An extreme internal solitary wave event observed in the northern South China Sea

With characteristics of large amplitude and strong current, internal solitary wave (ISW) is a major hazard to marine engineering and submarine navigation; it also has significant impacts on marine ecosystems and fishery activity. Among the world oceans, ISWs are particular active in the northern South China Sea (SCS). In this spirit, the SCS Internal Wave Experiment has been conducted since March 2010 using subsurface mooring array. Here, we report an extreme ISW captured on 4 December 2013 with a maximum amplitude of 240 m and a peak westward current velocity of 2.55 m/s. To the authors’ best knowledge, this is the strongest ISW of the world oceans on record. Full-depth measurements also revealed notable impacts of the extreme ISW on deep-ocean currents and thermal structures. Concurrent mooring measurements near Batan Island showed that the powerful semidiurnal internal tide generation in the Luzon Strait was likely responsible for the occurrence of the extreme ISW event. Based on the HYCOM data-assimilation product, we speculate that the strong stratification around Batan Island related to the strengthening Kuroshio may have contributed to the formation of the extreme ISW.


Results
Characteristics of the extreme ISW event. On 4 December 2013, an extreme ISW event was captured by the mooring M10 (120.22°E, 20.57°N) deployed in the northern SCS at the bottom depth of 3847 m (Fig. 1). Heavy instrumentations, including two 75-kHz Acoustic Doppler Current Profilers (ADCPs), five recording current meters (RCMs), five conductivity-temperature-depth (CTD) recorders, and dozens of temperature loggers, were mounted on the mooring M10 (see Methods). Temperature observations showed that surface-layer water with high temperature sank into the lower layer during the ISW's passage (Fig. 2a), indicating a wave of depression. At the depth of 300 m, the temperature exhibited a maximum increase of over 6 °C at the wave trough. The temperature increase exceeded 0.5 °C even at 1000 m. From isotherm contours, we can infer that the water particle at 300 m prior to the wave arrival was displaced downward to 540 m by the wave trough within 15  With respect to horizontal current velocity of the extreme ISW, there existed a notably enhanced westward current zone, with a light-bulb shape around the wave trough (Fig. 2b). A peak westward current velocity of 2.55 m/s was found at 130 m at the wave trough. The strong westward current anomalies with magnitudes larger than 2 m/s extended to 190 m. At 130 m, the westward current anomalies that exceeded 2 and 1 m/s lasted for at least 5 and 12 minutes, respectively. The 4771 ISWs observed during the SIWE have a mean maximum current velocity of 0.64 m/s towards the west. So, the maximum current velocity of the extreme ISW is four times as large as the mean. Vertically, strong downward currents with a peak of 0.35 m/s were observed at the leading edge of the wave, following which the upward currents with comparable velocity magnitudes were observed at its trailing edge (Fig. 2c). Strong vertical velocities with magnitude exceeding 0.2 m/s can be found over a broad depth range between 100 and 900 m.
In the deep water between 1565 and 3803 m, notable eastward currents with magnitude of 6-8 cm/s (blue dots in Fig. 3a) were observed 6 min prior to the wave trough arrival by the RCMs working at a burst mode. The zonal current velocity in the lower layer showed opposite direction to that in the upper layer, corresponding to the mode-1 baroclinic structure. With sampling time interval of 30 min, the measurements of the RCMs missed the peak current velocity of the ISW at the wave trough. Here, we estimate the ISW current velocity from 1565 to 3803 m at the wave trough using the mode analysis method (see Methods). As shown in Fig. 3a (gray shadings), the estimated maximum eastward current velocity associated with the extreme ISW could reach 0.2 m/s. In the meantime, the deep-water CTD measurements with sampling interval of 2 min revealed significant temperature increases (Fig. 3b) during the passage of the extreme ISW at the depths of 1570, 2180, 2787, 3294, and 3808 m, respectively. The maximum temperature increases at these depths corresponded to downward isotherm displacements of 77, 57, 35, 23, and 19 m, respectively, on the basis of temperature gradient that was calculated using the winter data of the World Ocean Atlas (WOA). Based on the above results, we suggest here that the extreme ISW exerted great influences not only on the upper ocean but also on the deep ocean.  Following the strongest ISW, six trailing waves were observed; each was weaker than its predecessor (Fig. 3c). Previous studies reported that such multi-wave ISW packets generally occurred west of 118°E around the continental shelf of the northern SCS [19][20][21] . The extreme ISW reported here was captured east of 120°E, quite close to the originating site of internal waves in the Luzon Strait (LS). Amplitudes of the 2 nd , 3 rd and 4 th waves in the ISW packet still reached 120, 90 and 60 m, respectively. This is, therefore, another indicator for the intensity of the ISW.
