*3.1. Spatial Distribution of ISWs*

Figures 1 and 2 show dozens of ISWs, whose crests appear as northward convex arcs, covering the vast region of the BS from the southern LS, to the shallow continental shelf, to the west of the Kangean Islands. The crests of those ISWs almost bordered Bali Island on the left and Lombok Island on the right in the LS, and they diverged significantly during the northward propagation in the BS, passing through almost the entire basin. For the wave (S4-b) observed from the MODIS image taken at 12:40 on 14 April (Figure 1d), its crest line spanned about 1.5 degrees of longitude in the BS basin with a length of nearly 200 km.

Moreover, most ISWs in the BS appeared in the form of multi-wave packets that contain a number of rank-ordered solitons. For example, there existed more than 20 solitons in the packet S4-b, and those solitons spanned more than 60 km along their propagation direction and filled nearly half of the area between the LS and the Kangean Islands. The distances between the solitons in the ISW packets decreased from the front to the rear of the packet, and solitons were highly concentrated in the packet rear. Comparisons between Figure 1c,d also demonstrate the evolution process of S4, featuring the newborn solitons in the packet rear during propagation.

Up to three multi-wave ISW packets appeared simultaneously in one satellite image. In the VIIRS image of 15 April (Figure 2a), three distinguishable wave packets (S7, 8 and 3-c) were distributed in the LS, the BS basin and the continental shelf to the west of Kangean Islands, respectively, occupying a large portion of the BS. Actually, in the majority of the satellite images presented in Figures 1 and 2, two multi-wave ISW packets are easily seen, suggesting the prevailing solitary waves in the BS near the time of the submarine wreck.

The locations of all leading ISW crests in 10 remote sensing images were extracted and plotted together to exhibit the distribution of ISWs (coloured curves in Figure 3a). It can be seen that, near the time of the submarine wreck, ISWs generally propagated toward the northwest, and thus, the ISWs were concentrated in the area north of Bali Island where the submarine wreck occurred. However, in the SAR images collected by Karang et al. from 2006 to 2011 and Karang et al. from 2014 to 2015 [14,29], most of ISWs propagated northeastward after being emitted from the LS, and those waves were mainly distributed in the area to the north of the Lombok Island rather than the Bali Island. This phenomenon indicates that the spatial distribution of ISWs in the BS has significant temporal variability, which may be modulated by dynamic processes such as mesoscale eddies. As is clear to all, ISWs in the area to the north of Bali Island were extraordinarily active in April 2021, which significantly increased the likelihood that submarines would encounter internal waves.
