Application of tidal harmonic analysis based on iteratively reweighted least squares method in the Qiantang River

Zhou Huamin; Pan Haidong; Chen Lixiao; Sun Maoming; Gu Jiali; Liu Yong; Wang Jiaqing

doi:10.12284/hyxb20250129

Volume 47 Issue 12

Dec. 2025

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Zhou Huamin，Pan Haidong，Chen Lixiao, et al. Application of tidal harmonic analysis based on iteratively reweighted least squares method in the Qiantang River[J]. Haiyang Xuebao，2025, 47(12)：150–164 doi: 10.12284/hyxb20250129

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Application of tidal harmonic analysis based on iteratively reweighted least squares method in the Qiantang River

doi: 10.12284/hyxb20250129

1.
Zhejiang Institute of Hydraulics and Estuary (Zhejiang Institute of Marine Planning and Design), Hangzhou, 310020, China
2.
First Institute of Oceanography, Ministry of Natural Resources, Qingdao, 266061, China
3.
Yangtze River Delta Estuarine Tidal Bore-Geomorphology-Ecology Observation and Research Station, Ministry of Water Resources, Hangzhou, 310020, China

Received Date: 2025-09-18
Rev Recd Date: 2025-12-15

Available Online: 2025-12-31

Publish Date: 2025-12-31

Abstract

Abstract

Traditional harmonic analysis based on the ordinary least squares (OLS) method is sensitive to noise and susceptible to contamination by measurement errors and strong non-tidal processes. Harmonic analysis utilizing the iteratively reweighted least squares (IRLS) method reduces the influence of outliers by assigning them smaller weights, thereby effectively improving accuracy and stability compared to the OLS method. However, a systematic comparison of the precision of these two methods in tidal-level analysis within tidal rivers is still lacking. This study systematically compares the two methods using measured water level data from the Qiantang River in Zhejiang Province, China, through both idealized and practical experiments. The results indicate that: (1) For short time series (<3 months), the IRLS method yields more accurate results than OLS, with the mean vector difference reduced by over 2 cm, while the difference between the two methods diminishes as the time series lengthens (>3 months). (2) In the lower reaches of the Qiantang River, the difference between the two methods is minimal. However, in the middle to upper reaches (e.g., from Cangqian to Tonglu), where the river is strongly influenced by freshwater runoff, the IRLS method improves the harmonic analysis results, particularly for long-period constituents. (3) The IRLS method significantly enhances the stability and accuracy of harmonic analysis results for tidal stations along the Qiantang River by effectively suppressing high-level noise and outlier interference. Therefore, the IRLS-based harmonic analysis method holds significant application value in regions with poor data quality or high background noise, such as tidal rivers.
- harmonic analysis,
- ordinary least squares (OLS),
- iteratively reweighted least squares (IRLS),
- Qiantang River,
- tidal river reach

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References(15)

References

[1]	吕咸青, 潘海东, 王雨哲. 潮汐调和分析方法的回顾与展望[J]. 海洋科学, 2021, 45(11): 132−143. Lü Xianqing, Pan Haidong, Wang Yuzhe. Review and prospect of tidal harmonic analysis method[J]. Marine Sciences, 2021, 45(11): 132−143.
[2]	Rajabi M, Hoseini M, Nahavandchi H, et al. Tidal harmonics retrieval using GNSS-R dual-frequency complex observations[J]. Journal of Geodesy, 2023, 97(10): 94. doi: 10.1007/s00190-023-01782-6
[3]	Pan Haidong, Sun Junchuan, Xu Tengfei, et al. Extraction of ocean tides in the Bohai Sea from GFO satellite altimeter via a modified tidal harmonic analysis algorithm[J]. Continental Shelf Research, 2024, 276: 105231. doi: 10.1016/j.csr.2024.105231
[4]	Leffler K E, Jay D A. Enhancing tidal harmonic analysis: robust (hybrid L¹/L²) solutions[J]. Continental Shelf Research, 2009, 29(1): 78−88. doi: 10.1016/j.csr.2008.04.011
[5]	Guo Leicheng, van der Wegen M, Jay D A, et al. River-tide dynamics: exploration of nonstationary and nonlinear tidal behavior in the Yangtze River estuary[J]. Journal of Geophysical Research: Oceans, 2015, 120(5): 3499−3521. doi: 10.1002/2014JC010491
[6]	Cai Huayang, Li Bo, Garel E, et al. A data-driven model to quantify the impact of river discharge on tide-river dynamics in the Yangtze River estuary[J]. Journal of Hydrology, 2023, 620: 129411. doi: 10.1016/j.jhydrol.2023.129411
[7]	Pan Haidong, Lü Xianqing, Wang Yingying, et al. Exploration of tidal-fluvial interaction in the Columbia River estuary using S_TIDE[J]. Journal of Geophysical Research: Oceans, 2018, 123(9): 6598−6619. doi: 10.1029/2018JC014146
[8]	Pan Haidong, Wang Dingqi, Li Bingtian, et al. Timing errors in global sea level observations[J]. Ocean Dynamics, 2025, 75(1): 5. doi: 10.1007/s10236-024-01652-5
[9]	武家兴, 张卓, 陈鹏, 等. 考虑流量变化影响的西江感潮河道潮汐特征分析[J]. 海洋学报, 2023, 45(7): 8−24. doi: 10.12284/hyxb2023101 Wu Jiaxing, Zhang Zhuo, Chen Peng, et al. Analysis of the tidal characteristics along the tidal reach of Xijiang River considering river discharge variation[J]. Haiyang Xuebao, 2023, 45(7): 8−24. doi: 10.12284/hyxb2023101
[10]	欧素英, 田枫, 郭晓娟, 等. 珠江三角洲径潮相互作用下潮能的传播和衰减[J]. 海洋学报, 2016, 38(12): 1−10. doi: 10.3969/j.issn.0253-4193.2016.12.001 Ou Suying, Tian Feng, Guo Xiaojuan, et al. Propagation and damping of tidal energy in the Pearl River Delta[J]. Haiyang Xuebao, 2016, 38(12): 1−10. doi: 10.3969/j.issn.0253-4193.2016.12.001
[11]	Gan Min, Chen Yongping, Pan Haidong, et al. Study on the spatiotemporal variation of the Yangtze estuarine tidal species[J]. Estuarine, Coastal and Shelf Science, 2024, 298: 108637. doi: 10.1016/j.ecss.2024.108637
[12]	Cao Yu, Zhang Wei, Zhu Yuliang, et al. Impact of trends in river discharge and ocean tides on water level dynamics in the Pearl River Delta[J]. Coastal Engineering, 2020, 157: 103634. doi: 10.1016/j.coastaleng.2020.103634
[13]	Xie Dongfeng, Wang Zhengbing, Huang Junbao, et al. River, tide and morphology interaction in a macro-tidal estuary with active morphological evolutions[J]. CATENA, 2022, 212: 106131. doi: 10.1016/j.catena.2022.106131
[14]	Zhou Huamin, Pan Haidong, Gan Min, et al. Study on the tidal variability related to flooding and hydroelectric operations in the Qiantang river estuary[J]. Estuarine, Coastal and Shelf Science, 2024, 305: 108845. doi: 10.1016/j.ecss.2024.108845
[15]	潘存鸿, 韩曾萃, 2017. 钱塘江河口保护与治理研究[M]. 北京: 中国水利水电出版社. Pan Cunhong, Han Zengcui, 2017. Research on Conservation and Regulation of Qiantang Estuary[M]. Beijing: China Water & Power Press.