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A Practical Guide to Discrete Wavelet Decomposition of Hydrologic Time Series

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  • Yan-Fang Sang

Abstract

Discrete wavelet transform (DWT) is commonly used for wavelet threshold de-noising, wavelet decomposition, wavelet aided hydrologic series simulation and prediction, as well as many other hydrologic time series analyses. However, its effectiveness in practice is influenced by many key factors. In this paper the “reference energy function” was firstly established by operating Monte-Carlo simulation to diverse noise types; then, energy function of hydrologic series was compared with the reference energy function, and four key issues on discrete wavelet decomposition were studied and the methods for solving them were proposed, namely wavelet choice, decomposition level choice, wavelet threshold de-noising and significance testing of DWT, based on which a step-by-step guide to discrete wavelet decomposition of hydrologic series was provided finally. The specific guide is described as: choose appropriate wavelet from the recommended wavelets and according to the statistical characters relations among original series, de-noised series and removed noise; choose proper decomposition levels by analyzing the difference between energy function of the analyzed series and reference energy function; then, use the chosen wavelet and decomposition level, estimate threshold according to series’ complexity and set the same threshold under each level, and use the mid-thresholding rule to remove noise; finally, conduct significance testing of DWT by comparing energy function of the de-noised series with the reference energy function. Analyses of both synthetic and observed series indicated the better performance and easier operability of the proposed guide compared with those methods used presently. Following the guide step by step, noise and different deterministic components in hydrologic series can be accurately separated, and uncertainty can also be quantitatively estimated, thus the discrete wavelet decomposition result of series can be improved. Copyright Springer Science+Business Media B.V. 2012

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  • Yan-Fang Sang, 2012. "A Practical Guide to Discrete Wavelet Decomposition of Hydrologic Time Series," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(11), pages 3345-3365, September.
    • Handle: RePEc:spr:waterr:v:26:y:2012:i:11:p:3345-3365
    DOI: 10.1007/s11269-012-0075-4
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    1. Silvia Meniconi & Bruno Brunone & Marco Ferrante & Christian Massari, 2011. "Small Amplitude Sharp Pressure Waves to Diagnose Pipe Systems," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 25(1), pages 79-96, January.
    2. Wensheng Wang & Shixiong Hu & Yueqing Li, 2011. "Wavelet Transform Method for Synthetic Generation of Daily Streamflow," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 25(1), pages 41-57, January.
    3. Chien-ming Chou, 2011. "A Threshold Based Wavelet Denoising Method for Hydrological Data Modelling," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 25(7), pages 1809-1830, May.
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    4. Jinjie Miao & Guoliang Liu & Bibo Cao & Yonghong Hao & Jianmimg Chen & Tian−Chyi Yeh, 2014. "Identification of Strong Karst Groundwater Runoff Belt by Cross Wavelet Transform," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(10), pages 2903-2916, August.
    5. Hafiza Mamona Nazir & Ijaz Hussain & Muhammad Faisal & Alaa Mohamd Shoukry & Showkat Gani & Ishfaq Ahmad, 2019. "Development of Multidecomposition Hybrid Model for Hydrological Time Series Analysis," Complexity, Hindawi, vol. 2019, pages 1-14, January.
    6. Djerbouai Salim & Souag-Gamane Doudja & Ferhati Ahmed & Djoukbala Omar & Dougha Mostafa & Benselama Oussama & Hasbaia Mahmoud, 2023. "Comparative Study of Different Discrete Wavelet Based Neural Network Models for long term Drought Forecasting," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 37(3), pages 1401-1420, February.
    7. Salim Djerbouai & Doudja Souag-Gamane, 2016. "Drought Forecasting Using Neural Networks, Wavelet Neural Networks, and Stochastic Models: Case of the Algerois Basin in North Algeria," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(7), pages 2445-2464, May.
    8. Yan-Fang Sang & Zhonggen Wang & Changming Liu, 2015. "Wavelet Neural Modeling for Hydrologic Time Series Forecasting with Uncertainty Evaluation," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(6), pages 1789-1801, April.
    9. Duong Tran Anh & Thanh Duc Dang & Song Pham Van, 2019. "Improved Rainfall Prediction Using Combined Pre-Processing Methods and Feed-Forward Neural Networks," J, MDPI, vol. 2(1), pages 1-19, February.
    10. Yongtao Wang & Jian Liu & Rong Li & Xinyu Suo & EnHui Lu, 2022. "Medium and Long-term Precipitation Prediction Using Wavelet Decomposition-prediction-reconstruction Model," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 36(3), pages 971-987, February.
    11. Haijiao Yu & Xiaohu Wen & Qi Feng & Ravinesh C. Deo & Jianhua Si & Min Wu, 2018. "Comparative Study of Hybrid-Wavelet Artificial Intelligence Models for Monthly Groundwater Depth Forecasting in Extreme Arid Regions, Northwest China," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(1), pages 301-323, January.
    12. Alpaslan Yarar, 2014. "A Hybrid Wavelet and Neuro-Fuzzy Model for Forecasting the Monthly Streamflow Data," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(2), pages 553-565, January.

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