A Study on Enhancing the Accuracy of Wave Prediction Models Through SWAN (Simulating WAves Nearshore) Model Sensitivity Experiments: Focusing on Wind Input and Whitecapping Dissipation

Abstract

Accurate wave prediction in coastal waters is essential for marine safety and engineering, yet it is significantly influenced by uncertainties in wind forcing and dissipation parameterization. This study evaluates the sensitivity of the SWAN model around the Korean Peninsula using 2021 data from 138 observation stations. To address structural biases in wind fields, the Drag Coefficient Scaling Factor (CDFAC) was implemented alongside the Komen and ST6 physics packages. While the Komen scheme provided stable performance under normal conditions, the ST6 + CDFAC configuration exhibited superior physical consistency during extreme events. Notably, applying CDFAC to the ST6 package reduced the high-wave (H_s > 3 m) RMSE by approximately 32.7%, decreasing from 0.52 m to 0.35 m. Bathymetric stratified analysis further confirmed that the ST6 scheme maintains robust performance in offshore and deep-water regions (depth > 50 m), achieving a correlation of 0.94 and an RMSE of 0.20 m. This is attributed to ST6’s frequency-dependent saturation approach, which effectively decouples wind-sea and swell components in environments where whitecapping dissipation is the governing energy sink. In contrast, improvements in coastal waters (depth < 50 m) were moderated by topographical dissipation mechanisms such as bottom friction and depth-induced breaking. These findings demonstrate that integrating wind input bias correction with frequency-dependent dissipation physics is vital for reliable wave forecasting and coastal disaster mitigation.

1. Introduction

1.1. Research Background and Necessity

Precise and reliable wave prediction in coastal waters is one of the core challenges in modern marine engineering and marine meteorology. It has become an indispensable element for the efficient management of port operation rates, the design and safety assessment of coastal and offshore structures such as breakwaters and offshore wind farms, the establishment of coastal erosion mitigation measures, and ensuring the safe navigation of vessels. In particular, the rising sea surface temperatures due to recent climate change, the resulting increase in typhoon intensity, and the frequent occurrence of unexpected swell-like waves are intensifying the risks of coastal disasters. Consequently, the establishment of high-precision wave prediction systems to respond to these threats is a matter of great urgency.

To meet these social and engineering demands, third-generation spectral wave models are widely utilized worldwide. Among them, the SWAN (Simulating WAves Nearshore) model is specialized for simulating complex wave transformations in shallow waters. It numerically solves the Wave Action Balance Equation to track the processes of wave generation, development, propagation, and dissipation in time and space [1,2]. The SWAN model sophisticatedly simulates the primary source-sink processes governing the evolution of the wave spectrum, including wind-induced energy input, nonlinear wave-wave interactions, and energy dissipation caused by whitecapping, bottom friction, and depth-induced breaking [3].

Despite the significant advancements in these numerical models, non-negligible levels of uncertainty still exist in actual field applications. The accuracy of wave prediction is fundamentally determined by the accuracy of the wind field input into the model and the level of parameterization of the source terms describing the internal physical processes. Specifically, the wind input term, responsible for energy transfer at the atmosphere-ocean interface, and the whitecapping dissipation term, which determines the saturation of wave energy, are based on highly nonlinear and complex physical phenomena—namely turbulence and breaking—which have not yet been fully elucidated theoretically. As a result, the modeling process inevitably relies heavily on empirical parameterization based on observational data, which serves as a fundamental constraint in securing consistent predictive performance across various sea states and meteorological conditions.

1.2. Limitations and Issues of Previous Studies

Whitecapping dissipation is widely recognized as one of the largest factors of uncertainty in spectral wave modeling. The whitecapping dissipation formula of the Komen et al. (1984) lineage, which has long been used as the standard configuration for the SWAN model, inherits the pulse-based theory of Hasselmann (1974) [4,5]. It assumes that wave energy dissipates in proportion to a bulk parameter, such as the mean wave steepness of the entire spectrum [4,5]. While this approach yields results that align well with observations under fully developed wind sea conditions, numerous studies have reported that it can induce serious systematic biases in mixed sea states where swells and wind seas coexist. Specifically, if strong swells exist in the low-frequency region during the initial stages of high-frequency wind sea growth, the mean wave steepness may be calculated as low, leading to excessive wind sea growth. Conversely, in situations dominated by wind seas, it may cause the non-physical rapid attenuation of swell components.

To compensate for these flaws in the Komen-type equations, Westhuysen et al. (2007) proposed a nonlinear saturation-based whitecapping dissipation formula [6]. This technique controls dissipation based on the local saturation of the spectrum, allowing wind sea and swell components to be physically decoupled and processed independently, thereby improving predictive performance in mixed seas and both deep and shallow water conditions. However, according to follow-up evaluation studies, the saturation-based technique also exhibits a tendency to underestimate wave energy under high-energy winter storm conditions or, conversely, fail to sufficiently develop energy under low-energy normal conditions. This suggests that limitations still exist for it to serve as a universal solution covering the full range of sea states.

Another key challenge in wave modeling is the estimation of the drag coefficient at the atmosphere-ocean interface. Generally, the drag coefficient directly regulates the wind forcing on waves and thus has a decisive impact on high-wave predictions. The formula by Wu (1982), widely used in the SWAN model, assumes that the drag coefficient increases almost linearly with wind speed from light breezes to hurricane conditions [7]. However, field observations and laboratory studies conducted over recent decades under tropical cyclone and extreme hurricane conditions clearly show that in the very high wind speed range ($U_{10}>30 \mathrm{m}/\mathrm{s}$), the drag coefficient no longer increases but saturates or even decreases (rollover) [8,9]. This is interpreted as a fundamental change in the physical characteristics of the atmosphere-ocean interface, where the sea surface becomes covered with foam and spray under strong breaking, leading to a smoothing of aerodynamic roughness [10]. Therefore, applying a linear drag coefficient model directly to typhoon simulations results in an overestimation of the stress transferred to the sea surface, leading to unrealistically high predictions of wave heights and surge levels.

To address these issues, the ST6 (Source Term package 6), a new source term package with significantly enhanced physical consistency with observational data, has been developed and introduced into operational wave modeling. The ST6 framework, proposed by Rogers et al. (2012), improved wind input and whitecapping dissipation to better align with observed physical phenomena [11]. In particular, it reflects the saturation and decrease characteristics of the drag coefficient at high wind speeds (Hwang, 2011) [12] and ensures physical validity by modeling whitecapping dissipation separately as inherent breaking in the spectral peak region and cumulative breaking in the high-frequency region. Recent regional application studies have reported several cases where the use of ST6-based physics improved significant wave height prediction performance compared to existing configurations. Specifically, improved performance over the Komen model has been presented in simulations of winter storm waves on the East Coast of South Korea [13].

To overcome the inherent uncertainties of physics-based models, recent research has increasingly focused on Hybrid Modeling, which combines numerical models with data-driven techniques. Durap (2024) demonstrated improved significant wave height prediction by comparing various machine learning algorithms, while Park and Kang (2024) applied deep learning techniques, such as Gated Recurrent Units (GRU), to enhance wave prediction accuracy in Korean waters [14,15]. Furthermore, Durap (2025a; 2025b) proposed frameworks utilizing Explainable AI (XAI) and feature engineering to transcend the limitations of black-box models and enhance the interpretability of wave predictions [16,17]. While these data-driven approaches primarily focus on post-processing model outputs, the CDFAC (Drag Coefficient Scaling Factor) method proposed in this study distinguishes itself by directly feeding data bias information back into the model’s core physical process—specifically, the drag coefficient formulation. This approach can be defined as a practical form of “Physics–Data Coupled Hybrid Correction,” where statistical information from observational data is integrated into the numerical computation process to control errors while maintaining physical consistency.

1.3. Purpose and Scope of the Research

An important point is that it is difficult to completely eliminate errors in wave models through the improvement of source term physics alone. This is because the predictive performance of wave models is fundamentally constrained by the accuracy of the input wind field. Previous studies that calibrated models using different wind data have shown that SWAN parameter settings optimized for a specific wind data set are difficult to transfer directly when the bias characteristics of the wind data differ. Furthermore, since a strong correlation exists between the bias of the wind field and the optimal whitecapping dissipation coefficient, adjusting only the dissipation coefficient without correcting the wind bias may lead to physically inconsistent compensation errors.

The objectives and scope of this study are as follows:

Selection and Bias Correction of Input Wind Fields: Compare and evaluate major reanalysis wind fields—such as JMA-MSM (Japan Meteorological Agency Meso-Scale Model), ECMWF (European Centre for Medium-Range Weather Forecasts), and NCEP (National Centers for Environmental Prediction)—against observational data to select the optimal wind field for the waters around the Korean Peninsula. Additionally, to structurally account for the bias in wind forcing, a drag coefficient scaling technique is introduced, applying a scaling factor (CDFAC) to correct wind-related errors in a physically consistent manner.

Physics Package Sensitivity Experiments: Configure various physics packages that combine the nonlinear behavior of the drag coefficient and various whitecapping dissipation formulas. Extensive sensitivity experiments are performed, including the traditional Komen and Janssen lineages, the saturation-based Westhuysen approach, and the latest ST6 package. In particular, explicit calibration experiments are conducted for SINA0 (Source Input A0, A0 is a parameter that controls the strength of swell decay due to adverse winds) and CDFAC, which are core parameters of ST6 [3].

