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Abstract

Mangroves thrive in the intertidal areas (interface between land and sea) of tropical and sub-tropical belt and play an important role in overall attenuation of nearshore waves. Multiple interactions of waves with mangrove trunks and roots and bottom friction are the two primary mechanisms responsible for wave attenuation in mangrove forests. Earlier studies, comprising both analytical and experimental, reported an exponential decay in wave height for waves propagating over vegetation with idealized bottom topography and a few on sloping bottom. But hardly studies have attempted to characterize the wave attenuation by vegetation over varying seabed slopes since mangroves generally grow luxuriantly on gradual topography having large tidal amplitudes. Nowadays, several studies are being carried out on development of artificial mangroves to reduce the coastal hazard risks; thenceforth, there is an imperative requirement to study the wave damping characteristics of mangroves on varying seabed slopes. Consequently, this study performs sensitivity experiments to analyze the wave attenuation over mangroves with different sea-bottom slopes using a third-generation wave model. The study exposes sensitivity of wave attenuation characteristics to different beach slopes in the presence of mangroves and aims at understanding how the wave attenuation characteristics by mangroves differ with varying bottom slopes. The total percentage energy reduction for waves reaching the shoreline after propagating through mangroves on mild slope (1:80, 1:40) is observed to be 93%–98%, nearly 84% for 1:20 slope, and 67% for steep slope (1:10). The study reveals that the wave height decays exponentially for the mild slope and found to be consistent with the earlier studies, but as the degree of bottom steepness increases, the wave height reduction becomes gradual, and this can be attributed to the water depth variation, shoaling, breaking, and reflection characteristics associated with different slopes, in the presence of mangroves.

Keywords

Wave attenuation mangroves bottom slopes sensitivity study wave height

Introduction

In the aftermath of the 2004 Indian Ocean tsunami, compelling evidence has emerged from field studies in several affected countries, indicating that the mangrove forests played a crucial role in saving human lives and property (Environmental Justice Foundation (EJF), 2006). While the mechanism of wave attenuation in mangroves has been studied earlier, the extent of protection they offer is still not clear due to their inherent complexity and high regional variability (Narayan et al., 2010). Mangroves thrive on low wave energy coasts, namely, Sundarbans, West Bengal where tidal amplitude is high and the topography is gradual. However, in the Pichavaram mangrove wetlands of Tamil Nadu, wave energy along the coast is high and tidal range is low, but a sandy beach located between the mangroves and the sea protects the mangrove wetland, allowing the propagules to settle and grow (Selvam and Karunagaran, 2004). In a global perspective, Naskar and Mandal (1999) reported that small pockets of mangrove woodland are widely distributed even in steep slope shoreland near Tupi Island and swampy areas at Tigak Archipelago between New Ireland and New Hanover. Even though mangrove forests on steep slopes are rarely reported, one cannot ignore the possibility of mangroves thriving on steep slopes, and it opens up a new prospect of coastal hazard risk reduction by reducing the wave attack on high wave energy coasts. By mimicking the essential conditions, mangroves can be grown or artificial mangroves/patches/island can be implemented on high-energy coasts that can potentially replace the existing conventional coastal structures for coastal protection. There are various natural mangrove rehabilitation techniques developed to adapt the mangrove seedlings to different conditions in the field. Nevertheless, wherever the above techniques fail, the artificial mangroves made of biodegradable and environmental friendly materials can be used after experimental and field studies. However, it is imperative to understand how these mangrove structures behave on a steep topography and its efficiency in wave damping encountering high-energy waves. Also, in certain mangrove locations, the natural slope of the coast (bathymetry) is subjected to varying climate change and associated environmental factors and it can adversely affect the attenuation efficiency of mangroves and its ecosystem. Hence, this study finds its importance on mangrove coasts that eventually may turn steeper in future due to severe erosion caused by climate change and natural and anthropogenic hazards. Several studies (Burger, 2005; Meijer, 2005; Oude, 2010) have conducted extensive sensitivity analysis of wave attenuation by vegetation where the role of waves and vegetation characteristics on the wave damping were analyzed, but scarcely studies have paid attention to the variation of wave attenuation pattern resulting from varying bottom slopes and sediment characteristics. Therefore, in this study, we have conducted synthetic experiments to simulate the characteristics of wave attenuation through vegetation over varying bottom topography using a third-generation numerical wave model. It exposes the sensitivity of wave attenuation characteristics to different bottom slopes in the presence of mangroves and aims to understand how the wave attenuation characteristics by mangroves differ with varying bed slopes during extreme wind-wave climate.

