Analysis of the tidal characteristics along the tidal reach of Xijiang River considering river discharge variation
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摘要: 本文基于2015−2017年西江感潮河道的潮位数据，应用非平稳潮调和分析模型NS-TIDE，研究了不同周期分潮振幅和迟角的时空变化特征、潮汐动力构成变化和潮波变形特征，并讨论了感潮河道中的潮位变形、极低潮位颠倒等现象的形成原因。结果表明，不同于全日、半日分潮振幅的沿程衰减和迟角的沿程递增，浅水分潮振幅先增后减，MSf分潮振幅呈递增趋势、迟角有显著的增减交替变化；各个分潮的振幅洪季衰减速率大于枯季，迟角在洪季变化较大，表明径流顶托作用下的潮波向上游传播速度较慢。受径流、地形等因素的影响，在洪季和上游河段，MSf分潮振幅更大，潮汐动力由主分潮向次分潮转移，M4和M2分潮振幅比的变化表明潮汐变形显著，MSf与M2、S2分潮的振幅比较大时有最低低水位的颠倒现象。Abstract: Based on the tide level data along the tidal reach of Xijiang River from 2015 to 2017, we applied the nonstationary tidal harmonic analysis model NS-TIDE to study the spatial and temporal variation characteristics of the amplitude and phase of different cycles of tidal constituent, the change of tidal dynamics composition and tidal wave deformation characteristics, and discussed the causes of tidal level deformation and the reversal of the lowest low waters along the tidal reach. The results show that, unlike the diurnal constituent and semi-diurnal constituent along the tidal reach that have amplitude decay and phase increment, the shallow water component amplitude increases and then decreases, the amplitude of MSf is increasing, and the phase is changing alternately; the decay rate of each tidal amplitude is higher in the flood season than in the dry season, and the phase changes more in the flood season, indicating that the tidal wave propagates upstream more slowly under the top support of river discharge. Due to the influence of river discharge and topography, the amplitude of MSf is larger in the flood season and upstream section of the river, and the tidal dynamic composition changes from the main tidal constituent to the secondary tidal constituent; the change of amplitude ratio of M4 and M2 indicates significant tidal deformation, and the reversal of the lowest low waters when the amplitude ratio of MSf to M2 and S2 is relatively large.
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图 2 模型计算断面及网格
a. 一维区域局部图；b. 二维区域局部图
Fig. 2 Model calculation section and grid
a. Partial view of 1D area; b. partial view of 2D area
图 3 西江感潮河道潮位验证
Fig. 3 Verification of tidal level along the tidal reach of Xijiang River
图 6 2015−2017年西江感潮河道不同周期分潮振幅时间序列沿程分布
Fig. 6 Distribution of amplitude time series of tidal constituents with different periods along the tidal reach of Xijiang River from 2015 to 2017
图 8 2015−2017年西江感潮河道不同周期分潮迟角时间序列沿程分布
Fig. 8 Distribution of phase time series of tidal constituents with different periods along the tidal reach of Xijiang River from 2015 to 2017
图 7 西江感潮河道洪季（a）、枯季（b）典型时段分潮振幅沿程变化
Fig. 7 Variation of tidal constituents amplitude along the tidal reach of Xijiang River in typical periods of flood season (a) and dry season (b)
图 9 西江感潮河道洪季（a）、枯季（b）典型时段分潮迟角沿程变化
Fig. 9 Variation of tidal constituents phase along the tidal reach of Xijiang River in typical periods of flood Season (a) and dry season (b)
图 10 西江感潮河道洪季（a）、枯季（b）典型时段分潮振幅占比沿程变化
Fig. 10 Variation of tidal constituents amplitude proportion along the tidal reach of Xijiang River in typical periods of flood season (a) and dry season (b)
图 11 2015−2017年西江感潮河道M4分潮和M2分潮振幅比时间序列沿程分布
Fig. 11 Time series distribution of M4 constituent and M2 tidal constituent amplitudes ratio along the tidal reach of Xijiang River from 2015 to 2017
图 12 潮汐变形系数较大时潮位沿程变化
