An architectural understanding of natural sway frequencies in trees

Abstract

<jats:p>The relationship between form and function in trees is the subject of a longstanding debate in forest ecology and provides the basis for theories concerning forest ecosystem structure and metabolism. Trees interact with the wind in a dynamic manner and exhibit natural sway frequencies and damping processes that are important in understanding wind damage. Tree-wind dynamics are related to tree architecture, but this relationship is not well understood. We present a comprehensive view of natural sway frequencies in trees by compiling a dataset of field measurement spanning conifers and broadleaves, tropical and temperate forests. The field data show that a cantilever beam approximation adequately predicts the fundamental frequency of conifers, but not that of broadleaf trees. We also use structurally detailed tree dynamics simulations to test fundamental assumptions underpinning models of natural frequencies in trees. We model the dynamic properties of greater than 1000 trees using a finite-element approach based on accurate three-dimensional model trees derived from terrestrial laser scanning data. We show that (1) residual variation, the variation not explained by the cantilever beam approximation, in fundamental frequencies of broadleaf trees is driven by their architecture; (2) slender trees behave like a simple pendulum, with a single natural frequency dominating their motion, which makes them vulnerable to wind damage and (3) the presence of leaves decreases both the fundamental frequency and the damping ratio. These findings demonstrate the value of new three-dimensional measurements for understanding wind impacts on trees and suggest new directions for improving our understanding of tree dynamics from conifer plantations to natural forests.</jats:p>

Time for a Plant Structural Economics Spectrum

“…Recently, a first synthesis effort (Jackson et al, 2019) on more than 1,000 TLS scanned trees from multiple locations across the globe was done to study wind-tree interactions and natural sway frequencies. Based on the structural metrics from that study, we can demonstrate the existence of a SES using a principle component analysis (PCA) (Figure 2).…”

“…The included architectural metrics are: Top-heaviness (ratio of total woody volume in the crown to the stem woody volume), relative crown width (ratio of maximum crown width to tree height), aspect ratio (ratio of maximum crown width to crown height), crown area (maximum ground area covered by the crown viewed from above), DBH (stem diameter at breast height), crown density (ratio of crown area to woody volume in the crown), height (total tree height), mass taper exponent (exponent of a power law fit to the vertical profile of volume), path fraction (ratio of mean to maximum base-to-twig path length), crown asymmetry (the reatio of maximum to mean of 8 angular crown segments) and branching angle (the average angle between two cylinders at each branching point). More information on the underlying data can be found in the original study of Jackson et al (2019). woody ecosystems in a much more general way, crucially allowing testable predictions to be made about the relationships between ecosystem structure and function and vice versa.…”

Time for a Plant Structural Economics Spectrum

“…In conclusion, we expect that the structural economics spectrum will help to functionally describe tree species and FIGURE 2 | Illustration of how a multidimensional structural trait space can be decomposed in a few dominant axes which form the basis of a structural economics spectrum. This figure is modified from Jackson et al (2019). The figure shows the two main axes of variation resulting from a principal component analysis executed on structural trait data extracted from cylinder models of TLS 3D point clouds from 1,213 trees from temperate and tropical ecosystems.…”

“…The included architectural metrics are: Top-heaviness (ratio of total woody volume in the crown to the stem woody volume), relative crown width (ratio of maximum crown width to tree height), aspect ratio (ratio of maximum crown width to crown height), crown area (maximum ground area covered by the crown viewed from above), DBH (stem diameter at breast height), crown density (ratio of crown area to woody volume in the crown), height (total tree height), mass taper exponent (exponent of a power law fit to the vertical profile of volume), path fraction (ratio of mean to maximum base-to-twig path length), crown asymmetry (the reatio of maximum to mean of 8 angular crown segments) and branching angle (the average angle between two cylinders at each branching point). More information on the underlying data can be found in the original study of Jackson et al (2019).…”

Monitoring Tree Sway as an Indicator of Water Stress

“…The oscillating behavior that follows has a natural sway frequency. Models have related the dominant natural sway frequency to tree architectural parameters, including the diameter at breast height (DBH), height, mass, and stiffness (Jackson et al, 2019;Moore & Maguire, 2004). We employ a relationship that assumes a tree can be modeled as a cantilever beam with distributed mass and without a top load (Gardiner, 1992):…”