Multi-frequency variability and mechanism of intra-seasonal sea surface height in the Sulawesi Sea
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摘要: 本文利用1993–2022年卫星高度计观测数据，分析苏拉威西海海面高度多频率季节内变化信号的时空特征，利用罗斯贝标准模理论给出动力解释。谱分析显示，苏拉威西海海面高度变化存在很强的30～90 d的季节内信号，其平均功率谱密度为半年内信号平均功率谱密度的13倍。这些季节内信号具有离散、不连续的谱峰周期，其中54.0 d和64.4 d的峰值最大，分别为30～90 d信号平均谱值的28倍和23倍。罗斯贝标准模态理论分析显示，近封闭的苏拉威西深海盆存在离散的罗斯贝标准模态。卫星高度计观测的季节内变化与罗斯贝标准模态结果的二维空间结构演化、周期以及西传速度一致，罗斯贝标准模态解的叠加呈现出与海面高度变化相似的方差分布，这说明苏拉威西海海盆的固有振荡是其季节内变化特征形成的重要机制之一。Abstract: Based on the satellite altimeter observation data from 1993 to 2022, this paper analyzes the temporal and spatial characteristics of the multi frequency seasonal variation signal of sea surface height in the Sulawesi sea, and gives the dynamic interpretation by using Rossby standard mode theory. The spectral analysis shows that there is a strong intra-seasonal signal of 30–90 days in the sea surface height variation of Sulawesi sea, and its average power spectral density is 13 times of the average power spectral density of the signal in half a year. These seasonal signals have discrete and discontinuous spectral peak periods, and the peaks of 54.0 d and 64.4 d are the largest, which are 28 times and 23 times of the signal of 30–90 days, respectively. The theoretical analysis shows that the existence of Rossby standard modes in the nearly closed Sulawesi deep-sea basin. The seasonal variation observed by satellite altimeter is consistent with the two-dimensional spatial structure evolution, period and westward propagation velocity of Rossby standard mode results, the superposition of Rossby standard mode solutions presents a variance distribution similar to the sea surface height variation field. This shows that the inherent oscillation of Sulawesi Sea basin is one of the important mechanisms that contribute to its intra-seasonal variation.
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图 1 研究区域周边海域（a）和苏拉威西海（b）水深地形
b中红色矩形框区域为计算罗斯贝标准模的理论封闭海盆
Fig. 1 Bathymetry of the study area (a) and Sulawesi Sea (b)
The red box in b indicates the theoretical closed basin for calculating the Rossby normal modes
图 2 苏拉威西海深海盆n = 1的前3个正压罗斯贝标准模态（a–c）和前3个斜压罗斯贝标准模态（d–f）的归一化海面高度分布，T为罗斯贝标准模态周期
Fig. 2 Normalized sea surface height distributions of the first 3 barotropic (a–c) and first 3 baroclinic (d–f) Rossby normal modes for the deep basin in the Sulawesi Sea when n = 1, with the Rossby standard mode period denoted as T
图 3 1993年1月1日至2022年12月31日苏拉威西海海面高度异常SLA时间序列功率密度谱
蓝色代表功率谱，红线代表频谱密度的平均值，白线代表各周期处所有格点频谱密度的均值，黑色线代表罗斯贝标准模态$ {\zeta }_{mn} $周期，绿色为0.95的置信下限
Fig. 3 Power spectral density of sea surface height anomaly (SLA) in Sulawesi Sea from 1993−01−01 to 2022−12−31
The blue color represents the power spectrum. The red line represents the average spectral density. The white line represents the mean spectral density at each period for all grid points. The black lines represent the periods of the Rossby normal modes $ {\zeta }_{mn} $. The green line represents the 0.95 confidence lower limit
