Computing factors of safety against wind-induced tree stem damage

The drag forces, bending moments and stresses acting on stems differing in size and location within the mechanical infrastructure of a large wild cherry (Prunus serotina Ehrh.) tree are estimated and used to calculate the factor of safety against wind-induced mechanical failure based on the mean breaking stress of intact stems and samples of wood drawn from this tree. The drag forces acting on stems are calculated based on stem projected areas and field measurements of wind speed taken within the canopy and along the length of the trunk. The bending moments and stresses resulting from these forces are shown to increase basipetally in a nearly log-log linear fashion toward the base of the tree. The factor of safety, however, varies in a sinusoidal manner such that the most distal stems have the highest factors of safety, whereas stems of intermediate location and portions of the trunk near ground level have equivalent and much lower factors of safety. This pattern of variation is interpreted to indicate that, as a course of normal growth and development, trees similar to the one examined in this study maintain a cadre of stems prone to wind-induced mechanical damage that can reduce the probability of catastrophic tree failure by reducing the drag forces acting on older portions of the tree. Comparisons among real and hypothetical stems with different taper experiencing different vertical wind speed profiles show that geometrically self-similar stems have larger factors of safety than stems tapering according to elastic or stress self-similarity, and that safety factors are less significantly influenced by the 'geometry' of the wind-profile.     

Analysis and simulation of dynamic response behavior of Scots pine trees to wind loading

This paper presents an empirical approach for the decomposition, simulation, and reconstruction of wind-induced stem displacement of plantation-grown Scots pine trees. Results from singular spectrum analysis (SSA) allow a low-dimensional characterization of the complex and complicated tree motion patterns in response to non-destructive wind excitation. Since motion of the sample trees was dominated by sway in the first mode, the application of SSA on time series of sample trees’ stem displacement yielded characteristic and distinguishable non-oscillatory trend components, quasi-oscillatory sway, and noise, of which only the non-oscillatory components were correlated directly with wind characteristics. Although sway in the range of the dominant damped fundamental frequency dominated the measured stem displacement signals, it was almost decoupled from near-surface airflow. The ability to discriminate SSA-components is demonstrated based on correlation and spectral analysis. These SSA-components, as well as wind speed measured in the canopy space of the Scots pine forest, were used to train neural networks, which could then reasonably simulate tree response to wind excitation.     

Size-dependent Allometry of Tree Height, Diameter and Trunk-taper

The allometry of tree height with respect to trunk diameterand the allometry of trunk diameter with respect to distancefrom the top of the tree (i.e. trunk taper) were determinedfor 27 Robinia pseudoacacia trees differing in age and sizegrowing in an open field. The allometric (scaling) exponentfor height was > 1 for small and young trees and decreasedto 2/3 and then 1/2 as tree size and age increased. Similarly,the exponent for taper was > 1 near the tips of young andold trunks and converged onto values of 2/3 and 1/2 toward thebase of mature tree trunks. These observations indicate thata single 'optimal mechanical design principle' (i.e. elastic,stress or geometric self-similarity) neither holds true throughoutthe lifetime of R. pseudoacacia trees, nor does a single designprinciple govern the taper of a trunk throughout its entirelength. Rather, over the course of growth and development, theallometry of R. pseudoacacia tree height and trunk taper progressivelychanges, complying with geometric self-similarity for youngplants (and young portions of old plants) and subsequently givingthe appearance of elastic or stress self-similarity as plants(or portions of plants) get older and therefore larger. Analysesof published (and new) data suggest that the conclusions drawnfor R. pseudoacacia trees are likely to hold true for othertree species because stem growth in diameter is 'indeterminate'whereas growth in overall tree height is asymptotic and thereforeessentially 'determinate'.Copyright 1995, 1999 Academic Press Scaling, woody plants, Robinia pseudoacacia     

Effects of individual size,local competition and canopy closure on the stem volume growth in a monoclonal Japanese cedar (<Emphasis Type="Italic">Cryptomeria japonica</Emphasis> D. Don) plantation

