Distortion and broadening of internal solitary wavefront in the northeastern South China Sea deep basin. Institute of Technology, Lianyungang, China

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1 PUBLICATIONS Geophysical Research Letters RESEARCH LETTER Key Points: A peculiar ISW front across northeastern SCS deep basin is reported and explained by developing a nonlinear refraction model Strong mesoscale current leads to distortion, while different transformation across variable bottom topography results in broadening Simulated characteristics of distortion and broadening are consistent with the SAR-observed front Supporting Information: Supporting Information S1 Correspondence to: S. Cai, caisq@scsio.ac.cn Citation: Xie, J., Y. He, H. Lü, Z. Chen, J. Xu, and S. Cai (2016), Distortion and broadening of internal solitary wavefront in the northeastern South China Sea deep basin, Geophys. Res. Lett., 43, , doi:. Received 29 MAR 2016 Accepted 7 JUL 2016 Accepted article online 9 JUL 2016 Published online 25 JUL American Geophysical Union. All Rights Reserved. Distortion and broadening of internal solitary wavefront in the northeastern South China Sea deep basin Jieshuo Xie 1,2, Yinghui He 1, Haibin Lü 1,3, Zhiwu Chen 1, Jiexin Xu 1, and Shuqun Cai 1 1 State Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology, CAS, Guangzhou, China, 2 University of Chinese Academy of Sciences, Beijing, China, 3 School of Geodesy and Geomatics Engineering, Huaihai Institute of Technology, Lianyungang, China Abstract Internal solitary waves (ISWs) with peculiar fronts are frequently observed in the world ocean by satellite images, though with quite few explanations. In this study a distorted and broadening ISW front across the northeastern South China Sea deep basin is presented by using synthetic aperture radar (SAR) image. To illustrate this peculiar front, a nonlinear refraction model is developed to simulate and evaluate the effects of realistic bottom topography, current, and stratification on its transformation. Simulated results in realistic oceanic environments show good agreements with this SAR-observed front. Based on separate and comparative results in different background environments, we demonstrate that the distortion is actually caused by the strong mesoscale currents at periphery of an anticyclonic eddy. Moreover, the broadening is due to the difference in change of wave half width at different rays, which is associated with the different transformation of ISWs across variable bottom topography in the deep basin. 1. Introduction Internal solitary waves (ISWs), with fronts extending for tens to hundreds of kilometers, are frequently observed in the northeastern South China Sea (SCS) by satellite images [Jackson, 2004; Huang et al., 2008]. These waves propagate westward from generation source sites at Luzon Strait, across the deep basin, and onto continental shelf [Alford et al., 2010]. In spite of their wide span and obvious scientific [Lamb, 2014; Alford et al., 2015] and societal [Moore and Lien, 2007; Wang et al., 2007] significance in the SCS, much remains unknown, especially with respect to waves dynamics and characteristics along their fronts. Satellite images show that near Luzon Strait the long ISW fronts tend to parallel to the line source sites [e.g., Zheng et al., 2007], as simulated in Zhang et al. [2011]. In the northeastern SCS deep basin, however, circular/cylindrical ISW fronts would appear more easily due to nonlinear effects [Zhao et al., 2004; Chen et al., 2011]. Moreover, due to refraction and diffraction effects of bottom topography, distorted/cusped ISW fronts could be frequently observed [e.g., Li et al., 2013] and well simulated [Zhang et al., 2011] after bypassing Dongsha Atoll and propagating onto continental shelf. Nevertheless, it is reported that in the deep basin ISW fronts with peculiar distortion could also be occasionally observed [Liu et al., 2004]. From the perspective of generation, simulated results in Zhang et al. [2011] suggested that the irregularity of source sites at Luzon Strait might cause distorted ISW fronts in the deep basin. Moreover, in terms of propagation, the linear ray tracing analysis in Park and Farmer [2013] showed that Kuroshio intrusions could lead to refraction of internal waves and then deformation of wavefronts. Recently, in terms of both propagation and evolution, the MITgcm simulations [Xie et al., 2015], performed in bottom topography with constant depth, suggested that variations of oceanic eddies, especially energetic eddies, might also play a role in forming this type of distortion. In this study, a nonlinear refraction model (NRM) similar to that in Small [2001a, 2001b] is developed