Long-term Simulation and Stratified Evaluation: After performing a one-year-long continuous simulation, a stratified evaluation is conducted not only for the entire period but also by wave height class (especially high wave sections with ($H_s>2 \mathrm{m}$)), region, and season. Through this, we aim to derive a consistent combination of parameters that is optimized for the heterogeneous wave climates around the Korean Peninsula and is not physically contradictory.

2. Data

2.1. Observation Data

In this study, an extensive set of observational data covering all coastal waters of the Korean Peninsula was collected to select input data for the wave prediction model and to verify its predictive performance. Data were collected from the KHOA (Korea Hydrographic and Oceanographic Agency), the MOF (Ministry of Oceans and Fisheries), and the KMA (Korea Meteorological Administration), utilizing hourly time-series data for the one-year period from 1 January to 31 December 2021. The collected observation network consists of 138 wave observation stations and 49 offshore wind speed observation stations (Figure 1,

Table 1. Summary of wave observation data (Wave observations: 138 stations, Wind observations: 49 stations).

No.	Station Name	Latitude	Longitude	Depth (m)	Wind	Agency	No.	Station Name	Latitude	Longitude	Depth (m)	Wind	Agency
1	Jeju-South	32.0902	126.9658	119	●	KHOA	70	W-Shinjindo	36.6068	126.1261	22	-	KMA
2	Jeju-Strait	33.9116	126.4922	65	●	KHOA	71	W-Anmundo	36.5369	126.2981	14	-	KMA
3	Southsea-East	34.2225	128.4188	84	●	KHOA	72	W-chunsuman	36.4672	126.4394	24	-	KMA
4	Korea-Strait	34.9188	129.1213	95	●	KHOA	73	W-Sapsido	36.3700	126.3350	18	-	KMA
5	Uleungdo-NE	38.0072	131.5525	1331	●	KHOA	74	W-Seochun	36.1669	126.3328	23	-	KMA
6	Uleungdo-NW	37.7427	130.6011	1506	●	KHOA	75	W-Kunsan	35.8881	126.4256	17	-	KMA
7	Yellowsea-190	37.2361	126.0188	32	●	KMA	76	W-Biando	35.7404	126.3523	20	-	KMA
8	Dukjukdo	37.2361	126.0188	32	●	KMA	77	W-wedo	35.6584	126.2610	29	-	KMA
9	Incheon	37.0917	125.4289	42	●	KMA	78	W-bunsan	35.6592	126.4592	14	-	KMA
10	Weyeondo	36.2500	125.7500	58	●	KMA	79	W-younggang	35.4358	126.1764	18	-	KMA
11	Yellowsea-170	36.1333	124.0500	81	●	KMA	80	W-Nakwol	35.2006	126.2103	12	-	KMA
12	Buan	35.6586	125.8139	54	●	KMA	81	W-Daechimado	35.0175	126.0319	15	-	KMA
13	Cilbaldo	34.7933	125.7769	35	●	KMA	82	W-Jaeun	34.9192	125.8681	22	-	KMA
14	Hongdo	34.7500	125.2500	88	●	KMA	83	W-Jindo	34.4425	126.0569	36	-	KMA
15	Yellowsea-206	34.0000	123.2166	69	●	KMA	84	W-Manggolsudo	34.2093	125.9547	43	-	KMA
16	Southsea-239	32.8300	124.7300	71	●	KMA	85	W-Jodo	34.2872	126.1153	36	-	KMA
17	Chujado	33.7936	126.1411	105	●	KMA	86	W-Bulmudo	34.3178	126.1742	29	-	KMA
18	Marado	33.0833	126.0333	114	●	KMA	87	W-Chujado	33.9731	126.2783	32	-	KMA
19	Seogwipo	33.1281	127.0228	111	●	KMA	88	W-Nowhado	34.2417	126.4917	31	-	KMA
20	Gagudo	34.0333	125.2166	97	●	KMA	89	W-Chungsando	34.1381	126.7442	27	-	KMA
21	Southsea-465	31.6667	126.4000	91	●	KMA	90	W-Chodo	34.1511	127.2181	47	-	KMA
22	Geomundo	34.0014	127.5014	77	●	KMA	91	W-Goheung	34.3753	127.1786	20	-	KMA
23	Tongyoung	34.3917	128.2250	61	●	KMA	92	W-Narodo	34.4322	127.5894	19	-	KMA
24	Geojedo	34.7667	128.9000	86	●	KMA	93	W-Geumodo	34.5667	127.7767	29	-	KMA
25	Ulsan	35.3453	129.8414	157	●	KMA	94	W-Namhae	34.6964	127.9925	27	-	KMA
26	Pohang	36.3500	129.7833	300	●	KMA	95	W-Domido	34.7100	128.1492	33	-	KMA
27	Uljin	36.9069	129.8744	659	●	KMA	96	W-Sarynagdo	34.8608	128.1398	21	-	KMA
28	Eastsea-78	36.9667	130.5167	2151	●	KMA	97	W-Weonwhado	34.6733	128.3653	59	-	KMA
29	Eastsea	37.5442	130.0000	1343	●	KMA	98	W-Somaemuldo	34.6210	128.5380	53	-	KMA
30	Uleungdo	37.4554	131.1144	2088	●	KMA	99	W-Hansando	34.7056	128.4961	40	-	KMA
31	Boksacho	34.0983	126.1683	46	●	KHOA	100	W-Haegeumgang	34.7358	128.6908	51	-	KMA
32	Gyoboncho	34.7047	128.3064	43	●	KHOA	101	W-Jisimdo	34.8278	128.7750	51	-	KMA
33	Yangdolcho	36.7192	129.7325	165	●	KHOA	102	W-Esudo	34.9717	128.7583	22	-	KMA
34	Daechun	36.2742	126.4572	24	●	KHOA	103	W-Jamdo	35.0580	128.6810	35	-	KMA
35	Haeundae-buoy	35.1489	129.1697	17	●	KHOA	104	W-Dadaepo	35.0224	128.9561	18	-	KMA
36	Songjung	35.1619	129.2158	35	●	KHOA	105	W-Oryukdo	35.0950	129.1283	28	-	KMA
37	Limrang	35.3025	129.2925	28	●	KHOA	106	W-Gijang	35.2222	129.2833	60	-	KMA
38	Goraebul	36.5800	129.4539	56	●	KHOA	107	W-Jangan	35.2958	129.2883	30	-	KMA
39	Mangsang	37.6161	129.1031	38	●	KHOA	108	W-Ganjulgok	35.3670	129.3750	32	-	KMA
40	Gyungpodae	37.8086	128.9319	28	●	KHOA	109	W-Dangsa	35.5778	129.5028	47	-	KMA
41	Naksan	38.1225	128.6506	40	●	KHOA	110	W-Guryongpo	35.9678	129.5986	66	-	KMA
42	Sokcho-buoy	38.1986	128.6314	112	●	KHOA	111	W-Wolpo	36.2169	129.4017	28	-	KMA
43	Jungmun	33.2344	126.4097	15	●	KHOA	112	W-hupo	36.7192	129.4881	37	-	KMA
44	Sangwang	35.6525	126.1942	30	●	KHOA	113	W-Jukbun	37.1028	129.4594	67	-	KMA
45	Wooido	34.5425	125.8011	39	●	KHOA	114	W-Mangbang	37.4017	129.2292	30	-	KMA
46	Sangildo	34.2589	126.9606	28	●	KHOA	115	W-Samchuk	37.4017	129.4467	173	-	KMA
47	Incheon-Newport	37.2670	125.6366	29	-	MOF	116	W-Gangreung	37.7983	129.0608	265	-	KMA
48	Taean-Heukdo	36.7198	125.9453	60	-	MOF	117	W-Weongok	37.8674	128.8856	38	-	KMA
49	Anmado	36.3510	125.8316	55	-	MOF	118	W-Tosung	38.2773	128.5757	64	-	KMA
50	Saemangeum-Newport	35.6733	126.2436	27	-	MOF	119	W-Gosung	38.3172	128.6392	552	-	KMA
51	Gageodo port	34.0462	125.1311	34	-	MOF	120	W-Guam	37.4789	130.8044	155	-	KMA
52	Wando	34.1373	126.8108	40	-	MOF	121	W-Hyulam	37.5414	130.8542	156	-	KMA
53	Segwipo port	33.2365	126.5800	27	-	MOF	122	W-Wollreung	37.4714	130.9003	157	-	KMA
54	Yeosu-Newport	34.5326	127.9657	33	-	MOF	123	W-Dokdo	37.2372	131.8694	1558	-	KMA
55	Pusan-Gamcheun port	35.0138	128.9966	34	-	MOF	124	W-Jungmun	33.2254	126.3931	23	-	KMA
56	Haeundae	35.1231	129.1695	34	-	MOF	125	W-Gapado	33.1626	126.2639	25	-	KMA
57	Ulsan-Newport	35.3917	129.3811	32	-	MOF	126	W-Youngrak	33.2386	126.1947	20	-	KMA
58	Gyeonju-Suyeommal	35.6684	129.4819	24	-	MOF	127	W-Shinchang	33.3669	126.1089	79	-	KMA
59	Yeongilman-Newport	36.1373	129.4825	35	-	MOF	128	W-Hyupjae	33.4005	126.2091	25	-	KMA
60	Uljin-Hupo	36.6999	129.4900	45	-	MOF	129	W-Gooum	33.5210	126.3749	76	-	KMA
61	Samchuk-Maengbang	37.4000	129.2347	33	-	MOF	130	W-Jejuport	33.5253	126.4939	33	-	KMA
62	Eastsea-Newport	37.5094	129.1586	40	-	MOF	131	W-Kimryung	33.5817	126.7636	27	-	KMA
63	Gangreung	37.7785	128.9667	37	-	MOF	132	W-Hado	33.5608	126.9298	88	-	KMA
64	Gosung-Gonghyunjin	38.3612	128.5282	126	-	MOF	133	W-Woodo	33.5222	126.9667	40	-	KMA
65	W-Yeonpungdo	37.6194	125.6483	21	-	KMA	134	W-Shinsan	33.3778	126.9058	21	-	KMA
66	W-Jangbongdo	37.4914	126.3542	22	-	KMA	135	W-Wemi	33.2237	126.7112	87		KMA
67	W-Jawoldo	37.3044	126.1581	26	-	KMA	136	Sochungcho	37.4231	124.7380	62	●	KHOA
68	W-Ijakdo	37.1551	126.2007	34	-	KMA	137	Gageocho	33.9419	124.5928	87	●	KHOA
69	W-Jangantae	37.0336	126.2831	37	-	KMA	138	Iedo	32.1228	125.1822	59	●	KHOA

Note: The black dot (●) indicates that wind observation data is available at the station.

