Descriptive Methodology for Risk Situation of Disastrous Sea Waves in the China Sea

Abstract

To meet the needs of marine disaster prevention and mitigation, this paper proposes a systematic methodological framework to describe the annual risk situation of Disastrous Sea Waves (DSWs) from four perspectives. Its application is demonstrated for the China Sea in 2023 as a case study. The systematic approach is reflected in the following: (1) a comprehensive description of DSW risks based on three dimensions: occurrence frequency, maximum intensity, and hazard index; (2) an overview of the DSW risk characteristics for the year through spatial and monthly distributions; (3) a comparative analysis of the year’s DSWs, with historical data based on anomalies and return periods used to assess the risk characteristics and extremities; and (4) an analysis of the causes of the year’s characteristics based on monthly anomalies and weather systems. Through its application to the China Sea in 2023, the analysis process is introduced as follows. (1) High-Frequency and Intensity Areas: DSWs frequently occurred in the northeastern South China Sea (SCS) and Taiwan Strait, exceeding 450 h. The maximum significant wave height (H_s), reaching 11.3 m, was recorded in the southern East China Sea (ECS) in August. (2) Extremity in Frequency and Attribution: The occurrence frequency was extremely high, with the cumulative hours exceeding the historical average by 159 h (9.1%). The southwestern SCS showed the most significant excess, up to 168 h (>120%). The reason for this was that DSWs in January caused by prolonged cold air lasted 236 h longer (121%). (3) Extremity in Intensity and Attribution: The maximum H_s in the southern ECS and Taiwan Strait was 2 m (30%) higher than the historical average. The intensified cold air waves caused the higher intensities. (4) Hazard Levels: Higher risk occurred in the southwestern SCS, southern ECS, and Taiwan Strait, while the highest extremity occurred in the Bohai Sea.

1. Introduction

Disastrous Sea Waves (DSWs) refer to waves generated by winds in the ocean that possess destructive potential. These waves are typically caused by intense atmospheric disturbances such as tropical cyclones (typhoons, hurricanes), temperate cyclones, or strong cold air [1]. DSWs generally do not include tsunami waves caused by underwater earthquakes. These waves can capsize ships, destroy marine and coastal engineering structures, and cause significant losses to navigation, offshore construction, military activities at sea, and fishing operations. DSW is a term frequently used in the context of marine disasters in China, but it is not commonly used internationally. Internationally, terms like “extreme sea waves” or “rogue waves” are more commonly used to describe potentially disastrous waves [2,3,4,5].

The quantitative definition of DSW generally refers to waves with a significant wave height (H_s) exceeding a certain threshold. Xu (1996) [6] analyzed DSWs in China’s offshore areas and considered DSWs to be waves with heights exceeding 6 m. According to the Chinese national standard, the issue of marine forecasts and warnings—part 2: the issue of wave forecasts and warnings (GB/T 19721.2-2017) [7],) if waves with H_s ≥ 2.5 m are expected in coastal waters, a wave warning needs to be issued. Meanwhile, the “China Marine Disaster Bulletin”, published annually by the Ministry of Natural Resources, refers to offshore waves with H_s ≥ 4 m as DSWs. Similarly, the Chinese marine industry standard, technical directives for risk assessment and zoning of marine disaster- part 2: waves (HY/T 0273-2019) [8], also sets H_s ≥ 4 m as the minimum threshold for identifying wave disasters. Based on existing research, adopting H_s ≥ 4 m as the threshold for DSW occurrence is a common practice. However, the threshold settings can be adjusted based on the actual conditions for specific regions or specific types of load-bearing bodies.

Current studies primarily analyze DSWs based on their occurrence frequency, generally represented by the number of DSW events [9,10,11]. This is a very vague statistical result that does not reflect the cumulative duration of DSW occurrences, the spatial distribution pattern of occurrence frequency, or the intensity information. Other studies on potentially disastrous waves, including analyses of large waves (H_s ≥ 2.5 m), typhoon waves, cold air waves, and extreme waves [12,13,14,15,16,17], focus on the characteristics or trends of long-term historical averages, but do not involve specific analyses of deviations or extremities in a particular year [18,19]. It is evident that existing studies on the characteristics of DSW are not comprehensive and an lack analysis of annual features and deviations from historical norms.

