An architectural understanding of natural sway frequencies in trees

Authors

Affiliations

Toby Jackson

School of Geography and the Environment, University of Oxford

Alexander Shenkin

School of Geography and the Environment, University of Oxford

John Moore

Scion, Rotorua, New Zealand

Amanda Bunce

Department of Natural Resources, University of Connecticut

Tim van Emmerik

Water Resources Section, Delft University of Technology

Brian Kane

Department of Environmental Conservation, University of Massachusetts Amherst

Daniel C. Burcham

Centre for Urban Greenery and Ecology, National Parks Board, Singapore

Ken James

Melbourne

John Selker

Department of Crop and Soil Science, Oregon State University

Kim Calders

Department of Environment, Ghent University

Niall Origo

National Physical Laboratory

Mathias Disney

Department of Geography, University College London

Andrew Burt

Department of Geography, University College London

Phil Wilkes

Department of Geography, University College London

Pausi Raumonen

Tampere University of Technology

Jose Gonzalez de Tanago Menaca

Laboratory of Geo-Information Science and Remote Sensing, Wageningen University

Alvaro Lau

Laboratory of Geo-Information Science and Remote Sensing, Wageningen University

Martin Herold

Laboratory of Geo-Information Science and Remote Sensing, Wageningen University

Rosa C. Goodman

Department of Forest Ecology and Management, Swedish University of Agricultural Sciences

Thierry Fourcaud

AMAP, University of Montpellier

Yadvinder Malhi

School of Geography and the Environment, University of Oxford

Abstract

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.

Illustrative figure

Figure 1: Simulated fundamental sway frequency of a tree. Finite-element simulation output showing the two extreme positions (blue and red) for a sycamore tree (Acer pseudoplatanus) swaying at its fundamental frequency, f₀ = 0.26 Hz.

Materials

• Paper (final version)

BibTeX citation

@article{Jacksonetal:2019,
    Author = {Toby Jackson, Alexander Shenkin, John Moore, Amanda Bunce, Tim van Emmerik, Brian Kane, Daniel C. Burcham, Ken James, John Selker, Kim Calders, Niall Origo, Mathias Disney, Andrew Burt, Phil Wilkes, Pausi Raumonen, Jose Gonzalez de Tanago Menaca, Alvaro Lau, Martin Herold, Rosa C. Goodman, Thierry Fourcaud, and Yadvinder Malhi},
    Doi = {10.1098/rsif.2019.0116},
    Journal = {Journal of the Royal Society Interface},
    Month = {6},
    Pages = {20190116},
    Title = {An architectural understanding of natural sway frequencies in trees},
    Volume = {16},
    Issue = {155},
    Year = {2019}}