In order to characterize the multi-wave ISW packet in this case, the dnoidal solution 22,23 to the Kortevrieg-de Vries (KdV) equation is adopted (see Methods). The calculation shows that newborn trailing waves continuously arise from the packet tail during the evolution, and the analytical packet waveform (dashed line in Fig. 3c) most closely matches the observations when the evolution time t approaches 6.6 h. Toward the packet rear, time intervals among successive waves exhibit a decreasing trend due to weakened nonlinearity. Moreover, compared to the ISW packets with smaller leading waves, the dnoidal solution reveals that the extreme multi-wave ISW packet exhibits a much more compact wave pattern (see Supplementary Fig. S1). According to the KdV theory, the strong nonlinearity of the leading wave would contribute up to 0.52 m/s to its propagation speed. With a linear propagation speed of 2.69 m/s, the propagation speed of the leading wave is estimated to be 3.22 m/s, which is 0.38 m/s faster than the mean ISW case with an amplitude of 67 m.
Energy in the ISW packet. Based on the moored temperature, salinity and velocity measurements, energy contained in the ISW packet was calculated (see Methods). At the trough of the leading wave, the maximum KE and APE densities were of 3.34 and 1.81 KJ/m 3 , respectively. The integrated KE and APE along the orientation of the ISW packet reached 3.84 and 4.29 GJ/m, respectively, which are two times of those of one prototypical ISW in the northern SCS reported by previous literature 15 . The energy of the baroclinic tides in the northern SCS, emanating from the LS that is known as the most energetic barotropic-to-baroclinic energy conversion region among the world oceans 24 , is considered to be the primary energy source for the enhanced vertical mixing and circulation in the deep SCS 25,26 . We should note that, the energy contained in this extreme ISW packet, which lasted only 3 hours, is comparable to the total energy in the diurnal and semidiurnal internal tides of a whole day.

Measurements near Batan Island.
It is generally accepted that the eastern ridge in the LS is the primary source region of ISWs 13,21,27,28 . To monitor the generation processes of ISWs, concurrent moored observations were conducted in the LS near Batan Island with the bottom depth of 329 m (mooring IW1 in Fig. 1b). By applying a band-pass filter to the time series of depth-averaged currents, the zonal semidiurnal (with periods of 9-15 h) and diurnal (with periods of 21-27 h) barotropic tidal currents at IW1 were obtained. Based on the stratification derived from the winter data of the WOA, we estimate that about 18.2 h is needed for ISW to propagate from IW1 to M10 according to the ratio between ISW propagation speed and linear phase speed 21 . Tracing back the extreme ISW signals at M10 to IW1, we find that the generation time of the extreme ISW well corresponded to the eastward total tidal current (marked by the magenta dashed line in Fig. 4a) over the generation site, consistent with previous studies 13,18,21 . No wave with such pattern as the extreme ISW at M10 was found in the baroclinic current measurements at IW1 (Fig. 4b). This result suggests that the generation mechanism of the extreme ISW might not be linked to the lee-wave generation mechanism.
