Barry Gardiner

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

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.

Management of forests to reduce the risk of abiotic damage — a review with particular reference to the effects of strong winds

Abstract This paper describes the process of managing risks to reduce abiotic damage to forests and gives particular emphasis to wind damage and to methods of risk assessment. A detailed description of the ForestGALES wind risk model is used to demonstrate the deterministic/probabilistic approach to risk assessment. The importance of quantitative risk estimation is illustrated by model output comparing a range of silvicultural strategies and site characteristics. The results illustrate how difficult it is to make general statements about risk and how management response has to be ‘context sensitive’. Any response must be appropriate to the level of risk, the options for risk reduction and the implications of damage. Mathematical models provide an opportunity for objectively calculating the risks to forests and will in the future allow forest managers to make informed decisions about how best to manage forests in order to minimise these risks.

THE EVOLUTION OF TURBULENCE ACROSS A FOREST EDGE

An experiment was set-up to investigate the adjustment of turbulence over a roughness transition (moorland to forest). Results from this experiment support the development of an internal boundary layer (IBL) at the transition, which propagates upwards by turbulent diffusion as a function of distance downwind from the transition. Spectra and length-scale results uphold the hypothesis that, over a transition to a rough surface, the variance distribution shifts towards smaller wavelengths/length scales. However, results suggest that the adjustment of streamwise velocity variance may be faster than the adjustment of the vertical velocity variance. The concept of an equilibrium layer developing above the new surface is supported. Fetch requirements for equilibrium are, however, found to differ between first order and second order (flux) statistics, with second order statistics requiring a longer fetch. Results indicate that fetch should exceed 25 times the height of the measurement above the zero plane, which is a 2° (±0.5) growth angle, for flux equilibrium.

WIND AND WIND FORCES IN A PLANTATION SPRUCE FOREST

Observations have been made of the tubulent structure within and above a dense (LAI=10.2) plantation spruce forest along with measurements of the movement of individual trees. The mean statistics of the turbulence and the turbulence spectra are compared with observations in other crops and complementary wind-tunnel studies using 1∶75 scale plastic trees. The measurements show that momentum transport and the subsequent motion of the trees is dominated by intermittent sweep/ejection events associated with ‘honami’ waves moving across the forest. The trees themselves act as forced damped harmonic oscillators and appear to short circuit the normal turbulent energy dissipation process by efficiently absorbing energy at their resonant frequencies. It is argued that understanding the nature and formation of ‘honami’ waves over forests and crops is a crucial problem in agricultural and forest meteorology because of their important role both in turbulent transport and in causing wind damage.

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.

Mechanisms Controlling Turbulence Development Across A Forest Edge

In this paper we discuss the development of turbulence back from the transition fromopen moorland to a forest. Data from a field study and a wind-tunnel experiment arepresented. These show that the variance in the streamwise velocity begins to adjust tothe new surface between 2 to 4 tree heights downwind of the transition. This is soonerthan either the vertical velocity variance or the shear stress, both of which begin to adjust in a zone 3 to 5 tree heights downwind of the edge. Key terms in the prognostic equations for streamwise and vertical velocity variance are evaluated in order to explain these differences. The flow distortion caused by the forest edge, which extends to 4 tree heights downwind of the forest edge, is shown to be crucial in the delayed turbulence development. Initially the shear production term, which is the dominant source for the streamwise velocity variance, is counteracted by a sink in the vertical advection term. After the flow levels out the pressure redistribution (return-to-isotropy) term becomes the main sink of streamwisevelocity variance and feeds energy into the vertical velocity component. Therefore, thedevelopment of the vertical velocity variance and shear stress cannot begin until afterdevelopment of an increase in the streamwise velocity variance. Results are comparedwith other experiments, including the flow across shelterbelts, and large-eddy simulations of forest flow.

