Overview on Mangrove Forest Disaster Prevention and Mitigation Functions

CHEN Xinping , YIN Ziqi , LI Zibin, WANG Bin, TAO Aifeng , GUO Zhixing,WANG Fei , AN Yanhong , and O’DRISCOLL Kieran

1) College of Harbour, Coastal and Offshore Engineering, Hohai University, Nanjing 210098, China

2) National Marine Hazard Mitigation Service, Beijing 100194, China

3) The People’s Government of Hainan Province, Haikou 570204, China

4) Hibernian Marine Systems Limited, Cork T12EDD8, Ireland

Abstract This paper provides a comprehensive overview on coastal protection and hazard mitigation by mangroves. Previous studies have made great strides to understand the mechanisms and influencing factors of mangroves’ protection function, including wave energy dissipation, storm surge damping, tsunami mitigation, adjustment to sea level rise and wind speed reduction, which are systematically summarized in this study. Moreover, the study analyzes the extensive physical models, based on indoor flume experiments and numerical models, that consider the interaction between mangroves and hydrodynamics, to help our understanding of mangrove-hydrodynamic interactions. Additionally, quantitative approaches for valuing coastal protection services provided by mangroves, including index-based and process-resolving approaches, are introduced in detail. Finally, we point out the limitations of previous studies, indicating that efforts are still required for obtaining more long-term field observations during extreme weather events, to create more real mangrove models for physical experiments, and to develop numerical models that consider the flexible properties of mangroves to better predict wave propagation in mangroves having complex morphology and structures.

Key words mangrove; coastal protection; disaster prevention and mitigation; disaster reduction value; coastal resilience

1 Introduction

Mangrove forests are one of the most important types of coastal ecosystems, consisting of a group of trees and shrubs living in the coastal intertidal zone. Mangroves grow in coastal saline or brackish water and have adapted to living in harsh coastal conditions, including high salinity, high temperature, high sedimentation rates and muddy anaerobic soils (Giriet al., 2011). Mangroves are typically located between mean sea level and highest spring tide (Alongi, 2009). In 2018, the Global Mangrove Watch Initiative released a new baseline of mangrove extent that assesses the global mangrove area as of 2010 at 137600 km2, spanning 118 countries and territories (Buntinget al.,2018; Friesset al., 2019). Mangroves are distributed worldwide in the tropics and subtropics and some temperate coastal areas, mainly between latitudes 30?N and 30?S (Giriet al., 2011; Friesset al., 2019). The largest mangrove area is located between 5?N and 5?S (Giriet al.,2011), containing two regional distribution concentrations in Southeast Asia and Central and South America (Alongi,2009; Friesset al., 2019). A previous study concludes that there are about 80 different species of mangroves found in the world, contained in 16 families and 24 genera, including 70 species of true mangroves in 11 families and 16 genera (including 12 varieties) and 14 species of semi-mangrove plants in 8 genera of 5 families (Tomlinson, 2016).

In China, mangroves are located on the northern edge of the global mangrove distribution areas, and are mainly distributed in the Guangdong, Guangxi, Hainan, Fujian and Zhejiang Provinces, as well as Taiwan, Hong Kong and Macau. According to the Third National Land Survey of China (Office of the Third National Land Survey Leading Group of the State Councilet al., 2021), the area of mangrove forests in China is about 271 km2. Moreover,the mangroves in Guangdong, Guangxi and Hainan provinces account for more than 80％ of the whole mangrove area in China (State Forestry Administration, 2014). One study has shown that 26 species of true mangrove plants and 12 species of semi-mangrove plants are found in the coastal region of China (Liao and Zhang, 2014). Mangrove area in China accounts for less than 0.2％ of the global total,whereas species account for over 1/3 of the global number (Li, 2020).

Mangroves provide numerous important ecosystem services that play an important role in protecting marine biodiversity and supporting the livelihoods of coastal and island communities: they provide essential habitat for thousands of species (e.g., breeding, spawning and nursery habitat for commercial fish species); filter water, guard shorelines (e.g., protection from floods and storms, provide erosion control, prevention of salt water intrusion); and they create opportunities for tourism and recreation (cultural services) (Spaninks and Van Beukering, 1997; Brownet al.,2006; Branderet al., 2012; Kumar, 2012). Besides, as a type of ‘Blue Forest’ (that includes mangrove forests, seagrass meadows and tidal salt marshes), mangroves are an important constituent of the blue carbon sink on Earth,through sediment burial, mineralization and organic export,which contributes to mitigating climate change (Alongi,2012; Duarteet al., 2013; Hamilton and Friess, 2018).

