Wetlands are key natural and nature-based features used to dissipate wave energy and reduce flood risk. Historically, the operational practice to account for wave energy reduction due to wetland vegetation was through bottom friction sink terms implemented in nearshore wave models. The formulations most often applied use Manning’s roughness coefficients n, which traditionally described bottom roughness in uniform flows for open channels and floodplains (Chow, 1959). These Manning’s coefficients n account for spatial variations tied to local terrain and roughness, and many numerical studies, particularly those coupling phase-averaged wave models to hydrodynamic models such as the ADvanced CIRCulation model (ADCIRC), select Manning’s n based on land-cover databases and standard hydraulic literature (Dietrich et al., 2011; Bender et al., 2013; Hope et al., 2013; Lawler et al., 2016; Bryant and Jensen, 2017). Controlled laboratory experiments continue to highlight the complexity of wave–vegetation interactions, most notably the effect of vegetation properties such as rigidity, height, density, and diameter on wave attenuation (Anderson and Smith, 2014; Ozeren et al., 2014; Luhar et al., 2017; Jacobsen et al., 2019; Phan et al., 2019; van Veelen et al., 2020). These studies suggest there are key physics that Manning’s n does not properly represent, such as the drag force exerted on the water column due to temporally and spatially varying immersed vegetation. These potential shortfalls of Manning’s n led to the derivation and subsequent implementation of vegetation-dissipation sink terms in widely used nearshore wave models, such as WWM-III (Roland, 2008), SWAN (Suzuki et al., 2012), STWAVE (Anderson and Smith, 2015), and XBEACH (Van Rooijen et al., 2015). These vegetation-dissipation sink terms are a function of the local hydrodynamic conditions and account directly for measurable vegetation characteristics. Both Smith et al. (2016) and Baron-Hyppolite et al. (2019) reported an underestimation of wave dissipation using enhanced Manning’s n to represent vegetation compared to vegetation-dissipation formulations that explicitly account for plant properties.

The fundamental formulation for wave dissipation through vegetation was derived by Dalrymple et al. (1984) for monochromatic waves using the conservation of energy flux equation, where the horizontal force F _x acting on the vegetation per unit volume is expressed in terms of a Morison-type equation neglecting swaying motion and inertial force: F x = 1 2 ρ C d b ν N u | u | (1) where ρ is water density, C _d is the depth-averaged bulk drag coefficient, b _v is stem diameter, N is plant density (stems/m ²), and u is horizontal velocity due to wave motion.

Although plant motion is neglected, Eq. 1 may still be applied to swaying plants because the bulk drag coefficient C _d accounts for our ignorance of plant motion, interactions between stems, and other unresolved processes. Indeed, Mendez et al. (1999) stated that using the relative velocity between the fluid and plant required a higher value of C _d to obtain the same amount of attenuation. Mendez and Losada (2004) expanded upon Dalrymple et al. (1984) and derived an analytical solution for random wave transformations over mildly sloped vegetation fields under breaking and nonbreaking conditions by assuming a Rayleigh distribution of wave heights. The modification by Mendez and Losada (2004) is incorporated into several phase-averaged nearshore wave models similar to Suzuki et al. (2012), with verification largely focused on laboratory studies, albeit field applications are now gaining traction (Garzon et al., 2019). As an alternative to field surveys to collect vegetation properties, Figueroa-Alfaro et al. (2022) proposed a modified parameterization using a leaf area index-based measurement that can be readily derived from satellite imagery, but its application is limited to emergent vegetation. While these developments are advancing wave–vegetation modeling, continued research into the drag coefficient C _d , which directly affects the dissipation rate, is critical given the growing concerns regarding its assumptions and derivations (Tempest et al., 2015).

This study is arranged as follows: a summary of the implementation of Mendez and Losada (2004) in WAVEWATCH III (WW3) is presented in Section 2; Section 3 provides a brief overview of the validation studies using laboratory data of homogeneous vegetation fields and field case application with observations in Virginia during Hurricanes Jose and Maria in 2017; and concluding remarks are provided in Section 4.

In spectral wave models such as WW3, the waves are defined in terms of wave action density spectrum N (σ, θ) as a function of angular wave frequency and wave direction: ∂ ∂ t N + ∇ x c g + U N + ∂ ∂ σ c σ N + ∂ ∂ θ c θ N = S σ (2) where N (k, θ) is the wave action density spectrum related to the wave energy density spectrum F (k, θ), where N (k, θ) = F (k, θ)/σ and c _g , U, c _σ , and c _θ are the group velocity, the current velocity depth-time averaged over the scales of individual waves, propagation velocity in frequency σ, and direction θ spaces, respectively.

The terms on the left-hand side of Equation 2 represent wave action density change in time, propagation in geographical space, shifting of the relative frequency due to changes in current and depth, and depth and current-induced refraction, respectively.

The energy density source term S is placed on the right-hand side of Eq. 2 and accounts for generation (i.e., by wind), dissipation (i.e., whitecapping, bottom friction, depth induced breaking), and nonlinear wave–wave interaction.

