A paradigm shift in the quantification of wave energy attenuation due to saltmarshes based on their standing biomass

Experimental set-up

Four vegetation species were selected: Spartina maritima, Salicornia europaea, Halimione portulacoides and Juncus maritimus. These species were chosen for a broad representation of the biomechanical properties and morphological characteristics of saltmarsh species^42,43. Plants were collected in Cantabrian estuaries in late summer and early autumn (from early September to late October) during low tide (please refer to the “Methods” section). A total of 105 boxes were collected, of which 94 boxes were used to build a 9.05 m long and 0.58 m wide meadow in a flume (Fig. 1). Five boxes were used to directly estimate the meadow standing biomass in the field (Sample 1 in Table 1), leaving 6 extra boxes for possible contingencies.

Experiments were conducted in a flume 20.71 m long and 0.58 m wide at the University of Cantabria. The flume is equipped with a piston wave maker at its left end and a dissipation beach at the rear end. The 94 vegetation boxes used to create a meadow were introduced into the flume following the pattern shown in panel A of Fig. 1 to minimize any edge effects along the edges of the boxes. To ensure a smooth transition from the bottom of the channel to the vegetated area, two false bottoms were constructed with wood, and a thin sediment layer was glued to the wood to mimic the field roughness.

Three meadow densities per species were considered. The meadow density directly determined in the field was chosen under the 100% density scenario. To consider a second meadow density, and therefore a second standing biomass value, plants were removed from half of the boxes following the pattern shown in Panel A of Fig. 1 to prevent creating preferential flow channels along the meadow. This case was considered the 50% density scenario. The study of these two biomass scenarios for each vegetation species is carried out with the aim of covering a wide range of standing biomass values, including low values that may be more representative of meadow winter conditions, thus facilitating the applicability of obtained results. Finally, a second cut was made, in which all plants were removed, resulting in the final scenario with a zero density. Plants were cut from above to avoid any damage along the meadow surface (as shown in Supplementary Fig. S2). In each cut, plants in 5 boxes along the leading edge and in 5 boxes at the center of the meadow were collected to quantify the standing biomass (Samples 2 and 3 for the first cut and Sample 4 and 5 for the second cut in Table 1). Therefore, the standing biomass could be monitored throughout the entire duration of the experiments, from the field until the second cut, when all plants were removed.

Once located in the flume, the meadow was evaluated under regular and random wave conditions considering three water depths, i.e., h = 0.20, 0.30 and 0.40 m. Regular waves were generated using Stokes II-, III- and V-order and Cnoidal theories when applicable. Wave heights ranging from 0.05 to 0.15 m and wave periods varying between 1.5 and 4 s were considered. Random waves were generated using a Jonswap spectrum with a peak enhancement factor of 3.3, a significant wave height varying between 0.05 and 0.15 m and a peak wave period ranging from 1.8 to 4.8 s (please refer to Supplementary Table S1). Additionally, all wave conditions were considered under the zero-density scenario with bare soil for each species. The wave height evolution along the flume was recorded using 15 capacitive free surface gauges, as shown in Fig. 1 (please refer to Supplementary Table S2 for detailed coordinates).

Meadow characteristics analysis

The characteristics of the vegetation meadows were analyzed by measuring the standing biomass throughout the full duration of the experiments and by measuring the individual plant height (please refer to the “Methods” section). The mean standing biomass value obtained for each species was considered the value associated with the 100% density scenario. Then, half of the standing biomass value was considered under the 50% density scenarios since half of the boxes was randomly cut, and the standing biomass values obtained after the second cut agreed with those obtained after the first cut and in the field, as indicated in Table 1. The plant height for each species was also measured (please refer to the “Methods” section), and the resultant mean value detailed in Table 1 was considered.

Wave height attenuation analysis

Wave height attenuation analysis was performed following previous studies reported in the literature assessing the capacity by fitting a damping coefficient^6,7,35,44. The¹⁸ formulation was used for regular waves, and that of¹⁹ was used for random waves (please refer to the “Methods” section). Cases with a zero density were also considered in this analysis to quantify the influence of bare soil friction by determining the corresponding damping coefficient, ({beta }_{B}). Consequently, β was obtained in the 100% and 50% density cases and the cases without vegetation (please refer to Supplementary Tables S3, S4 and S5 to find the obtained coefficients for all cases). This allowed the determination of a new damping coefficient isolating the effect of the standing biomass, ({beta }_{SB}), following²⁴ (please refer to the “Methods” section). Figure 2 shows an example of wave height attenuation analysis for the four species and the different densities under wave condition JS07 (Supplementary Table S1).

The damping coefficients for the bare soil cases shown in Fig. 2, ({beta }_{B}), are consistent with the soil properties observed in the field. Spartina sp. was collected in a muddy area, whereas the other three species were collected in areas with coarser sediments and exhibited a mixture of sand and mud. For all species, wave dissipation was significantly higher under the 100% density scenario than that under the 50% density cases, as expected, highlighting the importance of the standing biomass in wave energy dissipation. It was also observed that bottom friction-induced dissipation plays a more important role for the pioneer species, i.e., Spartina sp. and Salicornia sp., than for the upper marsh species, i.e., Juncus sp. and Halimione sp., which can dissipate wave energy to a greater extent.

