Analysis of Inter-Annual Climate Variability Using Discrete Wavelet Transform

  • Md. Khademul Islam MollaEmail author
  • A. T. M. Jahangir Alam
  • Munmun Akter
  • A. R. Shoyeb Ahmed Siddique
  • M. Sayedur Rahman


This chapter presents a data adaptive filtering technique to extract annual cycles and the analysis of inter-annual climate variability based on different climate signals using discrete wavelet transform (DWT). The annual cycle is considered as higher energy trend in a climate signal and separated by implementing a threshold-driven filtering technique. The fractional Gaussian noise (fGn) is used here as a reference signal to determine adaptive threshold without any prior training constraint. The climate signal and fGn are decomposed into a finite number of subband signals using the DWT. The subband energy of the fGn and its confidence intervals are computed. The upper bound of the confidence interval is set as the threshold level. The energy of individual subband of a climate signal is compared with the threshold. The lowest order subband of which the energy is greater than the threshold level is selected yielding the upper frequency limit of the trend representing annual cycle. All the lower frequency subbands starting from the selected one are used to reconstruct the annual cycle of the corresponding climate signal. The distance between adjacent peaks in the extracted cycles refers to the inter-annual variation of the climate condition. The experimental results illustrate the efficiency of the proposed data adaptive approach to separate the annual cycle and the quantitative analysis of climate variability.


Climate signal Discrete wavelet transform Fractional gaussian noise Multiband decomposition Time domain filtering 


  1. Bates BC, Charles SP, Hughes JP (1998) Stochastic downscaling of numerical climate model simulations. Environ Model Softw 13(3–4):325–333CrossRefGoogle Scholar
  2. Broughton SA, Bryan KM (2008) Discrete Fourier analysis and wavelets: applications to signal and image processing, 1st edn. John Wiley & Sons, Inc., Hoboken, New JerseyGoogle Scholar
  3. Dairaku K, Emori S, Nozawa T, Yamazaki N, Hara M, Kawase H (2004) Hydrological change under the global warming in Asia with a regional climate model nested in a general circulation model. In: Proceedings of the third international workshop on monsoons (IWM-III), Hangzhou, ChinaGoogle Scholar
  4. Flandrin P, Rilling G, Goncalves P (2004) Empirical mode decomposition as a filter bank. IEEE Signal Process Lett 11(2):112–114CrossRefGoogle Scholar
  5. Harrison DE, Larkin NK (1997) Darwin sea level pressure, 1876–1996: evidence for climate change? Geophys Res Lett 24(14):1779–1782CrossRefGoogle Scholar
  6. Mak M (1995) Orthogonal wavelet analysis: inter-annual variability in the sea surface temperature. Bull Am Meteorol Soc 76:2179–2186CrossRefGoogle Scholar
  7. Mallat S (2008) A wavelet tour of signal processing, 3rd edn. Academic Press, OrlandoGoogle Scholar
  8. Molla MKI, Rahman MS, Sumi A, Banik P (2006) Empirical model decomposition analysis of climate changes with special reference to rainfall data. Discrete Dyn Nat Soc 2006:1–17CrossRefGoogle Scholar
  9. Molla MKI, Ghosh PR, Hirose K (2011) Bivariate EMD-based data adaptive approach to the analysis of climate variability. Discrete Dyn Nat Soc 2011:1–21CrossRefGoogle Scholar
  10. Mpelasoka FS, Mullan AB, Heerdegen RG (2001) New Zealand climate change information derived by multivariate statistical and artificial neural networks approaches. Int J Climatol 21(11):1415–1433CrossRefGoogle Scholar
  11. Oh HS, Ammann CM, Naveau P, Nychka D, Otto-Bliesner BL (2003) Multi-resolution time series analysis applied to solar irradiance and climate reconstructions. J Atmos Solar Terr Phys 65:191–201CrossRefGoogle Scholar
  12. Rajagopalan B, Lall U, Cane MA (1997) Anomalous ENSO occurrences: an alternate view. J Climate 10(9):2351–2357CrossRefGoogle Scholar
  13. Rajagopalan B, Lall U, Cane MA (1999) Comment on reply to the comments of Trenberth and Hurrell. Bull Am Meteorol Soc 80(12):2724–2726Google Scholar
  14. Strang G, Nquyen T (1996) Wavelets and filter banks. Willesley-Cambridge University Press, WillesleyGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Md. Khademul Islam Molla
    • 1
    • 2
    Email author
  • A. T. M. Jahangir Alam
    • 3
  • Munmun Akter
    • 2
  • A. R. Shoyeb Ahmed Siddique
    • 2
  • M. Sayedur Rahman
    • 4
  1. 1.Department of Information and Communication EngineeringThe University of TokyoBunkyoJapan
  2. 2.Department of Computer Science and EngineeringThe University of RajshahiRajshahiBangladesh
  3. 3.Department of Environmental SciencesJahangirnagar UniversityDhakaBangladesh
  4. 4.Department of StatisticsThe University of RajshahiRajshahiBangladesh

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