Polarity Variations of Internal Solitary Waves over the ... - AMS Journals

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Polarity Variations of Internal Solitary Waves over the Continental Shelf of the Northern South China Sea: Impacts of Seasonal Stratification, Mesoscale Eddies, and Internal Tides XIAOJIANG ZHANG, XIAODONG HUANG, ZHIWEI ZHANG, CHUN ZHOU, JIWEI TIAN, AND WEI ZHAO Physical Oceanography Laboratory, Qingdao Collaborative Innovation Center of Marine Science and Technology, Ocean University of China, Qingdao, China (Manuscript received 5 April 2017, in final form 22 March 2018) ABSTRACT Spatiotemporal variations in internal solitary wave (ISW) polarity over the continental shelf of the northern South China Sea (SCS) were examined based on mooring-array observations from October 2013 to June 2014. Depression ISWs were observed at the easternmost mooring, where the water depth is 323 m. Then, they evolved into elevation ISWs at the westernmost mooring, with a depth of 149 m. At the central mooring, with a depth of 250 m, the ISWs generally appeared as depression waves in autumn and spring but were elevation waves in winter. Seasonal variations in stratification caused this seasonality in polarity. On the intraseasonal time scales, anticyclonic eddies can modulate ISW polarity at the central mooring by deepening the thermocline depth for periods of approximately 8 days. During some days in autumn and spring, depression ISWs and ISWs in the process of changing polarity from depression to elevation appeared at time intervals of 10–12 h because of the thermocline deepening caused by internal tides. Isotherm anomalies associated with eddies and internal tides have a more significant contribution to determining the polarity of ISWs than do the background currents. The observational results reported here highlight the impact of multiscale processes on the evolution of ISWs.

1. Introduction Internal solitary waves (ISWs) in the northern South China Sea (SCS) have the largest amplitude ever observed in the world’s oceans (Alford et al. 2015; Huang et al. 2016). They are remotely generated in the Luzon Strait (LS) through energetic surface tide–topography interactions (Zhao et al. 2004; Lien et al. 2012; Li and Farmer 2011; Alford et al. 2015). According to the Korteweg–de Vries (KdV) theory, ISWs may be either depression or elevation waves in waters of variable depth, depending on the sign of the nonlinear coefficient (Benjamin 1966; Helfrich and Melville 1986; Liu et al. 1998; Grimshaw et al. 2004). In the past decade, depression ISWs in the northern SCS have been a focus of attention (Ramp et al. 2004, 2010; Klymak et al. 2006; Alford et al. 2010, 2015; Huang et al. 2014; Dong et al. 2015). Observational studies have shown that the amplitude and current velocity of depression ISWs in the northern SCS can reach 150 m and 2 m s21, respectively (Ramp et al. 2004, 2010; Yang et al. 2004; Klymak et al. 2006; Denotes content that is immediately available upon publication as open access. Corresponding author: Wei Zhao, [email protected]

Alford et al. 2010; Zhao et al. 2012; Huang et al. 2014). Depression ISWs in the northern SCS have been demonstrated to play important roles in modulating the marine ecosystem (Wang et al. 2007; Dong et al. 2015), transporting energy and mass (Klymak et al. 2006; Huang et al. 2017), and triggering diapycnal mixing (St. Laurent et al. 2011). In addition, depression ISWs are considered to be a major hazard to submarine navigation and marine engineering (Cai et al. 2012). In the shallow water regions of the northern SCS, changes in water depth may cause polarity conversion, leading to elevation ISWs (Liu et al. 1998). Compared to depression ISWs, elevation ISWs have received much less attention during the past decade. However, elevation ISWs generally produce greater forces on man-made structures in the lower water column (Xu et al. 2012), break more easily, and thus enhance turbulent mixing (Klymak and Moum 2003; Bourgault et al. 2007). In a pioneering study of ISWs in the northern SCS, Zhao et al. (2003) reported that one satellite image showed both depression and elevation ISWs. They further suggested that the depression and elevation ISWs were separated by the 160-m isobaths. Based on shipboard tow-yo conductivity–temperature–depth (CTD) measurements, Long Ranger acoustic Doppler current profiler (ADCP) data, and high-frequency acoustic

DOI: 10.1175/JPO-D-17-0069.1 Ó 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

