Spatiotemporal Characteristics and Long-Term Variability of Large-Wave Frequency in the Northwest Pacific

Abstract

This study provides a systematic analysis of the spatiotemporal distribution and trends in the frequency of significant wave height (SWH) exceeding level 5 (SWH > 2.5 m) and level 7 (SWH > 6 m) in the Northwest Pacific (NWP) for 1993–2024, which are defined as f₅ and f₇, respectively, as well as their correlations with major climate indexes. Our results indicate that (1) the high-value zones for the annual mean f₅ and f₇ are both located in the south waters of the Aleutian Islands, with maximum values of 58.0% and 6.4%, respectively. Winter’s contribution is greatest (maximum values of 96.9% and 16.8% per year), while summer’s is the smallest. (2) f₅ exhibits a significant decline trend across the entire NWP basin (of −0.15 to −0.30%/yr), with the steepest decline occurring in autumn (−0.69%/yr) and the shallowest in summer. f₇ exhibits a significant linear decrease in the open ocean east of Japan (−0.08%/yr) while showing a significant linear increase in the waters east of the Kamchatka Peninsula (0.08%/yr). Both variations peak in winter (maximum values of −0.27% and 0.30% per year) and are smallest in summer. (3) Seasonal and regional variations in climate index–f₅ and f₇ relationships reflect large-scale atmospheric modulation of waves. For example, the Oceanic Niño Index shows a predominantly negative correlation with f₅ in winter (maximum correlation coefficient r_m = −0.70) around the Luzon Strait, shifting to a significant positive correlation in summer (r_m = 0.70) across the extensive region east of Taiwan Island and the Philippines. The Pacific Decadal Oscillation index shows a significant positive correlation with f₇ in summer and autumn (r_m = 0.69) east of Taiwan Island and a strong negative correlation in winter (r_m = −0.77) to the east of Kamchatka Peninsula.

1. Introduction

In the Northwest Pacific (NWP), a global shipping hub [1,2,3], the safety of maritime activities and the development of wave energy are closely linked to the occurrence of large waves [4,5,6,7]. According to the International Maritime Organization’s Guidelines for the Assessment of Ship Seakeeping Performance [8]: for sea state 5 (significant wave height SWH 2.5–4.0 m), medium-sized vessels need to activate anti-rolling devices; for sea state 7 (SWH 6.0–9.0 m), only large special-purpose vessels can operate under limited conditions. It can thus be concluded that the frequencies of sea states at level 5 and above (SWH > 2.5 m) and at level 7 and above (corresponding to SWH > 6 m) are core indicators for assessing the severity of the marine environment and conducting risk evaluations. In this study, these are defined as f₅ and f₇, respectively, and are taken as the primary research subjects. It is therefore crucial to systematically analyze the spatiotemporal distribution and trends of f₅ and f₇ in the NWP to ensure maritime safety, optimize operational scheduling and advance wave energy development.

Significant progress has been made in analyzing the long-term wave frequency trends and their spatiotemporal characteristics. The relevant research primarily covers two aspects: (1) examining trends in wave variations across different regions. For example, one study observed that, over the past 55 years, summer wave heights at mid-to-high-latitude coastal stations in China have decreased, while extreme wave heights at low-to-mid-latitude stations have increased [9]. Another study demonstrated a downward trend in extreme wave heights along the southeast coast of Hainan Island between 1949 and 2022 [10]. Research focusing on the Mediterranean Sea found that maximum SWHs increased across most regions from 1979 to 2020 [11]. Investigations in Kerala, India revealed that the 90th percentile SWH at ten observation points showed an upward trend from 1940 to 2022, with coastal average SWH also exhibiting a universal increase [12]. Several systematic studies pioneered the analysis of the variations in wave height and energy, focusing on global trends in both wind–sea and swell wave heights. Their results show that the global ocean SWH and swell wave height exhibited linear growth trends of approximately 4.6 cm/decade and 2–8 cm/decade, respectively, during the 1958–2001 period [13,14,15,16,17]. Recent research has established a theoretical system on the significant impact of swell propagation on global wave climate change, demonstrating that neglecting external swells (those from distant sources) introduces substantial biases into climate characteristics and may compromise subsequent analyses [18]. (2) Researchers have also explored the multiple factors influencing variations in wave trends. One study in the eastern tropical Atlantic reported positive growth trends in SWHs at inter-monthly and -annual scales, with stronger wave heights gradually approaching the coast. This change has been found to be jointly modulated by mid-latitude storm fields in both hemispheres [19]. Other researchers found that climatic conditions in the NWP significantly influence surface waves in the northern Indian Ocean [20]. Evidence indicates that the inter-annual variability in the wave climate in the New Caledonian atolls is closely linked to the El Niño–Southern Oscillation (ENSO) phenomenon [21]. Global wave pattern analysis has shown that the main component of SWHs during peak season (July–September) is significantly correlated with sea surface temperature anomalies in the equatorial Pacific. These variations are primarily influenced by tropical cyclone activity triggered by enhanced sea surface temperature anomalies [22,23]. Another study confirmed that variations in wave climate in the South China Sea are substantially modulated by strong El Niño signals [24].

However, systematic investigations of the spatiotemporal characteristics and long-term evolution of f₅ and f₇ in the NWP remain limited, which hampers the effective development and utilization of marine resources in this region.

To address these gaps, this study provides a comprehensive and application-oriented assessment of large-wave occurrence frequencies in the NWP. Specifically, based on SWH data from the European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis 5th Generation (ERA5) spanning 1993–2024, two frequency-based indicators, f₅ and f₇, are defined. These indicators are directly linked to operational sea states relevant to maritime safety and offshore engineering activities. The objectives of this study are to: (1) characterize the spatial distribution, seasonal variability, and long-term trends of f₅ and f₇ across the NWP basin; (2) quantify their relationships with major climate indices and elucidate the associated physical mechanisms; and (3) evaluate the implications of these relationships for marine risk assessment and the potential predictability of large-wave frequencies.

By introducing frequency-based wave indicators and systematically examining their climatic drivers, this study extends existing wave climatology research and provides a practical framework for linking large-scale climate variability to operationally relevant wave conditions.

2. Data and Methods

2.1. Data

2.1.1. ERA5 SWH

This study uses the ERA5 SWH data, which cover the period from 1993 to 2024 (32 years) in 3-hourly intervals. The spatial coverage extends from 0° to 60° N and from 95° E to 180° E, with a resolution of 0.25° × 0.25°. We justify starting at 1993 by the emergence of satellite-altimeter-constrained wave reanalysis in ERA5, which markedly improves reliability of SWH and other wave variables; pre-1993 wave fields are predominantly wind-driven and subject to larger biases and inhomogeneities due to limited observations. Several reanalysis datasets, including CFSR/CFSv2, JRA-55 and MERRA-2, also provide SWH data for the NWP [25,26,27,28]. However, ERA5 offers clear advantages in terms of higher spatial (0.25°) and temporal (hourly) resolution, a more comprehensive wave data assimilation system, and improved performance in representing extreme wave conditions, particularly under tropical cyclone influence [29,30]. As the successor to ERA-Interim, ERA5 assimilates over 20 times more satellite data. This expansion goes beyond mere quantity to encompass greater diversity, enhanced quality and improved processing methodologies. ERA5 achieves a qualitative leap in resolution, accuracy, number of variables, and uncertainty characterization through an advanced assimilation system, massive reprocessed observations, more robust bias corrections, and pioneering ensemble information [31,32,33].

