渤海湾M<sub>2</sub>分潮的季节变化：增强调和分析的应用

余鹰; 王道胜

doi:10.12284/hyxb2021063

渤海湾M₂分潮的季节变化：增强调和分析的应用

doi: 10.12284/hyxb2021063

余鹰^1,,
王道胜^{1, 2, ,}

1.
中国地质大学（武汉）海洋学院海洋地质资源湖北省重点实验室，湖北武汉 430074
2.
中国地质大学深圳研究院，广东深圳 518057

基金项目: 广东省重点领域研发计划（2020B1111020005）；广东省基础与应用基础研究基金（2020A1515110339）；深圳市基础研究资助项目（JCYJ20200109110220482）

详细信息

作者简介:
余鹰(1995—)，男，湖北省云梦县人，主要从事数据分析、潮汐变化特征研究。E-mail：yuying6d1p@163.com

通讯作者:
王道胜，硕士生导师，副教授，主要从事浅海动力学、数据同化研究。E-mail：dswangouc@163.com

中图分类号: P722.4
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出版历程
- 收稿日期: 2020-03-03
- 修回日期: 2020-05-07
- 网络出版日期: 2021-03-24
- 刊出日期: 2021-07-06

Seasonal variability of the M₂ constituent in the Bohai Bay: Application of enhanced harmonic analysis

Yu Ying^1
,,
Wang Daosheng^{1, 2
, ,}

1.
Hubei Key Laboratory of Marine Geological Resources, College of Marine Science and Technology, China University of Geosciences, Wuhan 430074, China
2.
Shenzhen Research Institute, China University of Geosciences, Shenzhen 518057, China

摘要

摘要: M₂分潮的季节变化对沿海的海洋环境有着重要影响。增强调和分析(EHA)既可以提取主要分潮时变的振幅和迟角，同时可以得到其他分潮不随时间变化的振幅和迟角。本文利用EHA分析渤海湾两个站点的水位数据，研究了渤海湾M₂分潮的季节变化。为了评估EHA方法的准确性，在理想实验中设计了人造“水位数据”。利用EHA分析得到的M₂分潮时变振幅和迟角以及S₂、K₁、O₁分潮不随时间变化的振幅和迟角均比其他方法得到的结果更接近给定值，表明了EHA的有效性和可用性。当使用EHA分析渤海湾实际海平面观测数据时，得到的M₂分潮振幅具有明显的季节变化特征：夏季较大，冬季较小。敏感性实验表明，分析所得渤海湾M₂分潮振幅的季节变化趋势不受实验设置的影响，是鲁棒的，能够反映该海域真实的M₂分潮季节变化。此外，渤海湾M₂分潮振幅的季节变化可能是东亚季风通过影响平均海平面、层化和涡动黏性系数的季节变化而引起的。
- M₂分潮 /
- 季节变化 /
- 增强调和分析 /
- 渤海湾
Abstract: The seasonal variability of M₂ constituent exerts a major influence on the coastal ocean environment. The enhanced harmonic analysis (EHA) can synchronously extract the temporally varying amplitudes and phase lags of significant constituent and the constant values of the other constituents. In this study, the seasonal variability of the M₂ constituent in the Bohai Bay, China, is investigated by analyzing one-year sea level observations at two stations with EHA. In order to evaluate the accuracy of EHA, artificial "sea level" is designed in the ideal experiment. Both the estimated temporally varying amplitude and phase lag of the M₂ constituent and constant values of the S₂, K₁ and O₁ constituents using EHA were much closer to the prescribed values than those obtained using the other methods, indicating the capability and efficacy of EHA. When the real sea level observations were analyzed using EHA, the estimated M₂ constituent amplitude has significant seasonal variability, with large values in summer and small values in winter. The sensitivity experiments show that the trend of seasonal variation of M₂ amplitude in Bohai Bay is not affected by the experimental settings, and it is robust and can reflect the real seasonal variation of M₂ constituent. The seasonal variations in the M₂ amplitude is possibly induced by the seasonally alternating Asia monsoon, as the Asia monsoon dominates the seasonality of mean sea level, stratification and eddy viscosity, which are main influence factors summarized in the previous studies.
- the M₂ constituent /
- seasonal variability /
- enhanced harmonic analysis /
- Bohai Bay