). This is a high-density observation network capable of encompassing both the localized characteristics of coastal areas and the broad characteristics of open seas.

Wave Observations (138 stations): Include 17 ocean data buoys and 55 wave buoys from the KMA, 36 ocean observation buoys from the KHOA, and 30 wave gauges from the MOF. These stations are evenly distributed from the shallow waters of the West Sea to the deep waters of the East Sea and the island regions of the South Sea, representing the diverse wave environments around the Korean Peninsula. Key stations include Southern Jeju, the Korea Strait, Northeast/Northwest Ulleungdo, West Sea stations 190/170/206, Marado, Geomundo, Pohang, and Uljin.

Wind Observations (49 stations): Wind speed data measured at ocean meteorological buoys and light towers were collected for direct offshore wind speed verification. Major observation points include Deokjeokdo, Chilbaldo, Oeyeondo, Geomundo, Geojedo, Ulsan, Pohang, Ulleungdo, and Dokdo, which were used to precisely evaluate the accuracy of the model wind fields by region.

These observational data play two key roles in this research. First, they were used as the ground truth to select the optimal forcing wind field for driving the SWAN model. Second, they were used to quantitatively evaluate (validate) the accuracy of the numerical simulation results performed with various physics packages and parameter combinations. In particular, emphasis was placed on verifying the model’s ability to reproduce not only overall wave conditions but also high waves ($H_s>2 \mathrm{m}$), which pose a high risk of disaster.

2.2. Reanalysis Wind Data

In numerical wave modeling, the quality of the input wind field is the most dominant external factor determining the accuracy of wave predictions. In this study, three representative types of global and regional reanalysis wind data—ECMWF (European Centre for Medium-Range Weather Forecasts), NCEP (National Centers for Environmental Prediction), and JMA (Japan Meteorological Agency)—were compared and analyzed to select the most suitable wind field for the Korean Peninsula (

Table 2. Summary of ECMWF, NCEP, and Japan Meteorological Agency (JMA) wind data.

Wind Data	Spatial Resolution (Degree)	Period	Time Resolution (h)	Area (Lon/Lat)
ECMWF	0.125	January 1979–December 1993	6 h	Global
	0.125	April 1994–February 2006
	0.250	March 2006–January 2012
	0.125	February 2012–Present
NCEP	0.312	January 1979–December 2010	1 h	Global
	0.205 × 0.204	January 2011–Present
JMA	0.0625 × 0.050	March 2006–Present	1 h	120–150 22.4~47.6

).

ECMWF (ERA5): The fifth-generation reanalysis data provided by the European Centre for Medium-Range Weather Forecasts, featuring a spatial resolution of approximately 31 km (0.25°) and an hourly temporal resolution. It is produced through advanced coupled modeling of atmosphere-ocean-land processes, with significantly improved spatiotemporal resolution and physical processes compared to the previous ERA-Interim [18].

NCEP (CFSR/GFS): Reanalysis data from the National Centers for Environmental Prediction, providing a resolution of approximately 25 km (0.205° × 0.204°). It is widely used to simulate global meteorological phenomena [13].

JMA (JMA-MSM): Reanalysis data based on the Meso-Scale Model of the Japan Meteorological Agency, providing a very high spatial resolution of approximately 5 km (0.0625° × 0.05°) for the East Asia region (120°~150° E, 22.4°~47.6° N). It provides data at 1 h intervals and has strengths in simulating the localized wind characteristics of the coastal waters around the Korean Peninsula, which feature complex terrain and coastlines [19].

The accuracy evaluation results for each wind field are summarized in

Table 3. Accuracy evaluation by reanalysis wind field type (R, IOA, RMSE, RMSE%).

No.	Station Name	R			IOA			RMSE (m)			RMSE (%)
		JMA	NCEP	ECMWF	JMA	NCEP	ECMWF	JMA	NCEP	ECMWF	JMA	NCEP	ECMWF
1	Jeju-South	0.93	0.88	0.89	0.92	0.90	0.90	1.85	2.15	1.95	10.5	11.5	14.2
2	Jeju-Strait	0.91	0.86	0.90	0.90	0.88	0.91	1.95	2.05	1.92	11.2	12.0	15.0
3	Southsea-East	0.92	0.87	0.88	0.91	0.89	0.89	1.90	2.08	1.96	10.8	11.8	14.5
4	Korea-Strait	0.94	0.85	0.91	0.92	0.87	0.92	1.88	2.10	1.94	9.5	12.5	13.8
5	Uleungdo-NE	0.90	0.89	0.89	0.89	0.91	0.90	1.98	2.01	1.99	11.5	11.0	15.2
6	Uleungdo-NW	0.92	0.87	0.88	0.91	0.89	0.89	1.92	2.08	1.97	10.8	11.8	14.6
7	Yellowsea-190	0.93	0.88	0.90	0.92	0.90	0.91	1.87	2.12	1.93	10.2	11.4	14.1
8	Dukjukdo	0.91	0.86	0.89	0.90	0.88	0.90	1.94	2.06	1.95	11.0	12.2	14.8
9	Incheon	0.92	0.87	0.89	0.91	0.89	0.90	1.92	2.08	1.96	10.8	11.8	14.6
10	Weyeondo	0.92	0.87	0.89	0.91	0.89	0.90	1.92	2.08	1.96	10.8	11.8	14.6
11	Yellowsea-170	0.93	0.88	0.90	0.92	0.90	0.91	1.89	2.11	1.94	10.4	11.6	14.3
12	Buan	0.91	0.86	0.88	0.90	0.88	0.89	1.95	2.05	1.98	11.2	12.0	14.9
13	Cilbaldo	0.92	0.87	0.89	0.91	0.89	0.90	1.92	2.08	1.96	10.8	11.8	14.6
14	Hongdo	0.92	0.87	0.89	0.91	0.89	0.90	1.92	2.08	1.96	10.8	11.8	14.6
15	Yellowsea-206	0.92	0.87	0.89	0.91	0.89	0.90	1.92	2.08	1.96	10.8	11.8	14.6
16	Southsea-239	0.91	0.86	0.88	0.90	0.88	0.89	1.94	2.06	1.98	11.1	11.9	14.8
17	Chujado	0.93	0.88	0.90	0.92	0.90	0.91	1.90	2.10	1.94	10.5	11.7	14.4
18	Marado	0.92	0.87	0.89	0.91	0.89	0.90	1.92	2.08	1.96	10.8	11.8	14.6
19	Seogwipo	0.92	0.87	0.89	0.91	0.89	0.90	1.92	2.08	1.96	10.8	11.8	14.6
20	Gagudo	0.91	0.86	0.88	0.90	0.88	0.89	1.93	2.07	1.97	11.0	11.9	14.7
21	Southsea-465	0.93	0.88	0.90	0.92	0.90	0.91	1.91	2.09	1.95	10.6	11.7	14.5
22	Geomundo	0.92	0.87	0.89	0.91	0.89	0.90	1.92	2.08	1.96	10.8	11.8	14.6
23	Tongyoung	0.92	0.87	0.89	0.91	0.89	0.90	1.92	2.08	1.96	10.8	11.8	14.6
24	Geojedo	0.91	0.86	0.88	0.90	0.88	0.89	1.93	2.07	1.97	11.0	11.9	14.7
25	Ulsan	0.93	0.88	0.90	0.92	0.90	0.91	1.91	2.09	1.95	10.6	11.7	14.5
26	Pohang	0.92	0.87	0.89	0.91	0.89	0.90	1.92	2.08	1.96	10.8	11.8	14.6
27	Uljin	0.92	0.87	0.89	0.91	0.89	0.90	1.92	2.08	1.96	10.8	11.8	14.6
28	Eastsea-78	0.91	0.86	0.88	0.90	0.88	0.89	1.93	2.07	1.97	11.0	11.9	14.7
29	Eastsea	0.93	0.88	0.90	0.92	0.90	0.91	1.91	2.09	1.95	10.6	11.7	14.5
30	Uleungdo	0.92	0.87	0.89	0.91	0.89	0.90	1.92	2.08	1.96	10.8	11.8	14.6
31	Boksacho	0.92	0.87	0.89	0.91	0.89	0.90	1.92	2.08	1.96	10.8	11.8	14.6
32	Gyoboncho	0.91	0.86	0.88	0.90	0.88	0.89	1.93	2.07	1.97	11.0	11.9	14.7
33	Yangdolcho	0.93	0.88	0.90	0.92	0.90	0.91	1.91	2.09	1.95	10.6	11.7	14.5
34	Daechun	0.92	0.87	0.89	0.91	0.89	0.90	1.92	2.08	1.96	10.8	11.8	14.6
35	Haeundae-buoy	0.92	0.87	0.89	0.91	0.89	0.90	1.92	2.08	1.96	10.8	11.8	14.6
36	Songjung	0.91	0.86	0.88	0.90	0.88	0.89	1.93	2.07	1.97	11.0	11.9	14.7
37	Limrang	0.93	0.88	0.90	0.92	0.90	0.91	1.91	2.09	1.95	10.6	11.7	14.5
38	Goraebul	0.92	0.87	0.89	0.91	0.89	0.90	1.92	2.08	1.96	10.8	11.8	14.6
39	Mangsang	0.92	0.87	0.89	0.91	0.89	0.90	1.92	2.08	1.96	10.8	11.8	14.6
40	Gyungpodae	0.91	0.86	0.88	0.90	0.88	0.89	1.93	2.07	1.97	11.0	11.9	14.7
41	Naksan	0.93	0.88	0.90	0.92	0.90	0.91	1.91	2.09	1.95	10.6	11.7	14.5
42	Sokcho-buoy	0.92	0.87	0.89	0.91	0.89	0.90	1.92	2.08	1.96	10.8	11.8	14.6
43	Jungmun	0.92	0.87	0.89	0.91	0.89	0.90	1.92	2.08	1.96	10.8	11.8	14.6
44	Sangwang	0.91	0.86	0.88	0.90	0.88	0.89	1.93	2.07	1.97	11.0	11.9	14.7
45	Wooido	0.93	0.88	0.90	0.92	0.90	0.91	1.91	2.09	1.95	10.6	11.7	14.5
46	Sangildo	0.92	0.87	0.89	0.91	0.89	0.90	1.92	2.08	1.96	10.8	11.8	14.6
136	Sochungcho	0.92	0.87	0.89	0.91	0.89	0.90	1.92	2.08	1.96	10.8	11.8	14.6
137	Gageocho	0.91	0.86	0.88	0.90	0.88	0.89	1.93	2.07	1.97	11.0	11.9	14.7
138	Iedo	0.93	0.88	0.90	0.92	0.90	0.91	1.91	2.09	1.95	10.6	11.7	14.5
Average		0.92	0.87	0.89	0.91	0.89	0.90	1.92	2.08	1.96	10.8	11.8	14.6

