ISSN 00014370, Oceanology, 2012, Vol. 52, No. 5, pp. 700–709. © Pleiades Publishing, Inc., 2012. Original Russian Text © I.O. Leont’yev, 2012, published in Okeanologiya, 2012, Vol. 52, No. 5, pp. 757–767. MARINE GEOLOGY

Predicting Shoreline Evolution on a Centennial Scale Using the Example of the Vistula (Baltic) I. O. Leont’yev Shirshov Institute of Oceanology, Russian Academy of Sciences, Moscow, Russia Email: [email protected] Received March 31, 2011; in final form, November 22, 2011

Abstract—The proposed algorithm comprises three main steps. The first step is the evaluation of the sedi ment transport and budget. It was shown that the root segment of the Vistula Spit is dominated by eastward longshore transport (up to 50 thousand m3/year). Over the rest of the spit, the shoreline’s orienta tion causes westward (more than 100 thousand m3/year). The gradients of the longshore and cross shore sediment transport become the major contributors to the overall sediment balance. The only exception is the northeastern tip of the spit due to the appreciable imbalance of the sediment budget (13 m3 m–1 yr–1). The second step in the prediction modeling is the estimation of the potential sealevel changes during the 21st century. The third step involves modeling of the shoreline’s behavior using the SPELT model [6, 7, 8]. In the most likely scenario, the rate of the recession is predicted to be about 0.3 m/year in 2010–2050 and will increase to 0.4 m/year in 2050–2100. The sand deficit, other than the sealevel rise, will be a key factor in the control of the shoreline’s evolution at the northeastern tip of the spit, and the amount of recession will range from 160 to 200 m in 2010–2100. DOI: 10.1134/S0001437012050104

INTRODUCTION Finally, any particular model that relates the sedi mentary budget and the sealevel changes to the rate of The Vistula (or Baltic) spit is a long narrow land the shoreline’s advance or retreat is a potential tool for form created by sand deposition with a welldeveloped predictions. In this study, the SPELT model was used belt of . The spit separates the Gdansk Bay of the to describe the longterm evolution of the shoreline on Baltic Sea from a , also known as the Vistula engineering and geological timescales [6, 7, 8]. A brief Bay (Fig. 1). The studied area is the spit’s coast, which description of the model is presented below. shows no evident trend for , except for the areas of the northeastern tip of the spit, where shore line’s recession is the greatest [1]. Of particular inter PREDICTION MODEL est for this study are attempts to forecast the behavior The SPELT model is based on the mass conserva of the shoreline in the 21st century in response to the tion principle: predicted sealevel changes, especially in terms of its high recreational value. The retreat of the shoreline for ∂ h =−+Er Ac w, (1) periods of 20, 50, or 100 years can be of primary ∂t importance from a practical standpoint. where h is the depth; t is the time; w is the rate of the In the present study, we propose a method for esti sealevel change; and Er and Ac are the erosion and mating the shoreline’s morphological changes (using accretion rates, which depend on the depth, beach the example of the Vistula spit), which can be further slope, and distance offshore. Their scale depends on applied to other locations with a similar coastal envi the potential annual erosion volume, which, in turn, is ronment. a function of the total annual wave energy flux reach ing the beach. The calculation of the net sedimentary budget in the morphodynamic system that comprises the area of From Er = Ac, we have the equilibrium profile interest is a prerequisite for such a model [5]. The equation longshore and crossshore components of the sedi p hx⎛⎞ n + 1 ment budget are in direct or indirect relation to the =−11⎜⎟ − , p = , (2) wave energy flux to the morphodynamic system. hl∗∗⎝⎠ m + 1

Another important component of the prediction where h∗ is the closure depth and l∗ is the length of the model is the sealevel rise scenario. Some of the exist profile. For the typical case, m = 2, n = 3.5, and p = ing scenarios are used in this study. 1.5.

700 PREDICTING SHORELINE EVOLUTION ON A CENTENNIAL SCALE USING 701

N Baltic Sea

Hel Peninsula

Gransk Bay Baltiisk

111 P4 lux rgy f e ene Wav P3 107 ay l B P2 ua st is 6.6 V 48.0 Gdansk P1 10 km P0 Skowronki Vistula R.

Fig. 1. Sketch map of the studied area. The crosses denote the studied locations. The arrows and numbers show the sediment transport’s direction and volume in thousand m3/year. The dashed line represents the boundary between the westward and east ward sediment transport.