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图 1 渤海湾观测站E1和E2的位置（红星），以及10 m和40 m水深线

Fig. 1 The locations of the observation stations (E1 and E2, red stars) in the Bohai Bay, and the isobathymetric lines at 10 m and 40 m

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图 2 E1（a）和E2（b）站的水位观测数据

洋红色实线描述了观测的时间段

Fig. 2 The observed sea level at E1(a) and E2(b) stations

The magenta solid lines describe the temporal locations of the observations

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图 3 E2站水位数据和人造“水位数据”的功率谱密度

黑色和红色虚线表示相应的95%置信值

Fig. 3 The power spectral densities of the observed sea level at E2 Station and the artificial sea level

The black and red dashed lines designate the corresponding 95% significance level against red noise

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图 4 使用SHA分析E2站水位观测数据所获得M₂分潮时变的振幅(a)和迟角(b)及其拟合值

Fig. 4 The temporally varying amplitude (a) and phase lag (b) of the M₂ constituent obtained by analyzing the observed sea level at E2 Station using SHA and their fitting values

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图 5 理想实验中给定的M₂分潮振幅（a）和迟角（b），以及使用SHA、采用5个独立点的OEHA、采用5个独立点的EHA和CHA得到的结果

Fig. 5 The amplitude (a) and phase lag (b) of the M₂ constituent prescribed in ideal experiments and the estimated values using SHA, OEHA with 5 independent points, EHA with 5 independent points, and CHA

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图 6 理想实验中给定的S₂分潮（a，b）、K₁分潮（c，d）和O₁分潮（e，f）的振幅和迟角，以及使用SHA、采用5个独立点的OEHA、采用5个独立点的EHA和CHA得到的结果

Fig. 6 The amplitude and phase lag of the S₂ (a, b), K₁ (c, d) and O₁ (e, f) constituent prescribed in ideal experiments and the estimated values using SHA, OEHA with 5 independent points, EHA with 5 independent points, and CHA

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图 7 理想敏感实验中给定的M₂分潮振幅（a）和迟角（b），以及使用SHA、采用5个独立点的OEHA、采用5个独立点的EHA和CHA得到的结果

b中的洋红色实线描述了理想敏感实验中人造“水位数据”的时间段

Fig. 7 The amplitude (a) and phase lag (b) of the M₂ constituent prescribed in ideal sensitivity experiments and the estimated values using SHA, OEHA with 5 independent points, EHA with 5 independent points, and CHA

The magenta solid line in b describes the temporal locations of the artificial sea level observations in the ideal sensitivity experiment

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图 8 理想敏感实验中给定的S₂分潮（a, b）、K₁分潮（c, d）和O₁分潮（e, f）的振幅和迟角，以及使用SHA、采用5个独立点的OEHA、采用5个独立点的EHA和CHA得到的结果

每个子图中的洋红色实线描述了理想敏感实验中人造“水位数据”的时间段

Fig. 8 The amplitude and phase lag of the S₂ (a, b), K₁ (c, d) and O₁ (e, f) constituent prescribed in ideal sensitivity experiments and the estimated values using SHA, OEHA with 5 independent points, EHA with 5 independent points, and CHA

The magenta solid lines in each panels describe the temporal locations of the artificial sea level observations in the ideal sensitivity experiment

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图 9 E2站基准实验的实验结果

蓝色实线展示了采用5个独立点的EHA得到的平均海平面高度（a）和M₂分潮振幅（b）的时变值，蓝色虚线为采用5个独立点的EHA得到的平均海平面高度（a）和M₂分潮振幅（b）的平均值，绿色星号表示常数形式的平均海平面高度（a）和M₂分潮振幅（b），蓝色阴影表示相应的95%置信区间

Fig. 9 The results of benchmark experiment at E2 Station

The blue solid line shows the time-varying values of mean sea level (a) and M₂ constituent amplitude (b) obtained by EHA at 5 independent points, the blue dotted line shows the average value of mean sea level (a) and M₂ constituent amplitude (b) obtained by EHA at 5 independent points, and the green stars describe the constant mean sea level (a) and M₂ constituent amplitude (b), the blue shadings indicate the corresponding 95% confidence intervals

