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) Spit 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 sediment transport (up to 50 thousand m3/year). Over the rest of the spit, the shoreline’s orienta tion causes westward sediment transport (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 dunes. The spit separates the Gdansk Bay of the to describe the longterm evolution of the shoreline on Baltic Sea from a lagoon, 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 erosion, 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 the Bruun rule [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 dune 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 OCEANOLOGY Vol. 52 No. 5 2012 702 LEONT’YEV 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).