The analysis of DSW risk situations is similar to the characteristics, but the former focuses more on the disaster-causing potential and severity of the waves, and it is more suitable for disaster prevention, mitigation, and emergency response needs. The analysis of DSW “risk” and “situation” reflects the disaster-causing potential and severity of waves. For “risk”, we consider using wave-related factors that cause disasters, such as the frequency of DSW occurrences and the maximum intensity. For “situation”, we consider using the state of the current year’s disaster-causing factors and their extremities, and compare them with historical averages. The annual risk situation analysis differs from the analysis of historical overall characteristics. The latter are an overview description of the long-term average state of DSWs, generally representing statistical averages over several decades. In contrast, annual risk analysis not only presents the current year’s state but also analyzes how it compares to historical data.

The conclusions drawn from the annual analysis of DSW risk situations have not only scientific value but also a wide range of applications. For example, the Ministry of Emergency Management of the People’s Republic of China holds annual and monthly summary meetings on the risk situation of natural disasters for the year or month, providing crucial reference points for the prevention and response to natural disaster emergencies in various provinces and cities. The National Marine Environmental Forecasting Center, as a national-level marine forecasting and disaster warning unit, is always invited to attend these meetings and reports on the DSW situation for the month or year, summarizing the risk characteristics. Additionally, in the “National Marine Disaster Prediction Consultation Meeting”, which all marine forecasting agencies in China participate in annually, the analysis of the previous year’s DSWs is also a key area of discussion.

We believe that DSW risk needs to be described from at least two perspectives: occurrence frequency and maximum intensity. This paper uses the number of hours in which H_s ≥ 4 m occurred during the statistical period to represent occurrence frequency, represented by the variable T_4m. This can be a statistical measure at spatial grid points or a cumulative statistic for the China Sea. T_4m can help capture more accurate spatiotemporal frequency information. DSW intensity is represented by the maximum H_s during the statistical period. Additionally, this paper will use a hazard index (HI), which comprehensively considers frequency and intensity, to assist in the analysis. The definition of HI comes from the Chinese marine industry standard (HY/T 0273-2019) [8].

This paper, by analyzing the China Sea in 2023, elaborates on the method used to analyze the annual risk situation of DSWs, focusing on three main aspects: (1) presenting the spatial distribution of T_4m and the maximum H_s in 2023 and the statistical values for each month; (2) analyzing the anomalies of T_4m and the maximum H_s compared to historical data, the corresponding historical return periods, and other extremities; and (3) analyzing the main or direct reasons for the significant anomalies of the year. This method systematically improves the current methods for analyzing annual DSW risk situations, and its application results can directly facilitate the annual disaster summary consultations of the Ministry of Emergency Management and the “National Marine Disaster Prediction Consultation Meeting”.

Section 2 introduces the data and methods used, Section 3 presents basic information on the frequency and intensity of DSWs in 2023, Section 4 analyzes the comparison and extremities of DSWs in 2023 relative to historical data, Section 5 analyzes the reasons for the main characteristics of DSWs in 2023, and Section 6 provides the conclusions.

2. Data and Methods

The data used for the analysis require the wave data of long-term historical periods, preferably in the form of reanalysis data at grid points. The ERA-5 wave reanalysis dataset is widely recognized for its high accuracy and extensive temporal coverage (1940 to the present, hourly). However, its spatial resolution of 0.5 degrees is more suitable for analyzing large sea areas and oceans. For smaller regions, especially coastal areas with complex dynamics, this resolution may limit the accuracy of localized DSW risk assessments. To address this, alternative data sources with a finer spatial resolution may be required for such analyses.

This study utilizes ERA-5 wave data from 1979 to 2023, with the historical period being from 1979 to 2022 and the analyzed year being 2023. The data extraction process includes the statistical analysis of the DSW occurrence hours (T_4m), the maximum H_s, and the Hazard Index (HI), which are analyzed both at each grid point and cumulatively for specific sea areas.

