The effect of sea level rise on beach morphology of caspian sea coast

Abstract

Study of beach morphology has been one of the most important issues in coastal engineering research projects. Because of the existence of two important coastal areas located in the north and south parts of the Iran, in the present study an analysis of the coastal zone behaviour is made. Bed level elevations are measured and compared with the theoretical equilibrium profile. It is shown that the behaviour of the coastal zone in the region is consistent with the Dean (1991) equilibrium profile. In the next stage, following extensive investigations, the bed level changes due to arise in sea level at different locations in the surf zone are estimated. The mechanism of beach re-treatment due to a rise in sea level is considered based on the simplified model of Dean (1991) in which the mass balance of the sediments is taken into account. Comparison of the equilibrium profiles for different cases of sea level rise, clearly shows that because of the sediment transport induced by the fluctuation of the water level, the beach profile in the surf zone changes accordingly resulting in an erosion in the inner region of the surf zone and an accumulation of sediments towards the offshore.

Keywords

wave / coastal zone / beach morphology / evolution / equilibrium profile / sea level rise

Introduction

Coasts are permanently subject to waves attacks, so their beach profile is alternatively changing. Since profiles of sandy beaches are permanently changing because of waves attack, observing a balanced profile in the stable mode for these kinds of shores is impossible.

Sediments move both landward and seaward depending on the beach gradient and wave energy. It is understood that when high energy waves (mostly during the winter), act on beaches by transporting the sediment from the steep beach, which is usually built in the summer, towards the sea causes a gentle beach to be constructed. The role of both energy level and beach gradient in determining the dominant direction of the sediment transport is evident. At the beginning of the low energy wave period (mainly summer) a gentle slope beach is exposed to waves. It is expected that the dominant direction of sediment transport will be shoreward. This process will construct a steep slope beach again. These general patterns were studied by several researchers to characterize the equilibrium beach profile.

The recent Caspian Sea level changes have created a new system of beach deposits and profiles but prediction of coastal changes related to sea level changes is fraught with difficulties. Predictive models are not being reliably generated due to a lack of knowledge of the interaction between coasts and energy sources. On the other hand, a model which is developed to forecast the behaviour of a particular coast cannot be applied to another because natural processes depend on coastal features which differ from one coast to another. Bruun (1962) proposed that the equilibrium beach profile does not change in response to sea level variations (Bruun Rule) and under sea level changes only a given volume of sand will move from the upper part and lies over the lower part of the profile.

Based on the Bruun Rule, since the shore-normal geometry of beaches remains unchanged under sea level rise conditions, the amount of shoreline retreat can be calculated if the amplitude of sea level rise and the form of the original profile are known. This rule ignores some main factors such as particle sizes, bottom currents, bed forms, and energy sources and assumed geometric rules are not valid; therefore, the Bruun Rule should be abandoned. Also, the estimated shoreline retreat for three depositional coasts of the Caspian Sea, over the period of the Caspian Sea level rise, showed overestimations of up to 600 percent by the Bruun Rule [1].

The effect of sea level change on the coastal morphology is based on reconstructions, not on real time observations. Because in on hand, the rate of present sea level change is so slight (about 10–20 cm per century), the present sea level has an upward trend, and the last low stand deposits can only be investigated by drilling or deep sounding and other similar methods. On the other hand, it is necessary to validate numerical models using real time data, and laboratory simulations are hindered by drawbacks such as downscaling. While the linkage between sea level changes and coastal landforms has not yet been completely understood, the Caspian Sea can play an important role in enhancing our knowledge of coastal behaviours in response to sea level variations.

Nevertheless, Dean’s studies (1991) showed that an equilibrium profile can always be defined for sandy beaches around which fluctuation of sea bed take place. It stands to reason that such a profile does not exist at all and it only shows average situation of bed behaviour affecting by waves attacks. In determining profile equations of sandy beaches, following conditions are assumed:

1) Beach is of sandy type so that average settlement velocity of particles is between 1 to 10 centimetres per seconds.