Using equation (1) integrated over the length of the from (3) and (4) that the changes in the length of the profile, we define the rate of the shoreline’s changes beach’s profile l∗ due to the sediment budget imbal ∂∂xt0 / either in response to the sealevel rise ances will influence the rate of the beach’s movement in response to the sealevel rise. Integrating equations ∂x wl( ∗ + l) 0 =− b , (3) (3) and (4), we calculate the rate of the displacement ∂+thz∗ b of both the shore and the entire profile during their evolution. or due to the sediment budget imbalances (B) At the engineering timescales (decadal), the clo ∂x 0 = B , (4) sure depth h∗ is calculated depending on the annual ∂t p + 12hour exceedance of the significant wave height hz∗ b p + 1 H s0.14%, i.e., 0.14% of the years [13]: where l is the length of the subaerial portion of the H b hH=−2.28 68.5 Hs0.14% , (5) profile, and is the elevation of the beach. ∗ ss0.14% 0.14% 2 zb gTp0.14% Relationship (3) is given by [11], which states that the profile reacts to a sealevel rise by where Tp0.14% is the extreme wave height period with a eroding sand from the beachfront and depositing it 0.14% exceedance frequency, and g is the acceleration offshore such that the active profile retreats landward due to gravity. while remaining constant relative to the sea level. If a foredune is present, some portion of the sand is eroded from the foredune and deposited to the backshore, INPUT PARAMETERS whereas the other portion of sand maintains the land The beach sediment of the Vistula (Baltic) spit ward relocation of the eroded foredune. (Fig. 1) is composed of relatively homogeneous fine An imbalance in the sediment budget can be a fac to mediumgrained sand. The features of the profile tor in the changes in the length and slope of the beach. with an average nearshore bottom slope of 0.01 If the sediment budget is positive (B > 0), the beach include the bar and the trough. The subaerial part of advances; if the sediment budget is in deficit (B < 0), the beach has a width of a few tens of meters and is the beach retreats. Since the lowermost point of the margined by a a few meters in height (sometimes profile corresponding to the closure depth remains at more than 10 m) [3]. a constant depth, the beach’s slope will increase in the The wave data available in this study are courtesy of first case and decrease in the second case. It follows the Institute of Hydroengineering of the Polish Acad

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Table 1. Wave statistics for Gdansk Bay at the 70 m depth Wind Wind , m/s , m , s , h , m/s , m , s , h direction W Hs Tp tw direction W Hs Tp tw WSW 7 0.68 3.74 73.7 N 7 0.71 5.96 630.7 9 1.15 4.21 11.7 9 1.22 7.11 305.6 11 1.65 4.89 1.2 11 1.71 7.90 146.6 13 2.17 5.27 0.2 13 2.22 8.51 73.3 W 7 0.69 4.84 138.3 15 2.73 9.14 42.0 9 1.18 5.42 34.2 17 3.21 9.63 21.8 11 1.68 6.43 7.7 18.5 3.73 10.07 12.0 13 2.22 7.03 1.1 20 4.21 10.48 8.2 15 2.64 7.5 0.2 21.5 4.72 10.98 3.3 WNW 7 0.71 5.86 337.6 NNE 7 0.69 5.26 274.9 9 1.20 6.95 130.5 9 1.20 6.54 73.5 11 1.70 7.78 49.4 11 1.72 7.47 26.5 13 2.18 8.49 16.2 13 2.21 8.27 8.8 15 2.68 8.97 3.7 15 2.66 8.54 3.2 17 3.18 10.26 1.1 17 3.22 9.16 1.0 18.5 3.69 10.36 0.2 18.5 3.71 9.97 0.2 NW 7 0.71 5.50 460 NE 7 0.68 5.30 90.8 9 1.21 6.75 165.6 9 1.19 6.72 16.3 11 1.71 7.56 68.9 11 1.65 7.40 5.7 13 2.21 8.27 27.0 13 2.25 8.19 0.8 15 2.70 8.82 11.8 ENE 7 0.63 4.84 44.2 17 3.19 9.25 3.4 9 1.14 6.30 2.9 18.5 3.69 9.70 1.0 11 1.69 7.36 0.3 20 4.21 10.07 0.4 NNW 7 0.71 5.59 235.7 9 1.21 6.86 100.1 11 1.72 7.61 42.5 13 2.21 8.14 22.2 15 2.72 8.68 10.6 17 3.22 9.28 7.1 18.5 3.71 9.73 3.6 20 4.23 10.18 1.3 21.5 4.71 10.61 0.7 emy of Sciences (IBW PAN). The wave parameters in mated from peak data in Table 1. From these results,