For the selection of the DSW occurrence threshold, we adopted the criterion established by the China Marine Disaster Monitoring and Early Warning Center, which defines DSW as H_s ≥ 4 m. This institution serves as the official marine disaster statistics agency in China, responsible for rigorously recording the losses caused by marine disasters off and along the Chinese coast. Utilizing this agency’s threshold of H_s ≥ 4 m ensures this research’s wider recognition and consistency with national standards. However, this paper primarily provides an analytical framework for DSW risk, allowing for the adjustment of DSW thresholds based on the wave resistance of vessels, docks, and other hazard-affected entities in the specific sea area. For instance, if small fishing boats or yachts, which are more vulnerable to waves over 3 m high, frequently operate in the area, the threshold for DSW occurrence can be appropriately lowered to H_s ≥ 3 m.

Assuming the total number of years involved in the statistics is yn years, and the grid points involved are M rows by N columns, for each grid point, the number of hours with H_s ≥ 4 m is extracted monthly, resulting in a matrix with dimensions M × N × yn × 12. For a specific sea area covered by grid points, if any grid point in that area reaches H_s ≥ 4 m at any given time, the T_4m for that sea area is increased by 1 h. This provides the cumulative monthly statistics for each year, with data dimensions of yn × 12. The statistical method for Max H_s is similar, obtaining the maximum significant wave height for each grid point annually and monthly (M × N × yn × 12) and the maximum significant wave height for a specific sea area annually and monthly (yn × 12). Figure 1 shows the geographical locations of six sub-sea areas in the China Sea.

The calculation of the Hazard Index (HI) follows appendix A of the Chinese marine industry standard (HY/T 0273-2019) [8]. The content is introduced as follows. Wave intensity levels are classified into four categories based on H_s at each grid point: extremely strong, strong, moderate, and general, corresponding to levels I, II, III, and IV, respectively. The classification is presented in

Table 1. Classification of wave intensity levels.

Intensity Levels	I	II	III	IV
Hs	Hs ≧ 14 m	9 m ≧ Hs < 14 m	6 m ≧ Hs < 9 m	4 m ≧ Hs < 6 m

.

Using historical sea wave datasets, we calculate the annual average occurrences (N₁, N₂, N₃, and N₄) for wave intensity levels, namely I, II, III, and IV, at each grid point. The wave hazard risk parameter ($H_w$) for each grid point is then derived using the following formula:

$$H_w=0.6N_1+0.25N_2+0.1N_3+0.05N_4$$

To normalize $H_w$ across grid points, a linear normalization function is applied as follows:

$$HI=\left(H_w-H_{wmin}\right)/(H_{wmax}-H_{wmin})$$

where $H_{wmin}$ and $H_{wmax}$ are the minimum and maximum values of $H_w$ across all grid points. This process yields the normalized hazard index (HI) for each grid point. Finally, HI values are extracted annually and monthly for individual grid points and averaged for specific sea areas within the same time frames.

When analyzing the trend in T_4m and the maximum H_s, the Sen slope estimation is applied. This method is considered a powerful tool for studying linear relationships. Compared with linear regression analysis, its advantage is not affected by the total data errors and outliers, and can effectively reduce the interference of noise [20,21].

3. Overview of DSW in 2023

The annual overview of DSW includes an analysis of the spatial and monthly distributions of T_4m, maximum H_s, and HI. The spatial distribution characteristics in 2023 were analyzed based on grid point statistics (Figure 2 and Figure 3). The monthly distribution characteristics were analyzed based on cumulative statistics for the whole China Sea (Figure 4).

3.1. Overview of Spatial Distribution

Figure 2 shows that the occurrence time of DSWs was the longest in the northeastern SCS, reaching over 500 h, followed by the Taiwan Strait, with 450 h. The western SCS and southern ECS experienced 250–350 h. The shortest duration was recorded in the Beibu Gulf, with less than 50 h for the whole year. The Bohai Sea, Yellow Sea, and southeastern SCS also had shorter durations, ranging from 50 to 100 h. The northern ECS had an occurrence time between 150 and 200 h. The spatial distribution of the maximum H_s indicates that the DSW intensity was strongest in the southern ECS, where the maximum H_s exceeded 11 m. This was followed by the northeastern SCS, northern ECS, and Taiwan Strait, with the maximum H_s ranging from 6 to 8 m. The Bohai Sea, Yellow Sea, and Beibu Gulf had the weakest intensities, with the maximum H_s ranging from 4 to 5 m.

