Field observations were conducted from 14:00 August 18, 2020, to 10:30 August 20, 2020, during Typhoon Higos. Two instrumented stations were deployed on the south (#1) and north (#2) sides of the mouth-bar region in the ME ( Figure 1C ). Acoustic wave and current (AWAC) measurements were taken to determine the significant wave height, wave period, and wave direction, with the sampling period and the number of observations per period set to 30 min and 1,024, respectively. The tidal effect from the observed data by the AWAC was removed by reducing the observed tide level at each sampling period based on Geng et al. (2014). The cross-zero method was applied to calculate the significant wave heights and wave periods. In addition, hourly significant wave height and wave direction data recorded at a long-term buoy station ( Figure 1A ) were collected for analysis.

The wave steepness is used to evaluate variations in wave conditions (Thompson and Reynolds, 1976). During wave propagation, the condition of the wave field can be described in terms of wave composition, including wind waves, swells, and immature swells. The wave steepness can be calculated as follows:

where δ is the wave steepness, H s is the significant wave height, L is the wavelength calculated using the wave dispersion equation, T is the significant wave period, k is the wavenumber, and h is the water depth. According to Thompson et al. (1984), δ ≥ 0.025 represents wind waves, δ < 0.01 represents swell, and 0.01 ≤ δ < 0.025 represents immature swell conditions.

When waves propagate into coastal and estuarine regions, depth limitation causes enhanced bottom friction, leading to the dissipation of the wave. Based on Kang and Di Iorio (2006), the dissipation rate induced by bottom friction was calculated from the energy conservation equation of steady-state waves:

where F is the energy flux, E is the total wave energy, c g is the wave group velocity, and x is along the direction of wave propagation. Although Equations 2 and 3 neglect the contributions of other wave dissipation processes, these calculations include observed wave information and reflect the temporal variation of wave dissipation. Thus, integrating Equation 2 along the direction of wave propagation x,

where <> represents the spatial mean, θ is the angle between the wave propagation direction and the line connecting two observation stations, and L s is the distance between the two stations. Equation 4 can be rewritten as

where the subscripts o and i represent the outer and inner locations, respectively.

As for the observation station where wave period information was not collected, the component F in Equation 5 is replaced by E because the evolution of wave energy was directly associated with the variation of wave height under the major effect of wave transformation (Pruszak et al., 2008). Thus, the wave energy dissipation rate < ϵ E > was calculated as follows:

Moreover, Normalized Dissipation Rate (NDR) is proposed to explore the relatively dominant variation of the wave dissipation and convergence processes between the analytical points and was calculated as follows:

where ∫ 0 t < ϵ f + > and ∫ 0 t < ϵ f - > are respectively the positive and negative temporal integration results of dissipation rate < ϵ f > at each profile. Therefore, NDR closer to 1 or −1 means dissipation- or convergence-dominant, respectively.

Numerical simulations were performed using the TELEMAC–MASCARET modeling system (www.opentelemac.org), which was developed by the Laboratoire national d’Hydraulique et Environnement (LNHE), a research department of Électricité de France (EDF). The TELEMAC system is an integrated modeling tool that includes free-surface hydrodynamics, sediment transport, water quality, and wave and groundwater flow modules in which simulation is conducted based on the finite element method, and the model domain is discretized in the form of an unstructured grid. This system is suitable for coastal and estuarine environments with irregular and complex geometries. In this study, we used the TELEMAC wave module TOMAWAC for simulation.

Wave heights at all stations increased significantly during the typhoon, showing patterns similar to wind speed, but with differing peak times ( Figures 4A, B ). Wave height increased sharply as the typhoon approached, reaching maxima of 4.80 m, 3.98 m, and 3.69 m on August 19, 2020, at 00:00, 04:00, and 05:30 at the buoy station, station #1, and station #2, respectively. Wind speed reached maxima of 26.60 m/s and 27.30 m/s on August 19 at 02:00 and 06:00 at the buoy and Macau stations, respectively. Thus, wave height peaked before wind speed. The time of peak wave height was 2 h earlier than the time of peak wind speed at the buoy station. At stations #1 and #2, the peak wave height occurred 2 h and 0.5 h earlier, respectively, than the time of maximum wind speed at the Macau meteorological station within the ME.