2) Balanced form of shore should be supposed proportional to the loss of energy caused by waves breaking.

3) Wave height in the surf zone after breaking should be a constant percentage of the water depth.

Using above-mentioned assumptions, the sandy beach profile equation can be defined as [2]:

(1)h=A{x}^{\mathrm{2}/\mathrm{3}}

In which h is water depth at any point with distance x from the shore line and parameter A is a coefficient that follows this equation:

(2)A=\mathrm{2.5}{\left({\displaystyle \frac{W^{\mathrm{2}}}{g}}\right)}^{\mathrm{1}/\mathrm{3}}

In Eq. (2), W is the settlement velocity of bed particles and depends on the average diameter of particles i.e., D₅₀ and it is calculated by following equations:

(3)D_{\mathrm{50}}>{\mathrm{1}}^{mm}\begin{array}{lll}, \hfill & \hfill & \hfill \end{array}W=\mathrm{1.1}{\left[(s-\mathrm{1})g{D}_{\mathrm{50}}\right]}^{\mathrm{0.5}}

In these equations, g is the gravity acceleration, s is the density of bed materials and υ is the kinematic viscosity of sea water [2].

The effect of sea level rise on coastal morphology was investigated by different researchers [3]. The results of the measurements on the southern coastlines of the Caspian Sea especially the Anzali region which located in Guilan province shows a parabolic behaviour of sandy coasts in this region [4]. Sea level rise which cause the variation of equilibrium beach profiles is one of the most important issues on coastal engineering projects. Investigation of sea level rise circumstance and its impressions such as beach drowning, causing to ruin farm lands, destructive environmental effects are the whole factors which should be considered by governments and researchers who research about relative subjects. Some of the factors which cause the sea level rising are, atmospheric rainfall, climate changes and tectonic movements [5]. In this paper, investigation of the equilibrium beach profile variation in consequence to storm during a short period of time is made.

The Caspian Sea is the largest enclosed body of water in the Earth by a surface area of 372000 square kilometres and a volume of 78200 cubic kilometres. Its latitude and longitude are 40˚ 0′ 0″ and 51˚ 0′ 0″, respectively. The lake accounts for 40 to 44 percent of the total lacustrine waters of the world. It has a maximum depth of about 1025 meters. The Caspian Sea is divided into three distinct physical regions: northern, middle and southern Caspian. The southern Caspian is the deepest, with a depth that reaches over 1000 meters; also the southern Caspian account 66 percent of the total water volume [5]. Fig. 1 shows the study region in this paper.

The dramatic level rise of the Caspian Sea (about 2.25 meters since 1978), as can be seen in Fig. 2, has caused serious concern to all five surrounding countries. Flooding over the coastal zone has ruined buildings and structures such as roads, beaches, and farm lands. Moreover, sea level rise result in changes in: water level, hydro chemical regimes of river mouths, sediment depositions, and groundwater characteristic. It seems very important to prepare a coordinated work plan on joint activities of the Caspian Sea adjacent countries to tackle the Caspian Sea level rise problems. The assessment of the role of various factors in sea level changes is essential to develop predictive models.

Due to the rapid Caspian Sea level changes which has observed during the last century, it is absolutely essential to provide a data-base for each coastal zone. One of the most important zones of Caspian coastlines is its south line which borders the north of Iran.

Materials and methods

The Caspian’s various coastal types were introduced in the previous section. Their responses to Caspian Sea level changes are discussed in this section.

a) Mud flats: this type of coast tends to lie beside the lowland areas. Mud flats stretched along the northeast, southeast corner, and northwest coasts of the Caspian Sea during the period of Caspian Sea level fall from 1930 to 1977. Also, in this period, mad flats surrounded all Bays of the Caspian Sea including Kirov Bay, Krasnovodsk Bay, Kizlyar Bay, and Komsomoletz Bay. The rate of shoreline migration differed. This situation changed in 1977 when the Caspian Sea started to elevate its water level. A dramatic passive (beach profiles did not change and sediments remained unchanged along the profiles) shoreline retreat occurred due to the gentle slope of the coasts (~0.0001). Bays were filled in again and their shoreline advanced [6].

