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Boundary-Layer Meteorology

, Volume 159, Issue 2, pp 391–406 | Cite as

The Analyses of Turbulence Characteristics in the Atmospheric Surface Layer Using Arbitrary-Order Hilbert Spectra

  • W. Wei
  • F. G. Schmitt
  • Y. X. Huang
  • H. S. Zhang
Research Article

Abstract

Turbulent characteristics in the atmospheric surface layer are investigated using a data-driven method, Hilbert spectral analysis. The results from empirical mode decomposition display a set of intrinsic mode functions whose characteristic scales suggest a dyadic filter-bank property. It can be concluded from the joint probability density function of the intrinsic mode functions that the turbulent properties are totally different under different stratifications: the amplitudes (or energies) are arranged according to the stability parameter Open image in new window for stable conditions, but tend to cluster randomly for unstable cases. The intermittency analyses reveal that second-order Hilbert marginal spectra display a power-law behaviour in the inertial subrange, and that the scaling exponent functions deviate from the theoretical values due to the strong intermittency in the stable boundary layer.

Keywords

Atmospheric boundary layer Intermittency Scaling Hilbert spectral analysis Stratification 

Notes

Acknowledgments

This work was jointly funded by R&D Special Fund for Public Welfare Industry (meteorology) by Ministry of Finance and Ministry of Science and Technology (GYHY201506001), the Public Welfare Projects for Environmental Protection (201409001, 201309009), the National Natural Science Foundation of China (41475007, 91544216) and The Research Fund for the Doctoral Program of Higher Education (20110001130010). This work was performed during a visit of the first author in LOG (Wimereux, France). The China Scholarship Council (CSC) is thanked for financial support for this study.

