Evaluating Vegetation Effects on Wave Attenuation and Dune Erosion during Hurricane

Abstract

This study employs the XBeach surfbeat model (XBSB) to explore the effects of vegetation on wave attenuation and dune erosion in a case study of Mexico Beach during Hurricane Michael. The XBSB model was validated against laboratory experiments of wave-induced dune erosion and wave attenuation by vegetation. In the case study of vegetation on dunes in Mexico Beach during Hurricane Michael, different vegetation drag coefficients were evaluated to investigate the effects of vegetation on wave attenuation and dune erosion. LiDAR data of dune profiles before and after Hurricane Michael were used for model validation. The findings reveal that vegetation on dunes significantly affects wave attenuation and dune erosion. Under vegetated conditions, as the vegetation drag coefficient value increases, wave attenuation also increases, leading to a reduction of dune erosion. An increase in vegetation density enhances wave attenuation in the vegetated area, including reductions in significant wave height and flow velocity. However, the rate of change in attenuation decreases as the vegetation density increases. Through simulations under regular wave condition on Mexico Beach, an optimal vegetation density was identified as 800 units/m². Beyond this density, additional vegetation does not substantially improve wave attenuation. Furthermore, the position of the dune crest elevation is related to the location where the alongshore flow velocity begins to decrease. The findings highlight the essential role of coastal vegetation in enhancing coastal resilience against hurricanes.

1. Introduction

Extreme weather events like hurricanes could cause significant erosion to coastal sand dunes in a short period time by inducing high water levels accompanied with high waves and strong currents [1,2,3]. Previous study of Shaw Alex et al. [4] has demonstrated that dune failure significantly increased flooding during storms, highlighting the crucial role of dune protection in coastal defense. D’Alessandro and Tomasicchio [5] conducted large-scale physical model tests to investigate the effects of wave period and water depth on the resilience of the exposed dune under irregular wave attacks. Aquatic vegetation contributes to protect dune systems and coastal protection by damping the incoming water [6,7,8,9,10,11]. The findings of Unguendoli et al. [12] indicated that seagrass was able to reduce beach erosion volumes up to 55% as well as produced an average attenuation of 32% of the storm peak. Jacob et al.’s study [13] also agreed that seagrass expansion could be a useful addition to engineered coastal protection measures. Consequently, with the impact of aquatic vegetation on wave attenuation receiving increasing attention in recent years, the strategy of using vegetation to protect coastal dunes and reduce erosion has been applied to many studies [14,15,16].

To investigate the mechanisms of wave energy reduction due to aquatic vegetation, various studies have been developed. Numerous laboratory experiments examine wave attenuation by vegetation [17,18,19]. For example, a large-scale experimental study was employed to study wave damping over artificial Posidonia oceanic meadow [20]. Besides, some studies combined laboratory experiments and numerical models to explore the interactions between wave and vegetation providing significant insights into the effects of vegetation on wave energy dissipation. Chalmoukis [21] used a porous medium model to simulate a three-dimensional, two-phase flow past coastal vegetation fields. The model, validated against experimental data, assessed the impact of equivalent porosity and cross-shore length on wave behavior over a sloped beach. Holzenthal et al. [22] studied the influence of flexible, buoyant submerged aquatic vegetation on localized velocity fields, circulation pathways, and overall tidal behavior by coupling a dynamic friction model with a depth-integrated circulation-wave model.

Additionally, some studies have used Manning’s roughness coefficients to represent vegetation in wave attenuation investigations [23,24,25]. For instance, Lapetina et al. [26] indicated that 2D storm surge models typically use an enhanced Manning’s coefficient to represent the effects of coastal vegetation on flow. Medeiros [27] suggested values of 0.138 for Manning’s n and 2.34 m for initial water level based on field investigations in mangrove-covered regions of southwest Florida. However, Baron-Hyppolite et al. [28] pointed out that simplistically treating vegetation as enhanced bottom roughness underestimated the complexity of wave-vegetation interactions, thereby underestimating wave energy dissipation (error > 30%) while those cases with explicit representation of vegetation showed good consistency with field data (error < 20%). Besides, Abdoali et al. [29] indicated that the Manning’s n cannot accurately represent all key physical phenomena of vegetation in water, prompting the use of numerical models that consider vegetation characteristics to estimate dissipation more accurately, such as the SWAN model [30] and XBeach model [31]. The vegetation dissipation formulas applied in these models are functions combined with local hydrodynamic conditions and can directly reflect measurable vegetation characteristics. For example, Musumeci et al. [32] used a coupled SWAN model and XBeach model to simulate the impact of vegetation on coastal erosion and flooding risks.

