3.1. Observational Data
The number of wave events that consistently had wave heights greater than 1 m for at least 12 h was 38 in BC and 27 in AC, as described in
Section 2. The selected events generally corresponded to the times when high waves, including storms, were present in Yeongil Bay, and
displayed increasing and decreasing patterns during these periods, as shown in
Figure 3. Therefore, there was a time when the
value became the maximum, and the
value at this time was selected as the representative value for each event. In
Figure 5, the maximum
values of all of the events are compared between W1 (outside Pohang New Port) and W2, W3, W4, and W5 (inside Pohang New Port) in BC and AC. Similarly, the representative values for the wave propagation direction,
, were selected at the same time at which the maximum
values for the corresponding events were observed. In
Figure 6, the representative
value measured in W1 is compared with the
value in W2, W3, W4, and W5.
In the case of wave height, the
varied with the wave events and showed similar patterns at all stations, as when the
value was high inside the port (W2, W3, W4, and W5), the
value was generally also high outside the port (W1). It is noted that the representative
values inside the port were mostly higher than 0.2 m, and ~50% of them were even higher than 0.4 m in BC. In contrast, in AC, the representative
values outside the port in 23 events out of a total of 27 events were lower than 0.4 m, and ~50% of them were even lower than 0.2 m, which indicates that the breakwater effectively reduced the wave energy inside the port. In the case of the representative
value, its correlation with the representative
was lower, as shown in
Figure 6. In the second period of BC (
Figure 6b), the representative
value in W1 showed a large discrepancy with the
measured inside the port. The
measured in W1 was greater than 40° in events #1–#7, whereas the
value became lower than 25° in events #8–#17. However, this pattern was not observed in terms of the
value inside the port. In AC, a similar conclusion was not easily found, because there were wave events such as #4, #6, #10, and #20 when the
value in W2, W3, W4, and W5 increased and the
value in W1 was also greater than 30°; thus, a correlation was observed between the wave direction and the height inside Pohang New Port.
In
Figure 7,
and
are compared between the measurements at the two stations, W0 and W1. It is noted that the waves were not measured in W0 during BC01 (2008–2009), meaning that
Figure 7 only compares the data at BC02 (2018–2019) and AC. In the case of
, the data between the two locations show relatively high correlation with an
, the coefficient of determination, of 0.84. However, the
for
was as low as 0.16 between W0 and W1, which indicates that the directions of the waves that approached Yeongil Bay were not correlated with those that approached the detached breakwater. Therefore, to carry out a detailed investigation, it was necessary to examine the impact of wave direction based on the data in W1, as proposed in
Section 1, in addition to the analysis based on the data in W0, which was conducted in [
17]. In the present study, therefore, the data in W1 were considered the primary wave measurements outside Pohang New Port.
The correlation between the wave parameters inside and outside Pohang New Port was examined by defining a new parameter, the wave height reduction rate (
).
was calculated from the ratio of
measured inside and outside the port (i.e.,
and
, etc.). The
parameters were estimated from the data sets of 38 and 27 wave events selected for BC and AC, respectively, as described in
Section 2.2, because the relationship between
and
was not clearly observed for waves with low energy. In
Figure 8 and
Figure 9, the distributions of
versus
in W1 for the data selected for the wave events are compared between BC and AC. In addition to the four stations inside the port, the
and
values were estimated outside the port as well. Considering that the wave energy inside the port decreased with the decreasing magnitude of
, the results in
Figure 8 and
Figure 9 clearly show that the wave energy was much reduced in AC compared to that in BC, confirming the effectiveness of the detached breakwater in reducing the wave energy inside the port. It is also interesting to see that the
value measured inside the port (
) tended to increase with
, showing that the
value increased as the wave direction in W1 changed from N to NE. In contrast, the opposite phenomenon occurred in W6, the station in front of Dogu Beach outside the port (
Figure 1c), at which the
value decreased with increasing
. On the other hand, the pattern in W7, the station in front of Yeongildae Beach, became similar to that inside the port, as the
value also increased with increasing
. The difference in the pattern of
with
in W6 and W7 might have been induced by their locations, which is discussed in
Section 4. The correlation between
and
in BC was repeated in AC. However, the magnitude of
measured inside the port was much lower in AC than that in BC, as its values in AC were ~50% of those in BC, which is discussed in
Section 4. In
Figure 8 and
Figure 9, the red lines show linear regressions and the regression coefficients are listed in
Table 3.