The importance of wave parameters in the resultant wave attenuation has been highlighted by several works in the literature. Therefore, not only vegetation characteristics but also incident wave conditions determine the coastal protection capacity. Figure 3 shows a comparison of the obtained wave height attenuation due to Halimione sp. under the different wave conditions.

The top panel in Fig. 3 shows two cases where H_s and T_p are equal, i.e., JS01 and JS08 in Supplementary Table S1, and two water depths are considered, namely, h = 0.2 and 0.3 m. As can be observed, wave damping is higher for the smallest water depth, where most of the water column is covered by vegetation since the mean vegetation height for Halimione sp. reaches 0.187 m (Table 1). The importance of the water depth with respect to the plant height in terms of wave height attenuation has been reported by several authors^44,45,46 who have highlighted this aspect based on the submergence ratio, i.e., the plant height divided by the water depth, revealing higher attenuation at lower submergence ratios on a consistent basis. Bottom friction attenuation is also higher for the smallest water depth, as expected.

The middle panel of Fig. 3 shows two cases with equal h and H_s but different T_p values, namely, JS10 and JS11 in Supplementary Table S1. Wave height attenuation is higher for the shortest wave period, as well as the damping produced by bottom friction. This is in line with previous studies, such as³⁵ and⁴⁴, who conducted experiments involving simulated and real saltmarshes, respectively. Finally, the bottom panel of Fig. 3 shows two cases with different H_s but equal h and T_p values, i.e., JS09 and JS12 in Supplementary Table S1. As widely reported in the literature, e.g.,^7,47,48, wave height attenuation increases with the wave height, as shown in the bottom panel of Fig. 3. Bottom friction also increases with the wave height, as expected.

A set of damping coefficients was obtained via the 288 tests conducted in the laboratory, 144 tests involving regular waves and 144 tests involving random waves. Additionally, in all cases, the damping coefficient considering the isolated effect of the standing biomass, ({beta }_{SB}), was determined. The relationship of these damping coefficients to the measured standing biomass is explored in the next section with the aim of establishing a new relationship to estimate the wave damping effect of the different saltmarsh species based on the standing biomass, without the need for data fitting.

Wave damping coefficient as a function of the standing biomass

The mean standing biomass obtained for the different species, Table 1, is considered here to analyze the relationship with the wave damping coefficients obtained by fitting¹⁸ formulation to wave heights measured along the meadow for regular waves and¹⁹ formulation for random waves. The plant height was highly variable among the different species (Table 1), ranging from 0.170 m for Spartina sp. to 0.714 m for Juncus sp. Then, some species were submerged at all tested water depths, while other species remained above water in all tests. In the latter cases, there remained a portion of each plant above the water level, thus not contributing to wave attenuation. To consider the actual interaction between the standing biomass and flow conditions and assuming a uniform vertical distribution, the effective standing biomass, (ESB), can be defined as follows:

where (DryWeight) denotes the measured dry weight for each species (g/m²), ({h}_{v}) is the mean plant height and (h) is the water depth. Additionally, in the submerged cases, the same (ESB) value will impact flow differently depending on the submergence ratio, (SR), as defined in Eq. (2). To consider this effect, the standing biomass ratio, (SBR) in Eq. (3), can be defined as follows:

Figure 4 shows the relationship between (SBR) and the measured wave damping coefficient, (beta ). The results for regular and random waves are displayed for each water depth, and a linear fit was found under each condition.

Under each wave condition, a linear fitting relationship between (beta ) and (SBR) was obtained for the eight (SBR) values, as shown in Fig. 4. For similar (SBR) values, the highest (beta ) values were consistently obtained at the smallest water depth, highlighting the notable influence of this parameter on the obtained wave attenuation. Following previous works, such as those of²⁴ and²⁵, who considered the vegetation submerged solid volume fraction to estimate the resulting wave attenuation and established a common relationship for different water depths, the volumetric standing biomass, (VSB), can be defined as follows:

(VSB) is expressed in units of g/m³, which is the weight per unit volume. Exploring the relationship of (beta ) with this new parameter, it was found that the results for the three water depths could be fitted with a single linear relationship, as shown in Fig. 5. However, despite the linear trend observed in Fig. 5, notable data scatter was observed for each (VSB) value. Each of these groups corresponds to a certain water depth and (SBR) value, which were determined under different wave heights and wave periods.

