The present study was conducted in the National Research Council of Canada’s (NRC) 63 m long by 14 m wide by 1.5 m tall Coastal Wave Basin (CWB). The CWB is equipped with a computer-controlled wave machine capable of generating irregular long-crested waves with significant wave heights up to ∼0.35 m (at model scale). The active wave absorption feature was not enabled during this study.

A length scale of 1/20 was adopted for the experiments, and Froude scaling was used to relate most (but not all) conditions in the model to corresponding conditions at full scale. The 1/20 scale factor, together with the chosen wave conditions and the fact that the surrogate plant stems in the model were purposely over-sized, ensured that the wave-driven flows around the model vegetation and model armour stones on the dyke surface remained rough-turbulent at all times, as in nature. Preserving rough-turbulent flow in the model was essential to minimizing scale effects and preserving the realism of the wave-plant and wave-structure interactions in the physical model.

The 14 m wide CWB was subdivided into four separate 1.22 m wide flumes by erecting parallel masonry block walls (see Figure 1). This setup created four identical test flumes and allowed four different marshes to be built and evaluated at the same time, one per flume, with identical incident wave conditions in front of each marsh. Each flume included an identical scaled reproduction of the typical sloping foreshore along the edge of the Tantramar Marsh on the Chignecto Isthmus, as well as an idealized model dyke structure (see Figure 2). A ∼1V:11H foreshore slope followed by a 4.75 m long (95 m at full scale) horizontal tidal flat was created by rigidly securing thick plywood sheets to the flume walls.

The floor of the wave basin at the toe of the sloping foreshore was assigned an elevation of −0.18 m (corresponding to −3.50 m at full scale), while the tidal flat elevation was +0.27 m (+5.40 m at full scale). Water depths on the tidal flat in this study ranged from 0.05 to 0.12 m (1.0–2.4 m at full scale). The bathymetry helped to ensure that wave conditions at the edge of the marsh in the physical model, including the distribution of wave heights and the percentage of breaking and broken waves, was similar to head-on wave conditions at the edge of typical marshes in upper Chignecto Bay.

Marshes comprised of S. alterniflora were simulated on the 4.75 m long tidal flat using idealized surrogate vegetation fixed to the plywood. During the study, several different marshes with different plant characteristics could be modelled in each flume by swapping the vegetated plywood panels between tests. The sensitivity to plant density, plant height (and submergence), stem stiffness and marsh cross-shore width were investigated in this way.

These experiments were conducted using idealized surrogate vegetation representing S. alterniflora. Several configurations of rigid (cylindrical birch dowels) and flexible (Tygon polymer tubing) model vegetation were used during the experiments. The birch dowels were 3/8 inch (9.5 mm) in diameter, while the flexible tubing had outer and inner diameters of 5/16 inch (7.9 mm) and 1/4 inch (6.4 mm) respectively. It should be noted that vertical variability in stem diameter (tapering) or frontal area was not captured in this study. A tensile strength test indicated that Young’s modulus of the Tygon tubing was approximately 4.5 MPa, equivalent to ∼90 MPa at full scale.

Vegetated meadows were constructed by inserting dowels or tubing into 19 mm thick plywood sheets following a staggered arrangement. These vegetated panels were pre-constructed and easily interchangeable so that different vegetation conditions could be investigated during the experiments. The staggered arrangement of model plant stems shown in Figure 3 corresponds to the following relationship between stem spacing, λ , and the vegetation density [from Ozeren et al., 2014]: N v = 2 3 λ − 2 (8)

Scaling the stem diameter according to the model length scale was impractical since it would involve replicating hundreds of thousands of wire-thin stems. Moreover, this approach would cause the stem Reynolds number in the model to be significantly smaller than in prototype. Previous studies suggest wave attenuation is predominately associated with vegetation drag, which is proportional to the vegetation frontal area. Therefore the stems were scaled to maintain an equivalent solid volume fraction, ϕ , where ϕ = a d π / 4 , d is the cylinder diameter and a is the frontal facing area (the cylinder area perpendicular to the direction of flow per unit volume, m²m⁻³). Following this approach, three different meadows of S. alterniflora stems were simulated in the experiments using a reduced number of oversized cylinders. The stem densities of these scaled meadows were N v = 125, 295, and 450 stems/m², representing meadows with low-, medium-, and high-densities, equivalent to 150, 350, and 550 stems/m² of live vegetation (see Figure 4). Two stem heights, h v = 0.090 and 0.025 m were investigated in the experiments, representing S. alterniflora meadow heights of 1.8 and 0.5 m respectively, nominally representing two different periods of the growth season.