Several studies have validated SWH data from the ERA5 reanalysis against observations from buoys and multiple satellites, including the CYGNSS, GF-3, and FY-3E missions [34,35,36,37]. Meanwhile, the ERA5 SWH data was assessed by comparing it with observations from 103 buoys from the U.S. National Data Buoy Center in the North Atlantic and Pacific between 1979 and 2019. The results indicate that the ERA5 SWH has a good agreement with the in situ observations, with a bias of −0.058 m, root mean squared error of 0.325 m, correlation coefficient of 0.961 and scatter index of 18.54%. The accuracy of ERA5 SWH is satisfactory under the most typical sea states (0.5 m < SWH < 4 m). The monthly analysis shows that the performance of ERA5 SWH in summer is the best. The water depth and offshore distance have also been identified to impact the reliability of ERA5 SWH. Although the statistics vary at different locations, the performances of ERA5 SWH at most stations are reasonable. In addition, an evident improvement in the validity over time is observed, which can be attributed to the assimilation of the altimeter wave height [38]. Overall, due to their high spatiotemporal resolution and long-term temporal characteristics, the ERA5 SWH reanalysis data have become an optimal choice for SWH studies. They have been widely used to investigate SWH characteristics [20,39,40], demonstrating high levels of accuracy and reliability. Therefore, ERA5 is adopted in this study to derive high-wave frequency indices such as f₅ and f₇.

2.1.2. Climate Index Data

This study uses three climate indexes to represent different aspects of the climate: the Arctic Oscillation (AO), Oceanic Niño (ONI) and Pacific Decadal Oscillation (PDO) indexes. The data span the period from 1993 to 2024, with monthly resolution. The AO index is sourced from the Climate Prediction Center (CPC) of the National Oceanic and Atmospheric Administration (NOAA), and it reflects the counter-phase oscillation between sea-level pressure in the mid-latitude Northern Hemisphere (approximately 35° N–45° N) and the high-latitude region (north of approximately 55° N). It represents the primary mode of extratropical atmospheric circulation variability in the Northern Hemisphere [41]. The ONI, defined as the three-month moving average anomaly of the mean sea surface temperature in the central-eastern equatorial Pacific (5° N–5° S, 170° W–120° W), is provided by the NOAA CPC. It is recognized internationally as a key indicator for identifying El Niño and La Niña events [42]. The PDO index is sourced from the NOAA Environmental Information Center (EIC). It reflects the spatial variability characteristics of Pacific sea surface temperatures on a decadal timescale, characterizing the long-term evolutionary background of the sea’s climate system [43]. All three indexes have been extensively validated and applied in climate research, demonstrating good accuracy and reliability [41,42,43].

2.2. Methods

2.2.1. Analytical Framework

Firstly, this study compares and analyzes the annual distribution and seasonal variations in f₅ and f₇ in the NWP from 1993 to 2024. This covers regional seasonal extremes and dominant seasonal characteristics, revealing their physical mechanisms. Secondly, linear regression methods are employed to separately calculate the long-term climate trends of f₅ and f₇. The seasonality and regional differences in these trends are analyzed, as well as their dominant seasons. Significance tests are conducted using t-statistics, and representative months for typical oceanic seasons are then selected. Pearson correlation coefficients (PCCs) are then used to examine the relationships between f₅ and f₇ and the AO, ONI and PDO indexes. Cumulative probability $p$-values are applied for significance testing and the underlying physical mechanisms are elucidated. Finally, the study’s conclusions are summarized, and future research directions are proposed. The specific statistical methods and significance tests employed in this study are described in detail in the following subsections.

2.2.2. Linear Regression Method and $t$-Statistics

(1)

Linear regression method

Linear regression is a commonly used statistical method for modeling the linear relationship between a dependent variable and one or more independent variables. In time-series analyses, time is typically treated as the independent variable, while the observed values are considered the dependent variable [44].

Assume a time series dataset $\left(t_1,y_1\right)$, $\left(t_2,y_2\right)$, …, $\left(t_n,y_n\right)$, where $t_i$ denotes time, $y_i$ represents the observed wave frequency, and $n$ is the number of data points. The objective of linear regression is to determine the best-fitting straight line:

$$y={\beta }_0+{\beta }_{1}t$$

(1)

where ${\beta }_0$ is the intercept and ${\beta }_1$ is the slope. The slope ${\beta }_1$ represents the temporal trend of the time series, indicating the rate of change per unit time.

The intercept ${\beta }_0$ and slope ${\beta }_1$ are estimated using the least squares method, which minimizes the Residual Sum of Squares (RSS):

$$RSS={\displaystyle {\sum }_{i=1}^n{\left(y_i-\left({\beta }_0+{\beta }_1{t}_i\right)\right)}^2}$$

(2)

By taking partial derivatives of the RSS with respect to ${\beta }_0$ and ${\beta }_1$ and setting them to zero, analytical solutions for the regression coefficients are obtained:

$${\beta }_1={\displaystyle \frac{{\displaystyle {\sum }_{i=1}^n\left(t_i-\overline{t}\right)\left(y_i-\overline{y}\right)}}{{\displaystyle {\sum }_{i=1}^n{\left(t_i-\overline{t}\right)}^2}}}$$

(3)

$${\beta }_0=\overline{y}-{\beta }_1\overline{t}$$

(4)

where $\overline{t}$ and $\overline{y}$ denote the mean values of time and observations, respectively.

(2)

t-statistics

The $t$-statistic is used to test whether the regression slope ${\beta }_1$ is significantly different from zero. If the absolute value of the $t$-statistic exceeds the critical value, the null hypothesis of no trend is rejected, indicating ${\beta }_1$ statistically significant trend [44].

The $t$-statistic is calculated as:

$$t={\displaystyle \frac{{\beta }_1}{SE\left({\beta }_1\right)}}$$

(5)

where $SE\left({\beta }_1\right)$ is the standard error of the slope, given by:

$$SE\left({\beta }_1\right)={\displaystyle \frac{s_e}{\sqrt{{\displaystyle {\sum }_{i=1}^n{\left(t_i-\overline{t}\right)}^2}}}}$$

(6)

and $s_e$ is the standard deviation of the residuals, calculated as:

$$s_e=\sqrt{{\displaystyle \frac{RSS}{n-2}}}$$

(7)

All statistical significance tests in this study are conducted using two-tailed tests with ${\beta }_1$ significance level of $\alpha =0.05$. For ${\beta }_1$ 95% confidence level, the critical value is $t_{\alpha /2,n-2}$, where $n-2$ denotes the degrees of freedom. If $\left|t\right|>t_{\alpha /2,n-2}$, the trend is considered statistically significant.

2.2.3. Pearson Correlation Coefficient and $p$-Value

(1)

Pearson correlation coefficient

The Pearson correlation coefficient measures both the strength and direction of linear association between two variables and ranges from −1 to 1, where positive (negative) values indicate positive (negative) correlations, and larger absolute values indicate stronger linear relationships [45].