We studied how the dominant factor affecting stem volume growth changes during stand development in a monoclonal stand of Cryptomeria japonica D. Don. Stem analysis was used to compare growth history of trees in an unthinned plot (closed canopy) and a thinned plot (open canopy). In the unthinned plot, the dominant factor affecting stem volume growth was basal area (BA) before canopy closure, whereas neighborhood competition index (CI) was the dominant factor after canopy closure. In contrast, the dominant factor affecting stem volume in the thinned plot was BA throughout stand development. Spearman’s rank correlation coefficient between BA and CI continued to increase after canopy closure and size rank among individuals became increasingly fixed. Our results indicated that stem volume growth shifts from size-dependent to competition-dependent growth at canopy closure. The apparent correlation between tree size and growth rate observed in many previous studies may be the result of competition-mediated positive feedback between size and growth.     

Effects of bending stress on taper and growth of stems of youngEucalyptus regnans trees

A glasshouse experiment investigated the effect of bending stress on stem radial and height growth and stem taper ofEucalyptus regnans seedlings. Eighteen-week-old, potted seedlings were bent continuously for 8 weeks with a static bending stress. The bending treatment was then removed and the seedlings grown for another 12 weeks. Other seedlings were stayed vertically throughout the experiment whilst control seedlings were neither bent nor stayed. Seedlings were rotated every 2 days to prevent reaction wood developing asymmetrically in the stems of bent trees. Bent trees had higher radial growth rates, developed more tapered stems and had higher safety factors (the ratio of stem radius to the minimum radius required to prevent the tree toppling over) than unbent seedlings. They produced a band of tension wood in their stems and ceased height growth whilst bent. When bending ceased, they resumed normal radial and height growth. Unbent trees developed more cylindrical stems. There were no differences in growth behaviour between stayed and control trees. Bent and unbent trees all developed a butt swell, the taper of which was not affected by treatment. It was concluded that bending stress has substantial effects on both the size and taper of tree stems. However, the development of butt swell is independent of the bending stress applied. The results were considered in relation to biomechanical theories of tree stem development.     

Analysing the mechanical performance and growth adaptation of Norway spruce using a non-linear finite-element model and experimental data

Thirteen Norway spruce [Picea abies (L.) Karst.] trees of different size, age, and social status, and grown under varying conditions, were investigated to see how they react to complex natural static loading under summer and winter conditions, and how they have adapted their growth to such combinations of load and tree state. For this purpose a non-linear finite-element model and an extensive experimental data set were used, as well as a new formulation describing the degree to which the exploitation of the bending stress capacity is uniform. The three main findings were: material and geometric non-linearities play important roles when analysing tree deflections and critical loads; the strengths of the stem and the anchorage mutually adapt to the local wind acting on the tree crown in the forest canopy; and the radial stem growth follows a mechanically high-performance path because it adapts to prevailing as well as acute seasonal combinations of the tree state (e.g. frozen or unfrozen stem and anchorage) and load (e.g. wind and vertical and lateral snow pressure). Young trees appeared to adapt to such combinations in a more differentiated way than older trees. In conclusion, the mechanical performance of the Norway spruce studied was mostly very high, indicating that their overall growth had been clearly influenced by the external site- and tree-specific mechanical stress.     

Relationship of Pruning and Growth Morphology with Hormone Ratios in Shoots of Pillar and Standard Peach Trees

