C R I T I C A L T U R N I N G M O M E N T S A N D D R A G E Q U A T I O N S F O R BRITISH C O L U M B I A CONIFERS by KENNETH EARL BYRNE B.S.F. (Forest Resources Management) University of British Columbia, 2001 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES (Forestry) THE UNIVERSITY OF BRITISH COLUMBIA April 2005 © Kenneth Earl Byrne, 2005 Abstract Tree winching experiments were conducted for 4 British Columbia (BC) tree species: western redcedar (Thuja plicata (Donn ex D. Don) Spach), western hemlock (Tsuga heterophylla (Raf.) Sarg.), and lodgepole pine (Pinus contorta Doug, ex Loud.), and hybrid spruce (Picea engelmannii Parry XPicea glauca (Moench) Voss). Strong linear relationships between stem mass and critical turning moments were found. Based on the slope coefficients, lodgepole pine (145.6), hybrid spruce (118.6), western redcedar (94.5), and western hemlock (77.4) have different critical turning moments with respect to mass. Comparison with results for trees in the United Kingdom (UK) tree winching database indicated that there is a difference between the slope coefficients for BC pine and pine grown in the UK on equivalent soils. Wind tunnel experiments with juvenile crowns of the hybrid spruce were compared with results from earlier experiments with redcedar, hemlock and lodgepole pine. Static and dynamic drag coefficients, and mass versus drag relationships were examined. Differences in drag coefficients exist for species with different foliage characteristics, however, differences in the mass/drag relationships were less pronounced. Critical turning moment and drag results were used to adjust selected parameters in the UK Forestry Commission's mechanistic windthrow risk model 'ForestGALES' to estimate critical wind speeds for the four BC species and for lodgepole pine and hemlock grown in the UK. UK grown trees have higher critical wind speeds than trees of the same species grown in BC. More work is required to adjust ForestGALES to reflect the differences in tree form and mechanical attributes for BC species and to validate model predictions. Table of Contents Abstract 'i Table of Contents i» List of Figures v List of Tables • vi Acknowledgements v ' i 1.0 Introduction 1 1.1.0. E X P E R I M E N T A L O B J E C T I V E S 2 2.0 Literature Review 3 2.1.0. N A T U R E O F W I N D T H R O W A N D P R E D I C T I O N A P P R O A C H E S 3 2.2.0. W I N D T H R O W M E C H A N I C S : R E S I S T I V E F O R C E C O M P O N E N T S 6 2.2.1. Stem Stiffness and Strain 6 2.2.2. Branch Stiffness and Strain-. 12 2.2.3. Rooting Strength and Strain / 3 2.2.4. Soil Strength 14 2.2.5. Damping 15 2.2.6.0. Techniques used to measure resistive force components / 6 2.3.0. W I N D T H R O W M E C H A N I C S : A P P L I E D F O R C E S 17 2.3.1. Drag Forces 18 2.3.2. Self-loading Forces 23 2.3.3. Sway Forces 24 2.3.4.0. Techniques used to measure drag forces 25 2.4.0. F O R E S T G A L E S M O D E L O V E R V I E W 26 3.0 Critical Turning Moments for four BC Conifer Species 27 3.1.0.0. M E T H O D S 29 3.1.1.0. Site Selection 29 3.1.2.0. Trial Procedures 32 3.1.3.0. Tree instrumentation 34 3.1.3.2. Measurements of tree and study site attributes 34 3.1.3.3. Calculated Variables 35 3.1.3.4. Analytical procedures 38 3.2.0.0. R E S U L T S A N D D I S C U S S I O N 39 3.2.1.0. Characterizing stem cwvature and pivot point 40 3.2.2.0. Selection of candidate predictor variables and comparisons between mode offailure, site, and year of winching factors 49 3.2.3.0. Critical turning moment regressions 51 3.2.3.1. Predictor variables for BC species •. 51 3.2.3.2. Differences between BC grown species '. 54 3.2.3.2. UK Species 56 3.2.4.0. Allometric equations for BC species 57 3.3.0.0. C O N C L U S I O N S 59 4.0 Drag relationships for four BC conifers 61 4.1.0.0 M E T H O D S 63 4.1.1. Wind Tunnel Description and Layout 63 4.1.2. Trial Procedures 64 4.1.2. Data analysis 66 4.2.0.0. R E S U L T S A N D D I S C U S S I O N 66 4.3.0.0. C O N C L U S I O N S 74 iv 5.0 Sensitivity of ForestGALES to Critical Turning Moments and Drag 77 5.1.0. I N T R O D U C T I O N T O F O R E S T G A L E S M O D E L 78 5.1.1. Calculation of critical wind speed 79 5.2.0. M E T H O D S 82 5.2.1. Adjustments to ForestGALES required to add new species 82 5.3.0. R E S U L T S A N D D I S C U S S I O N 85 5.3.1.0. Within species comparisons of critical wind speed predictions using the profile and roughness methods : 86 5.3.2.0. ForestGALES predictions among BC species 90 5.3.3.0. ForestGALES predictions for the same species in BC and the UK 92 5.4.0. C O N C L U S I O N 94 6.0 Conclusions and Recommendations 96 References 99 Appendix 1 - Detailed Explanation of "Spline Method" 102 Appendix 2 - Detailed Explanation of "Coordinate Method" 105 Appendix 3 - Detailed Explanation of the Calculation of the Critical Turning Moment 106 Appendix 4 - System diagram of ForestGALES modules ....108 Appendix 5 - Pearson's correlations for dendrometric variables 109 Appendix 6 - Tree Failure Modes 110 V List of Tables Table 3.1. Summary of trees winched with number and percentage uprooted and broken 40 Table 3.2. Differences between moments calculated for each species using the coordinate and spline methods. 46 Table 3.3. Table of differences between moments calculated for each species using an offset pivot and a pivot at the base [p-values] 48 Table 3.4. Pearson's correlation coefficients for the selected predictor variables and for critical turning moment. 49 Table 3.5. Summary of contrasts between broken and uprooted trees for all the predictors 50 Table 3.6. Summary of contrasts between the two spruce sites 50 Table 3.7. Table of contrasts for hemlock and redcedar winched in Year 1 and Year 2 51 Table 3.8. Table of regressions to predict critical turning moments for all British Columbia species using four predictors 52 Table 3.9. Summary of root and tree characteristics influencing stem breakage and uprooting 53 Table 3.11. Slope coefficients relating stem mass to critical overturning moments in Quebec and BC 55 Table 3.12. Summary of regressions for lodgepole pine from BC and the UK 56 Table 3.13. Summary of allometric regressions for BC species 58 Table 4.1. Average sample tree characteristics for hybrid spruce (S), western redcedar (C), western hemlock (H), and lodgepole pine (P) 66 Table 4.4. Models for predicting crown drag (units in Newtons) for spruce and compared with prior models for hemlock, redcedar and pine 71 Table 5.1 Comparison of existing parameters for UK grown species with same parameters adjusted for BC grown species 84 Table 5.2. Average differences between the profile minus the roughness method with respect to predictions of critical wind speed (a = 0.05) 87 Table 5.2. Return periods (years) for peak hourly mean wind speeds and peak gust speeds (Mitchell 1999).91 Table 5.3. Dynamic drag coefficients for BC tree species 94 vi List of Figures Figure 2.1 Diagram of a bent and snow-loaded tree. The weights of the snow (S), crown (C) and stem (T) all exert clockwise bending moments, given for each by the product of weight and lever arm (1). These are opposed by the resistive bending moment (M) produced by the elasticity of the stem (Petty and Worrell 1981) 9 Figure 2.2. Schematic representation of the contribution of components of anchorage to the total turning moment during uprooting (Courts 1983) 14 Figure 2.3. Velocity at which breakage or overturning will occur versus tree height for trees on different soil types (Fraser and Gardiner 1967) 18 Figure 2.4. Drag coefficients regressions for individual trees over a range of wind velocity (Mayhead 1973a). 21 Figure 2.5. Wind profile within and above a forest canopy (Oliver and Mayhead 1974) 22 Figure 2.6. Illustration of the bending moments imposed on a tree due to wind load where M w is the moment applied by the wind, M B is the moment applied by the displaced weight of the crown and M s (not shown) is moment applied by the displaced weight of the stem (Mayer 1989) 24 Figure 3.1. Site schematic showing the layout for each winching trial 33 Figure 3.2. Measurement axes of stem 35 Figure 3.3. Characterization of stem curvature for a single uprooted lodgepole pine tree, (a) calculated moments from recorded deflections and forces versus time, and estimated stem curvature using the (b) spline and (c) coordinate methods. The critical moment occurs at 0 43 Figure 3.4. Characterization of stem curvature for a single stem-broken spruce tree, (a) calculated moments from recorded deflections and forces versus time, and estimated stem curvature using the (b) spline and (c) coordinate methods. The critical moment occurs at 0 sec and stem failure occurs at 10 sec 44 Figure 3.5. Differences between total moments calculated for each tree using the spline and coordinate methods expressed as a percent of the moment calculated using the coordinate method 45 Figure 3.6. Differences between total moments calculated for each tree using the offset pivot and base pivot expressed as a percent of the moment calculated using the offset pivot and the coordinate method 47 Figure 3.7. (a) calculated moments from recorded deflections and forces versus time, and estimated stem curvature using the (b) spline and (c) coordinate methods. The critical moment occurs at 0 sec in Figure (3.7a).48 Figure 4.1. Layout of wind tunnel experimental setup at the UBC Mechanical Engineering Department.... 64 Figure 4.2. Frontal areas of redcedar, hemlock, pine and spruce adjusted to nominal wind speeds up to 20 m/s. Error bars are ±1 SE. Redcedar, hemlock and pine data from Rudnicki et al. (2004) 67 Figure 4.3. Redcedar, hemlock, pine and spruce static drag coefficients calculated based on the still-air frontal area for wind speeds between 4 and 20 m/s. Redcedar, hemlock and pine data from Rudnicki et al. (2004). (redcedar (0), hemlock (•), pine ( A ) , spruce ( x ) ) 68 Figure 4.4. Redcedar, hemlock, pine and spruce dynamic drag coefficients calculated based on speed-specific frontal area for wind speeds between 4 and 20 m/s. Redcedar, hemlock and pine from re-analyzed data in Rudnicki et al. (2004). [redcedar (0), hemlock (•), pine ( A ) , spruce ( x ) ] 69 Figure 4.5. Comparisons of drag per unit of branch mass for redcedar, hemlock, pine and spruce. Redcedar, hemlock and pine from re-analyzed data in Rudnicki et al. (2004). Error bars are +/- 1 SE 72 Figure 4.6. Comparisons of drag per unit of frontal area for redcedar, hemlock, pine and spruce. Redcedar, hemlock and pine from re-analyzed data in Rudnicki et al. (2004). Error bars are +/-1 SE 73 Figure 5.1. Schematic diagram of GALES (Gardiner et al. 2000a) 79 ** Indicates parameter values that were not changed in ForestGALES. Entire column of values not changed where this symbol is beside a column heading 84 Figure 5.1. Comparison of predicted critical wind speeds by dbh for western redcedar (A), BC western hemlock (B), BC lodgepole pine (C), and hybrid spruce (D) using the profile and roughness methods assuming recent exposure to a 100 m clearing, [profile method (0, • , A) and roughness method (•, • , A ) for all species except spruce profile (+) and spruce roughness ( x ) ] 87 Figure 5.2. Comparison of predicted critical wind speeds by dbh for UK lodgepole pine (A) and UK western hemlock (B) using the profile and roughness methods assuming recent exposure to a 100 m clearing, [profile method (A, • ) and roughness method ( A , B ) ] 88 Figure 5.3. Comparison of predicted critical wind speeds by slenderness for western redcedar (A), BC western hemlock (B), BC lodgepole pine (C), and hybrid spruce (D) using the profile and roughness methods assuming V l l recent exposure to a 100 m clearing, [profile method (0, • , A) and roughness method (•, • , A ) for all species except spruce profile (+) and spruce roughness (x)] 89 Figure 5.4. Comparison of predicted critical wind speeds by slenderness for UK lodgepole pine (A) and UK western hemlock (B) using the profile and roughness methods assuming recent exposure to a 100 m clearing, [profile method (A, •) and roughness method (•,•)] 89 Figure 5.5. ForestGALES predictions of critical wind speeds by dbh (A) and slenderness (B) for trees recently exposed to a 100 m gap on equivalent average sites in BC using the roughness method. [BC lodgepole pine ( A ) , western redcedar (•), BC western hemlock (•), hybrid spruce (+)] 90 Figure 5.6. ForestGALES predictions of critical wind speeds by dbh (A) and slenderness (B) for trees recently exposed to a 100 m gap on equivalent average sites in BC and the UK using the roughness method. [BC lodgepole pine ( A ) , BC western hemlock (•), UK pine (X),UK hemlock (o ) ] 93 Figure 5.7. Streamlining coefficient curves for lodgepole pine and western hemlock in BC and the UK. [UK pine (0), BC pine (•), UK hemlock (A), BC hemlock (x)] 93 Acknowledgements The completion of this work would not have been possible without the help of numerous people. I wish to begin by thanking my adviser, Dr. Stephen Mitchell, for his infinite patience and unfailing encouragement and guidance throughout my studies. This project was made possible through the financial support of the Network of Centres of Excellence - Sustainable Forest Management Network (NCE - SFMN). The Forest Engineering Research Institute of Canada (FERIC) provided equipment and technical support for the winching experiments. Canadian Forest Products (CANFOR) and the UBC Malcolm Knapp Research Forest (MKRF) provided the winching sites and helped with logistics in Prince George and Maple Ridge, respectively. In particular, I wish to thank Doug Bennett, Rob Jokai, and Seamus Parker from FERIC, Kerry Deschamps and the GIS staff at CANFOR, and Ionut Aaron, Rick St. Jean and Paul Lawson at MKRF. The Department of Mechanical Engineering at UBC provided the use of their wind tunnel and Pete Ostafichuk provided technical expertise during the wind tunnel experiments. I also wish to thank all the people who provided advice and helped me with the experimental work including: Dr. Jean-Claude Ruel, Dr. Michael Novak, Stephan Vollsinger, Leanne Helkenberg, Danielle Wensauer, Yun Hsien Choi, David Locke-Norton, Adrian Verster, Jenny Mitchell and Pascal Blanquet. Finally, this thesis should really include five more names as authors. In lieu of that I wish to dedicate this thesis to my mother and father, Donald and Shirley Byrne, my wife, Lynn Byrne, and my two boys, Tyler and Calum for their love, support and belief in my ability to succeed. I could not have done this without you. 1 1.0 Introduction Windthrow is a common natural disturbance that produces ecological impacts in forests and imposes economic costs. Therefore, forest managers need tools for predicting and limiting damage. Observational tools, and empirical and mechanical models have been developed to help managers predict the risk of windthrow. Of these tools, mechanical models are the most useful for investigating component processes, and making predictions for new management scenarios. Specific information is required to customize and validate these models in different forest types. The focus of this thesis will be on the resistance and loading components of windthrow risk. The goal of this the research was to begin adapting the mechanical model 'ForestGALES', which was developed by the UK Forestry Commission, for 4 major conifer species in BC. Two major components of the model are the equations related to wind loading and resistance. By adjusting these equations, critical wind speeds can be estimated for different tree types and locations. Static tree winching was used to gather data related to tree resistance while wind tunnel experimentation was used to estimate new parameters related to wind loading. The following approach was taken to solve this problem, and the thesis is structured along parallel lines: 1. I conducted a thorough literature review to identify techniques used to acquire loading and resistance data along with their advantages and disadvantages; 2. I then designed and conducted tree winching and wind tunnel experiments to expand the database related to tree resistance and wind loading for BC conifers; 3 . this database was used to develop new equations to be added to ForestGALES; 2 4. I ran ForestGALES with these newly incorporated equations to explore differences in critical wind speeds among B C species and between U K and B C species. The thesis concludes with a discussion of the implications of key results from each chapter and a series of recommendations for future work. Because Chapters 3, 4, and 5 are intended as manuscripts, there is some overlap with the literature review. 1.1.0. Experimental Objectives The specific objectives of the thesis experiments were to: 1. fit regressions relating maximum resistive moments to tree attributes based on field winching measurements; 2. document crown streamlining at different wind speeds and determine drag coefficients, drag per unit frontal area, and drag per unit mass relationships from measurements on real tree crowns in the wind tunnel; 3. evaluate the critical wind speeds for the same species grown in B C and the U K using ForestGALES with modified critical turning moment and drag equations. In the course of evaluating resistive moments, several methodological issues were identified and resolved. These are introduced and discussed in Chapter 3. 3 2.0 Literature Review 2.1.0. Nature of windthrow and prediction approaches Windthrow is a term used to describe the damage that occurs in forests when the force of wind knocks over trees. There are four main types of wind damage: 1) stem breakage, 2) stock breakage, 3) root breakage, and 4) tree throw (Mayer 1989). Mayer notes that it is sometimes difficult to distinguish between root breakage and tree throw unless the root system is analysed. Therefore, he makes only one distinction between wind breakage (stem and stock breakage) and windthrow (root breakage and tree throw). The latter is also an important pedological process in all forested landscapes called floralturbation (Schaetzl et al. 1986). Wind breakage occurs when the resisting strength of the roots is greater than the strength of the bole and windthrow (uprooting) occurs when the stem strength is greater than the root holding strength (Mergen 1954). Windthrow can also be classified according to whether it is catastrophic or endemic (Stathers et al. 1994a). Catastrophic windthrow is an infrequent occurrence associated with exceptionally strong winds that cause widespread and extensive damage. Characteristics of catastrophic damage include trees blown over in a single direction, a higher proportion of wind breakage, and wind damage on sites with a low windthrow hazard. There is usually little that can be done to prevent catastrophic windthrow. Endemic windthrow, however, is more preventable and is characterized by individual trees or small groups of trees that are blown over by frequently occurring peak winds in areas of recent harvesting or thinning. Forest management practices can worsen endemic damage if abrupt boundaries are created with poor orientation to the wind or on sites with poor rooting potential (Stathers et al. 1994a). Forest managers are concerned about the extent of windthrow damage. Mergen (1954) reported that the United States Forest Service estimated that timber loss due to wind damage represented 2.5% of annual timber resources. A windthrow survey in British Columbia (BC) in 1992 revealed that wind damaged a volume of timber equivalent to 4% of the annual allowable cut (AAC) by volume (Mitchell 1995a). Windthrown trees are salvaged wherever it is viable. This amounts to two-thirds of identified windthrow in coastal BC and 95% in the central interior where access is easier and the threat of bark beetle infestation higher. However, salvaging windthrow is more costly than standard harvesting and the log values are often lower due to breakage. It can also disrupt silvicultural planning and in some cases be disallowed, for example, along streamside buffer strips and wildlife corridors (Mitchell 1995b). The potential economic and ecological impacts of windthrow demand that forest managers continually acquire pertinent information about windthrow risk factors (Schaetzl et al. 1986). Their success in assessing the risk of wind damage will also depend on their ability to integrate the effect of these interacting factors (Ruel 1995). The knowledge acquired to-date has resulted in several methods for assessing the risk of wind damage in forests. These methods are divided into observational, empirical, and mechanical approaches (Mitchell 1999). The observational approach involves identifying presence and abundance of indicators for various environmental and management factors that are associated with windthrow risk. Broad predictions are then made about the damage being more or less likely to occur or damage being more or less severe based on the identified factors and indicators. An example of the type of plot card used in the observational approach can be found in (Stathers et al. 1994b). The advantages of this method are that it is easy to learn and apply, can quickly identify the most vulnerable areas and can be used with minimal staff and financial resources. However, the disadvantages are that the probability and severity of damage is not defined, the indicators are generic and do not account for local conditions and refinements are not possible unless a feedback step is included (Mitchell 1999). The empirical approach uses a quantitative model that predicts the proportion of wind damage given specific environment, stand and management factors. For example, Valinger and Fridman (1997) developed models for predicting damage using tree, stand and site characteristics from permanent sample plots in Swedish Scots pine (Pinus sylvestris L.) stands. These models are useful when enough data is available for a geographic area and the variables are strongly associated with damage. However, their effectiveness is limited to the landscape or forest types similar to where the data was obtained given limited management scenarios. Therefore, the model may not apply well to areas with different attributes (Mitchell 1999). However, even with weak associations, being able to determine the relative contribution of various factors is an improvement on the observational approach, where indicators are not weighted. The third approach to assessing windthrow risk is through mechanical modeling. Mechanical models estimate the critical wind speeds and critical stand heights where wind damage is likely to occur. Critical wind speeds are derived from loading and resistance models. Wind loading is determined in the wind tunnel by testing the drag force on tree crowns using a combination of measurements and calculations related to crown streamlining, drag equations and wind speed profiles within the canopy. Tree resistance to the drag forces exerted on the stem and crown is determined through static pulling tests that identify the maximum turning moment before the tree eventually falls under its own weight. The probability of wind damage occurring is then 6 connected to the average return period of critical wind speeds for a particular area using climatic data modified for local topography (Mitchell 1999). The study described in Smith et al. (1987) is a good example of a simple mechanical model. The detailed characterization of loading and resistance in more complex models requires an understanding of the functional components of windthrow and makes mechanical models useful to managers outside the development locations. 