International Journal of Biometeorology

, Volume 57, Issue 6, pp 819–833 | Cite as

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

Original Paper

Abstract

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.

Keywords

Tree vibration Wind load Singular spectrum analysis Neural network Pinus sylvestris 

References

  1. Akaike H (1974) On the likelihood of a time series model. Statistican 27:217–235CrossRefGoogle Scholar
  2. Almeida JS (2002) Predictive non-linear modeling of complex data by artificial neural networks. Curr Opin Biotechnol 13:72–76CrossRefGoogle Scholar
  3. Amtmann R (1986) Dynamische Windbelastung von Nadelbäumen. Forstl Forschungsberichte München No. 74, pp 218Google Scholar
  4. Baker CJ, Bell HJ (1995) The aerodynamics of urban trees. J Wind Eng Ind Aerodyn 44:2655–2666CrossRefGoogle Scholar
  5. Berry MW, Dumais ST, Obrien GW (1995) Using linear algebra for intelligent information-retrieval. SIAM Rev 37:573–595CrossRefGoogle Scholar
  6. Broomhead D, King G (1986) Extracting qualitative dynamics from experimental data. Phys D 20:217–236CrossRefGoogle Scholar
  7. Brüchert F, Gardiner B (2006) The effect of wind exposure on the tree aerial architecture and biomechanics of Sitka spruce. Am J Bot 93:1512–1521CrossRefGoogle Scholar
  8. Cattell RB (1966) The scree test for the number of factors. Multivar Behav Res 1:245–276CrossRefGoogle Scholar
  9. Clarke G, Berthier E, Schoof C, Jarosch A (2009) Neural networks applied to estimating subglacial topography and glacier volume. J Clim 22:2146–2147CrossRefGoogle Scholar
  10. Collineau S, Brunet Y (1993a) Detection of turbulent coherent motions in a forest canopy. Part I: wavelet analysis. Bound-Layer Meteorol 65:357–379Google Scholar
  11. Collineau S, Brunet Y (1993b) Detection of turbulent coherent motions in a forest canopy. Part II: time-scales and conditional averages. Bound-Layer Meteorol 66:49–73CrossRefGoogle Scholar
  12. de Langre E (2008) Effects of wind on plants. Annu Rev Fluid Mech 40:141–168CrossRefGoogle Scholar
  13. Feldman M (2008) Theoretical analysis and comparison of the Hilbert transform decomposition methods. Mech Syst Signal Process 22:509–519CrossRefGoogle Scholar
  14. Finnigan JJ (2007) The turbulent wind in plant and forest canopy. In: Johnson EA, Miyanishi K (eds) Plant disturbance ecology. The process and the response. Academic, Amsterdam, pp 15–58Google Scholar
  15. 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. Sauerländer, Frankfurt am Main, pp 40–61Google Scholar
  16. Gardiner BA (1994) Wind and wind forces in a plantation spruce forest. Bound-Layer Meteorol 67:161–186CrossRefGoogle Scholar
  17. Gardiner BA (1995) The interactions of wind and tree movement in forest canopies. In: Coutts MP, Grace J (eds) Wind and trees. Cambridge University Press, Cambridge, pp 41–59Google Scholar
  18. Gardiner B, Byrne K, Hale S, Kamimura K, Mitchell SJ, Peltola H, Ruel J-C (2008) A review of mechanistic modelling of wind damage risk to forests. Forestry 81:447–463CrossRefGoogle Scholar
  19. Graps A (1995) An introduction to wavelets. IEEE Comput Sci Eng 2:50–61CrossRefGoogle Scholar
  20. Hassani H (2007) Singular spectrum analysis. Comparison and methodology. J Data Sci 5:239–257Google Scholar
  21. Hassinen A, Lemettinen M, Peltola H, Kellomäki S, Gardiner B (1998) A prism-based system for monitoring the swaying of trees under wind loading. Agric For Meteorol 90:187–194CrossRefGoogle Scholar
  22. Hedden RL, Fredericksen TS, Williams SA (1995) Modeling the effect of crown shedding and streamlining on the survival of loblolly pine exposed to acute wind. Can J For Res 25:704–712CrossRefGoogle Scholar
  23. Hegger R, Kantz H, Schreiber T (1999) Practical implementation of nonlinear time series methods: the TISEAN package. Chaos 9:413–435CrossRefGoogle Scholar
  24. Kaimal JC, Finnigan JJ (1994) Atmospheric boundary layer flows: Their structure and measurements. Oxford University Press, Oxford, p 289Google Scholar
  25. Kerzenmacher T, Gardiner B (1998) A mathematical model to describe the dynamic response of a spruce tree to the wind. Trees 12:385–394CrossRefGoogle Scholar
  26. Liang YC, Lee HP, Lim SP, Lin WZ, Lee KH, Wu CG (2002) Proper orthogonal decomposition and its applications—part I: theory. J Sound Vib 252:527–544CrossRefGoogle Scholar
  27. Loskutov A, Istomin I, Kuzanyan K, Kotlyarov O (2001) Testing and forecasting the time series of the solar activity by singular spectrum analysis. Nonlinear Phenom Compl Syst 4:47–57Google Scholar
  28. Marrelli L, Bilato R, Franz P, Martin P, Murari A, O’Gorman M (2001) Singular spectrum analysis as a tool for plasma fluctuations analysis. Rev Sci Instrum 72:499–502CrossRefGoogle Scholar
  29. Mayer H (1987) Wind-induced tree sways. Trees 1:195–206CrossRefGoogle Scholar