Genotype and cultural management determine the shape of peach [Prunus persica (L.) Batch] tree canopies in orchards. Not well understood, however, is the relationship between terminal growth, lateral branching, and shoot hormone levels that can fundamentally affect tree canopy development. In this experiment, two peach cultivars with widely differing growth habits (Pillar, KV930479 and Standard, ‘Harrow Beauty’) were budded on ‘Lovell’ rootstock, planted in the field in 1998, and characterized for shoot morphology and hormone concentrations in 2002 and 2003 (the fourth and fifth leaf, respectively). Auxin (indole-3-acetic acid) and cytokinins (largely trans-zeatin riboside, dihydrozeatin riboside, and isopentenyladenosine) were measured in shoot tips (2002) and current-year shoots (2003) using mass spectrometry. In 2002, Pillar trees had less sylleptic branching, more upright growth, and higher auxin and auxin-to-cytokinin ratios than Standard trees. In Pillar trees in 2003, auxin concentrations and shoot growth were highest in current year shoots; in pruned trees, only auxin levels increased. Peach tree growth habits may be the result of altered hormone metabolism. Growth forms leading to superior production efficiency may be developed by selection based on specific target hormone concentrations and ratios.     

Phenotypic plasticity and integration across the canopy of Olea europaea subsp. guanchica (Oleaceae) in populations with different wind exposures

Woody plants, as sessile and long-lived organisms, are expected to have effective mechanisms for dealing with recurrent environmental stresses. In the present study, we hypothesized that phenotypic plasticity (the ability to express alternative phenotypes) and integration (covariation among functionally related traits) are elicited in plants under stressful wind speed conditions. We investigated the within-crown variation of nine vegetative traits of a tree species (Olea europaea subsp. guanchica) in six populations that represented a gradient of wind speed exposures. Wind-exposed twigs in outer-canopy layers had smaller leaves; thinner, lighter, and shorter internodes; and a larger internode cross-sectional area to leaf area ratio. Comparison between field and greenhouse trials revealed that field differences among populations were mediated by phenotypic plasticity. Outer-canopy twigs expressed plastic responses in populations exposed to high wind speeds, whereas inner-canopy twigs displayed high phenotypic convergence among populations. In addition, phenotypic integration increased with wind exposure (outer canopy > inner canopy > greenhouse) and was consequently affected by canopy openness. We conclude that exposure to wind above a certain speed threshold in this woody species elicits a plastic response that is associated with increased integration among traits and involves mechanical and hydraulic rearrangements in more exposed parts of the trees.     

Angle distribution of foliage in individual Chamaecyparis obtusa canopies and effect of angle on diffuse light penetration

 The vertical distribution of foliage angle and area of three Chamaecyparis obtusa trees was determined by the triangle method, which calculates foliage geometry using measured coordinates of the leaf ”corners”, in a 43-year-old plantation in central Japan. Vertical distribution patterns of leaf area were different depending on tree size, but the boundary heights, which divide the canopy into sunlit and shaded parts, were similar in the three sample trees. The value of the average foliage angle [I(Z)] at a given depth (Z) from the tip of the stem decreased continually from the upper to lower layers within the canopy. The vertical patterns of changes in I(Z) were different among the three trees, but could be expressed by the following allometric equation as a function of depth.

Vertical stratification of vascular epiphytes in submontane and montane forest of the Bolivian Andes: the importance of the understory

We studied species richness, composition, and vertical distribution of vascular epiphytes at two sites in the Bolivian Andes. To account for the epiphyte flora on understory trees, epiphytes on shrubs and small trees were sampled in 20 × 20 m² subplots around each sampled canopy tree; this understory zone U is introduced as an addition to the well-established five vertical Johansson tree zones. More than 20% of about 500 species recorded were found only in the understory subplots, including ca. 40% of aroids, 35%–40% of piperoids, and 25%–30% of ferns. Habitat generalists (occurring in three or more zones) were most common, contributing about 50% of all species, specialists (occurring only in two zones, or in three continuous ones) 34%–42%, and hemiepiphytes 6%–16%. Canopy epiphytes (occurring > 90% in tree zones Z3–5) were mainly represented by orchids and ferns, many with special adaptations to drought stress such as pseudobulbs, succulence, and poikilohydry. Trunk epiphytes ( > 90% in understory and tree zones Z1–2) reached highest relative species numbers among piperoids and ferns. Most hemiepiphytes were also trunk epiphytes, due to their characteristic growth pattern, and included mainly aroids. The vertical distribution of epiphytes within a tree is determined by several microenvironmental gradients, with light intensity, wind speed, and air temperature increasing and air humidity decreasing from the ground level to the canopy.     