The spatial distribution pattern of the maximum H_s in 2023 closely resembles patterns observed in prior studies, such as the N-year return H_s identified by Li et al. (2018) [3] and He et al. (2018) [4], as well as the 99.5th percentile H_s reported by Wang et al. (2021) [16]. These studies consistently show that extreme H_s values are highest in the southern ECS and gradually decrease toward the north, south, and coastal regions.

3.2. Overview of Monthly Distribution

By combining T_4m and the maximum H_s, the Hazard Index (HI) presents a spatial grid point distribution in Figure 3 that is very close to the distribution pattern of T_4m, while also considering the high intensity of maximum H_s in the southern ECS. The highest hazards are in the northeastern SCS, Taiwan Strait, and southeastern ECS, where the HI values range from 0.7 to 1. The remaining sea areas of the ECS and SCS are less hazardous, with HI values between 0.3 and 0.6. The Bohai Sea and Yellow Sea show low hazards, with HI values between 0.1 and 0.2, while the Beibu Gulf has the lowest hazard, with HI values below 0.1.

In terms of the monthly distribution of DSW in 2023, the cumulative T_4m and maximum H_s were calculated for each month in the China Sea to analyze the characteristics for each month. Figure 4 shows that DSWs occurred most frequently in January, with 431 h, accounting for 22.6% of the total 1908 h for the year 2023, followed by 323 h in December. The cold-air-dominated period of November (no typhoons recorded affecting the China Sea in November 2023), December, January, and February accounted for a total T_4m of 61.7% of the year, indicating that cold-air-induced DSWs accounted for more than 60% of the year’s events and were the dominant weather system affecting the China Sea in 2023. During the typhoon-prone period from June to October, the total T_4m accounted for 26.6% of the year, with August alone accounting for 14.2%. During the transition from cold air to temperate systems in March and April, DSW occurrences were minimal, with April being the month with the lowest occurrence, only 16 h.

The DSW intensity was highest in August, with a maximum H_s of 11.3 m in the China Sea. From May to July and in January, the maximum H_s ranged between 8 to 9.2 m. The minimum H_s was recorded in April, at only 4.2 m. From the perspective of weather systems, during the cold-air-dominated months of November, December, January, and February, the maximum H_s generally ranged between 6 to 8 m. During the typhoon wave-prone months from June to October, the maximum H_s ranged between 8 to 11.5 m.

3.3. Summary of DSW in 2023

In summary, the basic risk characteristics of DSWs in 2023 are as follows: (1) High frequency in the northeastern SCS and Taiwan Strait, with a total duration exceeding 450 h throughout the year; (2) The intensity of DSWs was highest in the southern ECS, where H_s exceeded 11 m, occurring in August; (3) DSWs induced by cold air accounted for 61.7% of the total duration for the year, with January alone accounting for 22.6%, while typhoon-induced DSWs accounted for 26.6%.

4. Comparisons of 2023 with Historical Averages

The comparisons are analyzed based on both the cumulative statistics and the spatial grid point statistics. The analysis includes anomaly analysis and a historical return period analysis for T_4m, the maximum H_s, and HI. Anomaly analysis is conducted by calculating the anomalies and anomaly percentages between 2023 and the historical average values from 1979 to 2022. The historical return period analysis is achieved by calculating the historical return period of T_4m and the maximum H_s, achieved in 2023, based on the extreme value analysis from 1979 to 2022.

4.1. Comparisons from Cumulative Statistics

The analysis of cumulative statistics for different sea areas provides a straightforward overview of how each sea area’s DSWs compare to the historical average. Based on the cumulative annual statistics of T_4m across the entire China Sea and six sub-sea areas, the annual variation trends, anomaly percentages for 2023, and corresponding return periods are presented (Figure 5, Figure 6 and

Table 2. Statistical table for the comparison of cumulative T_4m with historical averages, including anomaly percentage and return periods in 2023, historical averages from 1979 to 2022, and trends from 1979 to 2023.

