4.1. Maximum Winds and Water Elevations
As the counterclockwise wind pushes the ocean water above the land on the east side of the track, higher surges are expected to be on the east than on the west. For Case 1, the maximum wind intensity is above 40 m/s around the hurricane track line, and the maximum water elevation is above 1 m, mainly on the east side of the landfall area, as seen in
Figure 3a,b. For Case 2, the maximum wind intensity is increased to 50 m/s. A significantly larger domain around the east side of the track from the Texas to Mississippi coasts has a maximum water elevation higher than 1.5 m, as seen in
Figure 3c,d.
For Case 3, the maximum wind intensity went down to 35 m/s, and the maximum water elevation of 1 m has restricted only to the landfall area. Higher wind intensity means a stronger overland water push by the onshore wind on the east side of a hurricane. Similar effects of wind intensity of surges were observed in previous studies of Hurricane Irma and Hurricane Rita [
2,
3].
In
Figure 4, wind velocity vectors at the time of landfall for Cases 1, 2, and 3 are used to demonstrate further how wind velocity directions may impact storm surges. As shown in
Figure 1, Hurricane Harvey made landfall on 26 August at 0300 UTC when its center reached the northern end of San Jose Island, about 8 km northeast of Rockport, Texas [
18]. On the same day, after three hours at 0600 UTC, Harvey made a second landfall on the southeast of Refugio on the northeast coast of Copano Bay, west of Holiday Beach [
18].
Figure 4a–c show the first landfall, while
Figure 4d–f show the second landfall with different wind intensities. The strength of Harvey was more significant at the first landfall around Rockport than the second landfall around Copano Bay due to the land interactions in between. The arrows show the asymmetric and anticlockwise wind direction of the hurricane. The storm pushed the water up on the coast from the ocean to the east side of the hurricane, toward southeastern Texas, such as Seadrift, San Antonio Bay, the Freeport, Victoria, Galveston, and so on. This explains the high-water elevation of the east side of the hurricane, as seen in
Figure 3.
4.3. Water Level Timeseries for Observed and Model Predictions
The water level time series of Hurricane Harvey are compared with the observed water level at 12 locations in Texas. The identification number for the NOAA gauge stations and location bathymetric depths are presented in
Table 2. The stations are displayed on the map in
Figure 7a,b, and the stations, track, and wind vector snapshot at first landfall are shown in
Figure 7c.
The time series of water elevation for Hurricane Harvey in Case 1 and the observed data are displayed in red and black in
Figure 8(a1–a12), respectively. Additionally, the time series for different parametric cases are shown in
Figure 8(b1–b12). It is observed that the surges predicted by the model are generally underpredicted at most stations. A brief discussion of each station is given below. Please refer to
Figure 7a,b for each station’s geographical location and surroundings.
Bob Hall Pier is located on the left of the Hurricane Harvey track, on the east side of Padre Island, facing the Gulf of Mexico (see
Figure 7a). As shown in
Figure 8(a1), the time series for modeled storm surge closely matches the observed one, with some underpredictions between 0 m and 0.4 m. The surge at Bob Hall Pier is influenced by easterly and north-easterly hurricane winds pushing the water against the island, and the maximum surge recorded and modeled by Case 1 are about 1.3 m and 0.9 m, respectively. The tide frequency matches the observed data very well.
Corpus Christi station is situated by the mainland, in the inner part of Corpus Christi Bay, and is sheltered by Mustang Island. It experienced a lesser surge elevation and, in some instances, even a negative surge compared to neighboring stations such as Bob Hall Pier, which are located closer to the open ocean. The observed peak surge is about 0.4 m at Corpus Christie. Due to offshore winds on the west side of Hurricane Harvey, relatively mild flooding occurred in Corpus Christi Bay [
18].
Figure 8(a2) shows that the modeled storm surge time series matches the observed data with some overprediction between 0 m and 0.12 m. A receding pattern was observed once the hurricane made landfall due to westerly wind from the land to the ocean. To the west of the landfall location, the surge decreases with distance from the landfall, resulting from the competition between counterclockwise offshore winds and the storm’s forward motion [
2,
5,
25]. The tide frequency matches reasonably well with the observed data.
Aransas Pass, located northeast of Corpus Christie Bay, is open to the Gulf of Mexico. It experienced a similar surge as the Bob Hall Pier, but the sensor was not operational during the peak surge time, as depicted in
Figure 8(a3). Aransas Pass was very close to the center (eye) of Hurricane Harvey, which could have damaged the gauge and resulted in the absence of data during the peak surge [
26]. The surge peak modeled by Case 1 is approximately 1.2 m.
