the and effect,and low low the sea sea wind levellevel was conditionsconditions specified at as +1+ 10 m mm/s, a.s.l. a.s.l. and and and the −1 ice a.s.l.1a.s.l. conditions In Inthese these cases,were cases, − toidenticalto avoid avoid a multiplicationato multiplication previous cases. of of the Boththe e effect,ff casesect, the thecaused windwind intense was specified specified water dynamics as as 0 0 m/s, m/s, withinand and the the the iceice lagoon, conditions conditions resulting were were identicalfromidentical flow to to previousexchange previous cases.in cases. the Baltijsk Both Both casescases strait. causedcaused High water intenseintense levels water water at dynamicsthe dynamics sea is awithin withintypical the storm the lagoon, lagoon, condition resulting resulting for fromthefrom flowsouthern flow exchange exchange Baltic Sea; in in the thehowever, Baltijsk Baltijsk the strait. strait. water HighHigh surface water elevation levels levels at atrarely the the sea increases sea is is a atypical typical by 1 mstorm stormabove condition conditionthe normal for for thethe southern southern Baltic Baltic Sea; Sea; however, however, the the water water surfacesurface elevation rarely rarely increases increases by by 1 1m m above above the the normal normal

Water 2019, 11, 2297 13 of 16 Water 2019, 11, x FOR PEER REVIEW 13 of 16 levellevel inin thethe BayBay of of Gdańsk[ Gdańsk40 [40].]. The The described described scenario scenario is an is artificialan artificial case case referring referring to a 100-year to a 100-year storm stormcondition, condition, as determined as determined for the Portfor the of GdańskbyPort of Gda theńsk Institute by the ofInstitute Meteorology of Meteorology and Water and Resources. Water Resources.Resulting from Resulting the high from surge, the high a large surge, amount a large of amount sea water of sea inflow water entered inflow the entered lagoon the and lagoon ice cover and icewas cover pushed was from pushed the directfrom the vicinity direct of vicinity the Strait of of the Baltijsk. Strait of After Baltijsk. 24 h ofAfter steady 24 h high of steady water high level water at the levelsea side at the boundary, sea side significant boundary, displacement significant displaceme of the ice insident of the the ice lagoon inside was the observed. lagoon was Ice observed. was dragged Ice wasto the dragged lagoon shores,to the lagoon and thrusting shores, occurredand thrusting nearly occurred along the nearly entire along shore. the The entire largest shore. accumulation The largest is accumulationaffected by the is construction affected by ofthe the construction artificial island, of the which artificial stopped island, a largewhich amount stopped of icea large which amount jammed of iceagainst which the jammed eastern against bank ofthe the eastern island. bank The ofaccumulation the island. The reached accumulation up to0.5 reached m thick up (2.5to 0.5 initial m thick ice (2.5thickness) initial ice with thickness) a length with of the a length jam up of to the 20 jam km, up as to seen 20 km, in Figure as seen 12 in. ThisFigure ice 12. thrust This into ice thrust the island into 2 thecausing island a large causing force a of large up to force 100 N of/m upobserved to 100 onN/m the2 south-easternobserved on shore.the south-eastern It is noteworthy shore. that It the is noteworthyscenario did that not includethe scenario the wind did not eff ect,include which the may wind multiply effect, which the load. may multiply the load.

Figure 12. SimulationSimulation results results of of ice ice thickness thickness for a high water level at the Baltic Sea.

The case with a low sea level resulted in emptying the lagoon, and ice was pushed toward the Strait of Baltijsk.Baltijsk. DueDue toto thethe limited limited clearance clearance of of the the strait strait and and large large ice ice parcels parcels in thein the lagoon, lagoon, an icean jamice jamformed formed at the at lagoon the lagoon side ofside the of strait. the strait. As a consequence, As a consequence, only a only little amounta little amount of the ice of movedthe ice outmoved into outthe Balticinto the Sea, Baltic and afterSea, and 24 h after of simulation, 24 h of simulation, less than 2%less of than all ice 2% drifted of all downice drifted the strait down to the the strait sea. On to the entiresea. On lagoon, the entire the ice lagoon, was fractured the ice andwas was frac draggedtured and slowly was towarddragged the slowly strait; toward however, the no strait; other however,significant no accumulation other significant occurred, accumulation as seen occurred, in Figure as13 .seen A limited in Figure pile 13. was A limited formed pile on was the westernformed onshore the ofwestern the artificial shore islandof the andartificial this accumulationisland and this was accumulation dragged by was the movingdragged water by the and moving produced water a andload produced of up to 20 a Nload/m2 .of As up before, to 20 inN/m this2. simulation,As before, in the this wind simulation, effect was the omitted; wind effect therefore, was theomitted; effect therefore,could be expected the effect to could increase be expected in natural to conditions. increase in natural conditions.