The Pearson correlation coefficient $r$ is calculated as:

$$r={\displaystyle \frac{{\displaystyle {\sum }_{i=1}^n\left(X_i-\overline{X}\right)}\left(Y_i-\overline{Y}\right)}{\sqrt{{\displaystyle {\sum }_{i=1}^n{\left(X_i-\overline{X}\right)}^2}}\sqrt{{\displaystyle {\sum }_{i=1}^n{\left(Y_i-\overline{Y}\right)}^2}}}}$$

(8)

where $X_i$ and $Y_i$ represent paired observations of the two variables, $\overline{X}$ and $\overline{Y}$ are their respective sample means, and $n$ is the sample size.

(2)

p-value

The $p$-value is used to assess whether the Pearson correlation coefficient $r$ is significantly different from zero. Smaller $p$-values indicate stronger evidence against the null hypothesis of no correlation. In this study, correlations with $p<0.05$ are considered statistically significant [45].

The $p$-value is obtained from the $t$-distribution. For a dataset with sample size $n$ and correlation coefficient $r$, the corresponding $t$-statistic is calculated as:

$$t=r\sqrt{{\displaystyle \frac{n-2}{1-r^2}}}$$

(9)

where the degrees of freedom are $n-2$. For a two-tailed test, the $p$-value is computed as:

$$p=2\times \left(1-F\left(\left|t\right|\right)\right)$$

(10)

where $F\left( \right)$ denotes the cumulative distribution function of the $t$-distribution.

The linear regression and correlation analysis methods described above are widely applied in climate and oceanographic time-series studies, ensuring the robustness and reproducibility of the statistical results [44,45,46,47].

3. Results

3.1. Annual and Seasonal Distribution of f₅

The proportion of wave events of level 5 or higher relative to the total number of observations over the 32-year period was statistically analyzed based on wave observation data from various grid points in the NWP from 1993 to 2024. This yielded an annual mean spatial distribution of f₅, as shown in Figure 1. The results indicate that f₅ exhibits a spatial distribution pattern across the entire NWP region, gradually increasing from the south to the north and from the southwest to the northeast. The most pronounced gradient occurs in the area east of Japan, extending to 160° E. The entire NWP basin constitutes a high-value zone for f₅, with values consistently exceeding 20%. North of 30° N, f₅ generally exceeds 36%, peaking at 58.0% south of the Aleutian Islands. In the Okhotsk Sea region, f₅ rises from the coast to the open sea, reaching 35.0% in the central Kuril Island maritime area. In the Sea of Japan, f₅ increases gradually from west to east, reaching a maximum value of 16.8% in the maritime region to the west of the country. Additionally, there are high f₅ centers in the central Taiwan Strait and on both sides of the Luzon Strait, at 26.4% and 24.0%, respectively. Low-frequency zones (f₅ < 1%) are primarily found in the Gulf of Thailand, the Sulu Sea, the southern coastal areas of the South China Sea, and the equatorial maritime region. In the Strait of Malacca and the western Sulawesi Sea, f₅ is zero.

Based on wave observation data from various grid points in the NWP from 1993 to 2024 (winter data from 1993 to 2023, other seasons from 1993 to 2024), we statistically analyzed the spatial distribution of f₅ for different seasons (spring: March–May; summer: June–August; autumn: September–November; and winter: December–February of the following year), as shown in Figure 2. The analysis indicates that winter contributes most significantly to the annual mean distribution of f₅ in the NWP, with its spatial characteristics being highly consistent with the annual mean distribution (see Figure 1). During this season, f₅ reaches its peak value of 96.9% in the maritime region south of the Aleutian Islands. The second-highest proportion is contributed by autumn, followed by spring, with summer contributing the least. Moreover, during summer, the center of high f₅ shifts to the maritime region east of Japan, reaching a maximum of 15.3%. The annual maximum f₅ value in the Sea of Japan region is primarily influenced by the winter season. Similarly, the annual maxima in the central Taiwan Strait and on both sides of the Luzon Strait are dominated by winter, followed by autumn contributions. The seasonal maximums for f₅ are 64.3% in spring, 15.3% in summer, 62.2% in autumn and 96.9% in winter, with seasonal extremes and dominant seasons in major sea areas detailed in

Table 1. Seasonal extremes and dominant seasons of f₅ in major sea areas, 1993–2024.

Area	Annual Extreme Value	Spring Extreme Value	Summer Extreme Value	Autumn Extreme Value	Winter Extreme Value	Dominant Season
Waters south of the Aleutian Islands	58.0%	64.3%	12.8%	62.2%	96.9%	Winter
Sea of Okhotsk	35.0%	29.7%	3.0%	36.2%	50.4%	Winter
Sea of Japan	16.8%	10.1%	2.9%	17.3%	41.8%	Winter
Both sides of the Luzon Strait	26.4%	13.1%	13.8%	34.6%	51.2%	Winter
Taiwan Strait	24.0%	14.2%	6.8%	33.3%	46.6%	Winter

.

This distribution pattern is primarily governed by the combined influence of extratropical cyclones and monsoon systems. As a key component of the North Pacific winter-mean circulation [48], the Aleutian Low exerts its influence across an extensive zone of extratropical cyclonic activity. This extends from the mid-latitude seas east of Japan to the eastern coast of China and reaches northward to the Kamchatka Peninsula and southward to the region north of Taiwan Island and the Philippines. This activity range closely aligns with the high-frequency zones of f₅ in spring, autumn and winter (see Figure 2a,c,d). Temperate cyclones are most active from October to April; their intensity gradually increases in autumn (October–November) and peaks in winter (December–February), while the most frequent occurrence is seen in spring (March–May). This seasonal pattern aligns with the f₅ evolution characteristics. Temperate cyclones primarily form east of Japan, as well as along China’s eastern coast. Here, the continental cold air mass converges with the warm, moist air mass associated with the Kuroshio Current, creating favorable conditions for strong frontal cyclone formation [49,50]. These cyclones predominantly move in a northeast or eastward direction along the westerlies before merging into the Aleutian Low. This trajectory is consistent with the increasing distribution of f₅ from a southwesterly to a northeasterly direction. On the other hand, the monsoon system plays a pivotal role in generating waves in the South China Sea and near the Luzon Strait. The winter northeast monsoon (November–March) is characterized by high intensity and extensive coverage, with particularly strong winds and waves in the Taiwan Strait due to the “Venturi effect”. The summer southwest monsoon (June–September) can also generate large waves up to 4–6 m high. Thus, the monsoon, particularly the winter monsoon, is the dominant factor driving f₅ maxima along both sides of the Luzon Strait and in the central Taiwan Strait (see Figure 2c,d). Seasonal f₅ low-frequency zones predominantly occur near the equator and over continental shelves, where wind wave energy is significantly reduced due to weaker winds, land shielding or limited wind fetch.

