Advertisement

Tree Mechanics and Wind Loading

  • John Moore
  • Barry Gardiner
  • Damien Sellier
Chapter

Abstract

The response of trees to applied wind loads ranges from minor movement of leaves, branches and stems through to catastrophic failure in the form of stem breakage and uprooting. Catastrophic wind damage is a major source of economic loss in managed forests but is also an important ecological process in natural forests. Exposure to chronic wind stress results in a number of thigmomorphogenic responses including changes in tree shape and internal wood properties. In order to better understand the impacts of wind on trees, knowledge is required on wind loading of trees and their response to these loads. In this chapter, we provide an overview of the mechanics of wind loading of trees, starting with the drag force acting on trees for a given wind speed and how this wind speed varies within forest canopies. We then discuss how this load is resisted by the stem and root system, including tree dynamic response to fluctuating wind loads. Throughout the chapter, we focus on advances in instrumentation and modelling techniques that have aided our understanding of this complex phenomenon. We also highlight some of the key gaps in our knowledge and suggest future directions where research advances could be made. An improved knowledge of the mechanics of wind loading on trees aids the better management of the risk of damage to forests and a better understanding of the thigmomorphogenic responses of trees to wind stress and the biomechanical benefits these confer. It can also aid our understanding of the effects of wind exposure on wood properties and the potential consequences for the wood products sector.

References

  1. Aber J, Neilson RP, McNulty S, Lenihan JM, Bachelet D, Drapek RJ (2001) Forest processes and global environmental change: predicting the effects of individual and multiple stressors. Bioscience 51(9):735.  https://doi.org/10.1641/0006-3568(2001)051(0735:fpagec)2.0.co;2CrossRefGoogle Scholar
  2. Achim A, Ruel J-C, Gardiner BA, Laflamme G, Meunier S (2005) Modelling the vulnerability of balsam fir forests to wind damage. Forest Ecol Manag 204:35–50CrossRefGoogle Scholar
  3. Albrecht A, Badel E, Bonnesoeur V, Brunet Y, Constant T, Défossez P, de Langre E, Dupont S, Fournier M, Gardiner B, Mitchell SJ, Moore JR, Moulia B, Nicoll BC, Niklas KJ, Schelhaas M-J, Spatz H-C, Telewski FW (2016) Comment on “Critical wind speed at which trees break”. Phys Rev E 94(6).  https://doi.org/10.1103/physreve.94.067001
  4. Albrecht A, Hanewinkel M, Bauhus J, Kohnle U (2012) How does silviculture affect storm damage in forests of south-western Germany? Results from empirical modeling based on long-term observations. Eur J Forest Res 131:229–247CrossRefGoogle Scholar
  5. Arnold M, Steiger R (2006) The influence of wind-induced compression failures on the mechanical properties of spruce structural timber. Mater Struct 40:57–68CrossRefGoogle Scholar
  6. Badel E, Ewers FW, Cochard H, Telewski FW (2015) Acclimation of mechanical and hydraulic functions in trees: impact of the thigmomorphogenetic process. Front Plant Sci 6:266.  https://doi.org/10.3389/fpls.2015.00266CrossRefPubMedPubMedCentralGoogle Scholar
  7. Barton CVM, Montagu KD (2004) Detection of tree roots and determination of root diameters by ground penetrating radar under optimal conditions. Tree Physiol 24(12):1323–1331.  https://doi.org/10.1093/treephys/24.12.1323CrossRefPubMedGoogle Scholar
  8. Belcher SE, Harman IN, Finnigan JJ (2012) The wind in the willows: flows in forest canopies in complex terrain. Ann Rev Fluid Mech 44(1):479–504.  https://doi.org/10.1146/annurev-fluid-120710-101036CrossRefGoogle Scholar
  9. Blackburn P, Miller KF, Petty JA (1988) An assessment of the static and dynamic factors involved in windthrow. Forestry 61:29–43CrossRefGoogle Scholar
  10. Blackwell PG, Rennolls K, Coutts MP (1990) A root anchorage model for shallowly rooted Sitka spruce. Forestry 63(1):73–91CrossRefGoogle Scholar
  11. Blennow K, Sallnäs O (2004) WINDA—a system of models for assessing the probability of wind damage to forest stands within a landscape. Ecol Modell 175(1):87–99.  https://doi.org/10.1016/j.ecolmodel.2003.10.009CrossRefGoogle Scholar
  12. Bonan GB (2008) Forests and climate change: forcings, feedbacks, and the climate benefits of forests. Science 320(5882):1444–1449.  https://doi.org/10.1126/science.1155121CrossRefPubMedPubMedCentralGoogle Scholar