2.2.0. Windthrow Mechanics: Resistive Force Components The resistive components of windthrow can be divided into five broad categories: 1) stem stiffness and strain, 2) branch stiffness and strain, 3) rooting strength, 4) soil strength, and 5) damping influences. 2.2.1. Stem Stiffness and Strain The mechanical or strength properties of wood must first be considered before the resistance of stems, branches and roots can be discussed. Wood is an anisotropic and heterogeneous material that is subject to variation based on species, biotic and abiotic factors, and natural irregularities and defects, for example knots and burls. The Young's Modulus of Elasticity (MOE or E) provides a measure of resistance to extension or 'strain', therefore, larger E values mean that the material is stiffer (Cannell and Morgan 1987). Resistance to bending ('flexural rigidity') is equal to E times the second moment of area (I) where I is proportional to the fourth power of diameter for cylinders (Gardiner 1989; Neild and Wood 1999; Peltola et al. 2000). Due to the anisotropic nature of wood crushing across the grain, or parallel shear failure, will precede failure that occurs perpendicular to the grain (Wangaard 1950). Resistance to shear perpendicular to the grain is extremely high due to the alignment and structure of the longitudinal cells. 7 Metzger (1893), described in Assmann (1970), first proposed that the stem of a tree can be considered a cantilever beam, fixed at the base, free to move at the top, with uniform resistance to bending for a load applied to the free end. Petty and Worrell (1981) also used cantilever beam theory to calculate deflections under load, but this is only valid if the deflections are less than 25% of the length of the beam (Bisshopp and Drucker 1945). Analyzing the bending of stems and branches using the elementary cantilever beam theory beyond 25% deflection becomes more problematic. At this point complex solutions are required to accommodate patterns of taper and distributions of loads (e.g. Morgan and Cannell 1994). Investigations into the strength properties of wood show that conifers are roughly three times as strong in tension parallel to the grain as they are in compression parallel to the grain (Mergen 1954). Cannell and Morgan (1987) found that E along the grain of young living stems and branches is smaller than for green sawn timber from mature trees. It is suggested that these low E values occur because the bark does not contribute much to the overall rigidity. Cannell and Morgan added that when E was calculated using underbark diameters the E values more closely matched those for green timber. However, they did believe that since the bark is a part of a living tree that it would be included in the estimation of E in future work A summary of the variation of wood properties within a live stem can be found in Bruchert et al. (2000) who did static pulling tests on Norway spruce (Picea abies Karst)in the Black Forest area. They considered three main types of wood in the stem; 1) juvenile, 2) adolescent and 3) mature wood. However, the maximum compressive and tensile forces occur in the outer fibres of a bending beam which is mature wood in the lower bole. Petty and Worrell (1981) added that bending stresses increase from the centre to the periphery of the stem. Therefore, the strength of 8 wood in these outer fibres is most critical when it comes to bending resistance. Petty and Worrell (1981) calculated maximum tensile bending stress (Pm) using, Pm=a\, (2.D with the radius of the stem (a), the modulus of elasticity (E) and the radius of the curvature of the stem at each section (R). Equation 2.1 was rewritten as dx since — is approximately, given small deflections, equal to where y is stem deflection R dx from vertical and x is the distance from the tree tip. These equations assume that the stem is a cantilever beam that is rigidly attached at the base. Specifically, it is assumed that the tree is a cantilever and a column which is subject to an Euler buckling load (Figure 2.1). Calculation of the buckling load assumes a small lateral deflection of the column axis (Popov 1968). Other assumptions required to apply Euler buckling theory to tree stems are that there is a constant value for elasticity and that the stem is perfectly cylindrical. However, in the case of trees, they are neither perfectly cylindrical nor do they have constant elasticity. However, despite some of these assumptions being violated, the calculated curves compared well with observed curves of trees subjected to high winds in wind tunnel experiments (Petty and Worrell 1981). 9 Figure 2.1 Diagram of a bent and snow-loaded tree. The weights of the snow (S), crown (C) and stem (T) all exert clockwise bending moments, given for each by the product of weight and lever arm (I). These are opposed by the resistive bending moment (M) produced by the elasticity of the stem (Petty and Worrell 1981). Tree stems, however, do not always form a regular arc in bending but will often exhibit one or more sharp bends (Mayhead et al. 1975). This is likely because of irregularities and unique growth patterns that can occur due to knots, disease, injury or altered site conditions during the life of the tree. Morgan and Cannell (1994) looked at the hypothesis that the shape of a tree stem develops so that the bending and axial stresses are equalized along the length of the stem and used the transfer matrix method to examine this hypothesis. Their analysis supported this hypothesis, to an approximation with 10% error, for the stem above butt swell. They suggested that deviations from uniform stress on the outer surface of the stem are largely due to a lag between changes in the average forces on the crown of the tree and changes in the stem diameter. 10 Early studies of the resistance of trees to breakage and windthrow involved tree pulling experiments that applied an almost horizontal force to the tree using cables and winches (Fraser 1962b; Fraser and Gardiner 1967). The following equation, Mc=fd, (2.3) demonstrates how force (/) required to either uproot or break the tree was measured to calculate the critical turning moment (Mc) acting at the base where the distance (d) is the perpendicular distance from the point of force application to the tree base. These tests were used to determine the maximum resistance of the tree to turning at its base. Critical turning moment is used because it takes into account both the pulling force and the force of the tree's own weight as the angle of deflection increases. The use of empirical equations to estimate the maximum moment began when Fraser (1962b) conducted tree winching trials. He observed that graphs of the moment against defection have a characteristic shape where they rise to a maximum. Then, at the angle of maximum resistance the moment levels off. Using data from his winching trials Fraser estimated the critical turning moment (Ad), as shown in H WH M = P ^ f COS0 + — sine?, (2.4) is a function of Pmax (maximum resistance), 9 (angle of maximum resistance), and H (tree height) and If (tree weight) (Fraser 1962b). Fraser found, in his winching tests on Sitka spruce, that critical turning moment is related to tree mass. Fraser and Gardiner (1967) also found in the course of their work that there was a high correlation between stem mass and other tree size 11 attributes such as height, diameter and crown mass. The regressions that were subsequently fitted for maximum resistance versus stem mass had slopes that varied depending on soil type and root characteristics. Winching studies have since been used routinely to determine critical turning moments as a way of estimating tree stability. Smith et al. (1987) defined critical turning moment as the maximum turning moment a tree can withstand before windthrow occurs. Blackburn et al. (1988) found strong relationships between tree attributes, (eg. dbh3 (surrogate for volume), stem mass) and critical turning moment. Fredericksen et al. (1993) and Smith et al. (1987) also found very strong relationships between tree mass and size attributes (eg. stem mass, stem volume, dbh3) and critical turning moment in their studies of loblolly pine (Pinus taeda L.). More recently, winching tests were conducted on Douglas-fir to examine critical turning moments in relation to height and diameter (Mitchell 1999). The results of this study also showed a strong relationship between tree size (eg. dbh*ht, dbh3) and critical turning moment. Meunier et al. (2002) conducted winching tests on balsam fir (Abies balsamea (L.) Mill.) and white spruce (Picea glauca (Moench) Voss) and also found tree size variables (eg. dbh *ht, ln(diameter), ht) to be good predictors of the critical turning moment. However, the best predictor in this study was stem mass. Papesch et al. (1997) studied the stability of Radiata pine (Pinus radiata D. Don) at Eyrewell Forest on the Canterbury Plains in New Zealand also using a winch and cable to apply bending moments until the trees failed. The data from Eyrewell forest also indicate a relationship between tree height and stem deflection as shown in the following equations, 12 6Mc =-0.5416/2 + 21.099 R =0.52 and, (2.5) 0, =-1.2636/2 + 53.818 i?2 = 0.54. (2.6) These equations looked at angle of stem deflection at the maximum applied bending moment (OMC) and when the tree uprooted or the stem fractured (#). The results for height were much more significant with respect to stem deflection than dbh or dbh3 which had R2 values of 0.32 and 0.17, respectively. Papesch et al. (1997) suggest that the reason dbh is not related to stem deflection is that the stem does not behave like a rigidly attached cantilever beam due to root plate deformation under loading. They also identified the dependence of stem deflection on root characteristics as an area that requires more study. 2.2.2. Branch Stiffness and Strain The wind force acting on the crown of the tree (drag) is a function of the crown frontal area. The flexure of branches determines how the frontal area of the tree crown decreases with increasing wind speed. Furthermore, brittle branches will break more easily in collisions with other trees as the crown sways due to wind forces (Rudnicki et al. 2001). Hedden et al. (1995) simulated crown loss using model equations from Smith et al. (1987). It was found that a 50% reduction in crown weight was most effective at reducing mortality in hurricane force winds. Interestingly, a 25%) reduction in crown weight provided the greatest reduction in mortality at lower wind speeds. In this case height reduction due to stem bending and frontal area reduction due to streamlining was similar to a 25% reduction in crown weight. Streamlining occurs when branches that are perpendicular to the wind angle are bent in the direction of flow and is a function of flexural rigidity. The model used in this study assumes a linear relationship between 13 streamlining and frontal area reduction (Hedden et al. 1995). However, this is a complex process and there is a lack empirical data examining all factors associated with streamlining. For example, trees must be flexible enough to adapt to wind loads yet stiff enough to support the stem and foliage to maximize light interception and minimize the effects of snow loads and branch collisions during storms. 2.2.3. Root ing Strength and Strain The strength of individual roots in tension and bending follows the linear relationship of stress and strain up to the elastic limit where the relationship becomes non-linear and failure begins to occur (Coutts 1983). Therefore the flexural stiffness of roots, as in stems, is the product of their elastic modulus and their diameter taken to the fourth power. Roots can be classified into four main groups: lateral, oblique, sinker and tap roots (Somerville 1979). Somerville (1979) found in his research that lateral roots made up 66% of the total root weight followed by sinker roots (33%) and oblique roots (1-3%). As trees deflect in high winds, the lee side root of the root system is subject to bending and compression against the bearing surface of the soil while the windward side is lifted and is subject to tensile forces (Coutts 1983). Coutts (1983) found in his study of Sitka spruce that the lateral roots were most important to tree stability. Lateral roots on the leeward side act like a cantilever beam that resists the applied turning moment at the base of the tree. Since wood is weakest in compression, the limiting factor in root system stability is the ability of lateral roots on the leeward side to resist bending forces. Coutts suggested that any forking in the laterals reduces the stiffness of the beam by 50% assuming that the cross-sectional area is similar on both sides of the fork. This shortens the effective length of the resisting beam and draws the fulcrum closer to the stem, thus reducing 14 stability. Fewer but thicker lateral roots at the base of the stem that run in the direction of the wind will increase stability. Conversely, lateral roots on the windward side are lifted and subjected to tensile and possibly shear forces (Coutts 1983). 2.2.4. So i l Strength The resistance of non-rooted soil to shear and tensile strain is three to five orders of magnitude smaller than that of roots under tension. Additionally, higher soil moisture content lowers the resistance to shear while increased stress normal to the shear plane increases resistance to shear (Coutts 1983). Waldron and Dakessian (1981) also found that it is important to consider not only the strength of soil on its own but the strength of soil as it is reinforced by roots. Figure 2.2 shows how resistance to overturning is divided among the different components of the root system, including the weight of the root-system and entrained soil. Deflection of root-soil plate (°) Figure 2.2. S c h e m a t i c representat ion of the contr ibut ion of c o m p o n e n t s of a n c h o r a g e to the total turning momen t dur ing uproot ing (Cout ts 1983). 15 The root-soil system on the lee side undergoes bending and compressive forces against the underlying soil while the root-soil plate on the windward side is subjected to tensile and shearing forces due to lifting. Shallow root systems that have the main laterals near the surface tend to stiffen the soil more effectively on the windward side while root systems with deep horizontal roots reinforce the lee side when the roots "come under tension in the lower convex part of the bending root-soil plate" (Coutts 1983). Fraser (1962b) found that when root system depth was used to predict critical turning moment it accounted for only 10% of the variation. Moore (2000b) measured the maximum resistive bending moments of Radiata pine on six different soil types in New Zealand and used root depth and width as predictors. The contribution of root depth (R2 = 0.15) was comparable to that in Fraser; however, root plate width was found to have an even larger contribution (R = 0.53) to maximum resistive bending moment. Moore also noted that mode of failure was strongly related to soil type. Uprooting accounted for 92% of failures in non-cohesive soils but only 11% in clay soils. Anderson et al. (1989a) found that shear strength in the root plate-soil interface is important to windthrow susceptibility. Their study of Sitka spruce revealed that shear strength in brown earth was significantly greater than peaty gley or deep peat soil. This was mainly due to roots growing through the shear plane (e.g. a less distinct shear plane) and the lack of water saturation in the brown earth. 2.2.5. D a m p i n g Damping is the rate at which the oscillation of a swaying tree decays. Results from long duration sway tests indicate that oscillation increases over time due to a loosening root plate Rodgers et al. (1995) and that more damping exists in trees with a full crown than for stripped stems 16 (Gardiner 1989). Milne (1991) also measured sway damping on whole trees with some further refinements. He found that damping is a function of branch interference from neighbouring trees, aerodynamic drag on foliage, and damping of the stem. Branch interference was a function of distance between trees, and the energy lost due to aerodynamic damping was similar to that predicted using drag coefficients from wind tunnel research and other studies. 2.2.6.0. Techniques used to measure resistive force components Fraser and Gardiner (1967) used a tree-pulling technique that applied an almost horizontal force to the test trees at one-third of their height. More recently, Moore (2000b) performed winching tests in New Zealand using a hand winch, cable and pulley system. The height of cable attachment was 30-50% of the total tree height which is much less than the 80%) that Wood (1995) suggested as necessary to achieve uniform stress in the outer fibres. However, an attachment height of 30-50% is consistent with other studies (Fraser 1962; Fredericksen et al. 1993; Smith et al. 1987). Furthermore, a very long cable would be required to maintain a small angle between the point of attachment and the ground if it were attached at 80% of the tree height (Moore 2000b). The loading and resistance calculations associated with the deflection assume that the tree stem is a cantilever beam that bends in a way that produces a uniform stress on the periphery of the bole (Petty and Worrell 1981). Realistically, trees have complex taper patterns which result in different bending radii along the stem. Deflection calculations assume that the base of the tree is fixed and do not typically account for movement at the base (Morgan and Cannell 1994; Smith et al. 1987). For practical reasons the cable must be attached below the live crown, therefore, the 17 assumption must also be made that the resulting turning moment at the base is no different than when the wind force applies pressure at the centre of the crown. Dynamic forces including resonance are not reproduced by static winching, however this is not seen as problematic since it is rare that the gust frequency is in synchronization with the oscillation frequency of the tree (Oliver and Mayhead 1974). Furthermore, even in turbulent winds, the mean flow produces aerodynamic drag and limits oscillations of the tree to windward (Rudnicki et al. 2001). Static winching does not account for the gradual loosening of the root soil plate due to the swaying motion of a tree during prolonged storms. The process of windthrow involves a complex combination of meteorological, site, stand and tree conditions. Assumptions are made to hold some conditions constant while the effects of the other conditions are investigated. Specialists in such fields as engineering, soil science and meteorology may validate the assumptions underlying drag and turning moment studies in the future. However, a large body of knowledge exists based on the preceding assumptions. Error is associated with these assumptions however there is also error inherent in the variability of the more easily measurable tree and stand attributes. 2.3.0. Windthrow Mechanics: Applied Forces The critical wind speed is the speed at which the applied moment exceeds the resistive moment. Calculated critical wind speeds have been found to be inversely related to tree size for Sitka spruce over a range of soil types (Fraser and Gardiner 1967); Figure 2.3). The maximum applied moment is the combination of moment due to the wind drag on the tree and the self-loading moment due to the deflected weight of the tree at the instant of failure. 18 65 6 0 55 5 0 45 4 0 35 3 0 25 2 0 15 IO 5 BROWN EARTH DEEP PEAT v . SURFACEWATER ! G L E Y PEATY G L E Y 35 4 0 45 5 0 55 6 0 65 7 0 75 8 0 HEIGHT Figure 2.3. Velocity at which breakage or overturning will occur versus tree height for trees on different soil types (Fraser and Gardiner 1967). 