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flow visualization, Orr and Mignerey (2003) reported that the kinetic energy of ISWs significantly decreased from ;91.2 to ;32.3 MJ m21, after undergoing polarity conversion between the 150- and 180-m isobaths. Based on one-month-long moored observations, Duda et al. (2004) reported that a rearward energy flux can result in the broadening of the leading depression wave and the formation of trailing elevation waves during the polarity conversion process between the 200- and 110-m isobaths. Using 3-day moored observations, Fu et al. (2012) reported that polarity conversion processes occurred in water depths of 200 m and deeper, where large-amplitude elevation ISWs could exist. These shortterm observations have generally indicated that the water depth at which the polarity conversion occurs is variable. Although previous studies have demonstrated that the slope–shelf topography is the main reason for polarity conversion, the spatiotemporal variability in ISW polarity in the SCS is still poorly understood because of the lack of long-term observations. To the best of our knowledge, there are still no reports on the long-term variation in ISW polarity over the continental shelf regions. Investigating the spatiotemporal variability in ISW polarity can help us understand the shoaling process of ISWs over the continental shelf. From October 2013 to June 2014, a mooring array consisting of four moorings was deployed over the continental shelf of the northern SCS to monitor the evolution processes of ISWs. In this paper, we present the observed spatiotemporal variations in ISW polarity and investigate the possible factors affecting the polarity conversion of ISWs. The paper is organized as follows. In section 2, we introduce the data and methods. In section 3, we present the observed spatiotemporal variations in ISW polarity. We discuss the possible factors that affect ISW polarity in section 4 and summarize the study in section 5.

2. Data and methods a. In situ mooring data To investigate the shoaling processes of ISWs and their spatiotemporal characteristics, an array of four moorings was deployed over the continental shelf of the northern SCS (Fig. 1). The moorings were approximately along the main orientation of shoaling ISWs in synthetic-aperture radar (SAR) images (Zhao et al. 2004). Mooring IW6 was deployed at a water depth of 323 m from 14 April 2013 to 4 June 2014. This mooring was equipped with seven temperature loggers and three CTDs to record the stratification in the upper 260 m. Moorings IW7 and IW8 were located at water depths of 250 and 149 m, respectively. They were both equipped with an upward-looking 150-kHz ADCP (at 210 and 90 m beneath the sea surface, respectively) to measure

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current velocities with vertical bin of 8 m. The measurements of IW7 lasted for nearly eight months, from 19 October 2013 to 4 June 2014, while those of IW8 stopped only after one month of its deployment. The mooring IW9 (at a water depth of 95 m) was unfortunately damaged. To observe high-frequency ISWs, all the instruments (including ADCPs, temperature loggers, and CTDs) were set to have a 2-min sampling interval. Detailed mooring locations and configurations are shown in Table 1. Following previous studies, we used the following criteria to identify the occurrence of ISWs: the maximum horizontal velocity had to exceed 0.2 m s21 and the maximum displacement of the 208C isotherm had to exceed 20 m (Huang et al. 2014, 2017). At IW7 and IW8, where temperature measurements were absent, the vertical displacement was obtained based on ADCP-observed vertical velocity w using the following equation (Desaubies and Gregg 1981; Alford et al. 2010): j(tn11 ) 5 w[j(tn ), tn ]Dt 1 j(tn ) ,

(1)

where tn is the nth time. The initial time t0 is defined as 30 min before the ISW. The Dt is the sampling interval. The initial depths j(t0) at IW7 and IW8 were chosen as 120 and 60 m, respectively. The error in w due to the instrument’s vertical motion was corrected by subtracting the time derivative of the pressure field. Soliton-like waves with downward isotherm displacement and westward current velocities in the upper layer were regarded as depression waves, while soliton-like waves with opposite characteristics were regarded as elevation waves (Klymak and Moum 2003; Fu et al. 2012). Dramatic changes in waveform were characterized by irregular fluctuations in the isotherm with a broadening waveform (Fig. 2e); the polarity conversion occurred during this time (Liu et al. 1998; Zhao et al. 2003; Bourgault et al. 2007; Li et al. 2015).

b. AVISO SSH data and HYCOM assimilation product In addition to ISWs, the northern SCS also has abundant energetic mesoscale eddies (Zhang et al. 2013, 2016, 2017). Recent observations have revealed that mesoscale eddies can significantly modulate the amplitude, propagation direction, and speed of transbasin ISWs (Huang et al. 2017). To identify mesoscale eddies, the simultaneous altimeter sea surface height (SSH) data from the Archiving, Validation, and Interpretation of Satellite Oceanographic Data (AVISO) dataset are used in this study. We also use the global Hybrid Coordinate Ocean Model (HYCOM) assimilation product (http://hycom.org/) to investigate the potential impact of mesoscale eddies on ISW polarity in the northern SCS. The HYCOM product

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FIG. 1. (a) Bathymetry in the northern SCS. The locations of moorings IW6–IW8 are indicated by the red stars from east to west, respectively. (b) Topography along the line from mooring IW6 to mooring IW8.

provides daily SSH, temperature T, salinity S, and velocity fields with a fine horizontal resolution (1/128 by 1/128), which can resolve mesoscale eddies. Our previous observational study demonstrated that the HYCOM

product can well reproduce the temperature and velocity variations associated with the eddies in the northern SCS (Zhang et al. 2013), therefore providing a validation of this model product.

