Application of a modified tidal harmonic analysis method in the analysis of short-term tide levels offshore Zhejiang
-
摘要: 传统调和分析方法受限于瑞利准则，需半年数据以分辩八大主要分潮（M2，S2，N2，K2，K1，O1，P1，Q1）。对于短期潮位资料，未分辩的分潮需采用附近长期潮位站资料的差比关系来推算。而浙江近海公开的长期潮位资料匮乏，使得无法从短期资料中准确提取主要分潮。本文引入的新型潮汐调和分析算法，基于各主要分潮间内在联系所建立的平滑函数，突破瑞利准则限制，显著减少了所需潮位资料长度，特别适用于短期资料丰富的海域。本研究将该算法应用于浙江沿海多岛屿海域，对小于15天的潮位资料进行试验。结果表明：石浦站八大主要分潮的调和常数与传统调和分析方法得到的结果总体接近，而所需资料长度从
8760 小时减少至336小时，可用于理论深度基准面等特征参数的计算。采用该算法分析浙江沿海潮位的八大主要分潮时，建议数据长度在5天以上。Abstract: Due to the limitations of the Rayleigh criterion, classical harmonic analysis (CHA) model requires half a year of data records to analyze the eight main tidal constituents, namely, M2, S2, N2, K2, K1, O1, P1, Q1. For short-term tidal records, the unresolved constituents typically rely on the ratio differences from nearby long-term tidal stations for estimation. However, there is a scarcity of publicly available long-term tidal data in the coastal areas of Zhejiang, which currently prevents the accurate extraction of the main constituents from short-term records. This paper introduces a modified harmonic analysis model, referred to as the Modified Harmonic Analysis model based on the Credo of Smoothness (MHACS). Based on the smooth functions established by the intrinsic connections between major constituents, it breaks through the Rayleigh criterion, significantly reducing the length of tidal records required, especially suitable for coastal areas with abundant short-term data. This algorithm was applied to the multi-island area of Zhejiang offshore, using tidal records shorter than 15 days. The results show that the harmonic constants of the eight main constituents at the Shipu station are very close to the results obtained by the CHA method, and the required data length is reduced from8760 hours to 336 hours, which can be used to calculate characteristic parameters such as the theoretical depth datum. For analyzing the eight main constituents along the Zhejiang coast using MHACS, a minimum data length of 5 days is recommended.-
Key words:
- Zhejiang offshore /
- multi-island /
- short-term tidal records /
- harmonic analysis /
- tidal admittance
-
图 2 不同导纳形式下岭回归参数的比较
Fig. 2 Comparison of ridge regression parameters under different admittances forms
图 3 石浦站不同调和分析方法的回报结果
Fig. 3 336 hours records at Shipu and the hindcast of CHA and MHACS methods
图 4 浙江近海EOT20模型同潮图与MHACS结果（色差圆点）比较。（a）M2分潮；（b）S2分潮；（c）K1分潮；（d）O1分潮
Fig. 4 Co-tidal charts in the coastal area of Zhejiang based on EOT20 tide model and results of MHACS methods (colored dots). (a) M2 tide. (b) S2 tide. (c) K1 tide. (d) O1 tide
图 5 利用MHACS结果计算的浙江近海理论深度基准面
Fig. 5 Theoretical depth datum calculated using MHACS results in the coastal area of Zhejiang
图 6 利用MHACS结果计算的潮型系数分布
Fig. 6 Distribution of daily form factor (F) values using MHACS results
图 7 利用MHACS结果计算的月潮汐包络因子平面分布
Fig. 7 Distribution of monthly tidal envelope factor (E) using MHACS results
图 8 振幅比S2/M2（x轴）、N2/S2（y轴）与月潮汐包络因子E值（等值线）关系，以及浙江近海各站E值（蓝色点）分布
Fig. 8 Relationship between the S2/M2 and N2/S2 amplitude ratios (x and y axes respectively) and E values (shown as plot contours), with the distribution of E values (blue dots) at various stations in the coastal area of Zhejiang
图 9 石浦站采用MHACS方法（不同形式导纳）与CHA方法得到的平均矢量差随数据长度的变化
Fig. 9 The mean vector differences between tidal constants obtained by MHACS and CHA methods with different length of records at Shipu
A1 石浦站经典调和分析结果。(a)半日潮归一化振幅；(b) 半日潮迟角；(c) 全日潮归一化振幅；(d) 全日潮迟角。
A1 The CHA results at Shipu. (a) Normalized amplitudes for semi-diurnal tides. (b) Phase lags for semi-diurnal tides. (c) Normalized amplitudes for diurnal tides. (d) Phase lags for diurnal tides.