2.3.1. Drag F o r c e s The wind force or drag on a rigid and impermeable body generally varies with the square of the wind velocity. However, tree crowns deform and streamline with increasing wind speed (Fraser 1964). Additionally, trees are permeable and allow air to filter through the canopy (Mayhead et al. 1975). Fraser conducted wind tunnel studies to determine the relationship between wind velocity and the horizontal wind force for several tree species and crown densities. He found that drag on a tree increased linearly with wind velocity, as shown in Drag = mV + C, (2.7) 19 where m and C are constants. This equation is applicable to wind speeds greater than 9.3 m/s. Fraser also estimated m for any tree using the following, w = 0.029^ + 1.442, (2.8) where W is the total weight. This demonstrates that the linear relationship between wind velocity and drag could be described in terms of the tree's weight. Accordingly, Fraser proposed that drag could be estimated directly using wind velocity and tree weight. Fraser also noted that the resistive turning moment of a tree also increases linearly with size but at different rates depending on the site. Therefore, if resistance increases more slowly than drag in relation to tree size then the point where the two lines cross is mean gust speed where wind damage will occur. The next step in Fraser's work was to determine the variation in wind velocity over different plantations. He calculated the drag coefficient, which reflects the shape and permeability of trees, and found that it varied with wind speed. By contrast, solid objects have a constant drag coefficient because they are not permeable and do not change shape with wind speed. Some examples of drag coefficients for common shapes which are also solid objects include: a circular disk (0.56), a cylinder with its axis parallel to flow (0.43), a cylinder with its axis perpendicular to flow (0.37), and a streamlined foil (0.035) (Campbell 1977). Due to the changing characteristics of tree crowns with wind speed, the tree in Fraser's model was tested at a constant velocity of 15 m/s, the speed at which he observed that damage typically commenced. Drag coefficients were calculated using, 20 D (2.9) b , pV2A with the still-air frontal area (A), wind velocity (V), measured drag (D) and air density (p) in the classical drag formula for bluff bodies. Raymer also tested conifers at different wind speeds to determine the drag coefficients at the Royal Aircraft Establishment at Farnborough. Mayhead (1973a) used this data and some of his own to calculate drag coefficients for Sitka spruce (Picea sitchensis (Bong.) Carriere), Corsican pine (Pinus nigra var. maritime Melv.), lodgepole pine (Pinus contorta Dougl. ex. Loud.), grand fir (Abies grandis (Dougl. ex D. Don) Lindl.), Scots pine (Pinus sylvestris L.), Douglas-fir (Pseudotsuga menziesii (Mirbel) Franco) and western hemlock (Tsuga heterophylla (Raf.) Sarg.) using Equation 2.9. The non-linear regression lines for each tree took the generalized form, where Co is the drag coefficient (non-dimensional), U is the wind speed (ft/sec, m/sec.) and C, mi, and m2 are constants. Mayhead's main conclusions were that there is a large variation in drag coefficients between tree species and even within genus and species (Figure 2.4). Mayhead speculated that this variation could have been due to natural variation in the trees, or poor technique. He also demonstrated the inverse logarithmic decline in drag coefficient with increased wind velocity. Because of this decline, drag coefficients are difficult to use in tree-pulling and critical height assessments. Therefore, Mayhead suggested using drag coefficient CD =C + mJJ + m2U2, (2.10) 21 values for each species, fixed at the value obtained at a windspeed of 26 m/s. A t this speed the rate of decline in drag coefficient with increasing wind speed was low for most species tested. m u f e p u t fcs« * « 4 ! i « r i PJat Figure 2.4. Drag coefficients regressions for individual trees over a range of wind velocity (Mayhead 1973a). The tests used to determine the preceding drag coefficients were conducted in a wind tunnel where a uniform wind profile was assumed. The wind profile in a forest varies with height. Oliver and Mayhead (1974) took measurements of a pine forest during a gale to determine the natural wind profiles and estimate gust eddy sizes. The wind profile above a forest can be approximated using a logarithmic formulation, log. V * J V z o J (2.11) where uz is the wind speed (m/sec.) at height z (m), d is the zero plane displacement (m), zo is the roughness length (m), k is the universal (von Karman) constant (0.41) and u* is the friction 22 velocity (m/sec). The shape of the wind profile within the canopy (Equation 2.13) is approximated using an exponential formulation, uz = uhe -al - 2 (2.12) with h (height of the tree canopy), Uh (wind speed at height h), and a (constant; also termed the attenuation coefficient). Oliver and Mayhead found that the measured wind profiles within and above the forest were consistent with values obtained theoretically. Therefore, they determined that it is possible to estimate wind speeds within and above the canopy from measurements made at a single point using estimated values of d and z (Figure 2.5). It should be noted that the wind profile below the canopy base is an extrapolation. The true characteristics of this part of the wind profile are not entirely understood. Canopy basB / Velocity !U) Figure 2.5. Wind profile within and above a forest canopy (Oliver and Mayhead 1974). 23 Hsi and Nath (1970) studied local drag coefficients, aerodynamic roughness and wind velocity profiles using a simulated forest canopy in the wind tunnel. They found that the velocity distributions in the simulated canopy were similar to those measured in the field by other researchers. They also found that the local drag coefficient of the tree canopy is related to the longitudinal distance from the leading edge. Gardiner et al. (1994) also conducted wind tunnel tests on a 1:75 scale model to measure bending moments and wind profiles back from the forest edge. They identified problems associated with accurate representation of drag coefficient and crown clashing characteristics in the model trees with respect to full-scale trees. However, similar wind tunnel tests of model forests have been conducted since then which have shown that wind tunnel measurements of wind speed and turbulence agree well field measurements (Novak et al. 2000) 2.3.2. Se l f - load ing F o r c e s Once the tree is displaced by the wind, self-loading forces begin to contribute to the turning moment of the tree. The moment applied by the displaced stem can be determined by dividing the stem into segments and calculating the sum of the products of mass and horizontal deflection for each segment (Figure 2.6). 24 u Figure 2.6. Illustration of the bending moments imposed on a tree due to wind load where M w is the moment applied by the wind, M B is the moment applied by the displaced weight of the crown and M s (not shown) is moment applied by the displaced weight of the stem (Mayer 1989). 2.3.3. S w a y F o r c e s Realistically the forces exerted on the crown are not simply a result of the static wind pressure and self-loading forces. Assuming the tree is an elastic beam fixed at one end, the four basic kinds of tree sways that can occur are bending sways, torsion sways, longitudinal sways and coupled sways. Skatter and Kucera (2000) looked at the relationship of systematic crown asymmetry in Scots pine and torsional wind loading and suggest in their study that torsion may be as critical as bending with respect to tree breakage. However, this study is based on model predictions rather than physical tests. Subsequently, it has been found that trees act like damped harmonic oscillators where sudden increases in wind cause the greatest displacement to occur in the first cycle followed by a gradual return to the resting position due to damping forces (Peltola 1996). These dynamic forces, before the tree returns to the resting position, can be amplified if the wind gust frequency becomes synchronized with the sway frequency thus leading to increased stem deflection and loading on the root systems (Milne 1991). 2.3.4.0. T e c h n i q u e s u s e d to m e a s u r e drag f o r c e s Techniques used to measure drag forces on trees have predominantly been used in wind tunnels on juvenile crowns. Fraser decided that, despite their limitations, wind tunnels would provide a reasonable method to obtain enough information to "indicate the general pattern of wind forces in the forest" (Fraser 1964). Limitations of wind tunnel experiments include the difficulty in duplicating canopy wind profiles at the scale of individual tree crowns and the size of the tunnel which limits specimens to juvenile or small mature crowns (Rudnicki et al. 2004). Horizontal forces in the direction of the wind (drag), vertical forces (lift), and wind speed can be measured. Photographs and video can be used to estimate crown frontal area at various wind speeds to calculate drag coefficients (Fraser 1962a; Rudnicki et al. 2004). Wind profiles in the wind tunnel are assumed to be constant with height and the boundary layer along the sides of the tunnel is considered negligible. The measurement of wind forces applied to trees in the field requires expensive instrumentation and the measurement of a complex set of variables. Consequently, few full scale drag studies have been carried out in the field (Papesch 1984). Most field studies have been restricted to small and artificial trees in highly controlled conditions (Grant and Nickling 1998). The main assumption in any field study is the issue of site variability and the difficulty of comparing data between sites. There are also issues with wind field non-uniformity through space and time. 26 2.4.0. ForestGALES model overview The U K Forestry Commission developed ForestGALES to assess windthrow risk for commercial conifer species in U K forest plantations. Gardiner et al. (2000a) provide a detailed description of the model which uses relationships derived from winching and wind tunnel studies. The most complete data set from these studies is for plantation Sitka spruce in the UK. Critical turning moments are calculated and then related to crown and canopy drag characteristics to determine critical wind speeds for the average tree in the stand, assuming that all trees in the stand are of the same size. The probability of damage is then estimated using estimated local wind speed return periods derived from wind climate and topographic data. Since the development of ForestGALES, modifications have been made to extend the model to Eastern Canadian forests. For example, Ruel et al. (2000) have used balsam fir (Abies balsamea (L.) Mill.) data from Quebec to modify equations predicting crown characteristics and overturning resistance in the model. Currently there are no data available to make such modifications for BC tree species, grown in BC. Furthermore, most of the research available has examined trees in even-aged stands on homogenous site types. There are no studies that reflect the diversity of landscape and site conditions that exist in BC. These variations in site conditions affect the characteristics of individual trees within the same species. In addition to Sitka spruce, there is some data for western hemlock and lodgepole pine, however, it is a limited data set from plantation trees in the United Kingdom. Therefore, the acquisition of drag and resistance data for BC species grown on typical sites is a necessary step towards adapting ForestGALES to BC forests. 27 The two methods in ForestGALES that were used to predict critical wind speeds in this thesis were the 'profile' and 'roughness' methods. These will be discussed further in Chapter 5. Briefly, the profile method uses crown frontal area and the within canopy wind profile to calculate wind-loading while the roughness method estimates wind shear per unit area (and therefore per tree in a uniform stand) to determine loading. Gardiner et al. (2000) provide a detailed description of how wind loads and critical wind speeds are calculated using the roughness method. The profile method is functional in ForestGALES but is less well parameterized. 3.0 Critical Turning Moments for four BC Conifer Species The maximum resistance of trees to uprooting or breakage is required to calculate critical wind speeds in mechanistic models such as ForestGALES and HWIND (Gardiner et al. 2000a). Maximum resistance is the critical moment at the base of the tree for uprooting or maximum bending moment of the stem for breakage. Static winching is the standard test procedure (Blackburn et al. 1988; Fraser 1962b; Gardiner et al. 1997; Smith et al. 1987). Turning moment equations now exist for black spruce (Picea mariana (Mill.) B.S.P.) in Ontario (Smith et al. 1987); balsam fir (Abies balsamea (L.) Mill.) and white spruce (Achim 2004), and black spruce and jack pine (Pinus banksiana Lamb.) (Bergeron 2004; Elie 2004) in Quebec. BC species, including Sitka spruce (Picea sitchensis (Bong.) Carr.), lodgepole pine (Pinus contorta Doug, ex Loud.), and western hemlock (Tsuga heterophylla (Raf.) Sarg.), are represented in the UK tree winching database (Nicoll 2004) that was used to build the equations in ForestGALES. However, all these data are from winching experiments in UK plantations and 28 with the exception of Sitka spruce, there are few observations for each species. Mitchell (1999) winched interior Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco) on the BC central interior (Mitchell 1999). There is no UK or BC winching data for commercially important species such as western redcedar (Thuja plicata (Donn ex D. Don) Spach), and hybrid spruce (Picea engelmanni X glaucd). Furthermore, only a limited range of tree sizes is represented in the UK database. It is expected from past winching studies that relationships between critical turning moment and tree size attributes will be linear (Fraser 1962b; Smith et al. 1987). However, as trees grow larger they will become more root restricted relative to their size and, therefore, the critical turning moment versus size relationship may become non-linear. The purpose of this study was to use static winching to test the resistance of redcedar, hemlock, hybrid spruce and lodgepole pine over a range of tree sizes and fit equations that relate tree attributes to the critical turning moment. The following hypotheses will be tested: 1. There will be linear relationships between critical turning moment and tree attributes such as mass, diameter and height; 2. These relationships will be the same among western redcedar, western hemlock, lodgepole pine and hybrid spruce grown on typical sites for each species; 3. Western hemlock and western redcedar will have the same critical turning moment relationships in mixed stands; 29 4. There will be a maximum threshold tree size where the linear critical turning moment relationships break down and become non-linear; 5. BC species grown in BC and the UK will have the same critical turning moment relationships under equivalent site and stand conditions. Two methodological issues that could influence critical turning moment calculations, and which have not been explored in the literature were also examined: 1) the characterization of stem curvature at the time of failure; and, 2) the position of the actual pivot location for uprooted trees. 3.1.0.0. Methods Trees for this study were winched in the spring and summer of 2003 and 2004. The two coastal and two interior conifer species chosen are common species that occur in uniform stands and are the most economically important to forestry in British Columbia. Of these four species, lodgepole pine and western hemlock are represented in the UK tree winching database and in ForestGALES. 3.1.1.0. Site Se lec t ion This study took place at four sites. The cedar and hemlock were winched at the Malcolm Knapp Research Forest in Maple Ridge, approximately 50 km east of Vancouver. The site was on a gentle north facing slope in the Coastal Western Hemlock very moist montane variant (CWHvm 1; 122° 32' W , 49° 19' N). The CWHvm 1 variant occurs on the windward slopes of the coast mountains up to the middle elevations (approximately 900 m). It is characterized by 30 mean annual temperatures of about 8 °C with annual precipitation averaging about 2300 mm (Meidinger and Pojar 1991). Typical summers are cool with some hot, dry spells and winters are mild with snowfall amounting to about 15% of the annual precipitation. Soils are dominated by Humo-Ferric Podzols which often present an eluviated A horizon and thick organic layer (Meidinger and Pojar 1991). The CWHvml unit is the most widely distributed biogeoclimatic unit in the Vancouver region. The soils in the study area have a fresh soil moisture regime and a medium to rich soil nutrient regime (Green and Klinka 1994). The winching tests occurred in the early summer when the soils were still relatively wet. The spruce and pine study sites were located in the Sub Boreal Spruce (SBS) zone. This zone is primarily a montane zone that occupies the majority of the central interior of British Columbia. It is characterized by a continental climate with severe winters and relatively warm, moist summers. Mean annual temperatures range from 1.7 to 5 °C and mean annual precipitation ranges from 415 to 1650 mm (Meidinger and Pojar 1991). The differences in the pine and spruce sites reflect the variability of climatic norms in this biogeoclimatic zone. The spruce sites were in the very wet, cool subzone (SBSvk) whereas the pine site was in a warmer drier subzone (SBSdw). The spruce sites were approximately 120 km northeast of Prince George (121° 48' W, 54° 32' N). Both spruce sites are located within two kilometers of each other. The SBSvk subzone occupies the lower parts of the McGregor Plateau and many of the valleys of tributaries in the south-central portion of the Bowron Valley. It is the wettest and coldest biogeoclimatic unit in the SBS zone and has the most growing season precipitation. Forests are characterized by hybrid spruce and subalpine fir (Abies lasiocarpa (Hook) Nutt; (DeLong 2003). The study sites were on 31 a low-lying plain close to the Fraser River. Soils in the study areas were relatively coarse textured and of fluvial origin with a mesic soil moisture regime and a medium to rich soil nutrient regime. The pine site was located near the border of the SBSdw subzone variants 2 and 3 approximately 50 km south of Prince George, British Columbia (122° 53'W, 53° 32'N). These biogeoclimatic units are the warmest and driest areas in the SBS zone. Soils in the study area are typically Brunisols derived from till blankets, with a subxeric soil moisture regime and a poor nutrient regime (DeLong et al. 1993). The study sites were located along recently harvested road rights-of-ways in uniform stands. Rights-of-ways were used to facilitate access and ensure safety. Recent rights-of-ways were used because ForestGALES bases its predictions on data from stand-grown trees (Gardiner et al. 2000a). Therefore, potential winch trees should not be destabilized by nor acclimatized to higher than within stand wind regimes. The selected rights-of-ways were less than one tree height wide and had been harvested less than two years prior to the winching trial. It was not expected that edge trees experienced substantial increases in wind loading during this period because wind penetration in openings 1 tree-length wide is low (Novak et al. 2000). Furthermore, Mitchell et al. (2001) demonstrated that tree acclimation to new exposure takes up to 10 years. Stand edge trees were sought because of the cable clearances needed to safely winch the trees. Care was taken to ensure that trees selected for winching were well clear of areas where soil had been disturbed for road construction. 32 3.1.2.0. Trial Procedures Candidate trees of the desired species with single straight stems, no obvious crown damage, or pathological indicators over a range of sizes were identified. Trees whose crowns or proximal roots were closely intertwined with neighbour trees were not selected. Adequate clearance to winch was required for safety reasons and to avoid adjacent crown interference. Suitable candidates were assigned to 5 cm diameter classes and at least three of the candidates were selected from each diameter class for each species (total n=76). The trees ranged from 15 cm dbh and 16 m tall to 57 cm dbh and 33 m tall. The cable attachment point was at approximately one-third the height of the stem for most trees and was in no cases higher than 11 m up the stem. The horizontal distance to the anchor tree was slightly longer than one tree length for safety reasons (Figure 3.1). 33 Tree Winching Site Schematic P L A N V I E W Anchor Tree Load Cell and Tilt Sensor Data Transfer Cables (4-strand 22 gauge wire) C R 2 3 X Datalogger Winch Tree Data /Retrieval / Centre Notebook Approx 10 E L E V A T I O N V I E W 10,000 lb. Load Cell 150' (max) -7/16" Cable 5500 lb. Tirforjack Handwinch Tilt S e n s o r # 1 -#3 10.000 lb. Strap Figure 3.1. Site schematic showing the layout for each winching trial. Preliminary measurements of tree diameter and height, and distance and bearing to the anchor tree were taken and the tree was prepared by attaching all instruments and cables. Winching then commenced simultaneously with the electronic data capture routine. A Tirmaster 2500 kg manual winch was used to winch the tree to complete root or stem failure. The winching generally took less than five minutes. Tree level measurements including stem and crown dimensions and masses were taken after the tree had either safely fallen or been cut to the ground. 34 Modes of failure were recorded for each tree. These include uprooting, root collar breakage and stem breakage. Uprooting and root collar breakage were grouped as 'uprooted' for the purpose of analysis. Appendix 6 shows pictures of typical uprooted and stem broken trees. Trees with root collar breakage failed just below the surface and close to the stem but did not lift the root-soil plate out of the ground. 3.1.3.0. Tree instrumentation Tilt sensors (Seika N4 inclinometers +1-10°) were used to measure tree deflection from initial position. A load cell (BLH Type U3G1 10,000 lbs.) was used to measure tension in the winching cable. Data from the tilt sensors and the load cell was transferred to a datalogger (Campbell Scientific CR23X) and instantaneously uploaded to a notebook computer for processing by data acquisition software (Campbell Scientific PC208W Version 2.0 Datalogger Support Software). These measurements were recorded in real time at a sampling rate of 1 Hz. 3.1.3.2. Measurements of tree and study site attributes The following data were recorded for uprooted trees only: the maximum and minimum depths of the root-soil plate, the depth of the organic layers, and vertical and horizontal root plate width. Root plate surface area was calculated from the latter two measurements. The crown was divided into one-metre sections beginning at the base of the live crown. Branches were removed by section. For each section, the fully extended branch lengths of two median length branches oriented in the x and y directions were measured. Branches were placed in a plastic garbage can on a Champ-II scale to measure total sectional branch mass. Direct measurements of stem mass were not possible due to the large size of the trees and the desire of the forest managers to recover merchantable logs from winched trees. Therefore, stem disks (approximately 20 cm 35 thick) were cut from the stem at 5 metre intervals beginning at stump height (30 cm). Disk lengths and the inside and outside bark diameters in x and y directions were recorded for the top and bottom of the disk (Figure 3.2). The disk was weighed to enable calculation of green log density inclusive of bark. The volume of each 5 m log length was calculated using Smalian's formula (Marshall and LeMay 1990) and its mass was estimated by the product of log volume and green disk density. This method of estimating stem mass is similar to that used in (Moore 2000b). A minimum of three 7.98 m radius plots (200 m ) was located at each site. Species, heights, and dbh were recorded for each tree within the plot. Crown closure was estimated and the number of stems per hectare was calculated. Several soil pits were dug at each site to enable documentation of soil profiles. 