Evaluation of Wave Model Performance during Typhoon Event in Surrounding Korea Waters

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Abstract

1. Introduction

Typhoons play an important role as forcing events in generating extreme wave height in subtropical regions. In recent years, record-breaking maximum wave height during typhoon in surrounding Korea Waters observed can reach about nineteen meters (Moon et al., 2016). The typical spatial extent of a typhoon can exceed 320 kilometers (Tan et al., 2022). The waves generated by typhoons can even propagate away from the wind regions when the wind direction and direction of propagation of the typhoon are aligned, transforming into swell and hence impacting much larger regions than the intense winds (Young and Vinoth, 2013). Typhoon-generated waves present an immediate and severe threat to nearshore regions, leading to significant societal impacts. These impacts include damage to infrastructure, coastal flooding, and beach erosion (Thuan et al., 2016; Shimozono et al., 2020).

The study on such wind driven waves has been enhanced using wave models, satellite, and buoy data. The third- generation wind wave models, such as WAM (WAMDI, 1988), WAVEWATCH III® (WW3DG, 2019), and SWAN (Booij, et al., 2004) has consistently applied to achieve the accurate sea state predictions by enhancing the existing physical parameterizations (Ardhuin et al., 2010; Bidlot et al., 2005; Zieger et al., 2015; Son and Do, 2022) and thereby improving the wave model performance. WAM and WW3 are widely used for deep water wave modelling on a global and regional scale, while SWAN is well performed in simulating nearshore waves. It is important to note that nearshore regions demand high attention due to the dominant interaction between waves and currents (Cavaleri et al., 2018). These models are based on action balance equations and widely used in practical applications for global and regional operational forecasting of ocean surface waves.

The wave models that use the energy balance equations are considered effective tools for studying wind waves, as surface gravity waves on the open ocean can to a first approximation be regarded as linear wave phenomena (Janssen, 2008). Performance evaluation is an essential aspect of utilizing wave model outputs. The performance of the WW3 model in the waters surrounding Korea has been extensively studied (Park et al., 2009; Zhao et al., 2012; Zheng et al., 2014; Zheng et al., 2018; Roh et al., 2021). The capability of WW3 in simulating typhoon waves has been reported in several studies (Zhou, et al., 2014; Shao, et al., 2018; Sheng, et al., 2019; Qi and Wang, 2020; Hu, et al., 2020; Yao, et al., 2023). The latest version of WW3 model, 6.07, was released in March 2019 and introduces several improvements over its predecessor. The enhancements include updates to numerical methods, model structure, and physical parameterization (WW3DG, 2019).

Several studies have reported investigations into the performance of the WW3 model concerning atmospheric input and dissipation terms. Umesh and Behera, (2020) evaluated the WW3 model (v5.16) performances by examining the sensitivity of five input-dissipation source terms (ST1, ST2, ST3, ST4 and ST6) for the Indian seas using measurements from both deep and shallow waters in 2003 and 2004. Performance evaluation of different parameterizations was conducted using wind data from ERA-Interim. The results indicate that simulations using ST4 physics perform best across all seasons, while ST2 physics excelled in simulating rough weather conditions. Similarly, study by Sheng et al. (2019) found that under typhoon conditions around the Zhoushan islands, ST2 physics was the best option for simulating significant wave height during typhoon Fung-wong (2014) and Chan-hom (2015). Wang et al., (2017) evaluated the input/dissipation terms in WW3 using in-situ and satellite data in South China Sea during winter northeast monsoon January 2012. The comparison of Hs between model and observed data revealed that the ST2 source terms outperformed ST1 and ST3. Additionally, they noted that the model’s performance is greatly influenced by the atmospheric correction parameter. Qiao et al. (2019) also employed the WW3 ST2 physics package to model Typhoon Kalmaegi (2014) in the northwest Pacific Ocean. In a study by Liu et al. (2017) using the well-observed Hurricane Ivan (2004), the performance of the WW3 model with ST2 was found to be less accurate compared to ST3, ST4, and ST6. They also found that properly enhancing the strength of negative wind input can effectively improve model performance in such situations.