The performance of four different dyke designs located at the leeward end of the model test flumes was examined in these experiments (see Figure 5). The first design was considered typical for dykes throughout Atlantic Canada and featured an impermeable dyke core with two layers of riprap on the seaside only (herein referred to as a simply reinforced dyke). Three additional designs, representing various potential methods for upgrading the simply reinforced dyke, were also studied. The second design (armoured dyke) was created by adding two layers of riprap on the crest and leeside of the structure while maintaining the same crest elevation. The third design (widened reinforced dyke) was created by doubling the thickness of the seaside armour layer. The fourth design (simply reinforced dyke with berm) was created by adding a berm of armour stone on the seaside that was half the height of the structure and four armour stones in thickness. All four model dyke designs featured a crest elevation of +0.43 m (corresponding to +8.6 m above mean sea level at full scale), a typical crest elevation of older dykes in the Tantramar area (Lieske and Bornemann, 2012).

Each model dyke was constructed using carefully prepared stone materials and construction methods. The dyke cores were constructed using a fine gravel with low permeability, but also included impermeable wooden barriers which prevented water from seeping through the dykes into the inland areas. Furthermore, a thin, flexible plastic membrane was placed between the core and armour materials to prevent water from flowing into the core. This method of construction allowed overtopping flows to pass through or above the armour stone on the dyke crest as would occur in the prototype situation. The landward end of each test flume was sealed off so that the water level behind each model structure could be kept lower (using submersible pumps), thereby simulating the situation where the inland area behind the dyke structure is not flooded, which is expected to be the most critical condition for rear slope stability.

The sizing of armour stone was based on Hudson formula calculations and also informed by Nova Scotia Department of Transportation Guidelines. The required armour stone mass M 50 was calculated as 136 kg at full scale. The armour stone was assumed to have a wide gradation such that M 15 = M 50 / 2 and M 85 = M 50 × 2 . The corresponding values of M 15 , M 50 , and M 85 at model scale, accounting for the density difference between the freshwater used in the model and the seawater in prototype, were 7.5, 15.1, and 30.2 g. Model stone materials were prepared to closely replicate the gradation and characteristics of the prototype material. During construction of the various dyke structures, due care was taken to ensure that stones with aspect ratios greater than 3:1 were not used (i.e., stones where either the length, width or height was more than three times larger than any other dimensions). This was important since flatter stones are more likely to move or overturn under wave action.

Particulars of the marsh-dyke system in each test flume during each test series are given in Table 2. Each setup was chosen in order to obtain results needed to independently assess the influence of key variables including: vegetation density, vegetation (stem) height, cross-shore marsh width, type of vegetation (rigid or flexible), and dyke structure type. For Test Series 2, the dyke structures were replaced with gently sloping gravel beaches featuring less than 5% wave reflectance, so that wave conditions across the artificial marshes could be measured with minimal influence of reflected waves. Hence, much of the analysis concerning wave attenuation presented in the following Section is based on data gathered during Test Series 2.

The wave conditions and water levels selected for testing were generally representative of conditions along the Canadian Atlantic coast where marsh-dyke systems exist (see Table 3), with a particular focus on storm conditions (higher water levels and energetic waves) that could overtop and/or damage the dykes. Table 2 specifies the number of wave height, wave period, and water level combinations investigated in each test series. Overall, the testing program consisted of 141 unique tests.