Considering that the
value measured in W1 acted as a controlling factor on the wave reduction inside Pohang New Port, it was also necessary to examine the impact of the wave height on the wave reduction pattern.
Figure 10 and
Figure 11 show the scatter plots between
and
, measured in W1. It is observed that
did not show a clear correlation with
in W1 for both BC and AC. It is noted that the time variation pattern of
measured inside the port was similar to that of
in W1, as shown in
Figure 2 and
Figure 5. Therefore, the low correlation between
and
inside the port was an interesting result, indicating that the wave reduction process inside the port might not be dependent on the wave height, unlike the wave direction. The low correlation between
and
was not only observed inside the port but also outside the port in W6 and W7 in both BC and AC. The results in this section are important, because the effect of the breakwater was confirmed, as not only the magnitude but also the variance in
were significantly reduced in AC compared to those in BC, regardless of the wave height. In addition, the high dependence of the wave reduction process inside the port on the propagation direction of short waves outside the port required further analysis to understand the courses of wave propagation around the breakwater and the port, which was carried out using the BOUSS-2D model, which can simulate wave transformation around these complex structures, and the results are provided in the next section.
3.2. Numerical Model Results
The BOUSS-2D wave model was set up as described in
Section 2.3 for the two cases representing the wave propagation in BC and AC. The two cases were selected because they had the maximum wave heights during the period of the 38 (BC) and 27 (AC) wave events, as shown in
Figure 3a,b. The events with the maximum
were selected because the effect of the detached breakwater in reducing the wave energy inside Pohang New Port could be more clearly observed under higher wave energy conditions.
In
Figure 12, the wave conditions in W1 are compared between the observed and modeled data from 26 to 27 April 2009, which were selected from the BC events. Considering the computational domain shown in
Figure 4b, the location of W1 was close to the outside open boundary, and the modeled wave conditions were well matched with the observation data that were used for the boundary forcing conditions. The data show that the wave height increased to the maximum (
3.4 m) at 15:30 on 26 April 2009, and then, it gradually decreased. The wave period fluctuated between 9.2 and 12.2 s, and the
value gradually increased from ~N12°E to ~N40°E, indicating that the waves were mainly approaching from NNE~NE in W1 during this wave event.
Figure 13 shows the comparisons of the modeled wave heights with observations at the four wave stations (W2, W3, W4, and W5) inside Pohang New Port to validate the model performance. Reasonable agreement was observed among the four wave stations inside the port (marked in
Figure 4b), as the overall pattern of the
time variation generally agreed between the modeled and observation data, although the model results were underestimated, specifically in W3 and W5. The average error (
) was calculated, and it ranged from 12% to 23% (12.9%, 18.7%, 13.6%, and 22.7% for W2, W3, W4, and W5, respectively). It is noted that the errors were greater in the stations located outside the slits (W3 and W5) than those located inside the slits (W2 and W4). Although the reason for this is not yet clearly understood, the four wave stations were located in the corners of the slits where the incoming and reflected waves were interfered with in complicated ways, which could have increased the wave height compared to that in other areas near the slits and also could have increased the modeling errors. As the pattern of the
time variation of the model generally agreed with that shown in the observation, it could be concluded that the model was validated for the wave event, and the model results were further analyzed to understand the wave propagation pattern inside the port.