The wave and wind directions corresponded to the typhoon cyclone structure, and their fluctuations increased landward ( Figures 4C, D ). The wave direction captured at station #2 fluctuated strongly due to mouth-bar disturbance driven by the presence of an obstacle at the entry of the estuary. In contrast, the data captured at the buoy station and station #1 were relatively stable. However, the wave direction shifted significantly when the wind speed increased rapidly from 16.3 m/s and 14.4 m/s to its maximum at the buoy station and Macau station, respectively. Specifically, the wind and wave directions both shifted from northeastern to northwestern at the buoy station, while the wave direction shifted from southeastern to southern at station #1 with the wind direction transitioning from northeastern to southern at Macau station. The transition trend indicated that the directions of wind and wave vectors were comparable in this period due to the enhancement of wind force. With the typhoon decaying, the wind directions at both stations gradually transitioned to the east in the counterclockwise direction. The wave direction presented another shift from northwestern back to northeastern on August 19 at 15:00 at the buoy station, while the wave vectors remained in the south at station #1. Thus, the forcing intensity of wind to wave changes with typhoon movement; the significant transition of wind and wave directions aligned with the approach of typhoon cyclone structure. Moreover, the recovery period of wave direction was longer at the outlet of ME than in the open sea.

The temporal variation in the wave period had no apparent regularity but showed similar trends at stations #1 and #2 ( Figure 4E ). The average wave periods were 5.19 s and 3.96 s at stations #1 and #2, respectively, indicating a landward attenuation of the wave period. The wave period at stations #1 and #2 shortened during the peak wave height, which could be caused by the strong wave current interaction due to the current having a regulated effect on the wave period during typhoons (Cui et al., 2012).

Wind waves were the dominant component of waves while the typhoon approached at both stations ( Figure 5A ). The wave steepness sharply increased from 0.043 and 0.041 to 0.171 and 0.187 at stations #1 and #2, respectively, indicating enhanced instability of wave structure and the wind waves composing the wave field in the mouth-bar region of ME under the intense typhoon wind force. After the typhoon landfall, the wave composition remained wind wave-dominant at station #2, while the composition gradually transitioned to immature swell dominance at station #1. With the wind force continuously decaying, the wave steepness showed a declining trend, reducing to 0.019 and 0.066 on August 19 at 12:30 (i.e., 6.5 h after typhoon landfall) at stations #1 and #2, respectively. Subsequently, the wave steepness at station #1 remained below 0.025, while the value at station #2 stayed above 0.025. The decreased in wave steepness indicated a rapid decay of the intense wind wave component and the reappearance of the swell component in the coastal regions. Moreover, the spatial variation of wave composition pointed out that the wind waves persisted longer within the mouth-bar region compared to its outer area.

The intensity of wave dissipation and convergence increased as the typhoon approached ( Figure 5B ). The absolute value of the dissipation rate from the buoy station to station #1 increased from August 18 at 15:00 to August 19 at 01:00, with wave height reaching its maximum on August 19 at 00:00 at the buoy station. The absolute value of the dissipation rate from station #1 to station #2 increased from August 19 at 00:00 to August 19 at 14:30, with wave height reaching the maxima on August 19 at 04:00 and 05:00 at stations #1 and #2, respectively. Thus, the dissipation rate increased with the intensification of the wave field, which resulted from the approach of a typhoon.

Wave propagation from the buoy station to station #1 was dominated by the dissipation process ( Figure 5B ). The wave energy dissipation rate < ϵ E > reached its maxima of 4.40 J/m³ when the wave height was the highest at the buoy station. The temporal integration of the wave energy dissipation rate ∫ 0 t < ϵ E > was 7.17 J·h/m³, indicating that the positive component was much larger than the negative component ( Table 1 ). Thus, wave dissipation dominated the wave propagation from the open sea to the outer region of the mouth bar in ME.