b) Depositional coasts: the period during which the Caspian Sea level showed a decreasing trend is marked by an increase in the size and volume of depositional bodies such as dunes, barriers, and spits, except those which were being supplied by cliff erosion, because in this period cliffs were inactive resulting in a decrease in long shore drift causing erosion to spits. The behaviour of depositional coasts in response to the Caspian Sea level rise varied between different coastal segments depending on the near shore bottom slope. On the coasts where near shore slope was relatively gentle (tangent slope 0.0005–0.005), landward migration of these bodies occurred while their geometry remained almost unchanged. Also, on these coasts where wind-blown sediments are prevalent dunes began to grow during the period of both water level fall and water level rise [7].

Moderate near shore bottom slops (tangent 0.005–0.01) usually mark barrier coasts and under the Caspian Sea level fall its barriers increased their width and volume. Under rising sea level conditions however, sand ridges emerged on the coasts and a rise in the groundwater table formed a lagoon behind the ridges. On the coast with a steep backshore (tangent slope over 0.03–0.05) lagoons did not form. Steep near shore bottom slops (tangent slop over 0.01) caused intensive erosion to beaches leading to the formation of scarps of up to 1–1.15 m.

A proper example of barrier coasts was comprehensively studied by Kroonenberg et al., (2000). They investigated the barrier coast of Kaspiisk in Russia at the western Caspian Sea coast (Fig. 7) which had been monitored during the period of recent Caspian Sea level changes. Their study and findings are reviewed as follows. Three sandy bars which usually exist on the near shore zone (tangent slop 0.003) at depths of 0.6 m, 1.4 m, and 2 m moved landward during the period of water level rise. Storm directions are mostly SE and NW while incident waves are normal and parallel to the shore affected by the near shore topography. Affected by seabed friction and by breaking at far from the shore, waves reach the shore line with low amplitudes of up to 1.5 m. when the Caspian Sea level started to decrease (1930) the shoreline advanced and the cliffs were left. As a result, a coast with a width of 750 m was generated by 1977 when the sea level fall ceased and several small sandy-shelly bars were left formed probably by single storms (Fig. 8). The Caspian Sea level fall did not form lagoons on this coast while a lagoon was generated over the period of sea level rise. Soon after the sea level began to rise a barrier, and consequently a lagoon, were formed and this system moved shoreward as long as sea levels continued to increase (Fig. 8). The rise in sea level moved this barrier-lagoon system shoreward (18€m/yr) but not on its own. This system moved shoreward during the storms when the waves frequently washed over the barrier and caused erosion to its face. From 1988 however, the lagoon began to both widen and deepen, whereas the barrier decreased both in height and width. This was attributed to lack of the essential coarse material for formation of the barrier because the sea level rise increased the distance between the barrier and shell debris source which was the coarse material building the barrier.

The coarse grain sediment necessary for barrier formation was shell debris during the recent sea level changes while old barriers along this coast showed that gravel had been the dominant coarse grain during the Novo Caspian. This showed that the main sediment supply for the recent barriers was offshore sediments not long shore drift (Holocene) time [7].

c) Deltaic coasts: the main rivers feeding the Caspian Sea are the Volga, Ural, Terek, Sulak, and Kura whose deltas showed a notable response to the Caspian Sea level changes. When the Sea level began to decrease a passive emergence occurred on the deltaic coasts (Fig. 7). The Kura delta and the Sulak delta expanded up to 50–60 m/yr and 100–200 m/yr, respectively. The Volga delta together with the Ural delta located on the northern Caspian Sea coasts experienced a considerable expansion and caused the shoreline to move ahead by hundreds of kilometres. Since 1959, dam construction has resulted in a major decrease in the sediment discharge entering the Caspian Sea by the Kura River, leading to erosion in this delta. When the trend reversed and the Caspian Sea level started to increase deltaic shorelines retreated. The rate of the shoreline retreat was not as much as the shorelines advance in some deltas. While some areas were completely inundated the Volga delta retreated by only 2–4 m/yr, a main reason for this was the increase in sediment discharge. It is suggested that Volga sediment discharge increase by 33 percent due to an increase in its water discharge during the 1980s.