  13. Bonnesoeur V, Constant T, Moulia B, Fournier M (2016) Forest trees filter chronic wind-signals to acclimate to high winds. New Phytol 210(3):850–860.  https://doi.org/10.1111/nph.13836CrossRefPubMedGoogle Scholar
  14. Boudreault L-É, Bechmann A, Tarvainen L, Klemedtsson L, Shendryk I, Dellwik E (2015) A LiDAR method of canopy structure retrieval for wind modeling of heterogeneous forests. Agric Forest Meteorol 201:86–97.  https://doi.org/10.1016/j.agrformet.2014.10.014CrossRefGoogle Scholar
  15. Boudreault L-É, Dupont S, Bechmann A, Dellwik E (2016) How forest inhomogeneities affect the edge flow. Bound-Layer Meteorol 162(3):375–400.  https://doi.org/10.1007/s10546-016-0202-5CrossRefGoogle Scholar
  16. Butler DW, Gleason SM, Davidson I, Onoda Y, Westoby M (2012) Safety and streamlining of woody shoots in wind: an empirical study across 39 species in tropical Australia. New Phytol 193(1):137–149.  https://doi.org/10.1111/j.1469-8137.2011.03887.xCrossRefPubMedGoogle Scholar
  17. Byrne KE, Mitchell SJ (2007) Overturning resistance of western redcedar and western hemlock in mixed-species stands in coastal British Columbia. Can J Forest Res 37(5):931–939.  https://doi.org/10.1139/x06-291CrossRefGoogle Scholar
  18. Byrne KE, Mitchell SJ (2012) Testing of WindFIRM/ForestGALES_BC: a hybrid-mechanistic model for predicting windthrow in partially harvested stands. Forestry 86(2):185–199.  https://doi.org/10.1093/forestry/cps077CrossRefGoogle Scholar
  19. Ciftci C, Brena SF, Kane B, Arwade SR (2013) The effect of crown architecture on dynamic amplification factor of an open-grown sugar maple (Acer saccharum L.). Trees 27(4):1175–1189.  https://doi.org/10.1007/s00468-013-0867-zCrossRefGoogle Scholar
  20. Coutand C (2010) Mechanosensing and thigmomorphogenesis, a physiological and biomechanical point of view. Plant Sci 179(3):168–182.  https://doi.org/10.1016/j.plantsci.2010.05.001CrossRefGoogle Scholar
  21. Coutts MP (1983) Root architecture and tree stability. Plant Soil 71(1–3):171–188.  https://doi.org/10.1007/bf02182653CrossRefGoogle Scholar
  22. Crook MJ, Ennos AR (1996) The anchorage mechanics of deep rooted larch, Larix europea × L. japonica. J Exp Bot 47(10):1509–1517.  https://doi.org/10.1093/jxb/47.10.1509CrossRefGoogle Scholar
  23. Cucchi V, Meredieu C, Stokes A, Berthier S, Bert D, Najar M, Denis A, Lastennet R (2004) Root anchorage of inner and edge trees in stands of Maritime pine (Pinus pinaster Ait.) growing in difference podzolic soil conditions. Trees 18:460–466CrossRefGoogle Scholar
  24. Danjon F, Fourcaud T, Bert D (2005) Root architecture and wind-firmness of mature Pinus pinaster. New Phytol 168(2):387–400.  https://doi.org/10.1111/j.1469-8137.2005.01497.xCrossRefPubMedGoogle Scholar
  25. Dassot M, Colin A, Santenoise P, Fournier M, Constant T (2012) Terrestrial laser scanning for measuring the solid wood volume, including branches, of adult standing trees in the forest environment. Comput Electron Agric 89:86–93.  https://doi.org/10.1016/j.compag.2012.08.005CrossRefGoogle Scholar
  26. Davies NT, Altaner CM, Apiolaza LA (2016) Elastic constants of green Pinus radiata wood. N Z J For Sci 46(1).  https://doi.org/10.1186/s40490-016-0075-x
  27. de Langre E (2008) Effects of wind on plants. Ann Rev Fluid Mech 40(1):141–168.  https://doi.org/10.1146/annurev.fluid.40.111406.102135CrossRefGoogle Scholar
  28. Dellwik E, Mann J, Bingöl F (2010) Flow tilt angles near forest edges—part 2: Lidar anemometry. Biogeosciences 7(5):1759–1768.  https://doi.org/10.5194/bg-7-1759-2010CrossRefGoogle Scholar
  29. Dupont S (2016) A simple wind–tree interaction model predicting the probability of wind damage at stand level. Agric Forest Meteorol 224:49–63.  https://doi.org/10.1016/j.agrformet.2016.04.014CrossRefGoogle Scholar
  30. Dupont S, Brunet Y (2008) Influence of foliar density profile on canopy flow: a large-eddy simulation study. Agric Forest Meteorol 148(6–7):976–990.  https://doi.org/10.1016/j.agrformet.2008.01.014CrossRefGoogle Scholar
  31. Dupont S, Brunet Y (2009) Coherent structures in canopy edge flow: a large-eddy simulation study. J Fluid Mech 630:93.  https://doi.org/10.1017/s0022112009006739CrossRefGoogle Scholar
  32. Dupont S, Brunet Y, Finnigan JJ (2008) Large-eddy simulation of turbulent flow over a forested hill: validation and coherent structure identification. Q J R Meteorol Soc 134(636):1911–1929.  https://doi.org/10.1002/qj.328CrossRefGoogle Scholar
  33. Dupont S, Pivato D, Brunet Y (2015) Wind damage propagation in forests. Agric For Meteorol 214–215:243–251. https://doi.org/10.1016/j.agrformet.2015.07.010CrossRefGoogle Scholar