3.1.3.3. Calculated Variables The trees became noticeably curved under load and the tilt sensor readings indicated that some stem curvature remained at the critical moment. Therefore, it was necessary to characterize this curvature to properly locate the attachment point and tree centre of gravity, which is in turn 'disk Figure 3.2. Measurement axes of stem. 36 required to calculate the applied and gravitational moments. Two methods of estimating stem curvature were examined: the "spline method" (Appendix 1) developed by Vollsinger (2004) which used a combination of two third order polynomials to fit the curvature of the stem and the "coordinate method" which assumed a constant change in slope between the tilt sensors (Appendix 2). Both methods estimated stem curvature for the section of stem between the top and bottom tilt sensors, only. These methods also assume a smooth curvature with no abrupt changes. The distance between the top tilt sensor and the cable attachment point was very small; therefore, it was assumed no curvature existed between those two points. There will be some curvature between the cable attachment point and the top of the tree, due to the gravitational loading of the crown, which could not be estimated. Therefore, it was assumed that the angle of stem deflection above the cable attachment point was that recorded by the top tilt sensor. It was also assumed that no curvature existed between the bottom tilt sensor and the base of the tree at the point of germination. The location of the centre of gravity (COG) along the stem was calculated using the method of Wolfson and Pasachoff (1995), COG = ^ ' ' , (3.1) M where M is the mass of the tree, m, is the mass of each log section and /z, is height of each section.Once stem curvature was estimated using the spline or coordinate method and the assumptions were applied, the stem centreline was displayed on a high-resolution grid. The coordinates of the attachment point and COG were then located using the grid (Appendix 3). 37 The coordinates of the points of attachment and COG were used to calculate the applied and gravitational moments. These are added to determine the total moment. The total critical moment was assumed to have occurred at the time the maximum force in the cable was recorded. Due to observed fluctuations in deflection while winching, a sensitivity analysis was also performed to investigate the influence of attachment point position on the total calculated moment. Since the load cell and tilt sensors were recording simultaneously, the deflection analysis could be repeated for a series of time steps on either side of the maximum cable tension to identify the instant of maximum total moment. The position plots of the tree centre-line at each timestep produced by the spline and coordinate methods were visually compared. The difference between the two methods was quantified as a percentage of the turning moment calculated by the coordinate method as shown in, r^-rr ^-Coordinate ~ ^-Spline , „ . „ , %Dtfference = — x 100% . (3.2) M Coordinate The hypothesis that this difference was zero was evaluated with a t-test. As is the norm in the literature (eg. Fredericksen et al. 1993; Moore 2000b; Smith et al. 1987), for the preceding calculations it was assumed that the pivot point was located at the base of the tree (point of germination). However, observations of the base of the tree during winching, and of the final resting position of uprooted trees, suggest that the true pivot point for uprooted trees is located deeper and more towards the winch direction. To examine the influence of pivot point position, critical turning moments were re-calculated assuming an offset pivot point. The offset was derived from root-plate measurements and was assumed to be at the edge of the root system, in the direction of the winch, where compression failure of major structural roots was observed. 38 The difference between the offset and base pivot point with respect to calculated turning moment was expressed as a percentage of the moment calculated with the offset method as shown in, n,j^.rr ^OffsetPivot ^ BasePivot r n n o / %Difference = xl00% (3.3) MqffsetPivot The hypothesis that this difference was zero was evaluated with a t-test. 3.1.3.4. Analytical procedures The dataset was first inspected for anomalies and outliers. Of the 76 trees winched, 3 trees were discarded as outliers after consideration of regression residuals and re-evaluation of field observations. The spruce outlier had a much lower than expected critical turning moment. This tree was located in a depression that had a relatively high water table and low rooting depth. The hemlock outlier was considered suspect during winching. This tree brought up an adjacent stump when it uprooted and the turning moment was much higher than expected. The third outlier was a cedar that had a t-value of more than five on the studentized residuals. This difference between actual and predicted values caused the subsequent regressions to be disproportionately skewed towards the outlier. However, there were no field observations that supported exclusion as in the other two cases. All subsequent analyses used a sample set of 73 trees; 23 western redcedar, 20 western hemlock, 13 lodgepole pine, and 17 hybrid spruce. Linear regressions were fit and contrasted among species using SAS Version 8 (SAS_Institute_Inc. 1989) to determine the relationship between total critical turning moment and various tree attributes (a = 0.05). Pearson's correlation coefficients were used to help reduce the set of tree attributes to be investigated as predictors. The contrast function in the General Linear Model procedure (PROC GLM) was used to test for within-species differences between broken and uprooted trees, and between-sites for spruce only. This study spanned two field seasons on the coastal site. Eighteen redcedar and 15 hemlock were winched in the first season between May 2003 and June 2003. Six of each species were winched in the second season between June 2004 and July 2004. The site had been thinned during the summer of 2003 and some scattered windthrow occurred during the winter between field seasons. Therefore, contrasts were also used to compare yearly regressions to determine whether or not the root systems had loosened over the winter and whether yearly data could be pooled. The regression procedure (PROC REG) was then used to fit the regressions of greatest relevance. Additional data was acquired from the UK tree winching database to enable comparisons of regressions for lodgepole pine and western hemlock in BC and in the UK (Nicoll 2004). To match as closely as possible the conditions in the BC study, the selection of trees from the UK database was restricted to those grown in brown soils and podzols on non-cultivated sites. As will be seen in Chapter 5, ForestGALES uses easily measurable tree attributes to predict the parameters required to calculate such things as crown frontal area and stem mass. Therefore, Pearson's correlation was used to select the predictors for these allometric parameters in the model and SAS PROC REG was used to fit linear regressions based on these predictors. 3.2.0.0. Results and Discussion The primary goal of the winching experiments was to calculate the critical turning moments of the four BC species and explore how these moments relate to various predictor variables. A total of 73 trees were used for analysis (Table 3.1). The range in size of trees winched was representative of the range of trees at each study site. Since there are no replicate winching trials on other sites this analysis will focus on comparisons of species growing on typical sites. The largest coastal trees had greater diameters than the largest interior trees. The proportion of stems that broke varied from 0 for hemlock to 54% for pine. Peltola et al. (2000) winched Scots pine and Norway spruce in Finland and found that 14% and 22% failed due to stem breakage respectively. Stem breakage for black spruce was 19% (Smith et al. 1987) and for Radiata pine was 18%o (Moore 2000b). Peltola et al. (2000) also found that stem broken trees had typically higher slenderness ratios. T a b l e 3 .1 . S u m m a r y of t rees w inched with number and percen tage uprooted and broken. Species n dbh (cm) ht. range (m) slenderness % stems ratio range broken Cw 23 15-57 17-29 47.0-88.2 13% Hw 20 15-52 16-33 55.8- 102.0 0% PI 13 2 0 - 3 9 23 -33 77.5- 128.4 54% Sx 17 16-40 15-26 55.9-94.9 24% There are four main parts to the winching results. The first section deals with how accounting for stem curvature and pivot point location affects the determination of the critical turning moment. The second part explores within species differences between broken and uprooted trees, site differences and differences due to the year of winching. The third section fits regressions relating turning moment to four predictor variables and compares the best fits among B C and U K species. The final section fits allometric equations that will be required to adjust parameters in ForestGALES for B C species in Chapter 5 3.2.1.0. Characterizing stem curvature and pivot point Examination of the tilt sensor results revealed large fluctuations in the deflections recorded by each tilt sensor, and these were amplified in smaller more flexible trees. It is clear that the 41 rythmic movement of the hand winch was the source of this resonance. The left side of Figure 3.3a shows the applied and total moments and the associated deflections of the three tilt sensors before and after the critical moment for one of the sample pine trees. The critical moment is defined as the point (0 on the x-axis) when the maximum force is applied. The corresponding tilt sensor readings at the critical point are taken to calculate stem displacement and gravitational moment. Both the gravitational and applied moments were calculated based on the deflections recorded by the tilt sensors at the time of maximum applied load. There are some errors in this approach due to the fluctuating deflections. For example, peak moments sometimes corresponded with troughs in the tilt sensor deflection fluctuations. One possible reason for this could be, since the tilt sensors rely on fluid in bulbs flowing over contacts to record angle, that movement of liquid in the bulb due to the abrupt action of the winch is the cause of these fluctuations. Another possibility is that abrupt stop of the tree at the end of its back swing when the cable tightened (lowest relative deflection) induced a higher load than when it was at the end of the swing towards the winch when the cable was relatively slack due to the momentum of the tree (highest relative deflection). Alternative methods to deal with these fluctuations such as averaging the values around the maximum load also have errors and bias associated with them. For example, sometimes the maximum load was approached slowly and then dropped very quickly afterwards. Other times it took a long time for the load to decrease after the maximum had been reached. Therefore, how to decide over what time span to average values around the maximum load was problematic from both accuracy and bias standpoints. The sensitivity analysis revealed that there was less than 0.5% change in total moment for every metre the attachment point was moved laterally. Therefore, it was decided that errors due to fluctuations in deflection were minimal and that taking the deflections at the time of maximum load was the 42 most systematic and unbiased way of interpreting the data. Other researchers (Crook and Ennos 1996; Moore 2000b) have used a similar hand winch for static winching but issues surrounding fluctuations in deflection and methods of estimating stem curvature at the maximum load have not been addressed to this degree. Most (92%) of the nearly 2000 trees winched in the UK used a hand winch while power winches have been used there since 1993 (Nicoll 2005). However, there is no distinction in the ForestGALES critical moment equations to account for differences between power and hand winched trees. The total moment was the sum of the applied moment and the moment caused by the weight of the displaced stem. The two curves on the right side of Figure 3.3 represent the estimated curvature of the same pine tree using the spline and coordinate methods. 43 PI10 w i n c h e d o v e r t i m e 100000 I 80000 E 60000 40000 20000 0 (A) » o o o o o o o r m - y g ^ s ^ 10 -10 5 10 time (sec) 15 20 25 R10@rredrnum applied mcmert (spline) (B) mxrcnt (cocrclrcte) (C) Cettecticf>(m) Figure 3.3. Characterization of stem curvature for a single uprooted lodgepole pine tree, (a) calculated moments from recorded deflections and forces versus time, and estimated stem curvature using the (b) spline and (c) coordinate methods. The critical moment occurs at 0. Tilt and moment patterns over time differ between trees that uproot and those that fail due to stem breakage (Figures 3.3 and 3.4). Applied and total moments drop more rapidly on stem broken trees than uprooted trees and the bottom tilt sensor does not fluctuate throughout the trial. However, the top two tilt sensors continue to fluctuate and the spline method continues to deflect the tree more than the coordinate method. 44 Sx4 winched over time o E | 8000 / ';/ X (A) o 20 1 •s 15 T3 9d@mBMTuri appfied rt (spline) (B) Cfefledicn(m) 3d @frcpdrnum appfied mcment (oocrefnote) (C) CyJecocn(rT* Figure 3.4. Charac te r i za t ion of s tem curvature for a s ing le s tem-broken sp ruce tree, (a) ca lcu la ted momen ts f rom recorded def lect ions and fo rces ve rsus t ime, and es t imated s tem curvature us ing the (b) sp l ine and (c) coord ina te methods . T h e crit ical momen t occu rs at 0 s e c and s tem fai lure o c c u r s at 10 s e c . Coutts (1983) hypothesized that oscillations of the tree during winching mimic the soil and root abrasions that occur due to the dynamic forces of wind gusts. It should be pointed out that the oscillations observed during this experiment were much smaller than what would occur during a windstorm. 45 Figure 3.5. Differences between total moments calculated for each tree using the spline and coordinate methods expressed as a percent of the moment calculated using the coordinate method. There appeared to be more stem deflection using the spline method than the coordinate method (Figure 3.5). However, t-tests revealed that there were no significant differences between the moments calculated for spruce and western hemlock using each method. The moments calculated for western redcedar using the coordinate method were slightly larger than with the spline method, while moments calculated for lodgepole pine were slightly smaller (Table 3.2). The lower bound on the difference (Figure 3.5) increases as dbh increases indicating a small positive difference exists at the upper the range of the sample. This is interesting since the spline method deflects the trees more, presumably adding to the gravitational moment (average of 18% of total moment for all trees). 46 Table 3.2. Differences between moments calculated for each species using the coordinate and spline methods. Species Mean (%) n SE (%) Lower CL (%) Upper CL (%) p-value All -0.46 68 0.36 -1.18 0.25 0.206 Cw 1.03 20 0.49 0.01 2.06 0.048 Hw 0.25 18 0.59 -1.00 1.50 0.424 PI -3.19 13 0.56 -4.41 -1.98 <0.0005 Sx -1.00 16 0.84 -2.79 0.78 0.252 A possible explanation is that, if the spline method bends the tree higher up the stem, the centre of gravity would remain closer to the pre-winching central axis position thus reducing the self-loading component. The height to the centre of gravity was always less than the height of attachment: redcedar (66%), hemlock (81%), pine (85%), and spruce (63%). It is also true that the attachment point, calculated with the coordinate method, was always a little higher and little closer to the original central axis than with the spline method. The spline method appears to be bending the tree higher up the stem. Therefore, the applied horizontal moment, calculated with the coordinate method, was larger and the reverse was true for the applied vertical moment. Other techniques such as finite element modeling (Morgan 1989) or video capture (Achim 2004; Elie 2004) have been used to estimate tree curvature and deflection under load. Morgan modeled curvature based on the behaviour of tapered plastic rods, but these do not duplicate the anisotropic nature of wood and irregularities in stem form. Video capture may have parallax errors and curvature is difficult to estimate through dense canopies. Thus, every method of estimating curvature has sources of uncertainty and there seems to be no reason to consistently favour any one over another. In the end, the differences between the spline and coordinate methods were very small and since the coordinate method was functional for every tree, including those that broke, it was decided to use it for all subsequent analyses. 47 10.0% 5.0% 0.0% -5.0% -10.0% -15.0% -20.0% -25.0% -30.0% x 0 n * X n X X • • % A U * * • • o x • 0 o Q rj • • « a « Hw ° Cw - PI xSx 0.1 0.2 0.3 D B H (m) 0.4 0.5 0.6 Figure 3.6. Differences between total moments calculated for each tree using the offset pivot and base pivot expressed as a percent of the moment calculated using the offset pivot and the coordinate method. The effect of the pivot point on the calculation of the total moment was also examined (Figure 3.6). The moments calculated with the pivot point at the base of the tree were significantly larger than with an offset pivot and this difference increased with increasing tree diameter (Table 3.3). Al l trees that were greater than 40 cm dbh uprooted and they all had large plate root systems. Figure 3.7 shows that the offset pivot on one of the larger hemlocks has actually caused the gravitational component of the moment to be negative. 48 Hw18 winched over time 120000 -ty- • applied -total -••X-- • tiltl — tilt2 5 10 time (sec) KvW@rroarrijn^ paed rrorcrt (spline) (B) hWW (HJmadrrun ^ pfied moment (oocrdnde) (C) Deflection (m) Figure 3.7. (a) calculated moments from recorded deflections and forces versus time, and estimated stem curvature using the (b) spline and (c) coordinate methods. The critical moment occurs at 0 sec in Figure (3.7a). Coutts (1983) found that leeward lateral roots in Sitka spruce act as a cantilever beam upon which the mass of the root-soil plate acts to resist the overturning forces. Crook and Ennos (1996) agreed with Coutts' findings and added that windward lateral roots contribute up to one-third of resistive moment due to their tensile and shear strength. If negative self loading of stem mass at failure is true on a consistent basis with larger trees then it adds another dimension to how the design of root systems resists the overturning moment. More study of large or plate-rooted trees could provide better insight into the effect of an offset pivot on tree stability. Table 3.3. Table of differences between moments calculated for each species using an offset pivot and a pivot at the base [p-values]. Species Mean (%) n SE (%) Lower CL (%) Upper CL (%) p-value All -8.01 54 1.05 -10.11 -5.90 O.0005 Cw -7.89 19 1.94 -11.96 -3.81 0.0007 Hw -11.00 18 2.04 -15.29 -6.70 <0.0005 PI -6.68 6 1.07 -9.44 -3.93 0.0010 Sx -4.05 11 1.40 -7.18 -0.93 0.0030 49 Despite the differences that pivot-point location produces in calculated turning moments, the differences in the regressions of maximum moment versus stem properties were not significant, except for hemlock. Additionally, using the moment calculated with the offset pivot did not improve the fit of the regressions. A potential cause of this poorer fit is described in the last section of this chapter related to allometric regressions. All subsequent turning moment regressions therefore use the coordinate method with the pivot point at the base of the tree. 3.2.2.0. Selection of candidate predictor variables and comparisons between mode of failure, site, and year of winching factors Using Pearson's correlation, the best predictor variables for the critical turning moment (Mc) were stem mass (msterr), crown mass times the height to the centre of crown mass (mcrown(hmc)), 2 3 height times diameter squared (h(dbh )) and diameter cubed (dbh ;Table 3.4). Table 3.4. Pearson's correlation coefficients for the selected predictor variables and for critical turning moment. dbh3 matm » _ J A J M h(dbh2) 0.97224 0.92583 0.95603 0.87066 <.0001 <.0001 <.0001 <.0001 dbh3 0.83668 0.91927 0.78073 <.0001 <.0001 <0001 tnaem 0.93139 0.90327 <0001 <.0001 0.89285 <.0001 There were no significant differences between regressions for broken and uprooted trees for any of the predictors (Table 3.5). Therefore, broken and uprooted trees were pooled for all subsequent analyses. 50 Table 3.5. Summary of contrasts between broken and uprooted trees for all the predictors I n d e p . V a r i a b l e S p e c i e s frOhroken D1 broken frOuDrooted k 1 uprooted n p - v a l u e matm C w - 3 9 6 7 . 7 108 .1 6 2 0 7 . 5 93 .1 2 3 0 . 8 8 6 8 P I - 3 0 5 8 1 . 0 152 .1 - 2 7 3 2 8 . 6 1 4 4 . 9 13 0 . 8 4 2 9 S x 4 9 7 4 . 2 106 .4 - 8 5 1 2 . 1 1 2 3 . 0 17 0 . 4 3 8 1 h(dbti) C w 2 6 5 4 . 1 2 3 4 8 2 . 3 1 7 0 6 8 . 5 1 6 3 9 0 . 4 2 3 0 . 7 7 3 5 PI - 2 1 4 1 3 . 9 4 3 1 3 0 . 1 - 1 5 9 5 7 . 2 4 0 9 1 8 . 3 13 0 . 6 7 1 3 S x 5 7 4 . 5 3 2 7 2 8 . 0 104 .1 2 9 1 7 8 . 8 17 0 . 7 0 5 5 dbh3 C w 6 4 5 7 . 0 1 7 6 3 1 9 3 . 7 2 9 1 3 5 . 5 7 5 3 6 4 5 . 1 2 3 0 . 6 1 1 6 P I - 6 0 8 5 . 9 3 4 9 0 6 3 2 . 5 1 6 8 5 . 5 2 9 9 8 0 8 2 . 5 13 0 . 3 6 7 8 S x 2 9 5 0 . 7 2 1 3 6 7 1 4 . 2 8 4 3 9 . 0 1 6 5 4 1 3 1 . 2 17 0 . 5 8 3 7 mmwn(hmt C w - 3 6 0 . 3 2 8 . 5 2 1 2 9 4 . 2 2 0 . 5 2 3 0 . 7 5 5 7 P I 1 2 4 2 8 . 0 38 .1 2 4 9 6 9 . 1 3 4 . 9 13 0 . 8 2 2 7 S x 1 5 6 5 9 . 1 2 6 . 8 3 8 5 9 . 1 2 9 . 9 17 0 . 7 0 4 4 *p-value refers to difference between broken and unbroken trees. ** western redcedar (Cw), lodgepole pine (PI), hybrid spruce (Sx). Another issue to consider was the fact spruce was winched on two sites, two kilometres apart, with somewhat different soil properties. Contrasts were used to test for any site differences, and since none was detected, spruce trees were pooled for subsequent analysis (Table 3.6). Table 3.6. Summary of contrasts between the two spruce sites. I n d e p e n d e n t S i t e 1 S i t e 2 n p - v a l u e V a r i a b l e bo b , bo b, (d i f f . b e t w e e n s i tes ) mslem - 4 0 6 7 . 1 1 1 7 . 4 - 1 2 7 7 0 . 7 1 2 9 . 9 17 0 . 6 7 3 6 h(dbh2) 5 8 0 . 9 2 8 9 3 0 . 9 - 2 5 4 2 1 . 3 4 8 4 1 7 . 2 17 0 . 1 7 0 0 dbh3 6 8 7 8 . 9 1 6 7 4 4 1 5 . 4 - 1 6 1 3 7 . 2 3 1 9 6 3 1 3 . 1 17 0 . 1 9 0 3 2 8 2 0 . 6 3 5 . 2 6 0 9 0 . 5 2 4 . 3 17 0 . 