Water 2019, 11, 2297 14 of 16 Water 2019, 11, x FOR PEER REVIEW 14 of 16

Figure 13. SimulationSimulation results results of of ice ice thickness thickness for a low water level at the Baltic Sea.

4. Conclusions Conclusions The results of the two-dimensional numerical simulations of of the the ice dynamics of of the Vistula Lagoon induced by storms and strong winds allow the following to be concluded: • even though the Vistula Lagoon freezes nearly every year, the ice dynamics of the lagoon are • even though the Vistula Lagoon freezes nearly every year, the ice dynamics of the lagoon are limited only to the breakup periods andand areare oftenoften drivendriven byby strongstrong windswinds andand stormstorm surgessurges • for the calibration period, the comparison of calc calculatedulated and observed water levels in the lagoon • shows that the proposed mathematical model an andd its numerical solution ensure satisfactory accuracy of the results • ice hummockshummocks simulated simulated for for the the calibration calibration period period occurred occurred at locations at locations indicated indicated in the literature, in the • literature,and theirthickness and their wasthickness similar was to thatsimilar observed to that observed • the long-lasting NE winds can result in ice movementmovement towards the western and southern parts • of the lagoon and a jam will be formed at the shore of the proposed CDF site, which is being considered to be a HIP in the future • according toto the the simulation simulation results, results, the proposedthe propos armoringed armoring of the CDFof the site CDF will site need will to withstand need to • withstanda force of up a force to 260 of N up/m, to which 260 N/m, is caused which by is thecaus iceed load by the produced ice load byproduced ice thrusting, by ice thrusting, • in the case of a low low water water level level at at the the Baltic Baltic sea, sea, ice ice was was moved moved towards towards the Strait Strait of of Baltijsk, Baltijsk, and and • due to its limited width, ice may cause cause accumulation at the lagoon side of the the strait, strait, which which should should be relieved by icebreakers. Author Contributions: conceptualization, methodology, software, validation T.K.; formal analysis, investigationAuthor Contributions: T.K., M.S. Conceptualization,and P.Z.; data curation methodology, T.K.; writing—original software, validation draft prepar T.K.; formalation T.K.; analysis, writing—review investigation andT.K., editing M.S. and T.K. P.Z.; and data M.S.; curation visualization T.K.; writing—original T.K. draft preparation T.K.; writing—review and editing T.K. and M.S.; visualization T.K. Funding: This research received no external funding. Funding: This research received no external funding. Conflicts of Interest: The authors declare no conflict of interest. Conﬂicts of Interest: The authors declare no conﬂict of interest. References References 1. Kjerfve, B. Coastal Lagoons. In Elsevier Oceanography Series; Kjerfve, B., Ed.; Coastal Lagoon Processes; 1. Kjerfve, B. Coastal Lagoons. In Elsevier Oceanography Series; Kjerfve, B., Ed.; Coastal Lagoon Processes; Elsevier: Amsterdam, The Netherlands, 1994; Volume 60, pp. 1–8. Elsevier: Amsterdam, The Netherlands, 1994; Volume 60, pp. 1–8. 2. Chubarenko, B.; Margoński, P. The Vistula Lagoon. In Ecology of Baltic Coastal Waters; Schiewer, U., Ed.; Ecological Studies; Springer: Berlin/Heidelberg, Germany, 2008; pp. 167–195, ISBN 978-3-540-73524-3.