Wave propagation from station #1 to #2 was alternately dominated by the processes of dissipation and convergence ( Figure 5B ). When the wave height at station #1 reached its maximum, wave dissipation dominated the wave propagation with a dissipation rate < ϵ f > of 7.64 W/m². When the wave height at station #2 reached its maximum, wave convergence dominated the wave propagation, and the dissipation rate < ϵ f > was −4.79 W/m². After the typhoon landfall, the fluctuations of dissipation rate gradually weakened and remained in negative values as the typhoon decayed. The temporal integrals of the wave dissipation rates < ϵ f > and wave energy dissipation rates < ϵ E > were −27.08 W·h/m² and −12.99 J·h/m³, respectively, demonstrating that the negative components were greater than the positive components ( Table 1 ). Thus, wave propagation within the mouth-bar region was dominated by wave convergence, and enhancement of both wave dissipation and convergence occurred during typhoons.

Simulated wind fields during Typhoon Hagupit are shown in Figures 6A–H . The wind field before the typhoon landfall contained two regions of high wind speed, which coincided with the movement of the typhoon center. The maximum spatial area with wind speeds >20 m/s occurred on September 24, 2008, at 03:00 (3.75 h before typhoon landfall), covering the coastal areas from Jiangmen to Huizhou, and wind speed gradually decreased from west to east. Wind direction corresponded to the typhoon cyclone structure before landfall, while the study area was dominated by onshore wind after landfall.

Simulated wind fields during Typhoon Hato are shown in Figures 7A–H . The wind fields contained one region of high wind speed, which was located near the typhoon center and rotated counterclockwise. The maximum spatial area with wind speeds over 20 m/s occurred on August 23, 2017, at 09:00 (3.83 h before typhoon landfall), covering the coastal regions from Zhuhai to Shenzhen, with wind speed gradually decreasing from the typhoon center to the outer bands. Wind direction corresponded to the typhoon cyclone structure prior to landfall, whereas the western part of the study area was dominated by offshore and longshore winds, while the eastern part of the study area was dominated by onshore wind after landfall.

Simulated wind fields during Typhoon Higos are shown in Figures 8A–H . Their characteristics were similar to those during Typhoon Hato due to their similar tracks and landing locations. However, the maximum value of wind speed and the scale of typhoon cyclone structures were smaller than those during Hato due to the weaker intensity of Higos. Specifically, the maximum spatial area of the region with wind speeds over 20 m/s occurred on August 19, 2020, at 02:00 (4 h before typhoon landfall), covering the coastal region from Zhuhai to Hong Kong and with wind speed gradually decreasing from the typhoon center to the outer bands.

Typhoon-induced surface waves were predominantly composed of wind waves. The region with values exceeding 0.025 occupied over 99.37%, 99.82%, and 97.42% of the total study area at the landfall time of Typhoons Hagupit ( Figure 9C ), Hato ( Figure 9G ), and Higos ( Figure 9K ), respectively.

During Typhoon Hagupit, the region with wave steepness lower than 0.025 corresponded to the outer band of typhoon cyclone structures ( Figures 9A–C ), which were in lower wind speed before typhoon landfall ( Figures 6A–E ); subsequently, the values gradually weakened with typhoon decaying ( Figure 9D ). During Typhoon Hato, the wave steepness at the coastal areas from Jiangmen to Maoming was lower than 0.025 and gradually increased as the typhoon approached, while the values remained in high intensity in the rest of the study area ( Figures 9E–G ); then, the values decayed more rapidly in the open sea than in the estuarine regions after typhoon landfall ( Figure 9H ). During Typhoon Higos, the region with a wave steepness lower than 0.025 covered the coastal and offshore regions from Jiangmen to Zhanjiang, with values showing an increasing tendency before typhoon landfall ( Figures 9I–K ); subsequently, the values decreased after typhoon landfall, whereas the estuarine regions had higher values than the open sea ( Figure 9L ).

