The Nanliu Delta is dominated by irregular diurnal tides with an average and maximum tidal range of 2.46 and 5.36 m, respectively. The nearshore wave climate in this region varies seasonally with a maximum average wave height of 1.36 m (State Oceanic Administration, 1998), yet the maximum current speeds are 0.26–0.36 m/s (Huang et al., 2022). AC is dominantly distributed over Qixing Island, which is located at the delta center with scattered Cyperus malaccensis patches. The mean grain size of sediments over the AC tidal flat ranges from 0.2 mm in the seedling-sapling region to 0.04 mm in the sapling-adult region. A transverse transect through an AC tidal flat composed of 3 hydrological tripods was set up on the south side of Qixing Island ( Figure 1C ). Three tripods were positioned along a transect with a length of 1.275 km. The Tripod SC (109°2’12.69”E, 21°36’9.73”N), with a location height of 2.63 m above mean sea level in Beihai, was set at the upper part of the AC tidal flat, with mixed adults and saplings ( Figures 2C , F ). The Tripod SB (109°2’2.04”E, 21°35’39.03”N) with a relative location height of 1.17 m, was set at the transition region between the adult AC tree region and the seedling region. Additionally, tripod SA (109°1’58.48”E, 21°35’30.47”N), with a relative location height of 0.25 m, was set offshore in an area with mixed saplings and small seedlings. The distance from tripod SA to tripod SB was 0.275 km, and that from SB to SC was 1 km ( Figure 1D ).

Furthermore, wave recorders (RBR-2050 and RBR-solo3) were placed in line at these three tripods along the AC transect to obtain the wave and tide information from the 16th to the 29th of August 2019. These recorders are robust and have internal memory and battery housing so that they can collect the data autonomously. The sampling start time can be set at every deployment. Based on previous work conducted in mangrove tidal flats (Quartel et al., 2007; Horstman et al., 2014), the instruments logged data at 4 Hz over a consecutive 512 s (~8 min) period every 20 min (2,048 samples per burst), and they were fixed 10 cm above the ground, which can indicate the wave variation during an entire tidal period. The wave recorder used in this observation had an effective measuring range for wave heights of 0.005–10 m. The measured water depth was converted to the water level based on mean sea level.

AC along the selected transect from SA to SB covered seedlings of 1 year of age and sparse saplings of 2–3 years of age. Seedlings in this region were approximately 0.19 m high, with canopy sizes of 0.09 m in width and 0.09 m in length. Saplings in this region were 0.55 m high with a canopy size of 0.2 m in width and 0.3 m in length ( Table 1 ). Adults were distributed at a relative elevation of 2.63 m, which was above the mean high water level during spring tide (MHWS), with heights, widths, and lengths of 1.5, 1.7, and 1.7 m, respectively ( Figure 4 ).

Moreover, canopy locations of adult AC were slightly higher than the MHWS water level ( Figures 1D , 4A, B ), and canopies of saplings or seedlings still emerged when tides arrived at the mean high water level during neap tide (MHWN).

Furthermore, the mean water levels during the spring tide were 2.38, 1.46, and 0.73 m at the locations of tripods SA to SC ( Figure 4B ), respectively, indicating that the canopies of mangroves at SA and SB were submerged most of the time due to tidal level fluctuations. AC at the SC site could be inundated only to the branch position with the canopy part exposed to the air. The same situation also occurred at middle tide, with water levels of 1.99, 1.34, and 0.62 m ( Figure 4B ), respectively, from offshore to the inshore station. Moreover, during the neap tide, AC at the SA station was wholly submerged, as the depth was 1.17 m. The water level was 0.49 m at tripod SB, where branches of mangroves can be submerged. At tripod SA, a fully adult mangrove was almost exposed to the air since the water level was less than 0.07 m ( Figure 4D ).