Review of the literature

Wave attenuation by vegetation has been studied analytically and empirically (Feagin et al., 2011) since 1984. Mclvor et al. (2012) provide a comprehensive review on the wave attenuation characteristics in mangrove ecosystem and signify the importance of wave attenuation in multiple ways at different sites and postulated that it is not possible to present wave attenuation in a standardized way across different locations. The study by Mei et al. (2011) has highlighted the analytical and numerical solutions for wave attenuation on the macro-scale for different water depths and coastal forest configurations. Unlike the artificial barriers, a bio-shield of mangrove is quite effective (Muraleedharan et al., 2009; Noarayanan et al., 2012).The empirical model proposed by Noarayanan et al. (2012) finds practical application of a green belt as a bio-shield; moreover, the establishment and maintenance of coastal vegetation incur only low cost as compared to concrete structures used for coastal protection (Kathiresan, 2010). Motivated by the concept on the ability of mangrove plants to convert the mean kinetic energy into turbulent kinetic energy, Fatimah et al. (2008) proposed a numerical modeling approach for artificial mangrove root system (ArMS) as an alternative solution to solve coastal engineering problems in cohesive soil coastlines; the effort investigated the effect of mangrove-roots-like submerged breakwater. Kathiresan (2003) attempted on the tidal flows around mangrove vegetation and their role in the process of sedimentation. His study has provided a plausible mechanism on the role of mangrove forest on sedimentation.

Methodology

Several sets of numerical experiments have been conducted in this study to evaluate the impact of mangroves on wave height under varying bottom topography, that is, the influence of sea-bottom slopes on wave attenuation through mangroves using a third-generation wave model, SWAN (Simulating Waves Nearshore). The percentage rate of wave attenuation by mangroves, r, is defined by

$r = \frac{H - H_{0}}{H_{0}}$ (1)

where $H_{0}$ is the incident significant wave height at the offshore boundary and H is the significant wave height at the extreme nearshore end of the selected domain.

The SWAN model

The SWAN is a third-generation wave model developed at the Delft University of Technology, Netherlands that computes random, short-crested wind-generated waves in coastal regions and inland waters. The SWAN wave model is a discrete spectral model based on the action balance equation (Booij et al., 1996), which is mathematically expressed in the form

$\begin{array}{l} \frac{\partial N}{\partial t} + \frac{\partial}{\partial x} (c_{x} N) + \frac{\partial}{\partial y} (c_{y} N) + \frac{\partial}{\partial σ} (c_{σ} N) \\ + \frac{\partial}{\partial θ} (c_{θ} N) = \frac{S_{total}}{σ} = \frac{S_{in} + S_{nl} + S_{ds} + S_{bot}}{σ} \end{array}$ (2)

where $N (σ, θ)$ represents the total action density defined as $N = E / σ$ in which $E$ is the energy density and $σ$ is the intrinsic frequency, $t$ is the time, $θ$ is the wave direction, and $c_{x}$ and $c_{y}$ are the propagation velocities along the $x$ and $y$ directions, respectively. The terms on the right-hand side of equation (2) contain $S_{total}$ , which is the combined effect from various source/sink terms that represents all physical processes such as the generation by wind $(S_{in})$ , dissipative processes $(S_{ds} {and S}_{bot})$ , and overall redistribution of wave energy due to non-linear wave–wave interaction $(S_{nl})$ . To account for wave dissipative effects due to vegetation in SWAN, equation (2) will be extended with $S_{ds, veg}$ based on equation (4). The model includes wave damping over a vegetation field at variable depths using the cylinder approach suggested by Dalrymple et al. (1984) and modified by Mendez and Losada (2004) and The SWAN Team (2015). In this method, the vegetation is modeled as cylindrical obstacles causing a drag force and translated into an amount of energy that gives an energy dissipation term ϵ_v (Oude, 2010) as shown in equation (3)

$ε_{V} = \frac{2}{3 π} ρ C_{D} b_{v} N {(\frac{gk}{2 σ})}^{3} \frac{\sinh^{3} k α h + 3 sinhk α h}{3 {kcosh}^{3} kh} H^{3}$ (3)

The SWAN model utilizes a spectral version of the vegetation dissipation model of Mendez and Losada (2004) extended for full gravity wave spectrum (as mentioned in equation (4)) with the possibility to vary the vegetation vertically

$ε_{V} = \frac{1}{2 \sqrt{π}} ρ {\overset{ˇ}{C}}_{D} b_{v} N {(\frac{gk}{2 σ})}^{3} \frac{\sinh^{3} k α h + 3 sinhk α h}{3 {kcosh}^{3} kh} H_{rms}^{3}$ (4)

The physical mechanism behind wave dissipation by vegetation is detailed in previous literatures (Dalrymple et al., 1984; Kobayashi et al., 1993; Mendez and Losada, 2004; Suzuki et al., 2011). Several studies extensively validated the model against field studies and experimental observations in the past, and hence the model is assumed to extend reliable predictions and used in the present study.