TABLE 1. Information of moorings and detailed settings of instruments used to monitor ISWs.

Mooring

Lon, lat

Water depth (m)

Instrument

Instrument depth (m)

IW6

117.058E, 21.468N

323

Thermistor chain

20–260

IW7

116.708E, 21.658N

250

ADCP

210

IW8

116.518E, 21.698N

149

ADCP

90

Working time 14 Apr 2013– 4 Jun 2014 19 Oct 2013– 4 Jun 2014 18 Oct 2013– 12 Nov 2013

Record length (days)

Sample interval (min)

417

2

229

2

26

2

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FIG. 2. Two shoaling events of depression ISWs. (a)–(c) The ISW event on 22 Oct; (d)–(f) the ISW event on 8 Nov. The transmeridional current velocity anomalies associated with the ISW passing by (a),(d) IW8 and (b),(e) IW7. The black solid curves in (c) and (f) denote the 208C isotherm. The black solid curves in (a), (b), (d), and (e) denote the waveform estimated from vertical velocity w. The station locations are marked in (g).

c. Theoretical model To investigate the polarity conversion process, the extended Korteweg–de Vries (eKdV) equation (Holloway et al. 1997; Michallet and Barthélemy 1998; Helfrich and Melville 2006; Grimshaw 2001, 2015; Grimshaw et al. 2004) is used: ›h ›h ›h ›h ›3 h 1 c 1 ah 1 kh2 1 b 3 5 0, ›t ›x ›x ›x ›x

(2)

where h(x, t) is the vertical interface displacement; c is the linear long wave speed; and a, k, and b are the coefficients of quadratic nonlinear, cubic nonlinear, and

dispersion, respectively, which are computed using a continuous stratification (Grimshaw 2001, 2015; Grimshaw et al. 2004), ð0 3 a 5 ð2h 2 0 2h

ð0

1 b 5 ð2h 2 0 2h

(c 2 U)2 F3z dz , (c 2 U)F2z

(3)

dz

(c 2 U)2 F2 dz , (c 2 U)F2z dz

and

(4)

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FIG. 3. The case of ISWs in (a) depression form, (b) elevation form, and (c) in process of changing its polarity at IW7. The color bar is the same as that shown in Fig. 2b. (d) Temporal variation of the maximum westward velocity associated with elevation ISWs passing by IW8 during its observation period. (e) Temporal variation of the maximum westward velocity associated with ISWs passing by IW7 during its observation period. The black bars indicate that elevation ISWs played the leading role at IW7 in winter. The green bars indicate that depression ISWs were dominant at IW7 in autumn and spring. The red bars are the occurrences at IW7 when depression ISWs were followed by a wave in the process of changing its polarity 10–12 h later. (f) Amplitude of depression ISWs measured at IW8 during its observation period.

ð0 k5

2h

[3(c 2 U)2 (3Tz 2 2F2z )F2z 2 a2 F2z 1 a(c 2 U)(5F2z 2 4Tz )Fz ] dz . ð0 (c 2 U)F2z dz

(5)

-h

The linear long-wave speed c and vertical structure of vertical-displacement amplitude of wave mode F(z) are determined by the solution to the eigenvalue problem

[(c 2 U)2 Fz ]z 1 N 2 F 5 0,

(6)

where U(z) is the background shear current and N(z) is the buoyancy frequency. The T(z) is the nonlinear

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correction to the modal structure and is obtained by solving the inhomogeneous eigenvalue problem d d [(c 2 U)2 Tz ] 1 N 2 T 5 2a [(c 2 U)Fz ] dz dz 1

3 d [(c 2 U)2 F2z ]. 2 dz

(7)

3. Observational results a. Shoaling process of depression ISWs Using the measurements from IW6 to IW8, the shoaling process of ISWs over the continental shelf was examined. At IW7 and IW8, the velocity anomalies associated with ISWs were obtained after removing the background current (time-averaged current profile over the 30-min periods before and after the ISWs). Figures 2a–c present the evolution of a typical shoaling ISW from 22 to 24 October 2013. At IW6, a strong depression ISW arrived around 0430 local time (LT) of 22 October, which displaced the 208C isotherm from approximately 100 m before the wave’s arrival downward to below 200 m at the wave trough, indicating a depression ISW with an amplitude of approximately 100 m