Fig. 12 The tidal level variation for larger tidal deformation coefficient along the tidal reach
图 13 2015−2017年百顷头站枯季（a）、洪季（b）潮位48 h时间序列
Fig. 13 48-hour time series of tide levels at Baiqingtou Station in dry season (a) and flood season (b) from 2015 to 2017
图 14 2015−2017年西江感潮河道MSf分潮和S2分潮振幅比R1时间序列沿程分布
Fig. 14 Time series distribution of MSf constituent and S2 constituent amplitudes ratio R1 along the tidal reach of Xijiang River from 2015 to 2017
图 15 2015−2017年西江感潮河道MSf分潮和M2分潮振幅比R2时间序列沿程分布
Fig. 15 Time series distribution of MSf constituent and M2 constituent amplitudes ratio R2 along the tidal reach of Xijiang River from 2015 to 2017
图 16 2015−2017年马口站（a）和高明站（b）MSf、M2和S2分潮振幅时间序列
Fig. 16 Time series of MSf, M2, and S2 constituents amplitude from 2015 to 2017 at Makou Station (a) and Gaoming Station (b)
图 17 2015−2017年马口站和高明站最低低水位发生时间分布
Fig. 17 Distribution of the occurrence period of the lowest low water level at Makou and Gaoming stations from 2015 to 2017
图 18 马口站和高明站最低低水位颠倒发生时R1、R2值分布情况
Fig. 18 Distribution of R1 and R2 during the reversal of the lowest low waters at Makou and Gaoming stations
表 1 2015−2017年西江感潮河道沿程各站潮位均方根误差（RMSE）
Tab. 1 Root mean square error (RMSE) of tide level at each station along the tide reach of Xijiang River from 2015 to 2017
测站 实验一：指定分潮+0.1 实验二：不指定分潮+0.1 实验三：不指定分潮+0.15 马口 0.251 3 0.253 9 0.253 8 高明 0.184 9 0.188 7 0.188 0 甘竹 0.150 9 0.155 7 0.153 5 天河 0.140 6 0.148 8 0.146 2 百顷头 0.110 8 0.131 3 0.131 2 竹银 0.059 6 0.111 6 0.109 0 灯笼山 0.053 1 0.106 1 0.103 8 三灶 0.017 6 0.110 3 0.110 1 
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表 2 2015−2017年西江感潮河道沿程各站的P1与K1和K2与S2分潮时变迟角均值对比
Tab. 2 Comparison of mean values of P1 vs. K1 and K2 vs. S2 tidal constituents time-varying tide delay angles at each station along the tide reach of Xijiang River from 2015 to 2017
测站 P1 K1 K2 S2 马口 79.793 6° 87.087 5° 134.144 1° 137.938 1° 天河 77.017 3° 65.229 6° 43.303 4° 44.614 3° 灯笼山 322.557 5° 323.680 1° 348.114 2° 332.217 0° 三灶 300.176 8° 303.870 0° 308.689 3° 299.212 0°
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表 3 2015−2017年西江感潮河道沿程各站P1、K2和MSf分潮的振幅、迟角及其误差
Tab. 3 Amplitude, phase and their error of P1, K2 and MSf tidal constituents at each station along the tide reach of the Xijiang River from 2015 to 2017
测站 分潮 非稳态调和分析（取平均值） 经典调和分析 振幅/m 振幅误差/m 迟角/（°） 迟角误差/（°） 振幅/m 迟角/（°） 马口 P1 0.007 7 0.001 2 79.793 6 14.530 4 K2 0.003 6 0.000 5 134.144 1 10.005 8 MSf 0.040 4 0.016 3 236.484 7 55.229 5 天河 P1 0.056 3 0.003 4 77.017 3 5.247 2 K2 0.021 8 0.001 6 43.303 4 4.641 9 MSf 0.036 5 0.005 6 39.918 2 9.016 2 灯笼山 P1 0.099 4 0.002 2 322.557 5 1.269 9 0.101 2 322.117 7 K2 0.066 5 0.002 0 348.114 2 1.700 1 0.068 7 348.521 0 MSf 0.023 0 0.001 8 42.845 3 4.138 5 0.024 3 45.736 4 三灶 P1 0.110 8 6.044 7×10−4 300.176 8 0.345 3 0.110 5 300.384 9 K2 0.064 0 5.196 5×10−4 308.689 3 0.469 0 0.064 0 308.940 5 MSf 8.097 0×10−4 4.0736×10−4 296.694 6 61.735 1 2.2648×10−4 294.742 6
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表 4 潮汐分潮周期及频率
Tab. 4 Tidal constituent period and frequency
种类 名称 周期 频率/cph 全日分潮 Q1 26.868 4 h 0.037 218 O1 25.819 3 h 0.038 731 P1 24.065 9 h 0.041 552 K1 23.934 5 h 0.041 781 半日分潮 N2 12.658 3 h 0.078 999 M2 12.420 6 h 0.080 511 S2 12.000 0 h 0.083 333 K2 11.967 2 h 0.083 561 四分之一日分潮 MN4 6.269 1 h 0.159 511 M4 6.210 3 h 0.161 023 MS4 6.103 3 h 0.163 844 六分之一日分潮 M6 4.140 2 h 0.241 534 半月分潮 MSf 14.765 3 d 0.002 822
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