Hypothetic domains and boundary conditions

Four types of hypothetic domains (Figure 1) were considered in this experiment having a spatial dimension of 5 km × 5 km, based upon the degree of steepness, representing mild to steep slope (1:80, 1:40, 1:20, and 1:10, respectively).

Figure 1.

Schematic representations of bottom topography (in meters) used in sensitivity experiments (from left to right 1:80; 1:40; 1:20; 1:10).

The study domain assumes a maximum water depth corresponding to 50 m at the offshore boundary and the gradient of sea-bottom slope vary with depth from open boundary (offshore) to the coast (nearshore). The open ocean boundary condition in the experiment assumes a JONSWAP (Joint North Sea Wave Project) spectrum with the default peak enhancement factor, γ = 3.3. The waves are considered to approach the coast from offshore with a significant wave height and wave period of 9 m and 12 seconds, respectively. The model considered an extreme wave condition and used the boundary condition as specified in the work by Nayak et al. (2012). The effect of tides and current interaction with wave and vegetation are excluded assuming a small tidal range.

Implementation of mangroves in model

The first set of numerical experiments considered the case without vegetation for all the selected slopes and subsequently repeated after including the vegetation component. In the latter, the hypothetical mangroves were arranged in a tandem order in two vertical segments for a distance of 500 m from the coast. In this study, the mangrove forest has been provided for 500 m considering 10% of the total domain. As mentioned in a review work by Hashim et al. (2013), some Asian countries have outlined the minimum required width for mangrove forests. According to Lacambra et al. (2008), a mangrove belt between 500 and 1000 m width has been set as a buffer zone in Vietnam along the Mekong delta coastline. In Philippines, the buffer zone is 20 m and can reach up to 50 m in storm-prone areas. In Malaysia, the 1950s regulation specified 200 m mangrove buffer zone before any structures protecting agricultural land (Othman, 1994). The lower layer with a height of 0.5 m and diameter of 3 cm represented the root characteristics of the mangroves. The lower layer represents special roots known as pneumatophores or breathing roots. The heights of these aerial roots are reported differently for each region. Therefore, an average value of 50 cm has been selected for this study. It corresponds to a density of 100 no/m², and the upper layer consisted of a single mangrove stem having a height of 5 m and diameter of 0.2 m. Asano et al. (1993) proposed an adaptation to the formulation by Dalrymple et al. (1984) to include the sway motion of plants and thereby expand the range of the application from only stiff to flexible vegetation. The conclusions of physical modeling studies showed that varying the drag coefficient is sufficient to model flexible vegetation (Burger, 2005). This study has referred the previous literatures (Mazda et al., 1997; Narayan et al., 2010) to assign a drag coefficient of 1 to mangrove stem and 1.25 to roots in view of the flexibility of stem to account for swaying motion and the rigidity of roots.

Results and discussions

The simulated significant wave height corresponding to varying bottom slopes without mangroves and with mangroves (1:80, 1:40, 1:20, and 1:10) are shown in Figures 2 and 3, respectively.

Figure 2.

Computed significant wave height of the corresponding bottom slopes: (a) 1:80, (b) 1:40, (c) 1:20, and (d) 1:10 for experimental setup without mangroves.

Figure 3.

Computed significant wave height of the corresponding bottom slopes: (a) 1:80, (b) 1:40, (c) 1:20, and (d) 1:10 for experimental setup with mangroves.

Mangroves act as a buffer to the water surface from the effects of wind, thereby reducing the generation of wind-waves and wave setup and run-up, which make a substantial contribution to storm-surge flood levels and damage (Mclvor et al., 2012). From the synthetic experiments (Figures 2 and 3), it is clearly evident that the energy of the incoming waves is significantly dampened while propagating through the mangroves. The transmitted wave height across the mangrove forest on steep slope also exhibits considerable decrease in wave height in the presence of mangroves. However, the vegetated mild slope exhibits higher wave dissipation when compared to the steeper slopes having mangrove vegetation. Figure 4 details the variation in characteristics of wave attenuation for bottom slopes varying from mild to steep, with and without mangroves, respectively.

