Supplementary information
Seismic, satellite, and site observations of internal solitary waves in the NE South China Sea
Supplementary material
Qunshu Tang*, Caixia Wang, Dongxiao Wang, Rich Pawlowicz
Figure S1: Correspondences between seismic image and the vertical gradients of the acoustic impedance at two XBT stations (white lines). Inset in the left panel shows the near-field source wavelet of the GI gun during the experiment. Seismic image represents the convolution between the acoustic impedance contrast and the seismic source wavelet. The acoustic impedance is calculated from I=c*, where c and are the velocity and density of the water.
Figure S2: Potential temperature profiles (gray) and vertical gradients of temperature (dT, black), salinity (dS, blue), density (dR, purple), velocity (c, green), and acoustic impedance (dI, red), respectively, estimated from two in-situ XBT profiles as indicated both in Figure 2 and Figure S1. To indicate the relative contributions of the T, S, , and c to the I, amplitudes of the vertical gradients were scaledby their corresponding factors derived from Equation 5 of the reference:Ruddick et al., (2009), Water column seismic images as maps of temperature gradient, Oceanography, 22(1), 192-205. The salinities were estimated according to the reference: Kase RH, Hinrichsen HH, Sanford TB. Inferring density from temperature via a density-ratio relation. J Atmos Oceanic Technol 1996, 13(6): 1202-1208.
Figure S3:Model predicted barotropic tides near the study region (117.4E,21.25N). The black dot marks the approximate time when the studied ISWs were observed.
Figure S4: Diagram showing how ISW’s phase velocity is measured. Pentagons and dots are the sources and receivers, respectively. Their common mid-points (cmp1 and cmp2) are located at the crest/trough of the internal waves. Dashed arrows represent the coordinate with s2 as the reference point.
Figure S5: Velocity estimation of ISW1 from the common offset gathers (COGs). (a) Tracking the troughs of ISW1 for each COG; (b) Least squares criterion for linear regression; (c) Fitting of observations (black dots) using the linear regression (red line).
Figure S6: Same as Figure S5, but for a static seamount.
Figure S7: Diagram showing how an ISW’s vertical velocity is measured. η0: amplitude ofthe ISW; L: half width of the ISW, a horizontal distance over which the η0 decreases to η0/2. Therefore, the mean vertical velocity of the particle motion from A to B is w=η0V/L when the ISW moves from 1 to 2.
Figure S8: Analytical ISWs (blue) and their vertical velocities (green) at t=0. The three red stars from left to right represent the horizontal locations of characteristic width (x=1.0), half width (x=0.88), and maximum vertical velocity point (x=0.66) for an ISW, respectively, normalized by the characteristic with. The green areas are used for measuring the mean vertical velocities.
Table S1: Parameters observed/derived during wavelength estimation. H: water bottom depth; c: mode-one linear phase velocity, same as c in Table 1; KdV: nonlinear phase velocity estimated using continuous stratified ocean system; α: nonlinear parameter; β: dispersion parameter; L: half widthmeasured from seismic image; Δ: characteristic width.
H(m) / c
(m/s) / KdV
(m/s) / α / β / L
(m) / Δ
(m) / L/Δ
ISW1(XBT1) / 425 / 1.40 / 1.63 / -0.0119 / 10955 / 740 / 433 / 1.71
ISW2(XBT2) / 700 / 1.68 / 1.92 / -0.0121 / 32045 / 1262 / 730 / 1.73