The complexity of natural systems, combined with the extreme magnitudes of storm conditions—such as surges, wave heights, and wind speeds—presents substantial challenges. Meanwhile, this complexity results in a lack of comprehensive data needed for accurate validation [33]. Moreover, existing physical model experiments struggle to replicate the extreme hydrodynamic conditions of severe storms and the realistic growth patterns of vegetation [16]. These limitations hinder the accurate assessment of vegetation’s role in coastal defense [34]. Garzon et al. [35] investigated the ability of Spartina alterniflora saltmarshes to attenuate wave energy during storm surge conditions in the Chesapeake Bay. However, the research gaps remain in understanding the mechanisms by which vegetation affects wave attenuation and dune protection under extreme hydrodynamic conditions. To address the research gaps, our study aims to employ a one-dimensional XBeach model based on dune profile data collected pre- and post-hurricane to study the interactions between wave, dune, and vegetation. This method will enable us to investigate the protective functions of vegetation on dunes and its efficacy in wave attenuation during storm surge conditions. A detailed introduction to the XBeach model will also be provided in Section 2. The vegetation drag coefficient ($C_D$) is a critical parameter in the XBeach model for calculating vegetation-induced wave dissipation. In Section 2, this paper will thoroughly review the literature on determining $C_D$, aiming to identify the most suitable values for our study using the XBeach model.

The remainder of this paper is organized as follows: XBeach surfbeat model descriptions and a review of vegetation drag coefficient are presented in Section 2; Section 3 introduces the model validation of two laboratory experiments; Section 4 presents the XBeach surfbeat model application in real study case; and Section 5 and Section 6 present the discussion and conclusions, respectively. In this study, to aid readers in understanding the abbreviations used in the main text, a table listing each abbreviation used in this manuscript along with its full form is provided in Appendix A.

2. Model Descriptions and C_D Values Review

2.1. XBeach Surfbeat Model Descriptions

The XBeach surfbeat model (XBSB) is a two-dimensional, advanced numerical model that was developed for simulating nearshore hydrodynamics and morphodynamics under varying wave conditions [31]. The model employs shallow water equations, which assume a linear variation of pressure with depth and focus on depth-averaged hydrodynamics. This approach allows the XBSB model to efficiently simulate long-wave processes, including storm surges, tides, and tsunami inundation. While the model’s assumptions facilitate computational efficiency, they may limit its ability to capture detailed processes in regions with rapid changes in water depth. Nevertheless, the XBSB model is widely recognized for its ability to predict dune erosion, overwash, and coastal barrier breaches, offering valuable insights for coastal management and protection strategies [36,37,38]. For example, Sánchez-Artús et al. [39] used XBeach model to evaluate the performance of dunes as coastal protection measures for the barrier beach under three different storm events.

For modeling the interaction between vegetation and wave dissipation, XBeach utilizes the method proposed by Mendez and Losada [40], which was later adjusted by Suzuki et al. [41]to account for the effects of vertical heterogeneity introduced by vegetation. The dissipation of short waves caused by vegetation can be solved as a function of local wave height and several vegetation parameters. Vegetation can be represented by vertical elements of different properties, allowing for the simulation of damping effects of vegetation with characteristics like mangroves, which have densely packed roots but sparse stem areas. The total dissipation term can then be calculated as the sum of dissipation amounts for each vegetation layer as shown in Equation (1).

$$D_v={\sum }_{i=1}^{n_v}{D}_{v,i}$$

(1)

where $D_{v,i}$ is the dissipation amount in the vegetation layer i; $n_v$ is the number of vegetation layers.

The dissipation amount for each layer is calculated by the following equations:

$$D_{v,i}=A_v\times {\displaystyle \frac{\rho C_{D,i}{b}_{v,i}{N}_{v,i}}{2\sqrt{\pi }}}{\left({\displaystyle \frac{kg}{2\sigma }}\right)}^3{H_{rms}}^3$$

(2)

$$A_v={\displaystyle \frac{{(sinh}^{3}k{\alpha }_{i}h-{sinh}^{3}k{\alpha }_{i-1}h)+3(sinhk{\alpha }_{i}h-sinhk{\alpha }_{i-1}h)}{{3kcosh}^{3}kh}}$$

(3)

$${\alpha }_i=h_v/h$$

(4)

For the specific vegetation layer i, $C_{D,i}$ is the drag coefficient, $b_{v,i}$ is the diameter of the vegetation stems, $N_{v,i}$ is the vegetation density, $H_{rms}$ is the root-mean-square wave height, and ${\alpha }_i$ is the relative vegetation height in vegetation layer i.

In this paper, we only studied a single vegetation layer, assuming that the vegetation is vertically uniform. Therefore, when i = 1, the formula for the wave energy dissipation under the above vegetation field is as Equation (5).

$$D_v={\displaystyle \frac{{sinh}^{3}k{h}_v+3sinhk{h}_v}{{3kcosh}^{3}kh}}\times {\displaystyle \frac{\rho C_D{b}_v{N}_v}{2\sqrt{\pi }}}{\left({\displaystyle \frac{kg}{2\sigma }}\right)}^3{H_{rms}}^3$$

(5)

2.2. A Review of C_D Determination

The interaction between waves and coastal vegetation is a dynamic and multifaceted process that significantly influences coastal defense by modifying wave characteristics. Central to understanding this interaction is the vegetation drag coefficient ($C_D$), an empirical parameter critical for calculating the wave energy dissipation and the drag resistance presented by the vegetation [42,43,44].