Considering the previously discussed studies, it is noted that research focusing on the use of improved input-dissipation parameterization in the WW3 model for surrounding Korean waters is still needed. This study aims to address this by evaluating the simulation capabilities of WW3 version 6.07 in this area, investigating the model’s sensitivity to different available input and dissipation source terms. Specifically, the study will assess the accuracy of various source terms, including ST1, ST2, ST3, ST4, and ST6 particularly under rough sea conditions induced by super typhoon Hinnamnor in 2022.

2. Wave Model Overview

In order to simulate the wave field during typhoon conditions in surroundings Korea waters, this study employed the numerical wave model WAVEWATCH-III® (WW3). WW3 is a third-generation spectral wave model developed by NOAA/ NCEP that solves the action density balance equation:

where N(k, θ)≡ F(k, θ)/σ is the wave action density spectrum, which is a function of the wave number (k) and wave direction(θ), σ is the relative angular frequency, C_g is the group velocity, U is the depth-averaged current velocity vector and S represents the net source and sink terms for the spectrum F. The left-hand side of Eq. (1) expresses the evolution of the wave action density spectrum in terms of time, physical space, frequency, and direction, considering linear propagation. Meanwhile, the effects of physical processes including the nonlinear wave propagation and partial wave reflection arise by the net source and sink term S on the right side of Eq. (1). In deep water, three main components of net source terms are S_in, S_nl and S_ds which represent the atmosphere-wave interaction term, the nonlinear wave-wave interactions term, and the wave energy dissipation due to wave breaking term, respectively. In shallow waters, the most notable process is the wave-bottom interaction, defined as S_bot. For extremely shallow waters, triad wave-wave interactions (S_tr) and depth- induced breaking (S_db) should be considered as the additional source terms. Thus, the source terms in WW3 model are defined as follows.

Additional information about the WW3 model is provided in the user manual (WW3DG, 2019).

In this present study, version 6.07 of WW3 provides several options for input/dissipation source terms, namely ST1, ST2, ST2+STAB2, ST3, ST3+STAB3, ST4, and ST6. The source term package ST1 is based on the WAM3 cycle source term (Komen et al., 1984; Snyder et al., 1981). Tolman and Chalikov (1996) proposed the formulation for the ST2 package, and ST2+STAB2 provides a stable correction of ST2, which is calibrated for fetch-limited growth. The ST3 package includes the input source term by Janssen (2004) and the dissipation source term by Bidlot et al. (2005). Abdalla and Bidlot (2002) proposed the parameterization ST3+STAB3 to stabilize ST3 under unpredictable meteorological conditions. The ST4 source term package is recommended by Ardhuin et al. (2010), and ST6 is derived from laboratory experiments and measurements taken on lakes (Zieger et al., 2015).

3. Data and Methodology

3.1 Dataset Description

The study area is located between (21°N, 117°E) and (34°N, 131°E) and consists of two domains: the outer domain (D1), which covers the entire Northwest Pacific Ocean (0.5° x 0.5° (~ 55.56 km x 55.56 km) spatial grid domain; 5°- 55°N, 105°- 160^oE), and the inner domain (D2), which was used to validate the wave condition during typhoons in the surrounding Korea waters (0.05° x 0.05° (~ 5.5 km x 5.5 km) spatial grid domain; 23°- 42°N, 117°- 131°E), as shown in Fig. 1. The General Bathymetry Chart of Oceans 2023 (GEBCO_2023), the latest global bathymetric product with a spatial resolution of 15 arc second (~ 450 meters) is used as the bathymetric input and the Global Self-consistent Hierarchical High resolution (GSHHS) database was applied for the shoreline data.