Volga sediment discharge is composed of silt, clay, and very fine sand forming a gently sloping coast. Sea level rise and increasing Volga discharge worked together to vertically grow sediment bodies while sea level fall increased channel erosion leading to fast shoreline advances. The maximum level that the Caspian Sea experienced during the past century was 25 m below global Sea level and it has been suggested that it may increase to near this level again. If this is the case, a wide area will be inundated.

The present day Kura delta is composed of sandy and clayey bodies. The aggradation process, during the period of water level increase in the Caspian Sea resulting from flooding of the Kura River delta, and pro gradation over the period of sea level fall, both control the Kura River delta as much as do river dynamics.

d) Erosional coasts: these can be observed in the coasts of Azerbaijan, Russia, Kazakhstan, and Turkmenistan (Fig. 7). During the period of Sea level fall the cliffs were left behind and cliff erosion ceased because the causative waves broke over the newly emerged area. When this area was submerged again by an increasing Sea level, erosive waves attacked the cliffs and the result was an increase in the length of the erosional coasts of the Caspian Sea such that, for example, in Azarbaijan there was an increase from 20%–55% percent along the whole coastline.

For better analysis of sea level rise and its effect on the sea bed we need to sample several locations from several regions. In this paper, considering the consistency between initial coasts of southern Caspian Sea with the Dean’s equilibrium beach profile, the effect of sea level rise on equilibrium beach profile for each coasts were investigated. The beaches which have been investigated, from west to east, are Astara, Anzali, Tonkabon and Nour (Fig. 1). In this process, because of the short distance between the mountain and the sea, the soil in this region is more granular and from west to east by increasing the distance between the mountain and the sea in the area between Astara and Anzali the diameter of sediment particles decreases.

Therefore, in Anzali we have the least sediment particles diameters; whereas by moving toward east, the mountains in the Tonkabon coast are near to the sea and in comparison with Anzali coast in this region the sea bed soil is more granular. In Fig. 3 The correlation between median sediment grain size and beach face slope on the southern Caspian Sea coast is shown.

To have a better and more exact analysis of the profiles, the information of each region based on the specific characteristics and situation of that region is used. The results are tabulated in Table 1. These results obtained from the soil mechanics tests on different samples of sand taken from different locations across the beach profiles.

The equilibrium beach profile for each region is obtained based on geotechnical field measurements and using Dean’s equilibrium profile equation (Fig. 4). The actual bed elevations of beaches are measured using echo-sounder hydrography and justified with the GIS maps of the selected region.

Following Dean (1991), the important effective factors on the illustrated equilibrium profile are related to particle average size (D₅₀) and specific gravity (GS), so the main reason for differences is due to the characteristics of each region.

As the result of Table 1 and Fig. 3, it can be said that as much as sea bed sand include larger particles and the larger specific gravity, the beach slope can be steeper in comparison with the coast included smaller particle average sizeD₅₀ and specific gravity GS.

Structure of the model

In this paper, for modelling the profile of the studied coasts the ANPM (Advance Near Shore Profile Model) program is used [8,9]. This program consists of five predictive phases as follows:

1) Random wave transformation across the profile.

2) Long wave structure.

3) Hydrodynamics.

4) Sediment transport.

5) Profile development.

Basic background of the model

Beach profile change is the result of coastal sediment transport. Depending on the direction of sediment transport, it is usually designated as alongshore and /or cross-shore transport. For two-dimensional processes the alongshore transport rate assumed to be constant or zero such that no profile change will result from this component. The basic equation presently used by modellers is the vertically integrated continuity equation of sediment flux. The bed level changes are calculated based on the sediment continuity equation (mass balance), which reads as:

(4){\displaystyle \frac{\partial z_b}{\partial t}}+{\displaystyle \frac{\partial (S_b+S_{s,c}+S_{s,w})}{\partial x}}=\mathrm{0}

where z_b= vertical distance relative to a fixed datum; S_b= bed-load transport in x direction; S_{s,c}= current-related suspended-load transport in x direction; S_{s,w}= wave-related suspended-load transport in x direction.