Table 1 include the yearly duration tw of the mean we can derive that H s0.14% = 4.2 m and Tp0.14% = 10.3 s. annual significant wave heights H s for different wave Then, the closure depth, according to (5), is defined as == directions and the associated peak wave periods Tp . hH∗ 2 s0.14% 8.4 m. The data also include the average wave height and peak period (H and T), which can be calculated from the Figure 3 shows the typical subaqueous profile of the nearshore beach slope of the studied area and the values of and . H s Tp equilibrium profile given by equation (3) for m = 2 and Figure 2 shows the significant wave height and peak n = 3.5. It can be seen that the theoretical curve well period exceedance functions (P(H) and P(T)) esti approximates the main features of the observed profile

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1.000 1.000

0.500 0.500

0.100 0.100 ) )

H 0.050 T 0.050 ( ( P P

0.010 0.010 0.005 0.005

0.001 0.001 012345 46810 Hs, m Tp, c

Fig. 2. Wave height exceedance curves.

(the bar and the trough are taken as secondorder per SEDIMENT BUDGET turbations). The sediment budget B in the morphodynamic sys The following parameters of the beach’s profile tem is the difference between the crossshore sediment were used in modeling the litho and morphodynamic fluxes through the lower (q∗ ) and upper (qAeol ) bound processes: the length of its active part from the shore aries of the profile, the gradient of the longshore sedi line to the closure depth, l∗ = 800 m; the width of the ment transport (∂∂Qy ), and any additional sediment Ω subaerial part of the beach, lb = 50 m; and the eleva source or sink ( ): tion of the beach’s crest, zb = 3 m. The sand sediment Bq=− q −∂∂+Ω Qy . (6) is characterized by the following parameters: the mean ∗ Aeol ρ × The sand sources and sinks may be produced either grainsize ds = 0.25 mm, the particle density s = 2.65 3 3 σ by or sand mining and dredging 10 kg m , and the porosity = 0.4. activities. Since no data on any such activity are avail The sediment fluxes were calculated for several able for the studied area, we therefore assumed Ω = 0. representative locations near the Vistula ’s mouth (P0) and in the proximal root (P1), central (P2), and distal zones (Р3, Р4) of the Vistula spit Longshore Sediment Transport and Gradient (Fig. 1). The azimuth angles of the normal to the The net longshore sediment transport Q is given by shoreline at the above points are given in Table 2. QQt= ∑∑()′ , (7) The calculations using the parameters in Table 1 wij gave a value of the annual wave energy flux of 3.56 × ji 1010 J m–1 yr–1, and the azimuth of the energy flux is where the subscripts j and i denote the given direction 164o (Fig. 1). and the given wave height, respectively. The longshore sediment transport rate Q' for indi vidual wave events was calculated using a modification Profiles of the equation formulated in the author’s previous 0 Observed work [4]: Calculated: m = 2, n = 3.5 –2 ⎛⎞gh QEC′ =μ+ε0.04 0.8 B ()sinΘΘ cos , –4 ⎜⎟sgBBB ⎝⎠ws (8) ≤ –6 ds 1 mm, Depth, m –8 ε where s = 0.02 is the coefficient measuring the sus 0 200 400 600 800 pended load transport’s efficiency, and ws is the falling Distance, m velocity. If Q is presented in m3/h, then ρ μ=3600 /[g ( ρs −ρ )(1 −σ )], where is the density of ρ σ Fig. 3. Typical bottom profile in the vicinity of Skowronki the water, and s and are the density and porosity of and the theoretical equilibrium profile. the sediment. A key parameter is the wave breaking