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(Fig. 2c). As the ISW passed by IW7 at approximately 1130 LT, strong westward velocities existed in the upper layer above 140 m with a maximum of 0.8 m s21 (Fig. 2b). In the lower layer, strong eastward velocities were observed. The isotherm displacement estimated from w using Eq. (2) reveals that it was a depression ISW (black curve in Fig. 2b). At IW8, the ISW induced strong eastward current velocities above 65 m (Fig. 2a), in the opposite direction to those at IW7. In the lower layer, strong westward current velocities existed. The black curve in Fig. 2a shows that the isotherm at IW8 was displaced upward during the passage of the ISW, indicating an elevation wave. Figures 2d–f show the shoaling process of another ISW on 8–9 November 2013. Similar to the ISW event on 22–23 October 2013, this ISW appeared as a depression wave at IW6 and it evolved into elevation waves at IW8. At the central mooring IW7, the polarity conversion process was captured. During the polarity conversion process, the front face of the first wave became less steep and its rear face became steeper, and elevation ISW was born following the broadening leading wave. At IW8, the leading depression wave disappeared, but the following elevation waves became stronger, possibly because of the rearward energy flux from the leading depression wave to the

FIG. 4. The evolution of ISW polarity between 14 and 21 Dec. The red curve denotes the waveform estimated from the vertical velocity w.

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trailing elevation waves during the polarity conversion process (Duda et al. 2004).

b. Variations in ISW polarity To examine the spatiotemporal variability in ISW polarity over the continental shelf, we identified all the ISWs at the three moorings using the criteria introduced in section 2a. The results show that all the observed ISWs at IW6 were in depression form (Fig. 3f), and all the observed ISWs at IW8 were elevation waves (Fig. 3d). At the central mooring IW7, the polarity of ISWs exhibited remarkable temporal variations. As shown in Figs. 3a–c, mooring IW7 captured three types of ISWs, including elevation ISWs, depression ISWs, and polarity-converting ISWs. Figure 3e presents the maximum westward velocity associated with the ISWs at IW7. From 19 October to 18 December, 72 ISWs were observed at IW7, and 70 of them were depression waves, except for two polarityconverting ISWs in early November. From 19 December 2013 to 1 March 2014, a total of 46 ISWs were observed at IW7, and most of these ISWs were elevation waves. These results suggest that the polarity conversion process during this period occurred at water depths greater than 250 m, which is much deeper than the previously

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reported polarity conversion positions of ISWs (Orr and Mignerey 2003; Zhao et al. 2003). From 2 March to 4 June 2014, a total of 112 ISWs were captured at IW7. In contrast to the winter period, 100 ISWs during this period were depression waves, except for the two polarity-converting ISWs that occurred on 30 April and 1 May. Figure 4 presents an 8-day snapshot of velocity measurements at IW7 in December. Depression waves were observed before 18 December, while elevation ISWs were observed after 21 December. On 19–20 December, the observed waves were in the process of changing polarity from depression to elevation. The evolution of ISW polarity during the polarity-transition period (from depression to elevation) was quite different from previous fixed-point observations in which only one type of internal wave (depression or elevation) was captured (Klymak and Moum 2003; Fu et al. 2012). Figures 3e,f suggest that the oceanic conditions in winter were more favorable for the formation of elevation ISWs in the northern SCS. In autumn and spring, depression ISWs were dominant at IW7, but several polarity-converting ISWs were captured on a few days. At those times, both depression waves and polarityconverting waves were observed. Figure 5a shows the

FIG. 5. Correlation between the occurrence of ISWs and internal tides. (a) East–west current velocity of ISWs. Black curve denotes the wave form estimated from the vertical velocity w. (b) East–west component velocity of the internal tide. (c) The arrival-filtered 208C isotherm anomalies caused by internal tides. The dashed vertical lines indicate the times when depression ISWs were followed by a wave in the process of changing its polarity 10–12 h later on 7 Nov 2013.

