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Physiology and Biochemistry |
2Forest Research Institute Baden-Württemberg, Wonnhaldestr. 4, D-79100 Freiburg, Germany; 3Forest Research, Northern Research Station, Roslin, Midlothian, EH25 9SY, Scotland
Received for publication April 6, 2006. Accepted for publication July 27, 2006.
ABSTRACT
This paper reports on the effect of wind loading below damaging strength on tree mechanical and physical properties. In a wind-exposed Sitka spruce stand in western Scotland, 60 trees at four different levels of wind exposure (10 m, 30 m, 50 m, 90 m from edge) were characterized for stem and crown size and shape and mechanical properties, including structural Young's modulus (Estruct), natural frequency, and damping ratio. Estruct increased from the stand edge to the mid-forest, but with a large inter-tree variation. Swaying frequency and damping ratio of the trees also increased with distance from edge. Wind-exposed edge trees grew shorter, but more tapered with an overall lower Estruct, allowing for greater flexural stiffness at the stem base due to the larger diameter and for higher flexibility in the crown region of the stem. The trees at the middle of the stand compensated for their increased slenderness with a higher Estruct. Thus, for the different requirements for wind-firmness at stand edge and mid-forest, an adapted combination of tree form and mechanical properties allows the best withstanding of wind loads. The results show the requirement to understand the different strategies of trees to adapt to environmental constraints and the heterogeneity of their growth reactions in response to these strategies.
Key Words: architecture; biomechanics; crown size and shape; damping ratio; structural Young's modulus; swaying frequency
The relationship of tree architecture and tree biomechanics has been the subject of much discussion with respect to the risk assessment of storm and snow damage to forests in order to prevent economic losses (Everham, 1995
; Kellomäki and Peltola, 1998
; Quine and Gardiner, 1998
). Accurate modelling to predict wind and snow damage by overturning or stem breakage is based on understanding the influence of different elements such as stand structure, root anchorage, tree size and shape, and the mechanical characteristics of the stem and branch axis. Together these features define tree stability against mechanical constraints (Persson, 1972
; Petty and Worrell, 1981
; Petty and Swain, 1985
; Rottmann, 1985
, 1986
; Coutts, 1986
; Schmidt-Vogt et al., 1987
; Blackburn et al., 1988
; Nielsen, 1990
; Valinger et al., 1992
, 1993
, 1997
, 1999
; Wood, 1995
; Päätalo et al., 1999
; Talkkari et al., 2000
; Ancelin et al., 2003
; Cucchi and Bert, 2003
). Quantitative risk assessment for classification systems such as ForestGales (Dunham et al., 2000
), HWind (Peltola et al., 1999
), WINDA (Blennow et al., 2003
) implement mechanistic models that attempt to describe the effects of tree characteristics, climatological conditions, and the influence of the stand and site structure. These systems are built upon one or more components describing the temporal and spatial variation of strong winds and snow and submodels concerning the static and dynamic behavior of trees to wind or snow loads with respect to the aboveground tree components and the root anchorage system.
Trees have relatively limited options to adapt to the multiple mechanical constraints acting on them over time. Evolutionary adaptations to environmental constraints include changes to geometric, morphological, and structural characteristics. Mechanical loading fundamentally influences the development of the outer shape of the tree. The concept of adaptive growth was introduced by Schwendener (1874)
and adopted for forestry by Metzger (1893)
. The concept proposes that trees develop a trunk shape that is optimized to withstand vertical and horizontal mechanical loads. The basis is that at all stages the stresses at the surface of the trunk induced by external loads are evenly distributed (constant-stress theory, Mattheck, 1991
). Morgan and Cannell (1994)
reexamined the constant-stress theory and found that a tree is subject to a varying magnitude of constraints; hence the shape of the tree trunk has to compromise to average conditions. They formulated the uniform-stress theory: within the average range of mechanical loads, the stress will be uniformly distributed vertically due to the stem form, but in extreme conditions the stress distribution will be non-uniform along the stem. However, the stress distribution will vary with changes in the distribution of the stem and crown/branch mass under the influence of snow loading (Antoine, 1974
; Schmidt and Pomeroy, 1990
; Schmidt and Gluns, 1991
; Nykänen et al., 1997
) or wind loading (Gardiner, 1992
; Morgan and Cannell, 1994
; Stacey et al., 1994
; Wood, 1995
).