References

  1. Chen J, Zhang R, Wang H, Li J, Hong M, Li X (2014) Decadal modes of sea surface salinity and the water cycle in the tropical Pacific Ocean: the anomalous late 1990s. Deep Sea Res Part I Oceanogr Res Pap 84:38–49CrossRefGoogle Scholar
  2. Cohen L (1995) Time-frequency analysis. Prentice Hall, New Jersey, pp 153–161Google Scholar
  3. Dyer AJ (1974) A review of flux-profile relationships. Boundary-Layer Meteorol 7:363–372CrossRefGoogle Scholar
  4. Ferreres E, Soler MR, Terradellas E (2013) Analysis of turbulent exchange and coherent structures in the stable atmospheric boundary layer based on tower observations. Dyn Atmos Ocean 64:62–78CrossRefGoogle Scholar
  5. Flandrin P (1998) Time-frequency/time-scale analysis. Academic Press, San Diego, pp 12–18Google Scholar
  6. Flandrin P, Gonçalvés P (2004) Empirical mode decompositions as data-driven wavelet-like expansions. Int J Wavelets Multiresolut Inf Process 02:477–496CrossRefGoogle Scholar
  7. Flandrin P, Rilling G, Gonçalvés P (2004) Empirical mode decomposition as a filter bank. Signal Process Lett IEEE 11:112–114CrossRefGoogle Scholar
  8. Frisch U (1995) Turbulence: the legacy of AN Kolmogorov. Cambridge University Press, Cambridge, pp 72–97Google Scholar
  9. Garai A, Kleissl J (2011) Air and surface temperature coupling in the convective atmospheric boundary layer. J Atmos Sci 68:2945–2954CrossRefGoogle Scholar
  10. Haugen DA (1973) Workshop on micrometeorology. American Meteorological Society, Boston, pp 152–163Google Scholar
  11. Högström ULF (1988) Non-dimensional wind and temperature profiles in the atmospheric surface layer: a re-evaluation. Boundary-Layer Meteorol 42:55–78CrossRefGoogle Scholar
  12. Holtslag AAM, Nieuwstadt FTM (1986) Scaling the atmospheric boundary layer. Boundary-Layer Meteorol 36:201–209CrossRefGoogle Scholar
  13. Horiguchi M, Hayashi T, Adachi A, Onogi S (2014) Stability dependence and diurnal change of large-scale turbulence structures in the near-neutral atmospheric boundary layer observed from a meteorological tower. Boundary-Layer Meteorol 151:221–237CrossRefGoogle Scholar
  14. Hu W, Biswas A, Si BC (2014) Application of multivariate empirical mode decomposition for revealing scale-and season-specific time stability of soil water storage. Catena 113:377–385CrossRefGoogle Scholar
  15. Huang YX (2009) Arbitrary order Hilbert spectral analysis definition and application to fully developed turbulence and environmental time series. Université des Sciences et Technologie de Lille-Lille I, pp 31–32Google Scholar
  16. Huang NE, Shen SSP (2005) Hilbert–Huang transform and its applications. World Scientific, Singapore, 32 ppGoogle Scholar
  17. Huang NE, Shen Z, Long SR, Wu MC, Shin HH, Zheng Q, Yen N-C, Tung CC, Liu HH (1998) The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc R Soc A Math Phys Eng Sci 454:903–995CrossRefGoogle Scholar
  18. Huang NE, Shen Z, Long SR (1999) A new view of nonlinear water waves: the Hilbert Spectrum 1. Annu Rev Fluid Mech 31:417–457CrossRefGoogle Scholar
  19. Huang NE, Wu M-LC, Long SR, Shen SS, Qu W, Gloersen P, Fan KL (2003) A confidence limit for the empirical mode decomposition and Hilbert spectral analysis. Proc R Soc A Math Phys Eng Sci 459:2317–2345CrossRefGoogle Scholar
  20. Huang YX, Schmitt FG, Lu ZM, Liu YL (2008) An amplitude-frequency study of turbulent scaling intermittency using Empirical Mode Decomposition and Hilbert Spectral Analysis. Europhys Lett (EPL) 84:40010CrossRefGoogle Scholar
  21. Huang YX, Schmitt FG, Lu ZM, Liu YL (2009) Analysis of daily river flow fluctuations using empirical mode decomposition and arbitrary order Hilbert spectral analysis. J Hydrol 373:103–111CrossRefGoogle Scholar
  22. Huang YX, Schmitt FG, Lu ZM, Fougairolles P, Gagne Y, Liu YL (2010) Second-order structure function in fully developed turbulence. Phys Rev E 82:026319CrossRefGoogle Scholar
  23. Huang YX, Schmitt FG, Hermand J-P, Gagne Y, Lu ZM, Liu YL (2011) Arbitrary-order Hilbert spectral analysis for time series possessing scaling statistics: comparison study with detrended fluctuation analysis and wavelet leaders. Phys Rev E 84:016208CrossRefGoogle Scholar
  24. Huang YX, Biferale L, Calzavarini E, Sun C, Toschi F (2013) Lagrangian single-particle turbulent statistics through the Hilbert–Huang transform. Phys Rev E 87:041003CrossRefGoogle Scholar
  25. Imberger J, Boashash B (1986) Application of the Wigner–Ville distribution to temperature gradient microstructure: a new technique to study small-scale variations. J Phys Oceanogr 16:1997–2012CrossRefGoogle Scholar
  26. Iyengar RN, Kanth STGR (2006) Seasonal forecasting of Indian summer monsoon rainfall: a review. Weather 91:350–356Google Scholar
  27. Kaimal JC, Wyngaard Y, Izumi Y, Coté OR (1972) Spectral characteristics of surface layer turbulence over the sea. Q J R Meteorol Soc 98:563–589CrossRefGoogle Scholar
  28. Kaimal JC, Wyngaard Y, Haugen DA, Coté OR, Izumi Y, Caughey SJ, Readings CJ (1976) Turbulence structure in convective boundary layer. J Atmos Sci 33:2152–2169CrossRefGoogle Scholar