From satellite remote sensing images, previous study demonstrated that ISWs in the northern SCS are developed from the internal tides through the mechanism of nonlinear steepening 19 . This point has been confirmed by follow-up field 18,21,29 and numerical 28,30 studies. Previous studies further suggested that the semidiurnal internal tide in the northern SCS is able to disintegrate into ISWs while the disintegration of diurnal internal tide is largely restrained due to the dispersion effect of the Earth's rotation 29,31,32 . To examine the variation of the semidiurnal internal tide generation near Baton Island, a band-pass filter (with periods of 9-15 h) was applied to the time series of zonal baroclinic velocity measured at IW1. Fig. 4f shows that there existed a remarkable peak in the depth-integrated KE density of the semidiurnal internal tide in early-December, coinciding with the occurrence time of the extreme ISW at M10. Both semidiurnal and diurnal internal tides contribute to the formation of ISWs, but the former plays a dominant role, and therefore it is reasonable to attribute the occurrence of the extreme ISW at M10 to the powerful generation of semidiurnal internal tide in the LS.

Discussion
Changes of barotropic tide and stratification are known as decisive factors that can affect the generation of baroclinic tides. By examining the changes of barotropic tide at IW1, we find that the barotropic tide around 4 December was not stronger than those during other spring-neap cycles (Fig. 4c-e). This result suggests that the variation of barotropic tide could not account for the generation of strong semidiurnal internal tide. To diagnose the variability of stratification over the source site of ISWs, we employ the hybrid coordinate ocean model (HYCOM) product (see Methods) to compensate for the lack of long-term observational temperature and salinity data in the LS. Based on the HYCOM salinity and temperature outputs, the depth-averaged buoyancy frequency squared N 2 between 100 and 200 m around Batan Island (as marked by the black rectangle in Fig. 1b) was calculated. As shown in Fig. 5a, the value of N 2 reached a peak around early-December in 2013, which coincided well with the occurrence of the extreme ISW. An eastward background flow over the generation site can amplify the generation of internal tides and the amplitude of ISWs 29,33 . In early-December of 2013, however, a westward background flow was present over the generation site of internal tides around IW1 ( Supplementary Fig. S2), with a comparable magnitude to the average between March 2010 and June 2014. Hence, we think that the role of LS background flow in the formation of the extreme ISW was limited. Further, given that the observed barotropic tide at IW1 was not intensified, it is reasonable to consider that the increased stratification likely contributed to the formation of the extreme ISW in early-December of 2013.
It is noted that no ISW with a comparable amplitude as the extreme ISW was captured in 2011 and 2012 during the full-year measurements, indicating that there existed interannual variations of ISWs in the northern  Fig. 5a shows that the value of N 2 exhibited a significantly increasing interannual trend from 2011 to 2013. In early-December of 2013, the intraseasonal variation of N 2 further increased the stratification over the source site of ISWs. The superposition of the interannual trend and intraseasonal variation led to the peak of N 2 , the date of which matched the spring period of semidiurnal barotropic tide in early-December of 2013 (see Supplementary Fig. S3). We should note that large intraseasonal augments in stratification also occurred in 2011 and 2012 (e.g., April 2012). However, superimposed on a relatively lower level, the values of N 2 during 2011 and 2012 were not comparable to that in early-December of 2013. This result suggests that the 3-year interannual increasing trend of N 2 seemed to be a key basis for the generation of energetic internal tides and formation of the extreme ISW.
During the SIWE, mooring measurements over 25 months were collected in the eastern deep basin close to the LS (B3, from August 2010 to April 2011; M10, from April 2011 to April 2012, and from October 2013 to June 2014). In order to examine the long-term trend of ISWs, monthly-averaged maximum current velocity of ISWs were calculated, which show that the ISWs near the LS at B3 and M10 seemed to strengthen from late 2010 to early 2012, and reached a peak at the end of 2013 (Supplementary Fig. S4). Drawing an explicit conclusion that the ISWs continuingly became stronger from 2012 to 2013 requires the support of observations in 2013. However, considering that the barotropic tide in the LS varied little from year to year, we can safely assume that the strengthened ISWs from late 2010 to early 2012 near the LS at B3 and M10 were associated with the enhanced stratification near Batan Island.