Due to global and regional climate change, the risk of natural hazards, including floods and storm surges, have exhibited an increasing trend in recent decades in many coastal areas (P?rtneret al., 2022). By acting as natural barriers, the presence of mangrove ecosystems on coastlines can play an important role in protecting coastal regions, saving lives and property, and preserving communities during natural hazards such as cyclones and storm surges (Mcivoret al., 2012b). Previous studies have made the point that building defense systems against coastal hazards through the construction and restoration of coastal ecosystems such as mangroves can provide a more sustainable, cost-effective and ecologically sound option than through conventional coastal engineering (e.g., building seawalls) (Spaldinget al., 2014; Chávezet al., 2021).Popularly referred to as nature’s coast guards, mangrove ecosystems can, to some extent, improve the resilience of coastlines, by forming a natural protective buffer zone between land and sea.

Many studies in the literature have demonstrated and described the important role that mangroves play in natural disaster mitigation and coastal protection. The goal of the present study is to provide an overview on these related studies, including mechanisms and influencing factors of coastal protection and hazard mitigation by mangroves (Section 2), models on the dissipation of wave energy through mangroves (Section 3), and quantitative assessment methods for economic benefits of mangrove hazards mitigation (Section 4). Section 5 presents conclusions, in which we summarize the shortcomings of previous studies in order to provide suggestions for further study.

2 Mechanisms and Influencing Factors of Coastal Protection and Hazard Mitigation by Mangroves

2.1 Wave Attenuation by Mangroves

Theoretical analyses and field observations have demonstrated that ocean waves can be damped,i.e., their heights can be reduced over relatively short distances when passing through mangroves (Mazdaet al., 1997; M?lleret al.,1999; Mcivoret al., 2012a). The damage induced on coastal infrastructure by ocean waves can potentially be mitigated by mangroves due to wave damping and wave energy dissipation (Mcivoret al., 2012a).

The mechanisms of wave energy dissipation in mangroves have been widely studied in previous studies. In general, there are two dominant energy dissipation mechanisms in mangroves: one is dissipation due to the interactions of the flow with the mangrove vegetation, while the other is the dissipation due to wave breaking (Vo-Luong and Massel, 2008). Wave breaking is particularly important for wave attenuation in sparse trees, while the role of vegetation on water flow is dominant in mangroves with high tree density (De Vos, 2004; Quartelet al., 2007). Quartelet al.(2007) compared wave damping by mangrove vegetation and bottom friction at similar water depths, and found that damping by mangroves was 5 – 7.5 times larger than that by bottom friction only, confirming the importance of mangrove vegetation to coastal defence.

Several factors impact upon ocean wave attenuation through mangroves, including mangrove width, water depth,wave period, current-wave interaction, wave height, topography, tidal elevation and dynamics, and various characteristics of mangroves that most notably depend on the structure and morphology of mangrove trees associated with species, age and size (Mcivoret al., 2012a; Huet al.,2014) (Fig.1). Mangrove structure and characteristics, together with related water depth, are the major factors affecting wave attenuation rates in mangroves, and determine the nature of mangrove obstacles that waves encounter as they pass through the trees (Mcivoret al., 2012a).The density of mangrove obstacles encountered by ocean waves and the height of these obstacles relative to the water depth are among the key factors influencing the rate of wave attenuation with distance in mangroves (Mcivoret al., 2012a).

The complex root structure, trunks, branches and leaves of mangroves can form a solid barrier network in attenuating water movement (Spaldinget al., 2014). First, some species of mangroves have complicated, strong and extensive root systems, including aerial roots (Fig.1). For example,Rhizophoraspp. mangroves have prop roots,Avicenniaspp. mangroves have pneumatophores, whileBruguieraspp. mangroves have knee roots (De Vos, 2004).On a rising tide, the waves pass through the roots, thereby introducing considerable resistance to water flow, resulting in wave energy dissipation and wave damping (Mazdaet al., 2006). Masselet al.(1999) studied wave attenuation effects by prop roots in the mangroves located in Cocoa Creek in Australia, whereRhizophora stylosais the dominant species, and reported that about 60％ of peak wave energy was dissipated within the first 80 m along the extent of the mangrove of the mangrove forest. Second, when compared to mangrove root systems, the trunks normally present a lesser effect on wave attenuation, permitting waves to pass more easily (Mazdaet al., 2006). Third,when the waves reach the mangrove branches and leaves,wave damping is expected to increase again, due to the thick and flexibly spread branches and leaves that interact with waves, resulting in dissipation of wave energy (Mazdaet al., 2006). Moreover, mangrove tree size, shape and branch and aerial root density are age dependent. Mazdaet al.(1997) measured wave attenuation due to the influence ofKandelia candelin three groups of planted trees at different ages,i.e., 1/2-year-old trees, 2-3-year-old trees,and 5-6-year-old trees; and found that 5-6-year-old trees exhibited the greatest attenuation of waves.