3.2. Annual and Seasonal Distribution of f₇

We statistically analyzed the proportion of wave events of level 7 or higher relative to the total number of observations over the 32-year period based on wave observation data from various grid points in the NWP from 1993 to 2024. This yielded an annual mean spatial distribution of f₇, as shown in Figure 3. The results show that, compared to f₅, the distribution range of f₇ is significantly smaller and its values are generally lower overall. However, it still exhibits an increasing intensity trend from south to north and from southwest to northeast. The maximum gradient of f₇ concentrates in the region between 30° N and 45° N (spanning 160° E to 180° E). The annual mean f₇ is predominantly high in the northern part of the NWP Basin, generally exceeding 1.3%. North of 35° N, f₇ frequently exceeds 3.0%, with the highest value of 6.4% occurring in the maritime region south of the Aleutian Islands. In the Sea of Okhotsk, f₇ increases from the coast to the open sea, reaching a maximum value of around 1.5% in the central maritime region of the Kuril Islands. In the Sea of Japan, f₇ gradually increases from west to east, reaching a maximum of around 0.6% in the maritime region west of Japan. Another maximum of about 0.7% is also present east of Taiwan Island. By contrast, within the 0–15° N range, f₇ is generally below 0.1%, with large areas showing zero values.

Based on wave observation data from various grid points in the NWP from 1993 to 2024 (winter data from 1993 to 2023, other seasons from 1993 to 2024), we statistically analyzed the spatial distribution of f₇ for the different seasons (spring: March–May, summer: June–August, autumn: September–November and winter: December–February of the following year), as shown in Figure 4. The results indicate that the annual mean distribution of f₇ north of 25° N is primarily dominated by winter contributions and exhibits spatial characteristics that are most similar to the annual mean distribution of f₇ (see Figure 3). During winter, f₇ peaks to the south of the Aleutian Islands, and a significant high-value zone also forms in the Okhotsk Sea. The second-highest proportion is contributed by autumn, followed by spring, with summer contributing the least. Similarly, the annual maximum f₇ in the Sea of Japan originates primarily from the winter season. In the maritime region east of Taiwan Island, the annual maximum f₇ is mainly contributed to by summer and autumn together. The seasonal f₇ maxima are 4.8% in spring, 1.6% in summer, 5.9% in autumn and 16.8% in winter; these maxima and dominant seasons for major sea areas are detailed in

Table 2. Seasonal extremes and dominant seasons of f₇ in major sea areas, 1993–2024.

Area	Annual Extreme Value	Spring Extreme Value	Summer Extreme Value	Autumn Extreme Value	Winter Extreme Value	Dominant Season
Waters south of the Aleutian Islands	6.4%	4.8%	0.2%	5.9%	16.8%	Winter
Sea of Okhotsk	1.5%	1.2%	0.1%	1.7%	3.4%	Winter
Sea of Japan	0.6%	0.3%	0.03%	0.3%	1.9%	Winter
Waters east of Taiwan Island	0.7%	0.2%	1.6%	1.5%	0.1%	Summer and autumn

.

This distribution pattern is primarily governed by the combined influence of extratropical cyclones and typhoons. In the maritime region north of 25° N, sea waves of level 7 or higher in spring, autumn and winter are predominantly generated by extratropical cyclones. These waves form in a manner similar to level 5 or higher waves, which are closely related to mid-latitude strong westerlies, the Aleutian Low and sea–air interactions. In contrast, in the maritime region east of Taiwan Island, extreme waves primarily originate from typhoon activity. The NWP is the world’s most active tropical cyclone generation zone, accounting for approximately one-third of global tropical cyclones [51]. Although typhoons can occur at any time of year, they are most prevalent from July to October, with August and September being the busiest months. Their paths invariably traverse the maritime region east of Taiwan Island and the Philippines [52]. This pattern closely aligns with the emergence of high f₇ in the maritime region east of Taiwan Island during summer and autumn (see Figure 4b,c). Winter marks a period of reduced typhoon activity, characterized by a lower frequency of occurrences and southward-shifting paths. Systems predominantly affect the South China Sea, the Philippines and Vietnam’s coastal areas via westward trajectories, which also corresponds with the occurrence of f₇ regional maxima in the central South China Sea during winter (Figure 4d).

3.3. Annual Trend in f₅

To analyze regional variability patterns, this study employed LR methods based on data from 1993 to 2024 to calculate the long-term trend in f₅ in the NWP. The significance of this trend was tested using the t-statistic at the 95% confidence level, with the results shown in Figure 5.

In general, f₅ manifests a marked downward tendency across the majority of regions within the NWP basin. This trend is primarily concentrated within the triangular sea area bounded by the following coordinates: (30° N, 140° E), (12° N, 180° E) and (48° N, 180° E). Within this region, the rate of decline increases from the periphery towards the center, generally exceeding 0.15% per year, with a maximum value of 0.30%, which is indicative of a cumulative decrease of 9.6% over a 32-year period. Conversely, several regions exhibit a marked upward trend, principally in the waters adjacent to the Kamchatka Peninsula, southwest of Hokkaido, south of the Marshall Islands, and in the eastern and central Bohai Sea and northwestern Yellow Sea. The maximum rise rates in these areas are 0.49%, 0.18%, 0.11% and 0.05% per year, respectively, corresponding to cumulative increases of 15.68%, 5.76%, 3.52% and 1.6% over 32 years.

3.4. Seasonal Trend in f₅

To analyze the seasonal long-term variability characteristics of f₅ in the NWP, this study employed LR methods based on data from 1993 to 2024 (winter data from 1993 to 2023, and data for other seasons from 1993 to 2024). The trends for spring (March–May), summer (June–August), autumn (September–November) and winter (December–February) were calculated for each grid point, and their significance was determined via t-statistics at the 95% confidence level, with the results shown in Figure 6.

It is evident that, in general, the NWP basin demonstrates a marked downward trend. The most significant contribution to this annual mean decline is attributed to autumn, and its spatial distribution most closely resembles the inter-annual pattern depicted in Figure 5. The primary regions of autumn decline are situated within (12° N–32° N, 147° E–180° E) and (40° N–50° N, 147° E–180° E), with an increase in the rate of decline observed from the periphery towards the center. The maximum rate of interest reached 0.69% per year, corresponding to a cumulative decrease of 22.08% over the 32-year period. Spring ranks second, with the primary decline occurring in the (30° N–40° N, 150° E–180° E) region, where the maximum rate of decline is 0.50% per year, resulting in a cumulative decline of 16%. It is evident that winter exerts a substantial influence, manifesting as a pronounced decrease concentrated in (28° N–35° N, 143° E–175° E). Here, the maximum rate is 0.45% per year, resulting in a cumulative decrease of 14.4%. In contrast, the summer period exhibits no discernible trend and contributes almost nothing to the overall decline.

Meanwhile, certain sea areas exhibit notable upward trends. The annual mean rise near the Kamchatka Peninsula, southwest of Hokkaido, and south of the Marshall Islands is primarily driven by winter contributions. The maximum annual increase rates observed are 1.64%, 0.61% and 0.47%, respectively, with cumulative increases over a 32-year period reaching 52.48%, 19.52% and 15.04%. It is noteworthy that the annual growth rate of 1.64% is observed in the vicinity of (59.75° N, 170.75° E), with only 10 grid points surpassing a 1% growth rate. In order to emphasize the trend hierarchy in areas exhibiting growth rates below 1%, the color scale range shown in Figure 6 is set to [−1, 1]. Furthermore, the annual upward trend in the eastern and central Bohai Sea and northwestern Yellow Sea primarily originates from autumn, with a maximum annual increase rate of 0.18% and a cumulative increase of 5.76%.