T4m	Anomaly Percentage in 2023 (%)	Return Year for 2023 (Year)	Average of 1979–2022 (Hour)	Trends of 1979–2023 (Hour/Year)
China Sea	9.1	33.8	1749.0	+7.0
Bohai Sea	+169.0	42.7	35.7	−0.1
Yellow Sea	+2.3	25.0	178.9	+0.9
ECS	+1.7	24.7	725.4	+4.9
Taiwan Strait	+18.1	35.4	534.2	+3.1
SCS	+14.3	33.5	1132.1	+4.8
Beibu Gulf	−60.7	7.4	61.1	−0.3

). The historical average cumulative T_4m for the China Sea is 1749 h, and the 1908 h recorded in 2023 exceeded this by 159 h (9.1%). Additionally, the overall T_4m in the China Sea has shown an increasing trend in recent years, with an average annual increase of 7 h, which aligns with the positive anomaly observed in 2023.

Focusing on each sub-sea area, the Bohai Sea shows a positive anomaly of 60 h, with an anomaly percentage reaching 169%, corresponding to a return period of 42.7 years. This indicates that the DSW occurrence frequency in the Bohai Sea in 2023 was relatively extreme and significantly high compared to historical records. The cumulative T_4m in the Taiwan Strait and the SCS also significantly exceeded historical averages, with positive anomaly percentages above 14% and return periods of around 35 years. The Beibu Gulf is the only area in the China Sea where T_4m showed a negative anomaly, with a return period of only 7.4 years. Furthermore, in terms of the annual variation trends, the DSW occurrence duration in most sea areas is increasing, particularly in the ECS and the SCS, where the increase rate is about 5 h per year.

Based on the maximum H_s statistics for each sea area (Figure 7, Figure 8 and

Table 3. Statistical table for the comparisons of maximum H_s with historical averages, including anomaly percentage and return periods in 2023, historical averages from 1979 to 2022, and trends from 1979 to 2023.

Max Hs	Anomaly Percentage in 2023 (%)	Return Year for 2023 (Year)	Average of 1979–2022 (m)	Trends of 1979–2023 (cm/Year)
China Sea	−5.8	16.6	12.0	+2.3
Bohai Sea	+11.2	40.2	5.0	+0.3
Yellow Sea	−13.0	14.7	7.2	+2.1
ECS	−3.5	20.1	11.7	+2.8
Taiwan Strait	+1.8	26.6	7.5	+0.7
SCS	−5.8	17.1	9.7	+0.7
Beibu Gulf	−16.5	12.4	6.1	−2.0

), the historical average in the China Sea is 12 m, while the 11.3 m recorded in 2023 was 0.7 m lower than the historical average (5.8%). Breaking it down by sub-sea area, the Bohai Sea showed the highest positive anomaly of 11.2%, with a corresponding return period of 40.2 years, indicating that the intensity in the Bohai Sea in 2023 was relatively strong and extreme compared to historical records. Other sea areas showed either negative anomalies or slightly positive anomalies, with return periods all below 27 years, indicating that the DSW intensities were comparable to or lower than the historical averages. Notably, the Beibu Gulf and Yellow Sea had negative anomalies of 16.5% and 13%, respectively. Although the DSW intensity in 2023 was relatively low, the overall historical trend shows a slight increase, with an average enhancement rate of 2.3 cm per year. Among the sub-sea areas, the ECS showed the fastest increase, at 2.8 cm per year, followed by the Yellow Sea, while only the Beibu Gulf exhibited a weakening trend.

The positive trends identified in the ECS and SCS, as illustrated in Figure 8 and Table 3, align with findings from Osinowo et al. (2016) [18] and Wang et al. (2021) [16]. These studies similarly highlight a strengthening trend in extreme waves within these regions. However, we acknowledge that differences in data sources and the time span of the analysis years result in variations in the magnitude of these positive trends among the studies.

The primary driving force behind sea waves is sea surface wind. As highlighted by Wang et al. (2021) [16], the increase in extreme sea surface wind speeds in the ECS and SCS has directly contributed to the intensification of extreme waves. Additionally, studies on typhoon trends, such as those by Zhan and Wang (2017) [22] and Zhao et al. (2018) [23], indicate that climate warming has resulted in an increased frequency of strong typhoons in the northwest Pacific. This trend has indirectly amplified extreme wave intensities caused by typhoon activity. This addition provides a more comprehensive understanding of the environmental drivers behind observed wave anomalies and contextualizes our findings within broader climate-related trends.