A number of authors (e.g., Esser, 1946a
, b
; McMahon, 1973
; Petty and Worell, 1981; Mamada et al., 1984
; Morgan and Cannell, 1987
, 1994
; Cannell and Morgan, 1987
, 1989
; Milne and Blackburn, 1989
; Spatz and Bruechert, 2000
) applied engineering beam theory to analyze the bending of trees and the vertical distribution of the stresses within the tree to understand the static mechanical behavior of trees. The investigations included deductions of critical dimensions and safety factors (McMahon and Kronauer, 1976
; King and Loucks, 1978
; Dean and Long, 1986
; Mattheck et al., 1993
; Niklas, 2000
) and the validation of allometric power laws on tree size interrelationships (Bertram, 1989
; King, 1991
; Morgan and Cannell, 1994
; Moulia and Fournier-Djimbi, 1997
). Niklas and Spatz (2004)
, however, suggested that the proportional relationships of tree size are governed by hydraulic constraints rather than by mechanical stability. Nonetheless, forest practice found height-to-diameter ratio a good predictor of tree stability and consider trees with a relative large stem taper and a vigorous, long crown as particularly stable (Abetz, 1976
; Abetz and Unfried, 1984
; Rottmann, 1986
; Kellomäki and Peltola, 1998
). The physiological costs for the optimal stem shape and support costs of branches were examined by King (1981)
and Cannell et al. (1988)
. All these models form the basis for further understanding the dynamic behavior of trees, in particular in response to wind loading.
Trees are dynamic systems, and their response to mechanical loads varies with time. Considerable research into the interaction between wind and tree movement has been conducted to better understand the dynamic components (that is, swaying and damping) of the mechanical behavior of trees (e.g., Sugden, 1962
; Mayer, 1987
; Milne, 1991
; Peltola and Kellomäki, 1993
; Peltola, 1996
; Peltola et al., 1997
; Kerzenmacher and Gardiner, 1998
; Flesch and Wilson, 1999
; Neild and Wood, 1999
; Moore and Maguire, 2004
, 2005
). With respect to swaying, a tree responds most to wind gusts close to its resonant frequency and harmonics (Gardiner, 1992
), and the amplitude is therefore frequency dependent. Several authors report figures for the natural frequency of mature trees of different species, mainly conifers (Mayhead, 1973b
; Mayhead et al., 1975
; Milne, 1991
; Gardiner, 1992
; Flesch and Wilson, 1999
). Natural swaying frequency seems closely related to size characteristics of the tree, i.e., tree height and diameter close to the stem base (dbh1.3m) (Mayhead, 1973a
, b). Pruning experiments highlighted the effects of the crown mass and its vertical distribution on the natural oscillation frequency of trees; on removal of the branches from the tree as the swaying frequency increases (Milne, 1991
; Gardiner, 1992
; Moore and Maguire, 2005
). Snow will increase the overall mass and hence reduce swaying frequency.
Trees act as damped harmonic oscillators. The dissipation of the energy of a swaying tree arises from different sources, with the architecture of the tree playing an important role: clashing of crowns with neighbor trees, aerodynamic damping by drag of the crowns (Mayhead, 1973b
; Amtmann, 1986
; Wessolly, 1991
; Rudnicki et al., 2004
), structural damping (Niklas, 1992
; Kerzenmacher and Gardiner, 1998
; Moore and Maguire, 2005
), and internal friction or viscous damping of the wood (Milne, 1991
). In monocultural conifer stands, crown clashing and aerodynamic damping accounts for 50% and 40% respectively, of total damping; structural damping accounts for 10% of the damping according to Milne (1991)
.
All these models, however, are based on the assumption that woody plant stems can be treated as build of homogenous material. To the contrary, the physical and mechanical properties of wood vary greatly in the vertical direction of tree stems due to changes in density and annual ring width with age and growth space and to the presence of reaction wood (Rendle, 1959
; Telewski and Jaffe, 1986
; Timell, 1986
; Telewski, 1989
, 1995
; Lesnino, 1996
). These findings suggest that a Young's modulus Estruct. integrated over a cross section will not reflect the vertical differences in wood structure of a tree. Blackburn (1997)
and Brüchert et al. (2000)
found a highly variable structural Young's modulus Estruct. from butt to treetop with a general decrease in Estruct. with increasing tree height for Sitka spruce and Norway spruce [Picea abies (L.) Karst.], respectively. Spatz and Bruechert (2000)
showed that for branches, Estruct varied with branch diameter and vertical position on the tree. However, no useful relationship has been established so far to describe this variation in Estruct.