The wave signals for tests with irregular waves were synthesized from a family of JONSWAP-type spectra with a 3.3 peak enhancement factor approaching from a single direction. However, due to the shallow water conditions in the CWB and the natural growth of sub- and super-harmonics, the spectral shapes, and the distribution of energy with frequency in the experiments were typical of shallow water conditions. The test program included significant wave heights (H_m0) ranging from 0.05 to 0.15 m (corresponding to 1.0–3.0 m at full scale) and peak wave periods (T_p) ranging from 0.63 to 3.35 s (corresponding to 3–15 s at full scale). These conditions respect the guidance of Hughes (1993) and Heller (2011) for minimizing scale effects on wave propagation caused by surface tension. Water depths on the tidal flat ranged from 0.05 to 0.12 m (corresponding to 1.0–2.4 m at full scale). Each wave signal featured a non-repeating sequence of approximately 1,000 irregular waves, thus the duration of each wave signal and test varied depending on the peak wave period, ranging from ∼10.9 to 38.9 min long (corresponding to ∼0.8–2.9 h at full scale). One-thousand waves was selected to ensure that each signal included a statistically representative distribution of larger wave heights and crest elevations, since wave overtopping and armour stone stability are typically sensitive to the few largest waves in a sea state. Water levels were adjusted in the model by filling or draining the basin until the desired level was reached.

Twenty-two capacitance-type probes were used to measure water surface displacement at several locations of interest in each test flume. Two probes were located in deeper water near the wave generator to measure offshore wave conditions, while the others were positioned such that five probes were deployed inside each flume as shown in Figure 2 (one above the sloping foreshore and the other four distributed across the artificial marsh). The probes were configured to record water levels at a sampling frequency of 50 Hz and were (re)calibrated before each test series by changing their elevation with respect to a fixed (known) water level. The wave probes featured a highly linear and stable response, with calibration errors typically less than 0.5% over their calibration range. Comprehensive time-domain and frequency-domain analysis algorithms were applied to analyze the wave conditions measured in the model in detail.

Four simple, accurate and reliable overtopping measurement systems were deployed, one in each test flume. Each overtopping measurement system consisted of a collection tray positioned to collect water passing over the dyke crest and convey it to a water storage reservoir fitted with a capacitance water level gauge located on the leeside of the dyke. Wave overtopping was quantified as a volumetric flow rate per unit width passing over the top of the dyke crest. This overtopping measurement system was best suited for measuring moderate-to-heavy overtopping flows (e.g., greater than 1 L/s/m at full scale); measuring smaller volumes of splash and spray was less precise. The overtopping collection trays were positioned at the rear slope break of the dyke crest atop nominally two layers of armour stone. Small overtopping events in which the wave runup reached the crest elevation, generating overtopping flows through the armour stone on the dyke crest, were not captured by the overtopping measurement system. It is noted that typical dykes have a drainage ditch along their leeside which can handle some degree of overtopping flow. Only larger overtopping events featuring green water flowing over the crest and reaching the rear slope break were captured by the overtopping measurement systems in these experiments.

A photographic damage analysis system comprising four remotely-operated digital cameras was used to monitor the stability of the armour stones on each of the four dyke structures. Since each camera remained fixed throughout a test series, by comparing photographs taken before and after each test segment, damage could be assessed and quantified based on the number of individual stones that were displaced during each test segment. The effect of marsh vegetation on armour stone stability will be discussed briefly in the next section.

Previous research has identified a strong correlation between vegetation density and wave damping, and this correlation was further confirmed in these experiments. Not only did the rate of wave attenuation increase with increasing vegetation density, but the amount of wave overtopping recorded at the dyke, and the damage to the dyke itself was reduced as well. Figure 6 shows relative wave heights (wave height with vegetation normalized by corresponding wave height without vegetation) measured across the tidal flat comprised of medium-density vegetation for a range of wave conditions and water levels. Measurement locations are shown in Figure 2. This normalization of wave height is necessary to isolate the effects of vegetation, since the wave conditions across the artificial marshes in these experiments were generally strongly influenced by the effects of shoaling and depth-limited wave breaking, and, to a lesser extent, flume friction effects (Maza et al., 2019). For test flumes with vegetation, measured significant wave heights at each probe were normalized by H_m0 values measured at corresponding locations in the flume with no vegetation (i.e., Flume 1 in Test Series 2; refer to Table 2). Figure 6 shows the spread of observed wave attenuation for individual tests spanning a broad range of significant wave heights, peak wave periods, and water depths. For each test, the damping coefficient β ’ (Eq. 3) was evaluated by least squares regression to the significant wave heights measured across the model marsh canopy. Values from individual tests were averaged to permit comparison across different vegetation densities (discussed below).

