*4.1. Hydrodynamic Response*

Low-pass filtered water level variations during cold front and hurricane are shown in Figure 5a,b, respectively. Water level dropped about 15 cm after the cold front passage during northerly wind, so that one can see an obvious trough at 1500 UTC on 6 January. This is because northerly wind after the cold front passage continuously blew the water out of the bay, leading to the water level minimum. As northerly wind weakened, water level begun to rise. On the other hand, when the water level was under the influence of Hurricane Barry, it is found that there was a surge of 40 cm after the hurricane's landfall, when wind also reached the maximum of 14.5 m/s. The surge resulted from the southerly wind after Barry's landfall, which blew the water from the coastal ocean into the bay. Compared with the trough induced by the cold front, the surge caused by Hurricane Barry is about 3 times larger in terms of magnitude.

**Figure 5.** Water level variation during different weather types. (**a**) a cold front event and (**b**) Hurricane Barry.

Figure 6 shows the surface (Figure 6a) and bottom (Figure 6b) flows at 1200 UTC on 5 January 2014 before cold front passage when southerly wind dominated (with maximum magnitude of about 3 m/s). Flows inside the bay were in the wind's direction, flowing from south to north. Shallower and surface water had a larger magnitude of flows. Surface and bottom flows were unidirectional, while surface flow had a larger magnitude. After the cold front's passage (Figure 6c,d), when northerly wind dominated (maximum magnitude of 13.5 m/s), flows inside the bay were also in the direction of the wind, flowing from north to south. However, there existed a strong return flow in the middle of the bay where it had a greater water depth, which is consistent with previous studies in many systems: currents for shallower water tends to move in the direction of wind, whereas against the wind's direction for the region with a greater water depth (e.g., [49,56]). Again, surface and bottom flows were mostly uniform, except that surface flow had a larger magnitude. This is because bottom flow is decreased by bottom friction.

Figure 7 shows the surface (Figure 7a,c) and bottom (Figure 7b,d) flows prior (Figure 7a,b) and after (Figure 7c,d) Hurricane Barry's landfall. During Hurricane Barry, wind was rotating clockwise. Before Hurricane Barry's landfall, wind in the northern quadrant was dominating (with magnitude of 10 m/s). As a consequence, both surface and bottom currents were flowing in the direction of wind, from north to south in the shallow water region. An apparent returning flow against the wind's direction occurred in the deeper water region. After the landfall of Hurricane Barry, southerly wind dominated with the magnitude reaching 14.5 m/s. The surface and bottom flow in shallower water were flowing in the direction of the wind, moving from south to north, while in the deeper water region, they were flowing against the direction of wind, moving from north to south. Similarly, surface and bottom flows were mostly unidirectional, except that the surface flow had a larger magnitude.

**Figure 6.** Surface and bottom flows influenced by the cold front event in January 2014. (**<sup>a</sup>**,**b**) are surface and bottom flows on 1200 UTC, 5 January 2014; (**<sup>c</sup>**,**d**) are surface and bottom flows on 1800 UTC, 1 January 2014.

#### *4.2. Water Volume Transport*

To examine the water transport through multiple inlets, water volume fluxes are calculated using the following equation [50]:

$$\mathbf{V(t)}|\mathbf{r} = \int\_{-H}^{\zeta} (\int\_{0}^{L} V\_{n}(\mathbf{x}, y, z, t) |\mathbf{r} \, d\xi) dz,\tag{9}$$

where *V* is the water volume flux in cubic meters per second. Γ is the transect perpendicular to the along-channel direction, *H* is the water depth, and ζ is the surface elevation. *Vn*(*<sup>x</sup>*,*y*,*z*,*<sup>t</sup>*) is the low-pass filtered along-channel velocity in different water depths. A positive sign means water is transported into Barataria Bay.

Figure 8 shows the volume flux through Caminada Pass, Barataria Pass, Pass Abel, and Quatre Bayou. Positive value means water is flowing into the bay, while negative values means water is flowing out of the bay. During the cold front event in January 2014, the results indicate that water volume flux through Barataria Pass was the largest. Before cold front passage at 0000 on 6 January, water was flowing inside the bay through Caminada Pass and Quatre Bayou, while it was transported out of the bay through Barataria Pass and Pass Abel, which is consistent with mode 2a in Li et al. [50] under southerly wind. After the cold front's passage, as wind changed its direction from the south quadrants to north quadrants, volume flux through the four inlets began to decrease, then started to flow into the bay. Interestingly, volume flux changed the sign at different time stages: volume flux through Barataria Pass changed its sign first, followed by Pass Abel, Caminada Pass, and Quatre Bayou at last, which means there was a period (from 2000 UTC on 6 January to 0000 UTC on 7 January) when water was flowing out of the bay through Barataria Pass, while flowing inside of the bay through the other three inlets. From 0000 UTC on 7 January, water was transported into the bay through both Barataria Pass and Pass Abel, but it transported out of the bay through the other inlets, which is consistent with mode 2b in Li et al. [50] under northerly wind.

**Figure 7.** Surface and bottom flows under Hurricane Barry in 2019. (**<sup>a</sup>**,**b**) are surface and bottom flows on 0600 UTC, 11 July 2019; (**<sup>c</sup>**,**d**) are surface and bottom flows on 1800 UTC, 14 July 2019.

During Hurricane Barry, wind changed direction from the northern quadrants to southern quadrants. Therefore, the volume flux changed its sign after Barry's landfall on 13 July 2019, flowing into the bay through Barataria Pass, Pass Abel, and Quatre Bayou at first, then flowing out of the bay through these inlets afterwards. Note that Caminada Pass had the opposite condition: water was flowing out of the bay and then into the bay after Barry's landfall. This pattern is not included in any mode in cold front-induced flows [50]. Obviously, the mode of hurricane-induced flows can be different from that due to cold fronts. Before Barry's landfall, Pass Abel had the largest inward flux under northerly wind, and after Barry's landfall, Barataria Pass had the largest outward flux with a magnitude reaching 2500 m<sup>3</sup>/s, which was about 4 times of that induced by the cold front.

**Figure 8.** Volume flux through four inlets. (**a**) are fluxes in four passes during cold front, (**b**) are fluxes in four passes during Hurricane Barry.