Estimating $C_D$ has long been a focus in coastal engineering, with methodologies grounded in field observations, laboratory experiments, and numerical modeling. A notable study in the Yangtze Estuary in 2019 revealed that Phragmites australis outperformed Scirpus mariqueter in wave attenuation due to its greater biomass and structural strength, suggesting a mixed-species strategy could bolster coastal protection [45]. Zhang et al. [46] developed a new $C_D$ calculation formula through field observations. Ding et al. [47] established a new formulation for the $C_D$ based on biomechanical properties and field data from Terrebonne Bay, LA. Preliminary validation with laboratory experiments on synthetic vegetation confirmed the model’s improved accuracy in predicting hydrodynamic changes in marshes, highlighting its utility in assessing vegetation’s protective effects against waves and surges. Physical experiments were conducted [48] on idealized flexible vegetation in salt marshes to investigate the relationship between $C_D$ and other parameters such as the degree of submergence, stem density, and wave height. As for most existing numerical models for wave attenuation, such as SWAN [30], XBeach [31], and SWASH [49], they are typically combined with physical experiments to explore the estimation of $C_D$ value. In this paper, we will choose the XBeach model, which can explicitly represent vegetation characteristics, as the numerical model tool.

The $C_D$ is usually an empirical parameter used to calculate wave energy dissipation. The drag force exerted by the rigid vegetation on the currents differs significantly from that exerted by flexible vegetation due to differences in their deformation characteristics. For rigid vegetation, since its shape and position do not change with the current, the drag coefficient $C_D$ used to calculate the drag force is constant. Studies by Kothyari et al. [50] and Liu et al. [51] both examined the drag coefficient for rigid vegetation in open channel flow, with Liu’s research even investigating the calculation of $C_D$ under subcritical conditions in open channels. Other scholars, such as Hu et al. [52], Van Rooijen et al. [53], and Etminan et al. [54] have also developed formulations for $C_D$ of rigid vegetation. Additionally, some scholars have begun using artificial neural networks to estimate $C_D$ of rigid vegetation [55,56].

In contrast, for flexible vegetation, the deformation under the action of water flow will affect the resistance characteristics. The formation of the shear layer at the top of submerged flexible vegetation is a crucial characteristic of the flow [57,58]. Current physical experiments on the $C_D$ for flexible vegetation [59,60] have shown that the magnitude of $C_D$ is related to the Reynolds number (Re) [61] and the Keulegan–Carpenter number (KC) [40]. Typically, the Re parameter helps characterize the flow regime around the vegetation, distinguishing between laminar and turbulent flows and their respective impacts on wave interactions. The KC number is used to describe oscillatory flow conditions, reflecting the balance between inertia and drag forces acting on vegetation. These parameters are instrumental in predicting the $C_D$, providing a deeper understanding of the vegetative wave damping performance across different species and environmental conditions. Physical experiments found that $C_D$ decreases with the increase of the Re and the KC number [59,60]. Houser et al. [57] found that the relationship between the drag coefficient and the Re depends on the flexibility and morphology of the vegetation. The greater the flexibility, the more the drag coefficient is reduced. Their research also discovered that flexible vegetation has a smaller drag coefficient compared to rigid vegetation. In the studies conducted by José Francisco Sánchez-González et al. [62], a fitting relationship between $C_D$ and KC was obtained through best fit analysis of physical experiment data. Subsequently, Yin, Xu et al. [63,64] used this fitting relationship between $C_D$ and KC to establish semi-empirical formulas for the $C_D$ of flexible vegetation that can be applied to the XBeach model. Chen et al. [65] evaluated the effectiveness of two methods for determining $C_D$, which are crucial for assessing wave damping in vegetated coastal areas, and introduced a new $C_D$-KC relation for combined wave-current flows. The findings highlighted the superior performance of the direct measurement approach over the conventional calibration method in predicting wave dissipation, proposing a unified $C_D$-KC relation that could enhance the modeling of wave-vegetation interactions. Additionally, Wang et al. [66] provided a semi-empirical formula to estimate the $C_D$ for flexible vegetation. In addition to classifying vegetation as flexible or rigid, some scholars also study the impact of submersion on $C_D$. Some formulations specifically address either submerged vegetation [67,68] or emerged vegetation [69,70], while others encompass both [71,72].

Table 1. A review of C_D relations in vegetation-wave interaction and their deriving methods associated with Re or KC.