The amount of wave attenuation is also a function the horizontal extent of the mangrove forest along which the waves propagate. Mangroves can attenuate wind and swell waves within a relatively short distance: exponential wave damping dependent upon distance travelled through the mangroves has been demonstrated (Bao, 2011). Using wave measurement data, Bao (2011) studied the relationship between wave height and mangrove cross-shore distances,reporting that waves are approximately exponentially damped in the cross-shore direction. Additionally, Mcivoret al.(2012a) concluded that the rate of wave height attenuation with distance varies from 0.0014 m – 0.011 m, indicating that a 100 m wide long mangrove forest can reduce wave height by 13％ – 66％, while a 500 m wide long mangrove forest can damp wave height by 50％ – 99％ (Mazdaet al.,2006; Quartelet al., 2007).

Wave heights and periods are also factors that impact upon wave attenuation in mangroves. In general, the rate of wave damping is significantly affected by wave height,with higher amplitude waves being more attenuated (Mazdaet al., 2006; Mazaet al., 2019). Mazaet al.(2019) revealed a linear relationship between the wave damping coefficient and relative wave height (wave height/water depth),thereby demonstrating a strong correlation and reinforcing the idea that larger wave heights result in greater attenuation. However, the impact of wave period on wave attenuation is not prominently observed: the energy spectra for different periods waves did not significantly change when the waves passed through mangroves, implying that waves of different periods were attenuated at a similar rate(Brinkmanet al., 1997). In the study conducted by Mazaet al.(2019), the linear regression analysis for wave periods relative to wave height attenuation exhibited poor fitting performance, indicating that in some cases wave period is not a determining factor for wave damping.

Wave-current interaction plays a significant role in the process of wave attenuation. Li and Yan (2007) found that following currents (current velocity is in the same direction as wave propagation) promoted wave energy dissipation by vegetation (WDV), and WDV increased linearly with the velocity ratio of imposed current velocity to amplitude of horizontal orbital velocity. Huet al.(2014) conducted comprehensive flume experiments investigating the impact of following currents on wave dissipation within various canopies. Their study revealed a complex relationship between currents and waves, wherein following currents can either decrease or increase wave dissipation, contingent upon the ratio between current velocity and the amplitude of horizontal orbital velocity.

Another factor affecting wave energy dissipation by mangroves is forest floor slope, whereby changing water depth can cause wave shoaling, breaking and energy dissipation. Mangroves often grow on very gently sloping shores, where they can increase surface elevation by promoting sedimentation over the longer term, leading to decreased water depth, and hence an increase in wave shoaling and energy dissipation (Mcivoret al., 2012a). Utilizing analytical and experiment studies, Parvathy and Bhaskaran (2017) demonstrated the sensitivity of wave attenuation characteristics to beach slopes, with the aim of understanding how wave attenuation characteristics differ with varying bottom slopes in the presence of mangroves.The study reveals that wave height decays exponentially for mild slope, consistent with earlier studies, while wave damping extent becomes more gradual increasing degree of bottom steepness, and can be attributed to water depth variation, shoaling, breaking, and reflection characteristics, within mangroves.

2.2 Storm Surge Damping by Mangroves

Since mangroves are situated in tropical and subtropical coastal areas, they face high risks of damage from tropical cyclones and associated storm surges. There is scientific evidence that the complex network of roots, branches and leaves of the mangroves can provide measurable economic protection for coastal communities against storm surges, by slowing the flow of water and diminishing ocean waves (Hochardet al., 2019). This can also act to trap debris or even large moving objects caused by natural events including cyclones and storm surges, thus reducing potential damage from physical impacts of such events (Spaldinget al., 2014; Sakibet al., 2015). Evidence of this is provided in various reports, including Badola and Hussain (2005),Das and Vincent (2009), and Haqueet al.(2012).

The ability of mangroves to withstand storm surges is affected by a variety of factors, including mangrove characteristics (e.g., forest width extent, structural complexity,dominant species and the projected area of vegetation) and physical characteristics such as channels and pools as well as local topography (Mcivoret al., 2012b). Tidal channels located within mangroves normally reduce the ability of mangroves to withstand storm surges, since water can more easily flow inland along the channels (Mcivoret al.,2012b). Moreover, storm characteristics, such as direction of travel and speed, can affect the resistance of mangroves against storm surges. Zhanget al.(2012) demonstrated that mangroves cause more significant damping in surges of faster moving storms.