Using a numerical scheme, it is possible to solve this equation across the profile by discretizing the profile into a number of sections although some smoothing of the profile may be required after each time step. To solve this equation, a Lax-Wendroff numerical scheme is used. The scheme is explicit, second order accurate and ensures numerical stability of the sea bed development and conservation of the total amount of sediments. The initial beach profile levels must always be as input data, generally a profile can be described by 20 to 30 coordinates, considering a fixed boundary such as a seawall. With the designation of a variable grid width pattern in the profile input file, a subroutine further divides the profile into approximately 100 computational grid sections., The stability of the scheme is conditional on the model time step being less than a maximum value which is determined within the scheme [10].

The computational procedure for the Lax-Wendroff scheme is based on the selection of an automatic time step. After the hydrodynamic and sediment transport calculations have been performed, the maximum allowed time steps for the solution of equation 6 at each grid point across the profile are calculated from the local condition. The smallest of these is taken as the present morphodynamic time step ({{\displaystyle \mathrm{\Delta }t}}_m). If {{\displaystyle \mathrm{\Delta }t}}_m is less than the present hydrodynamic time step ({{\displaystyle \mathrm{\Delta }t}}_h), the sea bed levels are updated, and another model run is performed with the same hydrodynamic data input. This procedure is repeated until the cumulative morphological time step ({\displaystyle \Sigma {{\displaystyle \mathrm{\Delta }t}}_m}{{\displaystyle ={\displaystyle \Sigma {{\displaystyle \mathrm{\Delta }t}}_m}+\mathrm{\Delta }t}}_m) exceeds {{\displaystyle \mathrm{\Delta }t}}_h. When this occurs, {{\displaystyle \mathrm{\Delta }t}}_m is truncated such that {\displaystyle \Sigma {{\displaystyle \mathrm{\Delta }t}}_m}{{\displaystyle =\mathrm{\Delta }t}}_h. After updating the seabed levels, the model reads in the next set of wave data including the new{{\displaystyle \mathrm{\Delta }t}}_h, and the process is repeated. If an erodible surface is being considered, after each morphological time step the down cutting is determined in a subroutine for all exposed parts of the underlying profile till sections covered by less than a minimum protective layer of sand.

The program uses two input files; the first one contains the information of the beach profile including the components which forms the profile, beach slope, the density of soil, average particle size, internal friction angle, sediment fall velocity, sediment porosity and also the physical information of the region including, gravity acceleration, kinematic viscosity, water density, datum, and the wind angle toward north. The second file contains the wave data. The output files contain parameter of the profile such as beach profile variation after storm, velocity of sediment transport across the shore line and sediment transport rate at different points.

To investigate the equilibrium beach profile changes, the following storm with some defined characteristics occurred in Caspian Sea is used:

1) Storm duration: 12 hours.

2) Wave height (based on the conditions in Caspian Sea): 1 to 3 meters

3) Wind angle toward north: 340˚

Investigation of beach profile variation after storm

The results of comparing beach profiles of studied coasts are shown in Fig. 5.

Investigation of the bed level changes after wave attack

To investigate the variation between initial profile and the profile after wave attack, the bed level changes are shown in Fig. 6.

These curves clearly indicate that the rate of bed level changes in vicinity of shoreline is in the range of (0–15) cm and drops suddenly towards offshore. Different geotechnical and accompanying specific topography at each region are reasons of high or small fluctuation. As much as the rate of particle average size (D₅₀) and porosity (e) decrease, the rate of fluctuation bed level would be higher.