Figure 4.

Wave height decay computed with and without mangroves under breaking and non-breaking conditions for varying bottom slopes: (a) 1:80, (b) 1:40, (c) 1:20, and (d) 1:10.

It is clearly evident from this study that the type of wave attenuation is different for each case. The shoaling and breaking characteristics are different for various beach slopes. The relative contribution of damping by vegetation and breaking is represented in Figure 4. The breaker zone characteristics essentially depend upon the bottom slope, incident wave, and tidal variation. The distance of breaker zone from the coastline is dynamic in nature and changes with instantaneous water level variations. This study does not consider the time variation of water level elevation and assumes that the breaker zone for the respective beach slopes to remain constant. However, in the field, it changes for each tidal cycle that may alter the wave decay pattern depicted in Figure 4. For mild slopes, the waves propagate for longer distances. Tsai et al. (2002) found that the shoaling distance on steep slope becomes short, and the surface waves may be partially reflected from the steep bottom. Generally, spilling breaker dissipates the energy at a slower rate (Dally et al., 1985). The wave decay on mild slope occurs prior to the propagation of waves through the mangrove forest. In Figure 4(a), the wave height decays gradually for the mild slope, and in the presence of mangroves, the wave height decays exponentially. The presence of vegetation results in a drag force which greatly enhances wave attenuation compared to a smooth bed (Mclvor et al., 2012). In the case of steeper slopes, waves are found to decay at the entrance of the mangrove area, which is located before the breaker zone (Figure 4(d)). It is also noted that when the waves propagate through the mangroves on steep slope, the wave height reduction becomes gradual and the effect is similar to the attenuation on mild slope without mangroves.

For a mild slope (1:80), where the beach slope gradually varies, the percentage energy reduction is found to be 98% as the waves approach the shoreline from the offshore boundary. For 1:40 and 1:20 slopes, wave attenuation rate is indicated as 93% and 84%, respectively. As the bed slope gets steepened, the rate of wave dissipation due to mangroves on 1:10 slope marked an increase of 20% when compared with that of no mangroves. The attenuation rates are likely to differ with the variation in the incident wave characteristics and the vegetation parameters such as spacing, dimensions, and species. The study also solidifies the fact that the wave dissipation rate on mild slope is maximum for the first few 100 m of the mangrove forest, whereas the trend is reverse on the steep slope. The uniqueness of wave attenuation characteristics for each slope can be attributed to the water depth variation in different slopes. There exists an inverse relationship between water depth and rate of wave dissipation by mangroves. Since the water depth is lower in the nearshore regions of mild slope, the waves are attenuated more rapidly as they propagate through the exposed roots which offer more drag resistance. But in the case of a steep slope, the water level is higher and the roots are in submerged condition, and the waves are encountered on stem resulting in lesser attenuation rate. A similar kind of disparity in wave attenuation characteristics is observed in mangrove environments with high tidal range.

Kobayashi et al. (1993) assumed an exponential decay of local wave heights for the small amplitude waves propagating over vegetation

$H = H_{0} \exp (- k_{i} x)$ (5)

where $H$ is the local wave height (in meters), $H_{0}$ is the initial wave height at $x = 0$ , $k_{i}$ is the exponential decay coefficient, and $x$ is the horizontal coordinate considered positive in the direction of wave propagation. Anderson et al. (2011) also reported that the wave heights were observed to decay exponentially through vegetation beds with the most rapid reduction occurring within the first few meters of permanent vegetation cover. This study has computed the local wave height from model simulations and estimated the wave height decay as $H_{i} / H_{o}$ that was plotted against the distance of wave propagation ( $X$ ) as shown in Figure 4. The results obtained for mild or gradually varying slopes (1:80 and 1:60) have shown good consistency with the earlier studies, but contradict with that of steeper slopes. As the seabed slope steepens, the trend shifts from the expression as suggested by Kobayashi et al. (1993) as shown in Figure 4.

Figure 5 explains the dissipation due to mangroves on mild slope and steep slope, and also the dissipation by mangroves on steep slopes can be expressed.