  29. Kolmogorov AN (1941) Dissipation of energy in locally isotropic turbulence. Dokl Akad Nauk SSSR 32:16–18Google Scholar
  30. Kolmogorov AN (1962) A refinement of previous hypotheses concerning the local structure. J Fluid Mech 13:82–85CrossRefGoogle Scholar
  31. Klipp CL, Mahrt L (2004) Flux-gradient relationship, self-correlation and intermittency in the stable boundary layer. Q J R Meteorol Soc 130:2087–2103CrossRefGoogle Scholar
  32. Koracin D, Berkowicz R (1988) Nocturnal boundary-layer height: observations by acoustic sounders and predictions in terms of surface-layer parameters. Boundary-Layer Meteorol 43:65–83CrossRefGoogle Scholar
  33. Li X, Zhang H (2012) Seasonal variations in dust concentration and dust emission observed over Horqin Sandy Land area in China from December 2010 to November 2011. Atmos Environ 61:56–65CrossRefGoogle Scholar
  34. Mahrt L (1998) Nocturnal boundary-layer regimes. Boundary-Layer Meteorol 88:255–278CrossRefGoogle Scholar
  35. Mahrt L (2014) Stably stratified atmospheric boundary layers. Annu Rev Fluid Mech 46:23–45CrossRefGoogle Scholar
  36. Moeng C-H (1984) A large-eddy-simulation model for the study of planetary boundary-layer turbulence. J Atmos Sci 41:2052–2062CrossRefGoogle Scholar
  37. Molla MKI, Rahman MS, Sumi A, Banik P (2006) Empirical mode decomposition analysis of climate changes with special reference to rainfall data. Discret Dyn Nat Soc 2006:1–17CrossRefGoogle Scholar
  38. Panofsky HA, Dutton JA (1984) Atmospheric turbulence. Models and methods for engineering applications. Wiley, New York, pp 145–148Google Scholar
  39. Panofsky HA, Tennekes H, Lenschow DH, Wyngaard JC (1977) The characteristics of turbulent velocity components in the surface layer under convective conditions. Boundary-Layer Meteorol 11:355–361CrossRefGoogle Scholar
  40. Panofsky HA, Larko D, Lipschutz R, Stone G, Bradley EF, Bowen AJ, Højstrup J (1982) Spectra of velocity components over complex terrain. Q J R Meteorol Soc 108:215–230CrossRefGoogle Scholar
  41. Ramana MV, Krishnan P, Kunhikrishnan PK (2004) Surface boundary-layer characteristics over a tropical inland station: seasonal features. Boundary-Layer Meteorol 111:153–157CrossRefGoogle Scholar
  42. Rilling G, Flandrin P, Gonçalvès P (2003) On empirical mode decomposition and its algorithms. IEEE-EURASIP Work Nonlinear Signal Image Process NSIP-03 Grado 3:8–11Google Scholar
  43. Salmond JA (2005) Wavelet analysis of intermittent turbulence in a very stable nocturnal boundary layer: implications for the vertical mixing of ozone. Boundary-Layer Meteorol 114:463–488CrossRefGoogle Scholar
  44. Schmitt FG, Huang Y, Lu Z, Liu YL, Fernandez N (2009) Analysis of velocity fluctuations and their intermittency properties in the surf zone using empirical mode decomposition. J Mar Syst 77:473–481CrossRefGoogle Scholar
  45. Sun J, Mahrt L, Banta RM, Pichugina YL (2012) Turbulence regimes and turbulence intermittency in the stable boundary layer during CASES-99. J Atmos Sci 69:338–351CrossRefGoogle Scholar
  46. Vincent CL, Pinson P, Giebela G (2011) Wind fluctuations over the North Sea. Int J Climatol 31:1584–1595Google Scholar
  47. Weber S, Kordowski K (2009) Comparison of atmospheric turbulence characteristics and turbulent fluxes from two urban sites in Essen, Germany. Theor Appl Climatol 102:61–74CrossRefGoogle Scholar
  48. Wei W, Wu BG, Ye XX, Wang HX, Zhang HS (2013) Characteristics and mechanisms of low-level jets in the Yangtze River Delta of China. Boundary-Layer Meteorol 149:403–424CrossRefGoogle Scholar
  49. Wei W, Zhang HS, Ye XX (2014) Comparison of low-level jets along the north coast of China in summer. J Geophys Res Atmos 119:9692–9706CrossRefGoogle Scholar
  50. Wieringa J (1993) Representative roughness parameters for homogeneous terrain. Boundary-Layer Meteorol 63:323–363CrossRefGoogle Scholar
  51. Wu Z, Huang NE (2004) A study of the characteristics of white noise. Proc R Soc Lond A Math Phys Eng Sci 460:1597–1611CrossRefGoogle Scholar
  52. Zhang HS, Chen J, Park SU (2001) Turbulence structure in unstable conditions over various surface. Boundary-Layer Meteorol 100:243–261CrossRefGoogle Scholar
  53. Zhang HS, Zhu H, Peng Y, Kang L, Chen JY, Park SU (2007) Experiment on dust flux during duststorm periods over sand desert area. Acta Meteorol Sin 65:744–752Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • W. Wei
    • 1
  • F. G. Schmitt
    • 2
  • Y. X. Huang
    • 3
  • H. S. Zhang
    • 1
  1. 1.Laboratory for Climate and Ocean-Atmosphere Studies, Department of Atmospheric and Oceanic Sciences, School of PhysicsPeking UniversityBeijingPeople’s Republic of China
  2. 2.Laboratoire d’Oceanologie et de GeosciencesCNRS, Univ. Lille, Univ. Littoral Cote d’Opale, UMR 8187WimereuxFrance
  3. 3.State Key Laboratory of Marine Environmental ScienceXiamen UniversityXiamenPeople’s Republic of China

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