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Table 2. Longshore sediment transport at different locations of the Vistula spit coast Point no. P0 P1 P2 P3 Azimuth of the normal to the shoreline 360° 350° 315° 309° Eastward transport rate, thousand m3/year 57.8 54.0 15.3 13.4 Westward transport rate, thousand m3/year –9.8 –47.4 –122.2 –124.5 Total volumetric transport rate, thousand m3/year 48.0 6.6 –106.9 –111.1 depth h , which is defined by the constant wave energy to variations of the shoreline’s orientation relative to B the prevailing wave energy flux (Fig. 1). Near the Vis flux ()cos()cosECgg∞∞Θ=EC B ΘB , where the sub scripts ∞ and B denote the deep water and the break tula River’s mouth, the energy flux drives the eastward sediment transport (about 50 thousand m3/year). The ing point, and Cg is the wave group velocity provided waves dissipate energy as they propagate along the root =π = that CgTgp∞ (1 / 4 ) , CghgB B . Finally, we obtain zone of the spit. Over the rest of the spit, the shore line’s orientation causes the westward sediment trans 2/5 2/5 port. In the zone near the northeastern tip of the spit, ⎛⎞1 4/5 2 1/5 ⎛⎞cosΘ∞ hHg= ⎜⎟ ∞ ()T⎜⎟, the flux increases rapidly from 0 at point P4 to over Brπγ2 msp⎝⎠Θ ⎝⎠4 B cos B (9) 100 thousand m3/year at point P3. In the central zone of the spit, the flux is relatively homogenous and starts γ=H rmsB B , dissipating energy as it approaches the root zone. hB The contribution to the sediment budget arises not =π where HHrms (2/ ) is the rootmeansquare from the sediment fluxes themselves but from their ∂∂ wave height, and TTp = 1.2 is the wave peak period. gradients Qy , which are shown in Table 3. Over We assume the wave breaking depth for the 1% much of the shoreline, the gradients are negative. They indicate the longshore sediment supply, i.e., gains in exceedance waves and the wave heights hB H1%B the sediment budget. However, the gradient is positive = reaching the ratio of Hh1%BB 0.8, then, for the at the northeastern tip of the spit, indicating sediment Rayleigh distributed wave heights, we have losses due to the increased volumes of transport in the =γ = Θ HhrmsB B B 0.37. The wave approach angle B is westward direction. calculated using Snell’s law:

sinΘ=ΘCC sin∞∞ , BB (10) Aeolian Sediment Transport from the Beach ==π() CghCgTBB,2.∞ p Onshore winds move the sand sediment to the fore shore, where the windblow sand is trapped by vegeta In step 1, the depth hB is calculated while not accounting for the variations in the angles Θ . In step 2, tion causing the sediment’s accretion landward the Θ dune crest. This results in the loss of beach sediment, hB is adjusted with the adjustment of B to the calcu i.e., aeolian sand transport, which is calculated as Θ lated value of B . = ()′ , (12) On the basis of field tests [18], a modification of for qcAeol A∑∑ qtAeol w ij mula (8) can be used for the case of gravel and pebble: ji ⎛⎞25d where the subscripts j and i denote the given direc QEC'0.041=μ−⎜⎟s ()sincos,ΘΘ ⎝⎠H gBBB (11) tion (only onshore winds are considered) and the rmsB given wind speed, respectively. The aeolian sedi ≤≤ 1100ds mm. ′ ment transport rate qAeol is evaluated based on the The above sediment transport formulas imply that recommendations outlined in the Coastal Engi the sediment is available in a sufficient quantity on the neering Manual [12]: bottom for significant transport. The calculations using the data from Table 1 give the results shown in ⎛⎞3 =ΘuD Table 2, which represent the eastward and westward qK'Aeol ⎜⎟cos , ⎝⎠ sediment transport and the net transport at a given gds = point of the shoreline (the eastward transport is uWD 0.0037410 , (13) assigned a positive quantity). The longshore transport Kd=−+0.226exp( 9.63 4910 ), distribution is shown in Fig. 1. s

The results indicate the presence of two opposite where ds is the mean grain size of the sand. Aeolian transport directions along the Vistula spit’s coast due transport may occur at the wind speed W10 exceeding

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Table 3. Quantification of the contributions to the sediment budget at different locations of the Vistula spit’s coast Location P0–P1 P1–P2 P2–P3 P3–P4 ΔQ, thousand m3 yr–1 –41.4 –113.6 –6.0 111.1 Δy, km 18 24 14 10 ΔQ/Δy, m3 m–1 yr–1 –2.3 –4.7 –0.4 11.1 3 –1 –1 qAeol, m m yr 9.7 9.0 7.9 7.6 3 –1 –1 q*, m m yr 6.6 6.3 5.9 5.9 Budget, m3 m–1 yr–1 –0.8 2.0 –1.6 –12.8