Reference	Vegetation	Wave	Method	Re or KC Range	Formula
Hu et al. (2014) [52]	Rigid	R	Directed measurement	(300, 4700)	$C_D=1.04+{\left({\displaystyle \frac{730}{Re}}\right)}^{1.37}$
ROOIJEN et al. (2015) [73]	Rigid	I	Calibration	/	/
Mendez et al. (1999) [74]	Rigid	R	Calibration	(200, 15,500)	$C_D=0.08+{\left({\displaystyle \frac{2200}{Re}}\right)}^{2.2}$
Chen et al. (2018) [65]	Rigid	R	Calibration	(4, 120)	$C_D=1.17+{12.89KC}^{-1.25}$
Wu et al. (2016) [75]	Rigid	I	Calibration	/	/
Wang et al. (2020) [76]	Rigid	S	Directed measurement	(532, 8048)	$C_D=0.08+{\left({\displaystyle \frac{6436}{Re}}\right)}^{0.8957}$
Kelty et al. (2022) [77]	Rigid	I	Calibration	(4900, 190,000)	$C_D=0.6+\left({\displaystyle \frac{\mathrm{30,000}}{Re}}\right)$
Veelen et al. (2021) [78]	quasi-flexible	R	Calibration	(570,1500)	$C_D=1.04+{\left({\displaystyle \frac{730}{Re}}\right)}^{1.37}$
Kobayashi et al. (1993) [61]	flexible	/	Calibration	(2200, 18,000)	$C_D=0.08+{\left({\displaystyle \frac{2200}{Re}}\right)}^{2.4}$
Maza et al. (2013) [79]	flexible	R	Calibration	(2000, 7000)	$C_D=1.61+{\left({\displaystyle \frac{4600}{Re}}\right)}^{1.9}$
Anderson and Smith (2014) [34]	flexible	I	Calibration	(533, 2296)	$C_D=0.76+{\left({\displaystyle \frac{744.2}{Re}}\right)}^{1.27}$
Losada et al. (2016) [80]	flexible	R	Calibration	(4000, 160,000)	$C_D=0.08+{\left({\displaystyle \frac{\mathrm{50,000}}{Re*}}\right)}^{2.2}$
		I	Calibration	(20,000, 60,000)	$C_D=0.08+{\left({\displaystyle \frac{\mathrm{22,000}}{Re*}}\right)}^{2.2}$
Yin et al. (2022) [63]	flexible	R	Calibration	(0, 500)	$C_D={\left({\displaystyle \frac{150.5}{KC}}\right)}^{0.5952}$
Yin et al. (2023) [81]	flexible	R	Calibration	(28, 108)	$C_D=0.929+{\left({\displaystyle \frac{41.434}{KC}}\right)}^{5.663}$
Liu et al. (2023) [68]	flexible	R	Calibration	(75, 230)	$C_D={\left({\displaystyle \frac{25.4}{KC}}\right)}^{0.6}$
Garzon et al. (2019) [35]	flexible	/	Calibration	(100, 6000)	$C_D=0.411+{\left({\displaystyle \frac{514}{Re*}}\right)}^{0.5}$
Reis et al. (2024) [82]	flexible	R	Directed measurement	(22, 60)	$C_D=1.09+{\left({\displaystyle \frac{22}{KC}}\right)}^{5.56}$

Notes: R is regular wave; I is irregular wave; S is solitary wave. The $C_D$ formulation by Garzon et al. (2019) [35] was applied in this study. Re is Reynolds number and KC is the Keulegan–Carpenter number. In the 5th column, Ranges of KC number are marked with underline while ranges of Re are shown without underline. Re * means modified Re.

reviews $C_D$ relations in vegetation-wave interaction and their deriving methods. The research on empirical formulas for $C_D$ mentioned above mostly remains at the physical experimental stage and has not been applied to real engineering problems. Through this review, we determined that the findings of Garzon et al. [35] are the most suitable for application in our model because they used field observations under storm conditions to obtain the relationship of $C_D$ with the modified Re and KC.

3. Model Validation by Comparing to Laboratory Experiments

In this paper, we investigate the possibility of applying the $C_D$ values of empirical formulation to real-world scenarios by replicating and validating two classic physical flume experiments. The primary objective is to demonstrate the model’s capability to predict interactions between vegetation, waves, and dunes under extreme storm conditions. The first experiment focused on the model’s ability to accurately capture the evolution of dunes. The second experiment was chosen to validate XBSB’s ability to accurately predict the effect of vegetation on wave attenuation under regular wave conditions.

3.1. Case 1: Laboratory Experiment for Wave-Induced Sand Dune Erosion

In this case study, we conducted a comprehensive evaluation of XBeach surfbeat model, focusing on the erosion of sand dunes under storm surge conditions. Our approach replicated and validated the experimental setup detailed in Berard’s study [83], matching physical model parameters, including sediment characteristics and wave conditions.

We set the wave parameters to reflect the conditions in the reference study, with a significant wave height (Hs) of 0.16 m and a mean absolute wave period (Tm01) of 2.3 s. The model incorporated two still water levels, 0.40 m for the Low-water test (LW) and 0.47 m for the High-water test (HW), simulating different tidal conditions. This dual setup allowed us to simulate two scenarios: LWSB (Low-water) and HWSB (High-water), providing insights into dune erosion under varying hydrodynamic stresses. LWSB and HWSB simulated results in the collision regime and inundation regime, respectively. We refined some parameters in our simulations. The parameters are listed in

Table 2. Extended input parameters for dune morphology simulation.