1 0 2 5 The contrasts for hemlock and redcedar, using the year of winching as a factor, revealed that there were no significant differences for any of the predictor variables (Table 3.7). Had there been any significant decreases in moments for a given tree size in the year since harvest we would have suspected some confounding due to loosening of the root systems. The trees 51 winched in the second season were generally larger than those winched in the first year with an overlap in size at the lower end. T h e reason for this was to see i f the relationship between predictor variables and critical turning moment flattened out and became non-linear with increasing tree size. T h e non-linear fits that were attempted yielded no significant results and the linear contrasts from one year to the next d id not indicate a significant difference. Therefore, all subsequent regressions for the hemlock and redcedar were fit using a pooled dataset o f trees from both field seasons. Non- l inear regressions were attempted with the full dataset but d id not y ie ld any significant results. Table 3.7. Table of contrasts for hemlock and redcedar winched in Year 1 and Year 2. Indep. Variable Sp. bOvearl 1^ vearl b O v e a r 2 b 1 vear2 n *p-value Cw 6315.5 91.0 -25068.3 115.5 23 0.5858 Hw -1324.8 78.6 -73340.5 109.3 20 0.3754 h(dbh2) Cw 12910.2 17570.3 44606.9 12753.3 23 0.5293 Hw 3060.0 23435.6 54930.7 15603.1 20 0.4924 dbh3 Cw 19805.0 944158.1 84093.0 379811.4 23 0.1054 Hw 10918.2 1609127.7 92909.3 648587.3 20 0.1139 Cw 12972.0 24.0 53170.1 14.8 23 0.3131 Hw 8003.4 33.5 14693.8 22.6 20 0.1178 *p-value refers to the difference between regressions for trees winched in year 1 and year 2 by species. ** western redcedar (Cw), western hemlock (Hw). 3.2.3.0. Cr i t ica l turn ing m o m e n t r e g r e s s i o n s 3.2.3.1. Predictor variables for BC species Western redcedar and western hemlock were winched on the same site. T h i s makes direct species comparisons possible for these two species. G i v e n the ranges and site preferences o f the species tested, it is unusual to find all four species growing naturally o n the same site. Therefore, general species comparisons were made based on the assumption that the winched trees occur on sites that are typical for their respective species (Table 3.8). Ideally, I was looking 52 for one predictor variable that was universally relevant among all species to estimate critical turning moment. Therefore, the four predictor variables used to fit the regressions were ranked after averaging the root mean square error (RMSE) for all four species. Table 3.8. Table of regressions to predict critical turning moments for all British Columbia species using four predictors. dbh Indep. range Variable Sp. b0 b, SEbo SE b l RMSE R2 n (cm) Cw 4415.3 94.5a 8120.27 9.06 20721 0.83 23 15-57 Hw -1125.0 77.4a 7273.16 5.52 18738 0.91 20 15-52 P I -27333.0} 145.6b 10470.00 11.44 16023 0.93 13 19-39 Sx -5362.2 118.6c 4932.59 9.55 9378 0.91 17 16-40 h(dbh2) Cw 15175.0 16701.0a 8190.66 1818.38 23005 0.79 23 15-57 Hw 5149.0 22508.0b 8353.59 1953.61 22361 0.87 20 15-52 P I -17480.0} 41598.0c 4827.33 1576.79 7903 0.98 13 19-39 Sx 59.1 30204.0d 6369.18 3437.78 12712 0.83 17 16-40 dbh3 Cw 26685.0} 774488.0a 8078.38 95597.00 25369 0.75 23 15-57 Hw 18930.0} 1302242.0bd 8494.18 130342.00 25293 0.84 20 15-52 P I 792.6 3053567.0c 6093.93 170835.00 11592 0.96 13 19-39 Sx 8010.0 1745520.0d 7801.81 283327.00 16773 0.70 17 16-40 Cw 17723.0} 21.2a 7564.43 2.18 21989 0.81 23 15-57 Hw 20872.0} 22.6a 6196.80 1.65 19145 0.91 20 15-52 P I 14650.0 37.7b 11857.00 4.68 24204 0.84 13 19-39 Sx 6142.3 29.4b 5875.62 3.41 12910 0.82 17 16-40 *p-values were all <0.0001, slopes (b0 with different letters are significantly different, and intercepts (b0) with ($) beside them are significantly different from zero (a=0.05). * * western redcedar (Cw), western hemlock (Hw), lodgepole pine (PI), hybrid spruce (Sx). The best predictor variables ranked in order of average RMSE were: mstem (16215 Nm), h(dbh ) (16495 Nm), dbh3 (19757 Nm), and mcrown(hmc) (24711 Nm). Stem mass was the best predictor for every species except pine, for which variables representing tree size such as h(dbh ) and dbh were better predictors of turning moment. The breaking strength of a cylinder in bending is related to the Second Moment Area of Inertia, which is proportional to diameter cubed (Morgan and Cannell 1994; Neild and Wood 1999). Since more than half of the pine failed due to stem 53 breakage, it makes sense that dimensional characteristics provide good predictions (Peltola et al. 2000). Lower Modulus of Rupture (MOR), increased height to diameter ratio, and increased root depth all contribute to susceptibility to stem breakage (Cremer et al. 1982; Mitchell 1995a; Ruel 1995; Table 3.9) While pine in this study has a comparable published MOR to two of the other three species, it had higher H/D ratios and greater average rooting depths. Table 3.9. Summary of root and tree characteristics influencing stem breakage and uprooting. Species Height to diameter ratio (H/D) Minimum Maximum *MOR (MPa) **Avg. Rooting Depth Cw 47 88 36.6 0.93 (201 Hw 55 102 48.0 1.07 (19) PI 78 128 38.9 1.20 (6) Sx 55 95 35.1 0.65 (14) * Green sample values (Kennedy 1965). ** Numbers in brackets indicate trees that uprooted where root measurements were possible. The product of crown mass and the height to centre of crown mass was also a good predictor of critical moment, in spite of being the worst of the four based on average RMSE. This ratio was tested because it is logical to expect that tree resistance is proportional to potential wind loading. Crown mass has been found to be linearly related to drag (Mayhead et al. 1975; Rudnicki et al. 2004) and it is the drag force of wind on the tree multiplied by the height of that force which deflects the stem and produces applied moments. Furthermore, displaced crown mass contributes to the overall displaced stem mass in the gravitational component of total moment (Petty and Swain 1985). As noted above, the most consistently reliable predictor variable was stem mass. Many other researchers (Blackburn et al. 1988; Fraser 1962b; Fraser and Gardiner 1967; Gardiner et al. 1997) have also found stem mass to be the best predictor of the critical resistive moment. The reason why stem mass is the best predictor in this and many other studies is not entirely clear. One possible explanation is that diameter and height are related to volume which is related to mass. However, the regressions related to volume are not as good as mass. Another explanation could be that above ground growth is proportional to below ground growth, thus, as the stem grows so do the roots which affect resistance to overturning. There may also be an explanation related to the inertia of the tree as its mass is deflected by the wind. This is an interesting topic which warrants further investigation. 3.2.3.2. Differences between B C grown species The regressions for hemlock and cedar were not significantly different, however, the variability of the slope coefficient for cedar is nearly twice as much as hemlock. Therefore, it was decided to report separate regressions for western hemlock and western redcedar grown on the same site despite the fact they were narrowly insignificant with respect to each other. The two species are morphologically and silvically different with cedar having more taper, less wood density, and rooted in a wider range of microsites. Therefore, there is no biological logic to pool these two species. The slope coefficients for lodgepole pine and hybrid spruce in the BC interior compare well to results from winching studies in eastern Canada for jack pine, black spruce, white spruce and balsam fir (Achim 2004; Bergeron 2004; Elie 2004; Table 3.11). It should be noted that intercepts were included for the BC species but not the Quebec species. The intercept for lodgepole pine was statistically significant and negative while hybrid spruce was negative but not significant. 55 Table 3.11. Slope coefficients relating stem mass to critical overturning moments in Quebec and BC. Species Location Slope coefficient R 2 P i ' B C , Canada 145.6 0.93 Sx 1 B C , Canada 118.6 0.91 Sb 2 Quebec, Canada 148.2 * Sb 3 Quebec, Canada 108.9 0.84 Pj 3 Quebec, Canada 130.9 0.83 B-Sw 4 Quebec, Canada 100.9** 0.89 B 4 Quebec, Canada 147.8 0.81 1 Pine and spruce winched in B C fit with an intercept (this study). 2 Black spruce winched in central and eastern Quebec, fit without an intercept (Bergeron 2004). 3 Black spruce and jack pine winched in non-stony in central Quebec, fit without an intercept (Elie 2004). 4 Balsam fir and white spruce winched at Montmorency forest, Quebec fit without an intercept (Achim 2004). * not available. ** Rot found on 26 samples. Based on the regression coefficients, the resistive turning moments for trees of a given stem mass for trees grown on species typical sites are greatest for lodgepole pine, followed by hybrid spruce, western redcedar and western hemlock (Table 3.8). It is not possible to determine whether one species is generically better rooted than another using only the resistive moment data provided in this study. The resistance of trees to windthrow involves a combination of factors related to the type of soils in which they are rooted, tree attributes such as slenderness (Table 3.9) and the local wind loading to which they are acclimatized. For example, despite variability on the site, western hemlock was found to be mostly rooted in deep organic layers with the lower part of the root plate in poorly-drained mineral soil. Western redcedar microsites were more variable. For example, it was found on better drained sandy mounds and on poorly drained deep organics. 56 3.2.3.2. UK Species A sample of 8 western hemlock and 16 lodgepole pine from sites comparable to the BC sites was identified in the UK tree winching database supplied by Nicoll (2004). The UK hemlocks were winched in the Powys region of Wales and the UK pines were winched in the Inchnacardoch Forest in the Highland region of Scotland. While there were more observations for each of these species in the UK database, these were from sites that were cultivated or on peat-based soils and were therefore not comparable to the BC sites. I was unable to fit significant regressions using the UK hemlock. This is very likely due to the small number and narrow range of sizes of appropriate trees. However, a slope estimate for UK hemlock does exist in the ForestGALES code, as mentioned, and it is substantially (50%) higher than for BC hemlock. An intercept was used for BC hemlock but it was not statistically significant. Regressions, however, were successfully fit for BC pine and pine selected from the UK database (Table 3.12). The original ForestGALES turning moment equations assume that the intercepts are zero, however, the program has the capacity to accept intercepts. Therefore, the UK pine selected from the database was refit with intercepts to provide another basis of comparison with BC pine. Table 3.12. Summary of regressions for lodgepole pine from BC and the UK. Indep. Var. Location b0 b, SEb 0 SEb, RMSE R2 n dbh range (cm) dbh3 BC 792.6a 3053567.0a 6093.9 170835.0 11592 0.96 13 19-39 UK 13621.0Jb 1526813.0b 4021.9 152681.0 10154 0.87 16 15-41 h(dbh2) BC -18659.0}a 41660.0a 5095.5 1683.7 8441 0.98 13 19-39 UK 5988.0b 30138.0b 3608.1 2325.9 8038 0.92 16 15-41 BC -27333.0}a 145.6a 10470.0 11.4 16023 0.93 13 19-39 UK -2957.7b 125.2a 5206.3 12.0 9807 0.88 16 15-41 All regressions are significant (p<0.0001) and slope coefficients (bi) with a different letter are significantly different. Intercepts (b0) that are significant have (J) (a=0.05). •Intercepts where differences exist between UK and BC pine notated with different letter. 57 The regression slopes for UK pine and BC pine were not significantly different using stem mass as a predictor variable, however the intercepts were different. For this reason, the BC equations should be used for integration of BC pine into ForestGALES. There were also differences when the dimensional tree attributes, h(dbh ) and dbh , were used as predictors; BC pine had a steeper regression in both cases. Upon further analysis, it was discovered that the height to diameter ratio for BC pine (78 - 128) was larger than for UK pine (51 to 93), i.e., UK pine are more tapered. Given the similarity of the range of diameters selected from both areas, it is clear that the UK pines are shorter. 3.2.4.0. Allometric equations for BC species Since ForestGALES predicts tree attributes from input height and diameter only, regressions were also fit to estimate stem and branch properties from easily measured dimensional attributes. The best predictor of stem mass for all species was h(dbh2) which is also a surrogate for volume (Table 3.13). Therefore, it must also indicate stem density. The slope coefficients for western hemlock, lodgepole pine, hybrid spruce, and western redcedar are 301, 273, 258, and 174 respectively. The intercepts for all species were not significant except redcedar which had an intercept of 118. Therefore, by extrapolating between 0 and the minimum dbh, the relationship for redcedar is curvilinear down for trees up to approximately 15 cm dbh. This could reflect the change in form of redcedar from pole-like young trees more tapered older trees which sometimes had accentuated 'bottleneck' stems at the base. The slope coefficient for redcedar was significantly lower than all other species indicating that it is also less dense. This is supported by stem density estimates from the disk measurements. The slope coefficient for hemlock was significantly higher than all other species indicating higher density. This was also supported by the stem disk measurements. Pine and spruce estimates of stem mass with h(dbh2) as a predictor were not significantly different. However, estimates of stem density from disk measurements suggest that spruce is denser than pine. Therefore, the similarity of the slope coefficients, given different stem densities, may be function of more taper that was observed in spruce. Table 3.13. Summary of allometric regressions for BC species. Dependent Variable Independent Variable Sp. b0 b, SEbo SEbi RMSE R 2 p-value Icrown h(dbh2) Cw 9.17 0.80 0.66 0.14 1.87 0.57 <.0001 Hw 8.48 1.35 0.88 0.19 2.33 0.71 <.0001 ht PI 1.66 0.28 5.77 0.21 2.17 0.06 0.2087 Sx 0.17 0.55 2.66 0.13 2.20 0.49 0.0007 dvedcr0%vn dbh PI -11.33 113.00 8.05 26.41 6.32 0.59 0.0013 Sx 4.38 110.45 9.35 32.50 9.28 0.38 0.0037 h(dbh2) Cw 31.20 7.41 3.49 0.75 9.84 0.81 <.0001 Hw 14.20 11.14 3.24 0.76 8.68 0.92 <.0001 cown widthmax dbh PI -1.08 16.59 1.05 3.46 0.83 0.65 0.0006 Sx 3.28 6.61 0.73 2.54 0.72 0.25 0.0191 h(dbh2) Cw 5.36 0.46 0.23 0.05 0.64 0.79 <.0001 Hw 3.55 0.73 0.26 0.06 0.69 0.88 <.0001 Wrown(hm(J h(dbh2) Cw -116.83 789.62 130.91 28.18 369.40 0.97 <.0001 Hw -636.26 978.16 266.52 62.33 713.45 0.93 <.0001 PI -439.29 940.74 387.48 128.03 641.89 0.82 <.0001 Sx -44.14 943.27 244.77 120.25 526.17 0.78 <.0001 Wcrown dbh PI -135.88 744.58 33.65 110.39 26.42 0.79 <.0001 Sx -105.68 753.14 38.15 132.68 37.90 0.65 <.0001 dbh3 Cw 33.36 1890.10 8.33 95.18 26.25 0.94 <0001 *Hw 7.72 2551.13 8.64 132.58 25.73 0.95 <0001 h(dbh2) Cw 117.91$ 174.16a 37.67 8.11 106.29 0.95 <.0001 Hw 57.71 301.45b 42.73 9.61 115.09 0.98 <.0001 PI 95.46 272.83c 54.98 18.17 91.08 0.95 <.0001 Sx 44.26 258.19c 45.48 22.34 97.77 0.89 <.0001 mtree h(dbh2) Cw 127.21 213.88 39.50 8.50 111.46 0.96 <.0001 Hw 36.28 347.87 52.45 11.80 141.28 0.98 <.0001 PI 89.03 307.09 66.42 21.95 110.03 0.94 <.0001 Sx 64.73 306.28 57.21 28.10 122.98 0.87 <.0001 Slope coefficients (bi) for h(dbh2) predicting mslem that have a different letter associated are significantly different and ftistem intercepts (b0) that are significant have ({) (oc=0.05). 59 Pearson's correlation was used to reduce the set of easily measurable predictor variables for parameters of interest such as crown frontal area and stem mass (Appendix 5). Potential predictor variables for the pivot point location relative to the central axis were also explored. Recall that the determination of the pivot point location did not improve the fit of the critical turning moment regressions. One possible reason for this is that the Pearson correlations between the predictor variables and pivot point distance from the stem were good (< 0.80) relative to the correlation between stem mass and critical turning moment (> 0.90) which was very good. Therefore, inclusion of pivot point increased the variability. The primary intention of fitting these allometric equations is to incorporate more species-specific parameters into ForestGALES for critical wind speed predictions of BC species in Chapter 5 (Table 3.13). 3.3.0.0. Conclusions Winching results from all four BC species in this study indicate that the relationships between critical turning moment and stem mass, diameter cubed, and height multiplied by diameter squared are linear. Stem mass has also been found to be the best predictor in prior research and is the predictor incorporated into ForestGALES. Future research could focus on exactly why stem mass is consistently the best predictor of critical turning moment. The relationship between stem mass and critical turning moment was not the same for all species grown on species-typical sites. Despite the relationships of western hemlock and western redcedar being non-significantly different in mixed species stands, separate equations should be used because it was the variability of cedar that produced the overlap. A larger sample size would probably make the equations for these two species significant. Additionally, the equations should be different merely from the logic that these two species are expected to behave 60 differently on different sites. For the purpose of modifying ForestGALES for BC the two species should characterized separately. The slopes of the relationship between stem mass and critical turning moment for UK and BC pine were not significant. However, since the intercept was significantly negative for BC pine and not significant for UK pine, separate regressions should be maintained for these species, even under equivalent site and stand conditions. 61 4.0 Drag relationships for four BC conifers Calculation of the maximum turning moment is one requirement in evaluating the wind speed at which a tree will fail ('critical wind speed'), the other requirement is knowing how much drag is exerted on the crown at a given wind speed. In ForestGALES, drag is calculated using two methods, shear and profile. In the former method, species-specific equations are used to reduce crown frontal area reduction due to branch streamlining and increase canopy porosity. In the latter method, a drag coefficient of 0.30 is used for all species and wind speeds. While it is possible to do so, only one researcher (Papesch 1984) has reported measurements of drag for trees in-situ. More typically, drag is measured with cut specimens, either by placing them on trucks and driving at a fixed speed (Lai 1955), or by placing them in wind tunnels (Fraser 1962a; Fraser 1964). In the latter case, studies are typically with juvenile crowns due to the size restrictions of wind tunnels. The classic formula used to calculate drag on bluff bodies is, D = y2CdPAU2, (4.1) where Q is the drag coefficient (dimensionless), p is the air density (kg/m3), and U is the wind speed (m/s). Mayhead (1973a) and Smith et al. (1987) calculated drag coefficients and critical wind speeds assuming a fixed frontal area (A). Mayhead et al. (1975) also reported non-linear relationships between mass and wind speed, and drag for Sitka spruce and lodgepole pine. Rudnicki et al. (2004) ran wind tunnel experiments with sapling conifer crowns to explore the relationships between drag and crown mass, and drag and crown frontal area. They were also the 62 first to use wind speed-specific frontal area to better capture the effect of streamlining on drag coefficients. As was the case with critical turning moment equations, drag and crown streamlining equations for several BC species are already incorporated in ForestGALES, however these were obtained from Mayhead (1973a) and Mayhead et al.'s (1975) work with small samples of UK grown individuals. Work in obtaining results for BC species was commenced by Rudnicki et al. (2004). However they focused on species with widely differing foliage. Of the four species of interest in this thesis, they studied western redcedar (Thuja plicata (Dorm ex D. Don) Spach), western hemlock (Tsuga heterophylla (Raf.) Sarg.), and lodgepole pine (Pinus contorta Doug, ex Loud.). To complete the dataset for the four principal BC conifers, drag, crown frontal area, crown mass and branch mass relationships for hybrid spruce (Picea glauca (Moench) VossX Picea engelmannii Parry) were explored in this study using the same wind tunnel and identical methodology. The data for hybrid spruce was combined with data for the other three species obtained by Rudnicki et al. (2004) and was collectively analyzed and presented in order to facilitate comparison. The following hypotheses were tested: 1. Drag coefficients decrease with increasing wind speed. 2. Drag is linearly related to crown mass at a given wind speed. 3. Drag coefficients are different among species with different foliage properties. 4. Drag coefficients are similar for the similar species in BC and the UK. 63 4.1.0.0 Methods This experiment was a companion to earlier work reported by Rudnicki et al. (2004) and uses identical methods. 4.1.1. W i n d T u n n e l Descr ip t ion a n d L a y o u t The test section of the wind tunnel at the Mechanical Engineering Department is 1.65 m high, 2.44 m wide and 18.3 m long. It can produce a maximum laminar flow of 20 metres per second. The wind speed is uniform except for a thin zone near the walls, roof and floor of the tunnel. Wind speed (U) is calculated using the following equation, where the dynamic air pressure (AP) is measured at the opening of the test section using Bernoulli's law. Air density was calculated using the Ideal Gas Law, regularly throughout the trials using barometer and thermometer readings next to the tunnel and the ideal gas law. Barometric pressure (P), the gas constant for dry air (Rd), and the absolute air temperature ( I ) were used for this calculation. Drag forces were measured using a load cell (model PT-1000-30kg, Precision Transducers, Auckland). Sample trees were mounted in a bucket that was firmly attached to a near frictionless air table located under the tunnel floor. The air table then transferred the drag forces to the load cell. Al l instruments, including an S-type load cell (model AST-100, Precision Transducers, Auckland) to measure tree masses, were (4.1) (4.3) 64 monitored using a data acquisition computer through an analogue-to-digital interface card (Daqboard model DBK16, IOtech, Inc., Ohio, USA). A video camera was mounted 15 metres downstream of the tree in the wind tunnel to record the frontal area of the tree. To improve the contrast for subsequent image processing the tree was set against a black background. Figure 4.1 illustrates the layout of the wind tunnel and location of all relevant instruments and equipment. PLAN VIEW « 25 m , Mounting Bucket H 2.4 m j ' -^Wind tunnel Controls _ - Computer Monitor . DAQ Board & Computer ELEVATION VIEW Force Balance Video Camera A = Side Force Transducer Signal B = Drag Force Transducer Signal C = Dynamic Pressure Signal D = Load Cell (Tree Weights) Signal E = Data Acquisition Circuit Board (DAQ Board) Figure 4.1. Layout of wind tunnel experimental setup at the UBC Mechanical Engineering Department. 