Finally, to account for the characteristics of the incident wave conditions, including the wave height and period, two nondimensional parameters were considered. The first parameter, considering the wave height, is the relative wave height, defined as the ratio of the incident wave height to the water depth, (H/h). Previous studies have highlighted the importance of this parameter in the resultant wave attenuation (e.g.^24,44). Under random wave conditions, the considered wave height is ({H}_{rms}), according to wave attenuation analysis. The second parameter, considering the effect of the different wave periods and the importance of the number of wave lengths inside the vegetation length⁴⁹, is the relative meadow length, defined as the ratio of the meadow length to the wave length, ({L}_{v}/L). To ensure consistency with the above wave attenuation analysis, in which the wave damping amount per unit length was obtained, the unit meadow length was considered here. Thus, the hydraulic standing biomass, (HSB), can be defined as:

Figure 6 shows the relationship obtained between (beta ) and this new variable under all regular and random conditions following the linear fitting relationship of (beta =A*HSB+B), where (A) and (B) are fitting constants with units of (g/m²)⁻¹ and m⁻¹, respectively.

The linear fitting results obtained between (beta ) and (HSB) under regular and random wave conditions are shown in Fig. 6 as solid black lines and expressed as Eqs. (6) and (7), respectively, where values between brackets are the 95% confidence interval for each coefficient.

The inclusion of incident wave condition characteristics reduces the resulting data scatter, highlighting the role of the wave height and period in the obtained wave attenuation, as described in the previous section. An interesting aspect observed in Fig. 6 is that the four cases with the highest wave damping coefficients yielded similar values for the different (HSB) values. Under regular wave conditions, the mean (beta ) value for these four cases is 0.76, and under random wave conditions, the value reaches 0.68. This may indicate that the damping coefficient has reached its maximum value and no longer increases with increasing (HSB) value. To analyze this aspect in more detail, the wave height evolution measured for the four tests in which (beta ) reaches its maximum value are plotted (as shown in Supplementary Fig. S3). These tests correspond to Halimione sp. with a density of 100% and the shallowest water depth, h = 0.20 m. This species achieved the highest standing biomass value among the species considered in these experiments, and for h = 0.20 m, almost the entire water column was covered by vegetation. For these tests, a notable wave height attenuation was observed, where the wave height strongly decayed along the first 5 m of vegetation, and the wave height entirely dissipated along the last 4 m (as shown in Supplementary Fig. S3). The wave damping equation cannot suitably reproduce the strong wave decay within this few meters. Then, an almost constant wave damping coefficient value is reached under the different considered wave conditions, and a saturation regime is observed, in which the wave height beyond the meadow can be assumed to be negligible. To consider this phenomenon, a two-section fitting relationship is proposed, as shown in Fig. 6. The value of the saturation damping coefficient, chosen as the mean value of the four cases analyzed, is plotted as a dashed gray line, and a linear fit is obtained for the remaining data. The two-section fitting relationship is expressed in Eqs. (8) and (9) for both regular and random waves, respectively, where values between brackets are the 95% confidence interval for each coefficient.

All damping coefficients considered in the previous analysis were obtained without subtracting any additional source of dissipation such as bottom and wall friction. Previous works, such as²⁴, highlighted the high importance of considering any other sources of wave dissipation besides the effect of vegetation elements when quantifying the wave height attenuation capacity. In this case, the flume walls were made of glass, and the friction induced by these walls could be considered negligible. However, bottom friction could be significant, as observed in tests run after removing all vegetation stems. Then, the wave damping coefficient obtained after subtracting the bottom friction contribution, ({beta }_{SB}), is studied here. Figure 7 shows the relationship obtained between this damping coefficient, ({beta }_{SB}), and hydraulic standing biomass, (HSB).

A linear relationship was also obtained for ({beta }_{SB}), revealing correlation coefficients similar to those obtained when analyzing (beta ). The obtained linear relationships under regular and random wave conditions are expressed as Eqs. (10) and (11), respectively, where values between brackets are the 95% confidence interval for each coefficient. A two-section fitting relationship, Eqs. (12) and (13), was also included considering the saturation regime obtained in the Halimione sp. 100% density and h = 0.20 m cases with a ({beta }_{SB}=) 0.69 and 0.63 under regular and random wave conditions, respectively.

As can be noted, the ({beta }_{SB}) values are significantly lower than those obtained for (beta ), especially in the shallowest water depth cases where bottom friction is the highest, as discussed above. The estimation of (beta ) and ({beta }_{SB}) allows two possible approaches to determine the wave damping effect of a saltmarsh. The first approach, based on (beta ), includes wave damping induced by the combined effect of vegetation and bottom friction. Therefore, the consideration of (beta ) in analytical or numerical analysis could provide the total dissipation induced by the species under study, and sediment characteristics are not necessary for analysis. Considering that saltmarsh species grow in muddy to sandy environments and that the major contribution to the obtained wave attenuation is associated with vegetation, this approach may be the best option if soil properties are not thoroughly characterized.

The second approach relies on the definition of ({beta }_{SB}). In this case, the wave damping contributions of vegetation drag and bottom friction are separated. Then, ({beta }_{SB}) can be used in cases where the effect of both momentum sinks can be separately evaluated. To quantify the wave damping contribution of vegetation drag only, ({beta }_{SB}) can be used, and then, the additional friction due to the bottom effect can be added considering the soil properties in each case. This second approach assumes a linear sum of both momentum sinks and could be applicable when soil properties are thoroughly characterized.

Source: Ecology - nature.com