to investigate a distorted and broadening ISW front (Figure 1a) observed by the synthetic aperture radar (SAR). The NRM employs a nonlinear equation of the Korteweg-de Vries (KdV) type [Grimshaw et al., 2014] to describe wave evolution and a ray method [Pelinovsky et al., 1994] to describe distortion of fronts. Not only can the NRM present results in terms of both propagation and evolution, but it can isolate effects of various kinds of variable background environments. We herein use this NRM to study the SAR-observed front under realistic ocean environments and demonstrate that the distortion is caused by mesoscale currents associated with an anticyclonic eddy, while the broadening is due to the different transformation of ISWs across variable bottom topography. XIE ET AL. DISTORTION AND BROADENING OF WAVEFRONT 7617

2 Figure 1. (a) A distorted westward propagating ISW front shown by Envisat ASAR image acquired at 02:13:30 UTC on 18 June 2008 in the northeastern SCS and the contemporaneous background mesoscale variations shown by the GSVA (thin arrows) and SLA (color; cm); thin black lines depict water depth (m); blue dashed square region represents model domain; and thick black line represents the ideal initial front. Reconstructed current fields in (b) section N and (c) section N. Note that the inset in Figure 1c is the oceanic averaged stratification used for reconstructing. 2. Satellite Observations In Figure 1a, an Envisat advanced synthetic aperture radar (ASAR) image acquired at 02:13:30 UTC on 18 June 2008 is presented. In this image, a long ISW front D, propagating from generation source sites at Luzon Strait and across the deep basin while not reaching Dongsha Atoll, is observed near ~117.5 E. Different from most of the circular/cylindrical ISW fronts commonly observed in the deep basin, this recorded westward propagating ISW front has two special characteristics that are worthy of further study and evaluation. First, a concave wave fragment is formed at the southern half of ISW front D. This characteristic is different from most of the satellite observation or model prediction of fronts across the deep basin [Jackson, 2009]. For instance, based on an empirical model, Jackson [2009] showed that internal wavefronts generally still kept their circular waveforms near ~117.5 E (e.g., see the modeled front after propagating ~1.103 days away from the Luzon Strait in his Figure 7). Also, Figure 1a indicates that this concave wave fragment is formed at place where the local water depth is deeper than ~500 m, which is deeper than that at the northern half of this distorted front. Second, the width of ISW along this distorted front is broadened from the northern to southern end. Actually, Zhao et al. [2003] also reported one type of broadening on continental shelf in the northern SCS, though from south to north along the front; based on one-dimensional extended KdV equation in two-layer system, they attributed the broadening to polarity conversion across a turning point. In this study, however, based on the two-dimensional NRM we show a different mechanism responsible for the broadening of ISW front D. Moreover, we show that ISWs in a single long front may perform quite different evolution processes if they propagate in very inhomogeneous and complex ocean environments. The ISW front D is propagating across the deep basin and thus the single effect of inhomogeneous bottom topography cannot lead to such an obvious distortion, as implied in Jackson [2009]. Similar to the approach adopted in Xie et al. [2015], the contemporaneous merged altimeter data acquired on 18 June 2008 are further investigated (Figure 1a). Mesoscale eddies are detected by the geostrophic surface velocity anomaly (GSVA) and sea level anomaly (SLA) data, which are produced by Ssalto/Duacs and distributed by Archiving, Validation, and Interpretation of Satellite Oceanographic data (AVISO), with support from CNES ( aviso.altimetry.fr/duacs/). According to the GSVA, the magnitude of maximum surface velocity anomaly experienced by the long ISW front D can reach up to ~48 cm/s, which is associated with a background mesoscale anticyclonic eddy (see Figure 1a). Moreover, using the method proposed in Wang et al. [2013] we use the first baroclinic structure of quasi-geostrophic motions (see Text S1 in supporting information) to reconstruct the ocean s interior fields from surface data. Figure 1a indicates that the westward propagating ISW front D has experienced the strong mesoscale currents that are in an approximately opposite direction at the periphery of anticyclonic eddy. Therefore, the reconstructed current field in a southern section N across the periphery of anticyclonic eddy is shown (Figure 1b). For comparison, the reconstructed result in a northern XIE ET AL. DISTORTION AND BROADENING OF WAVEFRONT 7618

