**4. Formation of Shoreline Undulations Due to High-Angle Wave Instability** *4.1. Balili River Delta*

Figure 3 shows a satellite image of a rectangular area around the Balili River mouth, as shown in Figure 1, taken on 15 April 2006. In the lower Balili River, a minor distributary (R2) is separated from the main distributary (R1). In Figure 3, the Aringay River mouth was often closed by the elongation of a sandbar from the right bank, which was induced by the deposition of southward longshore sand transport. The shoreline extends straight southward in a 1.9 km stretch between the mouth of the distributary R2 and point A south of the mouth, and then the shoreline bends around point A at a right angle. The tip of the curved shoreline connects to point B at the jetty of the oil refinery factory with a wide

lagoon landward of the barrier island. Thus, a slender wetland separated by a barrier island extended in the west–east direction south of the distributary R2.

**Figure 3.** Satellite image of shoreline around Balili River mouth (15 April 2006).

Similarly, Figure 4 shows a satellite image, taken on 14 February 2014, of the same area. Points A, B, P, and Q are indicated in Figure 4 to explain, but in what follows, "point" is omitted for simplicity, and the shoreline configuration measured on 15 April 2006 is shown in each figure. In this case, the shoreline position was directly determined from the satellite images while leaving an occurrence of some error in determining the shoreline position because of the lack of field data, i.e., the tide level and beach slope.

**Figure 4.** Satellite image of shoreline around Balili River mouth (14 February 2014).

When referring to the tide level measured from January to December 2019 at San Fernando located at the entrance of Lingayen Gulf, the average of the monthly lowest and highest tide levels were −0.09 and +0.90 m, respectively, with a tidal range of 0.99 m. Detailed bathymetric surveys have not been carried out along the coast in Lingayen Gulf, but the berm height and foreshore slope were measured on a beach upcoast of a groin at Agoo, La Union near Narvacan on 23 February 2018, using two measuring staffs. The berm height and the foreshore slope were 2.0 m above mean sea level (MSL) and 1/7.7, respectively [11]. Given the tidal range of 0.99 m and the foreshore slope of 1/7.7, the maximum variance of the shoreline position becomes 7.7 m. This shoreline variance, however, is much smaller than the measured shoreline advance or the shoreline recession.

By 14 February 2014, a river delta had developed owing to the sediment discharge provided by the main channel of R1. Until this year, no shoreline changes were observed between P and A, although sediment supplied from the Balili River was deposited up to P. In contrast, a semicircular sandbar was newly formed with a shoreline protruding south of A. The formation of the sandbar clearly indicates that sediment supplied from the Balili River was transported southward and deposited as it turned around A. Until this time, the width of the sand spit increased because of the successive sand deposition along the shoreline of the sand spit, and in contrast, the lagoon width behind the sand spit decreased because of the deposition of sand from the distributary R2, as shown in Figure 4.

In Figure 5 showing an image taken on 11 June 2015, the river delta, which markedly protruded around the mouth, changed its form to a flat shape owing to erosion, and the curved sandbar south of A moved eastward as a whole.

**Figure 5.** Satellite image of shoreline around Balili River mouth (11 June 2015).

This sandbar further approached B until 20 February 2016 (Figure 6).

**Figure 6.** Satellite image of shoreline around Balili River mouth (20 February 2016).

A similar change continued until 1 December 2016, leaving an opening of the lagoon at the east end of the sandbar (Figure 7). In this year, a river delta was formed again around the mouth of R1 owing to sediment discharge from the river, indicating the occurrence of the intermittent sand supply from the Balili River.

**Figure 7.** Satellite image of shoreline around Balili River mouth (1 December 2016).

The village of Bauang, La Union south of B, indicated by a rectangular area in Figure 7, is shown in Figure 8.

**Figure 8.** Enlarged satellite image of rectangular area in Figure 7. Sites 1 and 2 are the locations where site photographs were taken in the field observation.

The center of the village is located 200 m north of the end of the coastal road. A concrete building destroyed by erosion remained in its vicinity, and five groins made of stones were constructed south of this building to maintain the shoreline. Figure 9 shows the coastal condition at Site 1 on the north side of the destroyed building.

**Figure 9.** North view from the second floor of a damaged building.

A wide sandy beach was formed upcoast of the groins because of the blockage of southward longshore sand transport by the groins. Similarly, Figure 10 was taken at Site 2 on top of groin No. 4, facing south. In this area, a wide sandy beach was formed in front of the village, indicating the effect of the groins that locally blocked longshore sand transport.

**Figure 10.** South view from groin No. 4.

In Figure 7, it should be noted that waves were obliquely propagating relative to the direction of the mean coastline in the offshore sea south of the Balili River, so the wave direction can be determined as the direction normal to the wave crestline. When setting the offshore point S at a location 3.2 km southeast of B, the wave direction at S was determined to be N37◦W. Since the direction normal to the straight shoreline between the mouth of R2 and A is N84◦W, waves were obliquely incident to the direction normal to the shoreline in a clockwise manner at an angle of 47◦. In Lingayen Gulf, waves of high directionality are incident from the north because of the shape of the gulf, and the wave direction determined from Figure 7 is in accordance with this general condition of wave direction. Since waves are obliquely incident at an angle over 45◦ to the direction normal to the shoreline, the shoreline undulation due to high-angle wave instability may develop, resulting in the development of a markedly protruded shoreline south of the Balili River.

When setting Q at a location where the shoreline most protruded in the south between A and B in Figure 7, the eastward distances of Q with reference to the location on 14 February 2014 were 910 m (June 2015), 970 m (February 2016), and 1020 m (December 2016). It was found that Q gradually approached the location by December 2016 as its movement velocity decreased. When the shoreline markedly protruded near A, as shown in Figure 7, the area near B was protected by a significant wave-sheltering effect of the sandbar itself against waves incident from the direction of N37◦W, and wave height decreases, resulting in the decrease in the movement velocity of the sandbar. Furthermore, when a sand body moves with the formation of a sand spit, the sand supply downcoast is suspended until the sand body reached downcoast, resulting in beach erosion. Because beach erosion has occurred in this manner in Bauang, La Union, it is considered that the groins have been constructed to protect the village against beach erosion.
