A mathematical model to describe the dynamic response of a spruce tree to the wind

Abstract

A mathematical, computer-based, dynamic sway model of a Sitka spruce (Picea sitchensis) tree was developed and tested against measurements of the movement of a tree within a forest. The model tree was divided into segments each with a stiffness, mass and damping parameter. Equations were formulated to describe the response of every segment which together form a system of coupled differential equations. These were solved with the aid of matrices and from the resulting modes, the transfer function of the tree was found and used to calculate the movement of the tree in the wind. Comparison of the modelled movement of a tree in response to the measured wind speed above a forest canopy gave good agreement with the measured movement of the top of the tree but less satisfactory agreement close to the base. The comparison also pointed to the complexity of tree response to the wind and inadequacies in the model. In particular, the branches need to be treated as coupled cantilevers attached to the stem rather than simply as masses lumped together.& k w d : Key words Wind Damage · Tree Movement · Modelling& b d y :

The periodic motion of lodgepole pine trees as affected by collisions with neighbors

“…In closed forest canopies, tree sway is thought to be mostly dampened by collisions with neighbors (Milne 1991) but this has not been effectively addressed in the literature. With little empirical evidence, theoretical sway models did not include collision damping but used sway data from isolated trees or parameterized the influence of collisions by inducing sway of a target tree with stationary neighbors (Baker 1995;England et al 2000;Kerzenmacher and Gardiner 1998;Saunderson et al 1999).…”

Influence of clear-cutting on the risk of wind damage at forest edges

“…In principle, the susceptibility of a stand to wind damage is controlled by tree and stand characteristics such as tree species, tree height, tree diameter, crown area, rooting depth and width, and stand density, which are in turn determined by forest management (Coutts, 1986;Gardiner, 1995;Gardiner et al, 1997;Lee and Black, 1993;Kerzenmacher and Gardiner, 1998;Peltola et al, 1999aPeltola et al, , 2000Dunham and Cameron, 2000;Zhu et al, 2000). Furthermore, large differences in the risk of wind damage can be observed between regions and locations that differ in their topography and/or climate (Copeland et al, 1996;Peltola et al, 1999b;Quine, 2000;Proe et al, 2001).…”

Modelling natural disturbances in forest ecosystems: a review

“…For example, Boose et al (2001) used a modified version of Fujita's (1987) scale, a widely applied descriptive system for assessing wind damage, which qualitatively accounts not only for stem breakage or uprooting but also for damages to leaves and branches in lower damage classes. The importance of branches and twigs and their behaviour under strong winds is, however, increasingly recognized also in mechanistic sway models (Kerzenmacher and Gardiner, 1998;James et al, 2006).…”