Without vegetation, wave energy flux remains constant if no energy is lost or gained. In the presence of vegetation, the wave energy flux, following Dalrymple et al. (1984), Kobayashi et al. (1993)m and Mendez and Losada (2004) becomes ∂ F ∂ x = − ϵ ν → ∂ ∂ x E . c g = − ϵ ν (3) where wave energy is defined as E = 1 8 ρ g H 2 (4) and ϵ _ν is a function of the drag force F _x (Equation 1) integrated over the height of the vegetation ϵ ν = ∫ − h − h + α h F x u d z ̄ (5)

Assuming linear wave theory is valid to calculate u, the horizontal velocity due to wave motion, the mean rate of energy dissipation per unit horizontal area ϵ _ν due to wave damping by vegetation becomes ϵ ν = 1 2 π ρ C d b ν N k g 2 σ 3 sinh 3 k α h + 3 ⁡ sinh k α h 3 k ⁡ cosh 3 k h H r m s 3 (6) where k is wave number, α is the ratio of plant height l _s to water depth h (L _s /h), and H _rms is root mean square wave height.

Combining Eqs (3)–(6), ∂ H r m s 2 ∂ x = − ϵ ν 1 8 ρ g c g = 2 3 π C d b ν N k sinh 3 k α h + 3 ⁡ sinh k α h sinh 2 k h + 2 k h sinh k h H r m s 3 (7)

A spectral version implemented in WW3 is divided by − ρg and written in a spectral/directional form: S v e g σ , θ = D t o t E t o t E σ , θ (8) D t o t = − 1 2 g π C d b ν N k ̄ g 2 σ ̄ 3 sinh 3 k ̄ α h + 3 ⁡ sinh k ̄ α h 3 k ̄ cosh 3 k ̄ h H r m s 3 (9) where the mean frequency σ ̄ , mean wave number k ̄ , and total wave energy E _tot are given by σ ̄ = 1 E t o t ∫ 0 2 π ∫ 0 ∞ 1 σ E σ , θ d σ d θ − 1 (10) k ̄ = 1 E t o t ∫ 0 2 π ∫ 0 ∞ 1 k E σ , θ d σ d θ − 2 (11) E t o t = ∫ 0 2 π ∫ 0 ∞ E σ , θ d σ d θ (12)

Finally, substituting H r m s 2 = 8 E t o t , the wave–vegetation sink term becomes (Suzuki et al., 2012) S d , v e g = − 2 π g 2 C d b ν N k ̄ σ ̄ 3 sinh 3 k ̄ α h + 3 ⁡ sinh k ̄ α h 3 k ̄ cosh 3 k ̄ h E t o t E σ , θ (13)

Although not currently in WW3, the spectral wave–vegetation sink term formulated by Suzuki et al. (2012) may consider different densities and stem widths between trunks and roots (i.e., mangrove trees) by considering layer schematization. Recent developments by Dalrymple et al. (1984) and Mendez and Losada (2004) include implementation into mild slope equation models (Tang et al., 2015) and the incorporation of wave–current interactions for both following and opposing currents (Losada et al., 2016).

After implementing the vegetation sink term in WW3, we verified for idealized laboratory experiments, consisting of 63 cases with homogeneous vegetation fields. Then, we progressed to the large-scale field test case for Hurricanes Jose and Maria (2017).

This study implemented wave–vegetation interaction in the WW3 model. The application is examined using a standard laboratory flume case for wave dissipation due to homogeneous vegetation fields. Different submergence ratios, densities were examined for single and double-peaks incident waves. The drag coefficients C _d were calculated using the empirical relationship based on Keulegan–Carpenter KC and Reynolds Re numbers, considering the correction due to the canopy submergence.

In addition to controlled laboratory experiments, we validated the model for a field application with spatially variable vegetation fields in a vegetated marshland during Hurricanes Jose and Maria, 2017. A well-known atmospheric model designed for hurricane modeling (HWRF) is used to drive the storm surge model (ADCIRC) to provide water level and current fields and the spectral wave model (WW3). These wind, current, and water level inputs were used to drive WW3 on a high-resolution triangular mesh with a ∼1 km resolution near the coast of the East Coast of the United States and a nominal resolution of ∼ 20 m in the Magothy Bay where wave height observations were available for validation. Such a resolution is required for resolving wave action in complex marsh environments (Deb et al., 2022a). WW3 simulations were conducted with the domain decomposition parallelization algorithm and the implicit numerical solver (Abdolali et al., 2020), making it possible to run the model on a high-resolution grid efficiently. The model skills and improvement due to the vegetation sink terms were examined and discussed using time series of high-frequency pressure gauges. We conclude that the wave attenuation due to vegetation is significant in marsh environments, and neglecting the vegetation sink term leads to a significant bias in the model outputs and observations. It is shown that WW3 skills are improved over areas with vegetation, with sufficient grid resolution and proper representation of spatially variable vegetation fields. Designing and evaluating wetlands as nature-based flood risk reduction features require accurate modeling of wave dissipation by vegetation. Updated WW3 with the vegetation sink term coupled with a storm surge provides the necessary capability to model wave attenuation in wetlands. Such implementation provides an opportunity to investigate the effect of seasonal variability of vegetation coverage on wave characteristics. Organic protection methodologies can be designed for beach and wetland erosion mitigation purposes. In addition, the changes in the stem characteristic (diameter, height, and density) and hydrodynamics can be investigated to identify the role of dry/wetland cover before, during, and after the occurrence of severe storm surges. Further improvement can be achieved by a two-way coupling between the storm surge and wave models, where depth-integrated wave radiation stresses in the presence of vegetation affect the storm surge model. In return, the updated water level and current fields derive the wave model dynamically. In this way, the model components interact with each other representing what occurs in nature (Moghimi et al., 2020).