  34. Dupuy L, Fourcaud T, Stokes A (2005) A numerical investigation into the influence of soil type and root architecture on tree anchorage. Plant Soil 278(1–2):119–134.  https://doi.org/10.1007/s11104-005-7577-2CrossRefGoogle Scholar
  35. Dupuy LX, Fourcaud T, Lac P, Stokes A (2007) A generic 3D finite element model of tree anchorage integrating soil mechanics and real root system architecture. Am J Bot 94(9):1506–1514.  https://doi.org/10.3732/ajb.94.9.1506CrossRefPubMedGoogle Scholar
  36. Duryea M, Kampf E (2007) Wind and trees: lessons learned from hurricanes. University of Florida, Gainsville, FLGoogle Scholar
  37. England AH, Baker CJ, Saunderson SET (2000) A dynamic analysis of windthrow of trees. Forestry 73(3):225–237CrossRefGoogle Scholar
  38. Ennos A (1997) Wind as an ecological factor. Trends Ecol Evol 12(3):108–111.  https://doi.org/10.1016/s0169-5347(96)10066-5CrossRefPubMedGoogle Scholar
  39. Ennos AR (1999) The aerodynamics and hydrodynamics of plants. J Exp Biol 202:3281–3284PubMedGoogle Scholar
  40. Everham EM, Brokaw NVL (1996) Forest damage and recovery from catastrophic wind. Bot Rev 62(2):113–185.  https://doi.org/10.1007/bf02857920CrossRefGoogle Scholar
  41. Finnigan JJ (2000) Turbulence in plant canopies. Ann Rev Fluid Mech 32:519–571.  https://doi.org/10.1146/annurev.fluid.32.1.519CrossRefGoogle Scholar
  42. Flesch TK, Wilson JD (1999) Wind and remnant tree sway in forest cutblocks. II. Relating measured tree sway to wind statistics. Agric Forest Meteorol 93:243–258CrossRefGoogle Scholar
  43. Foster DR, Boose ER (1995) Hurricane disturbance regimes in temperate and tropical forest ecosystems. In: Coutts MP, Grace J (eds) Wind and trees. Cambridge University Press, pp 305–339Google Scholar
  44. Fourcaud T, Blaise F, Lac P, Castéra P, de Reffye P (2003) Numerical modelling of shape regulation and growth stresses in trees. II. Implementation in the AMAPpara software and simulation of tree growth. Trees 17(1):31–39.  https://doi.org/10.1007/s00468-002-0203-5CrossRefGoogle Scholar
  45. Fourcaud T, Ji JN, Zhang ZQ, Stokes A (2008) Understanding the impact of root morphology on overturning mechanisms: a modelling approach. Ann Bot 101(8):1267–1280.  https://doi.org/10.1093/aob/mcm245CrossRefPubMedGoogle Scholar
  46. Fourcaud T, Lac P (2003) Numerical modelling of shape regulation and growth stresses in trees: I. An incremental static finite element formulation. Trees 17(1):23–30CrossRefGoogle Scholar
  47. Fournier M, Almeras T, Clair B, Gril J (2014) Biomechanical actions and biological function. In: Gardiner B, Barnett J, Saranpaa P, Gril J (eds) Biology of reaction wood. Springer-Verlag, Berlin, Germany, pp 139–169CrossRefGoogle Scholar
  48. Fournier M, Dlouha J, Jaouen G, Almeras T (2013) Integrative biomechanics for tree ecology: beyond wood density and strength. J Exp Bot 64(15):4793–4815.  https://doi.org/10.1093/jxb/ert279CrossRefPubMedGoogle Scholar
  49. Fournier M, Rogier P, Costes E, Jaeger M (1993) Modélisation mécanique des vibrations propres d’un arbre soumis aux vents, en fonction de sa morphologie. Ann Des Sci For 50(4):401–412.  https://doi.org/10.1051/forest:19930407CrossRefGoogle Scholar
  50. Fraser AI (1962) The soil and roots as factors in tree stability. Forestry 35(2):117–127.  https://doi.org/10.1093/forestry/35.2.117CrossRefGoogle Scholar
  51. Fraser AI, Gardiner JBH (1967) Rooting and stability in Sitka spruce, vol 40. HMSO, LondonGoogle Scholar
  52. Fredericksen TS, Hedden RL, Williams SA (1993) Testing loblolly pine wind firmness with simulated wind stress. Can J Forest Res 23(9):1760–1765.  https://doi.org/10.1139/x93-222CrossRefGoogle Scholar
  53. Gaffrey D, Kniemeyer O (2002) The elasto-mechanical behaviour of Douglas fir, its sensitivity to tree-specific properties, wind and snow loads, and implications for stability—a simulation study. J Forest Sci 48(2):49–69Google Scholar
  54. Gardiner B, Berry P, Moulia B (2016) Review: wind impacts on plant growth, mechanics and damage. Plant Sci 245:94–118.  https://doi.org/10.1016/j.plantsci.2016.01.006CrossRefPubMedGoogle Scholar
  55. Gardiner B, Blennow K, Carnus J-M, Fleischer P, Ingemarson F, Landmann G, Linder M, Marzano M, Nicoll B, Orazio C, Petron J-L, Reviron M-P, Schelhaas M-J, Schuck A, Spielmann M, Usbeck T (2011) Destructive storms in European forests: past and forthcoming impacts. European Forest Institute, Atlantic European Regional OfficeGoogle Scholar
  56. Gardiner B, Marshall B, Achim A, Belcher R, Wood C (2005) The stability of different silvicultural systems: a wind-tunnel investigation. Forestry 78(5):471–484.  https://doi.org/10.1093/forestry/cpi053CrossRefGoogle Scholar