Similarly, Figure 7 shows relative wave heights (wave height with vegetation normalized by corresponding wave height without vegetation) measured across the tidal flat as a function of vegetation density. Average β ’ values (derived by averaging results from multiple tests with different wave conditions and water depths) for the three different artificial marshes considered in these experiments are shown in Figure 7. Although different plant species were investigated by Maza et al. (2015), the β ’ values derived from the present experiments (0.149–0.346) are similar to those observed by Maza et al. at lower water depths (0.124–0.286), which involved submergence ratios similar to the present study (1.0 in Maza et al. compared to an average of 0.92 in the present experiments).

As shown in Figure 7, significant wave heights in the low-density, medium-density and high-density vegetation were 28, 40 and 46% lower (respectively) than those in the flume with no vegetation for the same test conditions. Therefore, higher vegetation density does lead to increased wave attenuation, as expected, but there appears to be a diminishing return on additional bio-mass leading to additional wave attenuation, at least for the range of densities tested in this study.

Looking at the data points along each individual curve in Figure 7, the majority of the wave damping occurs in the first third of the marsh (i.e., between Stations 2 and 3). Averaging over the full range of water level and sea state conditions investigated, there was a 19% reduction in significant wave height across the first 1.5 m of the low-density marsh, compared to a further 9% reduction across the following 3.25 m of marsh. For the high-density marsh, there was a 27% reduction across the first 1.5 m long section versus a further 19% reduction across the remainder.

Stakeholders looking to make use of vegetated tidal flats to augment shore protection should consider creating expansive marshes wherever possible, not only from a wave attenuation and flood risk reduction perspective but also for the environmental co-benefits they bring. Where expansive marshes are not possible, this data suggests that denser vegetation is preferred from a wave attenuation perspective, as opposed to sparser vegetation. Figure 7 shows that narrower denser marshes can be considered roughly equivalent to wider marshes with sparser vegetation. For example, 700 dowels placed in the low-density configuration (denoted by the blue ✕ in Figure 7) spans X = 4.55 m and yields ∼28% wave attenuation on average. However, 700 dowels placed in the medium-density configuration (denoted by the red ✕) occupies X = 1.95 m of horizontal distance and yields ∼29% attenuation on average across a broad range of wave conditions and water depths, while the same number of dowels in the high-density configuration (denoted by the green ✕) spans X = 1.25 m and yields ∼25% attenuation on average.

Figure 8 shows the observed variation in wave attenuation factor β ’ with peak wave period based on the present experiments. In this figure, symbols denote results for individual tests and dashed lines connect average wave attenuation factors for each wave period. For the range of conditions investigated in these tests, no clear dependence of attenuation factor on wave period was identified. While some wave period dependency was identified for specific test conditions (particular combinations of water depth and wave height), the trend was not consistent across all test conditions.

Contrary to the findings of Wu and Cox (2015b), no significant correlation between wave steepness and wave attenuation was observed across the range of conditions investigated in this study.

Based on a study by Maza et al. (2019), damping coefficients determined for various water depths, wave heights and wave periods indicated that, in general, higher damping coefficients are associated with higher wave heights and shorter wave lengths (i.e., smaller wave periods). In addition, higher correlations were found between the damping coefficient and wave height than with wave steepness, indicating that wave height has greater control than wave period in terms of attenuation capacity.