The energy density varied distinctly with the AC of different ages at each station ( Figures 5A, B ). Specifically, the wave spectra remained unimodal during spring and neap tides ( Figures 5A, C ) and bimodal ( Figure 5B ) during midtide. The wave energy densities increased with rising water levels ( Figure 5 , blue lines in boxes A, C) and decreased with falling water levels during spring and neap tides ( Figure 5 , red lines in boxes A and C). The energy density in the seedling-sapling region during the spring tide accepted the most powerful energy. The values varied from 0.03 to 0.055 × 10⁻³ m²s and decreased to 0.009 × 10⁻³ m²s from bursts of 90–94 ( Figure 5A , 1–5) to 95–98 ( Figure 5A , 6–9), respectively. For SB ( Figure 5A , 10–14), the value first increased from 0.005 to 0.013 and finally decreased to nearly zero ( Figure 5A , 15–18). Although the wave energy at SC was weak at every burst, its trend was the same as that of the other two tripods that were proportional to the water level ( Figure 5A , 19–23). Similar to the spring tide, the energy density changed from 0.21 to 1.18 × 10⁻⁶ m²s during rising water and declined to 0.18 × 10⁻⁶ m²s in SA.

The energy spectrum shape at the middle tide appeared bimodal, with the related high-frequency crest tending to occur during the falling water period ( Figure 5B , 7–9) in the seedling-sapling region, and the higher-frequency crest occurred first. The energy of the former crest decreased, while that of the latter increased. The interaction between waves and seedlings-saplings was drastic during the middle tide with a relatively constant water level ( Figure 4C ), resulting in a transition of wave composition from unimodal to bimodal, with the latter crest occurring at 0.4–0.6 hz ( Figure 5B , 10–18).

The wave environment during the observation period was dominated by a southwest (SW) wind with speeds of 0.15–0.32 m/s, indicating normal weather ( Figure 6A ). Significant wave heights showed distinct attenuation along the transect during different periods ( Figure 6B ). The average significant wave height was attenuated when it passed through every region during the spring tide. Specifically, from SA to SC, the wave height values were 0.1, 0.05, and 0.01 m, respectively. A similar declining trend was observed in every tidal period. At middle tide, the mean wave height along the transect decreased from 0.08 and 0.04 m to 0.008 m from SA to SC. Only wave data at tripod C were valid during neap tide, where the significant wave height was 0.02 m ( Figure 6A ). Limited by the low water level, no valid data were captured by the instruments at SB and SC in the neap tide. In summary, the wave height decreased by 58.33% in the SA–SB region and 80% in the SB–SC region on average during different tidal conditions.

However, wave periods did not exhibit the same trend from the SA to SC station as wave height did. During spring tide, the average wave periods from SA to SC were 5.07, 4.52, and 5.34 s, respectively. Periods shortened at the middle of the tide, when the values were 4.20, 2.31, and 4.04 s, respectively. Only the SA station had a 2.31 s wave period during the neap tide. The average wave periods of the SB station were the shortest of all tide periods. However, from spring to middle to neap tide, the wave periods all shortened at these observation stations ( Figure 6B ).

Moreover, the average wave energy dissipated along this transect under different tidal conditions ( Figure 6C ). During spring tide, the wave energy decreased from 7.44 J/m² at tripod SA to 5.65 J/m² at tripod SB and finally remained at 0.12 J/m² when the wave arrived at tripod SC, reducing nearly 98.39% of the incident wave energy. During the middle tide, the wave energy declined from 6.86 and 4.18 to 0.08 J/m² from SA to SC, reducing the incident wave energy by nearly 98.83%. During the neap tide, only tripod SA detected a faint energy of 0.48 J/m². Both the significant wave height and energy experienced an obvious decline when the waves spread from offshore to the AC tidal flat.

The wave height reduction rate along the AC transect was measured to evaluate the wave damping ability at these three tripods ( Figure 7 ). The rate of the incident wave height reduction experienced a declining process with a longer propagation distance under different tidal conditions. Specifically, during spring tide, the rate varied from 1.8 × 10⁻³ to 0.79 × 10⁻³ from the areas of SA–SB to SB–SC. The variation ranges were 2.3 to 0.8 × 10⁻³ in the middle tide from the SA–SB region to the SB–SC region. The rate was 3.0 × 10⁻³m⁻³/m from region SA to SB during the neap tide. The wave height reduction rate was negatively related to the water level during the whole tidal period along the observation transect ( Figure 7 ), indicating that deeper water may cause a weaker reduction rate. However, the region from SB to SC experienced an extremely low water level during the neap tide, and an emerged state of the AC ( Figure 3D ) was induced when no wave attenuation occurred.