  57. Gardiner BA (1992) Mathematical modelling of the static and dynamic characteristics of plantation trees. In: Franke J, Roeder A (eds) Mathematical modelling of forest ecosystems. Sauerlander’s Verlag, Frankfurt am Main, pp 40–61Google Scholar
  58. Gardiner BA, Byrne K, Hale SE, Kamimura K, Mitchell SJ, Peltola H, Ruel J-C (2008) A review of mechanistic modelling of wind damage risk to forests. Forestry 81(3):447–463.  https://doi.org/10.1093/forestry/cpn022CrossRefGoogle Scholar
  59. Gardiner BA, Peltola H, Kellomaki S (2000) Comparison of two models for predicting the critical wind speeds required to damage coniferous trees. Ecol Modell 129:1–23CrossRefGoogle Scholar
  60. Gardiner BA, Quine CP (2000) Management of forests to reduce the risk of abiotic damage—a review with particular reference to the effects of strong winds. Forest Ecol Manag 135:261–277CrossRefGoogle Scholar
  61. Gardiner BA, Stacey GR, Belcher RE, Wood CJ (1997) Field and wind tunnel assessments and the implications of respacing and thinning for tree stability. Forestry 70(3):233–252CrossRefGoogle Scholar
  62. Grace J (1977) Plant responses to wind. Academic Press, LondonGoogle Scholar
  63. Grace J (1989) Tree lines. Philos Trans R Soc Lon Ser B 324:233–245CrossRefGoogle Scholar
  64. Grace J, Morison JIL, Perks MP (2013) Forests, forestry and climate change. In: Fenning TM (ed) Challenges and opportunities for the world’s forests in the 21st century. Forestry sciences, vol 81. Springer, Dordrecht, pp 241–266.  https://doi.org/10.1007/978-94-007-7076-8_11Google Scholar
  65. Hale SE, Gardiner BA, Wellpott A, Nicoll BC, Achim A (2012) Wind loading of trees: influence of tree size and competition. Eur J Forest Res 131(1):203–217.  https://doi.org/10.1007/s10342-010-0448-2CrossRefGoogle Scholar
  66. Hanewinkel M, Peyron J-L (2013) The economic impact of storms. In: Gardiner B, Schuck A, Schelhaas M-J, Orazio C, Blennow K, Nicoll B (eds) Living with storm damage to forests: what science can tell us. European Forest Institute, Joensuu, pp 55–63Google Scholar
  67. Harman IN, Böhm M, Finnigan JJ, Hughes D (2016) Spatial variability of the flow and turbulence within a model canopy. Bound-Layer Meteorol 160(3):375–396.  https://doi.org/10.1007/s10546-016-0150-0CrossRefGoogle Scholar
  68. Hocking GH (1949) Compression failure in Pinus radiata stems exposed to strong wind. N Z J For 9(1):65–66Google Scholar
  69. Holbo HR, Corbett TC, Horton PJ (1980) Aeromechanical behaviour of selected Douglas-fir. Agric Meteorol 21:81–91CrossRefGoogle Scholar
  70. Jackson T, Raumonen P, Shenkin A, Malhi Y (2015) Modelling trees response to wind forcing using terrestrial LiDAR data. In: 8th Plant biomechanics international conference, Nagoya, Japan, 30 Nov–4 Dec 2015, p 253Google Scholar
  71. James K (2003) Dynamic loading of trees. J Arboric 29(3):165–171Google Scholar
  72. James KR, Haritos N, Ades PK (2006) Mechanical stability of trees under dyanmic loads. Am J Bot 93(10):1522–1530.  https://doi.org/10.3732/ajb.93.10.1522CrossRefPubMedGoogle Scholar
  73. Jones HG (1992) Plants and microclimate. A quantitative approach to environmental plant physiology, 2nd edn. Cambridge University Press, CambridgeGoogle Scholar
  74. Kamimura K, Gardiner B, Dupont S, Guyon D, Meredieu C (2016) Mechanistic and statistical approaches to predicting wind damage to individual maritime pine (Pinus pinaster) trees in forests. Can J Forest Res 46(1):88–100.  https://doi.org/10.1139/cjfr-2015-0237CrossRefGoogle Scholar
  75. Kamimura K, Gardiner B, Koga S (2017) Observations and predictions of wind damage to Larix kaempferi trees following thinning at an early growth stage. Forestry.  https://doi.org/10.1093/forestry/cpx006CrossRefGoogle Scholar
  76. Kamimura K, Kitagawa K, Saito S, Mizunaga H (2011) Root anchorage of hinoki (Chamaecyparis obtuse (Sieb. Et Zucc.) Endl.) under the combined loading of wind and rapidly supplied water on soil: analyses based on tree-pulling experiments. Eur J Forest Res 131(1):219–227.  https://doi.org/10.1007/s10342-011-0508-2CrossRefGoogle Scholar
  77. Kerzenmacher T, Gardiner BA (1998) A mathematical model to describe the dynamic response of a spruce tree to the wind. Trees 12:385–394.  https://doi.org/10.1007/s004680050165CrossRefGoogle Scholar
  78. Knight TA (1803) Account of some experiments on the descent of the sap in trees. Philos Trans R Soc Lond 93:277–289CrossRefGoogle Scholar