Fig. 1

Multi-grid domains for WW3 wave model: outer domain (D1) with spatial resolution 0.5^o x 0.5^o (~ 55.56 km x 55.56 km) and inner domain (D2) with higher spatial resolution 0.05^o x 0.05^o (~ 5.5 km x 5.5 km). The color represents the bathymetric topography provided by GEBCO 2023. The two observation points, marked by red dots, are Gageocho and Ieodo stations

The wind data used as the forcing input for the wave simulation were obtained from the ERA5 reanalysis dataset, featuring a spatial grid resolution of 0.25° (~ 27 km) and a temporal resolution of 1 hour. The ERA5 reanalysis data, produced by the European Centre for Medium-Range Weather Forecasts (ECMWF), represents the latest advancements in atmospheric reanalysis of the global climate. It offers hourly estimates of various atmospheric and oceanic climate variables starting from 1979 onwards (Hersbach et al., 2020). The wave model is capable of interpolating wind fields to the desired model grids, ensuring that the wind magnitudes align with the specified requirements. Fig. 2 illustrates the wind speed and direction over the seas adjacent to Korea during the peak of typhoon Hinnamnor from ERA5 dataset. It was observed that the maximum wind speed exceeded 25 m/s as the typhoon approached the Korean Peninsula.

Fig. 2

Wind fields of Typhoon Hinnamnor on September 4–5, 2022, over the seas adjacent to Korea (inner domain, D2). The colors indicate the wind speed

To validate the model results, we used observations data from Korea Hydrographic and Oceanographic Agency (KHOA). Significant wave height (H_s) and significant wave period (T_1/3) data obtained every 20 minutes from the middle of August to September 2022. Table 1 provides a summary of the wave buoy data and locations. Two wave buoys were deployed at the Gageocho and Ieodo station, which are located in the western part of Korea and the northern part of East China Sea, respectively. The locations of all buoys are indicated by red dots in Fig. 1. Unfortunately, the observed data at Ieodo station is unavailable for a certain period due to instrument failures. At Gageocho, no missing data or instrument failures were found.

Table 1

Summary of wave buoy data

3.2 Wave Model Setup

The wave model used in this study is a multi-grid version of WW3 that supports two-way nesting, allowing domains with different resolutions to be interconnected within a single model driver, greatly simplifying operational requirements (Chawla et al., 2013). The initial and boundary conditions for the inner domain (D2) are taken from the outer domain (D1), while a calm start condition is applied to the outer domain. All other settings used are the default values of version 6.07. Model simulations were performed over a one-month period from August 15 to September 15, 2022, starting 14 days earlier to allow for an initial spin-up period. The directional resolution was set to 10° and the initial frequency was 0.04118, discretized into 30 logarithmic increments. The nonlinear wave-wave interactions were modeled using the discrete interaction approximation (DIA) (Hasselmann et al., 1985), while the bottom friction was modeled using the JONSWAP (Joint North Sea Wave Project) parameterization. The linear input source term (Cavaleri and Malanotte-Rizzoli, 1981) allows for consistent model spin-up and improves initial wave growth behavior. In total, this study conducted five simulation experiments using different input-dissipation source term packages, namely ST1 (WAM3 Cycle), ST2 (Tolman and Chalikov, 1996), ST3 (Janssen, 2004; Bidlot et al., 2005), ST4 (Ardhuin et al., 2010), and ST6 (Babanin, 2011; Rogers et al., 2012; Zieger et al., 2015). Additional information on the input and dissipation terms can be found in Table 2.

Table 2

Input-dissipation source term package related to wind input and dissipation term in WW3

For the purpose of determining the best parameterization schemes during the typhoon conditions in surrounding Korea Waters, each option was independently evaluated by validating the model results in terms of significant wave height and significant wave period with observed data from buoy observations. The model outputs are derived from domain D2 (Fig. 1), the innermost domain with higher resolution. To obtain the model results at the buoy position, we utilized the output point feature of WW3 model. Statistical analysis was also conducted on the resulting simulation data by computing the statistical metrics for each different source term.