We report on investigations to describe static and dynamic properties of Sitka spruce in relation to the tree architecture and stem mechanical properties. Focus is given to the role of wind exposure because wind is an important component of the mechanical constraints imposed on trees. A detailed description of the size and shape of the individual tree allows understanding of the static and dynamic mechanical response to different wind loads with respect to internal structure of the supporting stem, to tree swaying and damping ratio.
MATERIALS AND METHODS
The study site was an even-aged stand of predominantly Sitka spruce [Picea sitchensis (Bong.) Carr) with small patches of lodgepole pine [Pinus contorta Dougl. ex Loud.) in Kilmichael Forest, Argyll Forest District, in western Scotland (56°04'25'' N, 5°22'05'' W). Only one site was chosen, defined by the following characteristics: mean wind speed, 5.5 m/s; slope, 16°; elevation, 150 m; accumulated temperature (degree days over 5°C), 1260; precipitation, 1800 mm/year. This was to keep as many site and stand characteristics constant when investigating the effect of wind exposure on tree growth and biomechanics. The stand was planted in 1953 at 1.5 m by 1.7 m (3900 trees/ha) and remained unthinned, which led to self-thinning, a distinct differentiation of the stocking density, and a wide range of diameter at breast height (dbh, i.e., 1.3 m). The site is characterized by a severe wind exposure to the west and a peaty gley soil.
Within a stand, the mean wind speed and subsequent bending moment on the individual tree decreases rapidly from the edge to the inner stand (Fig. 1) (Stacey et al., 1994
). Four distances (10 m, 30 m, 50 m, 90 m) from the edge to the mid-forest were chosen, representing different wind exposures for the trees. Sixty trees were selected for the experiments using stratified random sampling. In each line, 15 trees with diameters between 0.27 and 0.41 m dbh were selected, representing the most vigorous trees in the stand.
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), the external dimension and shape of each tree stem recorded by dbh (stem diameter at 1.3 m stem height, measured in two perpendicular directions), tree height (total length of the stem), stem taper (reduction of diameter in centimeters per meter stem length), height-to-diameter ratio, the size and shape of the crown, height to lowest green whorl (>
of branches alive) and crown length (length between lowest green whorl and treetop). In addition, the crown projection area (calculated from the windward, leeward, and two perpendicular crown extensions derived from the vertical projection of the outermost tip of the branches to the ground), crown asymmetry (largest crown radius/smallest crown radius of the four directions), position of whorls on the stem, and the mass of branches for each whorl were measured.
Mechanical tree characteristics: structural Young's modulus, swaying, damping ratio
The mechanical properties of the standing trees were characterized by bending stiffness, structural Young's modulus Estruct, and swaying frequency. Bending stiffness EI and Estruct were measured by static pulling tests using calliper type strain-gauge transducers (Blackburn, 1997
; Moore et al., 2005
) in wind-still conditions when the soil was saturated. Measurements were made at eight heights on the stem, equidistantly distributed between 1.5 m and the height where the stem diameter was reduced to 14 cm. A continuously increasing load was slowly applied by pulling a rope fixed at 1 m above the highest strain gauge, which caused a slight bending of the stem of less than 3° at the bottom of the tree. Loading to the maximum force lasted between 2 to 3 min and controlled release of the load for the static measurement between 1 to 2 min depending on the applied force. The recorded force and measured strain of the peripheral fibers of the stem allowed calculation of the bending stiffness of the stem and the elastic properties of the stem material (Estruct) (Niklas, 1992
; Wood, 1995
; Brüchert et al., 2000). The swaying frequency and damping ratio were recorded by releasing the tree from forced bending and letting it sway freely, avoiding crown contact with neighboring trees as far as possible, until no further movements were recorded by the strain gauges at all eight heights of the stem. Damping ratio 
was derived from these swaying experiments by individually fitting a model of damped oscillation for each swaying test and applying the swaying equation:
|
| (1) |
the natural frequency, and 
a time lag.
Internal stem structure
The internal structure of the stem was analyzed on a disc taken at 4 m stem height. At this height, heterogeneity in ring structure was felt to be less affected by buttressing and wavy pith than at 1.3 m height, and branches and whorls could be avoided as well. Annual radial increment was measured in four directions (windward, leeward, and two radii perpendicular) using the program WinDendro, version 6.4a (Regent Instruments, Quebec, Quebec, Canada). Mean ring width was calculated from individual ring measurements on all four radii. Radial eccentricity, as a measure of internal heterogeneity of the stem, was derived from the difference between the windward and the leeward radius and normalized to the total diameter.