3 section N, where the background anomalies are weak, is also shown (Figure 1c). Note that the oceanic averaged stratification N(z) calculated from the WOA09 in June [Locarnini et al., 2010] and the topography obtained from the 1 min gridded bathymetry (ETOPO1) [Amante and Eakins, 2009] are used for reconstructing. Because the southern section N passes through strong currents at the periphery of anticyclonic eddy, it is reasonable to see that the magnitude of reconstructed currents in section N is generally much larger than that in section N. Although the linear approach in Park and Farmer [2013] and the empirical model in Jackson [2009] can be used to illustrate the distortion to a certain degree, they fail to display evolution processes of ISWs. Also, because the nonlinear part of ISW speed depends on ISW amplitude, fronts with nonlinear part included will differ from results calculated with only linear speed, especially for large amplitude ISW on large distances [Xie et al., 2015]. Based on realistic oceanic environments, here we use the NRM to illustrate the two characteristics of ISW front D by examining both propagation and evolution processes. 3. Simulation and Evaluation Using NRM 3.1. Model Description To investigate the evolution of ISW fronts across two-dimensional bathymetry and isolate effects of various kinds of variable background environments, the NRM including spreading term [Pelinovsky et al., 1994] and employing KdV type equation [Grimshaw et al., 2014] at each ray is used. The model equation can be written as η T þ c η X þ αη η X þ β 3 η X 3 þ c dq 2Q dx η þ c dδ η ¼ 0; (1) 2Δ dx where η is the vertical displacement and X and T are the spatial and temporal range along the ray of interest. The environmental parameters c, α, and β are the linear speed, quadratic nonlinear coefficients, and dispersion parameter, respectively; Q is the amplification factor due to variable bottom topography, current, and stratification. A normal mode approach, as proposed in Grimshaw et al. [2004, 2014], is taken to compute these environmental parameters (see Text S2 in the supporting information) based on the following Taylor-Goldstein equation in the long-wave approximation [Apel et al., 2006]: d dz ðu B cþ 2 dφ dz þ N 2 Bφ ¼ 0 ; φ ¼ 0atz¼0; H; (2) where U B and N B are the reconstructed background current and stratification, φ is the related modal structure, and H is the water depth. Here because currents normal to rays generally have weak effects upon behaviors of ISW front (see Figure 4b in Xie et al. [2015] for instance), only currents projected on rays are used for calculating. Note that the last term in the left side of equation (1) depicts the spreading effect, and the factor Δ represents the wavefront length (i.e., differential width of ray tube), as described in Pelinovsky et al. [1994]. The NRM here adjusts the refraction model of Small [2001b] to deal with realistic oceanic environments including variable topography, current, and stratification. The square region marked in Figure 1a is selected as the computation domain. A single, first-mode ISW with straight-line front propagating westward from the deep basin (see thick black line in Figure 1a) is initialized at the east side of this domain by using KdV solution. The initial half width (L 0 ) and amplitude (A 0 ), consistent with the scale of in situ observations in the northeastern SCS deep basin [Alford et al., 2010] are set as 5 km and 50 m, respectively. Then a number of rays are constructed, each perpendicular to the prescribed front. For each ray, the initial ISW stated above is placed in the model domain such that its trough is just located at the position of prescribed front. The ray method and spreading algorithm (see Text S3 in the supporting information), as depicted in Small [2001b], are used to calculate the rays and ray tube s width Δ. Along each ray, the Fourier pseudospectral method with periodic boundary conditions and the fourth-order Runge-Kutta method for integration of time are used to solve equation (1) [Grimshaw et al., 2014] Model Results in Realistic Oceanic Environments The behavior of ISW evolution at each ray will depend on behaviors of each of the local environmental parameters in equation (1) [Grimshaw et al., 2010]. Therefore, using the bottom topography interpolated from XIE ET AL. DISTORTION AND BROADENING OF WAVEFRONT 7619