The role of mangroves in diminishing storm surges has been confirmed in the literature. Krausset al.(2009) found that the average rate of water level decline in the mangrove wetland reached 4.2 cm km?1– 9.4 cm km?1when the hurricane storm surge passed through the wetland. The simulation results of Zhanget al.(2012) showed that, without mangroves, the inundated area would extend an additional 70％ inland; due to the flooding ‘blockage’ effect by mangroves, the magnitude of storm surge at the leading edge of the forest increased by 10％ – 30％; storm surge depth was reduced by the mangroves; and the decay rate of surge amplitude in the central mangrove region was 20 cm km?1– 50 cm km?1. Furthermore, for some low-lying areas on the land side of the mangroves, a small drop in storm surge height (water level) contributed by mangroves can greatly reduce associated flooding (Thampanyaet al., 2006).

2.3 Mitigating Effect of Mangroves Against Tsunamis

Previous studies comprising field surveys, statistical analyses and numerical simulations, have improved our understanding of the role mangroves play in mitigating tsunami hazards (Kathiresan and Rajendran, 2005; Yanagisawaet al., 2009). Mangroves can attenuate tsunami associated waves and mitigate their impacts by reducing water flow velocity, height of water level increase, inundation range and destructive energy of water flowing onshore and inland (Spaldinget al., 2014). Numerical simulations have demonstrated that wide mangrove belts (several 100 m) can reduce tsunami-induced wave amplitudes by 5％ to 30％ (Spaldinget al., 2014). In some extreme cases, however, high-intensity tsunamis can damage or cause severe destruction to the mangroves, to some extent reducing their ability to mitigate tsunami associated hazards, where branches and trunks washed inland with the inundating seawater is likely to cause secondary disasters(Kathiresan and Rajendran, 2005).

The ability of mangroves to withstand tsunamis is influenced by several factors, including forest width; mangrove characteristics (e.g., tree density, tree diameter, tree height); soil texture; forest location; forest floor slope; tsunami size and speed; distance from tectonic tsunami source;and angle of tsunami incursion relative to the coastline(Alongi, 2008).

The 2004 Indian Ocean earthquake and tsunami provided clearly demonstrated the protective role of mangroves against the tsunami. The tsunami hit the coasts of several countries in South and Southeast Asia, killing around 200000 people in Indonesia, Sri Lanka, India, Thailand,and other countries. In India, it was stated that the small villages behind the Pichavaram mangrove wetland in the state of Tamil Nadu were physically protected from the tsunami, whereas settlements located on or near the beach,which were not protected by mangroves, were completely devastated (Kesavan and Swaminathan, 2006). Sri Lanka was also greatly impacted by the tsunami with water sweeping inland, especially along eastern and southern coasts. A survey carried out by the International Union for Conservation of Nature (IUCN) compared the losses of two villages after the tsunami hit, demonstrated that Wanduruppa village surrounded by degraded mangroves suffered 5000– 6000 deaths, whereas Kapuhenwala village, surrounded by 2 km2of dense mangrove forest, only two people were killed. Moreover, it was reported that Simeuleu Island in Indonesia near the epicenter of the earthquake (41 km from the epicenter), was partly saved by its substantial mangrove cover, coral reefs and seagrass beds, resulting in only 4 human deaths (EJF, 2006). Eyewitnesses on Simeuleu Island described the scene: no wave penetrated the mangroves, while instead the water level gently increased ‘like a rising tide’ (EJF, 2006). Similarly, the protective role of mangroves against the tsunami was also demonstrated in Thailand. Phang Nga, the most affected province in Thailand, was well protected by the large mangroves that significantly mitigated the impact of the tsunami, while coastal areas of Phang Nga unprotected by mangroves, were severely impacted (EJF, 2006).

2.4 Mangrove Adjustment to Sea Level Rise

Due to glacier melting and disappearance and thermal expansion from ocean warming caused by climate change,global mean sea level has risen since 1900, increasing by 0.20 [0.15 to 0.25] m between 1901 and 2018 (Masson-Delmotteet al., 2021) and continuing to increase at an accelerating rate. A variety of studies, published in the literature, have examined mangrove capacity to keep pace with rising sea level (Hashimotoet al., 2006; Cheonget al.,2013; Krausset al., 2014), demonstrating that the capacity is interactively influenced by hydrological, geomorphological and climatic processes together with plant processes.

Mangrove forests may directly or indirectly affect vertical changes of the soil surface, by producing and accumulating organic matter, as well as retaining and trapping sediment, due to both physical and biological processes(Krausset al., 2014). Mangrove vegetation can diminish wave energy, slowing the flow of water across the soil surface, thereby permitting suspended sediments to settle out of the water, and promoting the elevation of adjacent mudflats (Bird, 1980; Spaldinget al., 2014). A study found that up to 80％ of sediment delivered by tides can be captured by mangrove forests (Furukawaet al., 1997). For some extreme weather events, sediment deposition was observed to be largely stimulated. For example, during Hurricane Wilma, Smithet al.(2009) described the extensive sediment deposition in the mangrove area of Florida that reached up to 8 cm. Additionally, biological processes (e.g.,woody debris deposition, benthic algal matter growth, organic matter decomposition), are also important, but often under-appreciated, for contributing to elevation losses or gain (Krausset al., 2014). Normally, rates of surface elevation changes in mangroves are very slow, resulting in changes affecting the mangroves over long periods, ultimately determining whether the mangrove ecosystem survives (Krausset al., 2014).