Port Aransas is situated near Aransas Pass but is slightly inland, sheltered by Mustang Island and San Jose Island. As a hurricane circulates counterclockwise, water is carried on from the ocean to the west of the hurricane, where the station is located (see
Figure 7).
Figure 8(a4) shows that the observed peak surge is 1.75 m, while Case 1 underpredicted the surge by 0.5 m. A significant surge was anticipated at Port Aransas as it was along the track’s path just before the initial landfall. A study on Hurricane Ike’s storm surges also showed the highest peak near the landfall location, as it experienced strong winds during and shortly after landfall [
6]. The tide frequency matches well with the observed data.
Rockport is in the west of Aransas Bay, sheltered by San Jose Island from the Gulf of Mexico, the mainland to the west, and Aransas National Wildlife Refuge on the north. As shown in
Figure 8(a5), Rockport experienced negative and positive surges due to the change of wind direction as the hurricane moved towards small islands and bay pockets. The Rockport station was very close to the center (eye) of Hurricane Harvey; this could have damaged the gauge and resulted in no data after midday of 26 August [
26]. The surge predicted by Case 1 underpredicts the observed surge by about 0.2 m.
The Aransas National Wildlife Refuge is in the west of Espiritu Santo Bay, sheltered by Matagorda Island from the Gulf of Mexico. The peak surge for this station increases monotonously and then decreases afterward. The peak surge modeled by Case 1 underpredicts the observed peak by about 0.5 m and subsequently underpredicts the surge for about two days.
Seadrift is surrounded by San Antonio Bay from the west and by land from the north and east. Initially, during the incoming hurricane, a negative surge was observed until the wind started pushing from the west to raise the surge peak to approximately 1.75 m. Seadrift was located east of the hurricane, very close to the center during the first landfall, which is why it had the highest peak. The surge remained strong for two days when the hurricane hovered over Houston. Case 1 showed a similar pattern of the surges, albeit underpredicted by about 0.4 m.
Port O’Connor is open to Matagorda Bay from the north and east and is loosely sheltered by the narrow strip of Towns Island from the Gulf of Mexico. The station experienced a peak surge of approximately 1 m, and Case 1 underpredicted the peak by about 0.3 m. This station consistently gets wind from the waterside and experiences elevated surges for about five days.
Freeport is by the Gulf of Mexico, open to the ocean. It has a peak surge of about 1 m. The surges remained elevated for five days due to wind from the ocean. The surge predicted by Case 1 is similar to those observed but underpredicted by about 0.3 m.
Galveston Bay Entrance connects Galveston Bay with the Gulf of Mexico. The station is open to the Gulf of Mexico and susceptible to a hurricane’s direct hit. The surging water can move north and west through the connecting passage between the bay and the ocean. The peak surge reached approximately 1 m and remained elevated at around 0.75 m for about five days. Case 1 underpredicted the surge by about 0.25 m.
Texas Point, Sabine Pass is open to the Gulf of Mexico from the east and southeast. It is sheltered by land from the north and west. When the wind came from the ocean during the early part of the hurricane, a moderate surge of 0.5 m is visible in
Figure 8(a11). A zero or negative surge was observed when the wind was predominantly from the south. Interestingly, contrary to the observed data, Case 1 shows a different tidal pattern, suggesting that the bathymetry resolution used in the model is not accurate in that location.
Calcasieu Pass is west of the Louisiana–Texas border in Cameron, Louisiana. It is open to the Gulf from the south and sheltered from the north. Calcasieu Pass experienced a consistent surge of about 0.5~0.75 m throughout Hurricane Harvey until the hurricane approached its vicinity, causing the surge to rise above 1 m, as shown in
Figure 8(a12). Case 1 underpredicted the surge by about 0.25 m.
The discrepancies between model results and observed data can be attributed to various factors such as wind and pressure data, bathymetry, and mesh inaccuracies [
2,
3,
27]. The significant errors resulting from insufficient grid resolution are primarily attributed to the misrepresentation of large velocity gradients caused by the irregular coastline [
27]. The choice of model parameters, including bottom frictions and wind drag coefficients, could also contribute to the discrepancies. The exclusion of rain and river flows in the current study may have further contributed to the observed discrepancies.
4.4. Effects of Wind Intensity and Forward Speed
The effects of wind intensity and forward speed on storm surges are important factors to consider in analyzing the impacts of hurricanes. The time series of water elevation for the rest of the cases are displayed in
Figure 8(b1–b12). In the case of increasing wind intensity by 25%, the surges increase consistently. The most significant impact of higher wind intensity is observed at Freeport Harbor, Entrance Galveston Bay, and Seadrift. These areas, particularly around the first landfall and on the east side of the hurricane, experience a substantial increase in surges. However, even with higher wind intensity, the surges are still underpredicted to some extent at stations like Bob Hall Pier, Port Aransas, Rockport, Aransas Wildlife Refuge, and Port O’Connor.