A similar comparison between the modeled and observational data was carried out for the selected event case in AC. In
Figure 14, the observed and modeled wave conditions in W1 are plotted for the period of the wave event selected for AC, from 07:00 on the 22 to 21:00 on 23 September 2019. Similar to the event case in BC, the wave conditions in W1 were nicely matched between the model and observation due to the proximity of the location of W1 to the open boundary. It was shown that the wave height increased to become the maximum (
.8 m) at 19:00 on 22 September 2019 and then gradually decreased to ~2.5 m at 21:00 on the 23rd in W1. The wave period generally increased from ~8.5 s to ~11.0 s, and the
value fluctuated between 30
and 60
, showing that the waves generally approached from NE in W1 during the wave event.
Figure 15 compares the modeled wave heights with the observed data at the four wave stations (W2, W3, W4, and W5) inside Pohang New Port during the wave event selected for AC. It shows that the pattern of wave height time variation during the event was successfully generated by the model, although the errors estimated from the wave height were not improved compared to those in BC, as they were ~19.2%, 17.1%, 31.3%, and 19.2% for W2, W3, W4, and W5 respectively. The higher error range in AC was likely due to the lower magnitude of the observed
, which would increase the error for the same deviation between the model and observation data.
Once the BOUSS-2D model was validated, the next step was to analyze the course of wave propagation to understand how the wave energy was reduced inside Pohang New Port through a comparison between BC and AC. In
Figure 16 and
Figure 17, the contours of wave heights during the periods of the two wave events selected for BC and AC are compared. The contours are captured as a snapshot of the wave field at the time when the
value became the maximum for each event, as shown in
Figure 12 and
Figure 14. That is, in the case of BC,
Figure 16 shows the field of wave heights at 15:30 on 26 April 2009 when the
value became the maximum, 3.35 m (
Figure 14). Similarly, the wave height field is contoured in
Figure 17 at 19:00 on 22 September 2019, as it is the time when the
value became the maximum (4.84 m) during the wave event selected for AC. The input wave conditions for the two cases were based on the observations at corresponding times. The wave period was similar between the two cases, as the
value was 11.0 s and 10.9 s for BC and AC, respectively. The wave direction was N35.0°E for BC and N46.3°E for AC, as they were propagating in the NNE–NE directions. Along the open boundary that was rotated 40° in the NE direction (
Figure 4a), the incident wave direction was nearly normal to the boundary in both BC and AC (with a deviation of 5°–6°), indicating there were no significant discrepancies in terms of the input wave propagation direction between the two cases.
Both of the figures effectively compare the pattern of wave reduction inside Pohang New Port between the two cases. In BC (
Figure 16), the isolines of the wave height became parallel to the port entrance where the narrow navigation channel is connected to the inside of the port. At the port entrance, the
value was ~2.0 m (marked in a red rectangle in
Figure 16), indicating that the
value was reduced by ~40% from the input wave height at the outer open boundary (3.35 m). Once the waves entered the port, the wave height was rapidly reduced due to the combined effects of refraction and diffraction around the slits and other harbor structures, with
varying from ~2.0 m to ~0.3 m. The wave height was observed to be 0.3 m inside the slit where the wave stations W4 and W5 were located (marked in a blue rectangle). It is noted, however, that the
value was increased to 0.9 and 0.7 at the locations of wave stations W2 and W4, which was likely because the reflected waves were interfered with at the wall of the slits to increase the
value to higher than that calculated off the walls.
In
Figure 17, the
isolines are contoured for the wave event selected for AC, which occurred at 19:00 on 22 September 2019. Compared to the case of BC, the detached breakwater was constructed near W1, blocking the waves. Behind the breakwater, therefore,
was rapidly reduced, and the reduction rate was greater than that in BC. For example, the
value became ~2.0 m near the entrance of Pohang New Port (marked in a red rectangle), and the reduction rate was 59% considering that the input wave height on the boundary was 4.84 m in AC, which was ~19% greater than that in BC. In addition, in AC (
Figure 17), the red rectangle that marks the isoline position of
= 2.0 m is located ~0.2 km further offshore compared to that in BC (compare with
Figure 16), indicating that the wave heights inside the port would become lower than those in BC, assuming that the pattern of
reduction inside the port would be same between the two cases, which was also confirmed from a comparison of the observed and modeled wave heights between BC and AC in W2, W3, W4, and W5, as shown in
Figure 13 and
Figure 15.