表 1 潮位站信息
Tab. 1 The information of tide gauges
站点名称 编号 纬度（°N） 经度（°E） 站点名称 编号 纬度（°N） 经度（°E） 金塘 1 29.99 121.84 峙南 11 29.84 122.06 毛礁 2 29.93 121.87 黄牛礁 12 29.68 121.82 万华码头 3 29.94 121.95 西泽 13 29.63 121.85 定海 4 30.00 122.05 澉浦 14 30.37 120.90 双合 5 30.29 122.06 镇海口 15 29.95 121.72 衢山 6 30.44 122.28 石浦 16 29.23 121.96 泗礁 7 30.72 122.51 岱山 17 30.28 122.22 嵊山 8 30.72 122.80 下三山 18 29.94 121.85 独山码头 9 30.66 121.21 乍浦 10 30.59 121.10 石浦 16 29.23 121.96 
下载: 导出CSV
表 2 各回归方法下石浦站的调和常数矢量差统计（单位：cm）
Tab. 2 Vector differences of harmonic constants using different regression methods
插值函数 线性函数 二次函数 求解方法 普通最小二乘法 迭代重加权最小二乘法 岭回归法 普通最小二乘法 迭代重加权最小二乘法 岭回归法 矢量差 4.17 3.60 4.11 6.05 7.19 4.13
下载: 导出CSV
表 3 石浦站采用经典调和分析CHA方法（1年数据）、EOT20模型和新型调和分析MHACS方法（336小时数据）得到的调和常数（单位：cm，°）
Tab. 3 Estimated tidal amplitudes (cm) and phase lags (degree) at Shipu using CHA (one-year records) , EOT20 model and MHACS (336 hours records) methods
分潮名称 石浦站振幅（迟角） CHA方法 EOT20模型 MHACS方法 M2 145.23(246.08°) 145.00(246.10°) 140.87(244.05°) S2 60.65(291.02°) 60.08(290.16°) 61.25(290.42°) N2 26.86(227.94°) 27.34(224.05°) 33.89(227.42°) K2 16.65(285.47°) 15.94(286.90°) 17.36(294.00°) K1 29.93(209.30°) 29.34(208.12°) 32.15(205.73°) O1 21.58(169.07°) 21.01(168.11°) 22.88(164.01°) P1 8.69(207.32°) 8.68(203.41°) 10.05(202.56°) Q1 3.79(150.15°) 4.22(143.26°) 5.22(149.45°)
下载: 导出CSV
表 4 石浦站不同调和分析方法的回报结果比较
Tab. 4 The performances of CHA and MHACS methods at Shipu
方法 解释的信号方差 (%) 均方根误差 (m) 最大误差 (m) CHA方法 94.6 0.28 1.01 MHACS方法 94.7 0.29 0.94
下载: 导出CSV
表 5 MHACS方法与EOT20模型得到的18个站位分潮振幅误差比较
Tab. 5 Comparison of the amplitude errors of 18 stations obtained from the MHACS method and the EOT20 model
分潮名称 均方根误差RMSE（m） 最大误差MAE（m） M2 0.27 0.65 S2 0.12 0.25 K1 0.03 0.09 O1 0.02 0.03
下载: 导出CSV
表 6 利用MHACS结果计算的浙江近海理论深度基准面值(cm)
Tab. 6 Theoretical depth datum calculated using MHACS results in the coastal area of Zhejiang
站点名称 金塘 毛礁 万华 定海 双合 衢山 泗礁 嵊山 独山 理基值 −194 −185 −180 −181 −100 −204 −203 −208 −406 站点名称 乍浦 峙南 黄牛礁 西泽 澉浦 镇海 石浦 岱山 下三山 理基值 −428 −212 −256 −265 −499 −183 −283 −173 −181
下载: 导出CSV
表 7 浙江近海各站位潮汐类型及潮型系数
Tab. 7 Tidal types and daily form factor values using MHACS results in the coastal area of Zhejiang
站点名称 金塘 毛礁 万华 定海 双合 衢山 泗礁 嵊山 独山 F 0.56 0.60 0.63 0.59 0.67 0.47 0.42 0.42 0.24 类型 不正规半日潮 不正规半日潮 不正规半日潮 不正规半日潮 不正规半日潮 半日潮 半日潮 半日潮 半日潮 站点名称 乍浦 峙南 黄牛礁 西泽 澉浦 镇海 石浦 岱山 下三山 F 0.23 0.52 0.43 0.42 0.19 0.62 0.39 0.57 0.59 类型 半日潮 半日潮 半日潮 半日潮 半日潮 不正规半日潮 半日潮 不正规半日潮 不正规半日潮
下载: 导出CSV
表 8 浙江近海各站位月潮汐包络因子E值
Tab. 8 The monthly tidal envelope factor E at various stations in the coastal area of Zhejiang
站点名称 金塘 毛礁 万华 定海 双合 衢山 泗礁 嵊山 独山 E 0.91 0.91 0.92 0.91 0.87 0.87 0.84 0.84 0.91 站点名称 乍浦 峙南 黄牛礁 西泽 澉浦 镇海 石浦 岱山 下三山 E 0.91 0.87 0.86 0.86 0.91 0.93 0.86 0.90 0.92
下载: 导出CSV
-
[1] 方国洪, 郑文振, 陈宗镛, 等. 潮汐和潮流的分析和预报[M]. 北京: 海洋出版社, 1986.Fang Guohong, Zheng Wenzhen, Chen Zongyong, et al. Analysis and Prediction of Tides and Tidal Currents[M]. Beijing: China Ocean Press, 1986. (查阅网上资料, 未找到本条文献英文信息, 请确认) [2] 黄祖珂, 黄磊. 潮汐原理与计算[M]. 青岛: 中国海洋大学出版社, 2005.Huang Zuke, Huang Lei. Tidal Theory and Calculation[M]. Qingdao: China Ocean University Press, 2005. [3] Doodson A T. Perturbations of harmonic tidal constants[J]. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1924, 106(739): 513−526. [4] 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.Lv Xianqing, Pan Haidong, Wang Yuzhe. Review and prospect of tidal harmonic analysis method[J]. Marine Sciences, 2021, 45(11): 132−143. [5] Godin G. The Analysis of Tides[M]. Toronto: University of Toronto Press, 1972. [6] 徐晓庆, 方国洪, 王新怡, 等. 