Wave energy was calculated through the wave height, indicating that the temporal and spatial variations of wave height directly reflect the wave energy evolution within the study area during typhoons. The spatial extension of typhoon-induced wave fields coincided with the disturbance area of high wind speeds and the intense wave field located at the east side of the typhoon center ( Figures 6I–P , 7I–P , 8I–P ). The maximum wave heights within the study area were 5.74 m, 5.59 m, 6.39 m, 6.14 m, 5.88 m, 6.06 m, 5.68 m, and 5.28 m; 4.75 m, 5.79 m, 6.16 m, 6.49 m, 5.11 m, 3.84 m, 2.65 m, and 2.12 m; and 4.93 m, 5.47 m, 5.38 m, 5.23 m, 4.97 m, 3.75 m, 2.78 m, and 1.77 m sequentially at the simulated time during Typhoons Hagupit, Hato, and Higos, respectively ( Figures 6I–P , 7I–P , 8I–P ). The results were in positive correlation with the temporal variations of the highest typhoon wind speed, whereas the values of Hato were overall higher than those of Higos and comparable with Hagupit’s results before typhoon landfall and then reduced more rapidly when typhoons decayed.

The simulated wave fields during Typhoon Hagupit are shown in Figures 6I–P . Two regions of intense wind speed induced two regions of high wave height and then gradually merged as the typhoon moved landward. The maximum area with wave heights >2 m extended from the coastal regions of Maoming to Jieyang and covered over 79% of the coastline of Guangdong Province. Wave energy dissipations were centrally radiated, and the spatial dissipations were sharper toward the shore compared with those toward the open sea. Beyond that, the complex typhoon structures ( Figures 6A–H ) induced irregular wave fields, indicating that the spatial regularity of wave energy was changing with no apparent trend.

In contrast, the typhoon structures of Hato and Higos were regular and compact ( Figures 7I–P , 8I–P ). The induced wave fields were approximately circular, and their spatial expansions were smaller than those during Hagupit ( Figures 6I–P , 7I–P , 8I–P ). The region of wave heights >2 m kept expanding and covered over 45% and 30% of the coastline of Guangdong Province during Hato and Higos, respectively, while the significantly intense wave fields (i.e., wave height >4 m) had a slighter expansion and shifted corresponding to the typhoon movement. Along the moving tracks of typhoons, the waves propagated farther on their east sides and induced the non-negligible risks of intense waves attacks on the eastern coast of Guangdong, even though the typhoons did not directly make landfall in this region. Moreover, the wave height maintained two regions with high values within the offshore area of ME after Hato’s landfall ( Figure 7N ), the inner one located at the mouth-bar region and the second one located on the southwestern side of Da Wan Shan islands. The maximum wave heights in the inner and outer regions were 3.84 m and 3.59 m, respectively. In contrast, the wave field only maintained one region in high wave energy at the mouth-bar region of ME after Higos’s landfall, and the maximum wave height was 3.49 m ( Figure 8N ).

The PRE contains multiple estuarine configurations, mainly including the bell-shaped bays (i.e., LDY and HMH) and a prismatic estuary upstream into the mainstream of the Xijiang River (i.e., ME) ( Figure 1 ). In addition, the morphological changes from the open sea to the estuarine regions had critical effects on wave propagation and induced wave dissipation and convergence. Thus, three analytical profiles were set up in the central part of LDY, ME, and HMH, starting from the 50-m isobaths, with analysis points inside the 30-m isobaths spaced equally ( Figures 2 , 10A ). The NDR was calculated from 12 h before the typhoon landfall to 12 h after landfall ( Figure 10B ), and the temporal variation of wave dissipation rate < ϵ f > of each profile is shown in Figure 11 .