The main conclusions from the comparisons of the cumulative statistics in 2023 are as follows: (1) The cumulative T_4m for the entire China Sea increased by 9.1%, while the maximum H_s decreased by 5.8%; (2) The Bohai Sea exhibited the most significant increase in both the cumulative T_4m and maximum H_s, with return periods exceeding 40 years, indicating high extremity; (3) The Beibu Gulf showed the most significant decrease in both metrics.

4.2. Comparisons from Grid Point Statistics

While the cumulative comparison by sea area is straightforward and concise, it does not provide more precise and detailed information. Therefore, we conducted a comparative analysis with historical data at the spatial grid point level. According to the spatial distribution of anomalies and anomaly percentages (Figure 9 and Figure 10), it can be observed that in 2023, T_4m in most sea areas of the China Sea exceeded historical values, consistent with the conclusions from the cumulative analysis of the China Sea mentioned earlier. The most notable positive anomaly in T_4m was observed in the southwestern SCS, where the positive anomaly in some areas reached 168 h, with an anomaly percentage exceeding 120%. Following that, the surrounding sea areas of the Taiwan Strait and the northeastern SCS also had significant positive anomalies in T_4m, with a maximum local positive anomaly of 96 h (80%). Additionally, while the Bohai Sea’s positive anomaly in T_4m was only 48 h, its historical average is very low, leading to an anomaly percentage exceeding 200%, indicating a very significant relative increase in T_4m in some areas of the Bohai Sea. Regarding the maximum intensity of DSWs, some areas in the southern ECS and the Taiwan Strait showed a more considerable increase, with a maximum positive anomaly of 2 m (30%). Additionally, the Bohai Sea and southern SCS showed a mild increase in the maximum H_s, of approximately 0.5 m (around 10%). In contrast, the DSW intensity in the rest of the China Sea weakened in 2023.

From the above analysis, it is clear that the changes in the anomaly and anomaly percentage of T_4m are quite large, while the changes in the maximum H_s are relatively small. To achieve more comprehensive and intuitive comparative results, the HI anomaly was used for supplementary analysis. Figure 11 shows that the HI anomaly encompasses both the high anomalies of T_4m in the southwestern SCS and the Taiwan Strait and the high anomalies of the maximum H_s in the southern ECS, representing a good composite indicator. The maximum positive anomaly in these three sea areas was 0.3. Overall, in 2023, the DSW hazard level increased in most areas of the China Sea, with the most significant increases observed in the southwestern SCS, southern ECS, and Taiwan Strait. Other areas, such as the northeastern SCS, Bohai Sea, and Yellow Sea, also experienced varying degrees of increases.

Combining the historical return periods of T_4m and the maximum H_s in 2023 (Figure 12), it can be seen that the return periods of T_4m in the southwestern SCS, Taiwan Strait, and Bohai Sea exceeded 40 years for most grid points, indicating a relatively extreme and severe condition. In contrast, the return periods of the maximum H_s were generally shorter than those of T_4m, with a scattered spatial distribution and unclear characteristics. Only in the Bohai Sea, southern SCS, and a few other small sea areas did the return period exceed 40 years. Nearly half of the spatial grid points had return periods of less than 15 years, indicating that the extremity of the maximum DSW intensity was not significant.

Main conclusions of spatial distribution comparisons for 2023 vs. historical data:

(a)

The southwestern SCS showed the most significant positive anomaly in T_4m, with a maximum of up to 168 h (>120%), and a slight positive anomaly in the maximum H_s of 0.5 m (10%).

(b)

The maximum H_s increased significantly in the Taiwan Strait and southern ECS, with a maximum of up to 2 m (30%), while T_4m in some areas also increased by 72–96 h.

(c)

Most areas in the Bohai Sea experienced significant increases in both T_4m and the maximum H_s, with anomalies up to 200% and 20%, respectively.

(d)

The HI in the above-mentioned areas was 0.1–0.3 higher than historical values, with return periods generally between 35 and 40 years.

5. Causes for Significant Anomalies in 2023

The comparison between 2023 and historical data revealed that DSWs were stronger and more extreme in four sea areas. To analyze the reasons for this, we looked at the weather systems that cause DSWs. Since DSWs in the China Sea are mainly caused by cold air and typhoons—cold air prevailing from November to February of the following year, and typhoons occurring mainly from June to October—we analyzed the monthly anomalies to identify possible causes.