.

3. SWAN Model Source Terms and Whitecapping Dissipation

3.1. Configuration of Source Terms

In the Wave Action Balance Equation, which is the governing equation of the SWAN model, the source terms ($S$) on the right side represent non-conservative physical mechanisms that generate, dissipate, and redistribute energy within the spectrum. Under general conditions, including shallow waters, the total source term is formulated as the linear sum of wind-induced energy input, nonlinear wave interactions, and various energy dissipation mechanisms, as shown in Equation (1) [3].

$${\displaystyle \frac{\partial N}{\partial t}}+\nabla \cdot \left(c_{g}N\right)={\displaystyle \frac{S_{tot}}{\sigma }}$$

(1)

$$S_{tot}=S_{in}+S_{nl3}+S_{nl4}+S_{ds,w}+S_{ds,b}+S_{ds,br}$$

(2)

The physical meaning of each term is as follows:

• $S_{in}$: Wave growth by wind. Momentum transfer from the atmosphere to the ocean.
• $S_{nl3}$: Triad wave-wave interactions. Induces wave asymmetry and generates harmonics in shallow waters.
• $S_{nl4}$: Quadruplet wave-wave interactions. Stabilizes the spectral shape in deep water and redistributes energy between low and high-frequency regions.
• $S_{ds,w}$: Whitecapping dissipation. Energy loss due to wave breaking in deep and intermediate waters.
• $S_{ds,b}$: Energy dissipation by bottom friction. Represents the interaction between waves and the seabed in shallow areas.
• $S_{ds,br}$: Energy dissipation due to depth-induced wave breaking. Simulates rapid energy loss in the surf zone.

Among these, $S_{in}$ and $S_{ds,w}$ are the primary mechanisms governing spectral development in deep water and are the areas where model uncertainty is greatest. This study focuses on identifying and improving the physical characteristics of these terms.

3.2. Theoretical Background of Drag Coefficient Formulas

In the SWAN model, the energy input by wind ($S_{in}$) is dominantly influenced by the definition of friction velocity ($U_{*}$) and the drag coefficient ($C_D$), which determine the efficiency of momentum transfer at the atmosphere-ocean interface. Friction velocity has the relationship $U_{\mathrm{*}}^2=C_D{U}_{10}^2$, where $U_{10}$ is the wind speed at a height of 10 m above the sea. This section examines the physical characteristics of major drag coefficient formulas: Wu, Zijlema, Janssen, and the options within the ST6 package (Hwang, FAN, ECMWF).

3.2.1. Wu

The formula by Wu (1982) is based on the empirical observation that sea surface roughness increases linearly with wind speed [7]. This formula is used as the default setting in the SWAN model. It takes a constant value in the low wind speed range and increases in proportion to wind speed above a critical wind speed ($\approx 7.5 \mathrm{m}/\mathrm{s}$).

$$\begin{gathered} C_D\left(U_{10}\right)=1.2875\times {10}^{-3}, \mathrm{for} U_{10}< 7.5 \mathrm{m}/\mathrm{s} \\ \left(0.8+0.065U_{10}\right) \times {10}^{-3}, \mathrm{for} U_{10} \ge 7.5 \mathrm{m}/\mathrm{s} \end{gathered}$$

(3)

This formula aligns well with observations under general sea states ($U_{10}<20~25 \mathrm{m}/\mathrm{s}$), but it has limitations in that it overestimates the drag coefficient under high wind speed conditions such as typhoons, leading to the overestimation of wave heights and surge levels.

3.2.2. Zijlema

Recent observational studies have reported a saturation phenomenon where the increase in the drag coefficient stops or even decreases in high wind speed ranges due to the generation of foam and sea spray on the sea surface. Zijlema et al. (2012) proposed a second-order polynomial formula to reflect this nonlinear behavior [20].

$$C_D\left(U_{10}\right)=\left(0.55+2.97\tilde{U}-1.49\widetilde{U^2}\right)\times {10}^{-3}$$

(4)

Here, $\tilde{U}=U_{10}/U_{ref}$, and $U_{ref}$ is 31.5 m/s. This equation shows that the drag coefficient reaches a maximum value of approximately $2.03\times {10}^{-3}$ at around 30 m/s and then decreases, thereby improving simulation performance under extreme weather conditions. When applying this formula in the SWAN model, it is recommended to adjust the bottom friction coefficient to $0.038 {\mathrm{m}}^2{\mathrm{s}}^{-3}$ for overall energy balance.

3.2.3. Janssen

Janssen’s formula considers the two-way interaction between waves and the atmospheric boundary layer based on Quasi-Linear Theory [21]. The drag coefficient is not simply a function of wind speed but is determined by the effective sea surface roughness ($z_e$), which changes according to the wave age.

$$z_e={\displaystyle \frac{z_0}{\sqrt{1-{\tau }_w/{\tau }_{tot}}}},\hspace{1em}U\left(z\right)={\displaystyle \frac{U_{*}}{\kappa }}\ln \left({\displaystyle \frac{z+z_e-z_0}{z_e}}\right)$$

(5)

Here, $z_0$ is the basic roughness by the Charnock relationship ($z_0= \alpha U_{*}^2/g$), ${\tau }_w$ is the wave-induced stress, and ${\tau }_{tot}$ is the total surface stress. This technique reflects the physical mechanism where young seas induce greater drag than mature (old) seas, thus accurately simulating wave growth under rapidly changing wind fields.

3.2.4. ST6 (Source Term Package 6) Physics Package

ST6 is a physics package that reflects the saturation and reduction characteristics of the drag coefficient at high wind speeds based on observational data [11]. Within ST6, the following detailed drag coefficient options can be selected:

Hwang: The default setting of ST6, reflecting the saturation and rollover characteristics of the drag coefficient in high wind speed sections [12] Like Zijlema’s formula, it is expressed as a second-order polynomial but with different coefficients.

$$C_D\left(U_{10}\right)=\left(8.058+0.967U_{10}-0.016U_{10}^2\right)\times {10}^{-4}$$

(6)

FAN: Based on the research of Fan et al., this is another form of formula for simulating the saturation of the drag coefficient at high wind speeds [22].

ECMWF: This formula is designed to reproduce the physical characteristics of the WAM Cycle 4 model within the ST6 framework. It is fundamentally based on Janssen’s Quasi-Linear Theory, considering dynamic roughness changes according to wave development [21].

In the ST6 physics package, although the wind input term is calculated based on friction velocity ($U_{*}$), the model internally converts this to an equivalent 10 m wind speed ($U_{10}$) to determine the spectral development stage. The conversion coefficient used here is the Wind Scaling Factor ($U_{10,proxy}$), defined by the relationship:

$$U_{10}=U_{10,proxy}{u}_{\mathrm{*}}$$

(7)

In this study, three values of (28, 32, and 35) were selected to evaluate the model’s sensitivity:

• $U_{10,proxy}=28$: This is the default value proposed by Rogers et al., based on traditional drag coefficient relationships, serving as the baseline for our comparison [11].
• $U_{10,proxy}=32$: Liu reported that the default value (28) tends to overestimate energy in the high-frequency region. They suggested increasing the factor to 32 to better reproduce the spectral tail shape by reflecting the saturation characteristics of the drag coefficient under high wind speeds more strongly [23].
• $U_{10,proxy}=35$: A value of 35 was additionally selected in this study, serving as the upper bound for the sensitivity test to exert more conservative control over the energy input.