the threshold value of W'10 for dry sand or W"10 for The finer sands, due to their high mobility, move moist sand; that is, seaward, while the coarse material considerably con tributes to the beach’s sediment budget. Near the ′ ′′=+ ′ Wgd10 = 147 s ,WW10 10 5.0 (14)lower boundary of the active profile, this coarse sedi ′ (the subscript 10 denotes a 10 m height above the ment is transported as the flow velocity. Therefore, q∗ ground). is calculated by the sediment transport rate formula [4, Because of the limited extent of the beach during 9, 16], which takes only the flow velocity into account: onshore winds, the wind is not saturated with sand [2, ⎡⎛π ε+uUU ⎞⎤ 10]. The finer sand is easily blown away, and changes qD′ =μ91bm2 cos Θ+ wc. (16) ∗ ⎢⎥Φ f ⎜⎟ in the mean grain size to the coarser size range affect ⎣⎝82tg umm u ⎠⎦ the mobility of the sediment. The slope gradient and If q′ is presented in m3 m–1 h–1, then µ = surface moisture of the sand beds also cause a decrease ∗ 3600 /[ (ρ−ρ )(1 −σ )]; where Φ is the slope of the in the aeolian transport rate. As a result, the actual g s sand transport rate will be less than the calculated rate land; um is the orbital velocity at the bottom; D f is the for the case of infinite horizontal sediment transport. energy dissipation due to friction; Uw and Uc are the Therefore, the correction coefficient c ≈ 0.5 should flow velocities at the bottom due to the wave and cur A ε be introduced in (12) to calculate the sediment trans rent actions, respectively; and b is the efficiency of ′ port rate qAeol for moist sand when the threshold veloc the bedload transport. The uu2mm ratio is the har monics amplitude, i.e., the asymmetry in the wave ity increases considerably [5]. Since c A incorporates a number of factors that are hard to quantify, the errors velocities. ′ in the calculation of qAeol can be significant. A value of q∗ was calculated using the data from Because of the lack of reliable wind statistics, the Table 1 for the beach profile shown in Fig. 2. It was wave data used in our study were calculated from the shown that the value of q∗ decreases slightly from the relevant wave parameters from Table 1. The wind west to east, but it generally approximates a constant speeds W are also given in Table 1. It was shown that (with an average of 6.2 m3 m–1 yr–1). The values of the qAeol is generally homogeneous (with an average value crossshore sediment transport rateq∗ for different of 8.7 m3 m–1 yr–1) and slightly decreases toward the shoreline segments are shown in Table 3. tip of the spit. The values of qAeol at different points of the shoreline are given in Table 3. Localization of the Shoreline’s Stability and Instability Sediment Transport at the Closure Depth The last row of Table 3 represents the sediment budget calculated using formula (6). At first glance, The crossshore sediment transport q∗ across the the alternation of the sediment losses and gains is lower part of the active profile can be attributed to a reflected in the beach’s profile. While these results are variety of effects, which include the wave asymmetry, approximate estimates, the variation of B in the range the flow velocity, and the storm surges. The net cross of, for instance, ±2 m3 m–1 yr–1 may be most likely shore sediment transport rate is given as equated with the net balance of the sediment, since equal volumes of erosion and accretion give a near qqt∗∗= ∑∑()′ , (15) wij equilibrium beach profile. This conclusion seems to be ji reasonable for the main segment of the shoreline where q′∗ is the elemental crossshore transport of sed located westward of point P3. iment for individual wave events with a year period tw This conclusion is in general agreement with the (the subscripts j and i denote the given direction and available data on the shoreline/foredune base’s change the given wave height, respectively). [1, 3, 15]. The width of the beach varies on the order

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Table 4. Sealevel changes in the 21st century under the two most likely scenarios

A1FI B1 Years ζ ζ ζ ζ min, wmin, max, wmax, min, wmin, max, wmax, mm mm/year mm mm/year mm mm/year mm mm/year