The Biomechanics of Tree Fork Design

Two biomechanically different types of tree fork are described: the “compression fork” where the two jointed stems are pressed against each other at the contact face by the action of reaction wood, and the “tension fork” where the two connected stems are bent away from each other by gravity or wind action leading to tensile stresses in the connective zone. It is well known that trees permanently try to improve their own designs by adaptive growth in order to maintain a state of constant mechanical stress at the tree surface. In the case of these two different types of tree fork, adaptive growth also takes different ways in order to avoid high localized stress peaks which could lead to failure of the tree under wind loading. In this paper only the tension fork is assessed with respect to its shape optimization by computer simulation of adaptive growth. It is shown that the tensile fork is shape optimized in a very perfect way in order to avoid any dangerous localized stress peaks (notch stresses) which could lead to failure of the tree.     

Changes in the factor of safety within the superstructure of a dicot tree

The objective of this study was to determine whether the factor of safety for mechanical stability varied among stems differing in size and age within the superstructure of a large dicot tree. Two factors of safety were selected for study: the quotient of the critical buckling height and the actual length of stems, Hcrit/L, and the quotient of the modulus of rupture (the force per unit area required to break a stem) and the working stress (the force per unit area resulting from the biomass measured distal to a stem), M_R/σ_w. These two dimensionless safety factors were determined for a total of 420 shoot segments comprising much of the aboveground biomass of a Robinia pseudoacacia (Fabaceae) tree measuring 18.7 m in height and 1347 kg in mass, and 0.46 m in diameter (40 yr old) at 1.2 m from the ground. An S-shaped trend was observed when each of the two factors of safety was plotted as a function of stem age. Each factor decreased from a local maximum for the most distal (peripheral) stems in the canopy to a local minimum value for stems ∼10 yr old; each factor increased again to another local maximum for stems 11–18 yr old, and then decreased steadily toward the base of the trunk. This trend was the result of the allometric relationships among stem diameter, length, biomass, and material properties (stiffness and strength) with respect to stem age. Although they were disproportionately more slender than their older counterparts, peripheral stems were sufficiently stiff and strong to sustain the stresses resulting from their weight and that of foliage without deflecting under these loads, yet they were sufficiently flexible to easily bend and thereby presumably provide a mechanism to reduce the drag forces acting on the entire tree. In contrast, the internally imposed mechanical forces acting on progressively older stems increased at a greater rate than the observed rate of increase in stem stiffness, strength, or diameter. The probability of mechanical failure, which must be considered from a demographic perspective (i.e., an age-dependent phenomenon), thus increased from older branches to the base of the trunk. Reports of similar allometric trends based on interspecific comparisons among diverse dicot species comply with the allometry observed for the R. pseudoacacia tree and suggest that the S-shaped trend for the factor of safety holds for stems differing in age drawn from individual trees and for the trunks of conspecifics differing in age drawn from a dense population.     

Liana cover in the canopies of rainforest trees is not predicted by local ground‐based measures

Lianas (woody climbers) are structural parasites of trees that compete with them for light and below‐ground resources. Most studies of liana–tree interactions are based on ground‐level observations of liana stem density and size, with these assessments generally assumed to reflect the amount of liana canopy cover and overall burden to the tree. We tested this assumption in a 1‐ha plot of lowland rainforest in tropical Australia. We recorded 1072 liana stems (≥1 cm diameter at breast height {dbh}) ha^?1 across all trees (≥10 cm dbh) on the plot and selected 58 trees for detailed study. We estimated liana canopy cover on selected trees that hosted 0–15 liana individuals, using a 47‐m‐tall canopy crane. Notably, we found no significant correlations between liana canopy cover and three commonly used ground‐based measurements of liana abundance as follows: liana stem counts per tree, liana above‐ground biomass per tree and liana basal area per tree. We also explored the role of tree size and liana infestation and found that larger trees (≥20 cm dbh) were more likely to support lianas and to host more liana stems than smaller trees (≤20 cm dbh). This pattern of liana stem density, however, did not correlate with greater liana coverage in the canopy. Tree family was also found to have a significant effect on likelihood of hosting lianas, with trees in some families 3–4 times more likely to host a liana than other families. We suggest that local ground‐based measures of liana–tree infestation may not accurately reflect liana canopy cover for individual trees because they were frequently observed spreading through neighbouring trees at our site. We believe that future liana research will benefit from new technologies such as high‐quality aerial photography taken from drones when the aim is to detect the relative burden of lianas on individual trees.     

