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

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.