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FIG. 6. (a)–(c) Climatological seasonal mean temperature, density and buoyancy frequency profiles, respectively, at IW7 in the northern SCS. (d) The eigenfunction of vertical displacement of the mode-1 internal wave at IW7. The data are from WOA13. The black and red dashed curves denote the base of the winter/summer thermoclines.

zonal velocity on 7 November at IW7. Between 0130 and 0230 LT, a multiwave ISW packet with depression waves arrived at IW7, causing a strong westward current in the upper layer with a maximum of more than 0.8 m s21. Between 1130 and 1250 LT, another ISW was captured, which was characterized by a leading depression wave with a broadening waveform and a train of trailing elevation waves. This result indicates that the ISW was in the process of changing polarity from depression to an elevation wave. Occurrences such as the one shown in Fig. 5a (depression ISWs followed by polarity-converting waves 10–12 h later) were also observed in early November 2013 and late April 2014.

4. Possible mechanisms for polarity variations a. Effect of seasonal variations in the stratification Ocean stratification has a determinant role on internal wave properties. Figure 6 presents the temperature, density, and buoyancy frequency profiles and the eigenfunction of vertical displacement of mode-1 linear internal waves at IW7, calculated using the seasonal World Ocean Atlas 2013 (WOA13) dataset (Boyer and Levitus 1998). In summer, the maximum buoyancy frequency at IW7 is located at approximately 75 m and it can reach 0.021 rad s21, while in winter it deepens to approximately 100 m and decreases to 0.012 rad s21. The maximum calculated mode-1 vertical displacement is

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FIG. 7. The monthly coefficient of the eKdV equation based on the WOA13 data (black) and the moored T/S data at IW7 (red). The (a) linear wave speed c, (b) quadratic nonlinear coefficient a, (c) cubic nonlinear coefficient k, and (d) dispersion coefficient b.

located at 110, 100, 117, and 127 m in spring, summer, autumn, and winter, respectively. Thus, the maximum vertical displacement in winter is below the midwater depth at IW7. The quadratic nonlinear coefficient a, which principally determines the ISW polarity, was also calculated based on both the seasonal stratification from the WOA13 dataset and the moored T/S data (Fig. 7b). Because there were no T/S data at IW7, the upper-250-m T/S data from IW6 were used here. In spring, summer, and autumn, the a values calculated using the WOA13 dataset and moored data are all negative, but they becomes positive in winter. The positive monthly a values in January and February (Fig. 7b) are consistent with the occurrence of elevation ISWs at IW7 in these two months. The above results suggest that the predominant elevation ISWs in winter are closely associated with seasonal variations in stratification.

b. Impact of an anticyclonic eddy Figure 4 shows that the ISWs at IW7 changed polarity from depression to elevation over an 8-day period between 14 and 21 December. The AVISO SSH maps in the northern SCS show that moorings IW6 and IW7 were influenced by the northwest portion of an anticyclonic eddy with high SSH between 14 and 24 December

(Fig. 8). This anticyclonic eddy originated from the region southwest of Taiwan, and its three-dimensional structure, generation, and dissipation were reported in detail in our earlier papers (Zhang et al. 2016, 2017). Because of the propagation of the anticyclonic eddy, the observed thermocline depth, measured as the 208C isotherm depth, following Liu et al. (2001), varied significantly during this period (Fig. 9a). When the anticyclonic eddy approached IW6, the 1-day low-pass-filtered thermocline depth (black curve in Fig. 9a) at IW6 deepened from 120 m on 14 November to 145 m on 21 December. The thermocline then returned to its normal depth after propagated away from the mooring. The HYCOM thermocline depth (blue curve in Fig. 9a) showed variations similar to those observed at IW6, demonstrating that the HYCOM assimilation product can reproduce the thermocline variation associated with the anticyclonic eddy sufficiently well. Similar to that at IW6, the HYCOM thermocline depth at IW7 (red curve in Fig. 9a) also showed large variations associated with the anticyclonic eddy, which deepened from 110 m on 14 November to 139 m on 21 December and then gradually returned to its normal depth after 24 December. The thermocline depth variation associated with the anticyclonic eddy is

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FIG. 8. AVISO SSH in the northern SCS in December 2013. The solid (dashed) black line is the 1.2-m (1.1 m) SSH contour. Black circles with red filling denote the mooring locations. Date is marked in each panel.

