Geometrical Mangrove Models

Quantifying frontal surface area distribution for Avicennia marina vegetation: an important parameter for estimating wave attenuation

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Abstract

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.