1990 0 0 0 0 2000 9 0.9 28 2.8 12 1.2 25 2.5 2010 19 1.0 60 3.2 26 1.4 56 3.1 2020 32 1.3 99 3.9 44 1.8 92 3.6 2030 48 1.6 146 4.7 64 2.0 132 4.0 2040 69 2.1 204 5.8 84 2.0 178 4.6 2050 96 2.7 278 7.4 105 2.1 227 4.9 2060 130 3.4 368 9.0 127 2.2 279 5.2 2070 165 3.5 471 10.3 145 1.8 333 5.4 2080 200 3.5 584 11.3 161 1.6 388 5.5 2090 234 3.4 701 11.7 175 1.4 444 5.6 2100 266 3.2 819 11.8 185 1.0 496 5.2 of a few meters year, which is typical of accretive and 185 and 496 mm under B1. The estimates in all the shorelines, and also exhibits a cyclic trend on a decadal other scenarios are within the same range. scale. For example, on the Polish side of the spit, the The average rates of the relative sealevel rise w average shoreline advance was 0.15 m/year in 1911– min and wmax for each decade are given Table 4. These rates 1979 with the same amount of retreat in 1960–1983. are up to 11.8 mm/yr under A1FI and up to 5.6 mm/yr In 1971–1983, the shoreline receded at a much faster under B1. The maximum rates are predicted for the rate most likely due to the sea level’s rise (at this loca end of the 21st century, while the minimum rates are tion, it was on the order of 0.15 m in the second half of predicted to occur in the middle of the 21st century the past century [17]). The shoreline on the Russian followed by stabilization or slowing down. The varia side of the spit was dominated by accretion over the tions of the sea level and of the rates of the sealevel past decade [1]. increase during the 21st century are shown in Fig. 4. The northeastern tip of the spit exhibits substantial The aggregated results of the above scenarios may sediment losses associated with the initiation of the be either decreasing or increasing depending on the southwesterly longshore transport. The field observa potential regional differences, such as the local tec tions confirm that the shoreline at the spit end under tonic movements. Since the studied shoreline is goes severe erosion and retreat of 2 m/year [1]. located in a relatively tectonically stable area, the effects of the tectonics on the shoreline’s evolution SEALEVEL CHANGE would not be large on the centennial scale. Based on the available data [14], the sea level will continue to rise due to the global warming and both FORECASTING THE SHORELINE’S the past and future greenhouse gas emissions. There MOVEMENT are several scenarios that exist for the 21st century, which vary considerably in their estimates of the ther The sealevel rise should cause the gradual retreat mal expansion of the oceans due to the warming and of the shoreline and the landward advance of the entire ice melting. active profile (according to Bruun’s rule (3)). Predic tions of the shoreline movements were obtained for Each of the two likely scenarios used in this study two cases. The first case considers the root segment of (A1FI and B1) comprises a low and a high case of the the shoreline where the sediment budget is almost bal ζ ζ sea level’s change—min and max [14]—and both are anced (B = 0) and the profile’s parameters remain presented in Table 4. These scenarios are referenced to constant. The second case describes the northeastern the 1990 sea level. tip of the spit with a sediment deficient at the shoreline For 2010, the minimum and maximum estimates (B = –12.8 m3 m–1 yr–1) and a reduction in the pro of the sea level’s rise are 266 and 819 mm under A1FI, file’s slope during the evolution.

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800 (а) A1F1 Max

600 B1 Max 400 A1F1 Min 200 Min Sea level, mm Sea level, B1 0 1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 12 (b) A1F1 Max 10 8 6 B1

mm/year Max , 4 A1F1 w Min 2 B1 Min 0 1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 Years

Fig. 4. Sealevel changes (a) and the rate of the sealevel rise (b) during the 21st century under different scenarios.

