*3.1. Model Validation*

Considering that we only use barotropic tidal forcing to drive the model, the model run is primarily validated using TPXO7.2 data. Figure 3 gives the co-tidal charts for the first four tidal constituents derived through harmonic analysis over the final 30 days of the model results. The co-tidal chart of *M*<sup>2</sup> (Figure 3a) is in good agreement with previous tidal current measurements [29]. Our model also reproduced the degenerated counterclockwise amphidromic system of *K*<sup>1</sup> and *O*<sup>1</sup> near the northern tip of Luzon Island, which was

mentioned in previous simulations [23,30,31]. Notably, wave-like stripes exist in the modelpredicted amplitude and phase. These features are the manifestation of spatially coherent internal tide modulations with associated wavelengths [32].

**Figure 3.** The co-tidal charts calculated from model-predicted sea-level height for (**a**) *M*2, (**b**) *K*<sup>1</sup> , (**c**) *S*2, and (**d**) *O*<sup>1</sup> . Patched colors represent amplitude, gray lines represent phase (in deg and in reference to 0◦ ).

**Figure 4.** The root mean square difference between the model and TPXO7.2 data of zonal barotropic velocity for (**a**) *M*2, (**b**) *K*<sup>1</sup> , (**c**) *S*2, and (**d**) *O*<sup>1</sup> .

The root mean square difference *D* between the model and TPXO7.2 data for sealevel height and zonal barotropic velocity is used here [33]. The barotropic velocities *U* = <sup>1</sup> *H u* and *V* = <sup>1</sup> *H <sup>v</sup>* are defined as depth-averaged velocities, where (·) = <sup>R</sup> *<sup>η</sup>* −*d* (·)*dz* is the depth integration of a quantity from the bottom −*d* to surface *η* and the total water depth *H* = *η* + *d*.

$$D = \sqrt{\frac{1}{2}(A\_o^2 + A\_m^2) - A\_o A\_m \cos(\phi\_o - \phi\_m)}\tag{1}$$

where *A* and *φ* are the amplitudes and phases of a given constituent, respectively, and subscripts *<sup>o</sup>* and *<sup>m</sup>* refer to the TPXO7.2 data and our model, respectively. The domainaveraged *D* of sea-level height in areas deeper than 200 m is 3.03, 5.46, 1.34, and 2.78 cm for *M*2, *K*1, *O*1, and *S*2, respectively. The distributions of *D* of the zonal barotropic velocity

in the Luzon Strait for the first four tidal constituents (Figure 4) show small values in most regions, which indicates a good agreement between the model results and the TPXO7.2. Relatively larger *D* values appear mainly above ridges, where water is shallow. Our model is fully baroclinic and has a slightly different topography compared to the TPXO7.2 model, which has a stronger effect in shallow areas. Data assimilation is not included in our case but may also result in differences.

Figure 5 shows the comparison of time series of sea-level height *η* at L1 between our model prediction and TPXO7.2. L1 is located on the side of a seamount in the Luzon Strait and is hypothesized to be a generation source for internal waves [16]. These two time series are in good agreement, and both show well-recognized spring-neap characteristics. The heights of high tides and low tides are different, but the phases match very well. Therefore, our model is suitable for the simulation of tidal characteristics.

**Figure 5.** The time series of sea-level height at L1. The blue line represents the model results, the red line represents the TPXO7.2 results.