Considering that the current and thermal structures in the LS are largely impacted by the Kuroshio 34 , it is necessary to examine whether the increasing trend of N 2 from 2011 to 2013 was associated with the Kuroshio. As demonstrated in Fig. 5c, the averaged stratification of the Kuroshio along 18°N was obviously stronger than the water around Batan Island. From 2011 to 2012, mooring measurements 35 showed that the Kuroshio velocity at its origin at mooring KC1 increased by as large as 0.15 m/s (red line in Fig. 5b), which would have carried more warm water downstream into the LS. The 200-300 m averaged HYCOM meridional velocity at KC1 also exhibited an increasing trend from 2011 to 2012 (blue line). The HYCOM-simulated Kuroshio continued to strengthen in the year 2013, though it decreased a little bit over the last five months. Considering that the Kuroshio water was more stratified than the LS water, we speculate that the increasing trend of N 2 from 2011 to 2013 might be related to the strengthened Kuroshio.
Previous studies have shown that the Kuroshio at its origin strengthened during an La Niña event 36,37 . As we know that the La Niña event during 2011-2012 was one of the strongest on record, and the Niño 3.4 index continued to be negative in 2013. As the hotbed of highly stratified water, our analysis present here suggests that the variation of the Kuroshio might play the role of a bridge as the climatic-scale El Niño and Southern Oscillation (ENSO) event modulating weather-scale ISW event. Given the availability of the 4-year moored observations of ISWs, it is difficult to ascertain the response of ISWs in the northern SCS to the ENSO events. This, however, is an interesting topic that needs further study in future.

Methods
In-situ moored data. From 96°N, 122.93°E) at the depth of ~500 m, which recorded the velocity information from ~1100 m to near the surface. In this study, the above two moorings are regarded at the same position (called KC1) because they were not far from each other. For more detailed descriptions of the two moorings, readers are referred to the published papers 35,38 . Due to contamination by acoustic reflections near the air-sea interface, the velocity measurements of the ADCPs between the sea surface and 50-m depth were discarded. The vertical motions of the ADCPs were estimated by computing the time derivative of the pressure signals, and then they were subtracted from the vertical velocity records of the ADCPs to remove the influences of mooring tilt.
Vertical mode analysis. The theoretical structure of vertical velocity f n of mode-n internal wave can be obtained by numerically solving the Taylor-Goldstein equation: is the Brunt-Väisälä frequency and c 0 is the linear phase speed. Here, the density profile ρ(z) is computed from the daily-averaged temperature and salinity profiles measured by mooring M10. The lack of stratification data near the surface and bottom was made up by the winter data of the WOA. The velocity data 30 min prior to the ISW arrival measured by the ADCPs and RCMs are used to construct the background current profile U(z). The background currents near the surface, where the velocity measurements of ADCP were contaminated by acoustic refractions, are complemented by assuming that the velocity was constant from 50-m depth to the where η 0 is the wave amplitude.
is characteristic width and is wave propagation speed. However, due to the lack of information about trailing waves, the sech 2 solution to the KdV equation is not suitable to analyze the characteristics of the multi-wave ISW packet.
To interpret the dynamics of the multi-wave ISW packet in Fig. 3c, the Dnoidal solution to the KdV equation is applied. Here, k 0 is the wavenumber of the soliton at the packet rear, and t is the growth time of the packet. The Jacobi elliptic function dn s (X) of argument X is oscillatory quantity. The nonlinear parameter s is determined using the following equation, where τ is the space-time ratio, and K(s) and E(s) are complete elliptic integrals. The nonlinear parameter s decreases monotonically from unity at the leading edge to zero at the trailing edge, and the space-time ratio τ is verified to vary from 2/3 to − 1. The Supplementary Fig. S5a schematically shows the Dnoidal solution. The leading wave with the nonlinear parameter s that equals to unity has a fully-nonlinear wave shape. When τ is larger than 2/3, the solution is assumed to be one half of the sech 2 solution. In the Dnoidal solution, the nonlinear phase speed V is given by f 0 6 is adopted. As is shown in Supplementary Fig. S6, the trailing edge of the waveform returns to the starting position after the recovery.

Calculation of the Energy in the Isw Packet
The measured time series of velocity and temperature are transformed to the space coordinate in the wave's reference frame, ′ − = x x Vt. Then, the KE and APE of the ISW packet are computed through Here, ρ r (z) is the background density profile prior to the arrival of the ISW, and z ′ is the depth of the water particle in the background density profile. The velocity and stratification profile have been extrapolated to the surface and bottom using the mode analysis method.