4.1.2. Trial P r o c e d u r e s Seven interior spruce trees grown from a central interior British Columbia seed source were selected from the University of British Columbia South Campus field site in Vancouver. The stem bases were wrapped in plastic containing saturated sponges to minimize moisture loss in 65 transport and storage. Wind tunnel trials on the spruce were conducted within two days of sample collection. Prior to each trial, the sample was cut to a height of 1.9 metres and the lower branches trimmed to maintain a minimum 5-centimetre clearance from the tunnel floor and ceiling. After weighing the sample, it was mounted in the bucket below the tunnel floor. The video image was scaled using a two-metre scale bar held across the length and width of the tree to detect image distortion. Still air images were captured at this time by the video camera and the horizontal dimensions of the top, middle and bottom sections of the crown physically measured on four axes. The data acquisition software (Daqview Version 7.13.2) was then set up to record the wind tunnel trial after all pre-trial measurements were taken. The wind tunnel was stepped through nominal wind speeds of 4, 8, 12, 16, and 20 metres per second using a manual dial. Each wind speed setting was held constant for 30 seconds to allow 15 seconds for the wind tunnel to increase its wind speed and another 15 seconds of stable flow to sample the dynamic pressure and associated drag. After each trial, the stems and branches of the sample were weighed. Post-processing of the video images calculated the crown frontal area at each wind speed. The non-black portion of the image was cropped and pixilated, and unsupervised classification determined crown pixel counts using Geomatica (PCI Geomatics, Richmond Hill, Ontario, Canada). Prior to each trial, the image was scaled to determine pixel size. Therefore, crown frontal area at each wind speed was the product of pixel size and the crown pixel count. 66 4.1.2. Data analysis Linear regressions were fit using SAS PROC REG (SAS_Institute_Inc. 1989) to investigate the relationship between drag and the product of mass and wind speed. The relationship between drag and the product of frontal area and wind speed was also investigated. Due to the sensitivity of the manual dial to adjust the wind tunnel speed, the target wind speeds of 0, 4, 8, 12, 16 and 20 m/s could never be realized, exactly. Therefore, drag values have been adjusted to the target or nominal wind speeds by interpolation to produce the following histograms. The difference between actual and target wind speeds varied from 6.1% of the nominal wind speed at 4 m/s to 1.7% of the nominal wind speed at 20 m/s. To facilitate analysis and discussion of the four species of interest in this thesis, the data for interior spruce was combined into a single dataset with data for the other three species obtained by Rudnicki et al. (2004) prior to analysis. The unit of drag used throughout this paper is Newtons. 4.2.0.0. Results and Discussion The spruce crowns tested in this study were comparable in size to the species tested by Rudnicki etal. (Table 4.1). Table 4.1. Average sample tree characteristics for hybrid spruce (S), western redcedar (C), western hemlock (H), and lodgepole pine (P). Species n Bole diameter (cm) Full crown mass (kg) Bole only mass (kg) Frontal Area (m2) Full crown area/mass (m2/kg) S 7 4.19 (0.54) 5.69 (1.38) 1.64 (0.44) 0.80 (0.12) 0.14 *c 9 4.12 (0.33) 3.04 (0.42 1.36 (0.19) 1.05 (0.25) 0.35 *H 9 4.85 (0.74) 4.55 (1.09) 1.95 (0.41) 0.90 (0.20) 0.20 *p 9 4.16 (0.32) 4.53 (0.76) 1.62 (0.20) 0.93 (0.19) 0.21 Note: Standard deviations are in parentheses. •Results from (Rudnicki et al. 2004). 67 Spruce crown frontal area increased slightly at nominal wind speeds up to 8 m/s and then steadily dropped as wind speed increased to 20 m/s (Figure 4.2). This pattern, in which frontal area first increased at lower wind speeds, was noted by Rudnicki et al. (2004). However, the increase in frontal area for spruce continued until 8 m/s, whereas the frontal area of the other species began decreasing after 4 m/s. 1.2 -i 0 4 8 12 16 20 U (m/s) Figure 4.2. Frontal areas of redcedar, hemlock, pine and spruce adjusted to nominal wind speeds up to 20 m/s. Error bars are ±1 S E . Redcedar, hemlock and pine data from Rudnicki et al. (2004). Drag force and crown frontal area at 0 m/s, was substituted into the classical drag formula (Equation 4.1) to determine 'static' drag coefficients based on still-air frontal area. A s expected given the frontal area results, the static drag coefficient first increased, and then decreased with increasing wind speed as the crowns streamlined (Figure 4.3). 68 1.4 i 1.2 -o 0.8 -'in c <D E 0.6 -Jo, •o ° 0.4-0.2 -0 -0 2 4 6 8 10 12 14 16 18 20 U (m/s) Figure 4.3. Redcedar, hemlock, pine and spruce static drag coefficients calculated based on the still-air frontal area for wind speeds between 4 and 20 m/s. Redcedar, hemlock and pine data from Rudnicki et al. (2004). (redcedar (0), hemlock (•), pine (A), spruce (*)). 'Dynamic' or wind speed-specific drag coefficients were also calculated using wind speed-specific frontal areas (Figure 4.4). The resulting drag coefficients decreased more slowly as the wind speed increases. Because change in frontal area is already accounted for, the reduction in dynamic drag coefficient reflects the change in orientation and air-resistance of the drag elements produced as branches streamline. 69 1.2 n T J 0.4 -o 0.2 -0 -I 1 1 1 1 T 1 1 1 1 1 0 2 4 6 8 10 12 14 16 18 20 U (m/s) Figure 4.4. Redcedar, hemlock, pine and spruce dynamic drag coefficients calculated based on speed-specific frontal area for wind speeds between 4 and 20 m/s. Redcedar, hemlock and pine from re-analyzed data in Rudnicki et al. (2004). [redcedar (0), hemlock (•), pine (A), spruce (x)]. Of the three species tested by Rudnicki et al., the behaviour of the static and dynamic drag coefficients for spruce is more like lodgepole pine or western hemlock than western redcedar. However, the drop in dynamic drag coefficient was slower for spruce than for these species, suggesting greater stiffness and less branch re-orientation. Mayhead et al. (1975) obtained still air coefficients of 0.35 (n = 24) for lodgepole pine at 26 m/s and these were the values they recommended to calculate windthrow risk for that species. Recalculated static drag coefficients from data in Rudnicki et al. (2004) were 0.28, 0.54, and 0.49 for redcedar, hemlock and pine, respectively, at 20 m/s using still-air frontal area. Rudnicki et al. found their value for pine was comparable with that of Mayhead et al. (1975) over a similar range of wind speeds. Comparatively, the static drag coefficient for spruce at 20 m/s using still air frontal area was much higher than for any of these species at 0.69. Given the shape of the 70 curve, drag coefficients for spruce will likely continue to decline to wind speeds well above 20 m/s. The dynamic drag coefficients at 20 m/s, which have accounted for frontal area reduction, are 0.61, 0.89, 0.77, and 0.92 for redcedar, hemlock, pine and spruce, respectively. Several variations of mass versus drag and frontal area versus drag relationships for spruce were explored. The following linear models for spruce were compared to prior linear models for hemlock, redcedar and pine where: U is wind speed, As is still-air frontal area, Ad is dynamic frontal area, mc is the crown mass, and nib is the branch mass (Table 4.4). The linear regressions using wind speed and mass to predict drag did not fit as well for spruce as they did for the other species. However, the regression using dynamic frontal area and wind speed to predict drag for spruce was much better. A non-linear model was also fitted using a variation of the formula provided by Mayhead et al. (1975) to compare results for spruce, redcedar, hemlock and pine. The non-linear equation using mass and wind speed also produced a low RMSE for spruce but not as good as dynamic frontal area relative to the other species (Table 4.4). Vollsinger et al. (in press) tested drag on deciduous crowns using the same wind tunnel and techniques as in this study. They also found that models using branch or crown mass eliminated the variability associated with drag coefficients. Using mass as a predictor eliminates the need to estimate changing frontal areas associated with different wind speeds. 71 Table 4.4. Models for predicting crown drag (units in Newtons) for spruce and compared with prior models for hemlock, redcedar and pine. Independent variable Species bo b, SE b 0 SEbi RMSE R2 A. Linear regressions. U2Ad S 5.26ab 0.54c 1.55 0.01 5.4 0.99 C 6.0 lab 0.31a 1.12 0.01 4.3 0.96 H 3.08a 0.53c 1.88 0.01 7.2 0.97 P 7.43b 0.42b 1.74 0.01 6.9 0.97 Umb S -9.05ab 1.64a 5.85 0.11 16.5 0.86 c -2.91a 1.96b 1.78 0.08 5.7 0.93 H -8.43b 2.21c 2.69 0.08 9.0 0.95 P -11.39b 2.06d 2.76 0.07 8.6 0.94 Umc S -13.59b 1.19ac 4.82 0.06 13.3 0.91 c -3.93a 1.11a 1.61 0.04 5.0 0.95 H -10.74b 1.31bc 2.90 0.05 9.4 0.95 P -13.65b 1.36b 2.41 0.04 7.3 0.96 B. Nonlinear regressions. Co Cl SE c 0 SE c l RMSE */ U2(mJ2/3[coexp(clU'f\ S 0.2333a 0.00148b 0.0136 0.00019 8.9 0.96 c 0.2417a -0.00195a 0.0167 0.00023 6.6 0.91 H 0.2854b 0.00165b 0.0113 0.00013 6.3 0.98 P 0.2611a 0.00169ab 0.0118 0.00014 7.0 0.97 Note: Intercepts (b0, c0) and slopes {bh c;) that are significantly different between species. Results for C , H and P are from Rudnicki et.al. (2004). * Adjusted coefficient of determination Rudnicki et al. (2004) found that hemlock had a higher drag per unit mass at 20 m/s than pine and cedar. Hemlock also had the highest drag per unit of frontal area at 20 m/s, while pine and redcedar had intermediate and low drags, respectively (Figure 4.5). 72 45 i 4 8 12 16 20 U(m/s) Figure 4.5. Comparisons of drag per unit of branch mass for redcedar, hemlock, pine and spruce. Redcedar, hemlock and pine from re-analyzed data in Rudnicki et al. (2004). Error bars are +/-1 S E . The drag per unit of branch mass for spruce could not be distinguished from redcedar and pine at 20 m/s but was lower than hemlock. Spruce crowns also had significantly more mass than the other species but were not significantly larger. Bole diameter and mass was also not significantly different from the other species (Table 4.1). Therefore, it is reasonable to assume that spruce has a higher branch mass within a similar volume (e.g. a higher density of branches) than the other species. Yet despite this difference in mass concentration the drag versus mass relationship is similar to all but hemlock. Drag per unit of frontal area for spruce was comparable to western hemlock at 20 m/s. However, the increase in drag per unit of frontal area more closely matched pine up to 16 m/s (Figure 4.6). Therefore, at lower speeds, spruce crowns seem to change shape in a way similar to lodgepole pine. Rudnicki et al. (2004) suggested that pine crowns became more compact and less porous at higher wind speeds thus creating more internal shelter. Conversely, redcedar fronds streamlined, 73 resulting in increased crown porosity. The drag versus frontal area relationship was similar in both spruce and hemlock which were higher than both pine and redcedar. The alignment of redcedar fronds was most effective because its foliage took on plate-like properties under wind load, whereas pine and hemlock foliage adopted a more cylindrical shape under wind load (Rudnicki et al. 2004). Therefore, given the similarity between the spruce and hemlock drag versus frontal area relationships, it is reasonable to assume that spruce also adopts a more cylindrical shape when subjected to wind loads. It was also observed during the experiments that the spruce branches were not very well aligned with the laminar flow at the top wind speed. This could reflect greater stiffness in spruce branches and needles, or more branch interference as they move to streamline at increasing wind speeds. 250 i 4 8 12 16 20 U(nVs) Figure 4.6. Comparisons of drag per unit of frontal area for redcedar, hemlock, pine and spruce. Redcedar, hemlock and pine from re-analyzed data in Rudnicki et al. (2004). Error bars are +/-1 S E . Some qualifications are necessary before applying wind tunnel results to windthrow simulations. The wind tunnel tests occur with a uniform wind speed profile and laminar wind flow. They do 74 not capture the effect of wind speed profile in the canopy. They also do not replicate the vertical or cross-wind forces a tree would experience in a natural forest setting - however, these are minimal. While technically possible, techniques used to-date do not measure the turning moment at the base of the tree. This would be important if wind speed varied with height in the tunnel, or if winds were turbulent. The trees that have been tested in the wind tunnel are small due to size restrictions in the tunnel. There is no data on the drag of older trees. Vollsinger et al. (in press) compared their results for small deciduous trees with Lai's (1955) work with larger trees of the same species. Lai's large trees had much lower drag per unit branch mass than the small trees tested by Vollsinger et al. They suggested this was due to less exposure of leaves and branches in larger crowns, especially on the lee side. Rudnicki et al. (2004) ran trees in the wind tunnel with one-third and two-thirds of the branch mass removed and found that frontal area reduction with wind speed was similar among treatments suggesting that individual branches behave the same as drag elements. Therefore, some sheltering effects related to scale may exist that are not yet accounted for in the small crown mass versus drag equations. Similar experiments in a larger wind tunnel test section or with high density crowns may resolve some of these issues. 4.3.0.0. Conclusions Most species showed slight increases of frontal area at lower wind speeds, followed by decreases at higher wind speeds. Unlike the other conifers, hybrid spruce drag coefficients increased for wind speeds between 4 and 8 m/s. Above 8 m/s they decreased, as did the other species. This 75 result indicates that spruce branches are somewhat stiffer and streamline less readily at lower wind speeds than the other species. Drag was found to be linearly related to the product of mass and wind speed for all species. Both branch mass and crown mass were used in combination with wind speed and, on average, the product of crown mass and wind speed provided the best linear fit. However, non-linear equations using crown mass and wind speed proved to provide the best overall fits for all species, likely reflecting the region of non-linearity at lower wind speeds. The static and dynamic drag coefficients calculated at 20 m/s suggest that differences do exist among conifer species with different foliage properties. The static drag coefficients reflect crown frontal area reduction and element drag; whereas, the dynamic drag coefficients primarily reflect element drag. The dynamic drag coefficients represent crown streamlining effect as described in Rudnicki et al. (2004) where foliage elements re-orient and compact in the direction of the wind. This definition of streamlining should not be confused with the streamlining equations in ForestGALES which are curvilinear fits to the reduction of frontal area. Rudnicki et al. found that static drag coefficients for the only comparable species in the UK and BC, lodgepole pine, were similar over the same range of wind speeds. Differences in branch streamlining between species appear to reflect the flexibility and arrangement of the foliage, branches and stem. Spruce crowns appear to be less flexible than hemlock, redcedar and pine crowns. As would be expected for a stiffer tree, static and dynamic drag coefficients were much higher than for the other species. The static drag coefficient is still decreasing at the maximum speed of 20 m/s for spruce. It is risky to extrapolate a curvilinear trend, however it is of great value to have a fixed drag coefficient for simple wind loading calculations with high speed winds and for comparisons between species. Rudnicki et al. suggested fixed still-air drag coefficients of 0.40, 0.40, and 0.22 for pine, hemlock and redcedar, respectively, be used at wind speeds of 30 m/s and above. Using this same logic, I recommend a fixed still-air drag coefficient of 0.46 for spruce. 77 5.0 Sensitivity of ForestGALES to Critical Turning Moments and Drag The data compiled in the preceding two chapters enable the adjustment of resistive moment and drag parameters in ForestGALES for western redcedar, western hemlock, lodgepole pine, and hybrid spruce growing under BC conditions. In addition, the species-specific allometric parameters that were estimated in Chapter 3 can be adjusted in the model where relevant. ForestGALES predicts critical wind speed from tree and stand attributes, and the local probability of this wind speed occurring from geographic and topographic attributes. Since location-specific wind speed return period data was not yet available for BC, this chapter will focus on the sensitivity of predicted critical wind speed to the new mechanical and allometric parameters, rather than the prediction of windthrow probability. The following hypotheses were tested: 1. The critical wind speeds estimated by ForestGALES for BC species will be the same using the 'profile' and 'roughness' methods. 2. The critical wind speed calculated by ForestGALES for a given BC species under equivalent site and stand conditions will be the same whether United Kingdom (UK) or British Columbia (BC) derived regressions are used. While it is beyond the scope of this thesis, predictions generated using new turning moment and drag parameters for BC species can be validated using tree and stand-level datasets obtained during empirical windthrow risk modelling studies in various regions of the province (e.g. Mitchell et al. 2001, Scott and Mitchell 2005). 78 5.1.0. Introduction to ForestGALES model ForestGALES was developed in the UK to provide a windthrow prediction tool for forest managers, and to integrate 30 years of research results on windthrow mechanics. The publicly available version of the model (Dunham et al. 2000) requires the user to input a basic stand and site description. The model then derives additional tree and stand parameters from internal look-up tables and allometric relationships, conducts a series of mechanical calculations, and outputs the result to the screen (Figure 5.1). Critical turning moments and drag relationships were derived from winching and wind tunnel trials, respectively. The UK Forestry Commission provided the source code for version 2.0 of the software, written in Pascal. This object-oriented code was converted to Python. The model uses many tree and stand parameters and relationships to adjust the basic mechanical relationships for a variety of stand and site conditions. These include differences in soil type, soil drainage, thinning regime, and distance from the forest edge. The adjustment factors are based on empirical observations. Wood mechanical properties, such as modulus of elasticity (MOE) and modulus of rupture (MOR), are also incorporated to enable calculation of stem deflection and breakage under load. 79 INPUT DERIVED VALUES AND RELATIONSHIPS MODEL CALCULATION OUTPUTS Distance Irom stand edge Wind speed Snow depth Stand density Crown depth Crown width Aerodynamic roughness Zero plane displacement Mean wind profile Oust factor Crown streamlining '•'•'V''' ^ Sending moment and stem surface stress at tree base as a function of wind speed Specie* Tree height Wood density Stem diameter Modulus of rupture Strength of tree stem Maximum stem surface stress that tree can withstand Critical wind speed and snow loading for uprooting and breakage Root-soil plate anchorage as a lunction ol species Maximum resistive :g:::,mornent:oi-.tree roots;'; Figure 5.1. Schematic diagram of GALES (Gardiner et al. 2000a). 5.1.1. Calculation of critical wind speed The basic steps required to calculate the critical wind speed in ForestGALES are to: 1) estimate the maximum resistive moments of trees to breakage and uprooting; 2) calculate the canopy top wind speed that will supply enough drag force on the crown to create the total moments required to break or uproot the tree; 3) use an iterative approach using the first two steps to account for reduced crown frontal area due to streamlining as wind speed increases (Gardiner et al. 2000a). 