Parameter	Meaning	Value	Berard’s Study Value
wetslp	Critical wet slope for underwater avalanching	0.15	0.3
responseangle	Angle of repose affecting dune steepness	25 degree	30 degree
hswitch	Switch depth from wet to dry avalanche	0.005 m	0.005 m
form	Sediment transport formulation	vanthiel_vanrijn	vanthiel_vanrijn or soulsby_vanrijn
eps	Threshold water depth for cell inundation	0.09	0.09 or 0.02

including the comparisons with the referred paper. The one-dimensional model’s mesh, covering a 25 m cross-section, was configured for computational efficiency. From 3.8 m to 4.3 m, a 0.1 m grid was used; from 4.3 m to 20.4 m, a 0.5 m grid; and from 20.4 m to 25 m, a finer 0.025 m grid (Shown in Figure 1). All simulations share these parameter values, signifying a standardized approach.

In the hydrodynamic validation, the dune face was designated as a non-erodible layer. Figure 2 illustrates the cross-shore profiles of still water level (SWL) and observed significant wave height under low water (LW) and high water (HW) conditions, capturing the collision and overwash regimes, respectively. In Figure 2, LWSB and HWSB are simulated results by red dash lines. The sum of square residuals (SSR) is used to quantify the model performance, as shown in Figure 2c,d. The significant wave height (Hs) predictions from the XBSB model closely match the observed data, indicating the model’s superior capability to simulate the complexities of wave interaction with a static dune structure.

$$SSR=\sum {{(H}_{s,lab}-H_{s,mod})}^2$$

(6)

Building on the hydrodynamic validation, we assessed the morphological responses of the dune profile under various water levels. The morphological evolution of the dune profile was analyzed using simulations for low (LW) and high water (HW) tests, replicating dune responses over 510 min for LW and 270 min for HW. The model performance was evaluated using the Brier Skill Score (BSS) [84], which was applied as a quantitative measure of the model’s accuracy in simulating the morphological evolution of the dune profile. A BSS of 1 indicates high accuracy, while a BSS ≤ 0 indicates poor predictive capability. Scores below 0.3 are considered bad, 0.3–0.6 are fair, 0.6–0.8 are good, and above 0.8 are excellent. The BSS is calculated using Equation (7).

$$BSS=1-{\displaystyle \frac{\sum {\left(\left|{zb}_{post}-{zb}_{mod}\right|\right)}^2}{\sum {\left(\left|{zb}_{post}-{zb}_{pre}\right|\right)}^2}}$$

(7)

where ${zb}_{post}$ indicates the observed bed elevation post-hurricane, ${zb}_{mod}$ is the bed elevation results obtained from XBeach models, and ${zb}_{pre}$ represents the initial bed elevation pre-hurricane.

The comparative analysis of dune profile evolution during LW test scenarios (Figure 3a,b) reveals the capabilities of the XBSB model low-water level (LW test). Initially, at 4 min, the XBSB model shows significant precision with BSS values of 0.888. This accuracy persists until 270 min with a BSS of 0.863, indicating the model’s effectiveness in simulating early-stage erosive dynamics. However, by 510 min, the BSS diminishes to 0.767, suggesting decreased accuracy over time due to potential overpredictions of erosive processes. Analyzing the dune profile evolution during high-water level (HW) tests for the XBSB model, as shown in Figure 3c,d, highlights its performance in the overtopping regime. The model demonstrates high accuracy in the initial stages, with BSS values of 0.924 at 8 min. This indicates a strong ability to simulate dune erosion. However, accuracy declines at the 270-min mark, with a BSS of 0.875, suggesting the model initially overestimates erosion rates and underestimates dune face retreat over time. This analysis shows the XBSB model’s strong initial accuracy in simulating erosive processes under various water levels, with high BSS values.

3.2. Case 2: Laboratory Experiment for Regular Wave Attenuation over Vegetation

This section utilized the one-dimensional XBSB model to simulate and reproduce physical model experiments of the attenuation of regular waves under the influence of vegetation conducted by Yin et al. [63]. The numerical model setup was consistent with the physical setup of the laboratory experiment, and the configuration and calibration of model coefficients replicated the water level conditions along the physical flume. The XBeach model adjusted the length of the physical flume, selecting only the key flume before and after the vegetated area as the experimental cross-sections.

The entire experimental section was six meters long with a flat and fixed bottom. The first two meters of the area had no vegetation and was mainly used for stabilizing and calibrating wave conditions. This was followed by a 3.16 m vegetated area. The final 0.84 m also had no vegetation. The vegetation had a stem height of 0.25 m, a diameter of 0.0043 m, and a density of 1012 units/m². These vegetation parameters were consistent with the laboratory experiment. The drag coefficient $C_D$ was adjusted based on the results of the simulated wave heights. In the first scenario, the initial significant wave height was 0.08 m with a wave period of 1.4 s and the initial water level was 0.35 m. In the second scenario, the initial significant wave height remained the same at 0.08 m with a wave period also at 1.4 s, but the initial water level was increased to 0.4 m. The third scenario introduced changes in significant wave height, wave period, and initial water level. The grid spacing varied from 0.1 m to 0.03 m, with a total of 153 grid points. In the model, the vegetation zone spanned from 2 m to 5.16 m, consisting of 112 grid points, with vegetation present on 56 of those points. The total runtime of the model was 3000 s, and data were output every 0.35 s or 0.4 s. The sketch of the XBeach model and vegetation field is shown in Figure 4.