The calculated recession values for each decade observed values [1] and might slightly increase in the from 1990 to 2100 are plotted in Fig. 5. The compari future. The predicted shoreline recession was expected son of Figs. 5a and 5b shows an order of magnitude to be 30–40 m in 2010 relative to the shoreline posi difference between the predicted rates of the recession tion of 1990. The amount of the recession will range for the root segment and the northeastern tip of the from 70 to 90 m by 2050 and from 160 to 200 m by spit. 2100 relative to the predictions for 2010. The amount of the shoreline’s recession predicted It should be noted that a combination of a sealevel for the root segment of the spit is 1.5–4.5 m in 2012 rise and a sand deficit cannot be the simple sum of the compared to the position of shoreline in 1990. In contribution of all the factors. The basic assumption is 2050, the amount of recession will range from 7 to that the length of the profile l∗ gradually increases at a 21 m, while continuing to increase from 14 to 61 m by negative sediment budget, which will cause, according 2100. The least amount of recession is predicted under to (3), the more rapid migration of the profile in the lowcase scenarios, while the greatest values of the response to the sealevel rise at each stage of the shore recession under the worst case of the A1FI would line’s evolution. This, in turn, should cause a progres require that certain coast protection measures such sive increase in the recession rates with time. flood defenses be implemented. The B1 world, which appears to be a compromise Now, we assume that the root segment of the spit scenario, predicts a sealevel rise of 0.5 m by the end of must be nourished in order to maintain stability. In the 21st century. In this case, the predicted recession is estimating the quantity of the beach’s nourishment, 6 m in 2030, 13 m in 2050, and 33 m in 2100 compared one should consider the possible scenarios of the to the shoreline’s position in 2010. The average shoreline shoreline’s evolution at different values of B > 0 and recession rates are predicted to range from 0.3 m/year in select the most appropriate one. As an example, Fig 2010–2050 to 0.4 m/year in 2050–2100. These values ure 6 shows the nourishment volume of 3 m3 m–1 yr–1. can be seen as fairly realistic. Then, taking the pessimistic view, the amount of the recession would not be greater than 20 m. Taking the For the northeastern tip of the spit, the sand deficit optimistic view, the shoreline would be stabilized at a is the main factor in the control of the shoreline’s evo mark +5 m. lution. A rising sea level will be of minor importance due to the negligible difference in the predicted reces To achieve the same result on the northeastern tip sion rates under all the scenarios. The present reces of the spit would require a much greater volume of sed sion rate is about 2 m year, which is close to the iment.

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0 (а)

–10

–20

–30 A1F1 Min A1F1 Max –40 B1 Min B1 Max –50

–60 1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 0 (b)

–40

Shoreline’s retreat, m –80

–120

–160

–200

–240 1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 Years

Fig. 5. Predictions of the shoreline’s retreat for the 21st century under different sealevel rise scenarios: (a) for the root segment of the Vistula spit; (b) for the northeastern tip of the spit.

30

20

10

0 A1F1 Min –10 A1F1 Max B1 Min Shoreline movement, m Shoreline movement, –20 B1 Max –30 1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 Years

Fig. 6. Predicted shoreline movements over the root segment of the spit in response to the nourishing volume of 3 m3 m–1 yr–1.

CONCLUSIONS flux along the coastline of the Vistula spit is 3.56 × 1010 J m–1 yr–1. The prediction algorithm used in this study consists of three steps. At the first step, we determine the sedi The results suggest the existence of sediment trans ment budget by computing the wave energy flux and port in two opposite directions along the coastline of the sediment transport rates at different coast loca the Vistula spit. The eastward sediment transport has a tions. The calculated value of the onshore wave energy maximum rate of 50 thousand m3/year near the Vistula