80 The ForestGALES source code includes three methods of calculating drag: 1) 'roughness', 2) 'profile' and 3) 'Mayhead' methods (Gardiner et al. 1997; Mayhead 1973a; Mayhead et al. 1975). The third method, the Mayhead method uses non-linear equations for predicting drag from wind speed and crown mass, and is not yet functional in the Python version of the ForestGALES source code used in this thesis. The roughness method is the only one available to public users. A detailed description of the steps and equations used to estimate the critical wind speed with this method can be found in Gardiner et al. (2000). Briefly, the roughness method estimates how much momentum is transferred over an area of forest. Empirically derived parameters such as zero-plane displacement and aerodynamic roughness are important components of this calculation (Raupach 1992). Adjustments have since been made to account for gusting using spacing and distance from edge (Gardiner et al. 1997). Since the aerodynamic roughness and zero-plane displacement are derived from tree height, spacing and crown frontal area (Raupach 1992), it is necessary to account for the reduction in the crown frontal area due to branch streamlining as wind speeds increase. The resulting zero-plane displacement is also used to estimate the wind speed profile above and within the canopy. The profile method then uses the within-canopy wind speed profile as part of an iterative solution to calculate applied moments for the mean tree. Another difference between drag methods, is that the roughness method assumes a triangular shaped canopy whereas the profile method assumes a diamond shaped crown. Consequently, for the estimation of drag, crown frontal area seems to be the most critical species-specific parameter with respect to the adjustment of ForestGALES for BC species. Wind speed-specific crown frontal area was estimated using, 81 A = St Crown dCrown w (5.1) 2 where still air crown depth (CrownJ) and crown width (Crownw) are used with the streamlining coefficient (Sh dimensionless) to calculate wind speed-specific crown frontal area (A) (Equation 5.1). The streamlining coefficient is calculated using a non-linear empirical equation, of the form fit to species curves obtained by Mayhead (1973) using species-specific coefficients (c and ri) and wind speed (u; Equation 5.2). The applied moments calculated with the roughness or profile method are then equated to the maximum resistive moments for breakage or uprooting, to determine the critical wind speed for each mode of failure. Maximum resistance to stem breakage is dependent on the MOR and stem diameter (dbh) for each species while the resistance to uprooting depends on turning moment equations from tree winching trials. To solve for the critical wind speed, an iterative solution is required, beginning at an initial guess wind speed of 64 m/s at the canopy top. If the moment calculated from this initial value is greater than the moment required to break or uproot the tree, then the wind speed is reduced by half the starting value (eg. 64/2 m/s). Conversely, if the calculated moment is lower than what is required to break or uproot the tree, the canopy top wind speed is increased by half the starting value. -n (5.2) 5.2.0. Methods 5.2.1. Adjustments to ForestGALES required to add new species It is not possible to control the relationships used to calculate crown frontal area, stem weight, and the critical moments and wind speeds from the user interface in the publicly available software. Furthermore, the model produces warning statements for predictions for UK species greater than 30 cm dbh, except for Sitka spruce, because large trees are not represented in the underlying datasets. Therefore, it was necessary to change the algorithms directly in the source code. Adjustments to the model were limited to tree level attributes. Site parameters were not adjusted but were used to specify scenarios in which soil conditions were equivalent to the BC winching sites. For example, in order to compare predictions for BC lodgepole pine and UK lodgepole pine, the cultivation type in the input file was set to "notched", soil type was set to "brown earth", and drainage was set to "average". Since cultivation is not used in BC the equivalent condition in ForestGALES was 'notched' meaning that the tree is planted directly into uncultivated ground. The object-oriented source code provided by the UK Forestry Commission, was converted to open-sourced object-oriented Python code (Version 2.2; Active StateCorp. 2002). The basic structure of the underlying code was preserved during this conversion. The most relevant modules with respect to adding new species to ForestGALES were "FGTreeU" and "FGTreeMechanicsU" (Appendix 4). FGTreeU contains allometric relationships and arrays that identify species coefficients and is called on by FGTreeMechanicsU. FGTreeMechanicsU is the computational engine and contains the critical wind speed and probability of critical wind speed calculations, processes user inputs and generates model outputs. Critical turning moment 83 coefficients for BC grown species were added to the TreeU module. The critical turning moment equations in ForestGALES are for average sites. Multipliers of 0.8, 1, and 1.2 are then used to adjust turning moments for sites with poor, average and good drainage, respectively. BC hemlock and redcedar were winched on a site with poor drainage, therefore, the reciprocal of 0.8 was used as a multiplier to adjust the regression to represent average conditions. Hybrid spruce was winched on a site with good drainage, therefore, the reciprocal of 1.2 was used as a multiplier to adjust the regression to represent average conditions. Finally, lodgepole pine was winched on an average site, which allowed my empirically derived equation to be used directly. Streamlining coefficients (St) were used to reduce tree-frontal areas in lieu of using dynamic drag coefficients in the TreeMechanicsU module. Non-linear regressions were fit to the wind speed-specific crown frontal area data obtained in the drag experiments using PROC NONLIN in SAS to estimate c and n, which are in turn used to calculate St (Equation 5.2). Since the crown is reduced to a solid, ForestGALES uses a static drag coefficient of 1.0 for the profile method. An element drag coefficient of 0.30 is used for the roughness method for all species. Other parameters related to drag included still air canopy breadth and canopy depth. These crown dimensional properties were derived using allometric relationships specified in the TreeU module. Some parameters in ForestGALES were not adjusted for BC species. This was due to the inability to adjust the complex iterative solutions within an appropriate timeframe and because many adjustments within the model are reliant on local empirical fixes. Therefore, the adjustments made for BC species focused on equations that related to turning moments, crown streamlining, crown size estimates, and wood density and strength (Table 5.1). 84 Table 5.1 Comparison of existing parameters for UK grown species with same parameters adjusted for BC grown species. Species **UK pineBC pine **UK hemlock BC hemlock BC hybrid BC western redcedar Turning Moment Pred. Wstem Western P Astern Western P Moslem P P Equations b0 0 -27333 0.024 0 -1125 0.879 -5362 0.294 4415 0.592 b, 140.1 145.6 <.001 159.3 96.7 <.001 98.9 <.001 118.2 <.001 Streamlining C 2.48 2.06 1.51 2.53 3.18 2.81 Coefficients N 0.63 0.43 0.68 0.48 0.49 0.77 Canopy Breadth Pred. dbh dbh P dbh-1.1 h(dbh2) P dbh P h(dbh2) P b0 0.1022 -1.07 0.329 4.5 3.55388 <.001 3.27639 <.001 5.36432 <.001 b, 29.18 16.59 <.001 -40 0.7274 <.001 6.61266 0.019 0.45581 <.001 Canopy Depth Pred. ht ht P ht h(dbh2) P ht P h(dbh2) P b0 1.0356 1.6554 0.780 4.7828 8.4751 <001 0.17198 0.949 9.17465 <001 b, 0.4605 0.2756 0.209 0.1636 1.3504 <.001 0.54592 <.001 0.80216 <.001 Stem Density 850 805 850 880 825 640 *MOE 6.40E+09 8.83E+09 8.90E+09 1.02E+10 7.94E+09 7.26E+09 *MOR 4.60E+07 3.89E+07 4.10E+07 4.80E+07 3.51E+07 3.66E+07 * Published values (Kennedy 1965). ** Indicates parameter values that were not changed in ForestGALES. Entire column of values not changed where this symbol is beside a column heading. I was able to fit very good regressions for stem mass using h(dbh2) as a predictor, however, the procedure to estimate stem mass in ForestGALES is simplistic and relies on an iterative solution using the volume of stem sections and average stem density for the tree. More work will be required to fully integrate stem mass and taper data for BC trees into the TreeU module. Therefore, the only parameter with respect to stem mass that was adjusted for BC species was stem density, which was then converted to stem mass using the default volume calculation in ForestGALES. Crown mass regressions were also fit. These were not used because the Mayhead method (Mayhead et al. 1975) in the model was making critical wind speed predictions that were of the order of ten times higher than the other two methods. This appears to result from using Mayhead et al.'s non-linear drag vs wind speed and mass equations with trees much larger than those used in the wind tunnel tests. Accordingly, only the profile and roughness methods were used to predict critical wind speeds. 85 Critical wind speeds were simulated for each of the trees in the BC winching dataset using the adjusted ForestGALES. For this purpose, the diameter and height of each individual tree was entered. The user version of ForestGALES scales down the input height to represent the average stand height. However, this step was disabled in the Python version for simplicity. Therefore, each entered tree height represents the average stand height in this case with the default spacing that is provided in ForestGALES of 1.7 m. The critical wind speeds calculated for local trees were then compared to simulations with the UK grown western hemlock and lodgepole pine trees from the UK winching database used to fit the regressions in Chapter 3. This sample was chosen from sites in the UK that were comparable to BC based on the information regarding location, soils and cultivation in the UK winching database. For the simulations with UK trees, the parameters in ForestGALES were left unadjusted. For this comparison, cultivation and soils were specified as notched planting on Brown Earth (pine) or Podzols (hemlock) with average drainage. Given that critical wind speeds are normally positively related to tree size and negatively related to slenderness, the predicted critical wind speeds were plotted against dbh and against height-to-diameter ratio to display size-related trends. 5.3.0. Results and Discussion The critical wind speeds required for overturning were lower than required for breakage in nearly every case. Achim (2004) found a similar result with balsam fir. Therefore, all critical wind speed predictions given below are for uprooting. 86 5.3.1.0. Within species comparisons of critical wind speed predictions using the profile and roughness methods Perhaps the best way to compare predictions is to plot critical wind speeds for each species independently using the profile and roughness methods. Critical wind speed predictions for BC tree species (Figure 5.1) and UK species (Figure 5.2) were plotted against dbh given all other similarities except method. Western redcedar predictions show small differences between methods up to about 32 cm. However, critical wind speed predictions using the profile method become larger than the roughness method predictions with trees above 40 cm dbh (Figure 5.1 A). Since ForestGALES is a deterministic model, the place to begin looking for discrepancies between the profile and roughness method predictions is in how they are calculated. As mentioned, canopy breadth and depth are estimated differently and used differently. My equations used to predict canopy depth for pine and canopy breadth for spruce were not significant. Therefore, a possible fix for the discrepancies in pine and spruce could be to use the detailed crown dimension and mass information from this study to make better estimates of canopy depth and breadth. Alternately, regressions for predicting crown frontal area directly could be incorporated into the model. The predicted wind speeds using the roughness method were higher for both hemlock and spruce than with the profile method (Table 5.2). The substantial difference for hybrid spruce could be due to the regression for canopy breadth not being significant, the way spacing is used in the roughness method and not the profile method, or the difference in the way roughness is used in each method among other reasons. Also, recall the shape of the crown in the profile method is a diamond when normalized crown shapes in this study looked more like a diamond that was 87 truncated at the bottom. The assumption of a diamond shape places the maximum breadth, or the height of the applied forces, higher up in the crown and wind speed profile which would increase the incremental bending moments. A truncated diamond would lower the height of the applied forces into a more sheltered part of the canopy thus increasing the corresponding above canopy critical wind speed required to produce the same overall bending moment. This would apply to all species but may be most pronounced with spruce because the length of crown extended much further down the stem relative to the other species. Table 5.2. Average differences between the profile minus the roughness method with respect to predictions of critical wind speed (a = 0.05). Species Average Difference (km/h) Lower Confidence Limit Upper Confidence Limit BC western hemlock -7.2 -9.0 -5.4 hybrid spruce -23.6 -27.1 -20.0 1800--mo-E TT12Q0-S •D £ 800 5 2 eao-5 «o-200-A 300 cfch(cnt 50 1Q0 150 200 250 300 360 400 « 0 1800 1800 J-MOO E ^ 1 2 0 0 £ 800 i m 6Q0 430 2Q0 D x ++ + + + 300 drJi(cm) Figure 5.1. Comparison of predicted critical wind speeds by dbh for western redcedar (A), BC western hemlock (B), BC lodgepole pine (C), and hybrid spruce (D) using the profile and roughness methods assuming recent exposure to a 100 m clearing, [profile method (0, • , A) and roughness method (•, • , A ) for all species except spruce profile (+) and spruce roughness (*)]. Critical wind speed predictions for UK western hemlock and UK lodgepole pine were also plotted with respect to diameter. The profile and roughness method predictions diverge immediately for UK hemlock with the profile method estimates becoming much larger with diameter (Figure 5.2B). Divergent predictions with tree size are not obvious with UK pine but the critical wind speeds predicted with the profile method were on average about 14 km/h lower than the roughness method (Figure 5.2A). Figure 5.2. Comparison of predicted critical wind speeds by dbh for UK lodgepole pine (A) and UK western hemlock (B) using the profile and roughness methods assuming recent exposure to a 100 m clearing, [profile method (A, •) and roughness method ( A , a ) ] . Critical wind speeds were also estimated with respect to tree slenderness, by species, using both methods (Figures 5.3 and 5.4). Generally, the patterns are consistent with those found when the predictions were plotted against diameter. 89 180.0 160.0 J140.0 E ^ 120.0 I 80.0 i ™ 60.0 5 «° 20.0 0.0 180.0 160.0 J140.0 E ^ 120.0 S-100.0 1 80.0 j 60.0 3 «° 20.0 0.0 0.0 80.0 H/D ratio MB 0.0 80.0 100.0 120.0 140.0 H/D ratio 18001 160.0 3T 140.0-E ~120.0 1100.0 = 80.0 s S 60.0 • B 5 4 0 0 20.0 • • s 0.0 0 0 20.0 40.0 60.0 80.0 H/D ratio 100.0 120.0 140.0 Figure 5.3. Comparison of predicted critical wind speeds by slenderness for western redcedar (A), BC western hemlock (B), BC lodgepole pine (C), and hybrid spruce (D) using the profile and roughness methods assuming recent exposure to a 100 m clearing, [profile method (0, • , A) and roughness method (•, • , • ) for all species except spruce profile (+) and spruce roughness (*)]. Figure 5.4. Comparison of predicted critical wind speeds by slenderness for UK lodgepole pine (A) and UK western hemlock (B) using the profile and roughness methods assuming recent exposure to a 100 m clearing, [profile method (A, •) and roughness method (A,n)]. More work is required to determine which calculations in ForestGALES are causing these discrepancies. A sensitivity analysis of critical wind speeds to parameters that are repeated in the 9 0 calculations such as spacing, porosity, canopy depth, and canopy breadth could isolate where and how these estimates are diverging. It is also clear that critical wind speeds calculated with each method need to be tested against observed windthrow to validate the predictions. However, for the purposes of comparing species in this thesis, the roughness method will be used from this point forward. 5.3.2.0. F o r e s t G A L E S pred ic t ions a m o n g B C s p e c i e s Overall, the predictions are logical in the sense that critical wind speed is positively related to tree diameter as expected (Figure 5.5A). 120.0-1 1200. 100.0 A t 100.0 B n 1 80.0 i nd speed (kmfh) 1 B o 20.0 ? 1 « ° E u 20.0 0.0 0 0 10.0 200 30.0 40.0 500 600 0 0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 •ameter (cm) HelgmVTJameter Figure 5.5. ForestGALES predictions of critical wind speeds by dbh (A) and slenderness (B) for trees recently exposed to a 100 m gap on equivalent average sites in BC using the roughness method. [BC lodgepole pine ( A ) , western redcedar (•), BC western hemlock (•), hybrid spruce (+)]. Critical wind speeds were also plotted against slenderness ratios (Figure 5.5B). As expected (Ruel 1995), critical wind speeds decline with increasing slenderness. On species-typical sites, the order of windfirmness in descending order is spruce, redcedar, hemlock and pine for a given diameter. However, the species are more grouped with respect to slenderness where hemlock and pine are more windfirm than redcedar and spruce. Peak gusts and peak hourly mean wind speeds in BC are typically higher on the coast than the interior (Table 5.2; Mitchell 1999). Assuming that trees tend to acclimatize to mean winds and must withstand periodic peak winds it seems reasonable that coastal species will have higher critical wind speeds than interior species. Table 5.2. Return periods (years) for peak hourly mean wind speeds and peak gust speeds (Mitchell 1999). Location Hourlv mean wind speed (km/h) Peak §ust speed (km/h) 50 70 50 70 Abbotsford (c) 1.0 2.9 * * Vancouver (c) 1.0 13.0 * Quesnel (i) 3.0 80.0 1.0 1.06 Prince George (i) * * 1.0 1.01 * No data available * i indicates interior location * c indicates coastal location Many critical wind speed estimates appear too low given that most of the trees would blow down with the first annual peak wind if the predictions were true. In part this result reflects the manner of simulation. Trees were modeled as if they were in an even-aged stand of trees with the same physical attributes. In reality, the smaller, thinner winched trees used in these simulations were subdominants. While an entire stand of trees with those attributes would have very little resistance to windthrow, in unthinned stands, these trees are lower in the wind speed profile than their larger neighbours. The basic result that critical wind speed is negatively related to slenderness ratio is consistent with known risk factors for windthrow and the general magnitude of critical wind speeds is reasonable. Further study may reveal variation of critical wind speeds with regional wind regimes within the coastal and continental wind climates in BC. 92 5.3.3.0. ForestGALES predictions for the same species in BC and the UK U K pine predictions of critical wind speed were typically higher than BC pine yet BC pine had a higher slope coefficient for the turning moment equation in ForestGALES. BC pine had an average rooting depth of 1.2 m with no signs of depth restriction while average rooting depth of U K pine from the chosen site was 0.7 m. Since Moore (2000b) found significant relationships between root plate size and resistive moment it makes sense that the resistive moment in BC pine is larger. Therefore, the U K pines have higher critical wind speeds because of, among other reasons, the drag parameters and stem density used in ForestGALES. The regressions predicting canopy depth and height using the winched BC trees were not significant. This could be fixed by fitting a better regression using BC inventory data. Lodgepole pine and western hemlock grown in BC and the U K were compared using the profile and roughness methods and the results were graphed against diameter and slenderness. Critical wind speed predictions for U K trees BC trees were similar for a given diameter (Figure 5.6A). For trees from both locations, critical wind speed decreased with slenderness, as expected (Figure 5.6B). It is interesting to note that the same species grown in two separate locations have similar critical wind speed predictions with respect to diameter and slenderness. 93 140.0 120.0 • 100.0 I B 40.0 0 D OkU *A 10.0 20.0 30.0 40.0 Dameter (cm) 50.0 60.0 140.0 1200 r 100.0 I 3 £ 40.0 "6 A,o CP 0 0 20.0 40.0 100.0 120.0 1400 Figure 5.6. ForestGALES predictions of critical wind speeds by dbh (A) and slenderness (B) for trees recently exposed to a 100 m gap on equivalent average sites in BC and the UK using the roughness method. [BC lodgepole pine (A), B C western hemlock (•), UK pine (*),UK hemlock (o)]. UK hemlock is on a completely separate and higher curve than all other species with respect to diameter. This is, in part, due to a larger critical turning moment coefficient and greater reduction in crown area with increasing wind speed (Figure 5.7 using Equation 5.10) than BC hemlock in the model. Figure 5.7 illustrates the differences in crown frontal area reduction between BC and UK species. Streamlining coefficients for BC and UK species •UK pine •BC pine •UK hemlock •BC hemlock Figure 5.7. Streamlining coefficient curves for lodgepole pine and western hemlock in BC and the UK. [UK pine (0), BC pine (•), UK hemlock (A), BC hemlock (*)]. 94 Reduction in crown area is used as a surrogate for wind speed specific static drag coefficient in ForestGALES. Although UK hemlock streamlines better, the streamlining coefficients for UK hemlock were based on wind tunnel tests on only two hemlock crowns (Mayhead 1973a). Static and dynamic drag coefficients for BC trees were calculated from wind tunnel tests on juvenile crowns (Rudnicki et al. 2004). With the ForestGALES formulation, the streamlining coefficients estimate the reduction in crown frontal area and the dynamic drag coefficient is one. However, dynamic drag coefficients vary among species (Table 5.3) and are less than one for speeds above 4 m/s. Therefore, the present formulation likely over-estimates drag. Table 5.3. Dynamic drag coefficients for BC tree species. Species Dynamic drag coefficient western redcedar *0.61 western hemlock *0.89 lodgepole pine *0.77 hybrid spruce 0.92 * Results recalculated from data in Rudnicki et al. (2004). UK hemlock also has a higher resistive moment than BC hemlock. The regressions in ForestGALES for UK hemlock are based on winching tests of 44 trees on 5 different sites, some of which were cultivated (Nicoll 2004). There is reason to suspect that the turning moment equation coefficients derived from winching studies that included cultivated sites with better rooting will be higher than for BC grown trees. 5.4.0. Conclusion The basic trends in predicted critical wind speed versus diameter and slenderness are consistent with known relationships between tree attributes and the incidence of windthrow. However, the discrepancies between critical wind speeds predicted by the roughness and profile methods make comparisons among species problematic at this stage because differences between methods outweigh differences among species. The scatter of the profile method estimates is less than the roughness method. However, the profile method produces critical wind speeds that appear too low. Further examination of the calculations used in both methods, but particularly the profile method, is required before each method will produce similar critical wind speed predictions. There are trends indicating that UK species have higher critical wind speeds than the same species in BC. However, BC pine predictions are unrealistically low given that routine local peak winds would cause nearly all trees in the stand to fail. Better estimates of crown dimensions for BC pine and spruce may facilitate more accurate predictions, as would more data for UK hemlock. Sensitivity analyses would also be useful to test the assumptions related to spacing, gust factor and crown shape. Finally, model predictions should be tested against actual windthrow occurrence to determine if they are within an acceptable range for BC species on a range of sites. 