The modeled significant wave heights were in good agreement with the observed data in Figure 5, demonstrating that the XBSB model replicated the conditions of the physical flume well. Observations from Figure 5 clearly show that vegetation has a notable attenuation effect on waves across all three scenarios. In the first scenario, the wave height decreased by 0.013 m, in the second scenario it decreased by 0.011 m, and in the third scenario, the reduction was more significant, amounting to 0.022 m. Comparing scenarios 1 and 2, it is evident that an increase in water level leads to a decrease in the alongshore fluctuation of measured wave heights, with the percentage of wave height attenuation dropping from 16.8% to 14.1%. The third scenario shows the most significant wave height attenuation, reaching 18.5%. Meanwhile, given the low RMSE values (

Table 3. Boundary conditions and RMSEs for different scenarios.

Case No.	Hs (m)	SWL (m)	T (s)	${\mathit{C}}_{\mathit{D}}$	RMSE (m)
1	0.08	0.35	1.4	0.8	0.0025
2	0.08	0.4	1.4	0.8	0.0013
3	0.12	0.5	1.6	1.47	0.0055

) and the close match between the observed and modeled data points, especially within the region where vegetation is present (the green window), the conclusion is that the $C_D$ calibrated by the XBSB model can accurately reflect the wave attenuation characteristics of the vegetation in the flume, making it suitable for simulating the propagation process of waves in vegetated areas.

4. XBeach Modeling of Vegetation Effects on Wave Attenuation and Dune Erosion in Mexico Beach, FL

Building upon the foundation laid out in Section 2 and Section 3, we evaluated the capability of the XBSB model to simulate and forecast the interactions between waves, sand dunes, and vegetation. The good model performance in these sections provides a basis for the following application. In this section, we have applied the XBSB model to a one-dimensional dune setup located at Mexico Beach, Florida, USA (Figure 6), aiming to examine the wave attenuation and dune erosion under extreme storm conditions with different vegetation cover.

4.1. Model Setup

The bed elevation of dune profile data was sourced from NOAA LiDAR Database website [85], which offers pre- and post-hurricane LiDAR data. This dataset enables detailed analysis of geomorphic changes in response to Hurricane Michael. In our previous study, we have already validated a two-dimensional XBSB model on Mexico Beach, demonstrating strong performance [86]. Therefore, we used the best-performing parameters from that study in the present model and applied the same boundary conditions, including significant wave height and storm surge data (Figure 7). Unlike the previous large-scale study, which represented vegetation as bottom friction using Manning’s coefficient, this one-dimensional model features detailed vegetation parameters and higher grid resolution in vegetated areas. This approach provides a more accurate simulation of wave-vegetation interactions and wave behavior near dunes. Detailed model settings are provided below.

As depicted in Figure 8, the one-dimensional XBeach model has a span of approximately 310 m. The grid size varied across the model domain. From x = 0 to x = 156 m, the spatial resolution was set at 5 m. In the dune area, which extended from x = 156 m to x = 260 m, a finer spatial resolution of 0.5 m was employed to capture the intricate interactions. Beyond x = 260 m, the resolution was reverted to 5 m. Based on the field investigation and Google map, a 10-m vegetation section was set up on the dune crest, referred to as Veg area in Figure 7. The vegetation density (N) was estimated at 200 units/m² as well as a vegetation height (ah) of 0.7 m, with a stem diameter (bv) of 0.005 m based on natural conditions inferred from field surveys shown in Figure 9.

Table 4. The vegetation parameters for the different model cases.

Case No.	Parameter
	${\mathit{C}}_{\mathit{D}}$	N (Units/m2)	bv (m)	ah (m)
1	/	/	/	/
2	0.8	200	0.005	0.7
3	1.47	200	0.005	0.7

Note: Case 1 represents no-vegetation condition Model setup.

shows the vegetation parameters for the three model cases. The first case was without vegetation and was used as a comparison for the vegetation cases. In the second case, a drag coefficient of 1.47 was used, while in the last case, a $C_D$ of 0.8 was applied. Furthermore, a house structure was integrated into the model behind the dune. The structure stood 10 m in height and extended 20 m along the x-axis. The area under the house was designated as a non-erodible layer, suggesting no morphodynamical evolution here. Through these settings, the model aims to offer critical insights into the role of vegetation in enhancing dune stability during severe weather conditions.