  79. Koch G, Bauch J, Puls J, Schwab E (2000) Biological, chemical and mechanical characteristics of “Wulstholz” as a response to mechanical stress in living trees of Picea abies (L.) Karst. Holzforschung 54(2):137–143CrossRefGoogle Scholar
  80. Lanquaye-Opoku N, Mitchell SJ (2005) Portability of stand-level empirical windthrow risk models. Forest Ecol Manag 216(1–3):134–148.  https://doi.org/10.1016/j.foreco.2005.05.032CrossRefGoogle Scholar
  81. Larson PR (1963) Stem form development of forest trees. Forest Sci Monogr 5:1–42Google Scholar
  82. Larson PR (1965) Stem form of young Larix as influenced by wind and pruning. Forest Sci 11:412–421Google Scholar
  83. Lavers GM (1983) The strength properties of timber, 3rd edn. Building Research Establishment, LondonGoogle Scholar
  84. Lawton RO (1982) Wind stress and elfin stature in a montane rainforest tree: an adaptive explanation. Am J Bot 69(8):1224–1230CrossRefGoogle Scholar
  85. Lopes A, Oliveira S, Fragoso M, Andrade JA, Pedro P (2009) Wind risk assessment in urban environments: the case of falling trees during windstorm events in Lisbon. In: Střelcová K, Mátyás C, Kleidon A et al. (eds) Bioclimatology and natural hazards. Springer, Dordrecht, pp 55–74.  https://doi.org/10.1007/978-1-4020-8876-6_5CrossRefGoogle Scholar
  86. Lopes da Costa JC, Castro FA, Palma JMLM, Stuart P (2006) Computer simulation of atmospheric flows over real forests for wind energy resource evaluation. J Wind Eng Ind Aerodyn 94(8):603–620.  https://doi.org/10.1016/j.jweia.2006.02.002CrossRefGoogle Scholar
  87. Lopez D, Michelin S, de Langre E (2011) Flow-induced pruning of branched systems and brittle reconfiguration. J Theor Biol 284(1):117–124.  https://doi.org/10.1016/j.jtbi.2011.06.027CrossRefPubMedGoogle Scholar
  88. Manley B, Wakelin S (1989) Modelling the effect of windthrow at the estate level. In: Somerville A, Wakelin S, Whitehouse L (eds) Workshop on wind damage in New Zealand exotic forests. FRI Bulletin 146. Ministry of Forestry, Forest Research Institute, Rotorua, pp 66–72Google Scholar
  89. Martin TJ, Ogden J (2006) Wind damage and response in New Zealand forests: a review. N Z J Ecol 30:295–310Google Scholar
  90. Mattheck C (2000) Comments on “Wind-induced stresses in cherry trees: evidence against the hypothesis of constant stress levels” by KJ Niklas, H-C Spatz. Trees (2000) 14:230–237. Trees 15:63Google Scholar
  91. Mayer H (1987) Wind-induced tree sways. Trees 1:195–206CrossRefGoogle Scholar
  92. Mayhead GJ (1973) Some drag coefficients for British forest trees derived from wind tunnel studies. Agric Meteorol 12:123–130CrossRefGoogle Scholar
  93. Metzger C (1893) Der wind als massgebender Faktor fur das Wachstum der Baume. Mundener forstl Hefte 3:35–86Google Scholar
  94. Milne R (1991) Dynamics of swaying Picea sitchensis. Tree Physiol 9:383–399CrossRefPubMedGoogle Scholar
  95. Milne R, Blackburn P (1989) The elasticity and vertical distribution of stress within stem of Picea sitchensis. Tree Physiol 5:195–205CrossRefPubMedGoogle Scholar
  96. Mitchell SJ (2000) Stem growth responses in Douglas-fir and Sitka spruce following thinning: implications for assessing wind-firmness. Forest Ecol Manag 135(1–3):105–114.  https://doi.org/10.1016/s0378-1127(00)00302-9CrossRefGoogle Scholar
  97. Mitchell SJ (2012) Wind as a natural disturbance agent in forests: a synthesis. Forestry 86(2):147–157.  https://doi.org/10.1093/forestry/cps058CrossRefGoogle Scholar
  98. Mitchell SJ, Hailemariam T, Kulis Y (2001) Empirical modeling of cutblock edge windthrow risk on Vancouver Island, Canada, using stand level information. Forest Ecol Manag 154(1–2):117–130.  https://doi.org/10.1016/s0378-1127(00)00620-4CrossRefGoogle Scholar
  99. Moore JR (2000) Differences in maximum resistive bending moments of Pinus radiata trees grown on a range of soil types. Forest Ecol Manag 135:63–71CrossRefGoogle Scholar
  100. Moore JR, Cown DJ, Lee JR, McKinley RB, Brownlie RK, Jones TG, Downes GM (2014) The influence of stem guying on radial growth, stem form and internal resin features in radiata pine. Trees 28(4):1197–1207.  https://doi.org/10.1007/s00468-014-1030-1CrossRefGoogle Scholar
  101. Moore JR, Maguire DA (2004) Natural sway frequencies and damping ratios of trees: concepts, review and synthesis of previous studies. Trees—Struct Funct 18(2):195–203.  https://doi.org/10.1007/s00468-003-0295-6CrossRefGoogle Scholar
  102. Moore JR, Maguire DA (2008) Simulating the dynamic behavior of Douglas-fir trees under applied loads by the finite element method. Tree Physiol 28(1):75–83CrossRefPubMedGoogle Scholar