Various studies have noted that, in some mangrove areas, surface elevation increased at a rate similar to sea level rise, through the Holocene and also in recent years(McKeeet al., 2007; Ellison, 2009), indicating that these mangroves are able to adjust to sea level rise (Willard and Bernhardt, 2011; Mcivoret al., 2013; Krausset al., 2014).Moreover, mangroves are not passive to changes affecting them, rather, they are capable of modifying their environment, naturally promoting habitat persistence (Cheonget al., 2013). However, mangrove forests cannot survive if the rate of rising sea level becomes greater than their capacity to keep pace (Hashimotoet al., 2006). In addition, in some areas, such as in western Australia, mangroves can adjust to keeping pace with the rate of coastal erosion, by migrating and expanding inland (Willard and Bernhardt, 2011; Mcivoret al., 2013).

2.5 Surface Wind Reduction by Mangroves

Previous studies have shown that mangroves can reduce wind speeds, thus buffering wind-induced water surface movement. When winds blow against the mangrove forests, mangroves act as porous barriers, creating a wind reduction region on the windward side and a low-speed,turbulent wake zone in the lee, followed by a gradual wind speed recovery region (Takle, 2005). Considering the mangrove as an integrated feature of mangrove height, trunk and branch density, forest length, species composition,orientation, determines the effectiveness of mangroves in reducing wind speed reduction (Brandle and Finch, 1991).Moreover, by buffering the water surface from the effects of wind, mangroves can reduce the generation of windwaves, and can make a substantial contribution to storm surge flood levels and damage (Mcivoret al., 2012b).

The reducing effect of mangroves on wind speeds can be demonstrated from field observations. For example, Chenet al.(2012) collected wind-reducing data ofSonneratia apetalaandKandelia obovatain Dongzhaigang National Nature Reserve, Hainan. The results revealed that, when the wind speed was less than 5 m s?1, the average speed of wind that traveled 50 m within the mangrove forest belt was reduced by more than 85％, and mangroves can reduce the average wind speed by more than 50％ in extreme weather when wind speed is greater than 15 m s?1. Moreover, in 2008, Wanget al.(2012) also collected wind speed data when Typhoon ‘Raccoon’ passed through the studied mangrove forest area in the Dongzhaigang National Nature Reserve, Hainan. They concluded that wind speed decreased significantly after passing through the mangrove,with maximum speeds decreasing from 19.67 m s?1to 10.28 m s?1.

Rahumanet al.(2021) performed simulations and analyses with Computational Fluid Dynamics (CFD) techniques to study the effect of mangroves on reducing wind speeds. Results suggest that mangrove roots have demonstrated great resistance to wind, with a 70％ reduction of initial wind speed at 75 km h?1, 250 km h?1and 450 km h?1.Using the Advanced Circulation (ADCIRC) unstructured grid hydrodynamic model, Westerinket al.(2008) considered the variation of peak water levels in hindcasts of Hurricanes Betsy and Andrew whereby surface wind speeds were modified to reflect land cover differences, and pointed out that, comparing to the wind speeds assuming openocean marine conditions, peak water levels decreased more than 1 m in some areas within the mangrove forest, implying the effect of vegetation on wind speed significantly affects storm surge water levels.

3 Models on the Mechanism of Wave Propagation in Mangroves

Extensive physical models based on indoor flume experiments and numerical models that consider the interaction between plant and hydrodynamic parameters have been widely used to help understand and predict wave propagation and behavior through mangroves (Mazdaet al.,2006; Wu and Cox, 2015). Both physical model experiments and numerical simulations requirein-situobservation to support model calibration and validation. These observations are also used for visually observing and studying wave propagation process changes around mangroves.Insituobservations are expensive in terms of input effort,time and cost. In this section, we summarize models associated with the mechanism of wave propagation in mangroves, in term of both physical model experiments and numerical simulations.