Moreover, the trend of the wave height reduction rate showed a large difference during the different tidal periods. Sparse AC seedlings and a few saplings were observed in the SA–SB region ( Table 1 ), and the reduction rate increased nearly 27.78% from spring to middle tide and 30.43% from middle to neap tide. In contrast, in the SB–SC region, where dense adult trees of AC were vegetated ( Table 1 ), this rate increased by less than 5% during the entire tidal period. Obviously, the variation degree of the wave attenuation rate was impacted by the water level fluctuation, which caused the variational drag effect and indirectly dominated the intensity of the wave height reduction rate.

Coastal vegetation obstructs wave propagation via the drag effect caused by dense root or canopy systems (Augustin et al., 2009; Hu et al., 2014; Foster-Martinez et al., 2018; Devi et al., 2021). Moreover, the spatial distribution of vegetation densities may also play a crucial role in wave attenuation (Massel et al., 1999; Hashim et al., 2013). (Vo-Luong and Massel, 2008) indicated that wave breaking occurring in a sparse forest induced an obvious attenuation effect instead of the wave–trunk interactions that occur in a denser forest. Here, our results showed distinct differences in the wave attenuation process among the three tripods. During the entire tidal period, the wave height attenuated to an average of 2.37 × 10⁻³ m in the area of SA–SB and 0.82 × 10⁻³ m in the area of SB–SC per meter. The bed material from SA to SC was mainly composed of fine and very fine sand, indicating that the attenuation difference was caused by the plant drag effect rather than bottom friction.

However, the reduction rate from SB to SC was 50% less than the value from SA to SB during the entire tidal period. Furthermore, the rate from the SB to SC region rarely varied along with the SA to SB region, and the rate increased nearly 67% from the spring to neap tide ( Figure 7 ), illustrating the difference in the volumetric cover of AC to induce the change in the drag effect and higher wave energy attenuation. Specifically, the seedling and sapling volumetric cover below 0.5 H was 16.53 and 60.33% at the SA station, respectively. At the SB station, this value was 5.25 and 63.42%, respectively. Although adult trees at the SC station had a larger canopy, their volumetric cover of the stem part (below 0.3 H) was only 31% ( Figures 8A–C ). At a low water level, dense vegetation structures occupied more space in the SA and SB regions at a low water level, which generated a larger drag effect compared to the relatively sparse parts in the SC region. Therefore, there is an obvious attenuation phenomenon at a low water level that occurs in the seedling and sapling areas rather than in the adult area. According to Figures 9D, E , when the water level was shallower than 1.5 m, the mean drag coefficient generated by mangroves in the SA–SB region was 3.74, but the value in the SB–SC region was 1.48, indicating that seedlings and saplings contributed to the attenuation process; however, only the stem part of an adult contributed to this process. Additionally, the SC station was at the high tidal flat ( Figure 1D ), with adult mangroves emerging at most times during the observation period, when the canopy part did not submerge due to the water level; this induced no drag effect, which explains why smaller mangroves had more power for attenuating wave energy than larger mangroves because the parts of the adult trees that are most effective at attenuation did not participate in this process ( Figures 4D , 8E ).

The drag effect difference generated by vegetation mostly depends on the inundation state ( Figure 8 ). An abrupt change in the reduction rate occurred in the spring tide when the water rose up from the stem to the canopy ( Figures 9A, D ). In other words, the attenuation effect was distinctly different when the AC was in a shifted inundation state with different water levels. Particularly, if a typhoon event happens at a low water level when saplings and seedlings have submerged but the canopy parts of adults are emerged, the former can attenuate waves effectively, since adults always locate at the high part of a tidal flat.

