**1. Introduction**

When waves are obliquely incident to a slender water body at a large angle relative to the direction normal to the shoreline, shoreline undulation may develop owing to highangle wave instability [1], resulting in the formation of sand spits. Serizawa et al. [2] predicted beach changes under the condition that waves were obliquely incident to the direction normal to the shoreline at an angle over 45◦ using the BG model (a model for predicting 3-D beach changes based on Bagnold's concept) and showed that sand spits can develop by this instability mechanism. Although real examples of shoreline instability are limited in number because the wave incidence angle is ±20◦ at most on ordinary coasts, examples can be found in a slender water body. Since Lingayen Gulf in the Philippines is a slender bay, shoreline undulations caused by this instability mechanism occur downcoast of the river deltas, significantly affecting shore protection on the coast. Anthony et al. [3] described the formation of the sand spits associated with the Volta and Senegal River deltas, which show complex patterns of morphodynamic development while also strongly reflecting the recent impacts of human activities, such as the marked reduction in sand supply on the eastern coast of Ghana. In this study, the formation of the shoreline undulations downcoast of the river deltas of the Balili and Aringay Rivers was studied in

**Citation:** Uda, T.; Noshi, Y. Recent Shoreline Changes Due to High-Angle Wave Instability along the East Coast of Lingayen Gulf in the Philippines. *Geosciences* **2021**, *11*, 144. https://doi.org/10.3390/ geosciences11030144

Academic Editors: Jesus Martinez-Frias and Gianluigi Di Paola

Received: 14 December 2020 Accepted: 9 March 2021 Published: 22 March 2021

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the same manner using satellite images together with a field observation on 23 February 2018. The evolution of the shoreline undulation downcoast of the Aringay River delta was compared with the results of the numerical simulation using the BG model [4] on the formation of a sand spit at the point where an abrupt change of the shoreline configuration takes place. Furthermore, a sand spit at Santo Tomas located near the bottom of Lingayen Gulf was selected as another study site (Figure 1).

**Figure 1.** Satellite image of Lingayen Gulf (for location, 16◦30 45.27" N, 120◦7 11.62" E).

Similarly to the studies on the sand spits of the Rhône River delta by Sabatier and Anthony [5], the formation of the sand spits in relation with the evolution and morphology of the Danube mouths and deltaic lobes in the Black Sea basin [6], and the comparison of evolution and dynamics of selected representative deltaic spits [7], the evolution of the shoreline undulations was investigated using satellite images in this study. Furthermore, to predict shoreline changes of a sand spit and consider the measures against beach erosion on a coast around a sand spit, quantitative estimation of the rate of longshore sand transport is important, so the rate of longshore sand transport around this sand spit was estimated from the temporal change in the foreshore area of the sand spit. As mentioned by [5], understanding the functional aspects of spit formation and growth is important for the management of the delta shoreline and its sediment budget by public authorities. In this study, it is pointed out that useful information regarding shore protection of the coasts in Lingayen Gulf can be obtained by the analysis of topographic changes under high-angle wave conditions, given morphological characteristics of the bay shape and arrangement of rivers.