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图 10 E1站基准实验的实验结果

Fig. 10 The results of benchmark experiment at E1 Station

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图 11 分潮选择的敏感性实验结果

蓝色实线表示采用5个独立点的EHA在基准实验中的结果。带颜色的阴影表示相应的95%置信区间

Fig. 11 The results on the sensitivity of tidal constituent selection

The blue solid line represents the results of EHA with 5 independent points in the benchmark experiment. The shadings with colors indicate the corresponding 95% confidence intervals

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图 12 数据缺失和独立点数的敏感性实验结果

蓝色实线表示采用5个独立点的EHA在基准实验的结果。带颜色的阴影表示相应的95%置信区间

Fig. 12 The results on the sensitivity of missing data and independent points

The blue solid line indicates the results of EHA with 5 independent points in the benchmark experiment. The shadings with colors indicate the corresponding 95% confidence intervals

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图 13 北太平洋季风指数（WNPMI）与E1站和E2站M₂分潮振幅的相关性

黑点表示每天的WNPMI，黑圈表示WNPMI的月平均值，黑线为使用三次样条插值法对WNPMI的月平均值进行拟合的结果，蓝线为采用5个独立点的EHA得到的M₂分潮振幅，黑色竖线和蓝色阴影表示相应的95%置信区间

Fig. 13 The correlation between WNPMI and M₂ constituent amplitude of E1 and E2 stations

The black dot represents the daily WNPMI, the black circle represents the monthly average value of WNPMI, the black line is the result of fitting the monthly average value of WNPMI using cubic spline interpolation method, and the blue line is the M₂ constituent amplitude obtained by EHA with 5 independent points, the black vertical bars and the blue shadings indicate the corresponding 95% confidence intervals

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表 1 理想实验中的潮汐成分及其常数形式的振幅和迟角

Tab. 1 The prescribed constant amplitudes and phase lags of the constituents in ideal twin experiments

分潮	给定值
分潮	振幅/cm	迟角/(°)
S₂	20.69	273.88
K₁	27.19	75.46
O₁	20.45	14.70
MK₃	0.83	314.20
M₄	1.02	246.79
LF1	6.00	161.73
LF2	4.00	161.73

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表 2 基准实验中CHA和EHA分析所得4个主要分潮的振幅（单位：cm）

Tab. 2 The amplitudes of four main tidal constituents obtained by CHA and EHA in the benchmark experiment (unit: cm)

站点	分潮	CHA	EHA
E1	M₂	103.53	102.96
	K₁	29.04	29.14
	S₂	29.49	29.50
	O₁	22.89	22.90
E2	M₂	76.33	76.46
	K₁	27.19	27.21
	S₂	20.69	20.62
	O₁	20.45	20.44
注：由于M₂分潮的振幅是假定随时间变化的，因此使用EHA时列出其平均值。

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表 3 实际实验中的详细实验设置

Tab. 3 The detailed experimental settings of the practical experiments

实验名	分析的分潮	具有时变特征的分潮	有无缺测
基准实验	M₂, K₁, S₂, O₁	M₂	无
SE11	M₂, K₁, S₂, O₁	M₂, K₁	无
SE12	M₂, K₁, S₂, O₁	M₂, K₁, S₂	无
SE13	M₂, K₁, S₂, O₁	M₂, K₁, S₂, O₁	无
SE21	M₂, K₁, S₂, O₁, N₂, K₂, P₁, Q₁	M₂	无
SE22	M₂, K₁, S₂, O₁, N₂, K₂, P₁, Q₁	M₂, K₁	无
SE23	M₂, K₁, S₂, O₁, N₂, K₂, P₁, Q₁	M₂, K₁, S₂	无
SE24	M₂, K₁, S₂, O₁, N₂, K₂, P₁, Q₁	M₂, K₁, S₂, O₁	无
SE31	M₂, K₁, S₂, O₁	M₂	有（同E1）
SE32−SE35	M₂, K₁, S₂, O₁	M₂	有（大约占1/4）

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