4 Figure 2. Coefficients of the NRM equation in the model domain. (a) c TUN ; (b) α TUN ; (c) β TUN ; and (d) Q TUN. the ETOPO1 bathymetry and the above reconstructed ocean s interior fields from merged altimeter data, these parameters are computed. In Figure 2 we show the distribution of linear phase speed, c TUN, and parameters α TUN, β TUN, and Q TUN in the computation domain (here the index TUN represents combined effects of topography, current, and stratification). It is seen that the linear phase speed c TUN (Figure 2a) decreases from the eastern side to northwestern side/corner of the computation domain. Further, Figure 2b shows that the quadratic nonlinear coefficient α TUN is negative except at the upper left corner, where the local water depth (see Figure 1a) is shallower than ~150 m; Figure 2c shows that the dispersion coefficient β TUN decreases significantly from the southeastern to northwestern side. Besides, even though both cubic nonlinearity and background rotation are included in equation (1), their effects on simulated results are weak because of the quite small cubic nonlinear coefficient in the deep basin [see Grimshaw et al., 2014] and the quite minor role of rotation on the short length scale (i.e., L 0 = 5 km) ISW initialized above [Li and Farmer, 2011]. For instance, the Ostrovsky number [Famer et al., 2009], O s ¼ 24π2 c TUNα TUNA 0 (f is the local Coriolis parameter), from f 2 L 2 0 the south to north end for the initial front above ranges from ~4300 to ~3600 (O s 2), which implies that nonlinearity dominates while rotation plays a minor role here. First, we study the distortion of ISW front. Figure 3a shows results of ISW rays (thin back lines) and fronts (thick back lines). It reveals that ISW rays radiated within the range between 19.5 N and 21 N are gradually focused onto the selected southern section at ~20.23 N, where the mesoscale current associated with the anticyclonic eddy is very strong (see Figure 1b). Moreover, obvious concave fragments are formed at the southern half of ISW fronts when they arrive at ~118 E, and the degree of their distortion is gradually enhanced as they propagate westward. Overall, it is seen that the distorted characteristic of ISW fronts at the later time of simulation (i.e, at the time from about 18 h to 28.8 h) is quite consistent with the first characteristic, as shown above, of the SAR-observed front D. Next, we study evolution processes of ISWs. For this purpose the transformation of ISWs along four typical rays R1 R4 (see color lines in Figure 3a) are shown in Figures 3b 3e, respectively; here to make results easier to see, Figures 3g 3i show zoomed-in versions of Figures 3c 3e. Moreover, the wave amplitude A (normalized by A 0 ) versus the travel time in all four rays are shown in Figure 3f. It is seen that before ~10.8 h (or ~118.5 E) the solitary wave transformation is not obvious, and the ISWs maintain their soliton-like shape in all four rays because all background environmental parameters vary very slowly (see Figure 2). Correspondingly, Figure 3f shows that the ISW amplitude also has no obvious variation in all four rays before XIE ET AL. DISTORTION AND BROADENING OF WAVEFRONT 7620

5 Figure 3. Model results in realistic oceanic environments. (a) ISW rays (thin black lines) and fronts (thick black lines); four color lines depict typical rays R1 R4. (b e) Transformation of ISWs along the typical rays R1 R4; the amplitudes are incremented for each plot by +50 m, and X is the spatial range. (f) Wave amplitude A (normalized by A 0 ) versus travel time t in four typical rays R1 R4. (g i) Zoomed-in versions of Figures 3c 3e. Note that in Figures 3a 3e and 3g 3i, the travel time t (h) is denoted by red numbers. ~10.8 h. These results indicate that before ~118.5 E all background environments have weak effects on ISW evolution and thus the ISWs basically maintain their initial waveform. In the following evolution process, however, effects of background environments on ISW evolution at different rays become quite different. At ray R1, both the transformation of ISW (Figure 3b) and wave amplitude (see red line in Figure 3f) still have no significant variation throughout the whole evolution process, because both the quadratic nonlinear coefficient α TUN (Figure 2b) and dispersion coefficient β TUN (Figure 2c) are approximately constant at this ray. Nevertheless, at other three rays (i.e., rays R2 R4) they vary greatly. At ray R2, although the quadratic nonlinear coefficient α TUN is still approximately constant, the dispersion coefficient β TUN decreases greatly from position at ~118.5 E. These variations result in the destruction of balance between nonlinearity and dispersion at this ray. Therefore, Figures 3c and 3g show that at ray R2 the ISW with soliton-like structure is eventually transformed into a steep shock-like waveform at ~27 h, and Figure 3f shows that the wave amplitude increases