To estimate wave attenuation by mangrove forests, trees are often schematized as uniform cylinders (over the height) representing a tree’s stem. However, trees have more complex geometrical features that influence the interaction between waves and tree structures. Recent studies have shown that the frontal surface area distribution over the height Av(z) is a crucial parameter for estimating wave attenuation by vegetation (Kalloe et al., 2022; van Wesenbeeck et al., 2022) because it can account for complex geometrical features. This study aims to model the complex geometry of the Avicennia marina mangrove species. The research question then becomes: How to construct geometrical tree models of Avicennia marina vegetation and how to obtain the projected frontal surface area distribution over the height, Av(z)? In this study, manual measurements were performed to obtain tree structure parameters. Both canopy and root measurements were conducted for Avicennia marina vegetation with varying characteristics (age and density). Two saplings (approximately 1.5 years old) with variable canopy densities and two young trees (around five years old) with varying canopy densities were measured. We stored canopy measurements in a so-called tree data structure consisting of nodes (representing the branches) that contain information about the individual branches, such as branch orders, -lengths and -diameters and edges, which are links that establish direct relations from one branch to another. After that, we developed a search tree algorithm to loop through all tree data, compute parameters of interest and store the results in assigned data arrays. Parameters of interest to obtain after the data analysis were branch dimensions and diameter ratios of branches (between various branch classes). This information was necessary to create a blueprint for constructing geometrical tree models. Tree modelling started with the construction of a root (pneumatophore) model. Additionally, the frontal surface area of these roots was computed and displayed as a function of the height. In addition to the root model, we constructed two canopy models. The first model is based on relations between branches and can be called deterministic or dependent (canopy model 1). The second canopy model (canopy model 2) generates branch dimensions based on the normal distribution of branch diameters and is, therefore, more probabilistic with branches independent of each other. Both canopy models construct branches based on information travelling from preceding branches. The models account for the proper placement of branches within 3D space by rotations and translations. The algorithm computes and outputs the projected frontal surface area over the height of a system of branches for a given direction (XZ-plane projection or YZ-plane projection). We validated the two canopy/tree models against validation measurements. Three trees were divided into seven vegetation layers, and branches were registered that intersected with the layers. As a result, estimation could be made on the frontal surface area per layer. This study found that the frontal surface areas due to roots and canopies are significant and are well represented by the parameter Av(z). The contribution of the roots and canopy cannot be neglected in modelling wave dissipation by vegetation. The contribution of smaller branches to the total Av is significant, proving that considering only the tree stem is an underestimation. Moreover, the research shows that it is possible to develop a geometrical tree model based on a set of measurements and design rules that follow from observations, at least for the considered tree species. We could extrapolate and interpolate our results to generate tree models for a wide range of tree ages. Additionally, it is possible to create a forest by generating multiple trees. Both tree models (1 and 2) showed little differences in Av(z) during the model validation process. Moreover, the validation measurements led, in general, to an overestimation of the total frontal surface area. Consequently, model validation was inconclusive regarding both tree models. However, we found that constructing tree models according to tree/canopy model 1 is preferred because it resembles an L-system more and is more practically applicable in computer models. We can improve future tree models by collecting more measurements regarding branch structures and root distribution as a function of tree age. This will result in increased model reliability.

Conventional dike reinforcement measures do not take vegetation into account, while vegetation contains wave damping properties. Reasoning for this is that vegetation in general is seen as temporary and hence may be removed in the future. In this case study for the Dutch waterboard WDOD, the wave damping properties of vegetation in a floodplain along the river IJssel (Duursche Waarden) are studied. Duursche Waarden consists of mostly willow species and is adjacent to a dike. It is part of Natura2000 and hence it is a protected vegetation area and not considered to be temporal. A general approach is developed for similar sized (riparian) forests as Duursche Waarden (1.1 km2) to map the vegetation and obtain the vegetation parameters. This approach is also applied to Duursche Waarden. First of all the different vegetation areas within the riparian forest are identified with the help of aerial photos and field observations after which they are prioritised with the help of a Multi Criteria Analysis. The prioritised vegetation areas are divided into uniform and non-uniform areas and studied in detail. Uniform and non-uniform areas are distinguished based on tree species, structure, height and density with the help of field observations, aerial photos and airborne Light Detection and Ranging (LiDAR) data. A representative distribution of the vegetation parameters over the different vegetation areas is obtained with the help of one method. The vegetation parameters interesting for wave damping are the frontal area per volume and the bulk drag coefficient of leafless vegetation. Leafless vegetation is of interest since most extreme storms occur in winter. On top of that leaves seem to have insignificant contribution to wave damping in the full scale physical experiments of white willow trees conducted in the Delta Flume at Deltares. These experiments were performed in 2018. A new definition is introduced for the frontal area per volume. The frontal area density distribution over the height is estimated with the help of point clouds retrieved from TLS measurements and validated with hand measurements and studies of similar vegetation. Two methods are used in estimating the frontal area with the help of literature: the alpha shape and grid method. These methods are used for merged point clouds from Multiple Scanning Stations (MSS) and a point cloud from a Single Scanning Station (SSS). The SSS method includes a shadowing correction factor. Finally, the values of the frontal area per volume are chosen based on assessing the outcomes of the MSS method, SSS method and hand measurements. The bulk drag coefficient is estimated using selected values from literature. Dense vegetation contains relatively higher values for the vegetation parameters than sparse vegetation. This will result in more wave energy dissipation and hence more wave damping for dense vegetation. The frontal area per volume of sparse to moderate dense woody vegetation (values on average of about 0.01-0.20 m-1) in uniform areas is believed to estimated best and most efficiently with the MSS method. In non-uniform areas hand measurements are believed to be estimated best and most efficiently by hand measurements. The frontal area per volume of dense woody vegetation (values on average greater than 0.20 m-1) is most uncertain. Therefore, both hand and TLS measurements (with the SSS method) should be used to estimate the frontal area per volume. The wave attenuation by vegetation is estimated using the numerical wave model SWAN 1D and 2D computations including and excluding vegetation using the obtained vegetation parameters. No currents are included. Hydraulic conditions of Hydra-NL calculations using Bretschneider are used for both SWAN 1D and 2D computations. A comparison between Hydra-NL and SWAN 1D computations including model uncertainty for exactly the same conditions show similar outcomes for SWAN. SWAN 1D computations showed wave attenuation due to vegetation with a magnitude of 0 to about 44 cm for all dike locations adjacent to Duursche Waarden. SWAN 2D computations without vegetation show significantly lower outcomes than 1D computations without vegetation: on average about 12 cm. This difference is explained by refraction and directional spreading resulting from the spatial variability in water depth and fetch of the studied area. Therefore the studied area is believed to be better described by 2D computations. One combination of the wind direction and water level is proven to be governing for all dike locations. Following 2D computations, the failure mechanism ‘erosion of the outer slope’ with a return period of 66666 year results in an estimated maximum wave height of 77 cm for dike locations adjacent to Duursche Waarden. This is a reduction of about 23 cm compared to the results of Hydra-NL. Indicative calculations suggest that dike reinforcements are still needed at Duursche Waarden. The wave damping is estimated to be 16 to 24 cm at dike locations adjacent to relatively large vegetation areas of sparse to dense vegetation. Dike locations at which the significant wave height is the greatest are called critical dike locations. The wave damping for these critical dike points is estimated to vary between 4 to 7 cm. In a report by Deltares an overview is made of promising wave damping foreshores in the Netherlands. Rough estimations show possible wave damping at Duursche Waarden of about the same order of magnitude as found in this study. Also studies on similar vegetation show significant greater values for the wave damping, suggesting rather conservative than optimistic outcomes in this study.

