Woods versus waves: Wave attenuation through non-uniform forests under extreme conditions

Worldwide, communities are facing increasing flood risk, due to more frequent and intense hazards and rising exposure through more people living along coastlines and in flood plains. Nature-based Solutions (NbS), such as mangroves, and riparian forests, offer huge potential for adaptation and risk reduction. The capacity of trees and forests to attenuate waves and mitigate storm damages receives massive attention, especially after extreme storm events. However, application of forests in flood mitigation strategies remains limited to date, due to lack of real-scale measurements on the performance under extreme conditions. Experiments executed in a large-scale flume with a willow forest to dissipate waves show that trees are hardly damaged and strongly reduce wave and run-up heights, even when maximum wave heights are up to 2.5 meters. It was observed for the first time that the surface area of the tree canopy is most relevant for wave attenuation, but that the very flexible leaves hardly add to effectiveness. Overall, the study shows that forests can play a significant role in reducing wave heights and run-up under extreme conditions. Currently, this potential is hardly used but may result in considerable cost savings in


Introduction
Vegetated foreshores, such as marshes and mangroves, are promoted globally for their capacities in reducing impacts of waves, winds and surges [1][2][3][4][5][6] . Besides along coastlines there is also potential for reducing wave heights and run-up in rivers and lakes by floodplain vegetation and riparian forests 7,8 .
Although the capacity of trees to reduce hydrodynamic energy is intuitive, their effectiveness under more extreme events is not well substantiated with quantitative evidence. Numerical models generally oversimplify vegetation by representing it as rigid cylinders 9,10 . Laboratory-flume studies with scaled forests result in parameterized bulk drag values, but these cannot be readily used for realscale extreme situations. Small-scale experiments suffer from scale-effects, such as flow around natural trees representing a multiscale problem, with a large range of length scales of leaves, branches and stems of varying flexibility and higher influence of wall friction from the flume affecting drag coefficients 11,12 .
Previous field and laboratory-flume measurements on wave attenuation over grassy vegetated foreshores and plants show that energy dissipation depends on incident wave energy, ambient water depth, and the (vertical) structure and flexibility of vegetation [13][14][15][16][17]  for forests no such large-scale quantitative evidence exists for storm conditions. Current field observations represent relatively mild conditions with significant wave heights in the range of 0.1 to 0.5 m [19][20][21] . To obtain a quantitative understanding of wave-attenuation capacity of forests under more extreme conditions, we ran real-scale flume tests with various water levels and significant wave heights up to 1.5 m, using both intact and defoliated 15 years old willows (Salix alba) trees.

Experimental set up
We constructed a real-scale willow forest in a wave flume of 300 m long, 5.0 m wide and 9.5 m deep.
The forest existed of 32 willow trees that were placed in 16 rows of 2 to build a 40-meter long forest on an 85-meter-long platform ( Figure 1). The pollard willows (Salix alba) existed of stems that were 15 years old and branches that were 3 years old since the last cutting. Willows were placed with their roots (in a clod) in the sandy base of the platform and fixated by applying a concrete layer of 20 cm as bed. At the back of the forest a concrete levee slope was present ( Figure 1). Wave attenuation by the willow forest and associated run-up on the slope were measured for different water levels in the forest (h = 3.0 and 4.5 m), significant wave heights at the start of the forest at WHM 6 (H m0 = 0.2 m-1.5 m) and different steepness (Sop = 0.02 -0.06). All tests were performed with a JONSWAP wave spectrum and a duration of 500 waves per test to allow for a proper statistical analysis of the wave characteristics. Test series on willows with leaves, without leaves, with a thinned branch density and, as control, without any willows (bare platform) were executed (Table 1, for all tests see Supplementary Information). Wave characteristics were measured in front of the platform, in front of the forest and behind the forest using resistance wave gauges and radar wave gauges. Wave run-up on the slope was measured using cameras, a laser scanner and visual recordings.