consistent with the period of polarity conversion from depression to elevation waves (Fig. 4). To further investigate how the anticyclonic eddy influenced the ISW polarity conversion at IW7, we calculated the daily quadratic nonlinear coefficient a using the HYCOM stratification and the upper-250-m T/S data at IW6 with (without) the ADCP-observed background current (daily averaged velocity profile) at IW7 (Fig. 9b). Because of the rapid thermocline deepening associated with the anticyclonic eddy, the quadratic nonlinear coefficients at IW7 calculated from the HYCOM output and moored data both changed sign from negative to positive on approximately 19 December, which led to the change in ISW polarity. The calculated quadratic nonlinear coefficients a with and without the background current (solid and dashed black curve in Fig. 9b) are very similar, suggesting that the eddy-induced thermocline variations played a dominant role in the variations of the quadratic nonlinear coefficient, while the

role of the eddy-induced current anomalies was secondary. The above results indicate that mesoscale eddies can affect the ISW polarity conversion process by changing the stratification.

c. Impact of internal tides To investigate the role of internal tides in modulating ISW polarity, we analyzed the current velocities and thermocline fluctuations associated with internal tides (with periods between 11.3 and 27.0 h) at IW7 on 7 November, when both depression waves and polarityconverting waves were observed within one day (Fig. 5a). As shown in Fig. 5b, the internal tide had weak zonal velocities when the depression ISW reached IW7. When the polarity-converting ISWs arrived, the internal tide had strong westward and eastward velocities above and below 150 m, respectively, indicating a mode-1 internal tide. Figure 10 shows the background shear current during the period when the

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FIG. 9. Effects of mesoscale eddy on ISW polarity. (a) The depth of the 208C isotherm at IW6 and IW7. The blue and black curves are the calculated isotherm using the HYCOM output and the moored T/S data, respectively, indicating the thermocline depth at IW6. The red curve denotes the HYCOM result at IW7. (b) The quadratic nonlinear coefficient a at IW7 calculated using the HYCOM stratification and the upper-250-m T/S data at IW6 with (without) the ADCP-observed background current (daily averaged velocity profile) at IW7. The black (dashed) curve is the daily quadratic nonlinear coefficient a calculated with (without) the background current. The red curve denotes the coefficient calculated using the HYCOM output.

two ISWs arrived. The background shear current was dominated by the internal tide, which had stronger vertical shear during the periods when conversion waves were present than during periods when depression waves were present (Figs. 10a,b). Note that the locations of IW6 and IW7, which were separated by 41.9 km, were roughly located along the propagation path of the internal waves in the SAR images (Zhao et al. 2004). It is therefore reasonable to assume that the internal tide-induced thermocline fluctuation at IW7 was similar to that at IW6. Here, the thermocline depth fluctuation of the internal tides is defined by the bandpass-filtered [0.9–1.1 cpd for diurnal and 1.83–2.03 cpd for semidiurnal motions (Xu et al. 2014)] 208C isotherm. The time lag of the internal tides between IW6 and IW7 is estimated through DT 5 L/cp ,

(8)

where L is the distance between the two moorings and cp is the phase speed of internal tide. With the rotational

effects taken into account, the phase speeds of semidiurnal and diurnal internal tides around 218N in the SCS are (Alford et al. 2010) M

cp 2 5 1:07c K cp 1

5 1:5c,

and

(9) (10)

respectively. In the observation region, c is computed by solving the Sturm–Liouville equation using climatological stratification and high-resolution bathymetry following Alford et al. (2010) (Fig. 11a). Then, the thermocline fluctuation associated with internal tides at IW7 can be obtained by adding the arriving semidiurnal and diurnal internal-tide components (Fig. 11b). To investigate the role of the tide-induced thermocline fluctuation in modulating the polarity of ISWs, the hourly temperature profiles at IW7 on 7 November were reconstructed. The full-depth isotherm displacements h(z, t) are computed as in Desaubies and Gregg (1981):

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FIG. 10. (a) The background shear current during the period when depression ISWs were followed by a wave in the process of changing its polarity 10–12 h later on 7 Nov 2013. (b) Internal tide component (with periods of between 11.3 and 27 h) of the background shear current. (c) Steady component (periods greater than 27 h) of the background shear current. Both (b) and (c) are averaged over corresponding ISW periods. The blue curve is the background shear current during the period of the depression waves, and the red is during the period of polarity conversion.

h(z, t) 5 h(z0 , t)F(z)/F(z0 ) ,

(11)

where F(z) is the mode-1 baroclinic mode for vertical displacement as introduced in Eq. (6) and z0 is the mean 208C isotherm at IW7. The temperature anomalies associated with internal tides are calculated through DT(z, t) 5 h(z, t)Tz(z), where Tz(z) is the vertical temperature gradient at IW7 derived from the monthly WOA13 data. Then, the temperature field T(z, t) is obtained by adding DT(z, t) to the initial temperature profile T(z, t0) extracted from the monthly WOA13 data. As shown in Fig. 12b, fluctuations in the reconstructed temperature profiles at IW7 corresponded to the

internal tides on 7 November 2013. Based on the background current profiles (Fig. 10a) and reconstructed stratification profiles, the time series of the nonlinear coefficient on 7 November 2013 were calculated. The quadratic nonlinear coefficient a, calculated with the background current taken into account, showed only slight differences from the coefficient calculated without the background current (see the black vs red curves in Fig. 12c), indicating that the tide-induced isotherm anomalies, rather than the background current, were the main factor modifying the quadratic nonlinear coefficient. Between 0130 and 0230 LT, the displacement of the internal tide was at the equilibrium depth