greatly up to ~1.9A 0 (see blue line). Similar evolution processes of ISWs resulted from the destruction of balance between nonlinearity and dispersion also exist at rays R3 and R4. At these two rays, not only the dispersion coefficient β TUN (Figure 2c) decreases greatly from an earlier position at ~119 E, but the quadratic nonlinear coefficient α TUN (Figure 2b) increases greatly from ~ s 1 to ~ s 1. Therefore, at these two rays, not only steep shock-like waves are formed, but their formation times are brought forward in comparison with that at ray R2. In detail, at ray R4 (Figures 3e and 3i) shock-like waves are formed from ~19.8 h (~7.2 h earlier than that at ray R2), while at ray R3 (Figures 3d and 3h) they are formed from an earlier time at ~18 h (~9 h earlier than that at ray R2). Meanwhile, Figure 3f shows that at ray R4 the wave amplitude gradually increases to ~ 1.6A 0 and at ray R3 it increases up to ~ 2.6A 0. Furthermore, we study the variation of wave width. It is seen that because the steep shock-like waves and wave trains at the two northern rays R3 (Figures 3d and 3h) and R4 (Figures 3e and 3i) are formed much earlier due to the shallower bottom topography at the northwestern side of computation domain, the wave half width at these two rays decreases greatly from an initial value of 5 km to ~500 m. Particularly, at ray R3, XIE ET AL. DISTORTION AND BROADENING OF WAVEFRONT 7621

6 Figure 4. ISW rays and fronts affected by (a) only bottom topography, (b) both bottom topography and background current, and (c) both bottom topography and background stratification. Linear phase speed anomaly fields: (d) Δc UN, (e) Δc U, and (f) Δc N. the half width at 18 h (or at position near ~118 E) decreases to about half of the initial width. It is worth mentioning that this variation trend of half width at the two northern rays is comparable to that of in situ observations in Alford et al. [2010, Figure 9a], where their results are observed along a track (~21 N) near to the path of ray R3. However, at the two southern rays R1 (Figure 3b) and R2 (Figures 3c and 3g), where the concave fragment is formed, the width changes little (except at the later stage of ray R2 when the shock-like waves begin to form), and thus the wave width here will be much broader than that at two northern rays. It is seen that this broadening characteristic from the northern to southern rays is also consistent with the variation trend of the SAR-observed front D. Moreover, this variation trend can also be explained by using the following simple expression of half width [e.g., Apel et al., 2006] sffiffiffiffiffiffiffiffiffiffiffiffiffiffi 12β L ¼ TUN : (3) Aα TUN Because of the shallower bottom topography at the northwestern side of computation domain the β TUN (α TUN ) decreases (increases) greatly at two northern rays, whereas their variations at two southern rays are weak (Figures 2b and 2c). Thus, the width at northern rays is narrower than that at southern rays according to (3). In summary, these results indicate that the broadening characteristic of ISW front D is due to the difference in change of wave half width at different rays, which is associated with different transformations of ISWs across variable bottom topography in the deep basin Evaluating the Distortion of ISW Front In this subsection, the effects of bottom topography and background current and stratification on the distortion of ISW front are investigated separately and comparatively. Figure 4a shows results of ISW rays and fronts only affected by bottom topography. It indicates that the initial ISW fronts propagating in the deep basin will have no further distortion if only the effect of bottom topography exists; actually, this point can also be seen in Jackson [2009]. Further, Figure 4b shows results affected by not only bottom topography but also background current and reveals that a significant distortion very consistent with that in Figure 3a happens to the ISW fronts. Correspondingly, Figure 4c shows results affected by variations of both bottom topography XIE ET AL. DISTORTION AND BROADENING OF WAVEFRONT 7622