Reduction in wave height and run-up through the forest
The wave attenuation effect of the forest was represented as the measured transmitted wave height behind the willow forest (i.e., with leaves, without leaves, reduced branch density), in reference to the case with bare platform (without willows) (Equation 1 in Methods). Plotting the wave attenuation as function of the significant wave height, H m0,i , shows that for constant water depth the wave damping increases as a function of wave height ( Fig. 2A). The maximum wave attenuation by the willow forest is approximately 22% over 40 meters. Maximum attenuation is found for the willow forest with leaves and full canopy (Series 2), as could be expected based on the amount of frontal surface areas around the water line. Wave damping with leaves is 1.5% to 4% (percent point) higher than for a canopy without leaves (i.e., approximately 20% over 40 meters). Wave attenuation with full canopy density but without leaves is 3% to 7% (percent point) larger than with a reduced canopy density (i.e., approximately 15% over 40 meters). Wave attenuation was found to be strongly dependent on water depth. Attenuation for a water depth of 3m is significantly larger than for 4.5m.
As effects of the bottom are already accounted for in our calculation method for wave attenuation, this likely is explained by the fact that the strongest wave damping occurs when the water depth is around the middle of the canopy height (above the trunk), where the tree has most frontal surface area. The loss of biomass during different test series was relatively small. Limited breaking of stems or branches was recorded throughout repeated extreme tests, including average wave heights of 1.5 meter and maximum wave heights of 2.5 meter. It seems that the extreme flexibility of the willow branches limits the amount of actual breaking. The wave attenuation by the willows was also assessed using the measured (reduction in) wave runup on the dike ( Figure 2B). Plotting the relative reduction in wave run-up height (z 2%,no_willows -z 2%,willows ) / z 2%,no_willows ) against the wave attenuation reveals a clear linear relation, and thus a similar magnitude of the reduction effect (i.e., up to 20%). Also, the observed trends are similar, such as an increase in run-up reduction for increasing wave heights and lower run-up reduction for reduced canopy density. Note that in most cases the wave attenuation based on the wave run-up is somewhat lower than the wave attenuation based on the incident wave height. The lower outliers in the graph correspond to tests with a wave height of H m0,i =1.5m, the largest wave heights. For these tests the wave damping based on the wave run-up is somewhat larger than the damping based on the incident wave height.

Implications of measurements for wave-vegetation modelling
Until now, uneven biomass distribution over the vertical and differences between stems, branches and leaves is limitedly included in numerical models. Furthermore, trees are mostly assumed to behave as a rigid material under extreme hydraulic forces. We utilized the new measurements, to validate models representing wave attenuation by vegetation. For this, the spectral wave model SWAN (Simulating Waves Nearshore) 22 was used. This model was used in similar studies on wave attenuation over vegetated foreshores 8,10,14 and is frequently used in engineering practice. Suzuki et al. (2011) implemented the effects of vegetation in SWAN based on the phase-averaged wave energy dissipation model due to rigid stems for irregular waves 23,24 . The vegetation model is based on bulk wave dissipation (integrated over all wave frequencies), which is dependent on the incoming wave energy, the water depth and the vertical structure of the vegetation (Equation 2 in Methods).
In previous work the vegetation is described by a single branch diameter (b v ; m) and density (N v ; m -2 ) per vertical elevation level 10,24 . However, plants have different branches of different sizes and densities. Therefore, this was rewritten into a single parameter f i (z) (m 2 /m 3 ), which described the total frontal area per unit volume, instead of b v N v (m/m 2 ), that is generally used. This parameter is determined for the present trees by counting all branches at breast level, measuring their diameter and then applying the branching model of Jarvela (2004) 25 (Figure 3a). Only branches larger than 3 mm were considered.
For vegetation-wave models, especially the value of the bulk drag coefficient (̃) has been subject to debate. For flexible vegetation the value of this factor is reduced compared to the value for rigid cylinders because flexible vegetation moves with the flow, which results in less drag force experienced by the vegetation 26 . The ̃ parameter relies on complex physics (e.g., skin friction, pressure differences, swaying of vegetation), which in turn depend on the vegetation properties in relation to the hydraulic conditions 14 . Therefore, instead of determining the ̃ values a-priori, several studies have attempted to calibrate the ̃ values to measurements and relate them to the Reynolds number [27][28][29][30] or the Keulegan-Carpenter number KC 24,31-33 .
Here, the ̃ versus the KC number, ̂ ⁄ was obtained for the present tests ( Figure 3b). The KC number that is used here is based on the spatial weighted average of branch diameter and velocity, With: H m0 the significant wave height behind the forest This method to assess wave attenuation proved most reliable, since it allowed us to exclude effects of wave reflection and damping effects of the platform (which resulted in additional wave attenuation of 2 to 18%). Also, wave run-up on the slope was measured using cameras, a laser scanner and visual recordings. ) (see Figure S4 in Supplementary Information). Relevant tree data was gathered manually, among which: the total number of branches per class for each tree at breast height, the and branch length for 340 branches, and detailed sketches of 9 primary branches. The total amount of leaves were gathered and dried (at 60 °C for 48 hrs) in order to measure the total dry weight. Also, bending tests were conducted to obtain the flexural rigidity for different segments of the primary branches. (