Water 2019, 11, 2297 15 of 16

2. Chubarenko, B.; Margoński,P. The Vistula Lagoon. In Ecology of Baltic Coastal Waters; Schiewer, U., Ed.; Ecological Studies; Springer: Berlin/Heidelberg, Germany, 2008; pp. 167–195. ISBN 978-3-540-73524-3. 3. Kruk, M.; Kempa, M.; Tjomsland, T.; Durand, D. The use of mathematical models to predict changes in the environment of the Vistula Lagoon. In Vistula Lagoon—Natural Environment and Modern Methods of His Research Project on the Example of Visla; Publishing PWSZ: Elbl ˛ag,Poland, 2011; pp. 165–180. 4. Nadolny, A.; Samulak, M. Construction of a Waterway Connecting the Vistula Lagoon with the Bay of Gdańsk; Maritime Office: Gdynia, Poland, 2017; pp. 1–14. 5. Shen, H.T. Mathematical modeling of river ice processes. Cold Reg. Sci. Technol. 2010, 62, 3–13. [CrossRef] 6. Girjatowicz, J.P. Ice thrusting and hummocking on the shores of the Southern Baltic Sea’s coastal lagoons. J. Coast. Res. 2014, 30, 456–464. 7. Girjatowicz, J.P. Ice Cover Atlas for Polish Baltic Coastal Waters, 2nd ed.; ZUT, Maritime Office: Szczecin, Poland, 1990. 8. Girjatowicz, J.P. Ice condition in the Vistula Lagoon. Pol. Geogr. Rev. 1994, 66, 119–132. 9. Herman, A. Ice cover of the Vistula Lagoon. In Vistula Lagoon; Wydawnictwo Naukowe PWN: Warszawa, Poland, 2018; ISBN 978-83-01-19974-6. 10. Chubarenko, B.; Chechko, V.; Kileso, A.; Krek, E.; Topchaya, V. Hydrological and sedimentation conditions in a non-tidal lagoon during ice coverage—The example of Vistula Lagoon in the Baltic Sea. Estuar. Coast. Shelf Sci. 2019, 216, 38–53. [CrossRef] 11. Zhelezova, E.; Krek, E.; Chubarenko, B. Characteristics of the polynya in the Vistula Lagoon of the Baltic Sea by remote sensing data. Int. J. Remote Sens. 2018, 39, 9453–9464. [CrossRef] 12. Jevrejeva, S.; Drabkin, V.V.; Kostjukov, J.; Lebedev, A.A.; Leppäranta, M.; Mironov, Y.U.; Schmelzer, N.; Sztobryn, M. Baltic Sea ice seasons in the twentieth century. Clim. Res. 2004, 25, 217–227. [CrossRef] 13. Liu, L.; Li, H.; Shen, H.T. A two-dimensional comprehensive river ice model. In Proceedings of the 18th IAHR Symposium on River Ice, Sapporo, Japan, 28 August–1 September 2006. 14. Szymkiewicz, R. A mathematical model of storm surge in the Vistula Lagoon, Poland. Coast. Eng. 1992, 16, 181–203. [CrossRef] 15. Catewicz, Z.; Jankowski, A. Model H-N of stationary flows in Vistula Lagoon. Podstawy Gospodarki w Srodowisku´ Morskim III. Studia i Materiały Oceanologiczne 1983, 40, 223–249. 16. Szydlowski, M.; Kolerski, T.; Zima, P. Impact of the artificial strait in the vistula spit on the hydrodynamics of the Vistula Lagoon (Baltic Sea). Water 2019, 11, 990. [CrossRef] 17. Chubarenko, B.V.; Chubarenko, I.P. Regionalization of river Pregel estuary and Russian part of Vistula Lagoon on hydrophysical parameters. In Proceedings of the International Conference on Regionalization in Hydrology, Braunschweig, Germany, 10–14 March 1997; pp. 41–44. 18. Kwiatkowski, J.; Rasmussen, E.K.; Ezhova, E.; Chubarenko, B. The eutrophication model of the Vistula Lagoon. Oceanol. Stud. 1997, 26, 5–33. 19. Chubarenko, I.; Tchepikova, I. Modelling of man-made contribution to salinity increase into the Vistula Lagoon (Baltic Sea). Ecol. Model. 2001, 138, 87–100. [CrossRef] 20. Chubarenko, B.V.; Leitsina, L.V.; Esiukova, E.E.; Kurennoy, D.N. Model analysis of the currents and wind waves in the Vistula Lagoon of the Baltic Sea. Oceanology 2012, 52, 748–753. [CrossRef] 21. Bielecka, M.; Kazmierski, J. A 3D mathematical model of Vistula Lagoon hydrodynamics-general assumptions and results of preliminary calculations. Ground Water 2003, 80, 2–4. 22. Shen, H.T.; Liu, L. Shokotsu River ice jam formation. Cold Reg. Sci. Technol. 2003, 37, 35–49. [CrossRef] 23. Shen, H.T. River Ice Processes. In Advances in Water Resources Management; Handbook of Environmental Engineering; Springer: Cham, Poland, 2016; pp. 483–530. ISBN 978-3-319-22923-2. 24. Knack, I.M.; Shen, H.T. A numerical model study on Saint John River ice breakup. Can. J. Civ. Eng. 2016, 45, 817–826. [CrossRef] 25. Shen, H.T.; Gao, L.; Kolerski, T.; Liu, L. Dynamics of Ice Jam Formation and Release. J. Coast. Res. 2008, 52, 25–32. [CrossRef] 26. Kolerski, T.; Shen, H.T. Possible effects of the 1984 St. Clair River ice jam on bed changes. Can. J. Civ. Eng. 2015, 42, 696–703. [CrossRef] 27. Knack, I.M.; Shen, H.T. Numerical modeling of ice transport in channels with river restoration structures. Can. J. Civ. Eng. 2017, 44, 813–819. [CrossRef] Water 2019, 11, 2297 16 of 16