3.1 Theoretical Research of Wave Dissipation in Mangroves

Many previous studies have undertaken theoretical research into vegetation wave dissipation, employing a range of fluid mechanics and thermodynamics theories such as linear wave theory, potential flow theory, and laws of energy and momentum conservation. For example, using hydrodynamics, Dalrympleet al.(1984) analyzed wave motion in vegetated regions to explore the influence of vegetation resistance on wave behavior and thus quantify the resistance to develop a comprehensive model that describes the propagation characteristics of waves in vegetated areas. Based on Dalrymple’s theory, Kobayashiet al.(1993) developed a vertically-averaged momentum equation describing the propagation patterns of waves in mangroves to address situations involving submerged rigid plants. Mendez and Losada (2004) investigated the characteristics of wave breaking on gentle slopes to predict wave height attenuation in irregular waves within vegetated areas. Many studies have developed theories of porous media (e.g., Iimura and Tanaka, 2012; Suzukiet al.,2019) to characterize the movement of water flow within mangrove areas. Based on nonlinear shallow water equations, Suzukiet al.(2019) revealed that porosity effects induce wave reflection, and subsequently contribute to reduce wave height within and behind vegetation fields.

Extensive research efforts, including theoretical analyses, have been dedicated to investigating the role of drag forces in the equations of wave motion within vegetation areas. These have resulted in the development of expressions for the drag coefficient under varying hydrodynamic conditions and vegetation morphology. Many previous studies have employed theoretical analyses to investigate interactions among drag forces, hydrodynamic conditions,and vegetation morphology, presenting calculation methods for the drag coefficient under different scenarios. Kobayashiet al.(1993) proposed a direct relationship between the drag coefficient and the Reynolds (Re) number, which has been widely adopted several research projects: Huet al.(2014) combined experimental data and theoretical analysis to develop a method for calculating the Reynolds number, and derived an empirical equation that captures the relationship between the drag coefficient and the Reynolds number in the context of wave-current-vegetation interactions; Wanget al.(2022) established a highly correlated empirical relationship with the drag coefficient in the presence of complex mangrove root systems, by introducing a new effective characteristic length and a modified KC number.

3.2 Physical Model Experiments

Physical model experiments are established tools for studying complex interaction problems involving plants and hydrodynamics. They have been widely used to quantitatively assess the attenuation of wave propagation in mangrove areas. To set up such experiments, researchers generally need to design and build idealized model trees based on real mangrove plant characteristics; in term of plant shape, trunk diameters and other parameters.

For example, Struveet al.(2003) carried out physical experiments to investigate the additional resistance to wave propagation created by mangrove model trees. They set the model trees, made from dowels of mixed diameters, onto the channel bottom in a regular grid with varying tree densities in a hydraulic flume, thus suggesting that model tree diameter and density are the most important factors affecting the increase in velocity.

Wu and Cox (2015) conducted physical model experiments to investigate the effects of wave nonlinearity on the attenuation of irregular waves passing through mangroves. Plastic strips, used as model trees and, attached to a metal sheet in a uniform arrangement with a certain density in a rectangular water tank. The results indicated that steepness across the range of relative water depths, from shallow to deep water, determines the wave damping factor. Moreover, the authors also analyzed drag force coefficient of plants in relation to Reynolds (Re) number, Keulegan-Carpenter (KC) number and Ursell (Ur) number.They pointed out that KC and Ur were better predictors of the drag coefficient than the Re when considering wave nonlinearity effects.

Physical model experiments can also be used to study the effects of wave dissipation by mangroves on tsunami waves (solitary waves). Yaoet al.(2015) conducted a wave flume experiment to investigate the interaction of solitary waves with emergent and rigid plants on a slope. The results suggest that the ratio of runup to incident wave height,determined by plant density, is constant. Iimura and Tanaka (2012) studied the mitigation effects of different vegetation densities on tsunamis by means of physical model experiments. In their experiment setup, the plants were modelled by wooden cylinders in a staggered arrangement,and a long solitary wave, corresponding to a tsunami height of approximately 3 m offshore, was generated at the boundary. The results reveled that, due to dense vegetation, an obvious increase in the reflected wave height was found to the front of the vegetation, while, behind the vegetation,water level and velocity were reduced resulting from resistance due to the vegetation.

Recent research studies have developed mangrove models that consider complex mangrove structures to investigate wave attenuation in mangroves. For example, Heet al.(2019) considered the impact of three components of mangroves (roots, trunks, and canopies), on wave attenuation by conducting physical experiments. They demonstrated that the canopy of mangroves generally exhibited more effective wave energy reduction compared to the roots and stems. Wanget al.(2022) focused on detailed three- dimensional complex root modeling of Rhizophora mangrove species, exhibiting that mangrove roots significantly impacted upon wave attenuation, especially in shallow water conditions.

Overall, physical model experiments are powerful tools for investigating mechanisms and quantification of wave attenuation by mangroves, that consider mangrove characteristics of species, densities and width, as well as various hydrodynamic conditions. However, such models used in previous studies were mostly simplified as cylinder,plastic strips or other simple shapes, which are much simpler than the complex structures and characteristics of mangrove root systems, branches and leaves. Thus, physical models that are closer to real mangrove morphology and structures need to be developed to support more realistic conditions for physical experiments, and can be accomplished by means of 3D printing and other new techniques.