Figure 16 and
Figure 17 show the model that simulated the wave propagation patterns using the input conditions based on the observational data, and the input wave directions on the open boundary were similar between BC and AC, as they were N35.0°E and N46.3°E, respectively. Therefore, the impact of wave directional change on the wave pattern inside Pohang New Port could not be examined using these model results, although it was observed from the observational data, as shown in
Figure 8 and
Figure 9. In
Figure 18, the two additional cases that were tested for BC by assuming extreme cases in the wave propagation direction are shown. It is noted that most of the measured
values in W1 ranged between N15.0°E and N55.0°E in the case of AC, as shown in
Figure 9. In
Figure 18, therefore, the results of two model runs are shown with
set as N15.0°E (
Figure 18a) and N55.0°E (
Figure 18b), as they represent the extreme wave directions for NNE and NE waves, respectively. Except for the wave direction, the other input wave conditions were the same as those given for the case of BC in
Figure 16. The results of these two extreme cases in
Figure 18 could help us to understand the different patterns in the wave energy reduction rate inside Pohang New Port, according to the changes in
in W1, as observed in
Figure 8 in the case of BC. In the extreme NNE case (
= N15.0°E), the propagating waves outside the port mainly passed by the entrance of the port, and only the diffracted waves could enter the port, which increased the wave height reduction near the port entrance (
Figure 18a). For example, the
value was as high as 2.0 m just outside the port entrance, but it was reduced to 1.0 m just inside the port, as the distance between the two positions was only ~0.5 km (marked with two red rectangles). The high wave reduction rate near the port entrance meant that
ranged from 0.2 to 0.7 m inside the port, and the estimated wave height reduction rate (
) was 5–20%. On the contrary, in the extreme NE case (
= N55.0°E) shown in
Figure 18b, the wave reduction near the port entrance was less severe compared to that in
Figure 18a, as shown in the two marked red rectangles (the
value was reduced from 2.0 m to 1.4 m for ~0.5 km). Therefore, the
value inside the port was also higher compared to those in
Figure 18a, with a range of 0.4–1.2 m in the areas, providing
= 12–35% inside the port.
Figure 19 shows the model results of the two extreme wave directions that were tested for AC as well. That is, the other wave conditions were identical to those used in
Figure 17, except that
was set as N15.0°E (N55.0°E), which represented an example of extreme conditions of NNE (NE) waves, as shown in
Figure 19a (
Figure 19b). Similar to the cases in BC, the wave propagation pattern inside Pohang New Port was affected by the different
input conditions at the open boundary, regardless of the existence of the detached breakwater. When
was N15.0°E, the
value was significantly reduced in the lee area of the breakwater, as it was ~4.6 m offshore of the breakwater but decreased to ~2.0 m just outside the port, as shown in
Figure 19a (marked with a red rectangle). The waves were then diffracted near the entrance of the port, where strong
reduction occurred for the waves entering the port, as the
value was reduced to ~1.0 m just inside the port (marked with a red rectangle). The range of
was then 0.2–0.7 m inside the port, leading to
= 5–15% inside the port. In the case of extreme NE waves (
= N55.0°E in
Figure 19b), the waves approached the port from the NE direction, meaning the detached breakwater became less effective in reducing the wave height. For example, the
value was reduced from ~2.0 m to ~1.4 m (marked in the red rectangles in
Figure 19b) for the similar distance marked in
Figure 19a. As a result, the
value became higher inside the port, compared to that of
with N15.0°E, with the
range of 0.4–1.2 m inside the port, providing
of 8–25% (
Figure 19b). The impact of wave direction in the case of AC is further discussed in
Section 4.