图 4 苏拉威西海30～90 d带通滤波海面高度异常的方差分布（1993–2022年）
紫红色点线所围区域为方差大于7 cm2的高值区域，A点（海盆西侧3.125°N ，118.375°E）、B点（海盆中央3.125°N，120.875°E）以及C点（海盆东侧3.125°N，124.625°E，3 000 m以深）为小波分析所选的3个典型站位
Fig. 4 Variance distribution of sea surface height anomalies in the 30–90 day bandpass filtered Sulawesi Sea (1993−2022)
The purple-red dotted line encloses the high-variance area where the variance exceeds 7 cm2. Coordinates for point A (3.125°N, 118.375°E) on the western side of the basin, point B (3.125°N, 120.875°E) in the central basin, and point C (3.125°N, 124.625°E, at a depth of 3 000 m) are the three typical locations selected for wavelet analysis
图 5 SLA方差高值区（a）和低值区（b）的功率密度谱
蓝色代表功率谱，绿色为0.95的置信下限
Fig. 5 Power spectral density spectra for the high SLA variance region (a) and the low SLA variance region (b)
The blue color represents the power spectrum. The green line represents the 0.95 confidence lower limit
图 6 海盆西侧（a）、海盆中央（b）和海盆东侧（c）SLA小波分析结果
黑色实线为0.95置信曲线，白色实线为影响锥曲线，白色虚线分别对应图3中最大峰值周期54.0 d和64.4 d，能量结果以10为底取对数
Fig. 6 Wavelet analysis results at the western side of the basin (a), the center of the basin (b), and the eastern side of the basin (c)
The black solid line represents the 0.95 confidence curve. The white solid line represents the cone of influence. The white dashed lines correspond to the peak periods of 54.0 d and 64.4 d in Fig. 3. The energy results are logarithms to the base 10
图 7 2019年12月26日至2020年2月19日，
$ {\zeta }_{11}^{0} $ 对应FSLA变化Fig. 7 FSLA changes corresponding to
$ {\zeta }_{11}^{0} $ from 2019−12−26 to 2020−02−19
图 9 2001年12月22日至2002年2月26日，
$ {\zeta }_{21}^{0} $ 对应FSLA变化Fig. 9 FSLA changes corresponding to
$ {\zeta }_{21}^{0} $ from 2001−12−22 to 2002−02−26
图 8 2000年11月24日至2001年1月18日，
$ {\zeta }_{11}^{1} $ 对应FSLA变化Fig. 8 FSLA changes corresponding to
$ {\zeta }_{11}^{1} $ from 2000−11−24 to 2001−01−18
图 10 3.375°N纬线上的FLSA变化Hovmöller图
白色矩形区域为$ {\zeta }_{11}^{0} $、$ {\zeta }_{11}^{1} $和$ {\zeta }_{21}^{0} $模态FSLA相位交替变化显著时间段：a. 2019年12月10日至2020年2月18日，b. 2000年12月1日至2001年2月11日，c. 2001年12月31日至2002年3月31日，用以计算相位传播速度
Fig. 10 Hovmöller diagrams of FLSA changes along 3.375°N
The white rectangular areas represent significant periods of alternating phase changes in the $ {\zeta }_{11}^{0} $, $ {\zeta }_{11}^{1} $, and $ {\zeta }_{21}^{0} $ modes. These periods are: a. 2019-12-10 to 2020-02-18; b. 2000-12-01 to 2001-02-11; c. 2001-12-31 to 2002-03-31. They are used to calculate phase propagation velocity
图 11 模态海面高度变化方差分布
Fig. 11 Variance distribution maps of modal sea surface height changes
表 1 对应图 2中6个模态的波参数
Tab. 1 Wave parameters corresponding to the 6 modes shown in Fig. 2
模态 行波纬向波长$ {\lambda }_{mn}/ $km 周期$ {T}_{mn}/ $d 西传速度$ {C}_{mn} $/ （cm∙s−1） $ {\zeta }_{11}^{0} $ 823.18 48.8 –19.53 $ {\zeta }_{21}^{0} $ 625.51 64.2 –11.28 $ {\zeta }_{31}^{0} $ 479.13 83.8 –6.62 $ {\zeta }_{11}^{1} $ 752.65 53.3 –16.33 $ {\zeta }_{21}^{1} $ 592.83 67.7 –10.13 $ {\zeta }_{31}^{1} $ 463.96 86.5 –6.21 
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