On the other hand, higher-intensity winds accurately predicted the surge at Seadrift, Freeport Harbor, Galveston Bay Entrance, and Calcasieu Pass. Over-prediction of the surge occurred with high wind intensity in Corpus Christi and Texas Point, Sabine Pass. Interestingly, the surge sometimes recedes due to the high wind intensity case at all stations. When higher-intensity winds blow onshore (from the ocean to the land), they increase the surge. Conversely, when the winds blow Offshore (from the land to the ocean), they recede the surge by pushing the water away from the station. Lower-intensity winds have the opposite effects on surge behavior.
Regarding the hurricane’s forward speed, a higher forward speed brings surges faster, and the peak is advanced from about 12 to 18 h. Conversely, slower forward speed delays the surge peak from about 18 to 30 h. A previous study on Hurricane Rita by Musinguzi et al. [
3] observed a phase lead of 36 h when forward speed was increased by 25%. Notably, at Corpus Christie and Port O’Connor stations, reducing forward speed had a more significant impact than increasing forward speed. This suggests that a slower hurricane gives some time for water to accumulate in the shallow estuaries while a fast-moving hurricane quickly passes over the region. The study on Hurricane Rita also found that increasing the storm’s forward speed reduces flooded volumes but increases peak surges by about 40% [
3]. These observations highlight the complex relationship between hurricane forward speed and storm surge characteristics.
4.5. High-Water Marks
High water marks (HWMs) left on structures and trees after hurricane storm surges dissipate provide valuable data for evaluating the performance of the ADCIRC + SWAN model. However, in the ADCIRC + SWAN domain, some HWMs locations remained dry for various reasons, such as lack of model mesh resolution, outdated bathymetry, or inaccurate input parameters [
2,
27]. Therefore, only the wet stations are considered for comparison with the observed HWMs.
Figure 9 displays the comparison between model HWMs and the observed data. The model HWMs are subtracted from the observed data, and a color-coded scheme is used to indicate the accuracy of the model predictions. Purple points represent well-predicted HWMs; the surge differences are within ±0.5 m. On the other hand, the dark-purple points indicate stations with surge differences of around ±1 m or higher, suggesting more significant discrepancies between the modeled and observed HWMs.
Figure 10, the scatter plots are used to visualize the comparison between the modeled and observed HWMs. These plots quantitatively assess the model’s performance in predicting the HWMs. The scatter plots help identify the extent of agreement or disagreement between the modeled and observed data points.
These visualizations and comparisons of the modeled and observed HWMs are crucial for evaluating the accuracy and reliability of the ADCIRC + SWAN model in capturing the storm surge impacts during Hurricane Harvey. They highlight areas where the model performs well (seven purple points) and areas where improvements are needed (dark-purple points) in predicting the HWMs.
In
Figure 10, the 45-degree red line is the parity line between the observed and modeled HWMs, as shown in
Figure 10. It serves as a reference for comparing the two datasets. The scatter plots also display the coefficient of determinations (R
2) and straight-line equations to quantify the relationship between the observed and modeled HWMs.
Based on the statistical analysis presented in
Table 3, Case 1 has an R
2 value of 0.6118, indicating a moderate correlation between the observed and modeled HWMs. The Mean Normalized Bias (B
MN) value of −0.337 indicates an overall underprediction by the model, and the Root Mean Square Error (E
RMS) is 0.17, suggesting an average deviation of the modeled HWMs from the observed data. It is worth noting that these statistical numbers and the quality of comparison between the model and observed data are considered reasonable based on previous studies [
2,
3,
27].
Comparing the different cases, Case 2 improved the HWMs comparison by decreasing the ERMS to 0.07. On the other hand, Case 3 increases the ERMS to 0.374, indicating more significant discrepancies between the observed and modeled HWMs.
Regarding the forward speed, Case 4 performed slightly better than Case 5 in terms of error, although both have higher ERMS values than Case 1.
These findings are consistent with previous studies on other hurricanes, such as Hurricane Irma [
2].
4.6. Wave Effects
In this study, the contribution of waves to the rise of ocean water levels during a hurricane is examined in addition to storm surge and tide. Waves increase ocean water rise through wave runup and wave setup [
7]. Wave runup occurs when waves break and propel water onto beaches, while wave setup happens when wave runup accumulates and has nowhere to go but onto the land. The hurricane storm surge is simulated in Case 6 using ADCIRC without considering any wave effects.