Statistical analysis
Statistical analysis was carried out using SAS version 8.01 software package (SAS Institute, Cary, North Carolina, USA). Differences in means between the different levels of wind exposure were tested by ANOVA using Scheffe's test, regarding differences as statistical significantly at P = 0.05. We used 
2-tests to test for the heterogeneity of Estruct. Linear regression models were fitted to predict Estruct, swaying frequency, and damping ratio from external and internal tree characteristics, using stepwise regression analysis with P = 0.15 for entry into the model.
RESULTS AND DISCUSSION
External characteristics: tree height, diameter at breast height, height-to-diameter ratio
At the experimental site, the treetop height generally increased with increasing distance from the edge, converging to approximately 27 m at mid-forest (Table 1). The same held true for the tested trees, sampled randomly within a particular diameter range to avoid too large a variation in dbh (Table 2). The mean tree height for the sample trees increased slightly from the edge to the stand center from 24.9 m to 27.4 m, with no statistically significant difference (P = 0.05). However, with regard to all trees in each exposure situation the difference between stand edge and mid-forest became significant. Height-to-diameter-ratio (h/d) rose from 75.5 to 87.6, indicating increasing slenderness of the centrally grown trees under sheltered conditions. The h/d ratio of exposed trees close to the edge in line "10 m" was significantly lower than for the sheltered lines "50 m" and "90 m."
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), leading to earlier branch death and self-pruning of the trees. Figure 2 shows the variation in the vertical and the horizontal crown projection areas and the crown asymmetry in relation to the distance from the edge. The average vertical crown area varied between 9.4 to 4.8 m2, with a significantly larger crown area for the trees close to the edge (P = 0.05). The horizontal crown projection area changed in a similar way, generally decreasing from 33 m2 in line "10 m" to 22 m2 in line "90 m." The mean crown asymmetry varied from 2.01 to 3.23, with no distinct tendency from the edge to the mid-forest due to the large variation between the trees within the individual lines. The vertical and horizontal mean crown projection area of the sample trees in line "10 m" (close to the edge) was therefore larger but less asymmetric than crowns of trees in the center of the forest.
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|
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|
| (2) |
|
1.0 GPa/m; (3) var < 0.5 GPa/m.
Figure 4 shows the distribution of the heterogeneity in these three classes. The proportion of very small changes of Estruct in axial direction increased slightly from 60% to 70% from line "10 m" to line "50 m" and "90 m." At the same time, the proportion of large changes of Estruct over 1 GN/m2 per m stem length in line "10 m" increased (16%) strongly from the values of 5–7% measure in lines "30 m," "50 m," and "90 m." The 2 tests for differences in the frequency showed that within each line the frequency of neglectable and small local changes in Estruct were similar, whereas the frequency of large local changes was significantly lower. The inter-line comparison showed that in line "10 m" the frequency of large local changes in Estruct was significantly higher than in lines "30 m," "50 m," and "90 m."
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Dynamic tree characteristics: swaying frequency and damping ratio
Swaying frequency varied for the individual tree between 0.13 Hz and 0.41 Hz (Table 3). The mean swaying frequency decreased from 0.27 Hz in line "10 m" to 0.22 Hz for line "90 m." ANOVA showed that there are statistically significant differences in the swaying behavior of the trees between line "10 m" at the stand edge and line "90" at the middle of the stand; lines "30 m" and "50 m" were intermediate (P = 0.05). The largest variation in swaying frequency within a line was found in line "10 m," close to the edge. The variation in swaying frequency is not related to the degree of wind exposure represented by line "10 m" to line "90 m," but is closely correlated to the height and the diameter at breast height of the tree as expected from theory (Gardiner, 1989
; Moore and Maguire, 2005
) (Fig. 5). Thus the swaying frequency decreased with increasing height, because taller trees act like a longer pendulum with a longer period and lower frequency, and increased with increasing dbh. Because tree height significantly increased from the edge to mid-stand, the swaying frequency also differs significantly between those two lines. The frequency measured in this trial was smaller than the values between 0.33 Hz and 0.37 Hz reported by Gardiner (1989)
and Milne (1991)
for Sitka spruce. However, the tested trees were taller than the trees measured by these two authors, which support the findings of this investigation.
|
, we developed a linear regression model to predict the swaying frequency from tree and crown characteristics (Table 6):
|
| (3) |
. The relationship for the 60 trees tested is statistically not as strong as reported in previous studies (Moore and Maguire, 2004
, 2005
). This is probably due to the overall large self-differentiation in crown size and shape, found for trees in the same stand due to the lack of thinning. Even though tree dimensions such as tree height, dbh, crown length, and crown mass explained a considerable part of the variation in natural swaying frequency, about 40% of the variation is not explained by aboveground architectural tree features or the variation of the Estruct along the stem.