Results

Fig. 7 shows the Bruun’s first theory about beach profile geometry. Later in 1962 Bruun proposed that the equilibrium beach profile does not change in response to sea level variations (Bruun Rule).

In this study the rate of sea level rise is in the order of 1m. Based on the rate of sea level rise, the sea water intrusion at each region is calculated. The slope of the coast depends on geotechnical characteristics at each region and the rate of intrusion was determined and tabulated in Table 2.

The beach profile changes are shown (before and after storm) in Fig. 8. The secondary profile represents the beach profile after the wave attack (storm).

Southern Caspian Sea Coast under water level variations

Table 3 shows the behaviour of beaches resulting from hydrodynamic influences. Some coasts such as Miankale are very sensitive to sea level changes.

There exist several lagoons and bays along the Southern Caspian coast the most important ones being Anzali lagoon in the west and Gorgan Bay in the east (Fig. 9). The recent Caspian Sea level rise, which occurred between 1977 and 1995, doubled the Anzali lagoon surface from 80 to 160 km. The Alborz mountain range governs the shore width throughout the coastline and the rivers feeding the Caspian Sea from the south contribute great amounts of sediment to the shores to expand their width.

In the east, where the coast is composed of fine grain sediment, waves are prevented from reaching the shore due to the gentle slope of the nearshore zone. Sandy beaches have stretched along the hundreds of kilometers of the southern Caspian Sea coastline and coarse grain beaches can be observed in some segments. These coasts were affected by the Caspian Sea level rise in accordance with their offshore and onshore slopes [11].

Fig. 9 illustrates the formation of southern Caspian Sea coasts under conditions of rising sea level. The variety of behaviors is due to the differences between offshore and shore gradients [12].

Studies related to the sea level rise conducted on the southern coasts of the Caspian Sea are limited and there is a gap in the information available for this area. Although Fig. 9 is a schematic representation of the behaviors prevailing on some coasts, it is not sufficient for a coastline of 700 km in length which has a wide variety of features [13].

Investigations of beach profile and bed level changes after sea level rise

Fig. 10 shows the effect of sea level rise on coastal morphology in studied areas. As can be seen in these figures, after the sea level rise, still the same behaviour can be expected for all studied beaches but with different magnitudes of erosion.

In recent years, the coastline of Caspian Sea in Guilan province, especially the mouth of big rivers such as Sefidroud delta has changed increasingly due to the environmental, continental and marine factors. The changes in the position of these coastlines have led to some damages. The changes of water level that come from the land, the differences in the land sediment levels and the situation of erosion in the coastline’s sediments such as continental factors and the changes of sea level and the patterns of current and Caspian Sea waves are some changes that occurs in Caspian Sea’s coastlines.

Fig. 11 indicate that the rates of bed level changes are more after the sea level rise. As can be seen, by increasing depth and distance from shoreline, the rate of bed level changes considerably reduces. The reasons of large bed level changes in the shoreline could be attributed to the wave breaking zone, great erosion due to wave set-up and scouring in coastal zone.

Fig. 12 and Table 4 show that the maximum scour and erosion happen on the shoreline, which is in the range of (0–15) cm; also the most rate of fluctuation related to Anzali coast with the amount of 18 cm and the least rate related to Astara coast with the amount of 10 cm. It can be found that as much as the sand of seabed included the smaller particles, it has more fluctuation in comparison with the coast included larger sediment size.

Conclusions

In this paper, the mechanism of beach retreatment due to a rise in sea level is considered based on the simplified model of Dean (1991) in which the mass balance of the sediments is taken into account. Comparison of the equilibrium profiles for different cases of sea level rise, clearly shows that because of the sediment transport induced by the fluctuation of the water level, the beach profile in the surf zone changes accordingly resulting in an erosion in the inner region of the surf zone and an accumulation of sediments towards the offshore. This result is in agreement with that of reported by Rosati et al. (2013) [14].

This study comes up with the following conclusions:

1. The coasts which are located near the mountain have larger particle average sizes and with the distance from the mountain these amounts are reduced. The studied coasts are in the same conditions, therefore, the coasts which are located far from the mountain have more critical conditions related in terms of the sea water intrusion.

