Decomposition of CI and ENSO signals using the wavelet-Based technique
Keywords:
CI, ENSO, wavelet transformation
Abstract
The study is focused on six solar cycles that are studied in a comparison of related ENSO signals by using the wavelet technique. The wavelet technique is a advanced method used to analyze and understand the dynamical behavior of signals in any dimension. In this work, Discrete wavelet transformation (DWT) is applied on sun and ENSO data signals. Using the Daubechies wavelet (db 2), the Solar and ENSO parameters are decomposed into their approximation (a) and detail (d) components. By this technique, dynamical changes in both studied parameters are found effectively. The variation of solar energy was observed at a different level detailed coefficient frequencies up to 5 levels. The decomposition at level 5 shows the original signal and lower variability. Further initial and middle phase solar variation was found in the change of ENSO variability. The variability of solar energy in contrast to climate signals will be helpful in the future to understand the dynamical signal process by wavelet transformation.
References
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[3]. Bray, R. J., Cram, L. E., Durrant, C., & Loughhead, R. E. (2006). Plasma loops in the solar corona (Vol. 18). Cambridge University Press.
[4]. Catalão, J. P. D. S., Pousinho, H. M. I., & Mendes, V. M. F. (2010). Hybrid wavelet-PSO-ANFIS approach for short-term electricity prices forecasting. IEEE Transactions on Power Systems, 26(1), 137-144.
[5]. Chou, C. M. (2007). Applying multi-resolution analysis to differential hydrological grey models with dual series. Journal of Hydrology, 332(1-2), 174-186.
[6]. Chou, C. M. (2011). Wavelet-based multi-scale entropy analysis of complex rainfall time series. Entropy, 13(1), 241-253.
[7]. Daubechies, I. (1998) Orthonormal Bases of Compactly Supported Wavelets. Communications on Pure and Applied Mathematics , 41, 909-996. https://doi.org/10.1002/cpa.3160410705.
[8]. Farge, M. (1992) Wavelet Transforms and Their Applications to Turbulence. A nnual Review of Fluid Mechanics , 24, 395-457. https://doi.org/10.1146/annurev.fl.24.010192.002143.
[9]. Fugal, D. L. (2009). Conceptual wavelets in digital signal processing: an in-depth, practical approach for the non-mathematician. Space & Signals Technical Pub.
[10]. Gkana, A., & Zachilas, L. (2016). Re-evaluation of predictive models in light of new data: Sunspot number version 2.0. Solar Physics, 291(8), 2457-2472.
[11]. Graps, A. (1995) An Introduction to Wavelets. IEEE Computational Science and Engineering , 2, 50-61. https://doi.org/10.1109/99.388960.
[12]. Grossman, A. and Morlet, J. (1984) Decomposition of Hardy Functions into Square Integrable Wavelets of Constant Shape. SIAM Journal on Mathematical Analysis , 15, 723-736. https://doi.org/10.1137/0515056.
[13]. IPCC, Technical Paper V.2002: Climate change and Biodiversity.
[14]. Mallat, S. (1999). A wavelet tour of signal processing. Elsevier.
[15]. Mallat, S.G. (1989) A Theory for Multiresolution Signal Decomposition the Wavelet.
[16]. Partal, T., & Küçük, M. (2006). Long-term trend analysis using discrete wavelet components of annual precipitations measurements in Marmara region (Turkey). Physics and Chemistry of the Earth, Parts A/B/C, 31(18), 1189-1200.
[17]. Popivanov, I., & Miller, R. J. (2002, February). Similarity search over time-series data using wavelets. In Proceedings 18th international conference on data engineering (pp. 212-221). IEEE.
[18]. Quiroz, R., Yarlequé, C., Posadas, A., Mares, V., & Immerzeel, W. W. (2011). Improving daily rainfall estimation from NDVI using a wavelet transform. Environmental Modelling & Software, 26(2), 201-209.
[19]. Santos, C.A.G., Galvao, C.O., Suzuki, K. and Trigo, R.M. (2001) Matsuyama City Rainfall Data Analysis using Wavelet Transform. Annual Journal of Hydraulic E ngineering , 45, 211-216.
[20]. Svalgaard L, Updating the historical sunspot record, in SOHO-23:Understanding a peculiar solar minimum.Proceedings of a workshop held 21–25September in Northeast Harbor, Maine,USA, ed. by SR Cranmer, JT Hoeksema,JL Kohl. ASP Conference Series,(Astronomical Society of the Pacific, San Francisco, 2010). 2009;428:297.
[21]. Torrence, C. and Compo, G.P. (1998) A Practical Guide to Wavelet Analysis. Bull etin of the American Meteorological Society , 79, 61-78. https://doi.org/10.1175/1520-0477(1998)079<0061:APGTWA>2.0.CO;2
[22]. Vonesch, C., Blu, T., & Unser, M. (2007). Generalized Daubechies wavelet families. IEEE Transactions on Signal Processing, 55(9), 4415-4429.
[23]. Wang, B., W. Renguang and K. M. Lan, (2001): Interannual Variability of the Asian Summer Monsoon: Contrasts between the Indian and the Western North Pacific–East Asian Monsoons. Journal of Climate, (14), 4073-4090.
Published
2026-08-02
How to Cite
Akhter, M., Abbas, S., & Hassan, D. (2026). Decomposition of CI and ENSO signals using the wavelet-Based technique. International Journal of Artificial Intelligence & Mathematical Sciences, 5(1), 1-11. https://doi.org/10.58921/ijaims.v5i1.180