3.5. Annual Trend in f₇

We employed LR methods based on data from 1993 to 2024 to calculate the long-term trend in f₇ in the NWP and analyze regional variability patterns. The significance of this trend was tested using the t-statistic at the 95% confidence level, with the results shown in Figure 7.

In the waters east of Japan (30° N–40° N, 150° E–180° E), f₇ exhibits a significant annual decline trend, with the rate of decrease increasing from west to east. The maximum annual decrease is 0.08%, corresponding to a cumulative reduction of 2.56% over 32 years. Additionally, the waters east of the Kamchatka Peninsula exhibit a marked upward trend, with the maximum increase rate also reaching 0.08% per year, resulting in a cumulative increase of 2.56%.

3.6. Seasonal Trend in f₇

To analyze the seasonal long-term variability characteristics of f₇ in the NWP, this study employed LR methods based on data from 1993 to 2024 (winter data from 1993 to 2023, and data for other seasons from 1993 to 2024). The trends for spring (March–May), summer (June–August), autumn (September–November) and winter (December–February) were calculated for each grid point, and trend significance was determined via t-statistics at the 95% confidence level, with the results shown in Figure 8.

It can be seen that winter contributes most significantly to the annual mean change in f₇. The sea area east of the Kamchatka Peninsula exhibits a pronounced upward trend, with a maximum annual increase rate of 0.30% and a cumulative rise of 9.6% over 32 years. In contrast, the triangular region bounded by the points (35° N, 172° E), (33° N, 180° E) and (42° N, 180° E) exhibits a pronounced decline, with a maximum annual decrease of 0.27% and a cumulative reduction of 8.64%. Spring contributes secondarily, with a decline observed in the waters east of Japan (30° N–40° N, 153° E–175° E) during this season. The maximum rate is 0.11% per year, corresponding to a cumulative decrease of 3.52% over 32 years. Autumn’s influence was weaker, with the decline trend concentrated in the (47° N–51° N, 162° E–175° E) region. The maximum decline rate was 0.16% per year, with a cumulative decrease of 5.12%. Summer showed no significant trend and contributed the least to the annual mean change.

4. Correlations Between f₅/f₇ and Key Climate Indexes

To investigate the underlying climatic drivers of spatial variations in the annual and seasonal trends of f₅ and f₇, we further analyzed the correlations between monthly f₅ and f₇ and key climate indexes (AO, ONI and PDO) over the 1993–2024 period. Due to space constraints and considering the representativeness of typical months for seasonal oceanic element distribution, February, May, August, and November are selected as representative months for winter, spring, summer, and autumn, respectively, for correlation analysis. These months correspond to the climatological peaks of seasonal oceanic conditions and effectively capture the typical characteristics of each season while minimizing transitional influences, thereby enabling a clear representation of seasonal variability with reduced redundancy and computational cost. Based on these results, the subsequent discussion further explores the potential physical mechanisms underpinning the observed relationships. It should be noted that the identified trends and correlations are subject to uncertainties related to data limitations, internal climate variability, and methodological choices, and, therefore, the results should be interpreted with appropriate caution.

4.1. Correlation Between f₅ and Key Climate Indexes

4.1.1. Correlation with AO

Based on monthly average data from February, May, August and November spanning 1993–2024, this study calculated the PCC between f₅ and the AO index in the NWP. Significance was tested using a $p$-value at the 95% confidence level, with the results shown in Figure 9.

The analysis indicates that the AO index exhibits clear seasonal variations in its impact on f₅. During the winter and spring months, positive correlations prevail, while negative correlations predominate in summer and autumn. In February, the region exhibiting a significant correlation is predominantly distributed in the central and southern South China Sea, as well as the waters between the Philippines and the Mariana Islands. By May, the correlation zone is concentrated around the Mariana Islands. In August, a significant correlation zone is observed to shift to the waters southeast of the Ryukyu Islands. By November, the influence expands to three maritime areas: south of the Kamchatka Peninsula, east of Japan and near the Marshall Islands. The maximum correlation coefficients for each month are detailed in

Table 3. Maximum correlation coefficient between f₅ and AO.

Correlation Coefficient	Feb	May	Aug	Nov	Maximum
Maximum positive Correlation coefficient	0.51	0.48	0.46	0.50	0.51
Absolute maximum negative Correlation coefficient	−0.53	−0.48	−0.54	−0.64	−0.64

.

February: When the AO is in its positive phase, the mid-latitude westerly jet stream intensifies and exhibits greater zonal extension, thereby facilitating the stable and efficient eastward and southeastward transport of cold air masses from the Asian continent. The robust northeast monsoon over the open waters of the central and southern South China Sea possesses sufficient fetch, promoting large-wave generation and development. After the northeast monsoon crosses the Luzon Strait into the open ocean, the fetch increases substantially in the waters between the Philippines and the Mariana Islands. Reduced surface friction and enhanced sea–air energy exchange in this region further facilitate giant wave formation. Consequently, the positive AO phase strengthens the wind field intensity in the relevant sea areas through the “winter monsoon intensification” mechanism, leading to a significant rise in f₅.

May: When the AO is in its positive phase, the mid-latitude westerly jet stream remains strong and exhibits pronounced zonal flow characteristics. This circulation pattern first suppresses the northward jump of the Western Pacific Subtropical High (WPSH), keeping its position south and east of the climatological average, before it intensifies the trade winds around the Mariana Islands. These stable, strong winds persistently act over the open ocean, providing ample energy for wave growth. The positive AO phase indirectly promotes increased f₅ in the relevant sea areas by suppressing the WPSH and strengthening the trade winds.

August: The waters southeast of the Ryukyu Islands serve as a critical region for typhoon formation and movement. When the AO index is in its negative phase, the meridional extent of mid-to-high-latitude circulation increases, facilitating the development of deep trough–ridge systems along the East Asian coast. This weakens the WPSH, potentially causing it to fracture or retreat eastward. This circulation adjustment diminishes its westward steering effect on typhoon tracks, making northward or northeastward deviations more likely. The weakened WPSH simultaneously provides broader development space for low-latitude and -pressure systems, favoring typhoon formation and intensification. Therefore, the AO negative phase enhances f₅ in the relevant sea areas through the physical mechanism of weakening the WPSH intensity and improving the circulation background for typhoon formation and movement.

November: When the AO is in its negative phase, the polar vortex tends to split, causing the center of cold air to shift southward and significantly increasing the meridional extent of the circulation. This facilitates the formation of a “high-pressure west, low-pressure east” pressure field configuration over Eurasia, specifically manifesting in the development of a blocking high over the Urals and a deepening of the East Asian trough. This promotes an early and vigorous southeastward surge of strong cold air (cold surges). The southward-moving cold air mass reaches the Sea of Okhotsk and the waters south of the Kamchatka Peninsula, triggering sharp temperature drops and strong winds. Sea ice formation gradually begins in these waters from November. The contrast between the cold land surfaces and sea ice-covered areas and the relatively warmer ocean surface creates a significant sea–air temperature gradient. This strongly enhances atmospheric instability, stimulates vigorous thermal convection, and subsequently triggers polar cyclones or explosive cyclonic activity, leading to a significant increase in f₅ in this region. This process represents a classic “cyclone development” mechanism. East of Japan, the leading edge of southward-moving cold air masses converges with the warm Kuroshio Current, generating intense heat and moisture exchange and providing favorable conditions for extratropical cyclone development. Concurrently, the deepening East Asian trough front exhibits strong positive vorticity advection, further promoting cyclone formation and intensification, which are also characteristic of the “cyclone development” mechanism. Near the Marshall Islands, negative AO phases can influence convective activity in the equatorial central and western Pacific by inducing global circulation anomalies. These anomalies alter the Walker circulation or trigger Pacific-North American (PNA) mode and other teleconnection waves. Such large-scale circulation adjustments enhance the probability and intensity of weather systems like easterly waves and tropical disturbances, significantly increasing f₅ over tropical oceans. This mechanism can be categorized as tropical weather system modulation.