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

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

Strain distribution during anchorage failure of Pinus pinaster Ait. at different ages and tree growth response to wind-induced root movement

Winching tests were carried out on 5- 13- and 17-year-old tap rooted Maritime pine (Pinus pinaster Ait.) in order to determine how the mode of anchorage failure changes throughout the life of a tree. As trees were pulled sideways, strain along the lateral roots was recorded using strain gauges attached to a strain indicator. Measurements of strain in the root system, taken during winching, provide information about root movement when loaded by wind. The mode of mechanical failure appeared to depend on tree age. The youngest trees bent over completely during winching, but did not break due to the plasticity of their trunks. The 13-year-old trees either broke at the base of the tree (due to the presence of grafting scar tissue) or at the base of the tap-root. The oldest trees broke at the base of the tap-root and sounds of roots breaking were also heard. Strain was twice as great in the trunk compared to the roots in the 5- and 13-year-old trees and was three times greater in the compression roots of 17-year–old trees compared to that in the trunk. In one 17-year-old tree, strain was found to increase at a distance of 35 cm in tension roots before decreasing again. Although the mode of failure changed with tree size, anchorage strength increased proportionally with the third power of trunk diameter, therefore another reason why failure differs with tree age must exist. In order to determine if different types of wood were being laid down in the lateral roots in response to wind loading, maturation strains, indicating the existence of mechanical stress in developing wood cells, were measured at different points along the roots. A high correlation was found between maturation strain and strain measured during winching, in roots that lay in the wind direction only. Therefore, trees appear to be able to respond to external loading stress, even at a local level within a root. This revised version was published online in June 2006 with corrections to the Cover Date.     

Size, composition and distribution of particles related to wind induced resuspension in a shallow tropical lagoon

The size, composition and distribution of particles in the watercolumn were surveyed in a shallow area (1 m depth) of a tropicallagoon (Cte d'Ivoire) during a sequence of wind-induced resuspension.Water samples were collected hourly near the surface duringone tidal cycle. Three characteristic periods were distinguished:a calm period with low wind speed (average 1.2 m s^–1 awindy period with wind speed >3 m^–1 s (range between4 and 6 m s^–1) inducing sediment resuspension and a relaxationperiod during the decrease of wind velocity. From the analysisof several parameters (particle size and volume, bacteria. pico-and nanophytoplankton, ciliates and detritus), sediment resuspensioncaused a regular injection of particles from the bed. The finestparticles (1.5–6 µm: chlorophytes such as Chiorellaspp., picocyanobacteria such as Synechococcus) were the firstto be affected by wind-induced turbulence, whereas large particles(6–12 µm: diatoms. cyanobacteria such as Lyngbiaspp.) were dispersed into the water column at the highest windspeed. The fate of the different seston components differedaccording to their size. Therefore, wind-induced resuspensioncould greatly influence the food web organization through thequantity, quality and size of edible particles available ata given time.     