4.2. Model Simulations under Wave Condition of Hurricane Michael

We used the empirical formulations of $C_D$ conducted by Garzon et al. [35] and Yin et al. [63] to calibrate the XBSB model. The full $C_D$ formulas are listed in Table 1. The resulting values were 1.47 and 0.8. Besides, based on Section 4.1, we compared the modeled dune elevations with the observed post-hurricane LiDAR data in Figure 10. Figure 10 illustrates the evolution of dune profiles under varying drag coefficients during Hurricane Michael. The figure presented five distinct profiles: the observed initial pre-hurricane profile, the observed post-hurricane profile, a modeled profile without vegetation, and two modeled profiles with vegetation of different $C_D$ values. The observed post-hurricane profile showed marked changes, indicating significant morphological activity caused by the hurricane. To validate the performance of the model, we calculated the Brier Skill Scores (BSS) for three cases. Among them, the case with vegetation and a drag coefficient of 1.47 yielded a BSS of 0.742, which is greater than 0.6. According to the BSS classification in Section 3.1, this indicates that the model performance is good. In contrast, the case with a $C_D$ of 0.8 resulted in a BSS of 0.518, indicating fair model performance. This also indicates that, in this specific field application, Garzon’s formula for the drag coefficient was more suitable than Yin’s formula. Therefore, we used the model with a $C_D$ of 1.47 for the sensitivity analysis in Section 4.3. Additionally, the modeled profile without vegetation demonstrates the most pronounced departure from the observed initial conditions. This profile exhibited the highest average deviation with an RMSE of 0.392 m and experienced the most substantial erosion at a depth of 1.105 m. This highlights the erosion vulnerability of dune beds in the absence of vegetation and underscores the stabilizing role that vegetation plays in dune ecosystems.

We compared the significant wave heights (Hs) along the profile at the peak storm surge level in Figure 11. Between 120 m and 160 m, Hs fluctuates around 1.7 m for all three conditions. However, beyond 160 m, particularly within the vegetated area from 218 m to 228 m, Hs significantly decreases. The no vegetation scenario consistently showed higher Hs, with a wave height reduction of 0.11 m, indicating less wave attenuation. In contrast, the $C_D$ = 0.8 scenario showed a moderate decrease in Hs, with a reduction of 0.15 m, while the $C_D$ = 1.47 scenario exhibited the most substantial wave height reduction of 0.46 m. This demonstrates that higher drag coefficients result in more wave attenuation.

4.3. Sensitivity Analysis of Vegetation Effects under Regular Wave Condition

In this section, we conducted a sensitivity analysis on the impact of vegetation density on dune erosion and wave attenuation under regular wave conditions. Based on the predicted results from the XBSB models in Section 4.2, we examined various vegetation cover scenarios. The various vegetation densities of study cases are listed in

Table 5. Different vegetation cover scenarios with various densities.

Case No.	Density N (Units/m2)
case 4	No vegetation
case 5	200
case 6	500
case 7	800
case 8	1200

. The input tide boundary condition was the peak storm surge of 4.76 m. The input wave condition was a significant wave height of 1.98 m during Hurricane Michael, as shown in Figure 7. The model ran for 3 h, simulating the evolution of the dune, the changes in flow velocities, and the changes in significant wave heights under different vegetation densities. The baseline parameters for the XBSB model remain consistent with those in Section 4.2, featuring a vegetation height of 0.7 m and a stem diameter of 0.005 m. This comprehensive suite of cases allows for an in-depth analysis of the interaction between vegetation and wave dynamics, highlighting the potential of vegetation in mitigating coastal erosion and enhancing dune protection under storm surge conditions.

Figure 12 illustrates the simulation results of the XBSB model for cases 4 to 8 with various vegetation densities. Figure 12a shows that as vegetation density increased, the attenuation of significant wave height within the vegetated zones became more pronounced. The x-coordinate at which this attenuation stabilized moves closer to the initial range of the vegetated area as density increases. The moving of the stabilization point reflects the increased efficiency of denser vegetation in absorbing and dissipating wave energy. Specific attenuation values are provided in

Table 6. Impact of density of vegetation on significant wave height reduction.

Distance	Significant Wave Height (m)
	No veg	N = 200 (Units/m2)	N = 500 (Units/m2)	N = 800 (Units/m2)	N = 1200 (Units/m2)
x = 218 (m)	1.74	1.72	1.72	1.72	1.72
x = 228 (m)	1.66	0.90	0.40	0.28	0.30
Reduction (m)	0.08	0.82	1.32	1.44	1.42
Rate (%)	0	47.73	76.92	83.88	82.67
$∆$ Rate (%)	0	47.73	29.19	6.96	−1.21