3.3 Numerical Models

In recent decades, numerical models have been well developed for quantitatively assessing the function of wave dissipation by of mangroves. Researchers have developed a variety of numerical models based on different theories and assumptions for various case applications.

One group of such numerical models is based on popular ocean wave models or storm surge models, such as the SWAN (Simulating WAves Nearshore) model (Booijet al.,1999) and the CEST (Coastal and Estuarine Storm Tide)model (Zhanget al., 2012), by including damping effects by vegetation into the models. For example, Chen and Zhao (2012) developed a new model for random waves propagating in vegetation areas based on the SWAN. The model considers energy dissipation of random waves due to bottom friction. Suzukiet al.(2012) extended the SWAN model to include a vertical layer schematization for vegetation. The model calculates two-dimensional wave dissipation over vegetation fields, including wave breaking and diffraction. Zhanget al.(2012) modified the Manning coefficients for various types of land covers to incorporate the drag force of mangroves into the bottom friction term in the CEST model. The modified model resulted in better estimation of mangrove attenuation effects against storm surges compared to statistical methods based on sparse samples. Chenet al.(2021) employed an improved drag force formula, that incorporates the porosity plus drag force method, and applied an improved abstract mangrove tree model in the CEST model. The authors conducted extensive comparisons with the Manning coefficient method, demonstrating that their proposed method provided more accurate quantification for attenuation effects of mangroves against storm surge. Suzukiet al.(2019) introduced a vegetation model integrated into the SWASH (Simulating WAves till SHore) framework that explicitly incorporates the effects of drag force from vertical and horizontal vegetation cylinders, as well as inertia force and porosity. In Van Rooijen’s study (Van Rooijenet al., 2015), formulations were introduced to the XBeach model to incorporate the effects of coastal vegetation on wave energy attenuation and coastal hazard reduction.

Another group of numerical models for illustrating wave attenuation in mangroves are those models specialized models for dealing with wave motions and interactions between plants and waves in mangrove areas. Models have been developed various ways, using differing assumptions. For example, Mendez and Losada (2004) proposed an empirical model to estimate wave transformation induced by a vegetation field, that includes wave damping and wave breaking over vegetation fields at variable depths.The model considers geometric and physical characteristics of the vegetation field, and depends on a single factor parameterized as a function of the local KC number for a specific type of plant, which is similar to the drag coefficient. By linearizing the non-linear governing equations for wave-trunk interactions based on the stochastic minimalization concept, Masselet al.(1999) presented a theoretical model for predicting attenuation of wind-induced random surface waves within the mangroves. The governing equations introduce interactions between mangrove trunks and waves through the modification of drag coefficients.Bao (2011) established an integrated exponential equation based on field observations of wave attenuation in mangroves, that includes coefficients of initial wave height,canopy closure, mangrove height and density. The integrated equation can calculate the appropriated mangrove band width at a predetermined level of attenuation, according to the maximum average wave height and the safe wave height behind forest band. Vo-Luong and Massel(2008) developed the WAPROMAN (WAve PROpagation in MANgrove forest) model for solving a full boundary value problem to predict the attenuation of waves propagating though non-uniform mangroves in arbitrary water depth. Additionally, some researchers introduced the porous medium theory that considers the plant zone as a porous medium to derive the fluid control equation for wave motions in mangrove areas (Brinkmanet al., 1997; Zou,2020). For example, Zou (2020) introduced drag and inertial forces into the governing equations, to characterize the wave abatement effect of vegetation in the flow field,and got reasonable model results.

Overall, in recent decades, numerical models have been greatly developed to understand the mechanism of planthydrodynamic interaction in mangroves. However, there are still some shortcomings in the current numerical models. For example, the drag force coefficients developed and in current use are, to some extent, too simple to simulate the complex morphology and structure of various species of mangroves. The flexible effects of branches and roots of mangroves have still not been sufficiently considered in most numerical simulations. Thus, models need to be further developed, so as to better parameterize the relationship between mangrove characteristics and friction.

4 Quantitative Approaches to Quantifying the Value of Coastal Protection Services Provided by Mangroves

Mangroves serve as important natural buffers, protecting coastal residents and infrastructure, and providing significant economic benefits in terms of hazard prevention and mitigation (Becket al., 2016; Losadaet al., 2018). In general, economic values of coastal protection services provided by mangroves are based on common tools and approaches, which can also be used as additional aids to the decision-making process, including costs avoided or savings provided by natural habitats (Naidooet al., 2008;Dailyet al., 2009). These tools and approaches can be separated into two main categories: index-based approaches and process-resolving approaches.