7 and stratification, and it is seen that similar to Figure 4a, there is still no significant distortion happening to initial fronts. Therefore, these comparative results imply that ISW fronts propagating in the northeastern SCS deep basin will generally keep their initial forms (e.g., circular/cylindrical form) if they are not affected by other background factors such as variable currents and/or stratifications. On the other hand, the above comparison indicates that the distortion of the presented ISW front D here is mainly caused by the strong mesoscale currents at the periphery of anticyclonic eddy rather than the bottom topography and/or background stratification. Because the linear phase speed is actually the first indication of distortion of ISW fronts, the dominated role of mesoscale current relative to stratification could also be seen from the linear phase speed anomaly fields Δc UN, Δc U, and Δc N, which are computed by subtracting the linear phase speed c T from the total linear phase speed c TUN, c TU, and c TN, respectively (i.e., Δc UN = c TUN c T, Δc U = c TU c T, and Δc N = c TN c T ). Here c T refers to linear phase speed calculated with effects of only bottom topography, while c TU (c TN ) refers to linear phase speed calculated with combined effects of bottom topography and background current (stratification). Thus, Δc UN in Figure 4d gives anomaly due to both background current and stratification, while Δc U (Δc N )in Figure 4e (Figure 4f) gives anomaly due to only background current (stratification). It is seen that because of the strong mesoscale currents at the periphery of anticyclonic eddy, Figures 4d and 4e show similarly and significantly negative anomalies here; correspondingly, these anomalies lead to the concave wave fragments in Figures 3a and 4b, respectively. Overall, these comparisons show that background mesoscale current variations play important roles in forming phase speed anomalies and thus further cause the distortion of ISW front D. Acknowledgments The authors thank Roger Grimshaw for valuable suggestions and comments. This work was supported by NSFC grants and , Strategic Priority Research Program of CAS (XDA ), National Basic Research Program (2013CB956101), NSFC grant , and Innovation Group Program (LTOZZ1502) of LTO. The altimeter products were produced by Ssalto/Duacs and distributed by AVISO, with support from Cnes ( The ASAR image was provided by European Space Agency through ESA-MOST Dragon Project. The source code for the model used in this study, along with the data and input files, is available from the authors upon request (caisq@scsio. ac.cn). Thanks to the two reviewers for their valuable comments and helpful suggestions. 4. Summary and Discussion ISWs with long peculiar fronts are frequently observed in the world ocean by satellite images, though with quite few explanations [e.g., Zhao et al., 2003; Xie et al., 2015]. In this study a distorted and broadening ISW front across the northeastern SCS deep basin is detected by the SAR image. Based on investigation of the contemporaneous merged altimeter data, we find that the mesoscale currents at the periphery of an anticyclonic eddy may play an important role in forming this distortion. Then to test this hypothesis and explain this SAR-observed peculiar front, a nonlinear refraction model employing KdV type equation at each ray and including spreading term is developed. Model results show that in realistic oceanic environments the simulated distorted ISW fronts near ~117.5 E have good agreements with the SAR-observed front. Based on separate and comparative results in different background environments, we demonstrate that the distortion of ISW front D is basically caused by the strong mesoscale currents at the periphery of an anticyclonic eddy, rather than the background stratification and/or bottom topography in the deep basin. It is worth pointing out that this realistic study supports the conclusion of an ideal analysis in Xie et al. [2015], where they show that the background mesoscale current variations lead to more than ~83% of the overall distortion of ISW fronts. Moreover, different from the broadening on continental shelf in the northern SCS [Zhao et al., 2003], another type of broadening of ISW front in the northeastern SCS deep basin is reported and explained. Model results reveal that at northern part of fronts the width decreases greatly because of the easy formation of steep shock-like waves and wave trains near the shallower bottom topography at northwestern side of computation domain. Variations of width at the northern part of front are very comparable to the in situ observations in Alford et al. [2010]. However, because ISW transformations are weak at the southern part of front, the width changes little there. These differences indicate that the waves characteristics (e.g., amplitude and width) and dynamics in propagation and evolution processes, even along a single uniform initial front, can be very different in the northeastern SCS. References Alford, M. H., R. C. Lien, H. Simmons, J. Klymak, S. Ramp, Y. J. Yang, D. Tang, and M. H. Chang (2010), Speed and evolution of nonlinear internal waves transiting the South China Sea, J. Phys. Oceanogr., 40, Alford, M. H., et al. 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