Development of an individual tree-based mechanical model to predict wind damage within forest stands
Résumé
Models predicting forest stand wind-firmness are usually based on the calculation of a critical wind speed above which the mean tree of a stand is broken or uprooted. This approach is well adapted to regular stands, but in heterogeneous stands, not all the trees are necessarily damaged at the same time. Models used to analyse the distribution of damage within a population of trees can be a good alternative. In this perspective we developed FOREOLE, an individual-based mechanical model of tree response to wind. FOREOLE is based on a numerical description of tree structure allowing both wind and self-weight loads to be calculated at every level of the stem, as well as the bending moment at the tree base and mechanical stresses along the stem.We use a static approach to model wind forces in which the turbulent aspect of wind is taken into account through a gust factor. Stem breakage or uprooting is then predicted from comparisons to failure criteria, i.e. critical bending moment and critical compressive stress, respectively. Implemented in the software called CAPSIS, FOREOLE is compatible with a model of coniferous forest stand dynamics and allows wind-firmness to be simulated both in measured and virtual populations of trees. On individual trees, FOREOLE provided predictions of critical wind speed comparable to the existing models known as GALES and HWIND, despite differences in the method used to describe tree shape and to solve mechanics. These predictions appeared particularly sensitive to the gust factor and the drag coefficient.We then analysed the influence of stand structure, wind speed and individual tree characteristics on the type and amount of damage. From simulations in stands representing three different structures (regular, intermediate and selection stands), we showed that irregular stands experience scattered damage for a relatively wide range of wind speeds, whereas regular stands tend to collapse as a whole above a critical wind speed. Irregularity also increased the ratio between loss in volume of wood and loss in number of trees. Regarding tree characteristics, the highest and the slenderest subjects were the most sensitive, both to stem breakage and to overturning. Sensitivity to breakage was also increased by shorter crowns. In addition, statistical analysis of the simulation results also showed that wind speed remained the most significant variable in explaining wind damage.