  103. Morgan J, Cannell MGR (1987) Structural analysis of tree trunks and branches: tapered cantilever beams subject to large deflections under complex loading. Tree Physiol 3:365–374CrossRefPubMedGoogle Scholar
  104. Morgan J, Cannell MGR (1994) Shape of tree stems—a re-examination of the uniform stress hypothesis. Tree Physiol 14:49–62CrossRefPubMedGoogle Scholar
  105. Moulia B, Coutand C, Julien JL (2015) Mechanosensitive control of plant growth: bearing the load, sensing, transducing, and responding. Front Plant Sci 6:52.  https://doi.org/10.3389/fpls.2015.00052CrossRefPubMedPubMedCentralGoogle Scholar
  106. Murphy KD, Rudnicki M (2012) A physics-based link model for tree vibrations. Am J Bot 99(12):1918–1929.  https://doi.org/10.3732/ajb.1200141CrossRefPubMedGoogle Scholar
  107. Neild SA, Wood CJ (1999) Estimating stem and root-anchorage flexibility in trees. Tree Physiol 19:141–151CrossRefPubMedGoogle Scholar
  108. Nicoll BC, Gardiner BA, Peace AJ (2008) Improvements in anchorage provided by the acclimation of forest trees to wind stress. Forestry 81(3):389–398.  https://doi.org/10.1093/forestry/cpn021CrossRefGoogle Scholar
  109. Nicoll BC, Gardiner BA, Rayner B, Peace AJ (2006) Anchorage of coniferous trees in relation to species, soil type, and rooting depth. Can J Forest Res 36(7):1871–1883.  https://doi.org/10.1139/x06-072CrossRefGoogle Scholar
  110. Nicoll BC, Ray D (1996) Adapative growth of tree root systems in response to wind action and site conditions. Tree Physiol 16:891–898CrossRefPubMedGoogle Scholar
  111. Niklas KJ, Spatz H-C (2000a) Response to Klaus Mattheck’s letter. Trees 15:64–65CrossRefGoogle Scholar
  112. Niklas KJ, Spatz H-C (2000b) Wind-induced stresses in cherry trees: evidence against the hypothesis of constant stress levels. Trees 14:230–237CrossRefGoogle Scholar
  113. O’Sullivan MF, Ritchie RM (1993) Tree stability in relation to cyclic loading. Forestry 66(1):69–82CrossRefGoogle Scholar
  114. Ormarsson S, Dahlblom O, Johansson M (2010) Numerical study of how creep and progressive stiffening affect the growth stress formation in trees. Trees 24(1):105–115.  https://doi.org/10.1007/s00468-009-0383-3CrossRefGoogle Scholar
  115. Papesch AJG (1974) A simplified theoretical analysis of the factors that influence windthrow of trees. In: 5th Australasian conference on hydraulics and fluid dynamics, Christchurch, New Zealand. University of CanterburyGoogle Scholar
  116. Patton EG, Finnigan JJ (2012) Canopy turbulence. In: Fernando HJS (ed) Handbook of environmental fluid dynamics, volume one. CRC Press, pp 311–328.  https://doi.org/10.1201/b14241-28CrossRefGoogle Scholar
  117. Peltola H, Gardiner B, Nicoll B (2013) Mechanics of wind damage. In: Gardiner B, Schuck A, Schelhaas M-J, Orazio C, Blennow K, Nicoll B (eds) Living with storm damage to forests: what science can tell us. Eur Forest Inst, Joensuu, pp 31–38Google Scholar
  118. Peltola H, Kellomäki S, Hassinen A, Granander M (2000) Mechanical stability of Scots pine, Norway spruce and birch: an analysis of tree-pulling experiments in Finland. Forest Ecol Manag 135(1–3):143–153.  https://doi.org/10.1016/s0378-1127(00)00306-6CrossRefGoogle Scholar
  119. Peltola HM (2006) Mechanical stability of trees under static loads. Am J Bot 93(10):1501–1511.  https://doi.org/10.3732/ajb.93.10.1501CrossRefPubMedGoogle Scholar
  120. Petty JA, Swain C (1985) Factors influencing stem breakage of conifers in high winds. Forestry 58(1):75–84.  https://doi.org/10.1093/forestry/58.1.75CrossRefGoogle Scholar
  121. Petty JA, Worrell R (1981) Stability of coniferous tree stems in relation to damage by snow. Forestry 54(2):115–128CrossRefGoogle Scholar
  122. Pivato D, Dupont S, Brunet Y (2014) A simple tree swaying model for forest motion in windstorm conditions. Trees 28(1):281–293.  https://doi.org/10.1007/s00468-013-0948-zCrossRefGoogle Scholar
  123. Poëtte C, Gardiner B, Dupont S, Harman I, Böhm M, Finnigan J, Hughes D, Brunet Y (2017) The impact of landscape fragmentation on atmospheric flow: a wind-tunnel study. Bound-Layer Meteorol.  https://doi.org/10.1007/s10546-017-0238-1CrossRefGoogle Scholar
  124. Quine CP (1995) Assessing the risk of wind damage to forests: practices and pitfalls. In: Coutts MP, Grace J (eds) Wind and trees. Cambridge University Press, pp 379–403Google Scholar
  125. Quine CP (2000) Esimation of mean wind climate and probability of strong winds for wind risk assessment. Forestry 73(3):247–258CrossRefGoogle Scholar
  126. Quine CP, Gardiner BA, Coutts MP, Pyatt DG (1995) Forests and wind: management to minimise damage. For Comm Bull 114. HMSO, LondonGoogle Scholar
