Signatures of tidal interference patterns in the South China Sea

Abstract

The formation of arc-type structures in the surface elevation and temperature fields due to internal tidal (IT) waves is studied in the region of the South China Sea (SCS) and Luzon Strait. It is demonstrated that these arc-type structures in the surface elevation and temperature at depth result from the merging of IT waves. Predictions of internal baroclinic tides are conducted with a nonlinear hydrostatic model, the Luzon Strait Nowcast/Forecast System, forced with tides, realistic surface forcing and stratification (Appendix 1). It is shown that IT waves generated by the undersea ridges near the Batan and Babuyan Islands in the Luzon Strait propagate westward and merge into arcs in the SCS. The superposition of IT waves is also investigated with a linear knife-edge model (Appendix 2). M₂ and K₁ tidal waves are considered. It is demonstrated that K₁, M₂ tidal waves from the Babuyan Islands combine with waves from the Batan Islands to form arc signatures in sea surface elevation and warm spots in the South China Sea. Possible modulation effects of K₁ waves on M₂ waves are shown. Dynamics of the nonlinear hydrostatic model shape the arc segments differently from the linear model. Arc lengths increase from the sources in nonlinear and linear models. The model-predicted merged IT waves are compared with SAR images.

Appendices

Appendix 1: Hydrostatic model (LZSNFS)

The LZSNFS (Luzon Strait Nowcast/Forecast System) is an integration of a data-assimilating, dynamical ocean model, a statistical data-analysis model, and various data streams for ocean bathymetry, climatological data, surface forcing, open boundary forcing, and observations for data assimilation (Ko et al. 2008). The dynamic ocean model in the system is the Navy Coastal Ocean Model (NCOM) (Martin 2000), developed at Naval Research Laboratory (NRL) and in operation at the US Naval Oceanographic Office in various configurations (Rhodes et al. 2002). NCOM is a hybrid sigma/z-level primitive equation, free-surface model, applying the hydrostatic, incompressible, and Boussinesq approximations. This model is similar in its physics and numeric to the Princeton Ocean Model (POM), but uses an implicit treatment of the free surface.

The LZSNFS model domain covers the Luzon Strait, northern South China Sea and part of the western North Pacific Ocean (Fig. 3) with ~2.3 km horizontal resolution. There are 41 sigma-z levels in the model; 19 sigma layers are used from the surface down to a depth of 147 m, and z-levels are used below. The model ocean topography is derived from the NRL global Digital Bathymetry Data Base 2-min (DBDB2) (http://www7320.nrlssc.navy.mil/DBDB2_WWW/), with improvement by blending high resolution bathymetry data from the Ocean Research Center at National Taiwan University.

The LZSNFS applies the East Asian Seas Nowcast/Forecast System (EASNFS; Ko et al. 2009; Lee et al. 2013; Ko et al. 2014) that covers entire East Asian Marginal Seas for open boundary conditions (BCs). The EASNFS for this application does not include tides. To simulate internal tides/waves, LZSNFS are forced with tidal heights and transport of eight tidal harmonics (K₁, O₁, P₁, Q₁, M₂, S₂, K₂, and N₂) taken from TPXO7.2 (Egbert and Erofeeva 2002). Tides are applied to model depth-averaged normal velocity u, with elevation η, at open boundary by combining forcing from EASNFS using a forced radiation BC modified from Flather and Proctor (1983):

$$u = (u_{R} + u_{t} ) \pm c [(\eta_{R} + \eta_{t} ) - \eta ]/h,$$

where subscript R and t denote variables from the regional model (EASNFS) and from the tidal model, respectively, and c is the barotropic wave phase speed: $c = \sqrt {gh}$, with g being the gravitational constant and h the water depth. For the BCs of tangential velocity, temperature and salinity, the first-order-upwind advection scheme was utilized.

The atmospheric forcing consists of air pressure, wind stress, solar radiation, and heat fluxes from Coupled Ocean/Atmosphere Mesoscale Prediction System (COAMPS), a high-resolution Navy operational regional weather forecast model.

LZSNFS assimilates satellite altimeter data to produce Kuroshio and mesoscale eddies that have been shown to have an impact on the generation and propagation of large amplitude internal waves (e.g., Ma et al. 2013). A vertical weighting function and a scale separation scheme are applied for the data assimilation to prevent attenuation of high frequency internal tides/waves (Chen et al. 2013; Ko and Wang 2014).

Appendix 2: Knife-edge model

The knife-edge model represents the baroclinic surface elevation in cylindrical coordinates as:

$$\begin{aligned} \varsigma (t,r,\theta ) = \varsigma_{0} \left(\frac{{r_{0} }}{r}\right)^{1/2} \exp (i\vec{k}_{r} {\kern 1pt} .{\kern 1pt} \,\vec{r} - {\text{iwt}} + \phi_{0} ) \hfill \\ for\;|\theta - \theta_{0} |\; < a_{0} /2\,r_{0} , \hfill \\ \end{aligned}$$

where r is the distance from the center, Ϛ ₀ amplitude of baroclinic surface elevation at r ₀ and ϕ ₀ arbitrary phase. Equation evaluated for r > r ₀ Wave is evaluated for r > r ₀. Wave is prevented from radiating in all directions by assigning length a ₀, direction ₀ with range $\;\theta_{0} \pm (a_{0} /2r_{0} ),\;{\text{and}}\;\varsigma = 0\;{\text{elswhere}}$.

A ridge where generation occurs can be represented by a line source. Generation from several ridges can be superposed with this knife edge model. Propagation angle is established by the strongest barotropic tidal current direction. The phase is chosen for baroclinc currents to have the same phase as the maximum cross ridge barotropic tide. The wavelengths are calculated based on stratification used in model. The surface elevation is determined for the generated wave at the line source to carry the energy across the channel predicted by the knife-edge model (Rainville et al. 2010). Phases ϕ ₀ are derived from the OSU (University of Oregon) tidal model.