4.1.2. Correlation with ONI

Based on monthly average data from February, May, August and November spanning 1993–2024, we calculated the PCC between f₅ and ONI in the NWP. Significance was tested using a $p$-value at the 95% confidence level, with the results shown in Figure 10.

The ONI exhibits distinct seasonal dependence on f₅: predominantly negative correlations prevail in winter and positive correlations dominate in spring and summer, while autumn shows scattered positive and negative correlations. In February, significant negative correlations were concentrated on both sides of the Luzon Strait (with maximum correlation coefficient r_m reaching −0.70), the Sea of Japan, waters east of Honshu Island and areas east of the Kamchatka Peninsula. By May, the influence shifted to the eastern and southeastern Kamchatka Peninsula, the Melanesian Basin, and surrounding seas. By August, the influence spread most extensively, covering most of the NWP east of Japan, Taiwan Island, and the Philippines, with approximately three-quarters of the region showing moderate to strong correlations (r_m as high as 0.70). By November, negative correlations were observed in the northern South China Sea and localized areas east of Hokkaido, while positive correlations appeared in parts of the waters east of the Philippines and sections of the Melanesian Basin. The maximum correlation coefficients for each month are detailed in

Table 4. Maximum correlation coefficient between f₅ and ONI.

Correlation Coefficient	Feb	May	Aug	Nov	Maximum
Maximum positive Correlation coefficient	0.60	0.59	0.70	0.53	0.70
Absolute maximum negative Correlation coefficient	−0.70	−0.47	−0.42	−0.64	−0.70

.

February: During El Niño events (positive ONI), elevated sea surface temperatures in the eastern Pacific caused convective activity to shift eastward across the western Pacific. This reduced the thermal contrast between the Eurasian continent and the Pacific Ocean, subsequently weakening the intensity of the East Asian winter monsoon. Additionally, the positive phase of the PNA index triggered by El Niño shifted the North Pacific storm track northeastward, reducing the extent and duration of strong wind zones affecting waters east of Japan. Although the positive PNA phase intensifies the Aleutian Low, its strongest pressure gradients are concentrated south and southwest of the low-pressure center. Since the waters east of the Kamchatka Peninsula lie north or northwest of the low, actual wind speeds and the duration of strong winds in this region actually decrease. In summary, through the combined mechanism of weakening the winter monsoon, altering the path of extratropical cyclones and adjusting the structure and intensity of the Aleutian Low, f₅ is significantly reduced in the relevant sea areas.

May: As a transitional season, the positive phase of the PNA triggered by El Niño continued to exert influence, steering the North Pacific storm track northeastward and directing more extratropical cyclones over the waters east of the Kamchatka Peninsula. Concurrently, the enhanced tropical–mid-latitude moisture and energy transport during El Niño years provided more abundant latent heat support for extratropical cyclone development. In the Melanesian Basin, El Niño caused tropical convective centers to shift eastward toward the central Pacific, triggering adjustments in atmospheric circulation. The southwest winds crossing the equator and the easterly winds south of the WPSH in this region may strengthen to maintain energy balance. Furthermore, the typhoon formation tendency further east during El Niño years became evident as early as May. This earlier exposure to tropical disturbances or the outer circulation of typhoons increases the likelihood of f₅ in the associated waters.

August: During El Niño years, the subtropical high strengthens and extends southeastward, expanding the coverage and intensity of its easterly and southeasterly wind belts along its periphery. Although the total number of typhoon formations may decrease, their locations shift significantly eastward, and their lifespans lengthen, favoring the development of stronger systems. Under the influence of airflow guided by the southern edge of the WPSH, typhoons moving northwestward generate persistent strong swells over vast ocean areas to their right, capable of long-distance propagation, significantly elevating f₅ across the entire NWP region.

November: As a transitional season, autumn ENSO signals are susceptible to modulation or cancelation by other factors, resulting in scattered correlations with f₅. During El Niño years, signals of weaker winter monsoons emerge in autumn, reducing wind and wave activity in regions like the northern South China Sea and east of Hokkaido that experience early winter monsoon influence. Concurrently, in some areas, the residual effects of summer circulation anomalies (such as enhanced easterly wind anomalies) persist. Combined with incompletely dissipated sea surface temperature anomalies, this maintains a certain level of wave activity east of the Philippines and in the Melanesian Basin.

4.1.3. Correlation with PDO

Based on monthly average data from February, May, August and November spanning 1993–2024, we calculated the PCC between f₅ and the PDO index in the NWP. Significance was tested using a $p$-value at the 95% confidence level, with the results shown in Figure 11.

In its influence on f₅, the PDO index exhibits distinct seasonal characteristics: its positive correlation is primarily concentrated during summer and autumn, while significant correlation zones are rarely observed during winter and spring. In August, a significant contiguous positive correlation zone appeared across the vast waters east of the Philippines to the Melanesian Basin, as well as the area from the Marshall Islands to the south of the Emperor Seamount Chain. By November, continuous positive correlations also emerged in the waters east of the southern Philippines, east of the Mariana Islands and north of the Marshall Islands. The maximum correlation coefficients for each month are detailed in

Table 5. Maximum correlation coefficient between f₅ and PDO.

Correlation Coefficient	Feb	May	Aug	Nov	Maximum
Maximum positive Correlation coefficient	0.47	0.52	0.63	0.64	0.64
Absolute maximum negative Correlation coefficient	−0.56	−0.46	−0.43	−0.50	−0.56

.

August: When the PDO is in its positive phase, sea surface temperatures in the tropical central and eastern Pacific rise. This triggers a PNA-like teleconnection wave pattern, strengthening the WPSH and extending its reach westward. This circulation adjustment expands the range of southeasterly to easterly trade winds south of the WPSH and lengthens the wind zone, thereby increasing wave-generating energy. Typhoons simultaneously form further east and south than average. As they track westward, stronger pressure gradient winds develop between the typhoon’s northern flank and the WPSH, generating persistent heavy swells across vast ocean areas to the right, which significantly elevates f₅ in these waters.

November: This month marks a transitional period between the summer and winter monsoons. During the positive phase of the PDO, the waters east of the Philippine Islands remain under the persistent influence of an abnormally strong WPSH, resulting in trade winds stronger than the climatological average. As cold air masses from the Asian continent frequently move southward, the leading edge of cold fronts interacts with warm ocean surfaces in this region, creating a strong thermal gradient that further intensifies surface wind speeds. Additionally, the PDO positive phase intensifies the subtropical westerly jet stream, inducing a stable and robust low-level easterly jet stream in the tropical waters to the south. This leads to increased wind speeds and an extended wind zone east of the Mariana Islands, which collectively contribute to a significant increase in f₅.