4. Result and Discussion

To investigate the model performance with respect to input and dissipation source terms, five numerical experiments were conducted using give different source terms (ST1, ST2, ST3, ST4, ST6) in WW3. The model is forced by hourly ERA5 reanalysis wind data during Typhoon Hinnamnor in August to September 2022. The simulation results for significant wave height and significant wave period were then analyzed by comparing them with in-situ measurements. Fig. 3 shows the comparison between model results and observed data at Gageocho and Ieodo station. During the typhoon period, the wave model successfully captured the significant increase in wave height from the early stages of the typhoon to its peak. The wave height reached nearly 7 meters, while the wave period exceeded 12 seconds at the peak of the typhoon. For both stations, the computed significant wave heights and wave periods with ST1, ST3, ST4, and ST6 source term packages generally exhibit good agreement with the observed values and highly consistent with each other. However, the model results using ST2 present lower peak values compared to all other simulations. This finding is consistent with previous studies conducted in Lake Michigan (Ardhuin, et al. 2010), the East Sea (Lee, 2015), and the Persian Gulf (Kazeminezhad and Siadatmousavi, 2017). This discrepancy may be due to ST2 being the most optimal for ocean-scale applications rather than semi-enclosed basins like the study area in focus.

Fig. 3

Comparisons of observed and calculated significant wave heights and significant wave periods (a) in Gageocho station (b) in Ieodo station during super typhoon Hinnamnor 2022. The five different colors indicate the results from five numerical experiments

To provide a general overview of the model performance using different parameterization schemes for wave simulation during a typhoon in the seas adjacent to Korea, frequency scatter plots are presented in Figs. 4 and 5. These plots provide a visual assessment of model performance across a wide range of observational data. In addition, Taylor Diagrams, presented in Fig. 6, visualize the model performance in terms of standard deviation, root mean square error, and correlation coefficient. Each color in the diagram is used to distinguish different source term packages of the model. The statistical summary for wave modeling results from five numerical experiments is also presented in Table 3.

Fig. 4

Frequency scatter plot of H_s model result vs observation data at Gageocho station based on different source term packages (a) ST1, (b) ST2, (c) ST3, (d) ST4, and (e) ST6

Fig. 5

Frequency scatter plot of H_s model result vs observation data at Ieodo station based on different source term packages (a) ST1, (b) ST2, (c) ST3, (d) ST4, and (e) ST6

Fig. 6

Taylor diagrams display statistical comparison with observation of five numerical experiments for significant wave heights (a) in Gageocho station (b) in Ieodo station and significant wave periods (c) in Gageocho station (d) in Ieodo station which indicated by colored dots. The radial distance from the origin is directly related to the standard deviation of each experiment. The centered RMS error, representing the gap between the observation value (depicted by the magenta dot on the horizontal axis) and the model result, increases proportionally with their separation. The correlation coefficient between the observed value and the model result is reflected by the azimuthal position of the model result. Each colored dot corresponds to the scenario of five numerical experiments. Both the standard deviation and the centered RMS errors share the same unit of measurement

Table 3

Statistical summary of H_s and T_p for five numerical experiments

At Gageocho (Fig. 3a), the computed significant wave heights and periods from the five experiments generally exhibit good temporal variations that are well-matched with the observed values. The computed wave period follows a similar trend to the other site, with one peak exceeding 12 seconds at the peak period. The resulting periods using ST3 are slightly higher compared to those using other source terms. Interestingly, the significant wave height notably increases by approximately 6 meters from the early stage of the typhoon to its peak, whereas the wave periods differ slightly by about 2 seconds. This implies that swells are still dominant at the typhoon early-stage period. Conversely, the sea surface responds directly to the strong winds generated by the typhoon, resulting in large wave heights exceeding 6 meters during the typhoon’s peak period.

At Ieodo (Fig. 3b), the overall features of the computed and observed significant wave height and wave periods are similar to those at Gageocho station, closely matching the observed values. However, the computed significant wave height from all numerical experiments before the peak of the typhoon shows a slight decrease compared to the observed values. The difference in wave height is approximately 2 meters. It also appears that the observed waves during that time are dominated by swells.