5.1. Analysis from Monthly Cumulative Statistics

A comparison of the cumulative T_4m and maximum H_s for each month in 2023 with historical data, along with their anomaly percentages for the China Sea (Figure 13), allows for a direct analysis of the monthly deviations in DSWs. This analysis, combined with the dominant weather systems for each month, helps identify the reasons for the strengthened DSW.

For T_4m, January shows the largest positive anomaly, reaching 236 h, significantly exceeding the annual cumulative positive anomaly of 159 h for the China Sea. Similarly, February and December also show significant positive anomalies. Since January, February, and December are months when cold air is prevalent, and considering that the Bohai Sea has the highest positive anomaly percentage, where DSWs are primarily caused by cold air, it is believed that the prolonged influence of cold air in January, February, and December is the main reason for the longer DSW duration in the China Sea in 2023. January, in particular, shows the most notable prolongation, with an anomaly percentage of 121%. Existing studies suggest that the extremity of cold air and the intensity of waves caused by cold air have a strengthening trend [24,25].

Regarding the maximum H_s, the historical average from 1979 to 2022 shows that September is the month with the highest H_s. However, in 2023, September had a negative anomaly of 3.4 m, with an anomaly percentage of 34%. In contrast, the negative anomaly for the maximum H_s in the entire China Sea in 2023 was only 0.7 m. Additionally, October also had a negative anomaly of 1.6 m. Considering that the main weather system in September and October is typhoons, it is believed that the weaker intensity of typhoon waves in September and October is the primary reason for the weaker DSW intensity in the China Sea in 2023.

Previous studies, such as those by Zhang et al. (2021) [24] and Johnson et al. (2018) [25], have highlighted that global warming has intensified extreme weather events, leading to stronger sea surface winds and consequently an increase in extreme ocean waves. Additionally, research by Wang et al. (2021) [16], Yao et al. (2024) [26], and Osinowo et al. (2016) [18] demonstrates seasonal variations in DSW occurrences, with significant increases observed in the ECS and SCS during the summer, autumn, and winter months. These findings align with the seasonal patterns and extreme event analysis presented in this study, further supporting our conclusions regarding the temporal variability in DSW risk.

5.2. Analysis from Monthly Spatial Grid Statistics

As noted earlier, the anomalies in January and September were significant, representing months influenced by cold air and typhoons, respectively. These months are highly representative for analyzing the regions with large deviations and understanding the underlying causes through spatial grid anomaly maps.

January Analysis:

Figure 14 shows that both T_4m and the maximum H_s in January had very significant positive anomalies across the entire China Sea. Notably, the T_4m positive anomaly in the SCS was particularly pronounced, with more than half of the SCS having positive anomalies exceeding 120 h, and some areas reaching up to 168 h. This represents the highest T_4m positive anomaly value for the entire year, consistent with the spatial distribution conclusions discussed in Section 4.2. Meanwhile, the positive anomalies in H_s for the Bohai Sea and ECS also exceeded 1.5 m in most regions, with a local maximum of up to 2.5 m, which aligns with the spatial distribution conclusions mentioned in Section 4.2. During the cold air wave influence period from November to February of the following year, the historical average maximum H_s was 7 m (Figure 12). Positive anomalies of 1.5–2.5 m correspond to percentages ranging from 24 to 36%. The significantly prolonged influence time and increased intensity of cold air waves in January directly resulted in a longer DSW duration across the China Sea, a stronger extremity of DSWs in the Bohai Sea, and a longer DSW duration in the SCS.

September Analysis:

Figure 15 shows that the T_4m in September generally had mild negative anomalies across the China Sea, with the negative anomalies being more pronounced in the ECS. Regarding H_s, the negative anomalies were even more significant in the ECS, with most grid points showing negative anomalies exceeding 2.5 m, and local maxima exceeding 3.5 m. This indicates that the significantly lower intensity of typhoon waves in September mainly originated from the ECS.