4.2. Correlation Between f₇ and Key Climate Indexes

4.2.1. Correlation with AO

Based on monthly average data from February, May, August and November spanning 1993–2024, we calculated the PCC between f₇ and the AO index in the NWP. Significance was tested using a $p$-value at the 95% confidence level, with the results shown in Figure 12.

It can be observed that the correlation between the AO index and f₇ is generally characterized by a spatially limited influence, with no significant correlation zones forming across large areas in any season. In February, significant negative correlations were only observed east of Minamitorishima and north of Wake Island; May showed almost no significant correlation zones; and August featured scattered correlations, with isolated negative correlations distributed from northeast of the Philippines to the sea south of the Emperor Seamounts, while positive correlations were sporadically distributed from east of Honshu to the Bering Sea, including a relatively large positive correlation zone in the latter. By November, a significant negative correlation zone appeared in the waters southeast of the Emperor Seamounts chain. The maximum correlation coefficients for each month are shown in

Table 6. Maximum correlation coefficient between f₇ and AO.

Correlation Coefficient	Feb	May	Aug	Nov	Maximum
Maximum positive Correlation coefficient	0.48	0.37	0.50	0.50	0.50
Absolute maximum negative Correlation coefficient	−0.62	−0.41	−0.49	−0.52	−0.62

.

February: When the AO is in its negative phase, the pressure gradient weakens in mid-latitudes, and the meridional extent of the westerlies increases. This favors the development and eastward movement of more frequent and stronger extratropical cyclones along a more southerly track, passing east of Minamitorishima and north of Wake Island, and thereby enhances f₇ in this region. Conversely, during positive AO phases, storm tracks shift northward, primarily affecting waters near the Aleutian Islands. This weakens cyclonic activity over mid-latitude oceans, leading to a corresponding decrease in f₇.

May: In this transitional period between winter and summer, atmospheric circulation is significantly disrupted by factors such as active local convection and shortwave trough–ridge activity. Against this backdrop, the AO signal struggles to form a sustained and stable circulation pattern, thus failing to exert a significant systematic influence on f₇.

August: The negative AO phase can influence the pattern of the WPSH and enhance mid-latitude trough–ridge activity through teleconnection processes. This favors typhoon tracks turning northward east of the Philippines, subsequently triggering intense wind fields in the waters to its right and enhancing f₇. During positive AO phases, the circulation tends to become more zonal, and the WPSH configuration is unfavorable for northward typhoon turns. However, at this time, the Bering Sea and the waters south of the Kamchatka Peninsula are at the edge of the subpolar low-pressure system, where average wind speeds increase. Combined with the continued development of extratropical cyclones, this leads to an increase in f₇ in this region.

November: An AO negative phase favors the development of meridional circulation, promoting a southward shift in the paths of extratropical cyclones and cold air activity to the southeast of the Emperor Seamount Chain. This enhances the sea surface wind field and increases f₇. Conversely, an AO positive phase suppresses cyclonic development in this region, leading to a decrease in f₇.

4.2.2. Correlation with ONI

Based on monthly average data from February, May, August and November spanning 1993–2024, we calculated the PCC between f₇ and ONI in the NWP. Significance was tested using a $p$-value at the 95% confidence level, with the results shown in Figure 13.

ONI exhibits distinct seasonal variations in its influence on f₇: consistent positive correlations prevail during summer and autumn, while winter and spring show scattered distributions, with negative correlations predominantly concentrated in coastal waters and positive correlations primarily occurring in the open ocean. More specifically, in February, small-scale negative correlations exist east and west of southern Kamchatka Peninsula, while a large positive correlation zone appears northeast of Wake Island. In May, significant negative correlations occur off Sakhalin Island and east of Japan, with scattered small positive correlation zones from the Mariana Islands to the Bering Sea. August shows no negative correlation zones, with positive correlations forming contiguous areas primarily between Taiwan Island and Minamitorishima (maximum correlation coefficient r_m reaching 0.67), extending to the open ocean east and west of Emperor Seamount. By November, negative correlation zones nearly vanish, with positive correlations appearing only sporadically on both sides of the Mariana Islands, the western Sea of Japan and the central Bering Sea. The maximum correlation coefficients for each month are detailed in

Table 7. Maximum correlation coefficient between f₇ and ONI.

Correlation Coefficient	Feb	May	Aug	Nov	Maximum
Maximum positive Correlation coefficient	0.49	0.49	0.67	0.57	0.67
Absolute maximum negative Correlation coefficient	−0.49	−0.55	NaN	−0.36	−0.55

.

February: The winter El Niño reaches its peak, while the East Asian trough typically weakens, leading to a reduction in the intensity of the East Asian winter monsoon. This is the primary reason for the negative correlation observed in the offshore waters of the Kamchatka Peninsula. Concurrently, the El Niño event deepens the Aleutian Low, increases the pressure gradient in the central-northern Pacific northeast of Wake Island and intensifies extratropical cyclone activity, resulting in elevated f₇ in this region.

May: The negative correlation observed in the waters off Sakhalin Island and east of Japan can be regarded as a continuation of the weakening effect of the winter monsoon. Meanwhile, the scattered positive correlations extending from the Mariana Islands to the Bering Sea reflect the combined influence of summer typhoon activity in low latitudes and the persistent presence of extratropical cyclones in mid-to-high latitudes.

August: The mechanism of influence is largely consistent with that of the ONI on f₅ in August. During El Niño years, the WPSH intensifies and retreats southeastward, leading to typhoons forming further east and south. Their lifecycles extend and they intensify. The waters between Taiwan Island and Minamitorishima lie within the critical zone for typhoons moving westward or northwestward, and are directly affected by their passage. Simultaneously, the strong swells generated on the typhoon’s right flank can propagate far to the Emperor Seamounts region. Together, these factors significantly enhance f₇ in the relevant sea area.

November: The positive correlation mechanism in the waters flanking the Mariana Islands is similar to that observed in August. Additionally, the developing autumn El Niño strengthens the East Asian trough, guiding more powerful cold air southward. After interacting with warm sea surfaces in the Sea of Japan, this cold air can generate more vigorous extratropical cyclones. El Niño also causes a northward shift in storm tracks over the North Pacific through teleconnections, allowing more intense extratropical cyclones to directly affect the Bering Sea. These factors collectively contribute to an increase in f₇ over the aforementioned region.

4.2.3. Correlation with PDO

Based on monthly average data from February, May, August and November spanning 1993–2024, we calculated the PCC between f₇ and the PDO index in the NWP. Significance was tested using a $p$-value at the 95% confidence level, with the results shown in Figure 14.

The PDO index generally exerts a positive influence on f₇ throughout the year, with a negative correlation appearing only in winter waters east of the Kamchatka Peninsula. More specifically, in February, the positive correlation zone is concentrated within the (25° N–35° N, 150° E–180° E) range, while waters east of the Kamchatka Peninsula exhibit a significant negative correlation (r_m as high as −0.77). In May, a localized positive correlation zone exists southeast of the Kuril Islands. By August, the primary positive correlation zone extends from the waters between Taiwan Island and the Northern Mariana Islands (with a maximum r_m of 0.69) to the vicinity of the central and southern Emperor Seamounts. By November, the positive correlation zone formed an L-shaped distribution extending from the southeastern Japan Trench through the northern Philippine Sea Basin to the Mariana Islands region (r_m as high as 0.63), while positive correlations also emerged in the southeastern waters of the Kamchatka Peninsula and the Kuril Islands. The maximum correlation coefficients for each month are detailed in

Table 8. Maximum correlation coefficient between f₇ and PDO.