The wave propagation and dissipation varied among the estuarine regions. First, the waves directly attacked ME with high intensity, while LDY and HMH prevented the intense waves from propagating into the other estuaries. The maximum wave heights at the time of landfall were 0.72 m, 1.05 m, 0.85 m, 0.72 m, 2.75 m, 1.47 m, 0.28 m, and 0.26 m; 0.74 m, 0.97 m, 0.95 m, 0.84 m, 1.41 m, 1.11 m, 0.52 m, and 0.64 m; and 0.46 m, 0.67 m, 0.66 m, 0.61 m, 1.80 m, 1.50 m, 0.29 m, and 0.33 m at the outlet of the estuaries from east to west during Typhoons Hagupit, Hato, and Higos, respectively ( Figures 1A , 6I–P , 7I–P , 8I–P ). Second, the upstream expansions of intense waves were stronger at LDY and HMH than at ME, pointing out that the wide outlets and gradual contraction of the bell-shaped bays were conducive to the landward propagation of typhoon waves. The farthest upstream extensions of the 1-m isoline of wave height were 4.95 km, 65.48 km, and 26.73 km at 4 h after Hagupit’s landfall ( Figure 6O ); 4.92 km, 69.97 km, and 33.60 km at 2 h after Hato’s landfall ( Figure 7N ); and 4.84 km, 67.62 km, and 27.72 km at 4 h after Higos’s landfall ( Figure 8O ) at ME, LDY, and HMH, respectively, indicating that the maximum upstream propagating distances within the bell-shaped bays could be tens of times greater than those within a prismatic estuary during typhoons. The results also pointed out that the typhoon-induced waves kept propagating upstream after the typhoon landfall. Third, the wave heights were larger in the western part of LDY and HMH, which were mainly induced by the blocking effect of islands located on the southeast side of the bays. In contrast, the waves were under similar conditions on both sides of ME ( Figures 6I–P , 7I–P , 8I–P ). Furthermore, the spatial variation of wave steepness indicated that the intense wind wave component dissipated more slowly in the estuarine regions than in the offshore regions ( Figures 9D, H, L ).

The landward wave propagation changed significantly during typhoons. First, the amplitudes of wave dissipation and convergence significantly increased with typhoons approaching and decreased rapidly after landfall along the analytical profiles ( Figures 5B , 11 ). Second, the temporal variation of < ϵ E > shifted from being convergence-dominated to being dissipation-dominated at almost all profiles, indicating the intense wave propagation was a short-term change ( Figure 11 ).

In addition, the morphological changes from the deep offshore areas to the shallow coastal regions influence the overall trend of wave-propagated variation. Wave energy evolution had a tendency to convert from being convergence-dominated to being dissipation-dominated when the wave propagated toward the PRE. The NDR gradually converted to being positively dominated within the 30-m isobaths, and the transition depths at profiles HMH, ME, and LDY were between 9.86 m and 30.02 m, 8.01 m and 29.96 m, and 14.07 m and 29.64 m during the selected typhoons, respectively ( Figure 10B ), indicating that the depth-limited dissipation gradually enhanced due to the wind wave–bottom interactions (Dolgikh et al., 2013). Moreover, wave heights had an increasing tendency toward the mouth-bar region due to the interaction between wave, jet spreading, and bottom friction under normal weather conditions (Nardin et al., 2013). Likewise, waves tend to converge as they pass through the mouth-bar region during typhoons ( Figure 5B ), and the wave heights remained relatively high after typhoon landfall ( Figures 7N , 8N ). Nonetheless, the dominant processes of wave propagation between each analytical point showed inconsistency during the selected typhoons ( Figures 10B , 11 ), which were related to the uniqueness of each typhoon-induced wave field based on the unstable typhoon intensity, track, and scale.

Typhoons are extreme weather events with unpredictable track, speed, intensity, and scale before generation. In this study, the track of Hagupit covered nearly the whole coastal region of Guangdong, whereas Hato and Higos had tracks covering only the central and eastern coastal regions ( Figure 1A ). The maximum wind speed of both Hagupit and Hato was over 50 m/s, and that of Higos was only 35 m/s. Thus, the typhoons selected for analysis are sufficiently representative for discussion of the dominant typhoon-related factors affecting the intensity, propagation, and dissipation of the generated wave field.