6. Conclusions

This paper proposes a systematic analysis method to describe the annual risk situation of Disastrous Sea Waves (DSWs) from four perspectives and demonstrates its application using the China Sea in 2023 as an example. The systematic approach is reflected in the following aspects: (1) Describing DSW risk from three dimensions: occurrence frequency, maximum intensity, and hazard index, providing a multi-dimensional perspective; (2) Presenting the spatial and monthly distributions of DSWs, offering an overview of the annual risk scenario; (3) Demonstrating the extremity of the year using anomaly analysis and return period analysis to describe the characteristics of DSW risk; (4) Analyzing the reasons behind the DSW risk characteristics for the year based on monthly anomaly analysis and the influencing months of weather systems.

The DSW occurrence frequency is represented by the total hours with H_s ≥ 4 m (T_4m), the maximum intensity is represented by the maximum H_s within the statistical period, and the hazard index (HI) is represented by a weighted normalization coefficient of the duration of different Hs levels. The basic steps for applying the method are as follows:

(a)

Data Preparation: Extract T_4m, maximum H_s, and HI for each grid point annually and monthly. For the sea areas of interest, calculate the cumulative annual and monthly values for the grid points they cover.

(b)

Basic Situation of 2023: Analyze the sea areas and months with a higher DSW risk based on the spatial grid distribution of T_4m, maximum H_s, and HI in 2023, as well as the cumulative statistics for each month in the China Sea.

(c)

Extremity of 2023: Analyze the differences and extremities in 2023 compared to historical averages based on the anomaly, anomaly percentage, and corresponding return period of DSWs.

(d)

Causes of Risk Characteristics: Based on the conclusions of the extremity analysis, analyze the reasons for the risk characteristics of 2023 by combining the monthly DSW anomalies, characteristics of the weather systems causing DSWs, and their influencing months.

Apply this methodological framework to 2023 DSWs, and provide a step-by-step introduction to the analysis perspective, methods, and conclusions of the framework.

(a)

Basic Situation: DSW occurred frequently in the northeastern SCS and the Taiwan Strait, with a total duration exceeding 450 h. The maximum intensity was recorded in the southern ECS in August, with the highest H_s reaching 11.3 m. The durations of DSWs caused by cold air and typhoons accounted for 61.7% and 26.6% of the year, respectively.

(b)

Extremity in Frequency and Attribution Analysis: The occurrence frequency was strong, with the cumulative occurrence duration in the China Sea exceeding the historical average (1979–2022) by 159 h (9.1%). The southwestern SCS showed the most significant excess, with a local maximum of up to 168 h (>120%), while the Bohai Sea had the most significant relative excess, with a local increase of over 200% and a return period exceeding 40 years. The prolonged duration of cold air waves, particularly in January, which lasted 236 h longer (121%), directly contributed to the strong extremity of frequency.

(c)

Extremity in Intensity and Attribution Analysis: The extremity in intensity showed significant spatial variability. Although the cumulative maximum Hs in the China Sea was 0.7 m (5.8%) lower than the historical average, the maximum Hs in the southern ECS and the Taiwan Strait was 2 m (30%) higher, and it was 20% higher in the Bohai Sea. The strong cold air waves in January were the direct cause of the stronger intensity in the southern ECS and the Bohai Sea. Meanwhile, the lower Hs of the typhoon waves in the ECS in September (3.4 m lower) was the direct reason for the lower overall DSW intensity in the China Sea.

(d)

Hazard Levels: The sea areas with significantly higher hazards in 2023 were the southwestern SCS, southern ECS, and Taiwan Strait, which were also the areas with higher frequency and intensity. However, the relative extremity was highest in the Bohai Sea.

The descriptive methodology can provide a comprehensive overview of the DSW risk situation in a certain year and highlight the areas that require particular attention in terms of marine disaster prevention and mitigation. The findings on the annual risk situation can help local marine departments analyze the causes of marine disasters in that year. The conclusions on the historical average risk characteristics can serve as a warning to the marine departments and local governments responsible for managing high-risk areas, and to arrange economic activities and disaster prevention and reduction in a reasonable manner.

The methodological framework presented in this study is versatile and can be applied to a broader range of datasets, such as hindcast simulation data, higher-resolution reanalysis data, or observational data, to validate and refine the conclusions. While the 0.5-degree resolution of ERA-5 data constrains the reliability of small-scale analyses, higher-resolution datasets can improve the accuracy of results in coastal and localized areas. Nonetheless, the results presented here remain a valuable auxiliary reference.