2)
Where 〈 〉 is the averaged wave energy dissipation due to vegetation, ̃ the bulk drag coefficient, the gravitational acceleration constant, the mean wave number, the portion of the water depth covered by vegetation for layer i, ℎ the water depth, the significant wave height, and f i the total frontal width of vegetation per surface area for layer i, which is equivalent to the generally used b v,i N v,i .
A correlation was found between the bulk drag coefficient (̃) and the KC number 34 , as shown in

Statement on plant materials
Experiments in this research were executed with cultivated willow species (Salix alba) of 15 years old that were obtained from a Dutch private site. Trees were replaced with new younger trees. Salix alba does not occur on the list of threatened species for the Netherlands and is labeled as stable.

Determination of frontal surface area distribution
According to the branching ordering scheme, based on the work of Jarvela (2004), the lowest order begins at the tip of the branches and approaches the highest order (usually the trunk). It requires the following initial parameters, namely: , ℎ ℎ , ℎ ℎ , ℎ ℎ , where d min is the diameter of the smallest branch, N high , d high and L high are respectively the number of branches, the diameter and the length of the highest order branches. A description of the steps can be found in the paper by Jarvela   In this study the values and method were adjusted to account for the branching structure of pollard willows. Firstly, the initial parameters were determined for each branch class as shown in Table S3. Secondly, instead of averaging the branching factors over all the orders, we maintained separate values for them as shown in Table S4. The branching factors ( , , ) were applied starting at the highest order branches (in this case, the primary branches extending from the trunk), to calculate the diameters (d), number of branches (N) and length (L) of the subsequent order branches till the lowest order branch with a diameter of d min =3 mm. The total frontal surface area for each branch class is calculated by N* d* L and taking the sum of the frontal area per order, an example for branches of class 1 is shown in Table S5. By repeating the same procedure for the other branch classes, and taking the sum of these areas, the total frontal surface area of one tree is determined (excluding the frontal area of the trunk). This method assumes linear decay of frontal area over the height and uses cylinder shapes for the branches in each order to calculate the frontal surface area. Therefore, we applied a factor of 0.5 to the frontal area results per order, to account for cone shapes instead of cylinders. Lastly, we used measurements from a single tree to determine the distribution of the total frontal surface area over the height.

Determination of KC
The KC number or period parameter defines the ratio of the distance traversed by a fluid particle during half a wave period to the diameter of the cylinder, according to the definition by Keulegan and Carpenter (1958). The table below shows an overview of the test conditions and ways in determining the KC number, used in some reference studies, indicating possible explanations for deviations seen in Figure 3b. For instance, other references use the total width per tree/plant, which has no direct physical meaning in the sense of the original definition of the KC number. is the maximum intensity of the sinusoidal current, T is the wave period and D is the diameter of the cylinder. This means that even though the scale is large, the boundary layer around the branches is still laminar, such that the drag crisis, a fluid dynamics phenomenon which can reduce the drag coefficient and thereby the energy dissipation by a factor of 4, was mostly not reached. The drag on the stem is expected to have reached the drag crisis for a small percentage of the most extreme waves.