96 6.0 Conclusions and Recommendations Winching experiments on four BC species revealed linear relationships between several tree attributes and the critical turning moment. The best predictor among these tree attributes was stem mass. Stem mass has also been found to be the best predictor in prior research and is incorporated into mechanistic models such as ForestGALES. Therefore, future research should continue to focus on stem mass as a predictor of critical turning moment. The question as to why stem mass is the best predictor deserves closer attention. An inertial model of resistance may provide a useful conceptual framework for this investigation. The relationship between stem mass and critical turning moment differed for BC species grown on species typical sites. Further study of BC hemlock and western redcedar is recommended to evaluate whether these species have different relationships in mixed species stands. For now, with respect to changing parameters in ForestGALES, these two species should have individual parameters. The only species common to the UK and BC with sufficient data for meaningful comparisons was lodgepole pine. Results indicate that separate turning moment equations for each location should be maintained even under equivalent soil and cultivation conditions. Overall, the winching techniques used to obtain data were satisfactory. The use of three tilt sensors between the base and attachment point provided ample data to accurately estimate stem curvature and deflection, on the assumption of uniform curvature. The manual winch used in this study was versatile and efficient but created stem vibration while winching. Sensitivity analyses suggest this resonance was not significant with respect to the calculated turning moments, but smoother winching would simplify the analysis. A power winch is recommended 97 for any experiments involving larger trees since the loads generated for the largest trees in this study were near the capacity of the winch and its operators. However, the size of any winch should be a major consideration with respect to ease of moving it within potentially rugged terrain. Future winching experiments are recommended to capture the variability among sites and effects of tree size. Differences in static and dynamic drag coefficients at 20 m/s exist among species with different foliage properties. However, differences between the lodgepole pine in BC and the UK were not found by Rudnicki et al. (2004). Drag was found to be linearly related to the product of mass and wind speed for each species. Non-linear equations using crown mass and wind speed proved to provide the best overall fits for all species, but appear to be producing errors when applied to very large trees in ForestGALES simulations. Static drag coefficients that were calculated at 20 m/s were still decreasing for many of the species at the top speed of the wind tunnel. Extrapolation of this curvilinear trend is problematic with both static and dynamic drag coefficients. However, given the difficulty in measuring wind speed specific frontal area and the strongly linear mass versus drag relationships, the latter may be preferable for drag analysis, once issues of scaling to larger crowns are addressed. The basic relationships of predicted critical wind speed with increasing diameter and slenderness are satisfactory. There are trends indicating that UK species have higher critical wind speeds than the same species in BC. However, UK hemlock predictions appear to be unrealistically high and BC pine predictions unrealistically low. However, there are discrepancies between critical wind speeds predicted by the roughness and profile methods and these methods differ in their sensitivity to crown parameters. More work is required to adjust ForestGALES for BC species with respect to crown and stem attributes. 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Wind tunnel measurements of crown streamlining and drag relationships for several hardwood species. Canadian Journal of Forest Research Waldron, L.J. and S. Dakessian 1981. Soil reinforcement by roots: calculations of increased soil shear resistance from root properties. Soil Science. 132:427-435. Wangaard, F.F. 1950. The Mechanical Properties of Wood. John Wiley and Sons, Inc., New York. 377 p. Wolfson, R. and J.M. Pasachoff 1995. Physics: with modern physics for scientist and engineers' Ed. D. Humphrey. Harper Collins College Publishers, New York, USA. 1243 p. Wood, C.J. 1995. Understanding wind forces on trees. In Wind and Trees Ed. M.P. Coutts, Grace, J. Cambridge University Press, Cambridge, pp. 133-146. 102 Appendix 1 - Detailed Explanation of "Spline Method" The following derivation outlines the logical steps used to develop the spline equations used to estimate stem curvature (Vollsinger 2004). The "spline method" begins with the following general formulae and given starting conditions Spline #1 (S,) y = a,x3 +b,x2 +c,x + d, Given: Spline #1 (Istderiv.) ($',) y'= 3a,x2 + 2b,x +c, - Starting coordinate = P ^ X i / y , ) Spline #1 (2nd deriv.) (s;) y" = 6a,x + 2b, - Slope of the top and middle tilt sensor = k1 ,k2 - Rate of slope change at P^ - Length between P^ (height of top tilt sensor) and P2 (height of middle tilt sensor) The equations for each spline indicated by the subscripts are as follows: Equation #1 P i (x i /yd e S, -> y , = a,xf + b,x2, + c,x + d, Step #1 Equation#2 S',(P,)=k, -> k, = 3a, xj + 2b,x, + c, Step #2 Equation #3 S"(P,)= x -> Xi = 6a,x,+2b, Step #3 Derive coefficients by substitution a, = Start value Equation #4 b,=^—3a,x, Using Equ. 3 Step #4 i 2 1 1 Equation #5 c, = 3a,x2, - XiX, + k, Using Equ. 2 & 4 Step #5 Equation #6 d, = -a,x3, +^-x2,-k,x, + y, Using Equ. 1, 4 & 5 Step #6 Using the values from the first spline equation (Si) the following calculates x 2 and y 2 for the second spline equation as follows: With S',(P,)=k7; k2 = 3 a /X2 + 2bjX2 + c, Then by substitution: k2 = 3atx22 + 2X2\^Y~ 3a,Xl \ +3a,x2 - %,x, + k, k2 = 3a,x2 + x2(z, -6a,x,)+{^a,*/ - xi*i + k,) 3a,x22 + x2(x, - 6 a , x 2 ) + ( 3 a , x 2 - x i*i + k, - k2)= <j> 'Xi -6a,x, 3a, J I 3a, 6a,x, - Xi 6a Equation #7 With P,(x, /y,)eS,; , ' 6aJ J \{ ' 6 a U {3a,x[-Xix,+k,-k2) Step #7 3a, y2 =a,x2 +b,x2 +c,x2 +d, Step #8 103 The preceding derivation assumes that the x variable is the vertical component of the arc and the y variable is the horizontal deflection of the tree. The arc length for each spline is divided into 100 segments and these segment lengths are then used to produce 100 x and y coordinate pairs. The following table is an example of how the curvature of one tree (PI 13) is estimated using the given k3 slope lowest tilt sensor k2 slope middle tilt sensor k1 slope top tilt sensor 11 distance between low and mid 12 distance between mid and top curvel 2nd derivate in spline begin 0.040648395 0.135192864 0.214127687 5.3 5.6 0 BC's / assumptions 1. ) slope continuous over whole stem 2. ) curvature at top = 0 3. ) curvature continuous over whole stem wanted P1 x1 y1 P2 x2 y2 P3 x3 coeffs a1, b1, d , di of spline 1 coeffs a2, b2, c2, d2 of spline 2 0.00000 0.00000 1.03353 5.50289 1.71021 10.75669 first spline general s1 sr s1" y = a1*xA3 + b1*xA2 + c1*x+ d1 y' = 3*a1*xA2 + 2*b1*x + d y" = 6*a1*x + 2*b1 with P1(x1/y1) element of s1: s1'(P1) = k1 c1=k1 s1 "(P1) = curvel b1 =(curve1 )/2 abscissa of spline begin ordinate of spline begin arc length of spline slope at begin slope at end curvature at begin curvature at end abscissa of spline end or ordinate of spline end or coeffs of spline intervalx step dx arc x= y= l= k= k= curve= curve= x= x= y= y= a= b= c= d= upper spline 0 0 5.6 0.214127687 0.135192864 0 -0.02868851 5.50288757 -5.50288757 1.033530768 -1.033530768 -0.000868893 0 0.214127687 0 -5.50288757 -0.055028876 5.6006 lower spline -5.50288757 -1.033530768 5.3 0.135192864 0.040648395 -0.02868851 -0.064679392 -3.477684755 -10.75668872 -0.843172439 -1.710213327 -0.002961916 -0.063241525 -0.291752963 -1.217514417 -5.253801152 -0.052538012 5.3000 0 0 0.0000 goalseeker -0.00055 0.00002 PI13 ht1 11.2 ht2 ht3 1 2 3 11 12 k1 k2 k3 5.6 0.3 12.0861 7.6993 2.3277 5.3 5.6 0.214128 0.135193 0.040648 name ID act tree: PI13 78 next tree: 79 •w saved? yes needed: given given given given 0.214127687 0.135193ok given 0.135192864 0.040648ok given -0.02868851 k2.chi1 k2, chil k2,chi1 k2, chil -0.02869 check! -0.06468 ok a1, k1 al, k1 al, k1 a t k1 start value chit, x1, k1, a1 chil, x1, k1, a1 chil, xl, y1, k1, a1 spline method (Vollsinger 2004). 104 The results of each run of the spline method produced 200 x and_y coordinate pairs used to approximate the curvature of the stem from the bottom tilt sensor to the top tilt sensor. The following figure is a graphical representation of the curve produced for PI 13 using the polynomial function with a sampling of the x and y coordinates used to determine curvature for x1 yi d ard x2 y2 d arc2 0 -0.05502888 0 -0.01178306 -5.50288757 -1.03353077 0.05627626 -5.55542558 -1.0406727 0.05302122 -0.11005775 -0.02356525 0.05627608 -5.60796359 -1.04789123 0.05303159 -0.16508663 -0.03534571 -0.04712356 -0.05889793 0.05627572 0.05627517 0.05627444 -5.6605016 -1.05518381 ""0.05304172 -0.2201155 -5.71303962 -5.76557763 -1.06254783 -1.06998074 0.05305159 0.0530612 -0.27514438 -0.33017325 -0.07066796 0.05627354 -5 81811564 -1.07747995 0.05307053 -0.38520213 -0.08243278 0.05627245 -5.87065365 -1.08504288 0.05307957 -0.44023101 -0.09419151 0 0562"I 17 -5.92319166 -1.09266695 0.05308832 -0 49525988 -0.1059433 0.05626972 -5.97572967 -1.1003496 0.05309676 " -0.55028876 -0.11768727 0.05626809 -6.02826769 -1.10808824 0 05310489 -0.60531763 -0.12942255 0.05626628 -6 0808057 -1.1158803 0.0531127 -0.66034651 -0.14114827 0.05626429 -6.13334371 -1 12372319 0.05312018 -0.71537538 -0.15286357 0.05626211 -6.18588172 -1.13161435 0.05312733 -0 77040426 -0.16456758 0.05625976 -6.23841973 -1.13955119 0.05313413 -0.82543314 -0.17625942 0.05625723 -6.29095774 -1.14753113 0.05314059 -0.88046201 -0.18793823 0.05625453 -6.34349575 -1.15555161 0.05314669 -0.93549089 -0.19960315 0.05625164 -6.39603377 -1.16361004 0.05315243 -0.99051976 -0.21125329 0.05624858 -6.44857178 -1.17170384 0 05315781 -1.04554864 -0.2228878 0.05624535 -6.50110979 -1.17983044 0.05316281 -1.10057751 -0.2345058 0.05624193 -6.5536478 -1.18798726 0.05316744 -1.15560639 -0 24610642 0.05623835 -6 60618581 -1.19617173 0 05317169 -1.21063527 -0.25768881 0.05623459 -6 65872382 -1.20438126 0 05317555 -1.26566414 -0.26925208 0.05623065 -6.71126183 -1.21261328 0.05317903 -1.32069302 -1.37572189 -0.28079537 -0.29231781 0.05622655 0.05622227 -6.76379985 -6.81633786 -6.86887587 -1 22086521 -1.22913448 -1.23741851 0.05318211 01)531848 -1.43075077 -0.30381853 0.05621782 0.0531871 -1.48577964 -0.31529666 0.05621321 -6.92141388 -1.24571471 0.053189 -1.54080852 -0.32675134 0.05620842 -6.97395189 -1.25402052 0.0531905 -1.5958374 -0.33818169 0.05620347 -7.0264899 -1.26233336 0.0531916 -1.65086627 -0.34958685 0.05619835 -7.07902792 -1.27065064 0.05319229 -1.70589515 -0.36096595 0.05619307 -7.13156593 -1.2789698 0.05319258 each spline equation (Vollsinger 2004). Abscissa is the horizontal or x-coordinate in a coordinate system Ordinate is the vertical or y-coordinate in a coordinate system 105 Appendix 2 - Detailed Explanation of "Coordinate Method" The "coordinate method" estimates stem curvature between the bottom and top tilt sensors by dividing the stem into one-metre segments and changing the angle at a constant increment for each segment. The following table is a working example of how curvature is estimated using this method. The adjoining figure is the resulting graph from these calculations. The dotted line on the graph is the estimated curvature using the "spline method" on the same tree, for comparison purposes. ht1 8.6~1 ht2 4.4 >- Height of each tilt sensor in metres ht3 0.3 _J tiltldefl 25.0821 ~~| tilt2defl 18.454 V- Angle of each tilt sensor in degrees tilt3defl 11.7366 _J curv1_2 1.578119048-* Incremental change of angle between top and middle tilt sensor in degrees per metre curv2_3 1.638390244-•Incremental ch jnge of angle between middle and bottom tilt sensor in degrees per metre tiltl deflrad 0.437765228 ~~1 tilt2deflrad 0.32208306 >— Angle of each tilt sensor in radians tilt3deflrad 0.204842313 _J curv1_2rad 0.027543373 -^Incremental change of angle between top and middle tilt sensor in radians per metre curv2_3rad 0.028595304-•Incremental ch ange of angle between middle and bottom tilt sensor in radians per metre 0_0.3angle 0.204842313 Iat0_0.3 0.293727922 ~ - Bottom segment between base and stump dep0_0.3 0.061023832 height assumes angle of bottom sensor 0.3_1.3angle 0.204842313 Iat0.3_1.3 0.979093072 - First one-metre segment assumes dep0.3_1.3 0.203412772 angle of bottom sensor 1.3_2.3angle 0.233437617 Iat1.3_2.3 0.972876944 - Every subsequent segment adds the incremental dep1.3_2.3 0.231323262 _ change of angle to its deflection 2.3_3.3angle 0.262032921 Iat2.3_3.3 0.965865357 -> Latitudes are distance up the stem on the y-axis dep2.3_3.3 0.259044614 Departures are the deflection across the x-axis 3.3_4.3angle 0.290628226 Iat3.3_4.3 0.958064044 dep3.3_4.3 0.286554162 4.3_5.3angle 0.31922353 Iat4.3_5.3 0.949479383 dep4.3 5.3 0.313829413 5.3_6.3angle 0.346766903 Iat5.3_6.3 0.940476423 dep5.3_6.3 0.339858938 6.3_7.3angle 0.374310276 Iat6.3_7.3 0.930760027 dep6.3_7.3 0.365630649 7.3_8.3angle 0.40185365 Iat7.3_8.3 0.920337567 dep7.3_8.3 0.391124997 8.3_9.3angle 0.437765228 Iat8.3_9.3 0.588705832 ~ - The final segment calculates latitudes and departures dep8.3_9.3 0.275545718 J between the last full segment and the attachment pt. 9.3_10.3angle 0.437765228 Iat9.3_10.3 0 dep9.3_10.3 0 10.3_11.3angle 0.437765228 Iat10.3_11.3 0 dep10.3_11.3 0 Remaining segments used in Excel file to facilitate 11.3_12.3angle 0.437765228 Iat11.3_12.3 0 higher attachment points dep11.3_12.3 0 12.3_13.3angle 0.437765228 Iat12.3_13.3 0 dep12.3_13.3 0 13.3_14.3angle 0.437765228 Iat13.3_14.3 0 dep13.3_14.3 0 14.3_15.3angle 0.437765228 Iat14.3_15.3 0 dep14.3_15.3 0 1 r sumlat 8.499386572 ~ Identifies the estimated location of the attachment pt. sumdep 2.727348357 _ on coordinate grid to facilitate calculation of applied and self-loading components of the critical moment Cw1 106 Appendix 3 - Detailed Explanation of the Calculation of the Critical Turning Moment The following figure is a graphical representation of the calculation of the moments for each tree. The component applied force vectors ( F a ( h 0 r i z ) and F a ( v e r t ) ) are calculated using the applied force along the cable and the cable angle which were measured directly in the field. The horizontal and vertical lever arm lengths are calculated by taking the differences of the x and y coordinates of the attachment and pivot points. The gravitational force vector ( F g ) is projected downward from the centre of gravity for the whole tree. The corresponding lever arm is calculated as the difference between the x-coordinates of the centre of gravity and pivot point. PI10 30 •] vertical projection of pivot point 25 Anchor Tree 20 A 15 10 J 0 5 offset pivot point 15 Cable 20 Cable angle (0)=16% 25 30 35 40 107 The moment was calculated using two different criteria for locating the pivot point. The first, referred to as the offset pivot, assumes that the pivot point is offset from the base of the tree in the direction of the winch. The second, referred to as the base pivot, assumes the pivot point occurs at the base of the tree. The offset pivot could only be estimated for uprooted trees. The x-coordinate of the offset pivot is the horizontal distance between the central axis of the stem and the point in the root-soil plate where major structure roots underwent compressive breaks. The broken roots were observed in the hollow created by all uprooted trees and generally occurred near the edge of the root-soil plate. Therefore, the minimum depth of the root-soil plate was used to estimate the depth of the break or y-coordinate of the pivot point. The base pivot simply uses the base of the tree (coordinate {0,0}) as the pivot point for calculating the turning moment. Trees with root collar breakage as a mode of failure also use the base of the tree as the pivot point. Stem-broken trees used the break height and method of estimating stem curvature to calculate the coordinates of the break and thus the pivot point. Most of the broken stems occurred at about one to two metres causing the x and y-coordinates to be minutely greater than zero and minutely smaller than the break height, respectively. Therefore, very little value would be derived from calculating the moment using a pivot along the central axis at the break height, in addition, for comparison. Appendix 4 - System diagram of ForestGALES modules t , System (Python system rile Imports) • Gales.py\ p i profile™] sys .] Configuration Gales Model Utilities ctgjorestgales (oohigu ration tie -for Forest Gales) t^ cirigB] i-Toil FGTreeU { (module free) j FGCultivation I (cuiivatxu) types) FGTestData (series of parameters* ~FGHolp t he $> encodes for /farameten) FGreport 1 FGreport2 (simplereporting) %| \(reporting (orparameter. S \ A • 1 M " " T G C U I . •• '; j i : ••• | -4 testing) FGgraph (ptots datapn ygtapii)'' tuenuuew .(irian ties) j FGConstants (constants) » viewer ] | FGSoil (module SailTy&) t imer t^ime stamps/ v,,een Kscreen oontrot) FCThinning (thinning regimes) .,(pp eratihg-system .^ dependemoonaams) F G C o n s t a n t s FOLitlli:itf? (damage status) j rewc \FGYieidtabic ->u»?r»'j. FGTreeMechanics U • (computath/aflengine)*'.' FGConstants ( FGTreeU FGConstants FGCultwjtnn FGSoiis MFOTreeMechanicsU j rC ?'FGTreelf J [FGutilities! L| FC-'vieiaable FGConstants " F©reportaFC*Yieldtal»le: corhme • : Appendix 5 - Pearson's correlations for dendrometric variables Pearson Correlation Coefficients, N = 73 Prob > Irl under HO: Rho=0 ht I crown cr_wmax dbh h(dbh2) dbh3 irlstem mcr(hmc) TTlfree areacr pivot J ht I crown crjvmax dbh hdbh2 dbh3 Western frlcrhmc Wlfree areacr pivot J 1 0.53321 0.38278 0.66748 0.7268 0.57303 0.81106 0.69176 0.79001 0.44868 0.52219 <.0001 0.0008 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 0.53321 1 0.63197 0.6425 0.652 0.60776 0.66855 0.65518 0.68326 0.79512 0.5319 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <0001 <.0001 0.38278 0.63197 1 0.79308 0.77755 0.78942 0.68321 0.78045 0.71484 0.90565 0.64742 0.0008 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 0.66748 0.6425 0.79308 1 0.96632 0.95127 0.87136 0.91075 0.89311 0.82318 0.79239 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 0.7268 0.652 0.77755 0.96632 1 0.97224 0.92583 0.95603 0.94278 0.84063 0.78842 <.0001 <.0001 <.0001 <0001 <.0001 <.0001 <.0001 <0001 <.0001 <.0001 0.57303 0.60776 0.78942 0.95127 0.97224 1 0.83668 0.91927 0.8657 0.85682 0.77044 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 0.81106 0.66855 0.68321 0.87136 0.92583 0.83668 1 0.93139 0.99725 0.76977 0.74528 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 0.69176 0.65518 0.78045 0.91075 0.95603 0.91927 0.93139 1 0.95369 0.85008 0.75047 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <0001 <.0001 <.0001 0.79001 0.68326 0.71484 0.89311 0.94278 0.8657 0.99725 0.95369 1 0.80171 0.75667 <.0001 <.0001 <.0001 <.0001 <.0001 <0001 <.0001 <.0001 <.0001 <0001 0.44868 0.79512 0.90565 0.82318 0.84063 0.85682 0.76977 0.85008 0.80171 1 0.65281 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 0.52219 0.5319 0.64742 0.79239 0.78842 0.77044 0.74528 0.75047 0.75667 0.65281 1 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 Appendix 6 - Tree Failure Modes The following two pictures illustrate trees that failed due to uprooting.
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Critical turning moments and drag equations for British Columbia conifers Byrne, Kenneth Earl 2005
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Title | Critical turning moments and drag equations for British Columbia conifers |
Creator |
Byrne, Kenneth Earl |
Date Issued | 2005 |
Description | Tree winching experiments were conducted for 4 British Columbia (BC) tree species: western redcedar (Thuja plicata (Donn ex D. Don) Spach), western hemlock (Tsuga heterophylla (Raf.) Sarg.), and lodgepole pine (Pinus contorta Doug, ex Loud.), and hybrid spruce (Picea engelmannii Parry XPicea glauca (Moench) Voss). Strong linear relationships between stem mass and critical turning moments were found. Based on the slope coefficients, lodgepole pine (145.6), hybrid spruce (118.6), western redcedar (94.5), and western hemlock (77.4) have different critical turning moments with respect to mass. Comparison with results for trees in the United Kingdom (UK) tree winching database indicated that there is a difference between the slope coefficients for BC pine and pine grown in the UK on equivalent soils. Wind tunnel experiments with juvenile crowns of the hybrid spruce were compared with results from earlier experiments with redcedar, hemlock and lodgepole pine. Static and dynamic drag coefficients, and mass versus drag relationships were examined. Differences in drag coefficients exist for species with different foliage characteristics, however, differences in the mass/drag relationships were less pronounced. Critical turning moment and drag results were used to adjust selected parameters in the UK Forestry Commission's mechanistic windthrow risk model 'ForestGALES' to estimate critical wind speeds for the four BC species and for lodgepole pine and hemlock grown in the UK. UK grown trees have higher critical wind speeds than trees of the same species grown in BC. More work is required to adjust ForestGALES to reflect the differences in tree form and mechanical attributes for BC species and to validate model predictions. |
Genre |
Thesis/Dissertation |
Type |
Text |
Language | eng |
Date Available | 2009-12-11 |
Provider | Vancouver : University of British Columbia Library |
Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
DOI | 10.14288/1.0075001 |
URI | http://hdl.handle.net/2429/16479 |
Degree |
Master of Science - MSc |
Program |
Forestry |
Affiliation |
Forestry, Faculty of |
Degree Grantor | University of British Columbia |
GraduationDate | 2005-11 |
Campus |
UBCV |
Scholarly Level | Graduate |
AggregatedSourceRepository | DSpace |
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