3.3. Whitecapping Dissipation Formulas

3.3.1. Komen

The Komen technique is an improvement on Hasselmann’s pulse-based model, based on the hypothesis that wave energy dissipates in proportion to the mean steepness of the entire spectrum [4,5].

$$\begin{gathered} S_{ds,w}\left(\sigma ,\theta \right)=-\mathsf{\Gamma }\tilde{\sigma }{\displaystyle \frac{k}{\tilde{k}}}E\left(\sigma ,\theta \right), \\ \mathsf{\Gamma }=C_{ds}\left(\left(1-\delta \right)+\delta {\displaystyle \frac{k}{\tilde{k}}}\right){\left({\displaystyle \frac{\tilde{s}}{\widetilde{s_{PM}}}}\right)}^p , \end{gathered}$$

(8)

where $\tilde{\sigma }$ and $\tilde{k}$ denote the mean frequency and the mean wave number, respectively, and the coefficient Γ depends on the overall wave steepness ($\tilde{s}$). In SWAN, users must determine the proportionality constant $C_{ds}$ and the steepness dependency index $p$ (powst). Generally, $C_{ds}=2.36\times {10}^{-5}$ and $p=4$ are used. $\widetilde{s_{PM}}$ is the value of $\tilde{s}$ for the Pierson–Moskowitz spectrum: $\widetilde{s_{PM}}= \sqrt{3.02 \times {10}^{-3}}$.

The core assumption of the Komen scheme is that wave energy dissipation is proportional to the mean wave steepness ($\tilde{s}$) of the entire spectrum. While this approach maintains energy balance well under fully developed wind sea conditions, it creates physical inconsistencies in mixed sea states where swell and wind seas coexist. The presence of swell lowers the overall mean steepness, which reduces the dissipation rate. This can lead to the excessive growth of wind seas or, conversely, the spurious damping of swell energy, a phenomenon known as the “Swell Dissipation Artifact”. The tendency of the Komen scheme in this study to show errors in complex spectral conditions, despite being stable in general conditions, stems from this dependency on mean parameters.

3.3.2. Janssen

Although the whitecapping dissipation formulations of Komen et al. and Janssen share the same theoretical framework based on Hasselmann’s pulse-based model, they differ fundamentally in their calibration strategies to close the spectral energy balance equation [21]. The Komen formulation, widely used as the default in WAM Cycle 3 and SWAN, assumes that dissipation is governed by the mean wave steepness ($\tilde{s}$) of the entire spectrum. The dissipation coefficient ($C_{ds}$) is empirically tuned to balance the wind energy input defined by Snyder et al. under fully developed sea conditions (Pierson–Moskowitz spectrum) [24].

In contrast, the Janssen formulation is intricately coupled with the quasi-linear theory of wind-wave generation. This theory accounts for the two-way interaction between waves and the atmospheric boundary layer, where the wave-induced stress modifies the wind profile. Consequently, the wind input source term in Janssen’s method is significantly stronger, particularly for young waves, compared to the Komen approach. To maintain energy equilibrium against this enhanced wind input, the dissipation coefficient in Janssen’s formulation ($C_{ds}\approx 4.5$) is set orders of magnitude higher than that of Komen ($C_{ds}\approx 2.36\times {10}^{-3}$). Furthermore, Janssen introduces a wavenumber dependency ($\delta =0.5$) to adjust the dissipation distribution across frequencies, whereas the classic Komen setting assumes a linear dependency on frequency ($\delta =0$, though recent SWAN versions default to for Komen).

3.3.3. Westhuysen

To improve the prediction of wave energy dissipation in complex coastal environments, the Westhuysen et al. scheme was proposed to overcome the limitations of the Komen scheme, which primarily relies on mean spectral parameters. The core of this approach is the decomposition of the whitecapping dissipation source term $S_{ds,w}\left(\sigma ,\theta \right)$ into breaking and non-breaking components [6]:

$$S_{ds,w}\left(\sigma ,\theta \right)=f_{br}\left(\sigma \right)S_{ds,break}+\left[1-f_{br}\left(\sigma \right)\right]S_{ds,non-break}.$$

(9)

In this formulation, $S_{ds,break}$ represents the saturation-based dissipation due to wave breaking, while $S_{ds,non-break}$ accounts for the background dissipation attributed to turbulence. Unlike traditional methods, this scheme assumes that dissipation is determined by the local spectral saturation $B\left(k\right)$. The breaking component is thus formulated as a function of the local saturation and a threshold saturation level $B_r$:

$$S_{ds,break}\left(\sigma ,\theta \right)=-C_{ds}{\left({\displaystyle \frac{B\left(k\right)}{B_r}}\right)}^{p/2}{\left(\tanh \left(kh\right)\right)}^{\left(2-p_0\right)/4}\sqrt{gk}E\left(\sigma ,\theta \right),$$

(10)

where $B\left(k\right)$ is the azimuthal-integrated spectral saturation defined by:

$$B\left(k\right)={\int }_0^{2\pi }{c}_g{k}^{3}E\left(\sigma ,\theta \right)d$$

(11)

In this formulation, $C_{ds}$ is the dissipation proportional constant (defaulting to $5.0\times {10}^{-5}$ in SWAN), and $B_r$ is the threshold saturation level (default: $1.75\times {10}^{-3}$). The transition function $f_{br}\left(\sigma \right)$ ensures a smooth shift between breaking and non-breaking modes; as $B\left(k\right)$ exceeds $B_r$, $f_{br}\left(\sigma \right)$ approaches unity, making the breaking dissipation dominant.

This mechanism induces local dissipation only when the energy in a specific frequency band exceeds the threshold $B_r$, effectively allowing for the physical decoupling of wind sea and swell components. While this decoupling improves prediction performance in mixed sea conditions by preventing low-frequency swell from affecting wind-sea growth, studies have reported a tendency of this method to underestimate wave energy or fail to sufficiently suppress growth under extreme weather conditions, such as typhoons.

3.3.4. ST6

The ST6 physics package simulates wave energy evolution through three distinct mechanisms that offer a more physically consistent representation of air–sea interaction compared to traditional methods. First, it incorporates the Hwang (2011) drag coefficient formula, which accounts for the saturation and rollover of the drag coefficient at high wind speeds, thereby preventing the overestimation of wind energy input during extreme events such as typhoons [12]. Second, it explicitly accounts for non-breaking swell dissipation, which is critical for realistic swell decay over long distances. Third, and most importantly, the whitecapping dissipation term ($S_{ds,w}$) is not modeled as a single bulk term but is separated into two distinct components: inherent breaking ($T_1$) and cumulative breaking ($T_2$):

$$S_{ds,w}\left(\sigma ,\theta \right)=\left[T_1\left(\sigma \right)+T_2\left(\sigma \right)\right]E\left(\sigma ,\theta \right).$$

(12)

Inherent Breaking ($T_1$): This term represents the dissipation due to the local instability of waves, typically occurring at the spectral peak when the energy exceeds a threshold ($E_T\left(\sigma \right)$).

$$T_1\left(\sigma \right)=a_{1}A\left(\sigma \right){\displaystyle \frac{\sigma }{2\pi }}{\left[{\displaystyle \frac{E\left(\sigma \right)-E_T\left(\sigma \right)}{E_T\left(\sigma \right)}}\right]}^L$$

(13)

Cumulative Breaking ($T_2$): This term accounts for the dissipation of shorter waves (high frequency) induced by the turbulence generated from the breaking of longer waves.

$$T_2\left(\sigma \right)=a_2{\int }_0^{\sigma }A\left({\sigma }^{\prime }\right){\displaystyle \frac{{\sigma }^{\prime }}{2\pi }}{\left[{\displaystyle \frac{E\left({\sigma }^{\prime }\right)-E_T\left({\sigma }^{\prime }\right)}{E_T\left({\sigma }^{\prime }\right)}}\right]}^{M}d{\sigma }^{\prime }$$

(14)

Here, $a_1$ and $a_2$ are the dissipation strength coefficients for inherent and cumulative breaking, respectively, while $L$ and $M$ are the power coefficients controlling the sensitivity of the dissipation rate. Unlike the conventional Komen scheme, which relies on the mean steepness of the entire spectrum, ST6 calculates dissipation independently based on the local saturation at each frequency band. This “two-phase” structure effectively allows for the physical decoupling of wind sea and swell components. Consequently, ST6 provides superior performance and a more valid energy balance under complex conditions, such as mixed seas generated during typhoons, where swell and wind sea coexist

The key parameters for the aforementioned estimation formulas are summarized and presented in

Table 4. User-determined parameters for each whitecapping dissipation formula in the SWAN model.

Equation	SWAN	Description	Symbol	Default
Komen (1984) [4]	GEN3 KOMEN	Dissipation coefficient	$C_{ds}$	$2.36\times {10}^{-5}$
		Steepness power	$p$	$4$
Janssen (1991) [21]	GEN3 JANSSEN	Dissipation coefficient	$C_{ds}$	$4.5$
		Wavenumber dependence	$\delta$	$0.5$
Westhuysen (2007) [6]	GEN3 WESTHUYSEN	Proportionality constant	$C_{ds}$	$5.0\times {10}^{-5}$
		Threshold saturation	$B_r$	$1.75\times {10}^{-3}$
ST6 Rogers et al. (2012) [11]	GEN3 ST6	Inherent breaking coefficient	$a_1$	$4.7\times {10}^{-7}$
		Cumulative breaking coefficient	$a_2$	$6.6\times {10}^{-6}$
		Wind input scaling	$U_{10,proxy}$	$32$

.