. Generally, higher vegetation densities resulted in a greater value of wave attenuation, with the maximum wave height reduction observed at N = 800 units/m². However, beyond a density of 800 units/m², the impact of density on wave reduction tended to decrease. This stabilization may be due to the drag effect of vegetation reaching a “saturation point”, where further increases in vegetation density had minimal additional impact on wave reduction. This indicated an optimal vegetation density threshold, beyond which extra vegetation could not significantly enhance wave energy dissipation. Figure 12b shows the variation in mean flow velocity along the cross-section during the model run. When the flow reached the vegetated area, all cases with different vegetation densities experienced an immediate drop in velocity, followed by slight fluctuations within the vegetated zone. Subsequently, the flow velocity increased again due to the decline in bed elevation behind the vegetation area. Figure 12c revealed the bed elevation along the cross-section under different vegetation densities. Without vegetation cover, the dune was almost entirely removed. With vegetation present, significant protection of the dune was observed. At a vegetation density of N = 200 units/m², the dune crest moved noticeably landward. As the density continued to increase, the dune crest position shifted forward again. This shift was related to the x-coordinate position where the flow velocity begins to drop, as shown in Figure 12b. Additionally, unlike the significant differences in wave height attenuation across various vegetation densities, the reduction in dune crest elevation does not show significant differences under different vegetation densities.

5. Discussion

In this paper, we applied the XBeach model to evaluate the effects of vegetation on wave attenuation and dune erosion. Because lab experimental data for vegetation on dune is not available, we used the experiment data from the work of Berard et al. [83] and Yin’s laboratory experiments [63] to validate the performance of the XBSB model in predicting and simulating the effects of vegetation on dune erosion and wave attenuation. The field application of XBeach to Mexico Beach under Hurricane Michael as described in Section 4.1 fills the current research gap on wave actions on sand dunes with vegetation. The data set of storm surges, waves, vegetation, beach, and dune profiles before and after Hurricane Michael from LiDAR surveys provided a good model validation for vegetation on dunes under hurricane wave conditions, as shown in Figure 8, Figure 9 and Figure 10. LiDAR data of dune profiles before and after Hurricane Michael were used for model validation (Figure 10).

As can be seen in Figure 10 and Figure 11, compared with the observed post-hurricane dune elevation, vegetation on dunes reduced dune erosion and enhanced coastal resilience. This conclusion aligns with the findings of some recent studies [87,88] that demonstrated that vegetation significantly reduces wave heights, thus lowering flooding and erosion risks and providing multiple ecosystem benefits. However, because the XBSB is based on some modeling simplifications, the actual applications of vegetating the sand dune warrants further exploration. One notable simplification in the XBSB model is the representation of vegetation as uniformly distributed, slender, cylindrical structures. In reality, the vegetation does not grow uniformly across the dune surface and has leaves that contribute to the complexity of their density distribution. For example, Suzuki et al. [89] pointed out that drag force induced by horizontal vegetation stems/roots and porosity are often neglected in numerical models. A more accurate method might be to set up horizontal vegetation fields with various densities in future studies.

Another important point to consider is that in real extreme hydrodynamic scenarios, storm surges and huge waves can uproot or flatten thin plants or cause vegetation to be dislodged from the dunes due to erosion. This reduction in vegetation cover can diminish the ability to attenuate wave energy and stabilize the sand substrate, thus exacerbating erosion. However, these factors are not accounted for in the XBSB simulations. A report on Indonesia [90] recommended the planting of shade vegetation and fruit trees in the costal front zone to reduce the impact of coastal erosion. These strategies suggested that trees can provide a green barrier due to their deeper root systems and more significant biomass, which may enhance dune stability and wave energy dissipation. Future research should investigate the effects of different types of vegetation, including shrubs and trees, under extreme hydrodynamic forces.

Based on the findings in Section 4.3, vegetation density plays a crucial role in wave attenuation and erosion resistance. However, the relationship is not linear. There is a critical density, beyond which additional vegetation does not significantly reduce wave energy or dune erosion, indicating that there is an optimal density for maximizing protective benefits. In practical engineering, when considering the planting of vegetation on dunes, it is essential to determine and implement this optimal density. This finding resonates with the findings of Chen et al. [88], which emphasizes that optimizing the location and size of vegetation is crucial to increasing efficiency. This study only presents one single case in Mexico Beach during Hurricane Michael. Therefore, the optimal density simulated could vary under different environmental conditions, vegetation types, and storm scenarios. Therefore, further study is necessary to establish a range of optimal densities across various contexts. For example, studies should examine regional variations in optimal vegetation density. Factors such as local climate, dune morphology, and typical vegetation type can influence the effectiveness of vegetation in mitigating erosion and attenuating waves.

6. Conclusions

This study applied the XBeach surfbeat model to evaluate the effects of vegetation on wave attenuation and dune erosion. Validation against laboratory experiments demonstrated the model’s reliability. The case study of vegetation on dunes during Hurricane Michael shows the importance of vegetation for dune morphology during hurricanes. Vegetation stabilizes dunes and reduces erosion, with vegetated dunes showing significantly less erosion. In general, an increase in vegetation density enhances wave attenuation and reduces erosion rates. A saturation point has been identified where additional density does not significantly increase wave attenuation. The implications of this study for coastal resilience planning are significant. XBeach surfbeat model that predicts and enhances the protective functions of coastal vegetation on sand dunes is valuable for coastal resilience planning. This study expanded the application range of laboratory vegetation drag force parameters to the field application to account for the interactions among waves, dunes, and vegetation under actual hurricane conditions.