渤、黄、东海潮汐的相对导纳及N2, K2, P1 和Q1分潮的经验同潮图[J]. 海洋科学进展, 2011, 29(3): 293−306.Xu Xiaoqing, Fang Guohong, Wang Xinyi, et al. Relative tidal admittances and N2, K2, P1 and Q1 empirical cotidal charts in the Bohai, Yellow and East China Seas[J]. Advances in Marine Science, 2011, 29(3): 293−306. [7] 徐晓武, 陈永平, 甘敏, 等. 基于非稳态调和分析和长短时记忆神经网络的河口潮位短期预报混合模型[J]. 海洋通报, 2022, 41(4): 401−410. doi: 10.11840/j.issn.1001-6392.2022.04.005Xu Xiaowu, Chen Yongping, Gan Min, et al. Hybrid model for short-term prediction of tide level in estuary based on LSTM and nonstationary harmonic analysis[J]. Marine Science Bulletin, 2022, 41(4): 401−410. doi: 10.11840/j.issn.1001-6392.2022.04.005 [8] Pan Haidong, Sun Junchuan, Xu Tengfei, et al. Seasonal variations of tidal currents in the deep Timor Passage[J]. Frontiers in Marine Science, 2023, 10: 1135911. doi: 10.3389/fmars.2023.1135911 [9] Pan Haidong, Xu Tengfei, Wei Zexun. A modified tidal harmonic analysis model for short-term water level observations[J]. Ocean Modelling, 2023, 186: 102251. doi: 10.1016/j.ocemod.2023.102251 [10] Pan Haidong, Xu Tengfei, Wei Zexun. Improved tidal estimates from short water level records via the modified harmonic analysis model[J]. Ocean Modelling, 2024, 189: 102372. doi: 10.1016/j.ocemod.2024.102372 [11] 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 [12] 陈倩, 黄大吉, 章本照, 等. 浙江近海潮汐的特征[J]. 东海海洋, 2003, 21(2): 1−12.Chen Qian, Huang Daji, Zhang Benzhao, et al. The research of the tidal features in the coastal zone of Zhejiang Province[J]. Donghai Marine Science, 2003, 21(2): 1−12. [13] 曹颖, 林炳尧. 杭州湾潮汐特性分析[J]. 浙江水利水电专科学校学报, 2000, 12(3): 14−16.Cao Ying, Lin Bingyao. Tidal characteristics of Hangzhou Bay[J]. Journal of Zhejiang Water Conservancy and Hydropower College, 2000, 12(3): 14−16. [14] Pawlowicz R, Beardsley B, Lentz S. Classical tidal harmonic analysis including error estimates in MATLAB using T_TIDE[J]. Computers & Geosciences, 2002, 28(8): 929−937. [15] Munk W H, Cartwright D E. Tidal spectroscopy and prediction[J]. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1966, 259(1105): 533−581. doi: 10.1098/rsta.1966.0024 [16] 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 [17] Hoerl A E, Kennard R W. Ridge regression: biased estimation for nonorthogonal problems[J]. Technometrics, 1970, 12(1): 55−67. doi: 10.1080/00401706.1970.10488634 [18] Hoerl A E, Kennard R W. Ridge regression: applications to nonorthogonal problems[J]. Technometrics, 1970, 12(1): 69−82. doi: 10.1080/00401706.1970.10488635 [19] Marquardt D W. Generalized inverses, ridge regression, biased linear estimation, and nonlinear estimation[J]. Technometrics, 1970, 12(3): 591−612. doi: 10.1080/00401706.1970.10488699 [20] Hart-Davis M G, Piccioni G, Dettmering D, et al. EOT20: a global ocean tide model from multi-mission satellite altimetry[J]. Earth System Science Data, 2021, 13(8): 3869−3884. doi: 10.5194/essd-13-3869-2021 [21] Byun D S, Hart D E. A monthly tidal envelope classification for semidiurnal regimes in terms of the relative proportions of the S2, N2, and M2 constituents[J]. Ocean Science, 2020, 16(4): 965−977. doi: 10.5194/os-16-965-2020 -
计量
- 文章访问数: 53
- HTML全文浏览量: 25
- PDF下载量: 10
- 被引次数: 0