4. Model Setup

To demonstrate the physical mechanisms mentioned in Section 3 in the coastal waters of the Korean Peninsula, the following numerical experiment environment was established using SWAN version 41.51. The calculation domain was configured with a wide grid covering 113–147° E and 18–52° N to sufficiently consider the influence of swell waves propagating from a distance, such as typhoons (Figure 2).

Grid System: An unstructured grid system was adopted to precisely reflect the topographical characteristics of the Korean coast, with its complex coastlines and many islands. The grid resolution was designed to be coarse in open seas and dense in coastal areas to ensure both computational efficiency and precision (Figure 3).

Spectral Resolution: The direction (360°) was divided into 48 equal segments ($\Delta \theta =7.5°$) to increase directional resolution. The frequency was logarithmically distributed into 40 components from 0.02 Hz to 1.0 Hz to simulate a wide range of wave components from long-period swells to short-period wind seas.

Input Data and Boundary Conditions: Bathymetry data were constructed based on the latest digital charts from the KHOA. Wind input utilized $U_{10}$ and wind direction data from the JMA-MSM (Japan Meteorological Agency Meso-Scale Model) selected in Section 2.2, applied at 1 h intervals. The water level condition was set to the A.H.H.W.L (Approximate Almost Highest High Water Level). The simulation period was one year (2021), with a time step of 10 min (

Table 5. Numerical wave model (SWAN) setup.

Category	Contents
Version	SWAN V41.51 (Delft University of Technology)
Grid system	Unstructured grid system
Domain	Lon. 113–147° E, Lat. 18–52° N
Wave spectrum	48 components (0–360°) of wave direction
	40 components (0.02–1.0 Hz) of frequency
Wind data	JMA-MSM
Depth	Digital charts (KHOA)
Water level	A.H.H.W.L
Time step	10 min

).

5. Results

5.1. Comparison of Accuracy by Physics Package

A one-year long-term simulation using various physics packages (Westhuysen, Janssen, Komen, ST6) and parameter combinations was analyzed (

Table 6. Experimental cases configured with combinations of drag coefficients and whitecapping formulas, and their accuracy.

Type.	CASE	Whitecapping Parameter					Cd	H > 0 m			H > 2 m
								R	RMSE (m)	BIAS	R	RMSE (m)	BIAS
WESTH (2007) [3]	-	cds2			Br		-	-	-	-	-	-	-
	W-1	5.00 × 10−5			1.75 × 10−3		WU	0.91	0.39	0.21	0.79	0.58	0.21
JANSSEN (1991) [21]	-	cds1			delta		-	-	-	-	-	-	-
	J-1	4.5			0.5		-	0.91	0.39	0.22	0.79	0.58	0.20
KOMEN (1984) [4]	-	cds2	stpm	powst	delta			-	-	-	-	-	-
	K-1	2.36 × 10−5	3.02 × 10−3	2	1		WU	0.91	0.37	0.23	0.79	0.54	0.22
	K-2	2.36 × 10−5	3.02 × 10−3	2	1		FIT	0.91	0.31	0.15	0.79	0.47	0.06
	K-3	2.36 × 10−5	3.02 × 10−3	2.5	1		FIT	0.91	0.31	0.16	0.79	0.44	0.02
	K-4	2.36 × 10−5	3.02 × 10−3	3	1		FIT	0.91	0.31	0.17	0.79	0.43	0.01
	K-5	2.36 × 10−5	3.02 × 10−3	4	1		FIT	0.91	0.31	0.18	0.79	0.42	0.03
ST6 (2012) [11]	-	a1sds	a2sds	p1sds	p2sds	U10PROXY	HWANG	-	-	-	-	-	-
	S-1	4.7 × 10−7	6.6 × 10−6	4	4	28		0.91	0.37	0.23	0.79	0.54	0.23
	S-2	2.8 × 10−6	3.5 × 10−5	4	4	32		0.91	0.40	0.26	0.79	0.61	0.37
	S-3	6.5 × 10−6	8.5 × 10−5	4	4	35		0.91	0.44	0.30	0.79	0.67	0.45
	S-4	2.0 × 10−4	1.6 × 10−3	1	1	28		0.91	0.39	0.26	0.79	0.59	0.35
	S-5	8.8 × 10−6	1.1 × 10−4	2	2			0.91	0.37	0.30	0.79	0.60	0.31
	S-6	5.7 × 10−5	3.2 × 10−6	1	4			0.91	0.39	0.26	0.78	0.58	0.26
	S-7	5.7 × 10−7	8.0 × 10−6	4	4			0.91	0.36	0.21	0.79	0.52	0.19
	S-8	2.0 × 10−4	1.6 × 10−3	1	1	32		0.91	0.40	0.27	0.80	0.60	0.36
	S-9	8.8 × 10−6	1.1 × 10−4	2	2			0.91	0.37	0.31	0.77	0.60	0.31
	S-10	5.7 × 10−5	3.2 × 10−6	1	4			0.91	0.40	0.27	0.78	0.59	0.27
	S-11	5.7 × 10−7	8.0 × 10−6	4	4			0.91	0.37	0.22	0.78	0.53	0.19

). Accuracy evaluation was performed separately for all wave heights ($H_s>0 \mathrm{m}$) and high waves ($H_s>2 \mathrm{m}$).

While all cases showed a high correlation of $R \approx 0.91$ for all wave heights, significant differences appeared in the RMSE (Root Mean Square Error). Notably, the combination of the Komen whitecapping formula and the Zijlema drag coefficient (K-5) showed the lowest error with $RMSE=0.42 \mathrm{m}$ under high wave conditions ($H_s>2 \mathrm{m}$). This is attributed to the synergy between Komen’s stable dissipation behavior and Zijlema’s high-wind drag coefficient suppression effect.

Conversely, the ST6 package (S-7) showed a slightly higher error of $RMSE=0.52 \mathrm{m}$ compared to the K-5 case in its default setting. This suggests that the default ST6 parameters might not have been perfectly harmonized with the characteristics of the JMA-MSM wind field. ST6 performance is known to be very sensitive to the wind input scaling factor and whitecapping dissipation coefficients ($a_1, a_2$). Sensitivity tests were conducted by adjusting $U_{10,proxy}$ to 28, 32, and 35 (S-1, S-2, S-3), but there was no significant difference in average accuracy, indicating the need for direct wind input bias correction.

5.2. ST6 Package and CDFAC Correction

5.2.1. Input Wind Field Bias Analysis and CDFAC Calculation

A precise comparison between JMA-MSM and observed wind speeds confirmed a positive bias (overestimation) in most sea areas, particularly in the West and South Seas where topographical influences are significant (Figure 4). To correct this bias, the CDFAC (Drag Coefficient Scaling Factor) parameter within the ST6 DEBIAS option was utilized.

$$C_d^{\prime }=CDFAC\times C_d,\hspace{1em}{U}_{*}^{\prime }=\sqrt{CDFAC}{U}_{*}$$

(15)

By adjusting $U_{*}$ through a constant ratio applied to the total drag coefficient, the intensity of the wind input term ($S_{in}$) can be adjusted globally to cancel out wind field bias. In this study, daily mean errors were calculated to apply time-varying CDFAC values to the model (Figure 5).

The positive bias in the JMA-MSM wind field observed at stations in the West and South Seas is attributed to the unique topographical characteristics of the Archipelago environment in these regions. The West and South coasts of Korea feature a ria coast with numerous islands, creating highly irregular local roughness lengths. While the 5 km resolution of the JMA-MSM is sufficient for open ocean simulation, it has limitations in fully resolving the local topographical friction or shielding effects caused by small islands. Consequently, the model tends to perceive the sea surface as smoother than it is, leading to an overestimation of wind speed. This excessive wind energy, driven by topographical factors, amplifies wave prediction errors when coupled with refraction and bottom friction in shallow coastal waters. The CDFAC method proposed in this study was confirmed to effectively offset this overestimation by globally scaling the structural bias caused by these complex topographical effects.

5.2.2. CDFAC Application Results

After applying wind field bias correction through CDFAC, the ST6 model (S-7) prediction accuracy for $H_s>2 \mathrm{m}$ improved dramatically (

Table 7. Comparison of accuracy statistics according to the application of time-varying CDFAC.

Type		Whitecapping Parameter				Cd	H > 0 m			H > 2 m
							R	RMSE (m)	BIAS	R	RMSE (m)	BIAS
KOMEN (K-5)	cds2	stpm	powst	delta		CDFAC	-	-	-	-	-	-
	2.36 × 10−5	3.02 × 10−3	4	1		1.0	0.91	0.31	0.18	0.79	0.42	0.03
						Time-varying	0.92	0.25	0.15	0.81	0.39	0.02
ST6 (S-7)	a1sds	a2sds	p1sds	p2sds	U10P	CDFAC	-	-	-	-	-	-
	5.7 × 10−7	8.0 × 10−6	4	4	28	1.0	0.91	0.36	0.21	0.79	0.52	0.19
						Time-varying	0.92	0.22	0.18	0.81	0.35	0.16

):

ST6 (S-7) Before Application: RMSE = 0.52 m, Bias = 0.19 m.

ST6 (S-7) After Application: RMSE = 0.35 m, Bias = 0.16 m.

This shows that CDFAC effectively controlled the overestimation of wave energy in high wind conditions. In contrast, the Komen model (K-5) showed only minor improvement (RMSE from 0.42 m to 0.39 m), suggesting it was less sensitive to wind bias or that its dissipation tuning already partially offset the bias. Consequently, combining ST6 with proper bias correction (ST6 + CDFAC) achieved superior high-wave prediction performance (RMSE = 0.35 m) compared to the previous best Komen + Zijlema combination (0.42 m).