This work seeks to expand on the research done previously by the WOODY group on the ability of vegetation as a form of wave damping. Specifically in this work, we are looking at pollard willow trees (Salix Alba) and the relationship between the motion of the object and the forces it can induce on the wave flow. This was done by testing a range of stiff and flexible conical mimics of three different sizes and varying moduli of elasticity across multiple water levels. The results were compared to commonly used relationships for predicting object motion such as Cauchy, KC, and CAL/KC (Jacobson). Due to the non-constant cross-sectional area of a conical object. However, the relationships could not fully capture the motion. As such a new equation was fitted and derived from the relationships that better captured the motion of the mimics under wave flow. This equation relates the peak forces felt by the objects to the peak deflection. Which can be used as an indicator of wave damping. Along with this number thresholds for motion were also derived from the data. It was found that when an object tip has deflected 2 degrees or less it can be considered completely stiff. If deflecting between 2 and 5 degrees it can be considered relatively stiff, however, high-frequency flow effects can cause discrepancies in the forces between tests.

The wave attenuation of vegetation plays an increasingly important role in flood control in coastal areas. Past studies have found that the interaction of waves with vegetation mainly depends on hydraulic conditions and vegetation characteristics. Therefore, it is necessary to build vegetation models and quantify vegetation characteristics related to wave attenuation. Mangroves are one of the typical tropical intertidal vegetation. This study aimed to test the potential of using a low-cost, convenient smartphone-based structure-from-motion with multi-view stereo-photogrammetry (SfM-MVS) to accurately measure mangrove parameters related to wave attenuation. SfM-MVS is a computer vision technique in which the point cloud coordinates of an object can be calculated from a series of 2D photos to generate a 3D point cloud model. This study first tested the optimal photography distance （about 25cm） and optimal weather conditions （cloudy and no sunlight） using the smartphone-based SfM-MVS method. Then, based on the optiaml usage conditions, 3Dpoint cloud models of 10 individual mangrove samples were reconstructed using this method, then the mangrove parameters related to wave attenuation were estimated according to the model: linear parameters (tree height, crown diameter, stem diameter, branches diameter) and the frontal area at a certain height. The true values of these parameters were measured using traditional hand measurements to evaluate smartphone-based SfM-MVS-derived parameter estimates. The results show that the estimation of the linear parameters of the mangroves generally achieves high accuracy (RMSE of tree height, canopy diameter, stem diameter and thick branch diameter are all lower than 15%). There were significant negative biases in the estimates of tree height and crown diameter, and no significant biases in the estimates of stems and branches. The results of linear regression show that there is a strong positive correlation between the estimated values of all parameters and the true values. There are large errors and negative biases in the estimates of the frontal area at different heights. Overall, RMSE of frontal area at a certain height is 45.58% with a bias of -38.83%. This result showed that the SfM-MVS model resulted in a large underestimation of the frontal area at each height. A series of analyses showed that the main reason for the large error in the frontal area at a certain height was that the terminal branches with the lowest branch order (smallest diameter) were difficult to visualize in the SfM-MVS model. And this part of the branches actually occupies a large proportion of the frontal area. This study demonstrates that smartphone-based SfM-MVS is capable of estimating mangrove tree height, canopy diameter, stem diameter, and thick branch diameter. Its accuracy is comparable to other existing methods such as TLS, ALS, camera-based SfM-MVS. However, the resolution is insufficient for very thin branches (<=5mm), which makes the method inaccurate in estimating the frontal area at a certain height. Factors such as photography distance and ambient lighting can affect the accuracy of the model. Compared with the currently used remote sensing technologies such as TLS, the smartphone-based SfM-MVS has the advantages of low cost, high flexibility, and low difficulty for those who lack professional knowledge or training, which makes it an alternative with great potential.