For H_s (see Figs. 6(a), 6(b), and Table 3), all model results at both stations present a correlation coefficient value greater than 0.9, standard deviation ranging between 0.48 and 0.61 meters. In general, the model performed statistically very well, although the overall bias indicates that the computed significant wave heights at both stations tend to be underestimated. In particular, the bias for ST3 and ST4 was within -0.22 m, reflecting higher accuracy compared to the other source term packages. Additionally, ST4 and ST6 exhibited lower RMSE values than the other simulations. As seen in Figs. 4 and 5, the correlation coefficients using ST4 and ST2 were greater than 0.92, indicating a good performance. In contrast, the bias and RMSE of ST2 at both stations were poorly estimated as compared to other simulations. The model performance in capturing large significant wave heights for each source term package shows that ST4 result performs better than other source term at both station Gageocho and Ieodo, as seen in Figs. 4d and 5d. Thus, it can be noted that in this case, ST4 is considered the most effective source term package for reproducing H_s. The results of this study are consistent with the findings of Umesh and Behera (2020). While the seas adjacent to Korea, particularly the Yellow Sea and East China Sea, are generally influenced by swell, under typhoon conditions, these regions experience highly energetic sea states. ST4 performs particularly well in these conditions due to its advanced parameterizations for wave dissipation, including larger drag coefficients at high wind speeds (Lin et al. 2020). Ardhuin et al. (2010) emphasize that ST4 accurately models dissipation rates based on the wave spectrum, wind speed, and direction, capturing observed behaviors of wave breaking and swell dissipation. Its nonlinear swell dissipation, proportional to swell steepness, and its ability to account for short-wave dissipation by longer waves further enhance its accuracy in extreme sea states.

With respect to T_1/3 in Figs. 6c, 6d and Table 3, all simulation results yielded correlation coefficients lower than 0.77, which was relatively worse compared to the results for H_s. In addition, the variations in the statistical values between simulations were significantly larger compared to those of H_s (Table 3). ST6 provided poor simulation results, with RMSE and correlation coefficients for T_1/3 greater than 1.79 meters and less than 0.6, respectively. In contrast, ST1 results obtained the lowest RMSE values, less than 2.02 meters, and a correlation coefficient greater than 0.7, even though the simulations tended to be underestimated based on bias values. This indicates that the ST1 shows the best model performance for simulating T_1/3. Moreover, the bias for ST4 was lower than -0.06 meters, which was smaller than those of other simulations.

5. Conclusions

In this study, we investigated the performance of the latest version of wind wave model, WW3 version 6.07, with respect to wind input and dissipation source terms, particularly under rough sea conditions induced by super typhoon Hinnamnor in surrounding Korea waters. We examined five wind input and dissipation source terms of WW3 namely ST1, ST2, ST3, ST4, and ST6. The model was simulated from mid-August 2022 to September 2022, using ERA5 reanalysis dataset as the wind forcing. Simulated significant wave heights and wave periods were compared to observed data obtained from Gageocho and Ieodo stations located in southern part of the Korea peninsula. The results indicated that the WW3 performance using ST1, ST3, ST4, and ST6 was practically similar, while using ST2 displayed lower values for both significant wave heights and period compared with other simulations. Among the five wind input and dissipation terms, it was found that the results from ST4 consistently outperformed the other simulation in terms of significant wave heights, at both measurements sites, Gageocho and Ieodo stations. Investigating the wind input and dissipation source terms scheme is essential in wind wave modeling, particularly under extreme conditions like typhoons. These findings not only contribute to advancing research in wave modeling around the waters of Korea during severe weather but also offer practical applications for coastal and offshore engineering projects. The improved accuracy of wave predictions from the ST4 package can enhance the design and safety protocols for offshore structures, ports, and marine operations.

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