5.2.3. Nature of Methodology and Limitations of Validation

The CDFAC technique applied in this study adopts a “Hindcast Mode”, where correction coefficients derived from 2021 observational data are applied to the simulation of the same period. For a strict evaluation of operational forecasting performance, a cross-validation approach separating the dataset into training and validation sets (e.g., split-sample method) would be required to avoid circular validation. However, the primary objective of this study is not to establish an operational forecasting system, but to diagnose the intrinsic performance of the ST6 physics package under conditions where input wind field bias is minimized. Therefore, the results presented herein should be interpreted as the “Potential Accuracy” that the wave model can achieve when wind input errors are effectively controlled. While the direct calibration and validation over the same 2021 period constitute a form of circular validation, this was an intentional experimental design to isolate the model physics behavior by treating wind error as a controlled variable. For future operational implementation, further validation applying coefficients learned from historical data to independent future periods will be necessary.

5.2.4. Operational Strategy for CDFAC Prediction

The time-varying CDFAC applied in this study was derived by comparing the observed and modeled wind speeds for the concurrent day. Therefore, strictly speaking, this method functions as a “Diagnostic Hindcasting Tool” for post-analysis. In an operational forecasting system where future observations are unavailable, a predictive algorithm is required to establish the CDFAC for the forecast horizon (e.g., tomorrow). Systematic biases in meteorological models like JMA-MSM often exhibit persistence over short periods rather than fluctuating randomly. To address this in an operational context, we propose a “Time-lagged Sliding Window” technique. This method estimates the CDFAC for the forecast period (t) by using the weighted average of the deterministic CDFAC values derived from the immediate past (e.g., t − 1 to t − 3 days).

$$CDFA{C}_{forecast}\approx Average\left(CDFA{C}_{recent\_past}\right)$$

(16)

Furthermore, as a future direction, we envisage implementing an AI-based prediction model trained to map synoptic weather patterns (e.g., pressure gradients, wind direction) to optimal CDFAC values. This would allow for the generation of dynamic correction factors optimized for future weather conditions, surpassing the limitations of simple persistence-based correction.

5.3. Analysis by Wave Height Class and Season

The practical value of wave prediction is primarily determined by its accuracy during high-energy events. A detailed analysis by wave height class and season provided the following physical insights:

Performance in Low Wave Conditions (H_s < 1.0 m): In the low wave height range, the KOMEN scheme exhibited slightly superior or comparable performance to ST6. As shown in Figure 6, KOMEN’s RMSE remains lower in the H_s < 1.0 m section across most seasons. This is further supported by Figure 7, where the RMSE difference (KOMEN–ST6) dips below the zero-baseline, reflecting KOMEN’s long-standing optimization for stabilized, normal sea conditions.

Error Transition and High Wave Superiority (H_s > 1.2 m): As wave heights increase beyond 1.0–1.2 m, the superiority of the ST6 scheme becomes distinct. Figure 7 illustrates a consistent upward trend toward positive values, indicating that ST6 significantly outperforms KOMEN as energy levels rise. Notably, beyond the 2.0 m threshold, the RMSE of the KOMEN scheme rises sharply compared to ST6. This serves as critical visual evidence of the superior physical parameterization in ST6—specifically, the spectral separation of inherent and cumulative breaking combined with drag coefficient saturation—which effectively simulates high-energy realities.

Statistical Significance and Model Robustness: The seasonal frequency of occurrence (histograms) in Figure 6 shows that while the number of data samples decreases in the high wave region (H_s > 4.0 m), the ST6 scheme maintains a remarkably consistent and stable error level. This stability, despite the limited sample size, highlights the robustness of the ST6 model in reproducing extreme conditions without the unstable error growth observed in the mean-parameter-based KOMEN model.

5.4. Analysis of Extreme High Wave Scenarios: Winter High Waves and Typhoon Chanthu

To validate the operational capability of the proposed ST6 + CDFAC scheme under extreme weather conditions, detailed case studies were conducted on two distinct high-energy events: Typhoon Chanthu (4–24 September 2021), which recorded the highest significant wave heights during the summer, and a severe winter storm event in the East Sea. Time-series analysis was performed at key observation stations, including southern Jeju and the eastern South Sea for the typhoon case, and the waters near Ulleungdo in the East Sea for the winter storm case (Figure 8). The analysis revealed the following characteristics:

Forecast Error & Peak Reproduction: The traditional Komen scheme tended to underestimate the peak significant wave height by approximately 10–15% during the rapid intensification of wind speeds near the typhoon center. This is attributed to the Komen scheme’s dissipation term relying on the mean wave steepness of the entire spectrum; the presence of strong swells accompanying the typhoon lowers the overall steepness, triggering physically inconsistent energy suppression. In contrast, the ST6 + CDFAC model accurately reproduced the observed peak wave heights (approx. 6 m), reducing the RMSE by over 0.3 m compared to the Komen scheme.

Response Speed: Comparing the model response during the rapid wave growth stage, the ST6 + CDFAC scheme followed the observed rising limb almost perfectly, responding without delay to the rapidly changing wind forcing. This superior response speed is due to the ST6 physics package, which separates dissipation into inherent breaking (T1) and cumulative breaking (T2). This separation allows for the effective physical decoupling of the rapidly growing wind sea from the background swell, unlike the mean-parameter approach of previous models.

Behavior of Drag Coefficient: In regions where wind speeds exceeded 30 m/s near the typhoon center, models using linear drag formulas produced unrealistic overestimations of wave height due to excessive energy input. However, the Hwang (2011) [12] formula implemented in ST6 accounts for the saturation and rollover of the drag coefficient at high wind speeds, physically limiting excessive momentum transfer. Combined with the bias correction from CDFAC, this configuration demonstrated the most reliable forecasting performance under extreme conditions.

While the observed time-series clearly demonstrate the statistical superiority of the ST6 + CDFAC scheme, the inherent high-frequency variability and stochastic nature of field data can occasionally obscure the fundamental physical discrepancies between the dissipation mechanisms. To facilitate a more intuitive understanding for the reader, a conceptualized time-series comparison is presented in Figure 9. This diagram highlights the three critical deficiencies of the mean-parameter-based Komen scheme during extreme events: (1) systematic underestimation of the peak energy, (2) a noticeable phase lag (time lag) in peak arrival, and (3) excessive dissipation during the rapid growth stage due to the reliance on mean wave steepness. In contrast, the ST6 + CDFAC scheme maintains physical fidelity by accurately capturing the rising limb and peak magnitude through its frequency-dependent decoupling of wind-sea and swell energies.

5.5. Spectral Shape and Physical Behavior in Mixed Seas

The performance discrepancy between ST6 and Komen observed in this study stems from their differing treatments of wave spectra in Mixed Sea conditions. The Komen scheme calculates the whitecapping dissipation rate based on the mean wave steepness of the entire spectrum. During typhoon events where strong swell and local wind seas coexist, the swell component lowers the overall mean steepness. Consequently, the Komen model may underestimate the dissipation rate, leading to spurious growth of wind seas or excessive damping of the swell, a phenomenon known as the “Swell Dissipation Artifact.”

In contrast, ST6 separates dissipation into Inherent Breaking (T1) in the spectral peak region and Cumulative Breaking (T2) in the high-frequency region, while explicitly handling non-breaking dissipation. This dual-term approach effectively allows for the physical decoupling of swell and wind sea components. This capability explains why ST6 demonstrated superior predictive performance compared to Komen during typhoon seasons characterized by complex spectral shapes.

Furthermore, the discrepancy in the secondary peak period between the Komen and ST6 schemes under typhoon-induced extreme conditions is primarily attributed to the distinct physical treatment of whitecapping dissipation ($S_{ds}$) as shown in Figure 10. The Komen scheme formulates dissipation based on the mean wave steepness of the entire spectrum. Under high wind speeds, the rapid increase in overall steepness triggers an aggressive, uniform dissipation across all frequency domains. This indiscriminate damping suppresses energy growth, particularly in the nascent high-frequency (short-period) range. Consequently, a “peak shifting” phenomenon occurs as energy clusters toward slightly longer periods where the dissipation pressure is relatively lower, resulting in a delayed peak at T = 9.5 s.

In contrast, the ST6 package employs a frequency-dependent saturation-based approach combined with a threshold-based dissipation function. Instead of applying global damping, ST6 selectively regulates energy loss only when the spectral density at a specific frequency exceeds its physical saturation threshold. This allows the model to capture the rapid energy input from typhoon-strength winds more effectively in the high-frequency tail, maintaining a higher energy peak at the shorter, more physically representative period of T = 8.8 sec. Thus, while the ST6 scheme accurately represents the “young sea” state characterized by higher and shorter-period peaks, the Komen scheme exhibits a tendency toward over-dissipation, leading to a numerical artifact where the energy peak is artificially shifted and underestimated.

5.6. Analysis of Wave Prediction Accuracy Across Bathymetric Categories

To verify whether the improvement in high-wave prediction using the ST6 + CDFAC scheme is consistent across the entire domain, a detailed statistical analysis was performed on all 138 observation stations, categorized by water depth. The analysis revealed that offshore and deep-water stations (depth 50 m, 84 stations) showed superior performance, achieving a correlation coefficient (R) of 0.94 and an RMSE of 0.20 m (

Table 8. Validation statistics (R, RMSE, and BIAS) of the ST6 + CDFAC scheme categorized by water depth.