  30. Mayhead GJ (1973) Some drag coefficients for British forest trees derived from wind tunnel studies. Agric Meteorol 12:123–130CrossRefGoogle Scholar
  31. Milne R (1991) Dynamics of swaying of Picea sitchensis. Tree Physiol 9:383–399CrossRefGoogle Scholar
  32. Moore JR, Maguire DA (2004) Natural sway frequencies and damping ratios of trees: concepts, review and synthesis of previous studies. Trees 18:195–203CrossRefGoogle Scholar
  33. Moore JR, Maguire DA (2008) Simulating the dynamic behavior of Douglas-fir trees under applied loads by the finite element method. Tree Physiol 28:75–83CrossRefGoogle Scholar
  34. Peltola H (1996) Swaying of trees in response to wind and thinning in a stand of Scots pine. Bound-Layer Meteorol 77:285–304CrossRefGoogle Scholar
  35. Petersen C (2000) Dynamik der Baukonstruktionen. Vieweg, BraunschweigGoogle Scholar
  36. Queck R, Bienert A, Maas H-G, Harmansa S, Goldberg V, Bernhofer C (2012) Wind fields in heterogeneous conifer canopies: parameterisation of momentum absorption using high-resolution 3D vegetation scans. Eur J For Res 131:165–176CrossRefGoogle Scholar
  37. Rodriguez M, de 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 95:1523–1537CrossRefGoogle Scholar
  38. Rudnicki M, Silins U, Lieffers VJ (2001) Measure of simultaneous tree sways and estimation of crown interactions among a group of trees. Trees 15:83–90CrossRefGoogle Scholar
  39. Rudnicki M, Lieffers VJ, Silins U (2003) Stand structure governs the crown collisions of lodgepole pine. Can J For Res 33:1238–1244CrossRefGoogle Scholar
  40. Rudnicki M, Mitchell SJ, Novak MD (2004) Wind tunnel measurements of crown streamlining and drag relationships for three conifer species. Can J For Res 34:666–676CrossRefGoogle Scholar
  41. Rudnicki M, Meyer TH, Lieffers VJ, Silins U, Webb VA (2008) The periodic motion of lodgepole pine trees as affected by collisions with neighbors. Trees 22:475–482CrossRefGoogle Scholar
  42. Scannell B (1984) Quantification of the interactive motions of the atmospheric surface layer and a conifer canopy. PhD Thesis, Cranfield Institute of Technology, Bedford, UKGoogle Scholar
  43. Schindler D (2008) Responses of Scots pine trees to dynamic wind loading. Agric For Meteorol 148:1733–1742CrossRefGoogle Scholar
  44. Schindler D, Vogt R, Fugmann H, Rodriguez M, Schönborn J, Mayer H (2010) Vibration behavior of plantation-grown Scots pine trees in response to wind excitation. Agric For Meteorol 150:984–993CrossRefGoogle Scholar
  45. Schindler D, Fugmann H, Schönborn J, Mayer H (2012) Coherent response of a group of plantation-grown Scots pine trees to wind loading. Eur J For Res 131:191–202CrossRefGoogle Scholar
  46. Sellier D, Fourcaud T (2009) Crown structure and wood properties: influence on tree sway and response to high winds. Am J Bot 96:885–896CrossRefGoogle Scholar
  47. Sellier D, Brunet Y, Fourcaud T (2008) A numerical model of tree aerodynamic response to a turbulent airflow. Forestry 81:279–297CrossRefGoogle Scholar
  48. Spatz H-C, Brüchert F, Pfisterer J (2007) Multiple resonance damping or how do trees escape dangerously large oscillations? Am J Bot 94:1603–1611CrossRefGoogle Scholar
  49. Thom AS (1971) Momentum absorption by vegetation. Q J R Meteorol Soc 97:414–428CrossRefGoogle Scholar
  50. Thomas C, Foken T (2005) Detection of long-term coherent exchange over spruce forest using wavelet analysis. Theor Appl Climatol 80:91–104CrossRefGoogle Scholar
  51. Thomas C, Foken T (2007) Organised motion in a tall canopy: temporal scales, structure spacing and terrain effects. Bound-Layer Meteorol 122:123–147CrossRefGoogle Scholar
  52. Usbeck T, Wohlgemuth T, Dobbertin M, Pfister C, Bürgi A, Rebetez M (2010) Increasing storm damage to forests in Switzerland from 1858 to 2007. Agric For Meteorol 150:47–55CrossRefGoogle Scholar
  53. Vautard R, Ghil M (1989) Singular spectrum analysis in nonlinear dynamics with applications to paleoclimatic time series. Phys D 35:395–424CrossRefGoogle Scholar
  54. 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 For Res 35:1238–1249CrossRefGoogle Scholar
  55. Wall ME, Rechtsteiner A, Rocha LM (2009) Singular values decomposition and principal component analysis. In: Berrar DP, Dubitzky W, Granzow M (eds) A practical approach to microarray data analysis. Springer, Dordrecht, pp 91–109Google Scholar
  56. Webb VA, Rudnicki M (2009) A linear analysis of the interaction between the atmosphere and an underlying compliant plant canopy. Bound-Layer Meteorol 133:93–111CrossRefGoogle Scholar

Copyright information

© ISB 2012

Authors and Affiliations

  1. 1.Meteorological InstituteAlbert-Ludwigs-Universität FreiburgFreiburgGermany

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