Figure 9 shows the variation in wave attenuation factor ( β ’ ) with incident wave height based on data from Test Series 2, where the dykes in each flume were replaced by absorbing gravel beaches with low wave reflectance. The results show that wave attenuation is, on average, greatest (largest β ’ ) for the highest incident waves investigated in this study, which is consistent with the results of Maza et al. (2019). However, further analysis (presented and discussed below) makes it clear that submergence ratio plays a more significant role and helps to explain the degree of scatter seen in Figure 9. Analysis to detect correlations between wave attenuation factor and wave steepness were undertaken, but no clear trends were evident for the range of conditions in Test Series 2.

The relationship between wave attenuation factor ( β ’ ) and the ratio of submergence derived from the present experiments is presented in Figure 10, where symbols denote results from individual tests spanning a range of wave conditions, while dashed lines connect average values for each submergence ratio. As seen in many previous studies, wave attenuation clearly increases as plant height (submergence) increases relative to the local water depth. Although results for only three submergence ratios are available from this dataset, the data suggests that the rate of increase with submergence ratio is greater for submergence ratios less than 0.9, decreasing as the vegetation becomes emergent in still water.

Using data from Test Series 2, the bulk drag coefficient, C D , was calculated according to the formula proposed by Sonnenwald et al. (2019), see Eq. 7. Figure 11 shows the resulting relationship between the bulk drag coefficient and the K C number defined in Eq. 6. These results suggest that for larger KC number ( K C > 80), the low-, medium-, and high-density marshes studied in these experiments are associated with bulk drag coefficients of approximately 1.47, 1.55, and 1.63, respectively, and that bulk drag coefficients for all three marshes increase gradually as K C number decreases towards K C ∼ 10. These results are generally consistent with the findings of Ozeren et al. (2014), who found that C D was dependent on K C when K C < 10. In these experiments, 12 < K C < 268, suggesting all were in the range where drag forces dominate and the drag coefficient is weakly dependent on K C . At field (full) scale, 268 < K C < 2,351 would be typical for the same range of wave and water level conditions, assuming stem diameters of 9.5 mm, and therefore bulk drag coefficients observed in the present experiments are expected to slightly over-predict field conditions.

Test Series 4 was conducted to investigate the effects of vegetation height (or submergence ratio) and stem flexibility on the resulting wave attenuation. Figure 12 compares wave attenuation across the model marsh for otherwise identical marshes comprised of rigid and flexible vegetation. In this figure, the wave height attenuation across the marsh platform for the no vegetation (NoVeg) case is primarily due to depth-limited wave breaking. Across the wide range of significant wave heights, peak wave periods and water depths investigated, the additional wave attenuation due to flexible vegetation is roughly 90% of the additional attenuation due to comparable rigid vegetation. Although plant stiffness was not the main focus of these tests, and plant flexibility was not modelled with strict parametric specificity, these results are consistent with the findings of Maza et al. (2015), where increased plant rigidity was shown to correlate with increased wave attenuation.

The influence of plant submergence ratio on wave height attenuation is plotted in Figure 10 and discussed briefly in the previous section, where it is shown that wave attenuation capacity increases with increasing submergence ratio. In a similar vein, Figure 13 shows the effect of plant submergence (or height) on wave attenuation across otherwise similar model marshes. As in Figure 12, the wave height attenuation curves in this figure are based on averaging results from several tests with different wave conditions, and include the effects of depth-limited wave breaking. Stems in the tall marsh were simulated using 0.09 m tall rigid dowels, whereas 0.025 m tall dowels were used in the short marsh (28% of the tall plant height). Figure 13 shows that the additional wave height attenuation due to the short stems (relative to the NoVeg case) was roughly 1/3^rd of the additional attenuation due to the taller ones. These results are consistent with the results shown in Figure 10 and the findings by other authors (Arkema et al., 2013; Anderson and Smith, 2014) who investigated the effect of water depth on wave attenuation capacity and found a significant influence on wave height decay, specifically that emergent conditions led to higher amounts of wave attenuation. Wave attenuation due to shorter, broken stems is an important topic, particularly for higher latitude regions where marsh plants tend to die off following the summer growing season, thus reducing their capacity to dissipate wave energy and limit flood risk.