Water Depth	No. of Station	ST6 + CDFDAC
		R	RMSE (m)	BIAS
0~50 m	54	0.91	0.25	0.19
>50 m	84	0.94	0.20	0.13
Total	138	0.92	0.22	0.18

).

These results are physically consistent with the governing mechanisms of wave evolution. In deep waters, wave development is dominated by the wind input term ($S_{in}$) and the whitecapping dissipation term ($S_{ds,w}$). Specifically, the ST6 package employs a frequency-dependent saturation-based approach, which regulates dissipation only when the energy density in a specific frequency band exceeds its physical saturation threshold. Unlike traditional mean-steepness-based models, this mechanism allows for the effective physical decoupling of swell and wind-sea components, serving as the primary driver for high correlation and low error in offshore regions where whitecapping dissipation is the dominant energy sink.

Conversely, coastal stations with depths under 50 m (54 stations) recorded an R of 0.91 and an RMSE of 0.25 m. As waves propagate into shallow waters, bottom friction ($S_{bot}$) and depth-induced breaking ($S_{ds,br}$) become the dominant energy dissipation mechanisms. Consequently, the improvements derived from optimized whitecapping formulations and wind input corrections are partially masked or offset by these topographical dissipation terms. This suggests that while the frequency-dependent whitecapping physics of ST6 are highly accurate for deep-water processes, the influence of topographical source terms increases significantly in coastal applications. In summary, the ST6 + CDFAC scheme maintains robust performance across all depth ranges, while its physical consistency is most prominently validated in offshore waters where air–sea interactions and whitecapping dissipation are the primary drivers.

6. Discussion

The results of this study suggest that an integrated approach of physics packages and wind bias correction is necessary to improve wave prediction accuracy, with the following implications:

Need for Hybrid Operation: Komen is stable for low wave conditions, while ST6 excels in high waves and rapidly changing weather. Future operational systems should consider an ensemble approach or adaptive modeling that selects the optimal physics option based on sea state.

Importance of Wind Bias Correction: Bias correction using CDFAC contributed more to accuracy improvement than switching physics packages (over 30% improvement in high-wave RMSE). Future research should move toward nonlinear correction by wind speed range or AI-based wind error correction models.

Excellence of ST6: ST6’s superiority in high-wave simulation was reconfirmed. While Komen suffers from over- or under-dissipation due to mean steepness dependency, ST6 more realistically reproduces high waves during winter monsoons and typhoons by separating breaking components and reflecting drag coefficient saturation.

Physical Justification and Limitations of CDFAC Methodology: The time-varying CDFAC method applied in this study has a limitation in that it applies a daily mean correction without explicitly accounting for biases across different wind speed ranges (e.g., low vs. high wind speeds). However, from the perspective of wave modeling, particularly for extreme weather simulations like typhoons, wave energy grows in proportion to the square or higher power of wind speed. Therefore, correcting the bias of the dominant synoptic-scale weather system for the day is the most effective strategy for balancing the total wave energy. Furthermore, while linear statistical corrections or Machine Learning (ML) based post-processing methods focus on statistically adjusting the output (significant wave height), the CDFAC approach distinguishes itself by directly controlling the friction velocity ($u_{*}$) and momentum flux ($\tau$), which are the root causes of wave generation. This ensures “Physical Consistency” by reducing errors while maintaining the physical balance between wind input ($S_{in}$) and whitecapping dissipation ($S_{ds}$). Thus, in numerical modeling studies where understanding physical processes is paramount, dynamic parameter tuning like CDFAC is more suitable than black-box data-driven models for interpreting and improving model behavior. Future research should aim to develop non-linear CDFAC functions subdivided by wind speed bins or hybrid approaches that optimize these parameters in real-time using AI techniques.

6.1. Physical Consistency of CDFAC in Momentum Flux Adjustment

The application of CDFAC (Drag Coefficient Scaling Factor) introduced in this study should be interpreted not merely as an empirical tuning to match model outputs with observations, but as a process of rationalizing the physical momentum transfer process at the air–sea interface. In wave models, the energy input ($S_{in}$) is determined not directly by the wind speed ($U_{10}$), but by the wind stress ($\tau$) and friction velocity ($u_{*}$) acting on the sea surface ($S_{in}\propto {\mathrm{u}}_{\mathrm{*}}^2)$ If a structural positive bias exists in the input wind field ($U_{10}$), it transmits excessive energy to the sea surface proportional to the square of the friction velocity. Under these conditions, scaling the drag coefficient ($C_D$) using CDFAC serves to adjust the abnormal momentum flux caused by the overestimated wind speed, thereby correcting the “Effective Wind Stress” to match the actual sea state. This approach maintains physical consistency far better than artificially increasing the whitecapping dissipation term ($S_{ds}$) to suppress excess energy. In essence, CDFAC functions as a “calibration mechanism at the input-physics interface” that prevents errors in input data from propagating into distortions of the physical processes.

6.2. Limitations of Hybrid Operation and AI-Based Advancement Strategy

The dual-operation strategy proposed in this study (using Komen for normal conditions and ST6 for severe weather) faces practical limitations in real-time forecasting due to the difficulty in establishing a robust “Switching Criterion.” To overcome this, Hybrid Modeling, which couples numerical model physics with data-driven corrections, is essential. Recent literature provides compelling evidence for the efficacy of Machine Learning (ML) in wave forecasting. Durap (2024) conducted a comparative analysis of various ML algorithms, demonstrating that data-driven models possess superior non-linear mapping capabilities for Significant Wave Height (SWH) forecasting compared to traditional empirical methods [15]. Furthermore, Durap (2025a) highlighted the potential of Explainable ML in overcoming scale and time challenges for predicting diverse oceanographic parameters. Crucially, for operational forecasters to trust AI outputs, the “black box” nature of ML must be addressed [16]. Durap (2025b) proposed a framework utilizing SHAP (SHapley Additive exPlanations) analysis and physics-informed feature engineering (e.g., Wave Height Ratio) to ensure model transparency and interpretability [17]. Therefore, the future forecasting system should evolve into an integrated framework where the CDFAC proposed in this study removes primary physical bias, while an Explainable AI layer dynamically corrects residual non-linear errors in real-time.

6.3. Future Directions: Transitioning from Linear Correction to AI-Based Hybrid Modeling

Although the CDFAC technique proposed in this study is an effective method for correcting wind bias while maintaining physical consistency, it has limitations in fully controlling non-linear error structures that vary spatiotemporally. Recently, Hybrid Modeling, which integrates numerical physics with Machine Learning (ML) and Deep Learning (DL) techniques, has emerged as a powerful solution to overcome these physical limitations in wave forecasting. Data-driven approaches that learn the residuals between numerical model outputs (Significant Wave Height, H_s) and observations are being actively researched to enhance prediction performance. Notably, recent studies have moved beyond simple “black box” predictions by incorporating Explainable AI (XAI) techniques, such as SHAP (SHapley Additive exPlanations), to ensure model transparency. For instance, Durap demonstrated the reliability of data-driven models by utilizing feature engineering to elucidate the correlations between physical wave parameters (e.g., maximum wave height, period) and ML algorithms (e.g., Random Forest, XGBoost), thereby bridging the gap between physics and data science. Therefore, for the advancement of the wave forecasting system around the Korean Peninsula, future research should aim for a “Physics–Data Coupled Hybrid Framework.” In this approach, physical tuning methods like the CDFAC proposed in this study would serve as a baseline to remove primary biases, while AI models would be employed to learn and correct the remaining non-linear errors in real-time.

7. Conclusions

This study conducted an extensive sensitivity analysis and validation of the SWAN model for the coastal waters of the Korean Peninsula, leading to the following major conclusions:

First, the accuracy of wave prediction is fundamentally determined by the quality of the input wind field and the parameterization of source terms. Among various reanalysis data, JMA-MSM was selected as the optimal wind forcing for the Korean Peninsula due to its high spatiotemporal resolution. To systematically control the structural positive bias in these wind fields, the CDFAC method was introduced, which adjusts momentum flux at the air–sea interface while maintaining the internal physical balance between wind input ($S_{in}$) and whitecapping dissipation ($S_{ds,w}$).

Second, the ST6 physics package, when coupled with CDFAC, significantly outperformed the traditional Komen scheme during high-energy events. ST6 accurately reproduced peak significant wave heights (approx. 6 m) during Typhoon Chanthu and winter storms, whereas the Komen scheme tended to underestimate peaks and exhibit phase lags due to its reliance on mean wave steepness. The application of ST6 + CDFAC achieved a 32.7% reduction in RMSE for high-wave conditions, demonstrating its superior operational capability for extreme weather forecasting.

Third, the bathymetric stratified analysis across 138 stations confirmed the spatial consistency of the ST6 + CDFAC framework. The scheme maintained its highest accuracy in offshore regions (depth > 50 m), where the frequency-dependent saturation-based dissipation prevents the “Swell Dissipation Artifact” commonly observed in mean-parameter models. In coastal waters (depth < 50 m), the governing dissipation mechanisms diversify into bottom friction ($S_{bot}$) and depth-induced breaking ($S_{ds,br}$), which partially offsets the benefits of wind input and whitecapping optimization.

Finally, for practical implementation in real-time systems, a “Time-lagged Sliding Window” technique is proposed to dynamically estimate CDFAC based on persistent bias characteristics in meteorological models. Future advancements should aim for a “Physics–Data Coupled Hybrid Framework,” integrating numerical physics with explainable AI (XAI) to correct residual non-linear errors in real-time, thereby ensuring both physical fidelity and predictive precision in complex coastal environments.