For the seedling-sapling region, seedling mangroves were approximately 55 cm ( Figures 3B–D ), which often flooded due to the mean water level of 117 cm at this location. Moreover, the Cd reduction rate decreased rapidly below the 150 cm water level, and then the decreasing rate slowed down when the water level was above 150 cm (k1 = −1.30 × 10⁻³ for L1 and k2 = −6.79 × 10⁻⁴ for L2 in Figure 8D ), inferring that seedlings have an effective wave attenuation ability below the 150 cm water depth. However, from SB to SC, with the height of standing adult AC greater than 150 cm, which is seldom flooded due to the average water level of approximately 73 cm in this area during the spring tide ( Figure 4B ), only the branches were submerged, and the canopies could not be reached. Taken together, the change in the drag force followed the inundated volume variation in AC and controlled the wave attenuation rate.

The wave height reduction rate was negatively correlated with the water fluctuations ( Figure 9 ) and water-level variations for different drag coefficients induced by mangroves with different inundation states ( Figures 8D, E ). Furthermore, the similar structure and distribution of mangrove forests produce similar drag effect values, in which water fluctuation works as a medium. Therefore, a similar vegetation distribution may generate a similar drag coefficient (Hu et al., 2014; Foster-Martinez et al., 2018), even though the water level fluctuates during one tidal cycle. Thereafter, a direct relationship between the wave height reduction rate and Cd can explicitly express the impacts of mangrove vegetation on wave height, while wave data from most field observations are extremely difficult to obtain because of the inaccessibility of dense mangroves.

As the seedling-sapling region had a more powerful ability to attenuate waves than the sapling-adult region ( Figure 7 ), the wave height reduction rate and Cd along this area during the spring tide were selected. An exponential relationship between these two parameters was deduced, which was R = -0.0023 × e ^{-0.64 Cd} + 0.0025. While the water level rose and the seedlings were not entirely submerged, an obvious increase in the drag effect accelerated the wave attenuation process (blue box in Figure 10 ). Although the drag effect increased weakly when the water level was higher than the height of a plant, the wave could still be disturbed and attenuated within a certain water level range, and the reduction rate rose slowly beyond the canopy height of plants. The mechanism for the wave attenuation effect of seedlings and saplings of the AC illustrated that water depths shallower than 0.7 m were the most effective range of damping wave energy ( Figure 10 ). Predictably, when a typhoon event happens during the spring tide, meeting the high fluvial discharge, such as in the case of Hepu County in 1986, the high tidal flat is submerged, and the canopy part of the AC plays a crucial role in this attenuation process.

Furthermore, (Massel et al., 1999) inferred that the wave attenuation mechanism was the same both with and without a typhoon event, demonstrating that both mangroves and bottom friction played important roles in the attenuation process regardless of whether short waves propagated in cyclonic weather or long waves propagated in normal weather. Similarly, the exponential relationship between Cd and the reduction rate for seedlings and saplings can also be adopted during the typhoon period. Since the location of SC is in the upper mudflat, no quantitative relationship for adult AC between Cd and the water level can be constructed. However, according to the dense canopy of an adult tree ( Figure 8C ), it can be speculated that the canopy part of an adult mangrove is of great significance in the wave attenuation process during an extreme event. Therefore, the “green-embankment” definition has been proposed (Temmerman et al., 2013) recently to defend against extreme events, replacing “hard engineering.” Our in-field observational data elucidated that the AC at different ages has distinct volumetric cover from the bottom to the canopy part, which can attenuate wave heights in stages via water-level variations. During normal or slight typhoon weather conditions, the number of seedlings can effectively attenuate the wave energy with lower economic costs and higher plant survival rates. When the weather conditions become more severe with greater wave energy, adult mangroves can participate in this attenuation process. Obviously, the distribution of mangroves for constructing a “green embankment” should consider the age of mangroves to cope with different attenuation effects with changing water levels from offshore to inshore to obtain a longer defense period with lower economic costs.