2. Based on the results, beach profiles with small particle average size (D₅₀) have more intrusion with sea level rise. Therefore, in the regions like Anzali which has the smallest particle average size, we should expect expedience and contraption.

3. The most bed deformation on the shoreline zone is about 18 cm. This is because the D₅₀ in that region is small (Anzali).

4. If each of the four geotechnical parameters, particle average size D₅₀), porosity (e), specific gravity (G.S) and internal friction angle (ϕ) increases, the resulting bed deformation and erosion would be decreased. The effect of (D₅₀) on beach morphology is larger than others parameters.

5. Among the studied coasts, Astara coast has the least rate of erosion and intrusion due to sea level rise. Therefore, this coast has larger potential and good condition to construct ports piers and other marine structures.

6. It is recognized that shore slope plays an important role in determining the behaviour of the southern part of the Caspian Sea coastline in response to water level changes.

References

[1] Short A D. Hand Book of Beach and shore face Morphodynamics, JohnWiley, 1999

[2] Dean R G. Equilibrium Beach Profiles, Characteristics and Applications. Journal of coastal Research, 1991, 7(1): 53–84.

[3] Nairn R B, Southgate  H N. 1993. Deterministic Profile Modelling of Near Shore Processes. Coastal Eng., 1993, 19(1-2): 57–96.

[4] Hoque M A, Asano  T, Lashteh Neshaei M A. Effect of Reflective Structures on Undertow Distribution, In: Proceedings of the Fourth International Symposium Waves. California, USA, 2001, 2: 1042–1051.

[5] Firoozfar A, Bromhead   E N, Dykes A P ,  Neshaei MAL . Southern Caspian Sea coasts, morphology, sediment characteristics, and sea level change. In: the 27^th annual international conference soil, sediments, water and energy, MA,USA, 2001.

[6] Holmes P, Balock  T E, Chan  R T C, Neshaei  M A L. Beach Evolution under Random Waves. In: Proceeding of the 25^th International Conference on Coastal Engineering, ASCE. Orlando, USA, 1996.

[7] Kamphuis J W. Alongshore Sediment Transport Rate. Journal of Waterway, Port, Coastal and Ocean Engineering Div. ASCE, 1999, 117(6): 624–640.

[8] NeshaeiM A L, Holmes  P, Salami M G . A semi-empirical model for beach profile evolution in the vicinity of reflective structures. Journal of ocean Engineering, 2009, 36(17-18): 1303–1315.

[9] Neshaei M A L ,  Mehrdad M A ,  Veiskarami M . The effect of beach reflection on undertow, Iranian Journal of Science and Technology, Transaction B, Engineering,  2009, 33(1): 49–60.

[10] Abedimahzoon N, Molaabasi  H, Lashteh Neshaei M A, Biklaryyan M . Investigation of undertow in reflective beaches using a GMDH-type neural network. Turkish J. Eng. Env. Sci. TuBitak, 2010, 34: 1–13

[11] NeshaeiM A L, Veiskarami  M, Nadimi S . Computation of shoreline change: A transient cross-shore sediment transport approach. International journal of physical science, 2011, 6(24): 5822– 5830.

[12] Khoshravan H. Beach sediments, morphodynamics, and risk assessment, Caspian Sea coast, Iran. Quaternary International, 2007, 167(3): 35–39

[13] Kroonenberg S B ,  Abdurakhmanov G M ,  Badyukova E N ,  van der Borg K ,  Kalashnikov A ,  Kasimov N S ,  Rychagov G I ,  Svitoch A A ,  Vonhof H B ,  Wesselingh F P . Solar-forced 2600 BP and Little Ice Age High stands of the Caspian Sea. Quaternary International, 2007, 173(5): 137–143

[14] Rosati J D, Dean  R G, Walton  T L. The modified Bruun Rule extended for landward transport. Marine Geology, 2013, 340: 71–81

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag Berlin Heidelberg