Correlating Stem Biomechanical Properties of Hawaiian Canopy Trees with Hurricane Wind Damage1

Hawaiian forests are subject to the effects of periodic hurricane conditions. Hurricane Iniki struck the island of Kauai, Hawaii on September 11, 1992 with winds exceeding 200 km/h and caused defoliation, felling of trees by snapping and uprooting, and standing tree mortality due excessive limb and leaf loss. The purpose of this study was to evaluate if measured wood mechanical characteristics could be correlated with stem failure of trees under windstorm conditions. A field survey indicated that post-hurricane stem condition (snapped, uprooted, or standing) differed among five common canopy species and was significantly correlated with stem apparent elastic modulus (relative flexibility). Species that tended to snap had significantly higher apparent elastic moduli than those that remained standing or were uprooted. Wood density and stem diameter were not significantly related to stem failure mode. Native trees had a higher percentage per species of standing individuals but also had increased uprooting. Nonnative tree species were more often snapped and fewer were standing after the hurricane. The higher incidence of stem failure for introduced canopy trees may increase the spread of alien understory species following wind disturbance events. These relationships provide a simple means to predict relative differences in stem failure due to high wind conditions and should be considered in planning reforestation efforts on the Hawaiian Islands.     

Phylogenetic Structure of Tree Species across Different Life Stages from Seedlings to Canopy Trees in a Subtropical Evergreen Broad-Leaved Forest

Investigating patterns of phylogenetic structure across different life stages of tree species in forests is crucial to understanding forest community assembly, and investigating forest gap influence on the phylogenetic structure of forest regeneration is necessary for understanding forest community assembly. Here, we examine the phylogenetic structure of tree species across life stages from seedlings to canopy trees, as well as forest gap influence on the phylogenetic structure of forest regeneration in a forest of the subtropical region in China. We investigate changes in phylogenetic relatedness (measured as NRI) of tree species from seedlings, saplings, treelets to canopy trees; we compare the phylogenetic turnover (measured as β_NRI) between canopy trees and seedlings in forest understory with that between canopy trees and seedlings in forest gaps. We found that phylogenetic relatedness generally increases from seedlings through saplings and treelets up to canopy trees, and that phylogenetic relatedness does not differ between seedlings in forest understory and those in forest gaps, but phylogenetic turnover between canopy trees and seedlings in forest understory is lower than that between canopy trees and seedlings in forest gaps. We conclude that tree species tend to be more closely related from seedling to canopy layers, and that forest gaps alter the seedling phylogenetic turnover of the studied forest. It is likely that the increasing trend of phylogenetic clustering as tree stem size increases observed in this subtropical forest is primarily driven by abiotic filtering processes, which select a set of closely related evergreen broad-leaved tree species whose regeneration has adapted to the closed canopy environments of the subtropical forest developed under the regional monsoon climate.     

��13C signature of tree rings and radial increment of Fagus sylvatica trees as dependent on tree neighborhood and climate

We conducted dendroecological analyses in 80-year-long tree ring chronologies to detect neighborhood effects (competition intensity, species identity) on the δ¹³C signature of tree rings and radial stem increment of Fagus sylvatica trees growing either in monospecific or mixed patches of a temperate forest. We hypothesized that tree ring δ¹³C is a more sensitive indicator of neighborhood effects and the impact of climate variability on growth than is ring width. We found a closer correlation of summer precipitation to δ¹³C than to ring width. While the ring width showed a decline over the test period (1926–2005), the mean curve of δ¹³C increased until the mid of the 1970s, remained high until about 1990, and markedly decreased thereafter. Possible explanations related to ontogeny and environmental change (‘age effect’ due to canopy closure; elevated atmospheric SO₂ concentrations in the 1960s–1980s) are discussed. Beech target trees surrounded by many allospecific trees had a significantly lower mean δ¹³C in the period 1926–1975 than beech with predominantly or exclusively conspecific neighborhood, possibly indicating a more favorable water supply of beech in diverse stands. Contrary to expectation, trees subject to more intense competition by neighboring trees (measured by Hegyi’s competition index) had lower δ¹³C values in their tree rings, which is thought to reflect denser canopies being linked to increased shading. We conclude that tree ring δ¹³C time series represent combined archives of climate variability, stand history and neighborhood effects on tree physiology and growth that may add valuable information to that obtained from conventional tree ring analysis.