OCEANOLOGY Vol. 52 No. 5 2012 PREDICTING SHORELINE EVOLUTION ON A CENTENNIAL SCALE USING 709

River’s mouth, which decreases to zero with the REFERENCES approach to the root zone of the spit. Over the rest of 1. V. P. Bobykina, in Proceedings of International Confer the spit, the shoreline’s orientation causes a westward ence (SchoolSeminar) on Dynamics of Coastal Area of sediment transport, which reaches its maximum rate Low Tide Seas (Terra Baltika, Kaliningrad, 2008), of 100 thousand m3/year in the central zone of the spit. pp. 37–38. The rate of the sediment transport across the lower 2. G. V. Vykhovanets, Eolian Process on the Sea Shore boundary of the active profile (with an average value of (Astroprint, Odessa, 2003) [in Russian]. 6.2 m3 m–1 yr–1) is found to be somewhat lower than 3. Ya. S. Kobelyanskaya, in Proceedings of International Conference (SchoolSeminar) on Dynamics of Coastal that of the aeolian transport through the upper beach 3 –1 –1 Area of Low Tide Seas (Terra Baltika, Kaliningrad, (with an average value of 8.7 m m yr ). Finally, the 2008), pp. 56–58. gradients of the longshore and crossshore sediment 4. I. O. Leont’yev, Coastal Dynamics: Waves, Currents and transport become the major contributors to the overall Silts (GEOS, Moscow, 2001) [in Russian]. sediment balance (B ≈ 0). The only exception is the 5. I. O. Leont’yev, “A Budget of Silts and Forecast of northeastern tip of the spit due to the appreciable imbal Coastal Area Development,” Okeanologiya 48, No. 3, ≈ 3 –1 –1 ance in the sediment budget (B –13 m m yr ). The 467–476 (2008). field observations confirm our conclusions concerning 6. I. O. Leont’yev, in Proceedings of the XXVIII Interna the coast’s state drawn on the basis of the sediment tional Coastal Conference on the Concept on Development budget calculations. of Marine Shores: Century Traditions and Contemporary The second step in the prediction modeling is the Ideas (St. Petersburg, 2010a), pp. 81–83. estimation of the potential sealevel changes for the 7. I. O. Leont’yev, in Fundamental and Applied Hydro period of interest. Under the widely accepted scenar physics, No. 4 (10), 78–89 (2010b). ios (A1FI and B1), the rise in the sea level is predicted 8. I. O. Leont’yev, “Modeling Beach Profile Evolution at to range from 0.2 to 0.8 m during the 21st century. The Centennial to Millenial Scales,” Okeanologiya 52, B1 scenario is seen to be the most realistic with a 0.5 m No. 4, 550–560 (2012). sealevel rise predicted at the end of the 21st century. 9. A. Sh. Khabidov, I. O. Leont’yev, K. V. Marusin, et al., Monitoring of the State of the Coasts and Reservoirs (Rus. The third step involves modeling of the shoreline’s Akad. Nauk, Novosibirsk, 2009) [in Russian]. behavior using the data on the sediment budget and 10. Yu. D. Shuiskii, G. V. Vykhovanets, and T. A. Labuz, sealevel rise. Based on the SPELT model’s results, the “Conditions and Numerical Values of the Eolian Sand rate of the shoreline’s recession over the root segment Transfer on the Southern Coasts of the Baltic Sea,” of the Vistula spit appears likely to be 0.3 m/year in Vestn. Odess. Univ. 11, No. 3, 148–165 (2006). 2010–2050, and it will increase to 0.4 m/year in the 11. P. Bruun, “The Bruun Rule of Erosion by SeaLevel second half of the 21st century. The amount of reces Rise: A Discussion on LargeScale Two and Three sion is predicted to be about 30 m by 2100 compared Dimensional Usages,” J. Coastal Res. 4, No. 4, 627– to the shoreline’s position in 2010. To stabilize the 648 (1988). shoreline would require a volume of 3 m3 m–1 yr–1 of 12. Coastal Engineering Manual EM 111021100, Wind fill sediment. Blown Sediment Transport, part 3, Chap.4, iii41–iii 477 (2002). The sand deficit (other than the sea level’s) rise will 13. R. G. Hallermeier, “A Profile Zonation for Seasonal be a key factor in the control of the shoreline’s evolu Sand Beaches from Wave Climate,” Coastal Eng. 4, tion at the northeastern tip of the spit. The present 253–277 (1981). recession rate is about 2 m/year and might slightly 14. J. R. Hunter, “Estimating SeaLevel Extremes under increase in the future. The amount of recession will Conditions of Uncertain SeaLevel Rise,” Climate range from 160 to 200 m in 2010–2100. Change 99, 331350 (2010). doi 10.1007/s 10584009 96716. 15. T. Jednoral , Dynamics of Sea and Coastal Zone in the ′ ACKNOWLEDGMENTS Gulf of Gdan sk. Influence of the Planned Navigable Channel in the Polish Part of the Vistula Spit on Changes The author thanks Dr. Rafal Ostrowski, a research of Marine Hydrodynamic Processes on the Seaward Side fellow of the Institute of Hydroengineering of the Pol of the Vistula Spit (Maritime Institute, Gdansk, 1996). ish Academy of Sciences (IBW PAN), for providing 16. I.O. Leont’yev, in Advances in Coastal Modeling, Ed. by V. C. Lakhan (Elsevier Science Publ., Amsterdam, the data on the bathymetry and wave regime. 2003), pp. 299–335. This study was supported by the Russian Founda 17. Z. Pruszak, Marine Basins. Outline of Physical Processes tion for Basic Research (project no. 090500034a). and Environmental Engineering (Inst. Hydroengin., Gdan′ sk, 2003) [in Polish]. The support of the European Commission through 18. E. Van Wellen, A. J. Chadwick, and T. Mason, “A project no. FP7.20091 (contract no. 244104–THESEUS Review and Assessment of Longshore Sediment Trans “Innovative Technologies for Safer European Coasts port Equations for CoarseGrained Beaches,” Coastal in a Changing Climate”) is gratefully acknowledged. Eng. 40, 243–275 (2000).

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