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was derived from the swaying experiments individually fitting a model of damped oscillation to each sway test. The values for the damping ratio integrated the external damping due to aerodynamic drag of the crown and crown clashing and the internal friction of wood and structural damping due to branch movement. Individual damping ratios varied for the tested trees between 0.093 and 0.351 (Fig. 7), with a mean value per line between 0.138 ± 0.038 in line "10 m" and 0.186 ± 0.048 in line "90 m" (Table 3), which is statistically significantly different (P = 0.05). These damping ratios are higher than those reported for Sitka spruce by other authors (Mayhead et al., 1975
; Blackburn et al., 1988
; Gardiner, 1989
, 1992
; Milne, 1991
), which vary on average between 0.044 and 0.123. However, those trees were younger and smaller when the investigations were conducted. Milne (1991)
found inter-branch damping was related to tree spacing. As the tested trees grew with the same initial spacing and silvicultural treatment as Milne's trees and assuming the same yield class for both sites, the canopy contact will close, as the tested trees are older. The individual space per tree shrinks, and the probability of crown clashing increases strongly. For older, taller trees as in the present experiment, the higher values of damping ratio are mainly due to closer inter-tree contact.
|
|
| (4) |
|
; Brunner, 1998
), increased spatial competition (Rouvinen and Kuulivainen, 1997
), and greater wind shelter, but trees vary much more individually within the same level of exposure than did the mean at each exposure. Tree mechanics are largely controlled by the outer shape of the tree and to a smaller degree by the stem material properties. Wind-exposed edge trees are shorter, and more tapered toward the top with an overall lower Estruct, allowing for flexural stiffness at the stem base due to the larger diameter and a higher flexibility in the crown region of the stem. Shorter, more tapered trees seem well adapted to wind exposure because these trees sway with a smaller amplitude and frequency, which might help prevent the root system from becoming weakened. Trees in the middle of the forest grow taller with a more slender stem, but develop a smaller crown. As they grow, these trees develop higher stem stiffness (Estruct) to compensate for the larger slenderness, which results in an equivalent stem rigidity against bending. As the trees grow taller in the middle of the forest, they would tend to oscillate with a larger amplitude, but due to stand structure and canopy closure, damping ratios are higher than at the stand edge. This above-ground tree architecture tends to prevent heavy rocking of the tree and loosening of the root plate. Thus, for both situations in the stand, tree form and mechanical properties of the stem are adjusted in combination to balance tree stability against wind forces and tree requirements for photosynthesis. This strategy is as another example of multifactorial modifications of tree growth and how trees adjust to differing requirements. Depending on wind load and light level, the tree either optimizes for stability or for light availability. At the stand edge, where wind loading is high, the trees have shorter, tapered stems. In contrast, in the middle of the stand, competition for light is a greater constraint (Cannell, 1993
; Pretzsch, 1995
; Brunner, 1998
) than wind loading (Gardiner, 1994
; Stacey et al., 1994
), so trees grow taller and are less tapered.
In addition, movement of the stem and of the root plate influence the development of the other organ. Adaptive root development, as a result of differential loading on both sides of a trunk, was reported by Nicoll and Ray (1996)
, Nicoll and Dunn (2000)
, and Stokes (2004)
. The root architecture of the trees in this study has not been measured; therefore, the consequences of the difference in wind exposure on these roots are unknown.
We have shown a strong individual reaction of the tree to its growth situation, reflected by the large variation of each feature measured in the tested trees. An obvious growth reaction of the trees to the influence of the wind is eccentric growth as found in the experimental trees (Table 2). Eccentricity was significantly higher in the exposed, edge situation than in the center of the site. The absolute difference in wind exposure, which affected tree growth, was not large enough to cause a general difference in wood properties when integrated over the stem. To test the effect of different wind exposures on trees independent of light and spatial competition still requires investigation sites that are less wind exposed than the site in this paper. However, the results of this study show the need to understand the different options of trees to adapt to environmental constraints and the heterogeneity of these growth reactions following these different adaptation strategies.
FOOTNOTES
1 The authors thank S. Mochan and D. Clark from Forest Reseach, Northern Research Station (NRS) and staff of TSU Cairnbaan for help and support throughout the fieldwork, and T. Connolly (NRS) for help with data analysis. The European Commission funded the project under the Marie Curie Mobility programme (FAIR CT 98 5038). 
4 Author for correspondence (Franka.Bruechert{at}forst.bwl.de
)
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