Skip to main content
Log in

Wavelet analysis of atmospheric turbulent data

  • Original Article
  • Published:
Environmental Fluid Mechanics Aims and scope Submit manuscript

Abstract

Wavelets are employed to study atmospheric turbulent data of three wind components, temperature and passive scalars CO\(_2\) and H\(_2\)O. The multiresolution analysis (MRA) based on maximal overlap discrete wavelet transform (MODWT) is used to separate turbulent fluctuations from the mean flow. These turbulent fluctuations are further partitioned into small scales \(\mathrm {x'}_s\) and large scales \(\mathrm {x'}_L\), and the fluxes are calculated by averaging over the given time interval. The large scales are responsible for much of the flux transport, while the small scales are fine scales consisting of non-transporting, nearly isotropic motions. The velocity spectrum for both small (non-coherent) and large scale (coherent) follow \(-5/3\) scaling, and the transfer efficiency \(R_{wa}\) similarity laws are better satisfied for the large scales. The velocity probability distribution of partitioned signals shows a narrower distribution for small scales compared to large ones. However, the flatness factor indicates deviation from Gaussianity. The joint probability distribution for large scales is skewed, suggesting the dominance of ejections and sweeps. Despite their wave-like nature, the large scales are not linear waves as indicated by the phase spectrum. The large scales are subjected to the continuous wavelet transform (CWT) to detect and isolate the strong localized events. The Mexican Hat (MHAT) wavelet transform and zero-crossing method is used to estimate the duration, separation, and frequency of occurrence of the detected events.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Data availability

The datasets analyzed during the current study are available from the corresponding author upon request.

References

  1. Aubinet M, Vesala T, Papale D (2012) Eddy covariance: a practical guide to measurement and data analysis. Springer, Berlin

    Book  Google Scholar 

  2. Audit B, Bacry E, Muzy JF, Arneodo A (2002) Wavelet-based estimators of scaling behavior. IEEE Trans Inf Theory 48(11):2938–2954

    Article  Google Scholar 

  3. Barthlott C, Fiedler F (2003) Turbulence structure in the wake region of a meteorological tower. Bound-Layer Meteorol 108(1):175–190

    Article  Google Scholar 

  4. Barthlott C, Drobinski P, Fesquet C, Dubos T, Pietras C (2007) Long-term study of coherent structures in the atmospheric surface layer. Bound-Layer Meteorol 125:1–24

    Article  Google Scholar 

  5. Van den Berg J (2004) Wavelets in physics. In: Wavelets in physics

  6. Brunet Y, Collineau S (1994) Wavelet analysis of diurnal and nocturnal turbulence above a maize crop. In: Foufoula-Georgiou E, Kumar P (eds) Wavelet analysis and its applications, vol 4. Elsevier, Amsterdam, pp 129–150

    Google Scholar 

  7. Cava D, Giostra U, Siqueira M, Katul G (2004) Organised motion and radiative perturbations in the nocturnal canopy sublayer above an even-aged pine forest. Bound-Layer Meteorol 112(1):129–157

    Article  Google Scholar 

  8. Chen J, Hu F (2003) Coherent structures detected in atmospheric boundary-layer turbulence using wavelet transforms at Huaihe river basin, china. Bound-Layer Meteorol 107:429–444

    Article  Google Scholar 

  9. Choi T, Hong J, Kim J, Lee H, Asanuma J, Ishikawa H, Tsukamoto O, Zhiqiu G, Ma Y, Ueno K et al (2004) Turbulent exchange of heat, water vapor, and momentum over a tibetan prairie by eddy covariance and flux variance measurements. J Geophys Res Atmosp. https://doi.org/10.1029/2004JD004767

    Article  Google Scholar 

  10. Collineau S, Brunet Y (1993) Detection of turbulent coherent motions in a forest canopy part i: Wavelet analysis. Bound-Layer Meteorol 65(4):357–379

    Article  Google Scholar 

  11. Collineau S, Brunet Y (1993) Detection of turbulent coherent motions in a forest canopy part ii: Time-scales and conditional averages. Bound-Layer Meteorol 66(1–2):49–73

    Article  Google Scholar 

  12. Daubechies I (1992) Ten lectures on wavelets. SIAM, New Delhi

    Book  Google Scholar 

  13. De Bruin H, Kohsiek W, Van Den Hurk B (1993) A verification of some methods to determine the fluxes of momentum, sensible heat, and water vapour using standard deviation and structure parameter of scalar meteorological quantities. Bound-Layer Meteorol 63(3):231–257

    Article  Google Scholar 

  14. Farge M (1992) Wavelet transforms and their applications to turbulence. Annu Rev Fluid Mech 24(1):395–458

    Article  Google Scholar 

  15. Farge M, Schneider K (2005) Wavelets: application to turbulence. University Warnick, lectures

  16. Farge M, Schneider K (2015) Wavelet transforms and their applications to MHD and plasma turbulence: a review. J Plasma Phys 81(6):435810602

    Article  Google Scholar 

  17. Farge M, Schneider K, Kevlahan N (1999) Non-gaussianity and coherent vortex simulation for two-dimensional turbulence using an adaptive orthogonal wavelet basis. Phys Fluids 11(8):2187–2201