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FIG. 11. (a) The phase speed (m s21) in the observation region. The red stars denote the positions of IW6 and IW7 from east to west, respectively. (b) Internal tide amplitude at IW7. The black circle is the corresponding displacement of the internal tides at the wave trough. The black boxes indicate the occurrences when depression ISWs were followed by a wave in the process of changing its polarity 10–12 h later.

(Fig. 5c), and the quadratic nonlinear coefficient ranged from 21.5 3 1023 and 22.1 3 1023 s21; hence, the arriving ISWs behaved as depression waves. Between 1130 and 1250 LT, the displacement of the internal tide at the isotherm depression was large to 8 m (Fig. 5c), making the upper layer thicker than the lower layer. During this period, the quadratic nonlinear coefficient with (without) the background current changed sign and reached a positive value of 3.2 3 1024 s21 (3.1 3 1024 s21); therefore, the arriving wave was forced to convert its polarity. The average of the quadratic nonlinear coefficient with (without) the background current on 7 November was 21.81 3 1023 s21 (21.82 3 1023 s21), which is consistent with the monthly value in November shown in Fig. 7b. The above results demonstrate that internal tides can affect ISW polarity by modulating the thermocline depth.

d. Numerical simulation Using the eKdV equation, we simulated the polarity variations of ISWs associated with internal tides with the initial conditions involving an elevation solitary wave. The coefficients in the eKdV equation used in the simulation are time-dependent variable as shown in Figs. 13a–d. The numerical scheme is a finite-difference

scheme second order in space and leapfrog in time (Li et al. 2015). As shown in Fig. 13e, the elevation wave was changing its polarity from 0000 to 0100 LT as the positive quadratic coefficient a changed from positive to negative. It became asymmetric at 0200 LT after the first polarity changed, followed by a series of elevation waves. Then, it maintained its asymmetric depression form until another polarity change occurred, owing to the reversed sign of the quadratic coefficient a at 1100 LT. The polarity change process lasts approximately 1 h. The new elevation waves at 1300 LT were more asymmetric than the initial waves. It again reversed the polarity at approximately 1400 LT and then behaved as a depression waves after 1500 LT. The simulation of the entire polarity change is consistent with the observed ISWs of different polarities (recall Fig. 5a), which also supports the conclusions mentioned above that mesoscale eddies, and internal tides can significantly affect ISW polarity by modulating the thermocline depth.

5. Discussion and summary In this study, 8-month-long observations from a mooring array over the continental shelf of the northern

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FIG. 12. Time series of the (a) east–west ISW current velocity, (b) reconstructed temperature, (c) quadratic nonlinear coefficient, and (d) cubic nonlinear coefficient. The black curve in (a) denotes the waveform estimated from the vertical velocity w. The solid black curve in (b) denotes the arrival of filtered 208C isotherm anomalies, and the dashed black line denotes its average depth. The black (red) curve in (c) and (d) denote the quadratic nonlinear coefficient calculated with (without) the background current. The dashed vertical lines indicate the times when depression ISWs were followed by a wave in the process of changing its polarity 10–12 h later on 7 Nov 2013.

SCS were used to investigate the shoaling processes of ISWs. The main cause of polarity change in the northern SCS was shoaling onto the shelf where the quadratic nonlinear coefficient was positive (Liu et al. 1998; Orr and Mignerey 2003; Zhao et al. 2003, 2004). However, we found that the polarity conversion process of ISWs over the continental shelf had strong temporal variations due to thermocline fluctuations over multiple time scales. On seasonal time scales, the winter stratification, characterized by a deep thermocline, was favorable for the formation of elevation ISWs. On intraseasonal time scales, an anticyclonic eddy between 14 and 21 December strongly modulated ISW polarity by deepening the thermocline (see Fig. 9). Statistical analysis shows that, in the northern SCS, there existed a strong anticyclonic eddy in winter almost every year (Zhang et al. 2017). As a result, we anticipate that at least an eddy can affect the polarity conversion process of ISWs in the shallow water every year. On daily time scales, internal tides could also move the thermocline to below the midwater depth,

