Improving statistical windthrow modeling of 2 Fagus sylvatica stand structures through mechanical analysis

Abstract

In 1999, the major windstorm, Lothar, damaged many beech stands on the French Lorraine limestone plateau. Some of them were coppices with standards (CWS) while others were high forest (HF) stands. The use of statistical models to compare the wind firmness of different stand structures is often limited by poor estimates of the individual wind loading. Available knowledge about the mechanics of windthrow processes such as wind loading could improve statistical modeling. Our aim was to identify the main trees and site risk factors for beech and to compare wind firmness of both stand structures by fitting such a model. We developed a windthrow model with mixed effects, which is based on a simplified mechanical analysis of the wind-induced stresses and Weibull’s theory of fracture. This analysis revealed the relevancy of including the product of the crown diameter and the square of the tree height, known as the bending moment coefficient, in the model. The Weibull-based model was compared with multiple logistic regressions. Both models were fitted using tree and site factors on 384 dominant beeches (196 in CWS and 188 in HF) from 51 plots with comparable site conditions between the two stand structures.Damage mainly increased with tree height, although it also slightly increased with crown width. The bending moment coefficient used in the Weibull-based model more effectively accounted for tree size and tree shape effects than the logistic regressions.Stand structure showed an interesting second-order effect since the increase of risk with the increase of the bending moment coefficient was higher for HF. Including a random plot effect significantly improved the model likelihood and, therefore, took partly wind-induced spatial variability into account. To apply Weibull’s theory to windthrow, many assumptions that require further investigation must be made regarding the brittle behavior and the distribution of stresses in the root-soil plate.