  127. Quine CP, White IMS (1994) Using the relationship between rate of tatter and topographic variables to predict site windiness in upland Britain. Forestry 67(3):245–256CrossRefGoogle Scholar
  128. Raupach MR (1992) Drag and drag partition on rough surfaces. Bound-Layer Meteorol 60:375–395CrossRefGoogle Scholar
  129. Raupach MR (1994) Simplified expressions for vegetation roughness length and zero-plane displacement as functions of canopy height and area index. Bound-Layer Meterol 71:211–216CrossRefGoogle Scholar
  130. Raymer WG (1962) Wind resistance of conifers. National Physical Laboratory, Aerodynamics Division, Middlesex, U.KGoogle Scholar
  131. Rodriguez M, Langre E, Moulia B (2008) A scaling law for the effects of architecture and allometry on tree vibration modes suggests a biological tuning to modal compartmentalization. Am J Bot 95(12):1523–1537.  https://doi.org/10.3732/ajb.0800161CrossRefPubMedGoogle Scholar
  132. Rudnicki M, Mitchell SJ, Novak MD (2004) Wind tunnel measurements of crown streamlining and drag relationships for three conifer species. Can J Forest Res 34(3):666–676.  https://doi.org/10.1139/x03-233CrossRefGoogle Scholar
  133. Ruel J-C (1995) Understanding windthrow: silvicultural implications. For Chron 71(4):434–445CrossRefGoogle Scholar
  134. Ruel J-C, Achim A, Herrera RE, Cloutier A (2010) Relating mechanical strength at the stem level to values obtained from defect-free wood samples. Trees 24(6):1127–1135.  https://doi.org/10.1007/s00468-010-0485-yCrossRefGoogle Scholar
  135. Saunderson SET, England AH, Baker CJ (1999) A dynamic model of the behaviour of Sitka spruce in high winds. J Theor Biol 200(3):249–259CrossRefPubMedGoogle Scholar
  136. Schaetzl RJ, Johnson DL, Burns SF, Small TW (1989) Tree uprooting: review of terminology, process, and environmental implications. Can J Forest Res 19(1):1–11.  https://doi.org/10.1139/x89-001CrossRefGoogle Scholar
  137. Schindler D, Fugmann H, Schönborn J, Mayer H (2011) Coherent response of a group of plantation-grown Scots pine trees to wind loading. Eur J Forest Res 131(1):191–202.  https://doi.org/10.1007/s10342-010-0474-0CrossRefGoogle Scholar
  138. Schmidt M, Hanewinkel M, Kändler G, Kublin E, Kohnle U (2010) An inventory-based approach for modeling single-tree storm damage—experiences with the winter storm of 1999 in southwestern Germany. Can J Forest Res 40(8):1636–1652.  https://doi.org/10.1139/x10-099CrossRefGoogle Scholar
  139. Schwager H, Masselter T, Speck T, Neinhuis C (2013) Functional morphology and biomechanics of branch-stem junctions in columnar cacti. Proc Biol Sci 280(1772):20132244.  https://doi.org/10.1098/rspb.2013.2244CrossRefPubMedPubMedCentralGoogle Scholar
  140. Sellier D, Brunet Y, Fourcaud T (2008) A numerical model of tree aerodynamic response to a turbulent airflow. Forestry 81(3):279–297.  https://doi.org/10.1093/forestry/cpn024CrossRefGoogle Scholar
  141. Sellier D, Fourcaud T (2009) Crown structure and wood properties: influence on tree sway and response to high winds. Am J Bot 96(5):885–896.  https://doi.org/10.3732/ajb.0800226CrossRefPubMedGoogle Scholar
  142. Sellier D, Fourcaud T, Lac P (2006) A finite element model for investigating effects of aerial architecture on tree oscillations. Tree Physiol 26(6):799–806.  https://doi.org/10.1093/treephys/26.6.799CrossRefPubMedGoogle Scholar
  143. Spatz HC, Bruchert F, Pfisterer J (2007) Multiple resonance damping or how do trees escape dangerously large oscillations? Am J Bot 94(10):1603–1611.  https://doi.org/10.3732/ajb.94.10.1603CrossRefPubMedGoogle Scholar
  144. Spatz HC, Theckes B (2013) Oscillation damping in trees. Plant Sci 207:66–71.  https://doi.org/10.1016/j.plantsci.2013.02.015CrossRefPubMedGoogle Scholar
  145. Stacey GR, Belcher RE, Wood CJ, Gardiner BA (1994) Wind flows and forces in a model spruce forest. Bound-Layer Meteorol 69:311–334CrossRefGoogle Scholar
  146. Stokes A (1999) Strain distribution during anchorage failure of Pinus pinaster Ait. at different ages and tree growth response to wind-induced root movement. Plant Soil 217(1/2):17–27.  https://doi.org/10.1023/a:1004613126353CrossRefGoogle Scholar
  147. Stokes A, Salin F, Kokutse AD, Berthier S, Jeannin H, Mochan S, Dorren L, Kokutse N, Ghani MA, Fourcaud T (2005) Mechanical resistance of different tree species to rockfall in the French Alps. Plant Soil 278(1–2):107–117.  https://doi.org/10.1007/s11104-005-3899-3CrossRefGoogle Scholar