WIND FLOWS AND FORCES IN A MODEL SPRUCE FOREST

Wind tunnel tests have been conducted on a 1:75 scale model of a Sitka spruce forest in a correctly scaled turbulent boundary-layer flow. 12000 tree models were manufactured with mass, flexibility and aerodynamic drag characteristics chosen to give dynamical similarity with typical 15 m trees in a 30ms−1 gale. To measure the dynamic response of a sample tree, set within this model forest, a miniature, fast response strain-gauge balance was designed and built. Linked to a computer for on-line data sampling, this balance provided measurements of the fluctuating along-wind and acrosswind components of the overturning moment at ground level, leading to values of mean and extreme moments and the frequency spectrum of the sway motion. Associated measurements of local wind flow characteristics were made with hot-wire anemometers and a laser anemometer. The response of the tree has the characteristics of classical lightly damped vibration and there is evidence that resonant sway motion increases the extreme overturning moments significantly above the values produced by wind gust forces alone.

The effect of wind exposure on the tree aerial architecture and biomechanics of Sitka spruce (Picea sitchensis, Pinaceae)

This paper reports on the effect of wind loading below damaging strength on tree mechanical and physical properties. In a wind-exposed Sitka spruce stand in western Scotland, 60 trees at four different levels of wind exposure (10 m, 30 m, 50 m, 90 m from edge) were characterized for stem and crown size and shape and mechanical properties, including structural Youngs modulus (E(struct)), natural frequency, and damping ratio. E(struct) increased from the stand edge to the mid-forest, but with a large inter-tree variation. Swaying frequency and damping ratio of the trees also increased with distance from edge. Wind-exposed edge trees grew shorter, but more tapered with an overall lower E(struct), allowing for greater flexural stiffness at the stem base due to the larger diameter and for higher flexibility in the crown region of the stem. The trees at the middle of the stand compensated for their increased slenderness with a higher E(struct). Thus, for the different requirements for wind-firmness at stand edge and mid-forest, an adapted combination of tree form and mechanical properties allows the best withstanding of wind loads. The results show the requirement to understand the different strategies of trees to adapt to environmental constraints and the heterogeneity of their growth reactions in response to these strategies.

4 - Understanding how the interaction of wind and trees results in wind-throw, stem break-age, and canopy gap formation

The interaction of wind and trees can result in substantial changes to forest structure and is of interest to many forest ecologists, but the complexity of the relationship has confounded many studies. The result of the interaction can take many forms across a range of scales, may have chronic and acute components, and can be exacerbated by other conditions, such as wet snowfall and salt deposition. Leaves may be abraded, causing subsequent desiccation; young trees may socket (that is, become loosened around the root collar by swaying) and in extreme cases topple because of inadequate rooting; leaders, branches, and crowns may break; older trees may be windthrown when stem and root plate overturn or may experience windsnap when the stem fails above ground level. However, many studies commence after the interaction is complete. Such post event investigation frequently seeks simple relationships and frequently yields disappointing results. There is no escaping the fact that the interaction is complex, and an understanding of the process and response requires the integration of multiple disciplines, such as soil science, physiology, ecology, mechanics, meteorology, and climatology. This chapter seeks to demonstrate that such integration, although difficult, is possible. The chapter also attempts to outline the processes and mechanisms of wind and tree interaction that can be used to understand the likelihood of wind disturbance.

A prism-based system for monitoring the swaying of trees under wind loading

This paper describes a prism-based system for accurate measurement of the stem movement and frequency response of trees under dynamic wind loading. Tree movement was measured along with wind speed at the edge of a stand of Scots pine (Pinus sylvestris L.) close to 11 m in height. A 16 m mast was erected just upwind of the edge and instrumented to measure wind profile and wind direction. One tree located close to the upwind mast was instrumented with a target prism and accelerometers at the mid-canopy level in order to study tree swaying and frequency response. The suitability of this system for measuring the frequency response of trees under field conditions was tested by comparing the mechanical transfer functions for the tree obtained in this way with those from the accelerometers. Good agreement was found at frequencies close to and above the trees natural frequency but differences emerged at low frequencies, suggesting that the accelerometers overestimate the low frequency response. The accuracy and repeatability of stem displacement measurements made using the prism-based system were found in laboratory tests to be very high. The new system can be adjusted quickly to make measurements at different heights on the same tree or on other trees by simply adding additional target prisms.