such as on 7 November 2013 (Fig. 12b). This movement led to a sign change in the quadratic nonlinear coefficient from negative to positive (Fig. 12c), and therefore the incident depression ISW evolved into elevation waves (Fig. 5a). During the spring tidal period, the tideinduced isotherm anomalies made a more significant contribution to changing the ISW polarity than did the background current (Fig. 12c). Because the coefficient of the quadratic nonlinear term of the eKdV equation is determined principally by the background fields, it is difficult to accurately determine the distribution of the critical position at which ISWs change polarity over the continental shelf of the SCS (Orr and Mignerey 2003; Zhao et al. 2003; Fu et al. 2012). Based on our observational results, as well as seasonal temperature and salinity from the WOA13 dataset, the critical position over the continental shelf was estimated; we also considered the factors that could influence the polarity process of ISWs. As shown in Fig. 14, the calculated critical position closely follows the isobaths, but the seasonal variations in

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FIG. 13. Numerical simulation using an elevation solitary wave initial condition (x, t 5 0) 5 asech2(x/L) with amplitude a 5 50 m and half wave width L 5 600 m on 7 Nov. Coefficients of the eKdV equation based on the reconstructed stratification including the (a) cubic nonlinear coefficient k, (b) quadratic nonlinear coefficient a, (c) dispersion coefficient b, and (d) linear wave speed c. (e) The numerical simulation results. The red and black curves in (e) indicate the elevation or polarity-converting wave and depression wave, respectively.

stratification could significantly affect its location. In winter, the critical position was more southeast than that in summer. Importantly, mesoscale eddies, internal tides, and other dynamic processes could cause the critical position to shift to deeper or shallower water. That is, shoaling depression ISWs could change polarity to elevation ISWs earlier or later than usual. The calculated critical position is consistent with our observational results (Figs. 3d–f). In summary, we showed that seasonal variations in stratification, mesoscale eddies, and internal tides can all modify the depth at which ISWs change polarity. Through quantitative analyses, we demonstrated that the impacts of an anticyclonic eddy and internal tides on ISW

polarity were primarily through changes in isotherm anomalies (or thermocline depth) rather than in currents. Given that the polarity of ISW is sensitive to temporal variations in background fields at near-critical positions as demonstrated in this study, we suggest that other dynamic processes may also influence polarity conversion of ISWs, such as cyclonic eddies and Rossby waves, which will be investigated when more observations become available. Acknowledgments. We thank the two anonymous reviewers for their insightful suggestions. The World Ocean Atlas 2013 dataset is downloaded from the NOAA website (http://www.nodc.noaa.gov/OC5/woa13). The altimeter

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FIG. 14. Distribution of the critical position in the northern SCS. The green, red, blue, and black solid lines indicate the zero isolines of the quadratic nonlinear coefficient in spring, summer, autumn, and winter, respectively. The black (red) dashed lines indicate that the critical position in winter (summer) are shifted to deeper water by the accompanying internal tides or other dynamic processes. The red stars represent the mooring array.

product was produced by SSALTO/DUCAS and distributed by AVISO, with support from CNES (available online at http://www.aviso.oceanobs.com/duacs). The HYCOM product is downloaded from their website (http:// hycom.org/). Professor Zhao was supported by National Key Research and Development Program of China (Grant 2016YFC1402605) and National Natural Science Foundation of China (Grant 41676011). Professor Tian was supported by National Key Basic Research Program of China (Program 973) (Grant 2014CB745003) and Qingdao National Laboratory for Marine Science and Technology (Grant 2015ASKJ01). Dr. Huang was supported by National Natural Science Foundation of China (Grant 41506011), National Key Research and Development Program (Grant 2017YFA0603201), and Global Change and Air–Sea Interaction Project (Grant GASI-IPOVAI01-03). Dr. Z. Zhang was supported by NSFC-Shandong Joint Fund for Marine Science Research Centers (Grant U1406402) and National Key Research and Development Program (Grant 2016YFC1401403). Dr. Zhou was supported by Foundation for Innovative Research Groups of the National Natural Science Foundation of China (Grant 41521091) and Global Change and Air–Sea Interaction Project (Grant GASI-IPOVAI-01-02). REFERENCES Alford, M. H., R.-C. Lien, H. Simmons, J. Klymak, S. Ramp, Y. Yang, D. Tang, and M. Chang, 2010: Speed and evolution of nonlinear internal waves transiting the South China Sea.

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