The time series of a hurricane storm surge at 12 stations are shown in
Figure 8 in the light-green line. From the comparison between the red (Case 1—with the wave) and light-green (Case 6—without wave) lines, it is evident that wave effects almost always increased the surge in the order of centimeters. However, the wave contribution to the surge varied and reached up to 0.2~0.3 m in most stations. The difference is pronounced during the peak hurricane duration. Compared with observed data, ADCIRC + SWAN and ADCIRC slightly underpredict the surge in all stations except for Corpus Christie and Texas Point, Sabine Pass, where the models overpredicted surges.
The wave results from ADCIRC + SWAN are compared against the NOAA tidal gauge station and buoy data.
Table 4 provides information about the NOAA tidal buoy stations used in the study, including their coordinates, bathymetry, and observed Significant Wave Height (SWH) and Average Wave Period (AWP) peaks, as well as case-simulated SWH and AWP peaks.
The analysis of the simulated wave focuses on comparing SWH and AWP three hours before the first landfall, during the first landfall, and during the second landfall.
Table 4 provides a summary of the observed SWH and AWP peaks, as well as the corresponding values for Case 1.
In
Figure 11, the first column (i.e.,
Figure 11a,c,e) demonstrates the SWH and the second column (i.e.,
Figure 11b,d,f) shows AWP. Before and during the first landfall, the SWH exceeded 7 m due to the long fetch of the Gulf of Mexico. The entire coastal area around the landfall experiences significant SWH due to uninterrupted fetch. Similar observations were made for Florida’s east coast during Hurricane Irma [
7]. During the second landfall, the SWH is around 6 m, slightly lower than the first landfall SWH. This decrease in SWH could be attributed to the fact that the hurricane weakened and slowed down as it moved back from the land to the ocean. Toward the southeast of Texas, an SWH of 3 m is observed, and the SWH decreases as it approaches land. The AWP is 11 s before and during the first landfall but decreases to 9 s before reaching Galveston during the second landfall. A higher AWP means higher energy in the swell and a larger wave.
The modeled SWH and AWP are compared with the buoy data at four stations. The locations of the stations are shown on the map in
Figure 12a. The comparisons between SWH and AWP for these stations are shown in
Figure 12b–e. The results suggest that ADCIRC + SWAN accurately predicts the SWH for the stations, although some of the frequency details may be lost in the modeling process.
It is observed that the peak height is overpredicted by approximately 1.8 m for buoy station 42020. This discrepancy indicates that SHW generally increases with greater water depth, a finding that aligns with previous studies [
7,
8]. As the waves approach the shallow water and coast, the SWH decreases. Stations 42020 and 42019, which have water depths close to 100 m and are situated near the hurricane path, exhibit SWH values close to 7 m. Station 4203, although near the hurricane’s path, is located near the coast in shallow water with a depth of 15.81 m resulting in an SWH of around 3.5 m. Station 42002, which is farther away from the hurricane’s path but in a deep ocean depth of 2727.9 m, shows a high peak SWH of nearly 5 m. These findings corroborate a previous study on Hurricane Irma, which concluded that SWH increases with ocean depth [
7]. Shallow water generally exhibits shorter SWH compared to deep water. A study on hurricanes on the Hawaiian island also supports this finding, indicating that open ocean and deep water experience greater SWH regardless of the specific detail of the hurricane [
8]. The station closest to the coastal region has the lowest SWH and AWP values.
The Simulated AWP profiles show a good match with the observed ones. However, the modeled AWP starts lower than the observed values, likely because the SWAN starts from scratch and takes a day or two for the wave to develop fully. Near the peak, the modeled AWP consistently overpredicts by about 2 s for all stations. The AWP peaks coincide with the SWH peaks, indicating that higher AWP values correspond to greater energy in the swell and a larger wave.
Stations 42019 and 42020, which are close to the hurricane’s path and have relatively deep water, exhibit AWP values exceeding 10 s. In the deep ocean but away from the hurricane’s path, station 42002 shows AWP peaks at around 7.5 s. In the shallow water along the hurricane’s path, station 42035 has an AWP peak of around 6 s.
These findings emphasize the importance of considering wave effects, such as AWP and surge amplification, and accurately modeling and predicting hurricane impacts, particularly in coastal regions with complex coastlines. Overall, these results provide valuable insights into the relationship between ocean depth, SWH, and AWP, highlighting the behavior of waves in different water depths and their impact on coastal regions during hurricanes.