28. Shen, H.T.; Lu, S.; Crissman, R.D. Numerical simulation of ice transport over the Lake Erie-Niagara River ice boom. Cold Reg. Sci. Technol. 1997, 26, 17–33. [CrossRef] 29. Liu, L.; Shen, H.T. Numerical Simulation of River Ice Control with Booms; Engineer Research and Developemnt Center, Cold Regions Research and Engineering Laboratory: Hanover, NH, USA, 2000; p. 38. 30. Szydlowski, M.; Kolerski, T. Numerical Modeling of Water and Ice Dynamics for Analysis of Flow Around the Kiezmark Bridge Piers. In Free Surface Flows and Transport Processes; Springer: Cham, Poland, 2018; pp. 465–476. 31. Kolerski, T.; Shen, H.T.; Knack, I.M. A nested model for river Ice dynamics. In Proceedings of the 20th IAHR Ice Symposium, Lahti, Finland, 14–18 June 2010. 32. Kolerski, T.; Shen, H.T. Ice Modeling for HIP in the Upper Niagara River. In Progress Report submitted to Gomez and Sullivan Engineers, PC; Clarkson University: Potsdam, NY, USA, 2008. 33. Kolerski, T.; Shen, H.T.; Kioka, S. A numerical model study on ice boom in a coastal lake. J. Coast. Res. 2013, 291, 177–186. [CrossRef] 34. Shen, H.T.; Su, J.; Liu, L. SPH simulation of river ice dynamics. J. Comput. Phys. 2000, 165, 752–770. [CrossRef] 35. Ji, S.; Shen, H.T.; Wang, Z.; Shen, H.H.; Yue, Q. A viscoelastic-plastic constitutive model with Mohr-Coulomb yielding criterion for sea ice dynamics. Acta Oceanol. Sin. 2005, 24, 54. 36. Wu, J. Prediction of near-surface drift currents from wind velocity. J. Hydraul. Div. 1973, 99, 1291–1302. 37. Liu, L.; Shen, H.T. A Two-Dimensional Characteristic Upwind Finite Element Method for Transitional Open Channel Flow; Clarkson University: Potsdam, NY, USA, 2003; p. 54. 38. Kolerski, T. Mathematical modeling of ice dynamics as a decision support tool in river engineering. Water 2018, 10, 1241. [CrossRef] 39. Girjatowicz, J.P. Forms of onshore ice thrusting in coastal lagoons of the southern Baltic Sea. J. Cold Reg. Eng. 2014, 29, 04014008. [CrossRef] 40. Szymkiewicz, R. Hydrodynamics of Vistula Lagoon; Polish Academy of Sciences: Warsaw, Poland, 1992.

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).