Comparison of two models for predicting the critical wind speeds required to damage coniferous trees

Abstract

Two independently developed mathematical models (GALES and HWIND) for predicting the critical wind speed and turning moment needed to uproot and break the stems of coniferous trees were compared and the results tested against field data on the forces experienced by forest trees and the wind speeds required to damage them. The GALES model calculates the aerodynamic roughness and zero-plane displacement of a forest stand. The aerodynamic roughness provides a measure of the stress (force/unit area) imposed on the canopy as a function of wind speed and the zero-plane displacement provides a measure of the average height on the tree at which the wind acts. Together they allow a calculation of the bending moment imposed on the tree for any wind speed. Data from almost 2000 trees uprooted during pulling experiments and destructive sampling of green wood then allow the model to make predictions of the wind speed at which the tree will be overturned and at which the tree will break for a number of coniferous species. The model assumes a linear relationship between tree stem weight and the maximum resistive moment that can be provided by the root system and it assumes that the stress in the outer fibres of the stem induced by the wind is constant with height. In the HWIND model the turning moment arising from the wind drag on the crown is calculated assuming a logarithmic upwind profile. Together with the contribution from the overhanging weight of the stem and branches caused by bending of the stem this provides the total bending moment. The angle of stem bend is explicitly calculated from the stiffness of the stem. The breaking strength of the stem and the support given by the root-soil plate are calculated from previous experiments on timber strength, and tree resistance to overturning by using root-soil plate mass to derive the resistive moment. This allows calculation of the wind speed required to break and overturn the tree. Model comparisons were performed for individual Scots pine (Pinus sylvestris L.) and Norway spruce (Picea abies L.) with varying tree height and stem taper (dbh/height). Tree location was at the forest stand edge on a podzolic soil. Model comparisons gave good agreement for the critical wind speeds at the forest edge required to break and overturn trees with a maximum difference in prediction of 26%. Slightly better agreement was obtained for Norway spruce (mean difference of 10.8%) than Scots pine (mean difference of 12.3%) and the best agreement was for trees with a taper of 100. At higher taper the GALES model generally predicted higher critical wind speeds than the HWIND model whereas at lower taper the reverse applied.

Introduction

The structure and functioning of the boreal forest ecosystem is strongly affected by wind (Ulanova, 2000), and wind damage to trees is a continuing cause of economic loss in managed forests (Gardiner and Quine, 2000). For example, Storm Vivian destroyed 0.46 million hectares (100 million m³ of wood) in Northern Europe on a single night in February 1990. The susceptibility of a stand to wind damage is controlled by the stand characteristics, such as tree height, stocking density, tree diameter, crown area and rooting depth and spread (Fraser, 1962a, Fraser, 1962b, Raymer, 1962, Walshe and Fraser, 1963, Fraser, 1964, Fraser and Gardiner, 1967, Mayhead, 1973a, Oliver and Mayhead, 1974, Papesh, 1974, Savill, 1976, Wangler, 1976, Petty and Worrell, 1981, Mayer, 1985, Petty and Swain, 1985, Coutts, 1986, Lohmander and Helles, 1987). Trees adapt their stem (Telewski, 1995) and root growth (Nicoll and Ray, 1996) in response to the wind loading to which they are subjected in order to resist breakage or overturning. Therefore, damage is most likely to occur where there are sudden changes in wind loading to which the trees are not acclimatised, such as in stands adjacent to recently clear-cut areas (Alexander, 1964, Neustein, 1965, Alexander, 1967, Flemming, 1968, Neustein, 1971, Persson, 1975, Elling and Verry, 1978, Laiho, 1987) or stands thinned intensively (Lohmander and Helles, 1987).

Until recently, studies on wind-induced forest damage have been mainly statistical and have indicated how the properties and position of a tree stand are related to the frequency and size of damage (Laitakari, 1952, Neustein, 1965, Alexander, 1967, Flemming, 1968, Neustein, 1971, Persson, 1975, Solantie, 1983, Miller, 1985, Solantie, 1986, Valinger, 1986, Laiho, 1987, Lohmander and Helles, 1987). By understanding the behaviour of trees in strong winds (Mayer, 1987, Gardiner, 1994, Gardiner, 1995, Peltola, 1996, Blackburn, 1997, Gardiner et al., 1997) and the mechanisms of root anchorage (Deans and Ford, 1983, Coutts, 1986, Ray and Nicoll, 1998) it has become possible to develop mechanistic models that predict the critical wind speeds for damage to occur and how these are affected by the properties of the trees within the stand. Such an approach allows predictions of the impact of any silvicultural operations on tree stability and the design of silvicultural strategies for reducing wind damage. This is not possible with statistical approaches because they do not define the causal links between tree parameters and susceptibility to wind damage, which can be explicitly described in a mechanistic approach.

The aim of this paper is to compare two independently developed mechanistic models for predicting the critical wind speeds and turning moments needed to uproot and break the stem of trees. The models were designed to deal with the particular wind damage problems and silviculture relevant to the country in which they were developed. The HWIND model (Peltola et al., 2000) was developed to predict wind damage to Finnish forests at the stand edge following the creation of new edges and after thinning. The GALES model, which has not previously been reported in the scientific literature, was developed to deal with wind damage in the interior of unthinned or lightly thinned British commercial conifer stands. In order to compare the models it has been necessary to make additions to the GALES model in order to calculate the critical wind speeds at canopy top at the stand edge that will cause damage to the stand edge trees.

Model comparisons were made on individual trees of Scots pine (Pinus sylvestris L.) and Norway spruce (Picea abies L.) of varying height and stem taper positioned at the forest stand edge on a podzolic soil. The sensitivity of each model has been determined by varying the values of each input parameter by set amounts. The predictions of the models have been tested against field data on the forces experienced by forest trees and the wind speeds known to cause wind damage in Scots pine, Norway spruce and Sitka spruce stands. Other model predictions, such as the stem angle at failure, have also been tested against measurements made in field experiments. The validity of the models to predict the risk of wind damage to forests in Great Britain and Finland has been investigated by comparison with the location of wind damage in forests in both countries.

The advantage of comparing two independently developed models is that it provides a test of the various calculation methods and assumptions inherent in each model. Furthermore, it provides a way of assessing the relative strengths and weakness of each approach and allows the possibility of constructing one combined model that is applicable over a wider geographic area.