Correlation Coefficient	Feb	May	Aug	Nov	Maximum
Maximum positive Correlation coefficient	0.55	0.54	0.69	0.63	0.69
Absolute maximum negative Correlation coefficient	−0.77	−0.52	−0.41	−0.38	−0.77

.

February: During PDO positive phase years, elevated sea surface temperatures in the tropical central and eastern Pacific weaken the Aleutian Low through atmospheric teleconnection processes. Within the (25° N–35° N, 150° E–180° E) region, this circulation configuration favors enhanced or prolonged cyclonic activity, thereby increasing f₇. However, within the core of the Aleutian Low east of the Kamchatka Peninsula, the weakening of the low directly led to a decrease in mean wind speed and reduced storm activity. Despite the strong winter background wind and waves, the f₇ in this region during the PDO positive phase year remained below the climatological average. Its strong negative correlation (r_m as high as −0.77) reflects the critical modulating effect of the PDO on the wind field within the core of the Aleutian Low.

May: During the winter–summer transition period, background wind fields are relatively weak, and the PDO exerts negligible influence on f₇ in most sea areas. In the southeastern waters of the Kuril Islands, the positive PDO phase may slightly increase cyclone development or passage frequency, leading to localized f₇ enhancement.

August: During PDO positive phase years, typhoons form predominantly in a more southeasterly position. Warm sea surface temperatures favor their maintenance or intensification, with paths typically moving northwestward before turning northeastward, a pattern that increases the frequency and intensity of typhoon impacts on waters from Taiwan Island to the Northern Mariana Islands, thereby elevating f₇. As typhoons turn northward, their outer circulation generates strong winds near the central and southern Emperor Seamounts, further boosting f₇ in this region.

November: In the L-shaped sea area, typhoon activity with a more eastward track persists during the PDO positive phase year. The configuration of the WPSH shifting eastward and northward concurrently facilitates the development of extratropical cyclones moving eastward over the continent, collectively contributing to an increase in f₇. In the southeastern waters off the Kamchatka Peninsula and the Kuril Islands, the established Aleutian Low, under the influence of the positive PDO phase, may undergo upstream circulation adjustments, potentially increasing cyclone intensity or frequency and thereby elevating f₇.

5. Conclusions and Outlook

We investigated the spatiotemporal distribution characteristics, seasonal variations, and long-term trends of f₅ and f₇ in the NWP based on the ERA5 global reanalysis data for SWH from 1993 to 2024. We also revealed their correlations with climate indexes such as the AO, ONI and PDO, along with the underlying physical mechanisms. Our research findings are as follows:

(1)

The region with the greatest annual gradient of f₅ is located eastward from Japan to 160° E. The highest annual mean value of f₅ occurs in the waters south of the Aleutian Islands, reaching 58.0%, while significant annual maxima are also present in the central Taiwan Strait and both sides of the Luzon Strait, reaching 26.4% and 24.0%, respectively. Winter contributes most significantly to the annual mean f₅, with seasonal maxima of 64.3%, 15.3%, 62.2% and 96.9%, respectively.

(2)

The region with the greatest annual gradient of f₇ is located between 30° N and 45° N (between 160° E and 180° E). The highest annual mean value is found in the waters south of the Aleutian Islands, reaching 6.4%, with the greatest contribution occurring in winter. An annual peak occurs in the waters east of Taiwan Island, reaching up to 0.7%, with primary contributions in summer and autumn. The seasonal maxima are 4.8%, 1.6%, 5.9% and 16.8%, respectively.

(3)

f₅ exhibits a significant decreasing trend in the NWP basin, with a maximum rate of 0.30% per year and a cumulative reduction of 9.6% over 32 years. The most pronounced decline occurs in autumn, reaching a maximum rate of 0.69% per year. Significant upward trends are observed in the coastal waters around the Kamchatka Peninsula, the southwestern coastal waters of Hokkaido, and the southern waters of the Marshall Islands, with maximum rates of 0.49%, 0.18% and 0.11% per year, respectively. The cumulative increases over 32 years are 15.68%, 5.76% and 3.52%. Winter contributes most to the annual increasing trends in these three regions, with maximum rates reaching 1.64%, 0.61% and 0.47% per year, respectively.

(4)

f₇ exhibits a significant decreasing trend in the eastern oceanic regions of Japan and a significant increasing trend in the Bering Sea, with maximum rates of decrease and increase both reaching 0.08% per year (accumulating to 2.56% reduction and 2.56% increase over 32 years). Winter contributes most significantly to the annual average changes in the decreasing and increasing regions, with maximum rates reaching 0.27% and 0.30% per year, respectively.

(5)

Seasonal and regional variations in climate index–f₅ and f₇ relationships reflect large-scale atmospheric modulation of waves. For example, the AO index and f₅ exhibit positive correlations during winter and spring, but negative correlations in summer and autumn. The ONI shows a predominantly negative correlation with f₅ in winter (r_m = −0.70) around the Luzon Strait, shifting to a significant positive correlation in summer (r_m = 0.70) across the extensive region east of Taiwan Island and the Philippines. The PDO index shows a significant positive correlation with f₇ in summer and autumn (r_m = 0.69) east of Taiwan Island and a strong negative correlation in winter (r_m = −0.77) to the east of Kamchatka.

(6)

The core mechanism lies in how phase shifts in climate indexes modulate Northern Hemisphere atmospheric circulation, thereby affecting the intensity and paths of the WPSH, typhoons, monsoons, and extratropical cyclones. This ultimately alters the structure of sea surface wind fields, modulating the generation and propagation of ocean waves. Compared to f₇, the correlations between various climate indexes and f₅ are more pronounced, manifesting in broader regions of association, larger areas of moderate to strong correlations, and clearer spatial patterns and seasonal evolution. Furthermore, the influence exerted by the same climate index on f₅ and f₇ exhibits certain similarities.

The results of this study have direct implications for operational wave forecasting, marine safety, and wave energy assessment in the NWP. The identified statistically significant trends in f₅ and f₇, together with their robust and seasonally dependent correlations with large-scale climate indices, indicate that large-wave frequency anomalies are not purely random but are partly modulated by predictable climate modes. This suggests that f₅ and f₇ can serve as effective indicators for anticipating hazardous sea states on seasonal to interannual timescales, thereby supporting improved early warning and risk management for shipping routes, offshore engineering operations, and marine spatial planning. Furthermore, the frequency-based framework adopted in this study is readily transferable to other ocean basins, offering a scalable approach for integrating climate information into operational wave monitoring and forecasting systems. Overall, this work provides both a scientific and practical foundation for the medium- to long-term prediction of large-wave occurrence in the NWP. However, research in this area can be further expanded and refined in terms of the following aspects: (1) investigations into nonlinear wave frequency trends; (2) investigations into the nonlinear climate indexes that influence long-term wave trend dynamics; and (3) the application of artificial intelligence methods—such as combining machine learning and relevant climate indexes—for large-wave forecasting.