    Article  CAS  Google Scholar 

  18. Farge M, Pellegrino G, Schneider K (2001) Coherent vortex extraction in 3d turbulent flows using orthogonal wavelets. Phys Rev Lett 87(5):054501

    Article  CAS  Google Scholar 

  19. Farge M, Schneider K, Devynck P (2006) Extraction of coherent bursts from turbulent edge plasma in magnetic fusion devices using orthogonal wavelets. Phys Plasmas 13(4):042304

    Article  Google Scholar 

  20. Feigenwinter C, Vogt R (2005) Detection and analysis of coherent structures in urban turbulence. Theoret Appl Climatol 81:219–230

    Article  Google Scholar 

  21. Feigenwinter C, Vogt R, Parlow E (1999) Vertical structure of selected turbulence characteristics above an urban canopy. Theoret Appl Climatol 62:51–63

    Article  Google Scholar 

  22. 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 Oceans 64:62–78

    Article  Google Scholar 

  23. Foken T, Göockede M, Mauder M, Mahrt L, Amiro B, Munger W (2004) Post-field data quality control. In: Lee X, Massman W, Law B (eds) Handbook of micrometeorology. A Guide for Surface Flux Measurement and Analysis. Kluwer Academic Publisher, Dordrecht, pp 181–208

    Google Scholar 

  24. Foufoula-Georgiou E, Kumar P (1994) Wavelets in geophysics, vol 4. Academic Press, New York

    Book  Google Scholar 

  25. Goel PK, Vidakovic B (1995) Wavelet transformations as diversity enhancers. Citeseer

  26. Grošelj D, Chen CH, Mallet A, Samtaney R, Schneider K, Jenko F (2019) Kinetic turbulence in astrophysical plasmas: waves and/or structures? Phys Rev 9(3):031037

    Article  Google Scholar 

  27. Grossmann A, Morlet J (1984) Decomposition of hardy functions into square integrable wavelets of constant shape. SIAM J Math Anal 15(4):723–736

    Article  Google Scholar 

  28. Inc TM (2023) Matlab version: 23.2.0.2365128 (r2023b)

  29. Katul G, Vidakovic B (1996) The partitioning of attached and detached eddy motion in the atmospheric surface layer using Lorentz wavelet filtering. Bound-Layer Meteorol 77(2):153–172

    Article  Google Scholar 

  30. Katul G, Vidakovic B (1998) Identification of low-dimensional energy containing/flux transporting eddy motion in the atmospheric surface layer using wavelet thresholding methods. J Atmos Sci 55(3):377–389

    Article  Google Scholar 

  31. Mahrt L, Bou-Zeid E (2020) Non-stationary boundary layers. Bound-Layer Meteorol 177:189–204

    Article  Google Scholar 

  32. Maurya S, Chandrasekar A, Namboodiri K (2023) On the nature of drag coefficient over a tropical coastal station. Meteorol Atmos Phys 135(6):1–8

    Article  Google Scholar 

  33. Maurya S, Chandrasekar A, Namboodiri K (2023) A quantitative study of turbulent fluxes over a coastal station. Bound-Layer Meteorol 188(1):55–74

    Article  Google Scholar 

  34. Meyer Y (1992) Wavelets and Operators. Volume 1. Cambridge University Press, Cambridge

    Google Scholar 

  35. Percival DB (2008) Analysis of geophysical time series using discrete wavelet transforms: an overview. Nonlinear time series analysis in the geosciences: applications in climatology. Geodyn Solar Terr Phys 112:61–79

    Google Scholar 

  36. Percival DB, Walden AT (2000) Wavelet methods for time series analysis, vol 4. Cambridge University Press, Cambridge

    Book  Google Scholar 

  37. Thomas C, Foken T (2007) Organised motion in a tall spruce canopy: temporal scales, structure spacing and terrain effects. Bound-Layer Meteorol 122:123–147

    Article  Google Scholar 

  38. Walker JS (2008) A primer on wavelets and their scientific applications. CRC Press, Boca Raton

    Book  Google Scholar 

  39. Wilczak J (1984) Large-scale eddies in the unstably stratified atmospheric surface layer. Part i: velocity and temperature structure. J Atmosp Sci 41(24):3537–3550

    Article  Google Scholar 

Download references

Acknowledgements

The authors are grateful to the reviewers whose suggestions helped us improve the manuscript significantly. The authors would like to acknowledge Vikram Sarabhai Space Center (VSSC), ISRO, for providing access to the instrumentation facility and data.

Funding

This research received no specific grant from the public, commercial, or not-for-profit funding agencies.

Author information

Authors and Affiliations

Authors

Contributions

S.M carried out the data analysis, prepared figures and wrote the main manuscript. A.C. and K.V.S.N. revised the manuscript and added in the discussion. All authors reviwed the manuscript.

Corresponding author

Correspondence to Sonali Maurya.

Ethics declarations

Conflict of interest

The authors declare that there is no Conflict of interest regarding the publication of this paper.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Maurya, S., Chandrasekar, A. & Namboodiri, K.V.S. Wavelet analysis of atmospheric turbulent data. Environ Fluid Mech 24, 247–264 (2024). https://doi.org/10.1007/s10652-024-09983-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10652-024-09983-z

Keywords

Navigation