Index-based approaches assess the benefits of hazard risk reduction by estimating the exposure and vulnerability of the mangrove area. The key indices required for the assessment can be calculated by using different configurations of natural habitats and environmental conditions(Becket al., 2016). For example, Arkemaet al.(2013) employed an index-based approach for assessing the vulnerability of flood-prone shorelines with and without coastal habitat in the InVEST (the Coastal Vulnerability Module of InVEST) economic value assessment model. The In-VEST rates seven variables (sea level, winds, wave surge,etc.) with five scales for determining shoreline vulnerability.

Process-resolving approaches consider processes such as sediment transport and wave-vegetation structure interactions, before applying parameters including waves,storm surges, currents, and tides in the analytical calculations (Becket al., 2016). Process-resolving approaches can be further divided into analytical approximation (semi- empirical formulation) and numerical modeling approaches.Less computational capability is required for the analytical approximation methods, so they can be implemented over a larger area. The numerical modeling methods, however, can resolve coastal processes with higher accuracy,even though they need more computational capability and expertise (Becket al., 2016). In particular, the World Bank recommended the Expected Damage Function (EDF)method for valuing coastal protection services from mangroves, which is also a process-resolving approach (Becket al., 2016). The EDF approach assumes the value of an ecosystem (e.g., mangroves) to reducing economic damage can be estimated and accounted for by the reduction in expected damage (Barbier, 2007; Becket al., 2016).

Based on valuation approaches, an assessment was implemented for valuing the economic benefits of coastal protection services from mangroves. Lewis III (2005) reported that global mangroves can protect 18 million people against the exposure to coastal hazards while reducing economic property damage by more than $82 billion annually. Without mangroves, more than 39％ of the population and 16％ of the property in the globe would be additionally affected by coastal hazards (Lewis III, 2005;Friesset al., 2019). Overall, assessments based on valuation approaches have revealed that mangroves can protect millions of coastal citizens globally while greatly reducing economic property damage annually.

5 Conclusions

This study summarizes the coastal protection function provided by mangroves against coastal threats, including,hazardous ocean waves, storm surges, winds and tsunamis.Mangroves can effectively reduce wind speeds and ocean wave heights over a relatively short distance. A 100-meter-wide mangrove belt can reduce wave height by 13％to 66％ depending on species and density (Mazdaet al.,2006; Mcivoret al., 2012a). Mangroves can also withstand storm surges or mitigate the hazard of tsunamis by reducing water flow velocity and destructive energy of water flowing inland (Thampanyaet al., 2006; Alongi, 2008;Krausset al., 2009). Moreover, mangroves can permit suspended sediments to accumulate and subside out of the water to raise the ground gradually, and thus own the potential ability adjusting to sea level rise (Ellison, 2009;Spaldinget al., 2014). Mangroves also provide significant economic benefits in terms of hazard mitigation (Becket al., 2016; Losadaet al., 2018).

Previous studies have greatly improved our ability to understand and predict the mechanism of behavior of wave propagation in mangroves, by means of observations,theoretical analysis, physical model experiments and numerical models. Idealized model trees are the fundamental tools for physical model experiments, which are designed and built based on real mangrove plant characteristics in term of plant shape, trunk diameters and other parameters. Moreover, numerical models have seen great developments by considering geometric and physical characteristics of the mangrove field. Many researchers have extended popular ocean wave models or storm surge models (e.g., the SWAN, the CEST, the SWASH, the XBeach),to introduce vegetation effects on water movements into the models. Additionally, many studies developed some specialized numerical models (e.g., the WAPROMAN) to deal with the interaction of plants and waves in mangrove areas.

Some aspects still require further study on the mechanisms of coastal protection and hazard mitigation by mangroves. Firstly, field observations have been reported in some previous studies, while they are still lacking, especially for long-term, multi-locations observations during extreme events. Secondly, mangrove models adopted in physical experiments in previous studies were mostly simplified as cylinder, plastic strips or other simple shapes,which are limited in their ability to represent the complex structures and characteristics of mangrove root systems,branches and leaves. Therefore, models that better represent real mangrove morphology and structures are required for further development. Thirdly, in numerical models, the flexible effects of branches and roots of mangroves have not been fully considered in previous studies that are needed to further study to better simulate the behavior of waves propagating in various species of mangroves with complex morphology and structures.

Acknowledgements

This research is funded by the National Key R&D Program of China (No. 2023YFC3007900), the Young Scientists Fund of the National Natural Science Foundation of China (No. 42106204), the Jiangsu Basic Research Program (Natural Science Foundation) (No. BK20220082), the National Natural Science Foundation of China (No. 5227 1271), and the Major Science & Technology Projects of the Ministry of Water Resources (No. SKS-2022025).