  148. Stull RB (1988) An introduction to boundary layer meteorology. Kluwer Academic Publishers, Dordrecht, The Netherlands.  https://doi.org/10.1007/978-94-009-3027-8
  149. Telewski FW (1995) Wind-induced physiological and developmental responses in trees. In: Coutts MP, Grace J (eds) Wind and trees. Cambridge University Press, pp 237–263Google Scholar
  150. Telewski FW (2006) A unified hypothesis of mechanoperception in plants. Am J Bot 93(10):1466–1476.  https://doi.org/10.3732/ajb.93.10.1466CrossRefPubMedGoogle Scholar
  151. Telewski FW (2012) Is windswept tree growth negative thigmotropism? Plant Sci 184:20–28CrossRefPubMedGoogle Scholar
  152. Telewski FW (2016) Flexure wood: mechanical stress induced secondary xylem formation. In: Kim YS, Funada R, Singh AP (eds) Secondary xylem biology: origins, functions and applications. Elsevier, Oxford, U.KGoogle Scholar
  153. Telewski FW, Jaffe MJ (1986) Thigmomorphogenesis: field and laboratory studies of Abies fraseri in response to wind or mechanical pertubation. Physiol Plant 66:211–218CrossRefPubMedGoogle Scholar
  154. Telewski FW, Moore JR (2016) Trait selection to improve windfirmness in trees. CAB Rev 11(50).  https://doi.org/10.1079/pavsnnr201611050
  155. Theckes B, Boutillon X, de Langre E (2015) On the efficiency and robustness of damping by branching. J Sound Vib 357:35–50.  https://doi.org/10.1016/j.jsv.2015.07.018CrossRefGoogle Scholar
  156. Theckes B, Langre E, Boutillon X (2011) Damping by branching: a bioinspiration from trees. Bioinspir Biomim 6(4):046010.  https://doi.org/10.1088/1748-3182/6/4/046010CrossRefPubMedGoogle Scholar
  157. Thom AS (1971) Momentum absorption by vegetation. Q J R Meteorol Soc 97:414–428CrossRefGoogle Scholar
  158. Ulanova NG (2000) The effects of windthrow on forests at different spatial scales: a review. Forest Ecol Manag 135(1–3):155–167.  https://doi.org/10.1016/s0378-1127(00)00307-8CrossRefGoogle Scholar
  159. Urban ST, Lieffers VJ, MacDonald SE (1994) Release in radial growth in the trunk and structural roots of white spruce as measured by dendrochronology. Can J Forest Res 24:1550–1556CrossRefGoogle Scholar
  160. USDA (1999) Wood handbook: wood as an engineering material. Forest Products Laboratory General Technical Report FPL-GTR-113, 486ppGoogle Scholar
  161. Virot E, Ponomarenko A, Dehandschoewercker E, Quere D, Clanet C (2016) Critical wind speed at which trees break. Phys Rev E 93(2):023001.  https://doi.org/10.1103/PhysRevE.93.023001CrossRefPubMedGoogle Scholar
  162. Vogel S (1994) Life in moving fluids—the physical biology of flow. Princeton University PressGoogle Scholar
  163. Vollsinger S, Mitchell SJ, Byrne KE, Novak MD, Rudnicki M (2005) Wind tunnel measurements of crown streamlining and drag relationships for several hardwood species. Can J Forest Res 35(5):1238–1249.  https://doi.org/10.1139/x05-051CrossRefGoogle Scholar
  164. Watt MS, Moore JR, McKinlay B (2005) The influence of wind on branch characteristics of Pinus radiata. Trees 19:58–65CrossRefGoogle Scholar
  165. Webb VA, Rudnicki M, Muppa SK (2013) Analysis of tree sway and crown collisions for managed Pinus resinosa in southern Maine. Forest Ecol Manag 302:193–199.  https://doi.org/10.1016/j.foreco.2013.02.033CrossRefGoogle Scholar
  166. Wood CJ (1995) Understanding wind forces on trees. In: Coutts MP, Grace J (eds) Wind and trees. Cambridge University Press, pp 133–164Google Scholar
  167. Yang B, Morse AP, Shaw RH, Paw UKT (2006a) Large-eddy simulation of turbulent flow across a forest edge. Part II: momentum and turbulent kinetic energy budgets. Bound-Layer Meteorol 121(3):433–457.  https://doi.org/10.1007/s10546-006-9083-3CrossRefGoogle Scholar
  168. Yang B, Raupach MR, Shaw RH, Paw UKT, Morse AP (2006b) Large-eddy simulation of turbulent flow across a forest edge. Part I: flow statistics. Bound-Layer Meteorol 120(3):377–412.  https://doi.org/10.1007/s10546-006-9057-5CrossRefGoogle Scholar
  169. Yang M, Defossez P, Danjon F, Fourcaud T (2014) Tree stability under wind: simulating uprooting with root breakage using a finite element method. Ann Bot 114(4):695–709.  https://doi.org/10.1093/aob/mcu122CrossRefPubMedPubMedCentralGoogle Scholar
  170. Zienkiewicz OC, Taylor RL, Fox DD (2014) The finite element method for solid and structural mechanics, 7th edn. Butterworth-Heinemann, Oxford, U.K.  https://doi.org/10.1016/b978-1-85617-634-7.00018-1CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.ScionRotoruaNew Zealand
  2. 2.UMR 1391 ISPA, INRA, Bordeaux Sciences AgroVillenave D’OrnonFrance
  3. 3.EFI AtlanticCestas cedexFrance

Personalised recommendations