The presence (or absence) of vegetation was a strong function of dyke performance. Figure 14 shows a comparison of two identical dykes built in the lee of salt marsh platforms subject to the same series of increasingly harsh sea states and water levels. At the end of the test series, the dyke without protective vegetation (shown on the left) suffered significant damage, exposing the core at the seaside crest and causing significant scouring on the leeside. In stark contrast, the dyke fronted by a 4.75 m length of low-density marsh (shown on the right) sustained only minor damage to the leeside crest. Identical dykes protected by medium-density and high-density marshes (not pictured) showed effectively no damage following exposure to identical test conditions. Figure 15 shows a comparison of the overtopping measured at four identical dykes fronted by varying vegetation fields. Out of the 41 sea states examined in Test Series 1, the dykes typically only experienced overtopping as a result of the largest wave heights in combination with extreme water levels. From Figure 15, it is clear that the NoVeg case not only saw overtopping in a greater number of these sea states, but that the overtopping volumes were also significantly larger. It is noted that these overtopping results are notably smaller than predicted by Equation 5.11 from EurOtop (Van der Meer et al., 2018), however this formula likely does not consider a dyke fronted by a long tidal flat. These results emphasizes the potential effectiveness of coastal salt marshes in dissipating wave energy, lessening overtopping and reducing damage of adjacent coastal infrastructure in storm conditions, provided that the marsh itself is able to survive the storm without being damaged.

A detailed investigation of wave overtopping and damage to the dyke structures was not the primary focus of this study; however, some general commentary based on observations made during the testing program is presented herein. Four different dyke structure designs (see Figure 5) were modelled and investigated in Test Series 3 with identical foreshore marshes to help inform decisions concerning potential upgrading of older dyke structures. Analysis of the wave data measured on the tidal flats suggests that the level of wave reflection was similar in each flume, and that the degree of wave attenuation across the model marsh was also similar in each flume.

However, clear differences in overtopping flowrates (and damage) were measured in each flume, depending on the dyke design (see Figure 16). The armoured dyke (requiring a rock armour volume of 15.4 m³ per linear metre of full-scale structure), will be considered as a base case for comparison. The mean overtopping discharge for the armoured dyke, averaged across a broad range of test conditions, was 1 L/s/m. Despite this overtopping, the armour on the leeside crest and slope sustained negligible damage. In comparison, the simply reinforced dyke, with a slightly wider crest but requiring only 7.5 m³/m of rock armouring, saw a 36% reduction in overtopping discharge. However the unprotected leeside crest and slope saw comparatively greater damage, though not serious enough to jeopardize the overall integrity of the dyke.

In comparison, significantly fewer overtopping events and smaller flowrates were measured at the simply reinforced dyke with berm and the widened simply reinforced dyke (74 and 86% reductions in mean overtopping discharge, respectively). Each of these dyke designs requires 15.0 m³ of armour stone per linear metre of structure. The berm was observed to trigger earlier wave breaking, and the additional volume of porous rock in the widened dyke was effective at reducing run-up and overtopping. In both cases, despite the lower overtopping volumes, damage to the leeside crest and slope was similar to that observed on the simply reinforced dyke (without berm), which may point to the high mobility of the impermeable core material under the conditions tested. Overall, the widened simply reinforced dyke was most effective in reducing mean overtopping discharge, however the armoured dyke provided the best protection in terms of leeside stability.

In all four cases, the seaside armouring saw only minor damage, in the form of rocking and/or small displacements. It should be noted that all four dykes saw effectively zero overtopping (or damage to the leeside) in all but the most energetic test conditions featuring the highest water levels combined with the largest wave heights. These results provide information on the relative ability of the upgraded structures to reduce overtopping and limit damage in extreme conditions. The relative benefits of each potential dyke upgrade must be balanced against the relative cost of implementation, which can be assumed to be roughly proportional to the volume of armour stone required.