For mild slope

$f (x) = a * \exp (- bx)$ (6)

For steep slope

$f (x) = a * \exp (bx)$ (7)

where f(x) is the total energy dissipation, “x” is the width of mangrove forest, and “a” and “b” are constants. The dissipation rate by vegetation is high on mild slope for the first 100 m of vegetation width, and for the steep slope, the dissipation rate increases exponentially as it moves through the vegetation, and the highest wave dissipation is observed 100 m away from the landward edge of mangrove forest.

Figure 5.

Dissipation on mild slope (left) and steep slope (right).

The mangrove-dominated Ganges Delta—the Sundarbans—is a complex ecosystem comprising one of the three largest single tracts of mangrove forests of the world. The Sundarbans mangrove forest which is a part of the head bay region situated in the north of Bay of Bengal is a low wave energy coast with gentle bottom slopes and high risk to extreme events, namely, cyclones, storm surge, sea level rise, so on, and vulnerable to changing climate. One of the recent studies by Patra and Bhaskaran (2016) provides clear evidence on the dipole nature in the wind-wave climate over this region. The eastern side of the head Bay region bordering Myanmar experiences an increased activity of both wind and wave climate, unlike the western side that borders the mainland of India. Interestingly, there is a shift observed in the mean sea-level pressure patterns over this region. More research is warranted to understand these observed trends in wind-wave activity over the head Bay region, considering both the atmospheric and oceanographic components together. Higher wave activity in the coastal regions along the eastern side is directly linked with changes in the bathymetric profile. Complex sedimentation patterns and sediment transport mechanisms play an important role in dynamic changes in the shoreline patterns and also the seabed slope. It is felt that some areas in the nearshore regions off Sundarbans are in a state of continuous change due to sediment transport process and tidal action. In the long run, these localized coastal processes can significantly change the topography resulting in steepening of the bottom slope in some regions. This may adversely affect the mangrove ecosystem, and the characteristic wave energy attenuation for the region may also vary. Therefore, the present hypothetical experiment has addressed on how the wave dissipation varies with abrupt change in natural slope of the region and quantified the wave height reduction for varying slopes during extreme waves. The flow field will be different for each slope and it further affects the sedimentation in that region. Implementing artificial mangroves on a steeper beach will significantly improve the devastating effect of erosion caused by high-energy waves and further helps in sedimentation.

Conclusion

The key findings from synthetic experiments reveal that the energy of the incoming waves significantly dampens while propagating through mangroves for all slope conditions considered in this study. The vegetated mild slope exhibits higher wave dissipation when compared to the steeper slopes having mangrove vegetation. The total percentage energy reduction for waves reaching the shoreline after propagating through mangroves on mild slope (1:80, 1:40) is observed to vary between 93% and 98%, nearly 84% for 1:20 slope, and 67% for steep slope (1:10). The quantitative and qualitative characteristics of wave dissipation by mangroves differ for each slope due to which the water depth, shoaling, breaking, and reflection phenomenon for each slope varies. This study highlights that the characteristics of wave height decay significantly depend upon the slope of sea bottom, and hence, bottom topography plays an important role in wave dissipation characteristics by vegetation. This study is an initial effort to understand how the wave attenuation characteristics change from mild to steep slopes in the presence of mangroves, and furthermore, it develops an idea about the efficiency and behavior of artificial mangroves on a high wave energy coast.

Footnotes

Funding

The author(s) received no financial support for the research,authorship,and/or publication of this article.

Author biographies

Parvathy K G graduated BTech degree in Civil Engineering from Kerala University,Thiruvananthapuram in 2012 and MTech degree in Marine Structures from National Institute of Technology Karnataka (NITK),Surathkal in 2014. Currently she is working as a Research Scholar in the Department of Ocean Engineering & Naval Architecture at Indian Institute of Technology Kharagpur. Her broad area of research is on Coastal Wave Modelling with particular interest on wind-waves,its variability and attenuation characteristics by mangrove vegetation for the Indian seas.

Prasad K. Bhaskaran is currently the Professor and Head in the Department of Ocean Engineering & Naval Architecture at Indian Institute of Technology Kharagpur. He earned his PhD degree from Kurukshetra University,Kurukshetra. His research interest includes Ocean Wave Modelling,Coastal Engineering,Physical & Dynamical Oceanography,Tropical cyclones,Bottom Boundary Layer Dynamics,Numerical Modelling of Coastal Processes,Sediment Transport Modelling,Coastal Hydrodynamics,Port & Harbour Engineering,and Wind-Wave climate projections for the Indian Ocean region.

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